A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.




A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.




Part A: What is the height of the box? Show your work. (5 points)


Part B: What is the approximate amount of cardboard used to make the sides of the candy box? Explain how you got your answer. (5 points)

Paulie's opportunity cost of producing a cup of ice cream is 4 T-shirts while Vinny's opportunity cost (C) of producing a t-shirt is 0.53

The table entries are given as:

          Ice Cream (cups) T-shirts (quantity)

Paulie 5.00                          20.00

Vinny 8.00                              15.00

Paulie's opportunity cost of producing a cup of ice cream is calculated by dividing the number of T-shirts by the cups of ice cream.

So, we have:

[tex]C = \frac{20.00}{5.00}[/tex]

[tex]C =4.00[/tex]

Similarly, Vinny's opportunity cost (C) of producing a t-shirt is calculated by dividing the cups of ice cream by the number of T-shirts

So, we have:

[tex]C = \frac{8.00}{15.00}[/tex]

[tex]C = 0.53[/tex]

Hence, Vinny's opportunity cost (C) of producing a t-shirt is 0.53

Read more about opportunity costs at:

https://brainly.com/question/8846809

Answer:

y = 7°

Step-by-step explanation:

By interior angle sum theorem of a triangle.

[tex]51 \degree + 87 \degree + 6y = 18 \degree \\ \\ \implies 138 \degree+ 6y = 18 0\degree \\ \\ \implies 6y = 180 \degree - 138 \degree \\ \implies 6y = 42 \degree \\ \\ \implies y = \frac{42 \degree}{6} \\ \\ \huge \red{\implies y =7 \degree} \\ \\ [/tex]

We know –

Question's given –

The equation (1+m) x²-2(1+3m) x +(1+8m) =0 has equal roots.That means, Δ Discriminant is 0.(D= b²-4ac)

According to the question –

Now, Δ Discriminant = 0

↠{-2(1+3m)}² -4 × (1+m) ×(1+8m)=0

↠4(1+3m)² - 4 (1+m)(1+8m) = 0

↠4(1+ 9m² + 6m - 1 -8m - m -8m²) =0

↠4 (1+ 9m² + 6m - 1 -9m -8m²)=0

↠m²-3m =0

↠m(m-3) = 0

↠m =0,3

Answer:

She can run 58.5 yards in 9 seconds.

Step-by-step explanation:

39/6=x/9

cross product

6*x=39*9

6x=351

x=351/6

x=58.5

Answer:

The answer to this question is 97.5

Step-by-step explanation:

A= 15x13/2=97.5

Answer:

3.5 : 7 > 1.2 : 2.5.

Step-by-step explanation:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5 and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

The L.C.M (least common multiple) of 5 and 3 is 15.

Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

Now, 12/15 > 10/15

Therefore, 4 : 5 > 2 : 3.

2. Compare the ratios 5 : 6 and 7 : 9.

Solution:

Express the given ratios as fraction

5 : 6 = 5/6 and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

The L.C.M (least common multiple) of 6 and 9 is 18.

Making the denominator of each fraction equal to 18, we have

5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18

Clearly, 15 > 14

Now, 15/18 > 14/18

Therefore, 5 : 6 > 7 : 9.

3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.

Solution:

1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7

1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2

[We removed the decimal point from the ratios now, we will compare the ratio]

Now find the L.C.M (least common multiple) of 25 and 2

The L.C.M (least common multiple) of 25 and 2 is 50.

Making the denominator of each fraction equal to 50, we have

= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50

Now, 25/50 > 24/50

Therefore, 3.5 : 7 > 1.2 : 2.5.

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}}\implies \cfrac{-15}{-2+5}\implies \cfrac{-15}{3}\implies -5[/tex]

[tex]\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}{6}=\stackrel{m}{-5}(x-\stackrel{x_1}{(-5)}) \\\\\\ y-6=-5(x+5)\implies y-6=-5x-25\implies y=-5x-19[/tex]

red

Step-by-step explanation:

i tink cus it looks like it

Answer:

B.

Step-by-step explanation:

Because of isosceles triangle, AB = CB.

Because of the median, AD = CD.

Because of congruence of segments being reflexive, BD = BD.

By SSS, the triangles BAD and BCD are congruent.

Answer: B.

Using congruence postulate SSS we can prove that,

ΔBAD is congruent to ΔBCD.

Option B is the correct answer.

There are ways to prove that two triangles are congruent.

- Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

- Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

- Angle-Side-Angle (ASA) Congruence.

The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

- Angle-Angle-Side (AAS) Congruence.

We have,

BD is the median of ΔABC.

ΔABC is isosceles.

