Answer:
The value of x is 3 ,
The measure of each side is 55 units .
Step-by-step explanation:
Given as :
The sides of the equilateral Triangle are pq , qr , pr
The measure of side pq = 18 x + 1
The measure of side qr = 24 x - 17
The measure of side pr = 15 x + 10
∵ The triangle is equilateral then all sides are equal
i.e pq = qr = pr
So, 18 x + 1 = 24 x - 17
Or, 24 x - 18 x = 17 + 1
Or, 6 x = 18
∴ x = [tex]\dfrac{18}{6}[/tex]
i.e x = 3
So, Putting the value of x
The measure of side pq = 18 × 3 + 1 = 55 unit
The measure of side qr = 24 × 3 - 17 = 55 unit
The measure of side pr = 15 × 3 + 10 = 55 unit
Hence The value of x is 3 ,
And The measure of each side is 55 units . Answer
Answer:
x = 3.
Measure of each side is 55 units.
Step-by-step explanation:
In an equilateral triangle, the length of all the three sides are equal.
Therefore, Side PQ = QR = PR.
⇒ 18X + 1 = 24X - 17
⇒ 24X - 18X = 18
⇒ 6X = 18
⇒ X = 3
Substituting the value of X, we get:
PQ = 18(3) + 1 = 55 Units.
QR = 24(3) - 17 = 55 units.
PR = 15(3) + 10 = 55 units.
We see the length of all the sides are equal.
Which system of linear inequalities is represented by the
graph?
Answer:
y<x+1 y>x-2
Step-by-step explanation:
upper line: (0,1) (-1,0)
y=x+1
Lower line: (0,-2) (2,0)
y=x-2
I did not see any solid boundry on the line
Shaded: y<x+1 y>x-2
Answer:
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]
Step-by-step explanation:
According to the graph, the system is formed by two inequalities. Let's find out the equation to each line in first place.
Notice that the upper line passes through points (-1,0) and (0,1). First, we find its slope
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-0}{0-(-1)}=\frac{1}{1}=1[/tex]
Then, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-(-1)\\y=x+1[/tex]
Now, the dashed line indiactes that the inequalities must have sings < or >.
Notice that point (0,0) is part of its solution, that means the inequality is
[tex]y <x+1[/tex]
We do the same process to find the other inequality.
The line passes through points (0,-2) and (2,0).
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-(-2)}{2-0}=\frac{2}{2}=1[/tex]
Then,
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
Notice that point (0,0) is part of its solution, so the inequality is
[tex]y>x-2[/tex]
Therefore, the system of inequalities is
[tex]y <x+1[/tex]
[tex]y>x-2[/tex]
destiny sells pencil cases for $5 each and mechanical pencils for $2 each at the school supply store. she sells p pencil cases and (p+4) mechanical pencils. which expression represents destiny's total sales
Answer:
Step-by-step explanation:
5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.
An engineering student answered 81 questons correctly on a 90 question test. What percent of the question did she answer correctly?
Answer:
90% of the questions she answered correctly
Step-by-step explanation:
%age = 81/90 * 100= 90 % correctness
Any help would be appreciated. Thank you!
Answer:
Area [tex]=62.5\sqrt{6}[/tex] square units
[tex]AB=5\sqrt{15}[/tex] units
[tex]BC=5\sqrt{10}[/tex] units
Step-by-step explanation:
In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.
So,
[tex]BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units[/tex]
a. The area of the triangle ABC is
[tex]A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.[/tex]
b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so
[tex]AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units[/tex]
PLEASE HELP number 5
Answer: Option 3, and 4
Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet the car in her sketch is 8 inches long what is the length in feet of the actual car
Answer:
The actual length of car is 48 feet.
Step-by-step explanation:
Given:
Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.
In her sketch the car is 8 inches long.
Now, to find the length in feet of the actual car.
Let the actual length of car in feet be [tex]x\ feet.[/tex]
And the length of car in her sketch is 8 inches.
