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4 years ago

Please help me out if possible!

Mathematics

1 answer:

oksano4ka [1.4K]4 years ago

3 0

Answer:

Step-by-step explanation:

Hi,

So lets answer this question;

Here we know that:

69° + z = 180° [Straight angle or Supplementary angle]

⇒ z = 180° - 69°

= <u>111°</u>

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An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn

Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43 inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24, this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative value ( -49.7) so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0

2 years ago

Forty students are In Science club. Of those 45% are girls. This percent increase 56% after new girls join the club. How many ne

stepan [7]

45% of 40 is 0.45×40=18 girls
if x girls join then 56% of 40+x is 0.56(40+x)=18+x
22.4+0.56x=18+x
put together like terms
4.4=0.44x
<span>x=10 girls joined</span>

8 0

3 years ago

Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate th

pochemuha

Answer:

Polynomial expression that represents the area of blanket:

$A(x)=(6x^2+5x-21)cm^2$

If $x=2$ : $A(2)=13cm^2$

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

$A=lw$

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

$l=(3x+7)cm$

$w=(2x-3)cm$

Substitute them into $A=lw$ :

$A(x)=(3x+7)(2x-3)$

Then:

Use Distributive property (Remember the Product of powers property: $b^a*b^c=b^{(a+c)}$ ):

$A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21$

Add like terms:

$A(x)=(6x^2+5x-21)cm^2$ (Simplied form)

Evaluate $x=2$ :

$A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2$

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4 years ago

Hey store gives away gift bags during a cell a visa gift bags 50% are green 20% are yellow and 30% or blue the average number of

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Answer:8

Step-by-step explanation:

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3 years ago

Jada is designing two new paths leading from park entrances to a fountain near the center of the park.

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Is there a question?

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3 years ago