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Tasya [4]
3 years ago
14

What is the gcf of 378,132

Mathematics
1 answer:
Semmy [17]3 years ago
3 0
First, find the prime factorization of both numbers.

378/2 = 189
189/3 = 63
63/3 = 21
21/3 = 7
7/7 1

378 = 2 * 3^3 * 7

132/2 = 66
66/2 = 33
33/3 = 11
11/11 = 1

132 = 2^2 * 3 * 11

For the GCF, choose the common factors with lower exponent.

378 = 2 * 3^3 * 7
132 = 2^2 * 3 * 11

From 2 and 2^2 choose 2.
From 3 and 3^2 choose 3.
7 and 11 are not common, so do not choose them.

GCF = 2 * 3 = 6
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If John can mow the lawn in 2/3 of an hour and George can mow the lawn in 1 hour, how long will they take to mow the lawn togeth
snow_tiger [21]
This is esay to do when you realize the the speed of mowing is addtive. This is if John mows at 1 lawn / (2/3) hour and Gerge mows at 1 lawn /  1hour, the total speed of mowing is:

1 / (2/3) + 1 = 3/2 + 1 = 5/2

=> 5/2 of lawn per hour

Now, the time is calcualted as the amount of lawn divided by the speed:

1 lawn / (5/2 lawn/hour) = 2/5 hour.

Answer: 2/5 of an hour.
8 0
3 years ago
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Given that h(x) = 3x −19, find the value of x that makes h(x) = 71.
rosijanka [135]

Keywords:

<em>Equation, variable, value, clear </em>

For this case we have an equation with a variable of the form y = h (x). Where h (x) = 3x-19. Given the value ofh (x) = 71, we want to find the value of the variable "x". So, we have:

h (x) = 3x-19\\71 = 3x-19

We must clear "x", for this, we add "19" to both sides of the equation:

71 + 19 = 3x-19 + 19\\90 = 3x

We divide between "3" on both sides of the equation:

\frac {90} {3} = \frac {3x} {3}\\30 = x

Thus, the value of the variable "x" is 30.

Answer:

x = 30

Option A

6 0
3 years ago
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A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mower
Anestetic [448]

Answer:

The number of small mowers are 19 and the large mowers are 11.

Step-by-step explanation:

Given:

A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.

Now, to find the number of each type of mower sold.

Let the number of small mower be x.

And the number of large mower be  y.

So, total number of mowers are:

x+y=30

x=30-y\ \ \ ....(1)

Now, the total sales of mowers are:

249.99(x)+329.99(y)=8379.70

Substituting the value of x from equation (1) we get:

249.99(30-y)+329.99y=8379.70

7499.7-249.99y+329.99y=8379.70

7499.7+80y=8379.70

<em>Subtracting both sides by 7499.7 we get:</em>

80y=880

<em>Dividing both sides by 80 we get:</em>

y=11.

The number of large mower = 11.

Now, to get the number of small mowers we substitute the value of y  in equation ( 1 ):

x=30-y\\x=30-11\\x=19.

The number of small mower = 19.

Therefore, the number of small mowers are 19 and the large mowers are 11.

6 0
3 years ago
33% X$90 rounded up to thr next highest dollar minus one cent
ivann1987 [24]
33% times 90 would be $29.7
6 0
3 years ago
Suppose that F(x) = x^3 and G(X) = -3x^3. Which statement best compares the
Alik [6]

Answer:

D. The graph of G(x) is the graph of F(x) flipped over the y-axis and

stretched vertically.

Step-by-step explanation:

since there is a negative, there must be a reflection. the reflection is over the y-axis because it is outside the x-value (-F(x) not F(-x))

the same goes for the vertical stretch. we know it is a vertical stretch because the 3 is outside the x-value (3F(x) not F(3x))

6 0
3 years ago
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