Mathematics High School

Solve the inequality
-8x - 10 > 7x + 20

A.) x < - 30
B.) x > - 2
C.) x > - 30
D.) x < - 2

Answers

Answer 1
Final answer:

To solve the inequality -8x - 10 > 7x + 20, combine like terms, isolate the variable term, and solve for x. The correct answer is D) x < -2.

Explanation:

We need to solve the inequality -8x - 10 > 7x + 20.

First, let's combine like terms by adding 8x to both sides. This gives us -10 > 15x + 20. Next, subtract 20 from both sides to isolate the variable term. This gives us -30 > 15x. Finally, divide both sides by 15 to solve for x. This gives us x < -2.

Therefore, option D.) x < -2 is the correct answer.

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Related Questions

There are 20 girls on the basketball team. of these, 17 are over 16 years old, 12 are taller than 170 cm, and 9 are both older than 16 and taller than 170 cm. how many of the girls are older than 16 or taller than 170 cm?

Answers

17 are older than 16 years old and 12 are taller than 170 cm

Final answer:

By using the principle of inclusion-exclusion, we calculate that all 20 girls on the basketball team are either over 16 years old or taller than 170 cm, as the sum of the individual criteria minus the intersection equals the total number of girls on the team.

Explanation:

To determine how many of the girls on the basketball team are either over 16 years old or taller than 170 cm, we can use the principle of inclusion-exclusion. According to the information provided, there are 20 girls on the team in total, of which 17 are over 16 years old, 12 are taller than 170 cm, and 9 satisfy both criteria. The principle of inclusion-exclusion states that the number of elements in the union of two sets is equal to the sum of the sizes of each set minus the size of their intersection.

Using this principle:

Number of girls over 16 years old: 17

Number of girls taller than 170 cm: 12

Number of girls who are both over 16 and taller than 170 cm: 9

The calculation would be as follows:

17 (over 16) + 12 (taller than 170 cm) - 9 (both) = 20

Therefore, there are 20 girls on the team who are either older than 16 or taller than 170 cm.

If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Answers

There are 13 hearts in a standard 52-card deck.

The probability of getting a heart on the first card is 13 / 52 = 1/4

Given that the first card was replaced, the probability of getting a diamond on the second card is 13 / 52 = 1/4

Therefore, the probability of getting a heart on the first card and a diamond on the second is given by 1/4 x 1/4 = 1/16.

write an equation of the line, in slope intercept form, that passes through the given point and has the given slope. point:(8,-8), slope:3

Answers

If m equals 3, and we have a y and x value of 8 and -8, all we have to do is solve for b.

-8 = 3(8) + b
Multiply 8 and 3.
-8 = 24 + b
Subtract 24 from both sides to isolate b.
-32 = b

Your equation would look like this:

y = 3x - 32

andy constructed a triangle angle 1 and 2 are the same but angle 3 has a measurement of 100 degrees what is the measurement of angle 1 and 2

Answers

The triangle has one angle of 100 degrees, and the other two are equal. 
We know that the angles of a  triangle always add up to 180. To find the measurement of angle 1 and 2, let's solve for this equation. 
2x + 100 = 180, where x=angle 1 = angle 2. Subtract 100 from both sides
2x = 80                                                           Divide both sides by 2
x = 40

Help please I’ll mark you brainliest

Answers

Subtract any number from the next one.
-1 - (-6)
4 - (-1)
9 - 4
14 - 9

All of the above subtractions give the same answer.
That answer is the common difference.

find m<G p//r. the diagram is not to scale. I believe it to be 146 but I'm not sure.

Answers

You know that line r and line p are parallel to each other. Therefore, the angle underneath H is also 34 degrees. 

Angle H would be: 
180-34=146 degrees. 

Angle G would be: 
180-146=34 degrees. 

Hope I helped :) 
Final answer:

The given information is not clear enough to determine the measure of angle G p//r.

Explanation:

To find m<G p//r, we need to understand the given diagram. However, the provided information is not clear enough to determine the measure of angle G p//r. More information or a clear diagram is needed to find the angle accurately. Please provide additional details or a clear diagram for further assistance.

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5377 people/km^2= how many people/m^2 ?

