1. Write the expression in simplified radical form. Show your work.
3-2 square root 11/ 2+ square root 11
2. Solve the equation. Show your check then write the solution set.
x - 1 = square root 6x + 10
Score for Question 3: ___ of 6 points)
3. Given the complex number, 5 − 3i:
(a) Graph the complex number in the complex plane.
(b) Calculate the modulus. When necessary, round to the tenths place.
Answer:
Answers
Answer:
1) 3
2) {x = 9 or x = -1}
3) (b) The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]
Step-by-step explanation:
Problem 1
3 - 2 [tex]\frac{\sqrt{11} }{2} + \sqrt{11}[/tex]
i) Cancelling out the 2's from the top and bottom of the middle term, we get
3 - [tex]\sqrt{11} + \sqrt{11}[/tex]
ii) Cancelling out -[tex]\sqrt{11}[/tex] and +[tex]\sqrt{11}[/tex], we get
3 as the simplified form
Problem 2
x-1 = [tex]\sqrt{6x+10}[/tex]
Our first goal is to get rid off the radical on the right side
i) Squaring both sides, we get
[tex](x-1)^{2}[/tex]=[tex](\sqrt{6x+10})^{2}[/tex]
ii) (x-1)*(x-1) = 6x+10
iii) Applying the distributive property (a+b)(c+d) = ac+ad+bc+bd to the left side of the equation, we get
(x)(x)+(x)(-1)+(-1)(x)+(-1)(-1) = 6x+10
=> [tex]x^{2}[/tex]-x-x+1 = 6x+10
=> [tex]x^{2}[/tex]-2x+1 = 6x+10
iv) Subtract 6x from both sides, we get
[tex]x^{2}[/tex]-2x+1-6x = 6x+10-6x
v) Cancelling out 6x and -6x from the right side, we get
[tex]x^{2}[/tex]-2x-6x+1 = 10
=> [tex]x^{2}[/tex]-8x+1 = 10
vi) Subtracting 10 from both the sides, we get
[tex]x^{2}[/tex]-8x+1-10 = 10-10
vii) Cancelling out 10 and 10 from the right side, we have
[tex]x^{2}[/tex]-8x-10+1 = 0
=> 1[tex]x^{2}[/tex]-8x-9 = 0
viii) Coefficient of the first term = 1
Multiplying the coefficient of the first term and the last term, we get
1*(-9) = -9
We need to find out two such factors of -9 which when added should give the middle term -8
So, -9 and +1 are the two factors of -9 which when added gives us the middle term -8
ix) Rewriting the middle term, we get
[tex]x^{2}[/tex]-9x+x-9 = 0
x) Factoring out x from the first two terms and factoring out 1 from the last two terms, we get
x(x-9)+1(x-9)=0
xi) Factoring out x-9 from both the terms, we get
(x-9)(x+1)=0
xii) Either x-9=0 or x+1=0
xiii) Solving x-9=0, we get x=9
xiv) Solving x+1=0, we get x= -1
So, solution set {x = 9 or x = -1}
Problem 3
5 − 3i
a) In order to graph the complex number 5-3i, we need to move right by 5 units on the real axis and then move down by 3 units on the imaginary axis.
See figure attached
b) A complex number is in the form of z= a+ bi
i) Comparing 5-3i with a+bi, we get a=5 and b = -3
The modulus is given by
|z| = [tex]\sqrt{a^{2}+b^{2} }[/tex]
ii) Plugging in a=5 and b=-3, we get
|z| = [tex]\sqrt{5^{2}+(-3)^{2} }[/tex]
iii) |z| = [tex]\sqrt{25+9} [/tex]
iv) |z| = [tex]\sqrt{34}[/tex]
The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]
Related Questions
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the diagonal of a square whose sides are of the given measure.
Given = 7√3
Answers
Answer: " 7√6 " .
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→ The answer is: " 7√6 units " .
__________________________________________________
Step-by-step explanation:
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Method 1:
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This will be a "45-45-90" triangle;
which means that in:
(two sides for triangle will be the same).
which is consistent with the information give:
(the two side of the triangle are sides of a "square" ,
and ALL sides of a square have the "square length" ;
and one side with be 90 degrees (a right triangle);
and the other angles will be 45 degrees (which is 1/2 of 90 degrees because the will cut into "1/2" of each of the "two other 90 degree angles" when a diagonal is drawn to form the "hypotenuse".