So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.
Now, to get the actual length of car by using cross multiplication method:
[tex]\frac{2\ inches}{12\ feet} =\frac{8\ inches}{x\ feet}[/tex]
⇒ [tex]\frac{2}{12} =\frac{8}{x}[/tex]
By cross multiplying we get:
⇒ [tex]2x=96[/tex]
Dividing both sides by 2 we get:
⇒ [tex]48=x[/tex]
⇒ [tex]x=48\ feet.[/tex]
Therefore, the actual length of car is 48 feet.
Help. Explain good for brainliest
The measure of m∠J=90°, m∠G=55° and m∠H=35°
Step-by-step explanation:
Inscribed angles subtended by a diameter are right angles. Hence angle GJH =90°
The diameter GH and chord GJ intercepts an arc with a measure of 70°.The measure of an arc of a circle is equal to the measure of the central angle that intercepts the arc. Hence angle GOJ=70°. Radius of circle GO=OJ, which means triangle GOJ is an isosceles triangle thus ∠OJG=∠OGJ =(180° -70°) /2 = 55°. m∠G=55°
m∠H = (180°-(90°+55°) ) = 180° - 145° =35°
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Keywords : measures, angles, diameter, chord, intercepts, arc
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You are gathering data in the cafeteria, recording which condiments are most popular on students' hamburgers. The data you gather is
A. quantitative.
B. categorical.
C. discrete.
D. bivariate.
Kris runs a 5 K (kilometer) race for charity. It takes her 1 hour. What is Kris' average speed?
Answer: 5 Kilometers Per Hour
Answer:
1/12 km per minute
Step-by-step explanation:
1 hour=60 minutes
5/60=1/12
Monica brought some donuts for $0.50 Each and a box of coffee for $5.
Write and solve an inequality to find the possible number of donuts,d, she brought if she spent less than $15. Then graph the solution set
Answer:
[tex]d < 20\ donuts[/tex]
The graph of the solution set in the attached figure
Step-by-step explanation:
Let
d ----> the possible number of donuts Monica brought
we know that
The number of donuts d multiplied by $0.50 plus the cost of a box of coffee for $5 must be less than $15
so
The inequality that represent this situation is
[tex]0.50d+5 < 15[/tex]
Solve for d
subtract 5 both sides
[tex]0.50d < 15-5[/tex]
[tex]0.50d < 10[/tex]
Divide by 0.50 both sides
[tex]d < 10/0.50[/tex]
[tex]d < 20\ donuts[/tex]
The solution is all whole numbers greater than zero and less than 20 ( I say greater than zero because the problem states that Monica brought some donuts)
The solution set is the interval {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}
Simplify the radicals.
Someone please help because my book doesnt explain how to do this.
Answer: [tex]6y^2i\sqrt{6}[/tex]
Step-by-step explanation:
For this exercise it is important to remember the following property:
[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]
Then, given the expression:
[tex]\sqrt{-216y^4}[/tex]
You can follow these steps in order to simplify it:
1. Descompose 216 into its prime factors:
[tex]216=2*2*2*3*3*3[/tex]
2. The Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then:
[tex]216=2^2*2*3^2*3[/tex]
3. Now you can substitute:
[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]
4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:
[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]
14 x 1 = 14 exemplifies which property
Answer:
multiplicative identity
Step-by-step explanation:
Anything that is divisible by 0 or 1 is called multiplicative identity.
which equation has only two solution x=3 and x=-3
Answer:
The equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x) = x^2 - 9[/tex]
Step-by-step explanation:
Here, the ONLY two rrots of the equation is given as:
x = 3 and x = -3
Now, if x = a is the ZERO of the polynomial, then x - a = 0 is the ROOT of the polynomial.