Answers

186 people / m^2. you're welcome

Answer:

0.005377 people/m²

Step-by-step explanation:

5377 people/km² can written as

5377 × [tex]\frac{people}{km^2}[/tex]

Now we have to find the value in [tex]\frac{people}{meter^2}[/tex]

Since 1 km = 1000 meter.

So 5377 × [tex]\frac{people}{km^2}[/tex] = 5377 × [tex]\frac{people}{(1000)^2met^2}[/tex]

= [tex]\frac{5377}{(1000)^2}[/tex] people per met²

=  [tex]\frac{5377}{(1000000)}[/tex]

= 0.005377 people/m²

HELP MEH PLEZ! When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there

Answers

The equation representing the number of people, y, at the fair x hours after the gates open:

y = 68 * 1.5^(x-1)

Initial number of people: 68 (given)

Growth factor per hour: 1.5 (given)

Number of hours since gates opened: x

The equation uses the following logic:

Start with the initial number of people (68).

Multiply by the growth factor (1.5) to account for the increase after the first hour.

Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.

Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.

Complete question:

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

If sin theta = 3/5 and cos theta <0 find tan theta

Answers

-3/4
Find cos to be -4/5
then
tan=sin/cos=(3/5)/(-4/5)=-3/4

What does the end behavior look like of the graph of the function f(x)=-8x^4-2x^3+x?
I know what the graph itself looks like but I have trouble explain its end behavior.
Thank you.

Answers

In this question, the highest power is x^4 which is an even number. In this case, the f(x) will be same for plus X or minus X.
The coefficient is -8 which is a minus. In this case, the f(x) will become minus: 

The result would be:
when X go the left end(X= -∞), the f(x) will become minus (f(x)→−∞)
f(x)→−∞, as x→−∞

when X go the right end(X= +∞), the f(x) will become minus (f(x)→−∞)
f(x)→−∞, as x→+∞

The longer leg of a right triangle is 4cm longer than the shorter leg the hypotenuse is 8 cm longer than the shorter find the side lengths of the triangle

Answers

Let x  be  length of shorter leg

4cm longer than the shorter leg x +  4 = length of longer leg
 
hypotenuse is 8 cm longer than the shorter 
x + 8  = length of  hypotenuse

phytagorus rule 

x^2  + (x+4)^2 = (x+8)^2 

x^2 + x^2 +8 x + 4^2 = x^2 + 16x +  8^2

x^2 - 8x - 48 =0

(x + 4 ) (x - 12) - 0 

x= - 4    we reject negative number

so  x= 12 



The side lengths of the triangle are 8 cm, 12 cm, and 16 cm

To solve for the side lengths of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as a^2 + b^2 = c^2.

Let's denote the shorter leg of the triangle as x. Then, according to the problem, the longer leg is x + 4 cm and the hypotenuse is x + 8 cm. Plugging these expressions into the Pythagorean Theorem, we have:

x^2 + (x + 4)^2 = (x + 8)^2

Expanding and simplifying the equation:

x2 + x2 + 8x + 16 = x2 + 16x + 64

2x2 + 8x + 16 = x2 + 16x + 64

x2 - 8x - 48 = 0

Solving this quadratic equation for x, we find:

x = 8 cm (shorter leg)

x + 4 = 12 cm (longer leg)

x + 8 = 16 cm (hypotenuse)

Therefore, the side lengths of the triangle are 8 cm, 12 cm, and 16 cm

Write -42/9 mixed in a reduced form

Answers

-42/9 = -4 6/9 = -4 2/3

hope it helps
Answer: 
–4 2/3

Explanation:  
To make –42/9 into a mixed number, you need to divide –42 by 9. 
–42 ÷ 9 = –4.66666, so the mixed number starts with –4. 
–4 • 9 = –36 
–42 – –36 = 6 
So the mixed number is now –4 6/9 
To reduce it, you simplify: 
–4 6/9 = –4 2/3

You know, this question "functions" just as well as the Kardashians. Not at all, at least to my brain! I definitely need help with this.

Answers

The answer is 2
The question is asking what is Y, when X equals 1. It is referring to the standard formula B(x). If x on the graph were to equal 1, what would be the Y?
For this just look at the horizontal x-axis and find 1.
*On the left side is negative numbers going from right to left  -1 to -4 and the right side from left to right  1 to 4
So when you look at the graph on line 1, there is a dot at the point (1,2)
Thus, 2 is the answer.

