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3 years ago

Please answer answer question

Mathematics

1 answer:

sertanlavr [38]3 years ago

7 0

Answer:

156.6 m²

Step-by-step explanation:

To find the surface area of this pyramid, we need to find the area of the base and the sides.

The base triangle has a length of 9 and a height of 7.8. So:

$\frac{bh}{2} = \frac{9\cdot7.8}{2} = \frac{70.2}{2} = 35.1$

Now, the length of the sides are 9 and the height is 9. So:

$\frac{9\cdot9}{2} = \frac{81}{2} = 40.5$

Since there are 3 identical sides:

$40.5\cdot3=121.5$

Add the values:

$121.5+35.1=156.6$

Hope this helped!

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Find the values of x for which the denominator is equal to zero for y=3x+6/x^2-5x+6

lilavasa [31]

Answer:

x = 2

and

x = 3

Step-by-step explanation:

The function given is:

$y=\frac{3x+6}{x^2-5x+6}$

In this fraction, the bottom part is the denominator. We need to set it equal to 0 and solve for 2 values of x.

$x^2-5x+6=0\\x^2-3x-2x+6=0\\x(x-3)-2(x-3)=0\\(x-2)(x-3)=0\\x=2,3$

This is middle term factorization process. Hence the 2 solutions (roots) of the denominator is:

x = 2, 3

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3 years ago

Which algebraic expression means “four less than three times a number”?

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It’s 3n-4

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3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

Daniel went to play soccer at a quarter to 6. His mom called him to come home for dinner at 20 minutes after 7. How many minutes

Minchanka [31]

Answer:

Daniel played soccer for 95 minutes

Step-by-step explanation:

1) If he started at a quarter to 6 this means he started at 5:45 as a quarter is 15 minutes.

2) If he finished 20 minutes after 7 he ended at 7:20

3) Add 15 minutes to get to 6:00.

4) Since 60 minutes are in an hour, add 60 minutes to get 7:00. This brings our total up to 75 minutes.

5) Add the last 20 minutes to get the total amount of 95 minutes spent playing soccer.

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3 years ago

6 x 6 x 6 x 6 x 6 x 6 x 6= 6^x

Vilka [71]

Answer:

$6^7$

Step-by-step explanation:

$6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 = 6^7 \\$

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3 years ago

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