So, for "45-45-90" triangles, the side lengths, are:
"x, x, x√2 " ; in which "x√2" represents the side length of the "hypotenuse" ; and the two "x" values represent the equal values for the other 2 (two) side lengths.,
We are asked to find the "diagonal" of the square; in which: "x = 7√3" ;
That is, we are ask to find the hypotenuse: "x√3" ;
Note: We are given: " x = 7√3 " ;
So: " x√3 " = " 7 *√3 *√2 = 7 *√6 = " 7√6 ".
____________________________________________
The answer is: " 7√6 units " .
__________________________________________________
Method 2:
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Use the Pythagorean theorem (for right triangles):
" a² + b² = c² " ;
in which: "c" represents the "side length" of the "hypotenuse" ;
or: the "diagonal" of the "square" ; for which we shall solve.
"a" and "b" represent the other sides of the right triangle.
In this case, "a" and "b" are equal;
since "a" & "b" are the side lengths of a square.
We are given: a = b = " 7√3 " .
We are to find "c" .
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" a² + b² = c² " ;
↔ " c² = a² + b² " ;
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→ c² = (7√3)² + (7√3)² ;
→ c² = (7²) * (√3)² + (7²) (*√3)² ;
→ c² = ( 49*3) + (49*3) ;
→ c² = (147) + (147) ;
→ c² = 294 ;
Take the "positive" square root of each side of the equation;
to solve for "c" ;
→ ⁺ √(c²) = ⁺ √294 ;
→ c = ⁺ √294
⁺ √294 = ⁺ √3 ⁺ √98 ;
→ √98 = ⁺ √49⁺ √2 ;
⁺ √294 = 7√3√2 = 7√6 .
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c = 7√6
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The answer is: " 7√6 units " .
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The values obtained by using "both" methods/ match!
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Hope this helps!
Best wishes in your academic pursuits
— and within the "Brainly" community!
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please help ill give brainliest
Answers
Answer: Second, third, fifth and sixth options are correct.
Step-by-step explanation:
Since we have given that
[tex]\frac{3}{4}+m=\frac{-7}{4}[/tex]
Now, we will solve it for the value of m :
[tex]\frac{3}{4}+m=\frac{-7}{4}\\\\m=\frac{-7}{4}-\frac{3}{4}\\\\m=\frac{-7-3}{4}\\\\m=\frac{-10}{4}[/tex]
Hence, the value of m is
[tex]\frac{-10}{4}[/tex]
and we can also apply m=[tex]\frac{-5}{2}[/tex]
if [tex]\frac{-5}{4}+m=\frac{-15}{4}\\\\m=\frac{-15}{4}+\frac{5}{4}\\\\m=\frac{-10}{4}\\\\m=\frac{-5}{2}[/tex]
And
[tex]m+2=-0.5\\\\m=-0.5-2\\\\m=-2.5\\\\m=\frac{-5}{2}[/tex]
Therefore, Second, third, fifth and sixth options are correct.
Given the position function, s of t equals t cubed divided by 3 minus 12 times t squared divided by 2 plus 36 times t , between t = 0 and t = 15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. (5 points)
0 < t < 6
5 < t < 15
t > 15
The particle always moves to the right.
Answers
Answer:
Option D is correct.
as the particle always moves to the right
Step-by-step explanation:
Given the function: [tex]s(t) = \frac{t^3}{3} - \frac{12t^2}{2} + 36t[/tex] , 0<t<15;
where
s(t) represent the distance in feet.
t represents the time in second.
Since, when the particle is moving to the right,
⇒ s(t) is increasing.
so, [tex]v(t) =\frac{ds}{dt} > 0[/tex]
Find the derivative of s(t) with respect to t;
Use derivative formula:
[tex]\frac{dx^n}{dx} = nx^{n-1}[/tex]
[tex]\frac{ds}{dt} = \frac{3t^2}{3}-\frac{24t}{2}+36[/tex]
Simplify:
[tex]\frac{ds}{dt} = t^2-12t+36[/tex]
As [tex]\frac{ds}{dt} > 0[/tex]
⇒[tex] t^2-12t+36 > 0[/tex]
[tex](t-6)^2 >0[/tex] [[tex](a-b)^2 = a^2-2ab+b^2[/tex] ]
⇒ this is always true because square of any number is always positive
Therefore, it means that the particle always moves to the right.