Using congruence postulate SSS.

We have,

ΔABC is isosceles.

This means,

AB = CB

AD = DC [ BD is median ]

BD = BD [ Common sides ]

ΔBAD is congruent to ΔBCD

Thus,

ΔBAD is congruent to ΔBCD

Learn more about triangle congruency here:

https://brainly.com/question/12413243

#SPJ5

Answer:

[tex]\frac{2x}{x-1}[/tex]

Answer:

a = [tex]\frac{9}{5}[/tex] or [tex]1\frac{1}{5}[/tex]

Step-by-step explanation:

15a = 27

a = [tex]\frac{27}{15}[/tex]

a = [tex]\frac{9}{5}[/tex]

a = [tex]1\frac{1}{5}[/tex]

Answer:

a = 9/5 or a = 1 4/5

Step-by-step explanation:

15a = 27

Divide both sides of the equation by 15.

a = 27/15

Reduce the fraction by dividing the numerator and denominator by 3.

a = 9/5 = 1 4/5

BC = 5√2

AC = 10

[tex]ac = \sqrt{ {ab}^{2} + {bc}^{2} } = \sqrt{2 \times {(5 \sqrt{2} )}^{2} } = \sqrt{100} = 10[/tex]

Answer:

10 and 5*[tex]\sqrt{2}[/tex]

Step-by-step explanation:

See attachment

Answer:

see explanation

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

(1)

a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then

[tex]a_{n}[/tex] = 2 [tex]-3)^{n-1}[/tex]

(2)

a₁ = 5 and r = [tex]\frac{10}{5}[/tex] = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

Answer:

-20

Step-by-step explanation:

12 times 5 - 100 divided by 2

Answer:

-68

Step-by-step explanation:

12(4+1)-100/2 = 12(4)+12(1)-100/2

48-12=36-100/2

36-100= -136/2

-136/2 = -68

Answer:

No

Step-by-step explanation:

It has a proportional relationship until x is 8 because in the other parts of the equation it is 1×2.5 for each equation while at 8=18 it does not follow the same pattern as the previous equations. also sorry if I don't use the right words im just trying to explain what I mean.

Answer:

600 $

Step-by-step explanation:

10 + 12x ≤ 75

12x ≤ 65

x ≤ 65 ÷ 12

x ≤ 5.416

5 whole friends

answer is A

Answer:

39 athletes

Step-by-step explanation:

There is a total of 45 people on the bus.  This INCLUDES the athletes (A), 2 coaches and 4 managers.

Therefore, we need to sum A, 2 and 4 and equal it to 45:

2 + 4 + A = 45  so we need to used equation d.

To calculate how many athletes are on the bus, find the value of A:

                                         2 + 4 + A = 45

Subtract 2 from both sides:  4 + A = 43

Subtract 4 from both sides:        A = 39

Answer:

12xy

Step-by-step explanation:

For rectangle A, the length would be (x+3x) and the width would be 3y, so 4x*3y = 12xy

Answer:

PQ = 98.21

Step-by-step explanation:

PQ/23 = 47/11

PQ × 11

23 × 47

11PQ = 1081

11PQ/11 = 1081/11

PQ = 98.21

Here is the answer with explanation

Answer:

9x² + 72x + 144    OR   x² + 8x + 16

Step-by-step explanation:

Data :

Sqaure has  a side  let say p = 3x + 12

As the formula for square area is

    Area = A = p² or length × width

As square  has all equal  side

So   ( 3x + 12 ) ( 3x + 12 )

   ⇒  9x² + 36x +36x + 144

         9x² + 72x + 144

    OR  take 9 common

   x² + 8x + 16

Answer:

Given below.

Explanation:

Coordinates given: W( -4, -3 ) , X( 1 , -2 ), Y(2, -7 ) , Z( -3, -8)

To find the distance we will use the formula: distance=√((x2-x1)²+(y2-y1)²)

WX = √((1--4)²+(-2--3)²)

      = √26

YZ = √((-3-2)²+(-8--7)²)

     = √26

XY = √((2-1)²+(-7--2)²)

     = √26

WZ = √(-3--4)²+(-8--3)²

      = √26

WY =  √(2--4)²+(-7--3)²

     = 2√13

XZ = √(-3-1)²+(-8--2)²

     = 2√13

Answer:

WX = √26

YZ = √26

XY = √26

WZ = √26

WY = 2√13

XZ = 2√13

hope this helps! <3

Answer:

Hii! so are you asking for the answer to a graph? do you want the point?

If you do then I think it is (7a, -3) I might be wrong let me know if I am and I'll fix it.

Step-by-step explanation: