1. The science club constructed a pyramid with a square base out of paper clips. The height of the pyramid is 2.5 feet. One side of the square measures 2.5 feet. What is the slant height of the pyramid?

2. A modern skyscraper is being built with triangular shaped windows. One window is a right triangle with the longest side measuring 24 inches and another side measuring 12 inches. What is the length of the third side of the window?

3. The height of a cone-shaped building is 50 feet, and the radius of its base is 20 feet. Find the building's slant height. Show all work

Answer:

Below.

Step-by-step explanation:

I can't read it very well but one equation might be

2x + 8 = 3x - 12

(because the opposite sides of a parallelogram  are congruent.

Explanation:

Opposite angles of a parallelogram are equal.

B. (3x - 12)° = (2x + 8)°

This equation can be used to solve x.

3x - 12 = 2x + 8

3x - 2x = 12 + 8

x = 20°

Verification:

3(20) - 12 = 2(20) + 8

60 - 12 = 40 + 8

48° = 48°

Hence, verified.

Answer:

$103

Step-by-step explanation:

192.62 divided by 1.87

answer is $103

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If the markup price of the shoes is $192.61 then the original price of the shoes will be equal to $25.04.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given information in the question,

Let the original price of the shoes is x.

Markup Price = $192.61, which is 87% more than the original price.

Price markup = 192.61 × 87/100 = $167.57

Original Price, x = $192.61 - $167.57

x = $25.04.

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If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees

Solution:

Given that:

[tex]cos x= sin (20 + x)[/tex]

We know that,

[tex]sin (a+b)=sin a \times cos b+cos a \times sin b[/tex]

[tex]cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x[/tex]

[tex]cos x-sin20 \times cos x=cos 20 \times sin x[/tex]

Taking cos x as common,

[tex]cos x(1-sin 20)=cos 20 \times sin x[/tex]

[tex]\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}[/tex]

By trignometric functions,

sin 20 = 0.34202

cos 20 = 0.939692

So,

[tex]tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002[/tex]

Therefore,

x = arc tan (0.7002)

x = 35 degrees

Therefore value of x is 35 degrees

cos x = sin (20 + x)

sin and cos are co - functions, which means that:

cos x = cos [90 - (20 + x)]

cos x = cos (90 - 20 - x)

cos x = cos (70 - x)

Therefore, x = 70 - x

x + x = 70

2x = 70

x = 35

Therefore value of x is 35 degrees

Answer:

Step-by-step explanation:

5 ÷ 1/3

= 5 × 3/1

= 15

Answer:

Step-by-step explanation:

first we need to find the slope using the slope formula :

slope = (y2 - y1) / (x2 - x1)

(-9,7)...x1 = -9 and y1 = 7

(-6,-3)....x2 = -6 and y2 = -3

now we sub

slope = (-3 - 7) / (-6 - (-9) = -10 / (-6 + 9) = -10 / 3

so our slope is -10/3

now we use y = mx + b....with m representing the slope

slope(m) = -10/3

use either of ur points....I will use (-9,7)...x = -9 and y = 7

we are solving for b, the y intercept

now we sub

7 = -10/3(-9) + b

7 = 30 + b

7 - 30 = b

- 23 = b

so ur equation is : y = -10/3x - 23

Final answer:

To find the equation of the line through (-9, 7) and (-6, -3), calculate the slope, which is -10/3, and then use the point-slope form to derive the equation y = -10/3 x + 23.

Explanation:

To complete the equation of the line through the points (-9, 7) and (-6, -3), we need to find the slope (m) and use one of the points to find the y-intercept (b) in the slope-intercept form y = mx + b.

Step 1: Find the slope (m):

Step 2: Use point-slope form to find equation:

The completed equation of the line is y = -10/3 x + 23.

Answer:

slope: 2/3

y intercept: - 2

x-0,3

y - 3 0

Answer:

graph C

Step-by-step explanation:

Answer: y = (4/3)x + 8

Step-by-step explanation:

If 3x-y=12, what is the value of 8x/2y?

Answer:

[tex]\frac{8x}{2y} =\frac{4x}{3x-12}[/tex]

Step-by-step explanation:

[tex]3x-y=12[/tex]

[tex]-y=12-3x[/tex]

[tex]y=3x-12[/tex]-------------------------(equation 1)

Now,

[tex]\frac{8x}{2y} =\frac{8x}{2(3x-12)}[/tex]---------(from equation 1)

[tex]=\frac{8x}{6x-24}[/tex]

[tex]=\frac{8x}{2(3x-12)}[/tex]

[tex]=\frac{4x}{3x-12}[/tex]

Therefore, the value of [tex]\frac{8x}{2y} =\frac{4x}{3x-12}[/tex]

Answer:(x,y)-(x+7,y+6)

Step-by-step explanation:

The equation is simplified to -x = 5, yet a negative x value indicates that the identity is not true. Hence, there is no solution to this equation.

