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2 years ago

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A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fenc

ing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.

1 answer:

Vaselesa [24]2 years ago

5 0

Answer:

$\frac{8h}{\sqrt{2}} + 16h$

Step-by-step explanation:

First we need to compute the side length as a function of h

So x be the side length of the right isosceles triangle, in Pythagorean formula we have

$x^2 + x^2 = h^2$

$2x^2 = h^2$

$x = \frac{h}{\sqrt{2}}$

The cost for the legs is

$C_l = 4*2x = \frac{8h}{\sqrt{2}}$

The cost for the hypotenuse is

$C_h = 16h$

So the total cost in term of h is

$C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h$

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There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been

slamgirl [31]

There are 400 balcony seats in the concert hall.

<u>Step-by-step explanation</u>:

Step 1 :

The number of lower seats = 450 seats

Total seats = Lower seats + balcony seats

Step 2 :

Tickets sold = 170 tickets
Total tickets = x

Tickets sold = 1/5 of total tickets.

⇒ 170 = (1/5)x

⇒ x = 5 $\times$ 170

⇒ x = 850 tickets

∴ Total seats in the concert hall is 850.

Step 3 :

Total seats = 450 + balcony seats

850 - 450 = balcony seats

∴ balcony seats = 400

7 0

2 years ago

Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are abou

wel

Answer:

5%

Step-by-step explanation:

Total 'halwa' made = 1

Divided into four equal portion = 1/4

Arrival of an unexpected guest = 1/5

By what percentage has each family member's share been reduced:

Change in the sharing proportion:

Previous share ratio - new sharing ratio

(1/4 - 1/5) = (5 - 4) / 20 = 1/20

That means total reduction in the sharing = 1/ 20

Since each member comes contributed equally:

Reduction in each family member's share ;

(1 / 20) ÷ 4

(1 / 20) * 1/4 = 1/ 80

Percentage reduction:

(Reduction / original share) * 100%

[(1/80) ÷ (1/4)] * 100

(1/80 * 4/1) * 100%

(1/20) * 100%

= 5%

Reduction in each family members share = 5%

3 0

2 years ago

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equati

amid [387]

In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
$f(x) = a(x - x_1)(x-x_2)(x-x_3)$

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form $(x_n , 0)$

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say $x_1 = 2 , x_2 = 3 , x_3 = 5$

So required equation is
$f(x) = a (x-2)(x-3)(x-5)$
              $= a[(x^2 - 2x - 3x + 6)(x-5)]$
              $= a[(x^2 - 5x+6)(x-5)]$
              $= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)$
              $= a(x^3 - 10x^2+31x-30)$
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
$-5= a (0-0+0 - 30)$
$-5 = -30a$
$a = \frac{-5}{-30} = \frac{1}{6}$
So required equation of cubic polynomial is
$f(x) = \frac{1}{6}(x^3 -10x^2+31x-30)$

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.

4 0

2 years ago

Read 2 more answers

Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Cre

weqwewe [10]

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

4 0

2 years ago

The members of a high school band asked a number of students whether they would like blue, gold, or both for the uniforms for th

MaRussiya [10]

The values of a and b are a = 33% and b = 43% ⇒ last answer

Step-by-step explanation:

The venn-diagram contains:

A circle labeled blue 32
A circle labeled gold 25
The two circles are overlap with label 12 on the overlap

The table:

→ Band : blue : N.b : total

→ gold : 16% : a : 49%

→ N.g : b : 8% : 51%

→ Total : 59% : 41% : 100%

We need to find the values of a and b

From the table

16% represents the percentage of blue and gold uniforms (2nd row with 2nd column)

From venn-diagram

The common part of blue and gold label with 12 (overlap of two circles)

∴ 16% of the total number of students = 12

∵ 16% × x = 12

∴ $\frac{16}{100}$ × x = 12

∴ 0.16 x = 12

- Divide both sides by 0.16

∴ x = 75

∵ x represents the total number of students

∴ The total number of students were asked is 75

From the table

b represents the percentage of blue but not gold uniforms (3rd row and 2nd column)

From venn-diagram

The part that has blue and not gold labeled with 32 (the part of the blue circle not in the gold circle)

∴ 32 of the total number of students like the blue but not gold

- Divide 32 by the total 75 , then multiply the quotient by 100%

to find the percentage of blue but not gold

∴ b = $\frac{32}{75}$ × 100% = 42.6666%

∴ b ≅ 43%

From the table

a represents the percentage of gold nut not blue uniforms (2nd row and 3rd column)

From venn-diagram

The part that has gold and not blue labeled with 25 (the part of the gold circle not in the blue circle)

∴ 25 of the total number of students like the gold but not blue

- Divide 25 by the total 75 , then multiply the quotient by 100%

to find the percentage of gold but not blue

∴ a = $\frac{25}{75}$ × 100% = 33.3333%

∴ a ≅ 33%

The values of a and b are a = 33% and b = 43%

To check your answer complete the table you will find the total of it is 100% ( for the columns 16% + 43% = 59% , 33% + 8% = 41% , then 59% + 41% = 100%, for the rows 16% + 33% = 49% , 43% + 8% = 51% , then 49% + 51% = 100%)

Learn more:

You can learn more about the probability in brainly.com/question/3756853

#LearnwithBrainly

4 0

2 years ago

Read 2 more answers