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
Answer:15
Step-by-step explanation:
A total of 56 students signed up to play in a flag football league. If each team has 10 students, how many more students will need to sign up so all of the students can be on a team?
A printer prints 75 pages in 5 minutes. At the same rate, how many pages does the printer print in 7 minutes?
a. Solve and show your work.
b. Explain how you solved using First, Next, and Last
Answer:105
Step-by-step explanation:
the question says it prints 75 pages in 5 minutes.
to find out how much it prints in 7 minutes you must find how much it prints in 1 minute.
1 minute=75/5=15
it prints 15 pages in 1 minute.
15*7=105 pages.
so it prints 105 pages in 7 minutes.
please mark brainliest if it helps and please like.
welcome!
Answer:
105 pages
Step-by-step explanation:
It prints 75/5 = 15 pages per minute.
So in 7 minutes 15*7 = 105 pages are printed.
Bob bought a megahunk chocolate bar that weighed 9/10 lb he has already eaten 1/3 lb how much chocolate dose he have left
A 7/15
B 17/30
NEED ANSWERS FAST
Hi there! :)
Answer:
The answer is B) 17/30
Step-by-step explanation:
In order to find your answer you need to subtract 1/3 from 9/10:
9/10 - 1/3 = chocolate left
Since theses fractions do not have the same denominators (bottom number), the key here is to rewrite both of the fractions so that they have the same denominator:
The denominator is going to be a common multiple of "10" and "3". Ideally it's going to be the least common multiple of "10" and "3".
Let's start with the larger of the two denominators, which is "10". You have to go through its multiples and and see when we get to one that's divisible perfectly by 3.
So 10 is not divisible perfectly by 3, neither is 20. 30 on the other hand is divisible perfectly by 3. 30 is three times 10.
So you can rewrite both of these fractions as something over 30.
1/3 = ?/30
To get from 3 to 30, we have to multiply by 10. So if you multiply the denominator by 10, if you don't want to change the value of the fraction, you have to multiply the numerator (top number) by 10 also.
1/3 = 10/30
Same thing with the other fraction:
9/10 = ?/30 → 3 × 10 = 30 / SO, you need to multiply the numerator by three also → 9 × 3 = 27
9/10 = 27/30
Now that your fractions both have the same denominator, you can subtract the numerators together and put the answer on 30.
27/30 - 10/30 = ?
27 - 10 = 17 → 17/30
Since the fraction is simplified, you are now done.
There you go! I really hope this helped, if there's anything just let me know! :)
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
Answer: Choice B)
an = 15 + a(n-1)
a1 = 250
============================================================
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
Which of the following circles lie completely within the fourth quadrant?
Check all that apply.
A. (X-12)^2 + (y+0)^2= 72
B. (X-2)^2 + (y+7)^2= 64
C. (X-9)^9 + (y+9)^2= 16
D. (X-9)^2 + (y+5)^2= 9
Answer:
C. (X-9)^9 + (y+9)^2= 16
D. (X-9)^2 + (y+5)^2= 9
Step-by-step explanation:
The formula for a circle is
(X-h)^2 + (y-k)^2= r^2
where (h,k) is the center of the circle and r is the radius
The 4th quadrant is where x is positive and y is negative
Add r to the y coordinate of the center and if it is still negative, the circle is still completely in the 4th quadrant
A. (X-12)^2 + (y+0)^2= 72
The center is at 12,0 and the radius is sqrt(72) = 6sqrt(2)
This will be positive so it goes into the 1st quadrant
B. (X-2)^2 + (y+7)^2= 64
The center is at 2,-7 and the radius is 8
-7+8=1 so it goes into the 1st quadrant
C. (X-9)^9 + (y+9)^2= 16
The center is at 9,-9 and the radius is 4
-9+4 = -5 so it is completely in the 4th quadrant
D. (X-9)^2 + (y+5)^2= 9
The center is at 9,-5 and the radius is 3
-5+3 = -2 so it is completely in the 4th quadrant
Answer:
C and D
Step-by-step explanation:
The fourth quadrant is the bottom, right quadrant. In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative.
For a circle to be completely within the fourth quadrant, the circle must have its center in the fourth quadrant, and the center has to be far away enough from the positive x-axis and from the negative y-axis, that no points on the circle are outside the fourth quadrant.
