In the given equation, k is a constant. If the equation has no solution, what is the value of k?

if your car gets 26 miles per gallon how much does it cost to drive 420 miles when gas is $2.80 per gallon

Kitty [74]

Answer:

$45.22

Step-by-step explanation:

The number of miles per gallon can be represented by the ratio:

$\frac{miles}{gallon}=\frac{26}{1}$

Since we know the unit rate of 26 miles per gallon of gas, we can set up a proportion, or equivalent ratios, to find the number of gallons needed for 420 miles:

$\frac{26}{1}=\frac{420}{x}$ , where 'x' is the number of gallons of gas

cross-multiply and divide: 26x = 420 or x ≈ 16.15 gallons

If gas is $2.80 per gallon, take the total number of gallons needed and multiply by $2.80:

16.15 x $2.80 = $45.22

5 0

3 years ago

A biologist has been observing a tree's height. This type of tree typically grows by 0.22 feet each month. Fifteen months into t

Lyrx [107]

Data:

x: number of months

y: tree's height

Tipical grow: 0.22

Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)

In this case the slope (m) or rate of change is the tipical grow.

m=0.22

To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):

$\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}$

Use the slope(m) and y-intercept (b) to write the equation:

$\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}$ A) This line's slope-intercept equation is: y=0.22x+17.2

B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:

$\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}$ Then, after 29 months the tree would be 23.58 feet in height

C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:

$\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}$ Then, after 58 months the tree would be 29.96feet tall

3 0

1 year ago

Find the equivalent ratio with greater terms. (show work)

kipiarov [429]

A 42 24÷16 =1.5 1.5×28 =42 b i think its 78.4 im not sure

4 0

3 years ago

The following menu items were ordered at a pizza parlor on Friday. 3 salads, 8 pizzas, 4 sides of breadsticks, and 5 pepperoni c

den301095 [7]

Answer:

Using proportions, the pizza parlor should expect 20 breadsticks and 25 calzone orders if there were 100 total orders.

Step-by-step explanation:

Orders:

Salads 3

Pizzas 8

Sides of breadsticks 4

Pepperoni calzones 5

Total orders: 20

Proportion of sides breadsticks=4/20=0.2

Proportion of pepperoni calzones=5/20=0.25

For 100 total orders:

Sides of breadsticks=0.2(100)=20

Pepperoni calzones=0.25(100)=25

6 0

3 years ago

if you deposit $8000 into an account paying 9% annual interest compunded semi anually how long will it take for your money to do

Anna007 [38]

Answer:

7.87 years

Step-by-step explanation:

#First we determine the effective annual rate based on the 9% compounded semi annual;

$i_m=(1+i/m)^m-1\\\\=(1+0.09/2)^2-1\\\\=0.09203$

#We then use this effective rate in the compound interest formula to solve for n. Given that the principal doubles after 2 yrs:

$A=P(1+i)^n\\\\A=2P, i=i_m\\\\16000=8000(1.09203)^n\\\\2=1.09203^n\\\\n=\frac{log \ 2}{log \ 1.09203}\\\\=7.87324\approx7.87 \ yrs$

Hence, it takes 7.87 years for the principal amount to double.

4 0

3 years ago