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Firlakuza [10]
3 years ago
9

Write the phrase “all real numbers that are greater than 24 and less than or equal to 7” as a compound inequality

Mathematics
1 answer:
fiasKO [112]3 years ago
6 0

We are given phrase " all real numbers that are greater than 24 and less than or equal to 7".

We need to write a compound inequality for this phrase.

Let us break it into smaller parts first.

<em>Let us assume a real number by n.</em>

n is greater than 24 could be written as

<h3>n > 24.</h3>

And n is less then or equal to 7 could be written as

<h3>n ≤ 7.</h3>

Now, we can write compound inequality by putting n in between, we get

<h2>   24 < n ≤ 7 </h2><h2>That is our final compound inequality.</h2>
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OLEGan [10]

Answer: А.

The function f intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

In the graph we can see f(x), first let's do some analysis of the graph.

First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.

The arms of the graph go up, so the leading coefficient of f(x) is positive.

The vertex of f(x) is near (-0.5, -2)

The roots are at x = -2 and x = 1. (intersects the x-axis at two points)

Now, we know that:

g(x) has a positive leading coefficient, and a vertex at (0, 3)

As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.

As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.

so:

f(x) intersects the x-axis at two points

g(x) does not intersect the x-axis.

The correct option is A.

6 0
3 years ago
A football field is 300ft long a sloth moving very quickly travels 60ft every 5 minutes based on this ratio how many minutes wou
Ipatiy [6.2K]

Answer:

25 minute

Step-by-step explanation:

Speed is the ratio of the total distance traveled  to the total time taken to reach this distance. The formula for speed is:

Speed = total distance / total time taken

The total distance covered by the sloth = 60 ft, and the time taken = 5 minutes, hence:

Speed = total distance / total time taken

speed of the sloth = 60 ft / 5 minutes = 12 ft per minute.

We can calculate the time taken for the sloth to travel the length of the football field (i.e. 300 ft)

speed = distance / time

12 ft/minute = 300 ft / time

time = 300 ft / (12 ft/minute)

time = 25 minute

4 0
2 years ago
You invest $350 in an account with an interest rate of 1.2% compounded continuously. How much money would be in the account afte
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You will get about 1300 a year

6 0
3 years ago
If cos(x) = Three-fourths and tan(x) &lt; 0, what is cos(2x)?
makvit [3.9K]

Step-by-step explanation:

The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

How to determine the value of sin(2x)

The cosine ratio is given as:

\cos(x) = -\frac 14cos(x)=−

4

1

Calculate sine(x) using the following identity equation

\sin^2(x) + \cos^2(x) = 1sin

2

(x)+cos

2

(x)=1

So we have:

\sin^2(x) + (1/4)^2 = 1sin

2

(x)+(1/4)

2

=1

\sin^2(x) + 1/16= 1sin

2

(x)+1/16=1

Subtract 1/16 from both sides

\sin^2(x) = 15/16sin

2

(x)=15/16

Take the square root of both sides

\sin(x) = \pm \sqrt{15/16

Given that

tan(x) < 0

It means that:

sin(x) < 0

So, we have:

\sin(x) = -\sqrt{15/16

Simplify

\sin(x) = \sqrt{15}/4sin(x)=

15

/4

sin(2x) is then calculated as:

\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)

So, we have:

\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗

4

15

∗

4

1

This gives

\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

6 0
2 years ago
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