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2 years ago

What is the solution set for the following inequality? 4x – 3 + 6x > 5x + 7

Mathematics

1 answer:

Arada [10]2 years ago

4 0

Answer: x > 2

Step-by-step explanation:

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A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i

astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

$-3t^2+24t\geq 36$

$-3t^2+24t-36\geq 0$

$-3(t^2-8t+12)\geq 0$

Splitting the middle term, we get

$-3(t^2-6t-2t+12)\geq 0$

$-3(t(t-6)-2(t-6))\geq 0$

$-3(t-2)(t-6)\geq 0$

The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

3 0

2 years ago

Which graph represents an odd function?

Nookie1986 [14]

Answer:

<h2>The first graph in the second image is an odd function.</h2>

Step-by-step explanation:

An odd function has a graph that it's symmetric about the origin, that is, the origin is like a mirror. In other words, the graph of an odd function has a specific symmetry about the origin.

So, we have to look for those graph that has symmetrical points in opposite quadrants, I and III or II and IV.

You can observe that the first graph of the second image has this behaviour. You can see that the points are symmetrical across the origin. If you graph a line defined as y=-x, you will observe that such line acts like a mirror.

Therefore, the odd function is the first graph in the second image.

8 0

3 years ago

Read 2 more answers

12. What's the simplified form of x − 1 + 4 + 7x − 3?

Leviafan [203]

The first one is B and the second is D

3 0

3 years ago

Read 2 more answers

Michael is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%, what is the sale

Anna35 [415]

Answer

Find out the what is the sale price of the jeans including tax .

To prove

Let us assume that the sale price of the jeans including tax be x .

As given

Michael is buying a pair of jeans that regularly cost $40.

They are on sale for 20% off.

If the tax rate is 8% .

20% is written in the decimal form

$= \frac{20}{100}$

= 0.20

8% is written in the decimal form

$= \frac{8}{100}$

= 0.08

Than the equation becomes

x = 40 - 40 × 0.20 + 40 × 0.08

x = 40 - 8 + 3.2

x = 43.2 - 8

x = $35.2

Therefore the sale price of the jeans including tax be $ 35.2 .

4 0

3 years ago

A group of 70 people attended a ball game. There were four times as many children as adults in the group. Set up a system of equ

anzhelika [568]

Answer:

4b+b=70

5b=70

b=14

Step-by-step explanation:

4(14)+(14)=70

3 0

2 years ago