So, here the only roots of the polynomial are : (x-3) and (x+3)
Also, the POLYNOMIAL = PRODUCT OF ALL ROOTS
So, [tex]P(x) = (x-3)(x+3) = x(x+3) -3(x+3) = x^2 + 3x - 3x - 9 = x^2 - 9\\\implies P(x) = x^2 - 9[/tex]
Hence, the equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x) = x^2 - 9[/tex]
The equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].
We have to determine, the equation which has only two solutions x = 3 and x = -3.
According to the question,
The two roots of the equation is x = 3 and x = -3,
if x = a is the zero of the polynomial, then x - a = 0 is the root of the polynomial.
So, here the only roots of the polynomial are : (x-3) and (x+3).
If the [tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation the product of roots can be written as,
[tex]Product \ of \ roots = \alpha \times \beta[/tex]
Substitute the values in the equation,
[tex]= (x-3 ) (x+3)\\\\= x (x+3) - 3(x+3)\\\\= x^2 + 3x -3x -9\\\\= x^2 - 9[/tex]
Hence, The required equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].
To know more about Quadratic Equations click the link given below.
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You sell small and large candles at a craft fair. You collect $144 selling a total of 28 candles. How many of each type of candle did you sell?
Final answer:
Without knowing the individual prices of small and large candles, we cannot solve for the exact numbers of each type sold. A system of equations would normally be used, but in this case, essential price information is missing.
Explanation:
You sell small and large candles at a craft fair and collect $144 selling a total of 28 candles. To solve how many of each type of candle you sold, let's set up a system of equations with two variables. Let x represent the number of small candles and y represent the number of large candles.
The first equation comes from the total number of candles:
x + y = 28
The second equation involves the total amount of money collected:
ax + by = 144
where a and b are the prices of small and large candles respectively.
Unfortunately, the question does not provide the individual prices of the small and large candles, so we cannot continue without that information. To solve this system correctly, you would need to know the price of at least one type of candle.
With the missing price information, we cannot define a and b and therefore cannot provide a numerical solution to this question.
The square has a perimeter of 160 cm if the square is dilated with a scale factor of 0.9 what is the length of each side of the dilated Square in centimeters
Answer: 36 cm
Step-by-step explanation:
Given : The square has a perimeter =160 cm.
Perimeter of square = 4 (side)
Therefore , the side of square = (Perimeter)÷ 4
= 160 ÷ 4 = 40 cm
The new length of side after dilation = (Scale factor) x (Length of original figure)
For scale factor = 0.9
The new length of each side of the dilated square = (0.9)x(40)=36 cm
Hence, the new length of each side of the dilated square= 36 cm
Answer:
36cm
Step-by-step explanation:
Given: The square has a perimeter of [tex]160\text{cm}[/tex] ,the square is dilated with a scale factor of [tex]0.9[/tex].
To Find: length of each side of the dilated square.
Solution:
Perimeter of square [tex]=160\text{cm}[/tex]
length of each side of perimeter [tex]=\frac{\text{perimeter of square}}{4}[/tex]
[tex]=40\text{cm}[/tex]
Now,
the square is dilated by scale factor [tex]0.9[/tex]
new perimeter of square [tex]=\text{old perimeter}\times\text{scale factor}[/tex]
[tex]=160\times0.9[/tex]
[tex]=144\text{cm}[/tex]
new length of each side of square [tex]=\frac{\text{perimeter}}{4}[/tex]
[tex]=\frac{144}{4}[/tex]
[tex]=36\text{cm}[/tex]
Hence the length of each side of dilated square is [tex]36\text{cm}[/tex]
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 22 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
10 small boxes and 11 large boxes were shipped.
Step-by-step explanation:
Given,
Total boxes shipped = 21
Total volume of shipped boxes = 342 cubic feet
Volume of each small box = 10 cubic feet
Volume of each large box = 22 cubic feet
Let,
Number of small boxes = x
Number of large boxes = y
According to given statement;
x+y=21 Eqn 1
10x+22y=342 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132[/tex]
Dividing both sides by 12
[tex]\frac{12y}{12}=\frac{132}{12}\\y=11[/tex]
Putting y=11 in Eqn 1
[tex]x+11=21\\x=21-11\\x=10[/tex]
10 small boxes and 11 large boxes were shipped.
