What is the sum of all integers $n$ that satisfy
$$-3n < 7n-20 < 3n~?$$

$($In other words, what is the sum of all integers $n$ that satisfy both of the inequalities
$$-3n<7n-20\text{~~and~~}7n-20<3n~?)$$

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Answers

Answer 1

Looks like the inequality is

-3n < 7n - 20 < 3n

Add 3n to each side:

0 < 10n - 20 < 6n

Solve the right inequality.

10n - 20 < 6n

Add -10n to both sides:

-20 < -4n

Divides both sides by -4:

5 > n

Now solve the left inequality, and take the intersection of the two solution intervals.

0 < 10n - 20

Add 20 to both sides:

20 < 10n

Divide both sides by 10:

2 < n

So 2 < n < 5. There are only 2 integers in this range (3 and 4), whose sum is 7.

Answer 2

Answer:

7

Step-by-step explanation:

We solve each of the two inequalities separately. To solve the first inequality, -3n<7n-20, we add 3n to both sides:

0<10n-20, then we add 20 to both sides to get

20<10n. Finally, dividing both sides by 10 gives 2<n, so n must be greater than 2.

For the second inequality, 7n-20<3n, we subtract 3n from both sides:

4n-20<0, then add 20 to both sides to get

4n<20. Finally, dividing both sides by 4 gives n<5, so n must be less than 5.

The only integers that are greater than 2 and less than 5 are 3 and 4. So, the sum of all possible integer values of n is 3+4=7.


Related Questions

What is the domain of the square root function graphed below?

Answers

Answer:

x ≥ 0

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

According to the graph, the line's x-values span from 0 to infinity. Since 0 is a closed dot, it is inclusive in the domain:

[0, ∞) or x ≥ 0

Compute the sum of the squares of the shorter lengths. Compute the sum of the squares of the shorter lengths. Compute the square of the longest length. Compute the square of the longest length. What kind of triangle is it? What kind of triangle is it? Acute triangle Acute triangle Right triangle Right triangle Obtuse triangle Obtuse triangle

Answers

The given triangle is a right triangle because it agrees Pythagoras theorem.

In the given triangle, the shorter lengths are 12 and 16.

The sum of square of shorter lengths:

[tex]= 12^2 + 16^2[/tex]

[tex]=144+256[/tex]

[tex]=400[/tex]

The longer length is 20.

Square of the longest length is [tex]20^2.[/tex]

[tex]20^2 = 20 \times 20[/tex]

=400

The sum of squares of shorter lengths is equal to Square of the longest length which obeys Pythagoras theorem.

400 = 400

As this is agreeing Pythagoras theorem it is a right angle triangle.

Hence, option B is correct. right triangle.

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Lucy spent $22.80 on Halloween candy. Tax is 5%. How much will she spend total including tax?

Answers

Answer:

23.94

Step-by-step explanation:

Before Tax Price: $22.80

Sale Tax: 5.00% or $1.14

After Tax Price: $23.94

PLZZZ HELP DUE IN 5mins

Answers

Answer:

y=-6x+360

Step-by-step explanation:

The y intercept, b, is easy; its already listed as 360.

The slope we find by using some points:

300-360

10-0

=

-60

10

=

m=-6

y=mx+b

y=-6x+360

20 points

When you find a point on a graph that you think is the intersection, the best way to double check your answer is to:

substitute in the x value to see if both of the y values of both of the equations match the one you approximated from the graph.


substitute in the x value to see if one of the y values of one of the equations matches the one you approximated from the graph.


substitute in the y value to see if one of the x values of one of the equations matches the one you approximated from the graph.


substitute in the x value to see if both of the x values of both of the equations match the one you approximated from the graph.

Answers

Answer: Substitute in the x value to see if both of the y values of both of the equations match the one you approximated from the graph.

Step-by-step explanation:

I guess that we are working with systems of equations like:

y = f(x)

y = g(x)

Where an intersection is a solution that works for both equations, which means that the graphs will intersect each other in that point.

This means that for a given value x = x0, we must have:

f(x0) = g(x0).

Now, when you find a point that you think that is an intersection, you should substitute the x value in both functions, and see if the y-values coincide.

This will be equivalent to look if f(x) = g(x) for that particular value.

then the correct option is:

substitute in the x value to see if both of the y values of both of the equations match the one you approximated from the graph.

solve for d:
d + (-5.004) = 2.826
PLease

Answers

Answer:

7.83

Step-by-step explanation:

d + (-5.004) = 2.826

d = 2.826 - (-5.004)

  = 7.83

Therefore d is 7.83 :)

where is alrquan07 ? Anyone know?