Choice A has center (12, 0), so it cannot be.
Choice B has center (2, -7) and radius 8. Many points will be past the axes.
Choice C has center (9, -9) and radius 4. All points will be in the fourth quadrant.
Choice D has center (9, -5) and radius 3. All points will be in the fourth quadrant.
Is the following expression true or false? [x^2 + 8x + 16] · [x^2 – 8x + 16] = (x2 – 16)^2
[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.
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 -
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.
A students cost for last semester at her community college was 2300 dollars. She spent 368 dollars of that on books. What percent of last semester college costs was spent on books
Answer:
16%
Step-by-step explanation:
To find this, we have to divide the amount spent on books by the total amount, then multiply by 100:
[tex]\frac{368}{2300} * 100 = 16[/tex]
So 16% was spent on books!
16% of last semester college costs was spent on books.
Explanation:To find the percent of last semester college costs spent on books, we need to divide the amount of money spent on books by the total cost of last semester and multiply by 100 to get a percentage.
Amount spent on books: $368
Total cost of last semester: $2300
Percentage spent on books: 368/2300 * 100 = 16%
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Find the slope of the line passing through the points (8,-6)
and (4,-8)
.
Answer:
1/2 is the slope of the line
Step-by-step explanation:
To find slope, use the following equation
slope (m) = (y₂ - y₁)/(x₂ - x₁)
First, set each coordinate. Let:
(x₁ , y₁) = (8 , -6)
(x₂ , y₂) = (4 , -8)
Plug in the corresponding numbers for the corresponding variables.
m = (y₂ - y₁)/(x₂ - x₁)
m = (-8 - (-6))/(4 - 8)
Simplify. Note that two negative signs would result in a positive sign.
m = (-8 + 6)/(4 - 8)
Combine like terms.
m = -2/-4
Simplify. Divide common factors from both the numerator and denominator.
m = (-2/-4)/(-2/-2) = 1/2
1/2 is the slope of the line
~
Find the sin(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).
Note: Answer choices are attached below
Answer:
B) -2/√5
Step-by-step explanation:
see attached
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.
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°.
Find the area of the rectangle. Round the answer to the nearest whole number.
Answer:
The area of the given rectangle is 51
Step-by-step explanation:
First we have to find the coordinates of the vertices of the rectangle.
Then the length and breadth of it using distance formula.
The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Finally calculate the area of rectangle using the formula,
Area of rectangle = Length * Breadth
From the given graph, we get the coordinates of the rectangle as
A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)
Breadth, AB = [tex]\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}[/tex]
Length, BC = [tex]\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}[/tex]
Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51
∴ The area of the given rectangle is 51
Answer:
51
Step-by-step explanation:
HELP NOW!!!!! now please
Answer:
first answer is -10
second answer is 10
third answer is -2
fourth answer is 2
Step-by-step explanation:
Explanation to get the answers:
you plug in the b c d and a
depending on what your abc and d are will depend on how the equation goes
like for example if the equation is
a x (c) - (-d) + b
and a=5, b=8, c=10, d=15
then you plug 5 where a is
plug in 10 where c is
plug 15 where d is as a negative
and lastly plug 8 where b is
if you have a calculator/graphing calculator i would use it to help answer these equations
a graphing calculator solves it for you without doing all the extra work like you would on a regular calculator
i use the graphing calculator to help solve equations like this specific one and it works very well
i hope my answers and explanation helps you :)
16. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y= -1/4 x + 8
-2x + 8y = 4
Answer:
Given equation are:
[tex]y = -\frac{1}{4}x+8[/tex] ......[1]
[tex]-2x+8y = 4[/tex] .....[2]
The two lines are parallel lines then their slopes will be equal.When two lines are perpendicular then, the slope of lines are the negative reciprocals of each other.Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.
Slope[tex](m_1)[/tex] of equation of line in [1] is;
[tex]y = -\frac{1}{4}x+8[/tex]
then;
[tex]m_1= -\frac{1}{4}[/tex]
Slope[tex](m_2)[/tex] of equation of line in [2];
[tex]-2x+8y = 4[/tex]
Add both sides 2x we get;
-2x + 8y + 2x = 2x + 4
Simplify:
8y = 2x +4
Divide both sides by 8 we get;
[tex]y = \frac{1}{4} x + \frac{1}{2}[/tex]
then;
[tex]m_2 = \frac{1}{4}[/tex]
Therefore, the given two lines are neither parallel nor perpendicular.
