All categories

3 years ago

Solve the inequality for x. 75+15x is greater than or equal to 140

Mathematics

1 answer:

Gre4nikov [31]3 years ago

8 0

75+ 15x ≥ 140
⇒ 15x ≥ 140 -75
⇒ 15x ≥ 65
⇒ x ≥ 65/15
⇒ x ≥ 13/3
⇒ x ≥ 4 1/3

The final answer is x ≥ 4 1/3~

You might be interested in

Which is the best approximation for the measure of angle ABC?

qwelly [4]

Answer:

58.3°

Step-by-step explanation:

Missing Information:

In this question the diagram is missing Following are the attachment of diagram of the given question.

As we seen that the vertex c is making the right angle i,e 90° also there is an acute angle the Hypotenuse: 20 cm and the perpendicular is 10.5 cm

Now we have find the best approximation of the angle ABC used the cosx trigonometric function.

$cos\ x\ =\ \frac{perpendicular}{Hypotenuse} \\$

Putting the value of perpendicular and hypotenuse in the previous formula we get

$cos\ x\ =\ \frac{10.5\ cm}{20\ cm} \\$

$x\ =cos^{-1}\ 0.525\\x \ = \ 58.33$

8 0

3 years ago

Determine whether the geometric series is convergent or divergent. 10 − 6 + 3.6 − 2.16 + convergent divergent Correct: Your answ

Misha Larkins [42]

Answer:

The series CONVERGES with the sum being 6.25.

Step-by-step explanation:

Given that the geometric series is 10 - 6 + 3.6 - 2.16 + ....

So the first term of the geometric progression is, $a_{1}$ = 10

The second term of the geometric progression is $a_2$ = -6 = $a_1$ × r = 10 × r

where r is the constant ratio.

Therefore r = $\frac{-6}{10}$ = -0.6

The third term of the geometric progression, $a_3$ = 3.6 = $a_2$ × r = -6 × -0.6 = 3.6

The fourth term of the geometric progression, $a_4$ = -2.16 = $a_3$ × r = 3.6 × -0.6 = -2.16

So the above confirms that the series is indeed a geometric progression with first term, $a_{1}$ = 10 and constant ratio, r = -0.6

Now to find if the series converges or diverges we can take sum of the series from first term to infinity.

We can already infer that the series is convergent since the constant ratio, r = -0.6 which is less than 1.

So from the formula for the sum to infinity of a geometric progression, S, we get

S = $\frac{a_1}{1 - r} = \frac{10}{1 - (-0.6)} = \frac{10}{1 + 0.6} = \frac{10}{1.6} = 6.25$

So the series is convergent with the sum being 6.25

7 0

4 years ago

Find the measure of each interior angle of a regular polygon with the following number of sides 10

mina [271]

Answer:

a regular polygon has all angles measure sum up to 360 degrees so each interior angle = sum of alll angles/no.of sides so it is 360/10= 36 degrees hope its clear now

Step-by-step explanation:

8 0

3 years ago

Anything to the power of 1 is what ?

sp2606 [1]

Answer: It can be any number, x^1=x

Step-by-step explanation: Say we have 5^1. It is 5. No powers added.

plz mark as brainliest

8 0

3 years ago

An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. what is a si

zhannawk [14.2K]

The volume formula for a square or a rectangle, even, is V=l*w*h
Here, we are given our volume as 675, now we just have to find everything else, right?! Well, if you have a square, all 4 sides are the same exact length, so the length and the width of our formula are going to be the same so we only have to worry about finding a value for one and then use it twice. If you have a square of side length x and you cut 2 squares out of each side measuring 3 inches each, you are cutting away 6 inches. So the side now reflects a length of x - 6. Which is used for the length and the width in our formula. The height of the box will be 3 inches, or in other words, what you cut away from each corner to make a box in the first place! So our formula will look like this: 675 = (x - 6)(x - 6)3. Easiest thing to do is to divide away the 3 to get 225 = (x - 6)(x - 6). Now expand that by FOILing:
$225= x^{2} -12x+36$
Set it equal to 0 to solve for x, the length and width of each side by moving the 225 over to the other side:
$x^{2} -12x-189=0$
Now you just have to factor this. When you do, you get x values of 21 and -9. But we all know that you cannot have a side length be a negative number so the x value is 21. That's the side length of the original paper before you cut 6 inches away.

8 0

3 years ago