Keywords: linear equation, subtraction
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What is the results of adding these two equations?
6x+2y=-2
3x-2y=-5
Answer:
x=-7/9, y=4/3. (-7/9, 4/3).
Step-by-step explanation:
6x+2y=-2
3x-2y=-5
-----------------
9x=-7
x=-7/9
6(-7/9)+2y=-2
-42/9+2y=-2
2y=-2-(-42/9)
2y=-2+42/9
2y=-18/9+42/9
2y=24/9
y=(24/9)/2
y=(24/9)(1/2)
y=24/18
y=4/3
HELP I WILL MARK YOU AS A BRAINLIEST!
At a grocery store, the price of 3 cans of
soup is $6.90.
At this rate, how much would 10 cans of
soup cost?
A. $4.30
B. $13.90
C. $20.70
D. $23
EXPLAIN HOW YOU KNOW.
Answer:
D. $23
Step-by-step explanation:
To find the answer, find how much a can costs at that rate and multiply it by 10.
This would be
10 × 6. 90/3=69. 0/3
=23
If you don't understand anything, ask.
Which of the following tables represents a function?
Answer:
B seems right
Step-by-step explanation:
Write the point-slope form of an equation of the line through the points at (-9,9) and (6,-6)
Answer:
y = -x
Step-by-step explanation:
Explained in picture:
SORRY IF INCORRECT!!!!!
Which dimensions cannot create a triangle?
three angles measuring 109, 25º, and 1450
three sides measuring 9 m, 15 m, and 9 m
• three angles measuring 40°, 70°, and 650
o three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
three angles measuring 109º, 25º, and 145º cannot create a triangle
three angles measuring 40º, 70º, and 65º cannot create a triangle
Step-by-step explanation:
Verify each dimensions
Part 1) three angles measuring 109º, 25º, and 145º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]109^o+25^o+145^o=279^o[/tex]
[tex]279^o> 180^o[/tex]
therefore
three angles measuring 109º, 25º, and 145º cannot create a triangle
Part 2) three sides measuring 9 m, 15 m, and 9 m
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 9+15 > 9 ---> is ok
2) 9+9 > 15 ---> is ok
therefore
three sides measuring 9 m, 15 m, and 9 m can create a triangle
Part 3) three angles measuring 40º, 70º, and 65º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
[tex]40^o+70^o+65^o=175^o[/tex]
[tex]175^o< 180^o[/tex]
therefore
three angles measuring 40º, 70º, and 65º cannot create a triangle
Part 4) three sides measuring 6 cm, 8 cm, and 10 cm
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is ok
2) 8+10 > 6 ---> is ok
3) 6+10 > 8 ---> is ok
therefore
three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle
Answer:
its c i promise
Step-by-step explanation:
d/dx(sin x/2+cos x) = (a + b cos x)/(2+cos x)^2 find a and b.
Answer:
a = 1 and b = 2
Step-by-step explanation:
Using the Quotient Rule>
d/dx[(sin x)/(2+cos x) ]
= [(2 + cos x) * cosx - sin x * - sin x)] / (2 + cos x)^2
= 2cos x + cos^2x + sin ^2 x) / (2 + cos x)^2
But cos^2x + sin^2x = 1 so we have:
(1 + 2 cos x) / (2 + cos x)^2
- so a = 1 and b = 2.