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answer:
The population of the town at the end of 2017 was 65,550.
Step-by-step explanation:
The population of the town was 60,000 in the beginning of 2016.
In 2016, the total population is increased by 15%.
[tex]60,000\times\frac{15}{100}=9000[/tex]
Therefore the population is increased by 9000 and the population of the town at the end of 2016 was
[tex]60,000+9000=69,000[/tex]
In 2017, the total population is decreased by 5%.
[tex]69,000\times\frac{5}{100}=3450[/tex]
Therefore the population is decreased by 3450 and the population of the town at the end of 2017 was
[tex]69,000-3450=65,500[/tex]
Therefore the population of the town at the end of 2017 was 65,550.
Karl drove 617.3 miles. For each gallon of gas, the car can travel 41 miles. Select a reasonable estimate of the number of gallons of gas Karl used. Mark all that apply A. 1.5 gallons B. 1.6 gallons C. 15 gallons D. 16 gallons E. 150 gallons
Answer:
The number of gallons of gas Karl used is 15 gallons.
Option (C) is correct.
Step-by-step explanation:
As given
Karl drove 617.3 miles.
For each gallon of gas, the car can travel 41 miles.
i.e
1 gallons = 41 miles
[tex]1\ miles = \frac{1}{41}\ gallons[/tex]
Now find out for the 617.3 miles.
Thus
[tex]617.3\ miles = \frac{617.3}{41}\ gallons[/tex]
[tex]617.3\ miles = 15.1\ gallons[/tex]
[tex]617.3\ miles = 15\ gallons\ (Approx)[/tex]
Therefore the number of gallons of gas Karl used is 15 gallons.
Option (C) is correct.
A train moving at a constant speed travels 180 mi in 4 h. How far does the train travel in 7 h? A. 360 mi B. 315 mi C. 280 mi D. 420 mi
Answer:
B. 315 mi.
Step-by-step explanation:
180 ÷ 4 = 45
45 x 7 = 315
or...
180 ÷ 4 = 45
45 x 3 = 135
135 + 180 = 315
I hope this helps!
Cheers, July.
The train travels option B. 315 miles in 7 hours.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Distance train travelled = 180 miles
Time taken to travel the distance = 4 hours
Speed = Distance / Time
= 180 / 4
= 45 miles per hour
Also, given that train travels at constant speed.
Distance = Speed × Time
Since speed is constant, the distance train travelled in 7 hours will be,
Distance = 45 × 7
= 315 miles
Hence the distance train travelled in 7 hours is 315 miles.
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Yu has $20.28 and spends $2.80 on a hot dog. He lends half of his remaining money to a friend. How much money does Yu lend his friend?
If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 4 units left.Shift 2 units up
A.g(x)=|x-4|+2
B.g(x)=|x+2|+4
C.g(x)=|x+4|+2
D.g(x)=|x+2|-4
Got the answer its C.
Answer: C
Step-by-step explanation:
The general form of the equation is: g(x) = a|x - h| + k ;
"a" represents the vertical stretch (or shrink)"h" represents the x-coordinate of the vertex (left and right)"k" represents the y-coordinate of the vertex (up and down)4 units left means h = 4
2 units up means k = 2
--> g(x) = |x - 4| + 2
Option: C is the correct answer.
C. [tex]g(x)=|x+4|+2[/tex]
Step-by-step explanation:The parent function f(x) is given by:
[tex]f(x)=|x|[/tex]
Now, we know that for any parent function f(x) the transformation of the type:
f(x) → f(x+k)
is a translation of the function f(x) k units to the right if k<0
and k units to the left if k<0
and the transformation of the type:
f(x) → f(x)+k
is a translation of a function f(x) k units upward if k>0
and k units downward if k<0
Now here it is given that:
The function f(x) is shifted 4 units left and 2 units up.
Hence, the transformed function g(x) is given by:
[tex]g(x)=f(x+4)+2\\\\i.e.\\\\g(x)=|x+4|+2[/tex]
Jerome has 1/4 of thw group's video games at his house. Mario has 2/5 of the group's video games at his house. What fraction of the group's video games is either at jeromes house or marios house
Answer:
[tex]\frac{13}{20}[/tex] of the group's video games is either at Jeromes house or Marios house.