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I have no clue where they are sorry

Answer:

hewo friend

Step-by-step explanation:

There are 914.4 millimeters in a yard . There are 3 feet in a yard . How many millimeters are in a foot !

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Answer:

304.8 millimeters

Step-by-step explanation:

Answer:

0.003

Step-by-step explanation:

Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

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Answer:

8,10,20 pls mark me as brainliest

Answer:

A triangle can not have a side that is longer than the sum of the other two sides.  In this case, the second answer does not fit a triangle, as 20 > 8 + 10.

Step-by-step explanation:

Lamar drinks 8 ounces of water with breakfast, 6 ounces of water with his vitamins, 16 ounces of water with his lunch, 16 ounces of water with his dinner, and 32 ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in ounces that he drinks in a week.

Answers

Given:

Lamar drinks water with,

Breakfast = 8 ounces

Vitamins = 6 ounces

Lunch = 16 ounces

Dinner = 16 ounces

Bottle = 32 ounces

To find:

The a numerical expression for the amount of water in ounces that he drinks in a week.

Solution:

One day consumption of water by Lamar is

[tex]8+6+16+16+32=78[/tex]

We know that,

1 week = 7 days

One day consumption of water = 78 ounces

1 week (7 days) consumption of water = 7× One day consumption of water

                                                               = 7×(8+6+16+16+32) ounces                                                                

                                                               = 7×78 ounces

                                                               = 546 ounces

Therefore, the required numerical expression for the amount of water in ounces that he drinks in a week is 7×(8+6+16+16+32) ounces and the value is 546 ounces.  

Need this it is due tomorrow please.

Answers

Answer:

a) parallel lines : CE and BF

b)perpendicular lines : DE and EF

c) is FE parallel to CA : no

Step-by-step explanation:

hope this helps

Answer:

a. CE║BFb.DA and BFc. No, because Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Step-by-step explanation:

Savelot offers two types of baseballs bats the wood bat sell for 24$ and the metal bats sell for 30 in one day save lots sold 23 base ball bats these recipts for those bats totaled $606 how many of each type of bat was sold

Answers

Answer:

Step-by-step explanation:

Let us represent

Let the wood bat = w

Let the base ball bats = b

Savelot offers two types of baseballs bats the wood bat sell for 24$ and the metal bats sell for 30 in one day save lots sold 23 base ball bats these recipts for those bats totaled $606 how many of each type of bat was sold

System of Equations

w + b = 23.... Equation 1

b = 23 - w

24w + 30b = 606..... Equation 2

We substitute:30 - w for b

Hence:

24w + 30(23 - w) = 606

24w + 690 - 30w = 606

24w - 30w = 606 - 609

-6w = -84

w = -844/-6

w = 14 wood bats

b = 30 - 14

b = 16 base ball bts

Rawr ... someone help me :) please it’s math and the last word says Box btw !

Answers

Answer:

4/7

Step-by-step explanation:

Have a nice day

Answer:

4/7

Step-by-step explanation:

I said so hun

6(3x - 2) = 18x + 6
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Answers

Step-by-step explanation:

6(3x-2)=18x+6

18x-12=18x+2

18x-18x=2-12

0 =-10

0

Answer:

This equation does not exist.

yooooooooooooooooooooooooooooooooooooooooooooooooooooo

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Answer:

yooooooooooooooooooooooooooooo

pllllllllllllllzzzzzzzzzzzzzzz
hhheeeellllllllpppppppppppp

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Answer:

I think it should be the third option

How much are these coins worth??

Answers

Answer:

quarters are worth 25 cents

dimes are worth 10 cents

nickels are worth 5 cents

pennies are worth 1 cent

that is a total of $1.48 there

Step-by-step explanation:

find the number of kilograms in 250 pounds. there are 1000 grams in a kilogram and 454 grams in a pound.

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3+(−4)−8−(−1)

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Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

What is the y-intercept of the equation?

Answers

The y intercept is 0
Y = mx + b
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What is X in feet

X= Ft

Answers

Answer:

x = 26ft

Step-by-step explanation:

[tex]A^{2}[/tex] + [tex]B^{2}[/tex] = [tex]C^{2}[/tex]

[tex]10^{2}[/tex] + [tex]24^{2}[/tex] = 676

[tex]\sqrt{676}[/tex] = 26

The senior class has 412 students. They are assigned to different homerooms. There are 28 students in the smallest homeroom and the remaining 12 homerooms have the same number of students. How many students are in each of remaining 12 homerooms?