PLEASE HELP!! EARN 50 POINTS!! WILL MARK BRAINLIEST!!!!
Fill in the reason for each step
Given - 2x-7= 1/3x-2
Prove - x = 3
statement - 2x-7= 1/3x-2
reason- (Given)
statement - 3(2x-7)=3(1/3x-2)
Reason -
statement - 6x-21=x-6
reason -
statement - 5x-21=-6
reason -
statement - 5x=15
reason -
statement - X=3
reason -
Answers
Answer:
Use demos it is reaaly helpful with this
To solve the equation 2x-7= 1/3x-2, we multiply both sides by 3, subtract x from both sides, add 21 to both sides, and then divide by 5 to isolate x, resulting in x = 3.
Explanation:For the given equation 2x-7= 1/3x-2, the goal is to prove x = 3. Here's how to approach it step-by-step:
Multiply both sides by 3 to eliminate the fraction: Doing this, the equation becomes 6x - 21 = x - 6, which simplifies the problem by removing the fraction.Subtract x from both sides: This leads to 5x - 21 = -6. It helps to move all x terms to one side of the equation.Add 21 to both sides: By doing so, 5x = 15 is obtained, which gathers the constants on one side of the equation.Divide both sides by 5: This results in x = 3, finding the value of x.After solving the equation, it is important to check if the answer is reasonable by substituting x back into the original equation to see if both sides equal.
Vito uses 9 L of water to water 24 flowerpots he is wondering how many liters of water it would take to water 40 flowerpots
Answers
Find ? : 40
Solving Steps-
40 / 24 = 1 2/3
1 2/3 • 9 = 15
ANSWER is 15 L
Answer:15
Step-by-step explanation:
Given that 2^A×3^B×5^13=20^D×18^12, where A,B, and D are postive integers, compute A+B+D.
Answers
Answer: 75
Step-by-step explanation:
[tex]2^A3^B5^{13}=20^D18^{12}[/tex]
⇒ [tex]2^A3^B5^{13}=(2^2\cdot5^1)^D(2^1\cdot3^2)^{12}[/tex]
⇒ [tex]2^A3^B5^{13}=(2^{2D}\cdot5^D)(2^{12}\cdot3^{24})[/tex]
⇒ [tex]2^A3^B5^{13}=2^{2D+12}\cdot3^{24}\cdot5^D[/tex]
Now compare the like bases:
[tex]2^A=2^{2D+12}[/tex] ⇒ A = 2D + 12
[tex]3^B=3^{24}[/tex] ⇒ B = 24
[tex]5^{13}=5^D[/tex] ⇒ D = 13
Next, let's solve for A:
A = 2D + 12
= 2(13) + 12
= 26 + 12
= 38
LAST STEP: Find the sum of A, B, and D
S = A + B + D
= 38 + 24 + 13
= 75
If I use 6 gallons of water on 20 plants in my garden at that rate how much water will it take to water 30 plants
Answers
Sandy has 16 roses, 8 daisies, and 32 tulips. She wants to arrange all the flowers in the bouquets. Each boquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?
Answers
If it was more than 8 then each bouquet wouldn't have the same number of flowers since you only have a total of 8 daisies.
The lengths of the sides of a triangle are in the extended ratio 7 : 8 : 9. The perimeter of the triangle is 72 cm. What are the lengths of the sides?
Answers
Answer:
a=21, b=24, c=27
Step-by-step explanation:
a= side 1, b= side 2, c= side 3
a+b+c=72
a/b=7/8 and b/c=8/9 (proportion it)
then cross multiply to get 8a=7b and 9b=8c---> divide to get a=7/8b and c=9/8b
put that into the first equation--> 7/8b+8/8b+9/8b=72
add the fractions to get 24/8b=72 (24/8 equals 3) so 3b=72 (divide to get b=24)
then fill that in to the above equations (8a=7b, 9b=8c)
8a=7(24) and 9(24)=8c---> 8a=168 and 8c=216
divide all that and get a=21 and c=27
with all the measurements, you can check the proportion to make sure it works (7:8:9-->21:24:27)
if you multiple 7, 8, and 9 by 3 then you get the numbers found so it works
The sides of the triangle in question, which are in a 7:8:9 ratio, are 21 cm, 24 cm, and 27 cm respectively when the perimeter is 72 cm.