Is this true or false 4/3 = 8/9
Santa’s elves are selling are selling cookies for a sale. on the first day they sold 120 peppermint cookies and 30 cinnamon sugar cookies for total of $81. the next day they made $60 by selling 70 peppermint cookies and 60 cinnamon sugar cookies. find total cost of each cookie
The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30
Step-by-step explanation:
Let,
Cost of 1 peppermint cookie = x
Cost of 1 cinnamon cookie = y
According to given statement;
120x+30y=81 Eqn 1
70x+60y=60 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(120x+30y=81)\\240x+60y=162\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](240x+60y)-(70x+60y)=162-60\\240x+60y-70x-60y=102\\170x=102\\[/tex]
Dividing both sides by 170
[tex]\frac{170x}{170}=\frac{102}{170}\\x=0.60[/tex]
Putting x=0.60 in Eqn 2
[tex]70(0.60)+60y=60\\42+60y=60\\60y=60-42\\60y=18[/tex]
Dividing both sides by 60
[tex]\frac{60y}{60}=\frac{18}{60}\\y=0.30[/tex]
The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30
Keywords: linear equation, elimination method
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3. Twenty-four students brought their permission slips to attend the class field
trip to the local art museum. If this represented eight tenths of the class, how
many students are in the class? Use a bar diagram to solve arithmetically. Then
use an equation to solve algebraically.
Answer:
x=30
Step-by-step explanation:
ratio: 8:10 as 24:x
8/10=24/x
10x * 8/10= 10x * 24/x
x * 8 = 10 * 24
8x = 240
8x/8 = 240/8
8x/8 = 30
x = 30
There are (53)2 ⋅ 50 hens in a bird enclosure. What is the total number of hens in the enclosure? (1 point)
0
55
56
530
Answer:
The correct answer is C. 5⁶
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Number of hens in a bird enclosure = (5³)² * 5⁰
2. What is the total number of hens in the enclosure?
Let's recall a couple of properties of the exponents:
1. When you raise any number to a zero power you'll always get 1, with the exception of zero itself.
x⁰ = 1, x ≠ 0
2. The power of a power property says that to calculate a power of a power you just have to multiply the exponents, this way:
(x⁴)⁵ = x ⁴°⁵ = x²⁰
Now, applying those two properties, we have:
(5³)² * 5⁰ = 5³°² * 1 = 5⁶
The correct answer is C. 5⁶
Answer:
c
Step-by-step explanation:
AN EASY PERCENTAGE PROBLEM. In a semiconductor companies quality control test machine found that 22 out of a sample of us 600 computer chips were defective how many of the three 36,000 computer chips the company makes each year would you expect to be defective???
Final answer:
To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion: 22 defective chips / 600 chips = x defective chips / 36,000 chips. Dividing both sides by 600, we find that x = 1,320. Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.
Explanation:
To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion:
22 defective chips / 600 chips = x defective chips / 36,000 chips
Cross-multiplying, we get 600x = 22 * 36,000
Dividing both sides by 600, we find that x = 22 * 36,000 / 600 = 1,320
Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.
How many real-number solutions does the equation have?
0=-5x2 +8x–7
one solution
two solutions
no solutions
infinitely many solutions
Answer:
I'm guessing none because the discrimant (sqrt of b squared - 4ac is less than zero, signifying it has no real roots
Step-by-step explanation:
have a happy holidays!
what solution is
y=9x+35
y=-8/9x+4/5
Answer:
x=-1539/445, y=1724/445. (-1539/445, 1724/445).
Step-by-step explanation:
y=9x+35
y=-8/9x+4/5
-------------------
9x+35=-8/9x+4/5
9x-(-8/9x)=4/5-35
9x+8/9x=4/5-175/5
81/9x+8/9x=-171/5
89/9x=-171/5
x=(-171/5)/(89/9)
x=(-171/5)(9/89)
x=-1539/445
y=9(-1539/445)+35
y=1724/445
3.
of
The completely factored form
2d4 - 6d - 18d2 - 54d is
Answer:
2d(d³-9d-30)
Step-by-step explanation:
2d⁴ - 6d - 18d² - 54d
= 2d⁴- 18d²-60d
=2d(d³-9d-30)