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2 years ago

11

Solve each system of equations below by the substitution method. And show your work.

1 answer:

Simora [160]2 years ago

7 0

Instead of typing it all on here, I included my explanations with the work.

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The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a f

tiny-mole [99]

Answer:

Amplitude = 3 feet; period = 8 hours; midline: y = 4

Step-by-step explanation:

sketch it....(see attached)

3 0

2 years ago

Read 2 more answers

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypo

kompoz [17]

Answer:

$h = 12$

$x = 9$

$y= 16$

Step-by-step explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

$A = \frac{1}{2} * 15 * 20$

$i.e\ height = 20$

$A = \frac{1}{2} * 300$

$A = 150$

Let the base of the triangle be 25.

So, the area is:

$A = \frac{1}{2} * 25 * h$

$i.e\ height = h$

$A = \frac{1}{2} * 25h$

Substitute $A = 150$

$\frac{1}{2}*25h = 150$

Solve for h

$h = \frac{150 *2}{25}$

$h = 6 *2$

$h = 12$

Considering the smallest triangle

$Hypotenuse = 15$

So:

$15^2 = h^2 + x^2$

$15^2 = 12^2 + x^2$

This gives:

$15^2 - 12^2 = x^2$

$81 = x^2$

Take square roots

$9 =x$

$x = 9$

Solving for y

$x + y = 25$

$y= 25 - x$

$y= 25 - 9$

$y= 16$

7 0

2 years ago

What is the surface area of the cylinder with height 4 km and radius 2 km? Round

saveliy_v [14]

I hope this helps you

7 0

2 years ago

Given the polynomial 2x3 + 18x2 − 18x − 162, what is the value of the coefficient 'k' in the factored form?2x3 + 18x2 − 18x − 16

s344n2d4d5 [400]

Answer:

$k=3$

Step-by-step explanation:

Let

$f(x)=2x^3+18x^2-18x-162$

We factor 2 to obtain;

$f(x)=2(x^3+9x^2-9x-81)$

We factor the polynomial within the parenthesis by grouping.

$f(x)=2(x^2(x+9)-9(x+9)$

$f(x)=2(x^2-9)(x+9)$

$f(x)=2(x^2-3^2)(x+9)$

We apply difference of two squares on the second factor: $x^2-3^2=(x-3)(x+3)$

$f(x)=2(x+3)(x-3)(x+9)$

We now compare to;

$f(x)=2(x+k)(x-k)(x+9)$

It is now obvious that $k=3$

6 0

2 years ago

Some people took part in a game. The frequency shows information about their scores.

Marizza181 [45]

Answer:

The mean = 17.54

Step-by-step explanation:

Form a table as below;

<u>Interval Frequency{f} Midpoint of frequency{x} fx </u>

1-7 19 4 76

8-10 14 9 126

11-15 15 13 195

16-20 20 18 360

21-35 10 28 280

36-50 13 43 559

Sum 91 1596

The mean of grouped data = Sum of { Interval Midpoint * Frequency } /Sum of frequency

The mean= 1596 / 91

The mean = 17.54

5 0

3 years ago