Explanation:The subject of this question is Mathematics, specifically related to the concept of ratios and the calculation of triangle side lengths. The triangle in question has sides in the ratio of 7:8:9. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is 72 cm. This means that the total ratio units (7+8+9 = 24 units) represent 72 cm in real lengths.
To find out how much each ratio unit represents, we divide the total perimeter by the total units. This gives us 72 cm / 24 units = 3 cm/unit. This means that each ratio unit represents 3 cm. Thus, the lengths of the sides following the 7:8:9 ratio would be 7*3=21 cm, 8*3=24 cm, and 9*3=27 cm respectively.
Learn more about Triangle Side Lengths here:https://brainly.com/question/24273594
#SPJ3
Ava has 20-foot length of wire.She cuts the wire into 6 pieces of equal length.The length of each piece of wire will fall between which two whole-number lengths?
Answers
When a 20-foot length of wire is cut into 6 pieces of equal length, each piece would be approximately 3.33 feet long. Rounding to the nearest whole numbers, this means the length of each piece will fall between 3 feet and 4 feet.
Explanation:To find the length of each piece of wire when a 20-foot length of wire is cut into 6 pieces of equal length, you divide the total length by the number of pieces. So, you calculate:
Divide the total length of wire (20 feet) by the number of pieces (6).20 feet / 6 pieces = approximately 3.33 feet per piece.Since we're looking for whole-number lengths that the length of each piece falls between, we can round 3.33 feet down to the nearest whole number (3 feet) and up to the next whole number (4 feet). Thus, the length of each piece will fall between 3 feet and 4 feet.
A rectangular flying carpet is 1 1/2 m wide and 2 m long what is the area of the carpet
Answers
Hi there! :)
Answer:
The area of the carpet is 3m².
Step-by-step explanation:
First off, the formula to calculate the area of a rectangle is this: A = L × W
Where "A" is the area, "L" the length and "W" the width.
Now that you have that, replace all the information you know in the equation in order to find the value of "A", which is what we are looking for:
- Just keep in mind that 1 1/2 is the same thing as 1.5
- The term "wide" is used to give the "width"
- The term "long" is used to give the "length"
A = L × W
A = 2 × 1.5
A = 3
There you go! I really hope this helped, if there's anything just let me know! :)
The area of the rectangular flying carpet is [tex]$\frac{15}{4} \text{ m}^2}$[/tex] or [tex]3.75 { m}^2}[/tex]
To find the area of a rectangle, one multiplies the length by the width. The width of the carpet is given as [tex]$1 \frac{1}{2}$[/tex] meters, which can be expressed as a fraction [tex]$\frac{3}{2}$[/tex] of meters. The length of the carpet is given as 2 meters.
Using the formula for the area of a rectangle [tex]A = l \times w$,[/tex] where [tex]$l$[/tex] is the length and [tex]$w$[/tex] is the width, we substitute the given values:
[tex]\[ A = 2 \text{ m} \times \frac{3}{2} \text{ m} \][/tex]
[tex]\[ A = \frac{2 \times 3}{2} \text{ m}^2 \][/tex]
[tex]\[ A = \frac{6}{2} \text{ m}^2 \][/tex]
[tex]\[ A = \frac{15}{4} \text{ m}^2 \][/tex]
[tex]\[ A = 3.75 \text{ m}^2 \][/tex]
Therefore, the area of the carpet is [tex]$\frac{15}{4}$[/tex] square meters or 3.75 square meters.
What is the y-intercept of the function, represented by the table of values below? x: -2,1,2,4,7 y: 14,8,6,2,-4
Answers
Answer:
The y-intercept is at y = 10.
Step-by-step explanation:
It will be between y = 14 and y = 7 because the corresponding x values are -2 and 1.
An increase of 3 units of x gives a decrease of 6 units of y fro the above values.
Then an increase of 1 ( 1 to 2) in x gives decrease in y of 2 (8 to 6). The other values show the same pattern.
So very unit increase in x, the y values change by -2.
So from x = -2 to 0 is +2 units for x and this will be -4 units for y so the y-intercept ( when x = 0) will be at y = 14-4 = 10
y-intercept is (0,10).
A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30°, how tall is the tree to the nearest foot?