Suppose you had d dollars in your bank account. You spent $12 but have at least $51 left. How much money did you have initially? Write and solve an inequality that represents this situation.

A.
d+12 51; d 75

B.
d + 12 51; d 75

C.
d-12 51; d 63

D.
d-12 > 51; d > 63

Answers

Initial amount =  d  dollars
Amount spent = $12

Because the amount left is at least $51, therefore
d - 12 ≥ 51
Add 12 to each side.
d ≥ 51 + 12
d ≥ 63

Note: The amount left is at least $51. Therefore the amount left should be $51, or greater than $51.

Answer:
d - 12 ≥ 51
d ≥ 63

Suppose a parabola has vertex (-3,7) and pass throught the point (-2,11). write the equation of the parabola in vertex form.

Answers

Write out the information in the vertex form;

y=a(x-h)²+k 
y=a(x+3)²+7 <-- substitute the other coordinates to find the value of a 
11=a(-2+3)²+7 
11=a(1)²+7 
11-7=a 
4=a 

Therefore, this equation is; 

y=4(x+3)²+7 

Hope I helped :) 

Parabola is a plane curve with a U shape.

The parabola equation is given as:

y = a (x – h)² + k

The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.

What is a parabola?

Parabola is a plane curve with a U shape.

The parabola equation is given as:

y = a (x – h)² + k

(h, k) is the vertex.

We have,

Parabola:

Vertex = (-3, 7)

Passes through the point = (-2, 11)

The equation of the parabola is y = a (x - h)² + k

(-3, 7) = (h, k)

Since the parabola passes through the point (-2, 11) we get,

11 = a (-2 - (-3))² + 11

11 = a (-2 + 3)² + 11

11 = a x 1 + 11

11 = a + 11

Subtract 11 on both sides.

0 = a

a = 0

Now,

y = 0 (x + 3)² + 11

y = 0 + 11

y = 11

Thus,

The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.

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1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11

Answers

write it down again
you mean (3-2√11)/(2+√11) I guess
(3-2√11)(2-√11)/(2+√11)(2-√11)
(28-7√11)/(-7)
therefore the answer is √11-4

ANSWER

[tex] \sqrt{11} - 4[/tex]


EXPLANATION

The given radical expression is

[tex] \frac{3 - 2 \sqrt{11} }{2 + \sqrt{11} } [/tex]

We rationalize the radical expression by multiplying both the numerator and denominator by the conjugate of
[tex]2 + \sqrt{11} [/tex]

which is

[tex]2 - \sqrt{11} [/tex]

This will give us,

[tex] \frac{3 - 2 \sqrt{11} }{2 + \sqrt{11} } \times \frac{2 - \sqrt{11} }{2 - \sqrt{11} } [/tex]


[tex] \frac{(3 - 2 \sqrt{11})(2 - \sqrt{11} ) }{(2 + \sqrt{11})(2 - \sqrt{11} ) }[/tex]
We expand the numerator and also apply difference of two squares to the denominator.


[tex] \frac{6 - 3 \sqrt{11} - 4 \sqrt{11} + 2(11)}{ {2}^{2} - { (\sqrt{11} )}^{2} } [/tex]

This simplifies to,


[tex] \frac{6- 3\sqrt{11} - 4 \sqrt{11} + 22}{ 4- 11} [/tex]


[tex] \frac{28- 7 \sqrt{11} }{ - 7} [/tex]


We now share the denominator for the numerators to obtain,


[tex] - \frac{28}{7} + \frac{7 \sqrt{11} }{7} [/tex]

This finally gives,

[tex] - 4 + \sqrt{11} = \sqrt{11} - 4[/tex]

   John buys big ice-cream cylindrical Jar and sells it for $1 each ice-cream cone.

Each cone has around 30 cubic cm of ice-cream in it.

  Jar has diagonal 20 cm. and its height is 3 times of width.

If he sells the whole jar, and He originally bought it for $7 does he make profit out of selling the jar?

Answers

John makes a profit. Volume of ice cream cylinder is pi, π (3.14) times radius (20cm/2) squared, time height (3 x 20cm) = 3.14 x 100 square cm x 60cm ≠18850 cubic cm. With 30 cubic cm per cone, a cylinder contains ice cream for about 628 cones, and sell for $628 dollars.

John can make a profit by selling ice cream from the cylindrical jar. After calculating the volume, he would earn approximately $15.70 in revenue, and by deducting the initial cost ($7), he makes a profit of around $8.70.

