All categories

3 years ago

four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.

1 answer:

7 0

The solution to the problem about the possible values of x in the inequality is as follows:

4(x+15) >= 120
x+15 >= 30
<span>x >= 15

Therefore, there are </span><span>x >= 15 possibilities in the inequality.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.
</span>

You might be interested in

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

Re-write the following problem using a different form of rational numbers. Then solve using that different form of rational numb

Effectus [21]

Answer:

-6.85

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

If y=6 when x=2 over 3 find x when y=12

AlexFokin [52]

Answer:

4/3 or 1 1/3

Step-by-step explanation:

So if y = 6, when x = 2/3. Then, x would equal 1 and 1/3, because 12 is twice the amount of 6, so you'd also multiply 2/3 by 2.

(To multiply a whole number by a fraction, first multiply the whole number by the numerator and then divide that by the denominator. For example: 2 × 2 = 4, since you can't really divide 4 by 3 it would stay as is, but you can turn it to a mixed number. 4/3 is the same as 1 whole and an extra 1/3, or in other words 1 1/3).

Hope this helped :)

6 0

2 years ago

Which relation is a linear function with the least slope?

mel-nik [20]

It would be the first graph because the slope would be zero making it the smallest

7 0

3 years ago

Need help in all please asap and is the graphing right ? If not please help me with that two ! :))

Bezzdna [24]

Yes your graphing right
Y intercept is -2 and the slope is 1
Y = X + -2

6 0

3 years ago