A) 75 feet
B) 87 feet
C) 106 feet
D) 212 feet
Answers
B) 87 feet
Step-by-step explanation:The mnemonic SOH CAH TOA reminds you the relationship between angle, adjacent, and opposite sides is ...
... Tan = Opposite/Adjacent
In this geometry, the side adjacent to the angle is marked 150 ft, and the side opposite the angle is the height we want to find. This means ...
... tan(30°) = height/(150 ft)
Multiplying by 150 ft, we get ...
... height = (150 ft)·tan(30°) ≈ 87 ft
Write a function rule for the data in the table. Determine if it's a direct variation, inverse variation or neither. Last, determine the value of x if y=10.
Answers
I'm assuming you meant to say "graph" instead of "table".
The function rule is y = x+2 because the y intercept is 2, where the graph crosses the y axis. The slope is 1 meaning we move 1 unit up and 1 unit to the right each time. You can use the slope formula to determine the slope, or simply make this observation of rise vs run.
-------------------------------
Because this line doesn't go through the origin, and because it's not in the form y = k*x, this means we do not have a direct variation equation.
We do not have an inverse variation equation either because it is not in the form y = k/x or x*y = k. A visual indication of this is that the graph isn't a curved hyperbola.
Therefore, this function is neither direct variation nor inverse variation
-------------------------------
Plug in y = 10 and solve for x
y = x+2
x+2 = y
x+2 = 10
x+2-2 = 10-2
x = 8
The value of x is 8
So if x = 8, then y = 10 meaning that (x,y) = (8,10) is on this blue diagonal line.
For every penny Sam puts into his bank, Tara puts 4 pennies into her bank. If Sam puts 10 pennies into his bank, how many pennies does Tara put into her bank? Answer options with 4 options
Answers
Answer: If Tara puts 4 pennies in for every one Sam does then after he puts in 10 she would of put 40.
She put in 40 pennies. Hope this helps ;)
Which equation can be used to solve the following word problem? Seth has 8 more nickels than dimes, and the total value of his coins is $2.35. How many nickels does he have? Let n represent the number of nickels.
Answers
Answer:
Seth has 21 nickels
Step-by-step explanation:
Let n represent the number of nickels. Since Seth has 8 more nickels than dimes, then (n-8) is the number dimes.
Nickel is worth 5 cents and dime is worth 10 cents. Thus, n nickels are worth 5n cents and (n-8) dimes are worth 10(n-8) cents. The total value of Seth's coins is $2.35 that is 235 cents, then
[tex]5n+10(n-8)=235.[/tex]
Solve this equation:
[tex]5n+10n-80=235,\\ \\15n=235+80,\\ \\15n=315,\\ \\n=21.[/tex]
Which graph shows the solution to the system of inequalities below?
x+y<3
-5x+2y<10
Answers
Answer:
The last graph
Step-by-step explanation: On edge.
Answer:
D or the last graph
Step-by-step explanation:
Edge 2022
Is the following expression true or false? [x^2 + 8x + 16] · [x^2 – 8x + 16] = (x2 – 16)^2
Answers
[tex](x^{2} +8x+16)(x^{2} -8x+16)\\(x+4)^{2} (x-4)^{2} \\(x^{2}-16)^{2} \\[/tex]
it is true; just work them out, you should get what they got :))
Answer:
True.
Step-by-step explanation:
We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.
To answer our given problem, we will simplify left side of our given equation using distributive property as:
[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]
[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]
Combine like terms:
[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]
[tex]x^4-32x^2+1256[/tex]
Now, we will expand right side of our given equation using perfect square formula as:
[tex](x^2-16)^2=(x^2)^2-2(x)(16)+16^2[/tex]
[tex](x^2-16)^2=x^4-32x+256[/tex]
Since both sides of our given equation are equal, therefore, our given statement is true.
In the coordinate plane shown, how far apart are points B and D? Explain how you can use the Pythagorean theorem to determine this.
Answers
Answer:
10.3 units
Step-by-step explanation:
From the given graph, we can see the coordinates of the points B (-2, 4) and D (3, -5).
To use the Pythagorean Theorem, we must have a right angled triangle. So we can select a point X (3, 4) to calculate the distance between B and D using the Pythagoras Theorem.
BX = 5, XD = 9
BD = [tex]\sqrt{BX^2+XD^2}[/tex]
BD = [tex]\sqrt{(5)^2+(9)^2} =\sqrt{106} =10.29[/tex]
Therefore, the points B and D are 10.3 units apart.
