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3 years ago

What is the volume of the prism below

Mathematics

1 answer:

Eddi Din [679]3 years ago

6 0

Answer:

18 cm³

Step-by-step explanation:

The volume of any prism is the area of the base multiplied by the height of the prism. In this case, the sides are the bases since they are of the same shape.

V= base area x height

In this case, the base is a triangle. The area of a triangle is

0.5 x length of the triangle x height of the triangle

The height is basically the distance between both bases, in this case, both triangles.

V= (0.5x4x3)x3 = 18 cm³

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Riaz wants to use the number sentence shown to solve a problem.

BARSIC [14]

B) A key chain can hold 3 keys. If there are a total of 12 keys, how many key chains are there?

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3 years ago

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This figure is made up of a quadrilateral and a semicircle.

Arturiano [62]

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of AB is

$AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}$

The length of AD is

$AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}$

Since AB=AD, therefore ABCD is a square. The area of the of square is

$A_1=a\times a=\sqrt{29}\times \sqrt{29} =29$

The area of square is 29 units².

The area of a semicircle is

$A_2=\frac{\pi}{2}r^2$

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

$r=\frac{d}{2}=\frac{\sqrt{29}}{2}$

The area of the semicircle is

$A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825$

The area of the figure is

$A=A_1+A_2=29+11.2825=40.3825\approx 40.4$

Therefore the area of the figure is 40.4 units². Option B is correct.

5 0

3 years ago

7p-(3p+4) = -2(2p-1)+10 Please answer!!!!!!!

Zanzabum

P=2
Work:
7p−(3p+4)=−2(2p−1)+107p−(3p+4)=−2(2p−1)+107p+−1(3p+4)=−2(2p−1)+107p+−1(3p)+(−1)(4)=−2(2p−1)+107p+−3p+−4=−2(2p−1)+107p+−3p+−4=(−2)(2p)+(−2)(−1)+107p+−3p+−4=−4p+2+10(7p+−3p)+(−4)=(−4p)+(2+10)4p+−4=−4p+124p−4=−4p+124p−4+4p=−4p+12+4p8p−4=128p−4+4=12+48p=168p8‌=‌168‌p=2

Hope this helps:)

8 0

4 years ago

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Find the equation of the line using the given information.

Dominik [7]

Answer:

x 1 = -3

x2 = -3

y1 = 0

y2 = 5

The slope of that equation is infinite and the equation is a perfectly vertical line at x = -3.

So, the equation is x = -3.

Step-by-step explanation:

6 0

3 years ago

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Find the roots of f(x)=x^2+10x−96

a_sh-v [17]

Answer:

x = -16 or x = 6

Step-by-step explanation:

To find the roots of a polynomial function, set the polynomial equal to zero and solve for x.

x² + 10x - 96 = 0

We need to factor the left side. The left side is a quadratic polynomial whose first coefficient is 1. We need two numbers whose product is -96 and whose sum is 10. The numbers are 16 and -6.

(x + 16)(x - 6) = 0

If a product of two factors equals zero, then one factor or the other or both must equal zero.

x + 16 = 0 or x - 6 = 0

x = -16 or x = 6

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3 years ago