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wolverine [178]

3 years ago

15

Find the volume of a pyramid with a square base, where the side length of the base is 7.5 cm and the height of the pyramid is 10

.2. Round your answer to the nearest tenth of a cubic centimeter

1 answer:

m_a_m_a [10]3 years ago

8 0

Answer:

The volume is 191.3 $cm^3$

Step-by-step explanation:

Recall that the formula for the volume of a pyramid is given by the formula:

$Volume=\frac{B\,*H}{3}$

where B is the area of the pyramid's base, and H its height. So, in our case, the base is a square of length 7.5 cm, which gives 56.25 cm^2

Now, we use this value and the height 10.2 cm to find the volume:

$Volume=\frac{B\,*H}{3}\\Volume=\frac{56.25\,*10.2}{3}\\Volume=191.25\,\,cm^3$

which rounded to the nearest tenth is: 191.3 $cm^3$

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16. Solve -3x2 - 9x + 12 = 0.

AURORKA [14]

Given :

-3x² - 9x + 12 = 0

To find :-

Value of x .

Solution :-

Given equation ,

-( 3x² + 9x -12 ) = 0
3x² + 9x - 12 = 0
3x² + 12x - 3x - 12 = 0
3x ( x +4) -3( x +4) = 0
(3x -3)(x +4) = 0
x = 3/3 , -4
x = 1 , -4

7 0

3 years ago

Using the functions presented in the example, how much can Cam expect to earn if he sells all the corn produced on 1.5 acres?

12345 [234]

Answer:

Cam expect to earn if he sells all the corn produced on 1.5 acres is $8725.

Step-by-step explanation:

Given : $C(a)=7500a-1500$ , $M(C)=0.9C- 50$ and $M(C(a))=6750a-1400$

To find : How much can Cam expect to earn if he sells all the corn produced on 1.5 acres?

Solution :

$C(a)=7500a-1500$

Substitute a=1.5,

$C(1.5)=7500(1.5)-1500$

$C(1.5)=11250-1500$

$C(1.5)=9750$

Now, taking function $M(C)=0.9C- 50$

Substitute C=9750,

$M(9750)=0.9(9750)- 50$

$M(9750)=8775- 50$

$M(9750)=8725$

Now, taking function $M(C(a))=6750a-1400$

Substitute a=1.5,

$M(C(1.5))=6750(1.5)-1400$

$M(C(1.5))=10125-1400$

$M(C(1.5))=8725$

Therefore, Cam expect to earn if he sells all the corn produced on 1.5 acres is $8725.

8 0

3 years ago

The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle

AVprozaik [17]

Answer:

Length of rectangle is 31 yards and Width is 24 yards.

Given:

The length of a rectangle is 7 more than the width.
The area is 744 sqaure yards

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

$\\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\$

On Substituting the required values, we get;

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\$

As we know that width of the rectangle can't be negative. So x = 24

<u>Hence</u>,

Width of rectangle = x = 24 yards
Length of the rectangle = x + 7 = 31 yards

$\therefore$ Length of rectangle is 31 yards<u> </u>and Width is 24 yards.

8 0

2 years ago

A village fete has a children’s running race each year, run in heats of up to ten children. For each heat the first three contes

bekas [8.4K]

Answer: 1) 1/3,654 2) 3/406 3) 72,684,900,288,000 4) 120

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

1) First and Second and Third

$\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}$

2) First and Second

$\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}$

$3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}$

$4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}$

8 0

3 years ago

Help please? thank you

Alexxandr [17]

9514 1404 393

Answer:

RS = √(b² +(c -a)²)

Step-by-step explanation:

Put the given point coordinates in the given formula:

R = (x₁, y₁) = (0, a)
S = (x₂, y₂) = (b, c)

RS = √((b -0)² +(c -a)²)

RS = √(b² +(c -a)²)

8 0

2 years ago