Just give me the equation.​

Answers

Answer:

There are 32 students in the other 12 homerooms.

Step-by-step explanation:

32x12=384

384+28=412

Full equation: 32x12=384 28=412

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Answer:

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Step-by-step explanation:

have a good day <3

Solve for g.

g - 15 = 4

Answers

Answer:

11

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

(ABCD) = (A'B'C'D'). If A is (6, −8), A' is (−2, 4), and B is (4, −6), what are the coordinates of B'?

Answers

Answer: (6, 6)

In this problem the point is moved over 2 up and 2 to the right form A to A'

The coordinates of B' are (-4, 6).

What is translation?

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation may alternatively be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Since (ABCD) = (A'B'C'D'), we know that corresponding points in the two quadrilaterals have equal coordinates.

Therefore, we can use the coordinates of A and A' to find the translation vector that takes A to A'.

We can then apply this same vector to B to find its image B'.

The translation vector that takes A to A' is given by the difference A' - A:

A' - A = (-2, 4) - (6, -8) = (-8, 12)

So, the same translation vector takes B to B', and we have:

B' = B + (-8, 12) = (4, -6) + (-8, 12) = (-4, 6)

Therefore, the coordinates of B' are (-4, 6).

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PLEASEE HELPPPP WILL GIVE BRAINLEAST IT IS URGENT!!!!

Which equation models the trend line?
A- y = –1.3x + 2
B- y = 1.3x + 2
C - y= –1.3x – 2
D- y = 1.3x – 2

Answers

Sorry if it’s wrong but i think it’s B
sorry if i got it wrong

Answer:

B. y = 1.3 + 2

Step-by-step explanation:

The slope is positive, and the y intercept is at positive 2.

Two forces of 25 pounds and 20 pounds act on a body with an angle of 25 degrees between them. What is the magnitude of the resultant force?

a) 13.23 pounds
b) 38.78 pounds
c) 43.95 pounds
d) 53.23 pounds

Answers

Answer:

C) 43.95 pounds

Step-by-step explanation:

got it right on edge :)

The magnitude of resultant force is 43.95 pounds.

The option c is correct.

Resultant force:

Two forces are given that,

[tex]F_{1}=25, F_{2}=20,\theta=25 degree[/tex]

The resultant force is calculated by using formula,

         [tex]F=\sqrt{F_{1}^{2}+F_{2}^{2}+2F_{1}F_{2}cos \theta } \\\\F=\sqrt{25^{2}+20^{2}+2*25*20*cos25 }\\\\F=\sqrt{625+400+906.307}\\ \\F=\sqrt{1931.307}=43.95[/tex]

Hence, the magnitude of resultant force is 43.95 pounds.

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Find the x-value for point C such that AC and BC from a 2:3 ratio.

Answers

Given:

Point C divides AB such that AC:BC=2:3.

To find:

The x-value for point C.

Solution:

Section formula: If a point divide a line segment in m:n, then

[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Form the given graph it is clear that the endpoints of the line segment AB are A(-3,5) and B(3,0).

Point C divides AB such that AC:BC=2:3. Using section formula, the coordinates of point C are

[tex]C=\left(\dfrac{2(3)+3(-3)}{2+3},\dfrac{2(0)+3(5)}{2+3}\right)[/tex]

[tex]C=\left(\dfrac{6-9}{5},\dfrac{0+15}{5}\right)[/tex]

[tex]C=\left(\dfrac{-3}{5},\dfrac{15}{5}\right)[/tex]

[tex]C=\left(-0.6,3\right)[/tex]

The x-value of C is -0.6.

Therefore, the correct option is B.

slope = 5, goes through the point (2, 7)

Answers

Y-7=5(x-2) -> y-7=5x-10 -> y=5x-3
Final answer is y=5x-3

Raja claims that to add two fractions with unlike denominators, first you need to determine the smallest number that is a multiple of both denominators. Then change the denominators in both fractions and keep the numerators the same.

Answers

Answer:

Incorrect

Step-by-step explanation:

This is incorrect. In order to add two fractions that have unlike denominators, it is true that you first need to find a common denominator. When you change a fractions denominator you must also change it's numerator in proportion to the change in the denominator. For example, if you change the denominator in the fraction [tex]\frac{1}{2}[/tex] into a 4 then you are multiplying the denominator by 2, therefore you will also need to multiply the numerator by 2 which would give you a new fraction of [tex]\frac{2}{4}[/tex]

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