To determine if John will make a profit by selling the entire ice-cream cylindrical jar, we first need to calculate the volume of the jar to find out how many cones he can fill. The jar has a diagonal of 20 cm and a height that is three times its width. Assuming the width is 'w' and height is '3w', we can use the Pythagorean theorem with the jar's diagonal to find 'w', since the diagonal forms a right triangle with the width and height of the cylinder.

The formula for the Pythagorean theorem is diagonal^2 = width^2 + height^2, which gives us 20^2 = w^2 + (3w)^2. Solving for 'w', we get w = 4 cm and height = 12 cm. The volume 'V' of the cylinder is given by V = π * radius^2 * height, which gives us V = π * 2^2 * 12, therefore, V = 48π cm^3. Then, we divide the jar's volume by the volume of each ice cream cone to find the number of cones, 48π cm^3 / 30 cm^3/cone ≈ 5π cones.

Given that John sells each cone for $1, the total revenue from selling all the ice-cream cones would be approximately $5π. Since π is approximately 3.14, his total revenue would be about $15.70. Subtracting the initial cost of the jar ($7), we find that John would make a profit of approximately $8.70.

Therefore, John will indeed make a profit out of selling the jar of ice cream.

a fishing lake was stocked with 300 bass. Each year, the population decreases by 25. the population of bass in the lake after x years is represented by the function f(x)=300-25x

Answers

Final answer:

The function f(x)=300-25x represents the decline of population in a fishing lake that was initially stocked with 300 bass. Each year, the population reduces by 25. For instance, after 4 years, the number of bass left in the lake would be 200.

Explanation:

The question is about a fishing lake that was initially stocked with 300 bass. As per the information given, the population of bass in the lake decreases by 25 each year. Therefore, if we let x represent the number of years, then every year, the number of bass decreases by 25x. This relationship is represented by the algebraic function f(x)=300-25x.

To provide a practical understanding, suppose you want to calculate the number of bass remaining after 4 years. You just substitute '4' in place of x in the equation. Hence, f(4) = 300 - 25 * 4 = 300 - 100 = 200. So, after 4 years, there would be 200 bass remaining in the lake.

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How many 3 letter "words" can be created from the letters abcdefg when 1. repetition allowed,?

Answers

46 check out this site : wordmaker.info

Newer stocks can be bought for $8 each, while older stocks can be bought for $4 each. The total cost, in dollars, of 10 stocks is represented by the expression 8s+4(10-s), where s represents the number of new stocks bought. how does changing the value of s change the value of the term 4(10-s)?

A.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.

B.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.

C.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.

D.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.

Answers

The correct option is D.
The equation given in the question is 8S + 4[10 -S], where S is the number of new stock bought.
Changing the value of S in the 4[10 - S] component of the equation will change the equation. To get the the correct option you have to considered individually all the options given in the question.
Let consider option D.
For value of S less than 10, the term will be positive. For instance, let use 6.
4 [10 - 6] = 16.
For value of S greater than 10 the value will be negative. For instance, let use 20.
4 [10 - 20] = - 40.
For value of S equal to 10, the value will be zero. For instance, let S = 0
4[10 - 10] = 0.

Mrs. Sage will print a copy of the class alphabet book for each student. The book is formatted in1/2 pages with a title page, a page for each letter and an end page. If there are 70 students, how many reams of paper will Mrs. Sage need for the books?

Answers

Note that
1 ream of paper  = 500 sheets (or pages printed)

Each book has
1/2 page for each letter of the alphabet = (1/2)*26 = 13 pages
A title page = (1/2)*1 = 1/2 page
An end page = (1/2)*1 = 1/2 page

Total pages per book = 13 + 1/2 + 1/2 = 14 pages.
There are 70 students, therefore the number of pages needed is
14*70 =  980 pages

The number of reams of paper required is
980/500 = 1.96 ≈ 2 reams

Answer: 2 reams

help will mark brainliest Jim Shu has the following work shown on their paper. The directions read “Simplify each radical.” Unfortunately, they have not simplified correctly.
A. Find their mistake and explain what they did wrong.

Answers

Final answer:

Jim Shu made two mistakes in simplifying radicals: they missed the initial steps and included an irrelevant step of checking the answer's reasonability.

