4

Do 3 lines always, sometimes or never intersect at one point?

Pie

Answer:

Sometimes

Step-by-step explanation:

Three line sometimes intersect

7 0

3 years ago

Sally has read one-third of her book. She finishes the book by reading the same amount each night for 5 nights. Part A. What fra

boyakko [2]

Answer:

2/15

Step-by-step explanation:

Given that she have already read one-third of the book.

The fraction f of the book that will remain is;

f = 1 - 1/3 = 2/3

Then she finishes the book by reading the same amount each night for 5 nights

That implies she reads the remaining 2/3 of the book at equal rates for 5 nights.

Let x represent the fraction rate read per night;

5x = 2/3

Divide both sides by 5

x = 2/3 × 1/5

x = 2/15

Therefore, she reads 2/15 of the book every night for 5 nights.

6 0

3 years ago

Eric took out an 80/20 mortgage to buy a house costing $175,000. The first (80%) mortgage has an interest rate of 4.75%, and the

Serhud [2]

Answer:

The total monthly mortgage payment for the house is $975.63

Step-by-step explanation:

The principle amount is $175000

80% of 175000 is = $0.8\times175000$ = $140000

20% of 175000 is = $0.2\times175000$ = $35000

Emi formula is :

$\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }$

For 1st part:

p = 140000

r = 4.75/12/100=0.00395

n = $30*12=360$

Putting values in formula we get

$\frac{140000\times0.00395\times(1.00395)^{360} }{(1.00395)^{360}-1 }$

= $729.508

For 2nd part:

p = 35000

r = 7.525/12/100=0.00627

n = $30*12=360$

Putting values in formula we get

$\frac{35000\times0.00627\times(1.00627)^{360} }{(1.00627)^{360}-1 }$

= $245.301

Adding both the monthly payments:

$729.508+245.301=974.809$ dollars

This is closest to option A.

So, option A is the answer.

And for 30 years the mortgage payment will be =

$975.63\times12\times30=351226.80$ dollars

5 0

4 years ago

Rita goes for a bike ride on a trail by her house. After 15 minutes of riding she sees a mile marker. When she reaches the third

lana66690 [7]

Given:

Rita covered 1 mile in 15 minutes.

She covered 3 miles in 30 minutes.

To find:

The rate at which she is riding.

Solution:

Let y be the number of miles covered in x minutes.

Rita covered 1 mile in 15 minutes. So, the point is (15,1).

She covered 3 miles in 30 minutes. So, the point is (30,3).

Slope of the line:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{3-1}{30-15}$

$m=\dfrac{2}{15}$

Therefore, she is riding $\dfrac{2}{15}$ miles per minute.

8 0

3 years ago

Solve the equations using substitution <br> 7x-2y=3<br> 14x+y=14

Setler79 [48]

Answer:

x = 31/35 , y = 8/5

Step-by-step explanation:

Solve the following system:

{7 x - 2 y = 3

14 x + y = 14

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for y:

{7 x - 2 y = 3

14 x + y = 14

Hint: | Solve for y.

Subtract 14 x from both sides:

{7 x - 2 y = 3

y = 14 - 14 x

Hint: | Perform a substitution.

Substitute y = 14 - 14 x into the first equation:

{7 x - 2 (14 - 14 x) = 3

y = 14 - 14 x

Hint: | Expand the left hand side of the equation 7 x - 2 (14 - 14 x) = 3.

7 x - 2 (14 - 14 x) = (28 x - 28) + 7 x = 35 x - 28:

{35 x - 28 = 3

y = 14 - 14 x

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{35 x - 28 = 3

y = 14 - 14 x

Hint: | Isolate terms with x to the left hand side.

Add 28 to both sides:

{35 x = 31

y = 14 - 14 x

Hint: | Solve for x.

Divide both sides by 35:

{x = 31/35

y = 14 - 14 x

Hint: | Perform a back substitution.

Substitute x = 31/35 into the second equation:

Answer: {x = 31/35 , y = 8/5

8 0

4 years ago