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2 years ago

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Karen found that the solution to x – 7 + 5x = 36 is x = 6. Which of these could be the way she found the solution? Add x + 5x, s

ubtract 7 from both sides of the equation Add x – 7 + 5x, add 36 to both sides of the equation Add –7 and 5x, subtract x from both sides of the equation Add x + 5x, add 7 to both sides of the equation

2 answers:

Scorpion4ik [409]2 years ago

6 0

X - 7 + 5x = 36

Combine like terms:
6x - 7 = 36

Add 7 on both sides:
6x = 43

Divide both sides by 6:
x = 43/6

<span>Answer: The steps are (1)Add x + 5x, (2) add 7 to both sides of the equation, then (3)divide both side by 6.</span>

umka21 [38]2 years ago

4 0

Answer:

add x + 5x, add 7 to both sides of the equation

Step-by-step explanation:

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Please see the attachment.

Step-by-step explanation:

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2 years ago

1. Mac is about to sue his contractor who promised to install a water tank that holds 1880 gallons of water. Mac knows that 1880

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Answer:

option C.

Yes, the water tank is about 245 cubic feet too small

Step-by-step explanation:

step 1

Determine the volume of the cylindrical tank

we know that

The volume of a cylinder is equal to

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Remember that

$1\ ft=12\ in$

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2 years ago

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At <em>x</em> = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at <em>x</em> = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at <em>x</em> = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

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2 years ago