Explanation:

The instructions provided to Jim Shu involve simplifying radicals, but there is an omission of the initial steps in the process.

The student proceeds with step 6 without detailing the necessary earlier steps in simplifying the algebraic expression.

This misstep results in an incomplete representation of the solution process.

Furthermore, step 7 introduces an unrelated directive, advising the student to check the answer for reasonability.

This step is incongruent with the task at hand, which is the simplification of radicals.

To address this error, Jim Shu should incorporate the essential preliminary steps for simplifying radicals, ensuring a comprehensive presentation.

Additionally, the extraneous step of checking reasonability should be omitted, aligning the solution process with the given directions.

Find the next term of the following sequence.

25, 10, 4,

Answers

The given sequence is 25, 10, 4.

Notice that this is a geometric sequence because here we have equal common ratio.

So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]

= [tex] \frac{10}{25} [/tex]

= 0.4

So, each term is 0.4 times of it's previous term.

Hence, to get the next term of this sequence, multiply 0.4 with the third term 4.

So, fourth / next term = 4* 0.4 =1.6

Hence, next term of this sequence is 1.6.

Hope this helps you!

Answer:

Step-by-step explanation:

the answer is 8/5 i just did it on my quiz and got it right.

Katie jogged 2.4 miles on Monday, 3.7 miles on Tuesday, and 2.9 miles on Wednesday. How many miles did Katie jog on Thursday if she jogged a total of 12.1 miles for the four days

Answers

  12.1 total
-   2.4 Monday
    3.7 Tuesday
    2.9 Wednesday
_______________
    3.1 Thursday
Heya!

Please refer the image for Answer!
Hope it helps...!!!

If the intercepts of a line are (a,0) and (0,b), what is the slope of the line?
Show how you solved it.

Answers

generally gradient = (Y2-Y1)/(X2-x1)
from the above
y2= b
y1=0
x2=0
x1=a
so gradient= (b-0)/(0-a) = b/-a =-b/a

evaluate the expression (18-6)÷(11-5), if possible

Answers

18-6= 12
11-5=6

12 divided by 6 = 2
(18 - 6) ÷ (11 - 5) ⇒ Work out the bracket first

12 ÷ 6

2

PLEASE HELP ME DO NOT HELP IF YOU DO NOT KNOW HOW TO DO IT

The state of Colorado had roughly the shape of a rectangle that is 3.8 x 10^2

2.8 x 10^2 miles high. What is the approximate area of Colorado? hint: the area of the rectangle is a product of its length and width.

Answers

Area of rectangle = length times width

Let 3.8 x 10^2 = width

Let 2.8 x 10^2 = length

Search your book or online for instructions on how to multiply in terms of scientific notation.

A = (2.8 x 10^2)(3.8 x 10^2)

Take it from here.

The Sheng family had dinner at their favorite restaurant. A 4% sales tax was added to their bill. Amy paid the bill with a $25 gift certificate plus $44.80. How much did the family's dinner cost before tax? Round your answer to the nearest penny.$ 71.59$ 66.01$ 67.12$ 67.01

Answers

The answer would be 67.12.
The total cost is 72.59 so it should be A I believe 

Can someone please explain this in a way my dumb brain would understand? WHY does 2 - (-8) = 10? Shouldn't it be decreasing to -6?

Answers

Hey! The most intuitive way I've been explained the idea of subtracting negative numbers is in terms of debts. Subtracting a debt from your bank account has the effect of adding money to it. Imagine you had $10 in your account, but you owed $8 in debt; your current balance would show $2 in your account. If you took away that debt, though, you'd be back up to $10. If we imagine your funds as positive numbers and your debts as negative numbers, we could express taking away that debt as:

2 - (-8) = 10

Hope that makes a little more sense!

The reasoning is because you are subtracting 2. If you were to be adding 2, then it would be -6.

Since you are subtracting 2 it = 10.

Glad to help a Senior mod out.

Thanks, Plip.

For the points M(-2,3), N(4,5), P(1,6) and Q(4,-3), what is the relationship between MN and PQ?

Answers

MN=sqrt((4+2)^2+(5-3)^2)=2*sqrt (10)
PQ=sqrt((4-1)^2+(-3-6)^2)=3*sqrt(10)

MN/PQ=(2*sqrt (10))/(3*sqrt (10))=2/3

[sqrt=square root]
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