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3 years ago

Determine the intercepts of the line that passes through the following points. (-10,-28) , (-6,-21) , ( -2,-14)

1 answer:

8 0

The line through (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

Picking the last two points,

(-2 - -6)(y - -21) = (-14 - -21)(x - -6)

4(y+21) = 7(x+6)

When x=0

4y + 84 = 42

4y = -42

y = -21/2

Answer: -21/2

We never used the first point, let's check it's on the line

4(y+21) = 7(x+2)

4(-28 + 21) = -28

7(-10 + 6) = -28, good

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Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 32 ft long. She wants to leave a uniform strip of floor aroun

Rainbow [258]

Answer:

The rug should be 15 ft wide and 28 ft long.

Step-by-step explanation:

I have attached a figure that represents the situation.

The the rug is $l$ by $h$ , the width of the strip of floor is $w$ .

We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that

$l*h=420$ <em>(this says the area of the rug must be 420 square feet)</em>

From the figure we see that

$l= 32-2w$

$h=19-2w$

Therefore,

$l*h=420\\\\(32-2w)(19-2w)=420$

We expand this equation and get:

$4w^2-102w+608=420\\\\4w^2-102w+188=0$

using the quadratic equation we get two solutions:

$w=2\\w=23.5$

since the second solution, namely $w=23.5$ , is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take $w=2$ to be our solution.

Now we find the dimensions of the rug:

$l=32-2(2)=28\\\\h=19-2(2)=15$

The rug is 15 ft wide and 28 ft long.

8 0

4 years ago

You are starting a babysitting business to earn enough money to buy a new iPhone 7 Plus, which costs $769. You already have $240

Zina [86]

Answer:

9 times 59 is 531. 531+240= 771 she needs to work 59 hours.

Step-by-step explanation:

5 0

3 years ago

What is the average (arithmetic mean) of the first 90 measurements in a certain list of 92 measurements? (1) the average of the

marishachu [46]

The sum of all the measurements is just the average times the number.

$\bar x = \frac{1}{n} \sum_{i=1}^n x_i$

$\sum_{i=1}^n x_i = n \bar x$

So if the average of all 92 is 7 the sum of those is $92 \times 7$

The average of the last two is 7.2 so their sum is $2 \times 7.2$

That means the sum of the first 90 is $92 \times 7 - 2 \times 7.2$

so the average of the first 90 is

$\dfrac{92 \times 7 - 2 \times 7.2}{90} = 6.99556$ cm

7 0

3 years ago

Henry's current age is 10 times Justin's current age. In 6 years Henry's age will be 4 times Justin's age. Which system of equat

Anna11 [10]

The answer is C: H=10J
H+6=4(J+6)

8 0

3 years ago

May runs 10/4 miles everyday after school. Beth says she runs further because she runs 5/2 miles everyday after school. Is her s

Andrew [12]

Answer:

Her statement is not correct.

Step-by-step explanation:

It is not correct because if you simplify 10/4 it comes out to 5/2 therefore 5/2=5/2.

Beth and May run the same amount.

4 0

3 years ago