To solve this equation, we should first try to simplify both sides of the equation.

On the left side, combine like terms. This gives us -6x - 7.

On the right side, we already have -5x - 12.

Setting these expressions equal to each other yields: -6x - 7 = -5x - 12.

Adding 5x to both sides gives us -x - 7 = -12.

Then adding 7 to both sides gives us -x = 5.

However, a negative x value would indicate that the identity is not true, thus the equation has no solution.

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Answer:

x = 7

Step-by-step explanation:

The inscribed angle (5x - 3) is equal to half the measure of the intercepted arc

5x - 3 = 0.5(9x + 1) ← multiply both sides by 2

10x - 6 = 9x + 1 ( subtract 9x from both sides )

x - 6 = 1 ( add 6 to both sides )

x = 7

Answer:

The sixteenth term is (7.5y - 6.5x).

Step-by-step explanation:

The first term of the A.P. is given to be x and the common difference is assumed to be d.

So, the third term = y = x + (3 - 1)d {Given that the third term is y}

Then, 2d = y - x

⇒ [tex]d = \frac{y - x}{2}[/tex]

Therefore, the sixteenth term of the A.P. will be = x + (16 - 1)d

= [tex]x + 15 \times \frac{y - x}{2}[/tex]

= x + 7.5y - 7.5x

= 7.5y - 6.5x (Answer)

Answer:

The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].

Step-by-step explanation:

Given,

[tex]a_1=x[/tex]

[tex]a_3=y[/tex]

And also given, [tex]T_n=a+(n-1)d[/tex]

We have to find out the 16th term of given A.P.

Firstly, we will find out the common difference(d).

Common difference(d) is calculated by given formula.

[tex]T_3=a+(n-1)d[/tex]

On putting the values, we get;

[tex]y=x+(3-1)d\\\\y=x+2d\\\\2d=y-x\\\\d=\frac{y-x}{2}[/tex]

Now the value of 'd' is calculated, so we can find out the 16th term by using the formula.

[tex]T_{16}=x+(16-1)\frac{y-x}{2}\\\\T_{16}=x+15\times\frac{y-x}{2}\\\\ T_{16}=x+\frac{15(y-x)}{2}[/tex]

Hence The sixteenth term is [tex]x+\frac{15(y-x)}{2}[/tex].

Answer:

1 11/20m

Step-by-step explanation:

4 times 5 is 20

3/4(5) 4/5(4) =

15/20m + 16/20m =

31/20m = 1 11/20m

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf \stackrel{\textit{x-intercept}}{(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})}\qquad \stackrel{\textit{y-intercept}}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{6}}}\implies -\cfrac{5}{6}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{5}{6}}(x-\stackrel{x_1}{6}) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6(y-0)=6\left(-\cfrac{5}{6}(x-6) \right)}\implies 6y=-5(x-6) \\\\\\ 6y=-5x+30 \implies 5x+6y=30[/tex]

The standard form of the line with an x-intercept of 6 and a y-intercept of 5 is -5x + 6y = 30.

The standard form of a linear equation is given by the equation Ax + By = C, where A, B, and C are real numbers and A and B are not both zero. To find the standard form of the line with an x-intercept of 6 and a y-intercept of 5, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope using the two intercepts. The slope is (y-intercept - x-intercept) / (0 - 6) = (5 - 0) / -6 = -5/6.

Now, we can substitute the slope and the y-intercept into the standard form equation to get: (-5/6)x + y = 5. Multiplying through by 6, we get -5x + 6y = 30. Therefore, the standard form of the line is -5x + 6y = 30.

Answer:

The required points of the given line segment  are ( - 7, - 4 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( - 2, 3 ) and point A is ( 3, 10), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex]  )then the mid points M are-  

M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex]  , [tex]\frac{ y_{1} + y_{2} }{2}[/tex]  )

Here,

Let A ( 3, 10 ), B ( x, y ) with midpoint M ( - 2, 3 ) -

then by the midpoint formula M are-

( - 2, 3 )  = ( [tex]\frac{ 3 + x}{2}[/tex] , [tex]\frac{ 10 + y}{2}[/tex] )

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{ 3 + x}{2}[/tex] = - 2  , [tex]\frac{ 10 + y}{2}[/tex] = 3)

( 3 + x = - 4, 10 + y = 6 )

( x = - 4 - 3, y = 6 - 10 )

( x = - 7, y = -4 )

Hence the required points  A are ( - 7, - 4 ).

We can also verify by putting these points into Midpoint formula.

Final answer:

To find the other endpoint of a line segment with a known endpoint (3, 10) and midpoint (-2, 3), use the midpoint formula in reverse to calculate the coordinates, resulting in the other endpoint being (-7, -4).