There are 4200 adults in lake view 3/8 of adults have no children how many adults have children
Answers
525 x 3 = 1575
4200 - 1575 = 2625
2625 adults have children
Hope this helps :)
What function equation is represented by the graph?
f(x)=−2x−2
f(x)=2x−3
f(x)=−2x−3
f(x)=2x−2
Answers
9514 1404 393
Answer:
(b) f(x) = 2^x -3
Step-by-step explanation:
The horizontal asymptote is y=-3, eliminating the first and last choices.
The curvature is upward, eliminating the third choice.
The graph is a representation of ...
f(x) = 2^x -3
Andy joins a social networking site. After day three, he has 25 friends; after day eight, he has 40 friends. Write the equation to show the number of friends he will have on day 18 if he continues to add the same number of friends each day.
Answers
Answer:
Point slope intercept form: The equation for line is given by; [tex]y-y_1=m(x-x_1)[/tex] ......[1] ; where m is the slope and a point [tex](x_1, y_1)[/tex] on the line.
Let x represents the number of days and y represents the number of friends.
As per the statement: After day three, he has 25 friends; after day eight, he has 40 friends.
⇒ We have two points i.e,
(3, 25) and (8, 40)
First calculate slope(m);
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we get;
[tex]m = \frac{40-25}{8-3}=\frac{15}{5}[/tex] = 3
now, substitute the given values of m=3 and a point (3, 25) in [1] we get;
[tex]y-25=3(x-3)[/tex]
Using distributive property; [tex]a \cdot(b+c) = a\cdot b + a\cdot c[/tex]
[tex]y-25 = 3x - 9[/tex]
Add 25 on both sides, we get;
[tex]y-25+25 = 3x - 9+25[/tex]
Simplify:
y =3x + 16
if x = 18 days, then;
y = 3(18) + 16 = 54+16 = 70
Therefore, he will have on day 18, if he continues to add the same number of friends each day is, 70 friends.
Help! Easy 20 points.
Please help I am have a time limit and I am stuck on this one part. Simple answers are okay just quickly.
Answers
Answer:
online
Step-by-step explanation:
insert the subject that is into the search bar on google and look for the pdf document. it will contain all the work and information needed
Answer:
Step-by-step explanation:
2. Conclusion: U is the mid point of RN.
Justification: From the figure, you can see that RU=UN which means U divides the line segment RN in two equal halves, thus by definition of mid point theorem, U is the mid point of RN.
3. From the given figure,
Conclusion: ∠7=∠5
Justification: From the figure, you can see that \overrightarrow{IK} bisects∠MIE. Therefore by the definition of bisector angle property, ∠MIK=∠KIE that is ∠7=∠5.
4. Conclusion: if l║m, and t is the transversal, then ∠3=∠7.
Justification: Since l║m and t is the transversal, then ∠3=∠7 as the alternate angles made by the transversal are equal.
5. Conclusion: If \overrightarrow{BD} bisects ∠ABC, then ∠ABD=∠DBC
Justification: Since, \overrightarrow{BD} bisects ∠ABC, then by the bisector angle property, \overrightarrow{BD} divides ∠ABC in two equal angles that is ∠ABD=∠DBC.
6. Conclusion: If ∠2+∠3= 180°,then ∠2 and ∠3 are supplementary angle pairs.
Justification: Since, ∠2 and ∠3 are supplementary angle pairs which are on the same side of the transversal t, their sum is equal to 180° that is ∠2+∠3= 180°.
Jerry is a judge. He hears 5 cases every 2\dfrac382 8 3 ? hours. Jerry hears cases at a constant rate. How many cases does he hear per hour?
Answers
Answer:
[tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.
Step-by-step explanation:
We are told that Jerry hears 5 cases every [tex]2\frac{3}{8}[/tex] hours.
To find the number of cases that Jerry hears per hour let us divide 5 by [tex]2\frac{3}{8}[/tex].
[tex]\text{Jerry hears cases per hour}=5\div 2\frac{3}{8}[/tex]
Let us convert our mixed fraction into improper fraction.
[tex]\text{Jerry hears cases per hour}=5\div \frac{19}{8}[/tex]
Since dividing a number by a fraction is same as multiplying the number by the reciprocal of the fraction.
