The table and the graph each show a different relationship between the same two variables, x and y:

Find the slope of the line passing through the points , −8−3 and , −34 .

alukav5142 [94]

Slope of the line passing through two points P=(x1,y1) and Q=(x2,y2) is given by m=y2−y1/x2−x1.

We have that x1=−8, y1=−3, x2=−3, y2=4.

Plug given values into formula for slope: m=(4)−(−3)/(−3)−(−8)=7/5.

Now y-intercept is b=y1−m⋅x1 .

b=−3−(7/5)⋅(−8)=41/5.

Finally, equation of the line can be written in the form y=mx+b.

y=7/5x+41/5

5 0

3 years ago

Solve for the smallest value of $x$ such that $24x^2 + 17x - 20 = 0.$ Express your answer as a simplified common fraction.

Gala2k [10]

X=5/8 or x=-4/3
here is the work if needed...
24x^2+17x-20=0
Step one: Factor left side of equation.
(8x-5)(3x-4)=0
Step two: Set factor equal to 0.
8x-5=0 or 3x-4=0
x=5/8 or x=-4/3

4 0

3 years ago

Last year, the average American used 167 disposable water bottles (16.9 oz or 0.132 gallons). If the cost of 1 gallon of tap wat

Mrrafil [7]

Answer:

The money that could be saved by drinking tap water is $165.46.

Step-by-step explanation:

Given:

Cost of 1 bottle of water = $1.00

Number of bottles consumed = 167

Volume of water used in 1 bottle = 0.132 gallons

So, volume of water used in 167 bottles = 167 × 0.132 = 22.04 gallons

Cost of 1 gallon of tap water = 7 cents = $0.07

In order to determine the money saved using tap water, we first find the cost of 167 bottles.

Using unitary method,

1 bottle cost = $1.00

167 bottles cost = Number of bottles × Cost of 1 bottle

= 167 × $1.00 = $167.00

Now, 167 dollars is spent for consuming 22.04 gallons of water.

Now, cost of 1 gallon of tap water = $0.07

So, cost of 22.04 gallons of tap water = 22.04 × 0.07 = $1.54

Therefore, the money saved by drinking tap water is given as:

Money saved = Money spent in bottles for 22.04 gallons - Money spent in tap water for the same volume

Money saved = $167.00 - $1.54 = $165.46

Hence, the money that could be saved by drinking tap water is $165.46.

8 0

3 years ago

For the rectangular prism shown, answer the following questions. Write your number

rewona [7]

The area is 20
The height is 5
The volume is 60
The surface area is 94

6 0

3 years ago

Jane is 5 times older than her sister. In 3 years, Jane’s sister will be 1/4 her age. Find the ages now

Korolek [52]

The present age of Jane is 45 years old and present age of her sister is 9 years old

Solution:

Let the present age of Jane be "x"

Let the present age of her sister be "y"

Jane is 5 times older than her sister

present age of Jane = 5(present age of her sister)

x = 5y ---------- eqn 1

In 3 years, Jane’s sister will be 1/4 her age

Age of sister after 3 years = 3 + y

Age of jane after 3 years = 3 + x

Age of sister after 3 years = 1/4(age of jane after 3 years)

$3 + y = \frac{1}{4}(3 + x)$

Substitute eqn 1 in above equation

$3 + y = \frac{1}{4}(3 + 5y)\\\\12 + 4y = 3 + 5y\\\\5y - 4y = 12 - 3\\\\y = 9$

Substitute y = 9 in eqn 1

x = 5(9)

x = 45

Thus present age of Jane is 45 years old and present age of her sister is 9 years old

3 0

4 years ago