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lesya692 [45]
2 years ago
9

Two integers, a and b, have a greatest common factor of 1. If a =12 and b is greater than 35 but no more than 40, what is the va

lue of b?
Mathematics
1 answer:
yarga [219]2 years ago
7 0

Answer: 37

Step-by-step explanation:

a=12

35 < b < 40

\wedge\ means\ GCF\\a\ \wedge\ b= 1\\12\ \wedge\ 37= 1\\12\ \wedge\ 38= 2\\12\ \wedge\ 39= 3\\

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4. Identify the zeros and the graph of the function y = x(x − 2)(x + 5).
Natalka [10]

The zeros of

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

are

x=0,x=-2,x=-5x=0,x=−2,x=−5

EXPLANATION

The given function is

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

To find the zeros of the above function, we just have to equate the function to zero and solve for x.

x(x + 2)(x + 5) = 0x(x+2)(x+5)=0

This implies that,

x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0

x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5

To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,

x < - 5x<−5

When

x = - 10x=−10

y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0

The graph is below the x-axis.

- 5 \: < \: x \: < \: - 2−5<x<−2

When

x = - 3x=−3

y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0

The graph is above the x-axis.

- 2 \: < \: x < \: 0−2<x<0

when

x = - 1x=−1

y = -1(1)(4) \: < \: 0y=−1(1)(4)<0

The graph is below the x-axis.

Finally the interval,

x \: > \: 0x>0

when

x = 1x=1

y = 1(3)(6) \: > \: 0y=1(3)(6)>0

The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above

3 0
2 years ago
How do I figure the equation out
Tatiana [17]

Answer:

<em><u>Answer for Parallel line:</u></em> y = 3x - 13

<em><u>Answer for Perpendicular line: </u></em>y = (-1/3)x +17/3

Step-by-step explanation:

<em><u>Parallel line</u></em>

For the slope of a line parallel to another (given) line, just read the slope of the given line. It (in this case) is the coefficient in front of the x.

m = 3

So far what you have is y = 3x + b

To find b, use the given point (2,5)

x = 2

y = 5  Substitute these values into the skeletal equation. y = 3x + b

2 = 3*5 + b     Subtract 15 from both sides.

2 = 15 + b

2 - 15 = b switch sides

b = - 13

Answer y = 3x - 13

Part B

<em><u>Perpendicular line</u></em>

The perpendicular line will have a slope determined by the following formula

m1 * m2 = - 1

m1 is the slope of the given line which is 3

3 * m2 = - 1

m2 = - 1/3

So far, what you have is

y = (-1/3)x + b To find b, use the same 2 givens as above.

y = 5

x = 2

Substitute into the skeletal equation.

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

5 = -2/3  + b  Switch sides.  

b - 2/3 = 5  Add 2/3 to both sides.

b = 5 + 2/3

b = 5 2/3 = 17 / 3

Answer

y = (-1/3)x + 17/3

If this doesn't seem right, and you have choices, could you please list them?

4 0
3 years ago
A regular pentagon ABCDE is shown work out angle x
kow [346]

Answer:

108 degrees inside each corner

Step-by-step explanation:

360/5=72

180-72=108

5 0
3 years ago
It takes three identical water pumps 8 hours to fill a pool.
vagabundo [1.1K]
10 hours and 40 minutes
4 0
3 years ago
Need help with this
Zigmanuir [339]
In the ones place its 1

hundreds =  5
thaosands = 4
3 0
3 years ago
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