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mafiozo [28]
2 years ago
5

4(x-6)<-2x+6 what is the solution to the inequality _

Mathematics
1 answer:
Cloud [144]2 years ago
7 0
Simplify both sides if needed. The left-hand side needs simplification.

4(x - 6) \leq -2x + 6
4x - 24 \leq  -2x + 6

All is left to do is add and subtract to get the x variable all alone.

4x - 24  \leq -2x + 6
6x - 24  \leq  6    <-- Add 2x to both sides
6x         \leq  30  <-- Add 24 to both sides 
x           \leq 5    <-- Divide both sides by 6

In order to be in the solution set, x has to be less than or equal to 5.

In interval notation: [5, -∞)
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Which statement is true?
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the last option

Step-by-step explanation:

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gal created a painting with an area of 56 square inches and a length if 7 inches. they create a second painting with an area of
qwelly [4]

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5 inches

Step-by-step explanation:

the length of painting is 56/7 = 8in. to find the length of the 2nd painting divide the area by the width: 40/8 = 5

3 0
1 year ago
7x - 2(3x - 5) = 26 ​
Reptile [31]

Answer:

x=16

Step-by-step explanation:

7x−2(3x−5)=26

Use the distributive property to multiply −2 by 3x−5.

7x−6x+10=26

Combine 7x and −6x to get x.

x+10=26

Subtract 10 from both sides.

x=26−10

Subtract 10 from 26 to get 16.

x=16

Graph if needed:

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2 years ago
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Determine whether the rule represents an exponential function. Explain why or why not.
Alenkasestr [34]

Answer:

Yes.

Step-by-step explanation:

Exponential Parent Function: f(x)= a(b^{x})

If we write out the equation:

y = 6(5)^{x}

Whenever we have an exponent of <em>x</em>, it is a exponential function. The 5 is simply the base of the exponent and the 6 means we are vertically stretching the graph by a factor of 6.

5 0
2 years ago
The function h(t) = -16t^2 + 16t represents the height (in feet) of a horse (t) seconds after it jumps during a steeplechase.
Vladimir79 [104]
A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.

h'(t) = -32t + 16

When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.

-32t + 16 = 0

-32t = -16

t = 0.5 seconds

b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.

h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet

If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.

c.) We know that the horse is in the air whenever h(t) is greater than 0. 

-16t^2 + 16t = 0

-16t(t-1)=0

t = 0 and 1

So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
7 0
2 years ago
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