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zysi [14]
3 years ago
7

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of

its square base. Nathan uses the formula for the volume of a pyramid to determine the dimensions of the sculpture:
Here, a is the side length of the pyramid’s square base and h is its height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x3 +
x2 +
= 0 can be used to find that the length of the sculpture’s base is
centimeters.

Mathematics
1 answer:
uysha [10]3 years ago
8 0
Let
x-----------> <span>the side length of a pyramid square base
h-----------> t</span>he height of the sculpture <span>in the shape of a pyramid

we know that
h=(x-3)
Volume=162 cm</span>³
Volume=x² *(x-3)/3
then
x² *(x-3)/3=162----------> x³-3x²=486----------> x³-3x²-486=0
x³-3x²-486=0-------- <span>this equation can be used to find the length of the sculpture’s base 

using a graph tool-----------> </span>to find the solution
x=9 cm -------------> see the attached figure
h=(x-3)-----> h=9-3--------> h=6 cm

the answer is
<span>the length of the sculpture’s base is 9 cm
</span>the height of the sculpture is 6 cm

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Answer: See pic above for answer. I got it from Photomath

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7 0
3 years ago
The points (6, -3) and (7, -10) fall on a particular line. What is its equation in point-slope form? Use one of the specified po
kumpel [21]

Answer:

Step-by-step explanation:

Given the coordinate points (6, -3) and (7, -10), we are to find the equation of a line passing through this two points;

The standard equation of a line is y = mx+c

m is the slope

c is the intercept

Get the slope;

m = Δy/Δx = y2-y1/x2-x1

m = -10-(-3)/7-6

m = -10+3/1

m = -7

Get the intercept;

Substitute the point (6, -3) and m = -7 into the expression y = mx+c

-3 = -7(6)+c

-3 = -42 + c

c = -3 + 42

c = 39

Get the required equation by substituting m = -7 and c= 39 into the equation y = mx+c

y = -7x + 39

Hence the required equation is y = -7x + 39

6 0
3 years ago
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinate
MatroZZZ [7]

Answer:

C. 10 000

Step-by-step explanation:

If we called:

x = children who have been vacinated against rubella only

2x = children who have been vaccinated against mumps

y = children who have been vaccinated agains both

Children who have been vaccinated against mumps only = x - y

And we know that y = 2*(x-y)

=> 2y = 3x

y = 5000

There fore x = 7500

The number of children who have been vaccinated against rubella

= 2x - y = 2*7500 - 5000 = 15 000 - 5000 = 10 000

4 0
3 years ago
It’s for my geometry class and I don’t know how to solve it. Can someone please help me?
dusya [7]

Answer:

Below in bold.

Step-by-step explanation:

Because the 2 sides marked with the double lines are equal:

5y-1 = 2y+11

3y = 12

y = 4.

Also :

3x-5 + 2(2x+5) = 180

3x - 5 + 4x + 10 = 180

7x = 180 + 5 -10

7x = 175

x = 175/7 = 25.

5 0
3 years ago
-6(x-3)<br><br><br><br><br><br><br><br><br><br><br> pls help me....
MariettaO [177]

Answer:

−6x+18

Step-by-step explanation:

-6(x-3)

(−6)(x+−3)

=(−6)(x)+(−6)(−3)

=−6x+18

4 0
3 years ago
Read 2 more answers
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