Explanation:

To find the other endpoint of a line segment when given one endpoint and the midpoint, you can use the midpoint formula in reverse. The midpoint formula in two dimensions is
( (x1+x2)/2, (y1+y2)/2 ), where (x1, y1) and (x2, y2) are the endpoints of the line segment. Given that (3, 10) is one endpoint and (-2, 3) is the midpoint, we can set up equations to find the coordinates of the unknown endpoint (x2, y2).

To find x2, we use the formula for x-coordinate of the midpoint: (-2 + 3)/2 = (x2 + 3)/2. Solving for x2 gives us x2 = -2 - 3 = -7.

To find y2, we use the formula for y-coordinate of the midpoint: (3 + 10)/2 = (y2 + 10)/2. Solving for y2 gives us y2 = 2*3 - 10 = 6 - 10 = -4.

Therefore, the other endpoint of the line segment is (-7, -4).

Answer: 250 grams.

Step-by-step explanation:

Let x be the weight of the solution.

Given : There are 80 grams of salt in a 32% solution.

That means , 32% of x = 80 grams

[tex]\Rightarrow\ 0.32x=80[/tex]  [convert percent into decimal by dividing it by 100]

[tex]\Rightarrow\ x=\dfrac{80}{0.32}=\dfrac{8000}{32}=250[/tex]

i.e. Total solution = 250 grams.

Hence, the weight of the solution = 250 grams.

Answer:

y = - 5/2 * - 2

y = 10/2

y = 5

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

72/2=36 50% of 72 is 36

Answer:

36

Step-by-step explanation:

72 divided by 2 to get a quotient of 36

Answer:

The top left graph is the correct one.

Step-by-step explanation:

The graph of y = 1/2x - 4 will rise to the right , have a slope of 1/2  and pass through the point (0, -4) on the y-axis.

Since the inequality sign is 'less than or equal to' the line will be continuous and the shading will be below this line.

Answer:

-216 has three real cube roots.

Step-by-step explanation:

Answer:

number of shells zoe gives to dev  = 7

number of shells zoe is left with  = 55-7= 48

number of shells dev has = 9+7=16

Step-by-step explanation:

let the initial number of shells that dev has be A, and initial number of shells that zoe has be B.

let the number of shells that zoe gives to dev be x.

after giiving x shells zoe is left with 3 times the number of shell as that of dev.

therefore number of shells with zoe = 3×number of shells with dev.

number of shells with zoe = initial shells - x = 55-x

number of shells with dev = initial shells + number of shells he gets

                                            = 9+x

therefore (55-x)=3×(9+x)

55-x = 27+3x

55-27=3x+x

4x = 28

x= 7

therefore number of shells zoe gives to dev  = 7

number of shells zoe is left with  = 55-7= 48

number of shells dev has = 9+7=16

Answer:

Zoe laverne!!~!!!!!!!~~~!~~!~!~!

Step-by-step explanation:

Evaluate.

Follow PEMDAS.

7+(10-4)²÷4×(1/2)³

parentheses and exponents first

7+36÷4×(1/8)

multiplication next

7+9×(1/8) ----> 7+(9/8)

addition

8 1/8

answer: third choice

33.3...% = 1/3.

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Answer: 33.3 or 1/3

Step-by-step explanation:

i really good at math so if you need help message me

Answer:

the answer will be -5 and 1/2

Answer:

5 is a regular number and 1/2 is a fraction

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Step-by-step explanation:

Final answer:

The ordered pair (2,5) satisfies the equation -3x+4y=14, making it the correct solution, while the ordered pair (4,6) does not satisfy the equation.

Explanation:

To determine which ordered pair is a solution to the given linear equation -3x+4y=14, we need to plug in the x and y values from each pair into the equation and see if the equation holds true.

For the ordered pair (2,5), substituting x with 2 and y with 5 gives us:

Since the equation is satisfied, (2,5) is a solution to the equation.

For the ordered pair (4,6), substituting x with 4 and y with 6 gives us:

Since -12 + 24 does not equal 14, the equation is not satisfied, and hence, (4,6) is not a solution to the equation.

Therefore, the correct answer is A- Only (2,5)

Answer:

26

Step-by-step explanation:

2(3y+12)=180

3y+12=90

3y=78

y=26

Answer:

Option c) is correct.

The value of y in the given equation is 26 ie., y=26

Step-by-step explanation:

Given equation is

[tex]2(3y+7+5)=196-16[/tex]

Now to the find the value of y in the above equation.

To find y simplify the above equation

[tex]2(3y+7+5)=196-16[/tex]

[tex]2(3y+12)=180[/tex]

Now apply distributive property

[tex]6y+24=180[/tex]

[tex]6y=180-24[/tex]

[tex]=\frac{156}{6}[/tex]

Therefore y=26

Option c) is correct.

The value of y in the given equation is 26 ie., y=26

Answer: 8 1/3 yards per second

500 yards/60 seconds=8 1/3 yards per second

Check Work:

8 1/3 yards per second*60 seconds=500 yards per minute.

Hope this helps!