105/8 as a mixed number

Write an equation of the line that is parallel to -x + y = 5 and passes through the point (2, -5).

marshall27 [118]

x= something so try to solve it without the x and y and then you can figure out what x and y equals

6 0

3 years ago

If f(x)=x^2 is vertically stretched by a factor of 9 to g(x). What is the equation of g(x)?

AlexFokin [52]

Given:

The function is:

$f(x)=x^2$

This function is stretched by a factor of 9 to g(x).

To find:

The equation of function function g(x).

Solution:

The vertical stretch is defined as:

$g(x)=kf(x)$ ...(i)

If $0$ , then the function f(x) compressed vertically by factor k.

If $k>1$ , then the function f(x) stretched vertically by factor k.

The given function f(x) is stretched by a factor of 9 to g(x). So the value of k is 9.

Substituting $k=9$ in (i), we get

$g(x)=9f(x)$

$g(x)=9x^2$ $[\because f(x)=x^2]$

Therefore, the required function is $g(x)=9x^2$ .

7 0

3 years ago

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a ye

zloy xaker [14]

Answer:

Number of restaurant-purchased meals eaten in a restaurant = 70

Number of restaurant-purchased meals eaten in a car = 22

Number of restaurant-purchased meals eaten in a home = 60

Step-by-step explanation:

Let the number of people that will eat in a restaurant be R.

Let the number of people that will eat in a car be C.

Let the number of people that will eat in a home be H.

From the information given in the problem we have,

R+C+H = 152 ____equation (1)

C+H-R = 12 ____equation (2)

R = H+10 ____equation (3)

1) Plugging in R=H+10 from equation 3 into the equation 2, we get

C+H-R=12

=> C+H-(H+10)=12

=> C+H-H-10=12

2) Cancelling out +H and -H, we get

C-10=12

3) Add 10 to both sides

C-10+10=12+10

4) Cancelling out -10 and +10, we get

C=22

5) Plugin C=22 in equation 1, we have

R+C+H = 152

=> R+22+H=152

Subtract 22 from both sides,

R+22+H-22=152-22

Cancelling out +22 and -22 from the left side, we get

R+H=130 ____let it be equation (4)

6) Plugin C=22 in equation 2, we have

C+H-R = 12

22+H-R = 12

Subtracting 22 from both the sides, we get

22+H-R-22 = 12-22

Cancelling out +22 and -22 from the left side,

H-R = -10 ____let it be equation (5)

7) Adding equation 4 and equation 5, we get

(R+H)+(H-R) = 130 + (-10)

=> R+H+H-R = 130-10

8) Cancelling out R and -R from the left side, we get

2H = 120

9) Dividing both sides by 2, we get

$\frac{2H}{2} = \frac{120}{2}$

10) Cancelling out the 2's from the left side, we have

H=60

11) Plugging in C=22 and H=60 in the equation 1, we have

R+C+H = 152

=> R+22+60=152

=> R + 82 = 152

12) Subtracting 82 from both the sides, we get

R + 82 -82 = 152 -82

13) Cancelling out +82 and -82 from the left side, we get

R = 70

So, C=22, H=60, R=70

8 0

3 years ago

Round 9.55555 to the nearest hundredths

Paraphin [41]

When you round 9.55555 to the nearest hundredth you would get 9.56 which you would then round to 10

3 0

3 years ago

Answer both please, the topic is linear inequalities, and please explain it to me.

Bogdan [553]

Question 1 solution:
You have two unknowns here:

Let the Water current speed = W

Let Rita's average speed = R

We are given two situations, where we can form two equations, and therefore solve for the two unknowns, W, R:

Part 1) W→ , R←(against current, upstream)
If Rita is paddling at 2mi/hr against the current, this means that the current is trying to slow her down. If you look at the direction of the water, it is "opposing" Rita, it is "opposite", therefore, our equation must have a negative sign for water:

R–W=2 - equation 1

Part 2) W→ , R→(with current)
Therefore, R+W=3 - equation 2

From equation 1, W=R-2,
Substitute into equation 2.
R+(R–2)=3
2R=5
R=5/2mi/hr

So when W=0 (still), R=5/2mi/hr

Finding the water speed using the same rearranging and substituting process:

1... R=2+W
2... (2+W)+W=3
2W=1
W=1/2mi/hr

7 0

3 years ago