Step-by-step explanation:
Given the statement: Jerome has 1/4 of the group's video games at his house.
Also,Mario has 2/5 of the group's video games at his house.
⇒ Jerome has group's video games at his house(J) = [tex]\frac{1}{4}[/tex]
and
Mario has group's video games at his house(M) = [tex]\frac{2}{5}[/tex]
To find the fraction of the group's video games is either at Jerome house or Mario house.
Between two they have = [tex]J+M[/tex] = [tex]\frac{1}{4} + \frac{2}{5} = \frac{5+8}{20} =\frac{13}{20}[/tex] of the group's video games.
Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the keys landed. Draw a right triangle that will help you solve the problem. Label each triangle with the information you know
Answer:
Δ ABC is the required triangle.
Step-by-step explanation:
Since the person is standing at the top of tower.
let the height of tower be 'h' and 'b' be the distance from base of tower to the point where keys are dropped.
Consider, ABC be the right angled triangle with AB be the tower and A be the point where person is standing and C denotes the point where keys dropped finally.
Alpha (α) be the angle at which keys is dropped.
BC denotes the distance from foot of tower to the keys.
Simplify 54/10*20/9*2/28
Answer:
The answer for fraction part is 6/7
If this helps please mark brainliest
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)?
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
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?
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.
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Every _____ tessellates.
pentagon
hexagon
quadrilateral
octagon
Hi there! :)
Answer:
B. hexagon
Step-by-step explanation:
Every hexagon tessellates. Hexagon is a plane figure having six sides.
I hope this helps you!
Have a nice day! :)
:D
-Charlie
Thank you!
Answer: hexagon
Step-by-step explanation:
We know that equilateral triangles, squares and regular hexagons are the only regular polygons that tessellate .
Hexagon is a six sided regular polygon having all its sides equal. It is one of the three regular polygons which tessellates.
Therefore, from all the given choices the correct answer would be "hexagon".
The complete statement :-Every hexagon tessellates.
How do i even do this ? plz help smarties
x = number of messages sent or received
y = total cost per month
Plan A costs $30 per month plus $0.10 per text message. So the cost for plan A is y = 0.10*x + 30. The portion 0.10*x represents just the cost of the 10 cents per message, and then we add on the fixed cost of $30 to get the total cost.
In a similar fashion, plan B's cost is y = 60. There is no cost per message, so we don't have to include x in the picture. The cost is a flat fee, which leads to a flat horizontal line graph (as shown in the attachment below)
Our two equations are: y = 0.10x+30 and y = 60. Let's use substitution to find x
y = 0.10x + 30
60 = 0.10x + 30 ... replace y with 60 (works because y = 60)
60-30 = 0.10x
30 = 0.10x
0.10x = 30
x = 30/0.10
x = 300
If you send or receive 300 messages, then both plans will cost the same. We can see this on the graph below where the two lines cross at (300,60). Note how plugging x = 300 into the first equation simplifies to y = 60.
PLEASE HELP!!!
This table shows the input and output values for an exponential function f(x) .
What is the ratio of outputs for any two inputs that are one value apart?
A. 2
B. 4
C. -2
D. -1/2
Answer:
A
Step-by-step explanation:
We find the ratio by dividing two y-values from 2 consecutive x values (1 unit apart). Notice that in the table, all x-values are 1 unit apart. We can choose any pair of consecutive points.
Let's choose: (2,-4) and (1,-2). We divide -4/-2=+2.
Answer A.
Given that 2^A×3^B×5^13=20^D×18^12, where A,B, and D are postive integers, compute A+B+D.
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
A kite flying in the air has a 10-ft line attached to it. Its line is pulled taut and casts a 9-ft shadow. Find the height of the kite.
The height of the Kite from the ground is √19 feet.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A kite flying in the air has a 10-ft line attached to it and its line is pulled taut and casts a 9-ft shadow.
The line can be thought of as a hypotenuse and the shadow as the base.
So, We have to find the height of the kite.
Therefore, From the Pythagoras theorem,
Base² + Height² = Hypotenuse².
9² + Height² = 10².
Height² = 100 - 81.
Height² = 19.
Height = √19.
learn more about Pythagoras' theorem here :
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