[tex]\text{Jerry hears cases per hour}=5\times \frac{8}{19}[/tex]
[tex]\text{Jerry hears cases per hour}=\frac{40}{19}[/tex]
[tex]\text{Jerry hears cases per hour}=2\frac{2}{19}[/tex]
Therefore, Jerry hears [tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.
What is the length of the diameter of a circle if the endpoints of the diameter are at the points (4, 2) and (–6, –1)?
Answers
Answer:
d= 10.44030651
Step-by-step explanation:
The diameter is the length between the endpoints. We can find it using the distance formula.
d= sqrt((x2-x1)^2+(y2-y1)^2 )
d = sqrt((-6-4)^2+ (-1-2)^2)
d = sqrt((-10)^2+(-3)^2)
d= sqrt(100+9)
d = sqrt(109)
d= 10.44030651
A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each of nitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-lb bag of Fertilizer A costs $30 and a 50-lb bag of Fertilizer B costs $20, find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements.
Answers
Answer: Fertilizer A = 20, Fertilizer B = 56
Step-by-step explanation:
Step 1: Set up the equations
[tex]\begin{array}{c|c|c|c}& FertilizerA&FertilizerB&Quantity Required\\Nitrogen&8&5&440\\Phosphorous&2&5&260\\Potassium&4&5&360\\\end{array}[/tex]
Nitrogen: 8x + 5y ≥ 440
Phosphorous: 2x + 5y ≥ 260
Potassium: 4x + 5y ≥ 360
Step 2: Find the vertices
It is easiest to graph the equations to find the vertices. (see attachment). You can also solve each system of equations to find the intersected points.
The following satisfy the "greater than or equal to" requirement:
(0, 88) → y-intercept of Nitrogen equation(20, 56) → intersection of Nitrogen and Potassium equations(50, 32) → intersection of Phosphorous and Potassium(130, 0) → x-intercept of PotassiumStep 3: Use vertices in cost function C(x) to find the minimum
C(x) = $30x + $20y
(0, 88): $30(0) + $20(88) = $1760
(20, 56): $30(20) + $20(56) = $1720 ← This is the minimum!
(50, 32): $30(50) + $20(32) = $2140
(130, 0): $30(130) + $20(0) = $3900
The minimum cost occurs when 20 bags of Fertilizer A and 56 bags of Fertilizer B are purchased.
This is a linear programming problem. The farmer needs to solve the system of inequalities that define the minimum nutrient requirements for the field and the cost function of the fertilizers to determine the least expensive way to meet the nutrient requirements.
Explanation:The subject of this problem lies in the realm of linear programming—a mathematical method for determining a way to achieve the best outcome in a given mathematical model.
To solve this problem, we need to find the quantities of Fertilizer A and Fertilizer B that meets the minimum requirements for the field at minimum cost. Let x be the quantity of Fertilizer A and y be the quantity of Fertilizer B. Then, based on the information provided in the problem, we can set up the following inequalities:
Nitrogen: 8x + 5y ≥ 440Phosphorus: 2x + 5y ≥ 260Potassium: 4x + 5y ≥ 360Given that a 50-lb bag of Fertilizer A costs $30 and a 50-lb bag of Fertilizer B costs $20, the total cost of the fertilizers can be represented by the equation C = 30x + 20y, where C is the total cost.
The goal is to minimize the cost C = 30x + 20y, subject to the constraints above.
Using graphing or mathematical software, we can construct a graph of these inequalities and find the solution that lies on the feasible region where the cost is minimized.
The farmer needs to solve this system to determine the least amount of each fertilizer to use while still meeting the minimum soil nutrient requirements.
Learn more about Linear Programming here:https://brainly.com/question/34674455
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You and your friend are selling magazine subscriptions for a fundraiser. After w w weeks, you have sold (3w+4) subscriptions and your friend has sold (5w+1) subscription . A.Write an expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold.
Answers
Answer:
The simplest form that represents the difference is ( 2w-3).
Step-by-step explanation:
In this sum after w weeks subscription sold by me = 3w+4
and the subscription sold by my friend =5w+1
so the difference between the numbers of my friend and me
⇒(5w+1)-(3w+4)
⇒5w+1-3w-4
⇒2w-3
So the simplest form is (2w-3).
