MATHEMATICS MIDDLE SCHOOL

Suppose v varies directly as g, and v=36 when g=4. Find v when g=11.

Answers

Answer 1
Answer:

Answer:

v=99

Step-by-step explanation:

We have been given that that v varies directly as g.

We can represent this information in an equation as:

v=kg

First of all, we will find constant of variation (k) by substituting v=36 and g=4 in our given equation.

36=k\cdot 4

(36)/(4)=(k\cdot 4)/(4)

9=k

So our equation would be v=9g.

Now, we will substitute  g=11 in the given equation:

v=9* 11

v=99

Therefore, the value of v is 99.
Answer 2
Answer: For a variable to vary directly to another is telling you to set up a proportion

v/g = v/g

36/4 = v/11

4v = 396

v = 99

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Convert the mixed number to an improper fraction. 4 7/8

A.11/8


B.19/8


C.28/8


D.39/8

Answers

4 7/8=(4*8+7)/8=(32+7)/8=39/8 ⇒ D
8*4+7=\boxed{ (39)/(8)}

Which expression is equivalent to (2to the third power) times -5?

Answers

2 to the third power is 2³

so 2 to the third power times -5 is 2³ * (-5)

which on simplification will be 8* (-5) =-40

How long will jesse take to run a total of 50 miles if she run 0.13 per hour

Answers

Jesse runs 0.13 miles per one hour.
She wants to run a total of 50 miles.

0.13 miles .... 1 hour
50 miles ... x hours

We would like to know how long this will take (x hours). You can calculate this in the following way:
0.13 * x = 50 * 1   /0.13
x = 50/0.13
x = 384.6153846153846154 (hours)

The result is 384.6153846153846154 hours.
384.61538462 hours is the answer.

a boy is 24 years younger than his father. In 2 years time the sun of their ages will be 40. Find the present ages of father and son

Answers

ooh fun

x=boy
y=father
x+24=y
(x+2)+(y+2)=40
subsitute x+24=y into equation
x+2+x+24+2=40
add like terms
2x+28=40
subtract 28 from both sides
2x=40
divide both sides by 2
x=son now=20
father=son+24
father=20+24=44

father=44
son=20
Let the age of the boy be x.
Therefore the age of the father = x + 24.  (The boy is 24 years younger implies that 
                                                           his father is older by 24 years).

In 2 years time:
The boy will be = (x +2).
The father will be (x +24 +2) = (x + 26).

Sum of their ages = 40.
Therefore            (x+2) + (x + 26) = 40.
                           x + x + 2 + 26 = 40
                                      2x + 28 = 40
                                              2x = 40 -28
                                               2x = 12.
                                                 x = 12/2 = 6.    x =6.
Present ages =  x , x +24.  =  6,  (6 +24) =    6, 30.
Boy = 6 years old.
Father = 30 years old.
Cheers.

Bert's cab company charges $1.00 plus an additional $3.00 per mile for a ride.Madeline,s cabs company charges $3.00 plus an additional $2.00 per mile fora ride. Write a system of linear equations that shows the cost in dollars,y, for a cab ride of x miles for each cab driver.

Answers

So our y value is the end cost, while our x value is the number of miles driven. Let's also add two variables, r and c. r stands for the rate, or the cost per mile, and c stands for the defined cost. So our function is y = rx + c. Remember that whenever we have a function, the y is replaced with f(x). No worries, they mean the same thing.So let's add the values into each variable for both companies. Bert's company would have a function of f(x) = $3x + $1, and Madeline's company would have f(x) = $2x + $3. So let's say you drove 5 miles in a cab from both companies. x would become 5, so put that into both functions. 3 times 5 plus 1 would end up being $16, so Bert's company costs $16 for a 5 mile drive. 2 times 5 plus 3 would end up being $13, so Madeline's company costs $13 for a 5 mile drive.

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.Can you calculate the dimensions of this box with the given data?

Answers

Let the three sides of the box be P, Q and R.

Now we know the area of rectangle is l* b.

P * Q = 240
P * R = 300
Q * R = 180

Let us multiply these three equations:
(P*Q) (P*R) (R*S) = 240 * 300 * 180
P^2 * Q ^2 * R^2 = 12960000
(P*Q*R)^2 = 12960000
P*Q*R = 3600

Now we know that P*Q = 240

Thus R = 3600/240 = 15.

Similarly putting and solving for other variables, we get
P = 20 units
Q = 12 units
R = 15 units
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