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3 years ago

Solve For x . Show all steps / work !

Mathematics

1 answer:

Paraphin [41]3 years ago

5 0

Answer:

x = 46

Step-by-step explanation:

sqrt(3x - 17) + 5 = 16

Subtract the numbers

sqrt(3x - 17) = 11

Square both sides

3x - 17 = 121

Solve the linear equation

x = 46

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What is the reciprocal of 6/9

neonofarm [45]

Answer:

Step-by-step explanation:

Remember that, to find the reciprocal of a fraction, just swap the numbers. So the reciprocal of 6/9 is 9/6.

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3 years ago

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If f(x)=-2x+5, what is f(-3x) equal to?

jekas [21]

Answer:

$f(-3x) = 6x + 5$

Step-by-step explanation:

<u>Step 1: Substitute -3x for x</u>

<u /> $f(x) = -2x + 5$

$f(-3x) = -2(-3x) + 5\\$

$f(-3x) = 6x + 5$

Answer: $f(-3x) = 6x + 5$

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3 years ago

How many significant digits are there in the number 5.0500? A. 3 B. 4 C. 5 D. 6

bixtya [17]

Answer:

Step-by-step explanation:

1)Non- zeros (1,2,3,....) are always significant.

2)Captive zeros are significant too( zeros between non- zeros ).

3)Trailing zeros (zeros at the end) aren't significant always unless if there is a decimal point.

Such this question we have decimal point so we count them

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3 years ago

the area of a window is 192 in squared. The width if the window is four inches more than half the length of the window. What are

Leya [2.2K]

Answer:

Length = 16 inches and width = 12inches

Step-by-step explanation:

A = 192 in² . The width is 4 + 1/2x. therefore let x = length

Area = LW

192 = x(4 + 1/2 x)

192 = 4x + 1/2x²

384 = 8x + x² Multiply each term by 2 to make a

384 + 16 = x² + 8x + 16 Complete the square

400 = (x + 4)²

$\sqrt{400} = \sqrt{(x + 4)^2}$

± 20 = x + 4

20 = x + 4 or -20 = x + 4

20 - 4 = x or -20 - 4 = x

16 = x or -24 = x reject the negative amount

Length = 16

width = 4 + 1/2(16); 4 + 8 = 12

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3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

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