Final answer:
The difference in the number of subscriptions sold by the friend and the student after w weeks is represented by the simplified expression 2w - 3.
Explanation:
To find the difference between the number of subscriptions your friend has sold and the number you have sold, you simply subtract your sales from your friend's sales. The expression for your sales is (3w + 4) subscriptions and for your friend's sales is (5w + 1) subscriptions. So, the expression representing the difference will be:
(5w + 1) - (3w + 4)
Distributing the negative sign across the terms in the second set of parentheses gives us 5w + 1 - 3w - 4. Combining like terms, which are the 'w' terms and the constant terms separately, we get:
(5w - 3w) + (1 - 4) which simplifies to 2w - 3.
This expression 2w - 3 is the simplified form representing the difference between the number of subscriptions sold by your friend and you after w weeks.
m∥n, m∠1 = 65°, m∠2 = 60°, and m∠6 = 85°. What is m∠DBC?
Answers
Answer:
∠DBC = 40°
Step-by-step explanation:
We are given a figure where we know that the angle m∠1 = 65°, m∠2 = 60° and m∠6 = 85°. With the help of these given measures of the angles, we are to find the measure of the angle m∠DBC.
Since the sum of angles in a triangle is equal to 180 degrees, so:
∠1 + ∠2 + ∠3 = 180
∠3 = 180 - (65 + 60)
∠3 = 55°
Also ∠6 and ∠B are alternate interior angles so if ∠6 = 85° then ∠B is also = 85°.
Now that we know ∠3 and ∠B, we can find ∠DBC:
∠DBC = 180 - (85 + 55)
∠DBC = 40°
Answer:40
Step-by-step explanation:
See angle 1 = 65°
Angle 2 = 60°
We know in a triangle all angle count 180°
So angle 3 = 55°
Now in a straight line all angle count 180°
So angle DBC + angle 3 + remaining angle along the line m will count 180°
Now angle 6 and remaining angle along the line m will be equal as 'm' ?and 'b' are parallel lines and t is intersecting them so it subtend equal angles.
Angle 6 = 85° so remaining angle along the line m is also 85°
We know angle DBC + angle 3 + rem. angle = 180°
Or 55° + 85° + angle DBC = 180°
Therefore, angle DBC = 40°
Hope it helps!!!
Please help! A new car that sells for $21,000 depreciates (decreases in value) 16% per year. Write a function that models the value of the car. Find the value of the car after 3 years.
A) $8,602
B) $11,779
C) $12,899
D) $12,447
Answers
Answer:
The function is:
21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{n}[/tex]
The price after 3 years would be D) $12,447
Step-by-step explanation:
Because the value is depreciating, the price will decrease.
The function formula is:
Amount x (1 ± [tex]\frac{percentage}{100}[/tex])[tex]^{n}[/tex]
Where n is the amount of years and the ± is a + if the value is increasing, and a - if the value is depreciating.
So plug the values in, with a minus:
21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{n}[/tex]
The price after 3 years would simply be the following equation:
21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{3}[/tex]
Which gives the result 12446.7 or 12447 to 1.d.p
This means that the answer is D) $12,447!
Hope this helps!
i think it is d, can someone tell me if I'm right?
Chenoa starts with $250 in her savings account. Each month she adds $15.
Which recursive function rule models the total amount in Chenoa’s savings account at the end of each month?
a. a n =15⋅ a n−1 and a 1 =250
b. a n =15+ a n−1 and a 1 =250
c. a n =250+ a n−1 and a 1 =15
d. a n =250⋅ a n−1 and a 1 =15
Answers
Answer: Choice B)
an = 15 + a(n-1)
a1 = 250
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The variable "a" is used to represent the terms. Since we have infinitely many terms to worry about, we won'd use "b, c, d, etc" for the other terms or else we'd run out of letters. So instead, we just stick a number next to "a" to help keep track of the terms
a1 = first term, a2 = second term, a3 = third term, etc
The first term is 250 because Chenoa starts off with $250, so a1 = 250. The answer is between A and B at this point.
The recursive step is how we generate each term. In plain english, the recursive step would be "add 15 to each term to get the next term". In an informal equation, it would look like this
term = (previous term) + 15
So that is why the nth term is
[tex]a_n = 15 + a_{n-1}[/tex]
which means "to get the nth term, we add 15 to the previous (n-1)st term"
This is why choice B is the answer