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alisha [4.7K]
2 years ago
9

Find the value of y when x equals 4. -3x + 9y = -57

Mathematics
2 answers:
ANTONII [103]2 years ago
4 0

Answer:

y = -5

Step-by-step explanation:

Isolate y:

-3x + 9y = -57

9y = -57 + 3x

y = (-57/9) + (3/9)x

Substitute for x:

y = (-57/9) + (3/9)(4)

y = (-57/9) + (12/9)

y = (-45/9)

y = -5

GalinKa [24]2 years ago
4 0

Answer:

\mathsf {y = -5}

Step-by-step explanation:

\textsf {Given :}\\\textsf {-3x + 9y = -57}

\textsf {Divide throughout by 3 :}

\mathsf {\frac{1}{3} \times (-3x + 9y) = \frac{1}{3} \times -57}

\mathsf {-x + 3y = -19}

\textsf {Substitute x = 4 :}

\mathsf {-(4) + 3y = -19}

\mathsf {3y = -15}

\textsf {Divide by 3 on both sides :}

\mathsf {\frac{3y}{3} = \frac{-15}{3} }

\mathsf {y = -5}

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The volume of a sphere whose diameter is 18 centimeters is _ cubic centimeters. If it’s diameter we’re reduced by half, it’s vol
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<h2>Answer:</h2>

<u>First Part</u>

Given that

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We have that

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<u>Second Part</u>

Given that

Volume = \frac{4}{3} \pi r^{3}

If the Diameter were reduced by half we have that

Volume = \frac{4}{3} \pi r^{3} =  \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}

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<h2>Step-by-step explanation:</h2>

<u>First Part</u>

Gather Information

Diameter = 18cm

Volume = \frac{4}{3} \pi r^{3}

Calculate Radius from Diameter

Radius = \frac{Diameter}{2} = \frac{18}{2} = 9

Use the Radius on the Volume formula

Volume = \frac{4}{3} \pi r^{3} =  \frac{4}{3} \pi 9^{3}

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3

We can see now that one of the 3s can be already divided by the 3 in the denominator

Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3

Finally, since we can't simplify anymore we just calculate it's volume

Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}

Volume \approx 3053.63 cm^{3}

<u>Second Part</u>

Understanding how the Diameter reduced by half would change the Radius

Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}

Understanding how the Radius now changes the Volume

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