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2 years ago

Without solving, determine whether the solution of x = 21 is greater than or less than 21. Explain.

Mathematics

1 answer:

astraxan [27]2 years ago

7 0

Answer:

Without solving, the solution is greater than 21. The can be proven because a fraction of x is equal to 21, therefore x cannot be less than 21.

Step-by-step explanation:

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Answers:

The direct variation equation is y = 5x
If x = 4, then y = 20

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Explanation:

Let's say that the letter k replaces the green box

We have the equation y = kx

Plug in (x,y) = (7,35) to get the equation 35 = k*7

Dividing both sides by 7 leads to k = 5

Therefore, the direct variation equation is y = 5x

We can check this by plugging in x = 7

y = 5x

y = 5*7

y = 35

So x = 7 leads to y = 35 as expected.

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Side note: direct variation equations always go through the origin.

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3 years ago

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Can someone please help me solve these two problems and explain them to me? About the one with proportions though... I've always

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Answers:

A) $-\frac{11}{4}$

C) $m_{1}=\frac{Fr^{2}}{G m_{2}}$

Step-by-step explanation:

Part 1:

We have the followig equation:

$\frac{x-1}{3}-\frac{x+4}{5}=\frac{4x-1}{8}$

Calculating the least common multiple (l.c.m) in the denominator in the left side of the equation, being l.c.m=15:

$\frac{5(x-1)-3(x+4)}{15}=\frac{4x-1}{8}$

Solving for the left part of the equation:

$\frac{2x-17}{15}=\frac{4x-1}{8}$

Operating with cross product:

$8(2x-17)=15(4x-1)$

Applying the distributive property:

$16x-136=60x-15$

Isolating $x$ :

$x=-\frac{121}{44}$

Dividing numerator and denominator by 11:

$x=-\frac{11}{4}$ Hence, the correct option is A

Part 2:

We have the followig equation:

$F=\frac{G m_{1} m_{2}}{r^{2}}$

Operating with cross product:

$Fr^{2}=G m_{1} m_{2}$

Isolating $m_{1}$ :

$m_{1}=\frac{Fr^{2}}{G m_{2}}$ Hence, the correct option is C

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3 years ago