Solve the inequality 5u≤8u−21 and write the solution in interval notation

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]5u\leq 8u-21[/tex]

Subtract 8u from both sides

[tex]-3u\leq -21[/tex]

Divide by -3 on both sides

[tex]u\geq 7[/tex]

Interval notation: [greater/less than or equal to], (greater or equal to)

[7,∞)

Answer 2

The solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).

What is inequality?

In mathematics, an inequality is a remark that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

Here,

To solve the inequality 5u ≤ 8u - 21, we can start by isolating u on one side of the inequality. We can do this by subtracting 5u from both sides:

5u ≤ 8u - 21

-3u ≤ -21

Divide both sides by -3. Note that dividing by a negative number will reverse the direction of the inequality:

u ≥ 7

Therefore, the solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).

Learn more about inequality here:

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Related Questions

What is the inverse of the function f(x) = 169x2 when x ≥ 0?

A- f−1(x) = 13‾‾
B- f−1(x) = √13
C- f−1(x) = 13x
D- f−1(x) = 113

Answers

Answer:

[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]

Step-by-step explanation:

Inverse function:

Suppose we have a function y = f(x). To find the inverse, we exchange the y and the x values, and then isolate y.

Function:

[tex]f(x) = 169x^2[/tex]

That is:

[tex]y = 169x^2[/tex]

Exchanging x and y:

[tex]x = 169y^2[/tex]

Isolating y:

[tex]y^2 = \frac{x}{169}[/tex]

[tex]y = \sqrt{\frac{x}{169}}[/tex]

[tex]y = \frac{\sqrt{x}}{13}[/tex]

[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]

A box with a square base and open top must have a volume of 97556 c m 3 cm3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x x .] Simplify your formula as much as possible.

Answers

Answer:

S(x)  =  x²  +  390224/x

Step-by-step explanation:

Volume of the open box  =   V  = 97556 cm³

Material needed:

Let´s call x the side of the square base then  the  area of the base is

A(b) = x²

For the sides of the box, we have 4 sides each one with area of x*h

where h is the height of the box

The volume of the box    V(b) = 97556 = x²*h   then    h  =  97556/x²

S(x,h) = x²  +  4*x*h*

The surface area of the box as function of x is:

S(x)  =  x²  + 4*x*97556/x²

S(x)  =  x²  +  390224/x

What is the slope of a line perpendicular to the line containing the points (4,-7) and (-5,-1)? Express your answer as a common fraction.

40 POINTS!!!!!!

if not right i report

Answers

Answer:

3/2

Step-by-step explanation:

Slope 1 = (-1+7)/(-5-4) = 6/(-9) = -2/3

Slope 2 perpendicular to Slope 1 :

-1 ÷ -⅔ = 3/2

What are the coordinates of point K?

Answers

Answer:

Option A; [tex](\frac{5}{8} , -\frac{1}{4} )[/tex]

Hope this helps!

Answer:

i wanna say A but im not for sure

Step-by-step explanation:

A circle has an area 20 cm2. It is enlarged three times. What is the area of the enlarged circle?

Answers

Answer:

A = 60 cm²

Step-by-step explanation:

Given that,

The area of a circle, A = 20 cm²

It is enlarged 3 times.

We need to find the area of the enlarged circle.

Area of the enlarged circle,

A = 20×3

= 60 cm²

So, the area of the enlarged circle is equal to 60 cm².

Find x if x-log 48 + 3 log 2 = 1/3log125 - log3

Answers

Answer:

Step-by-step explanation:

x−log(48)+3(log(2))=

1

3

(log(125))−log(3)

Simplifies to:

x−0.778151=0.221849

Let's solve your equation step-by-step.

x−0.778151=0.221849

Step 1: Add 0.778151 to both sides.

x−0.778151+0.778151=0.221849+0.778151

x=1

Answer:

x=1

 

It takes Miguel 18 minutes to finish reading 4 pages of a book. How long does it take him to finish reading 30 pages

Answers

Answer: 135 minutes or 2 hours and 15 minutes  

Step-by-step explanation:

4/18 = 30/ x

Solve for duh 'x'

it should be 135 minutes, cuz you get 4.5 with 18 and 4

each exterior of a regular polygon is 30 degree find the sum of interior angles of the polygon​

Answers

Step 1: 360÷30(exterior angle)= 12 sides

Step 2: (12-2)×180= 1800 (sum of the interior angles of the polygon)

Test: 1800÷ 12 sides= 150 ( 1 interior angle)

Solve (x + 5)∕3 = 4 for x.

Answers

4+5=9 • 3 =27/4= 6.75

Answer:

7

Step by step explanation:

1. multiply both sides by 3

          3(x+5)/3 =4 x 3

2. Simplify

   x + 5=12

3. Subtract 5 from both sides

   x+5-5=12-5

4. Simplify

  7

Emelyn is comparing the rates of two different gardening companies for her camp site. The table below shows the rates for Log Edge Landscaping. Log Edge Landscaping Hours Worked 1.5 3 3.5 4.5 Total Cost $26 $44 $50 $62 The equation below represents the rates for Gatewood Gardening Services, where x represents the hours worked and y represents the total cost, in dollars. Compare the rates of both companies, and graph the relationship that represents the cost for the company with a greater rate of change.

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

Edge Landscaping:

[tex]\begin{array}{cc}{Hours} & {Total} & {1.5} & {\$26} & {3} & {\$44} & {3.5} & {\$50} & {4.5} & {\$62} \ \end{array}[/tex]

The rates (m) of the above table is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the table, we have the following points

[tex](x_1,y_1) = (1.5,26)[/tex]

[tex](x_1,y_1) = (4.5,62)[/tex]

So, the rate is:

[tex]m = \frac{62 - 26}{4.5 - 1.5}[/tex]

[tex]m = \frac{36}{3.0}[/tex]

[tex]m = 12.0[/tex]

This means that the rate of edge landscaping is $12.0 per hour

The equation for Gatewood is not given. Hence, the rate cannot be calculated. However, the general procedure of calculating rates from a linear equation is as follows;

A linear equation is of the form:

[tex]y = mx + b[/tex]

Where:

[tex]m \to slope\ or\ rates[/tex]

In other words, if the equation is:

[tex]y = 20x + 5[/tex]

Then the rate is: 20 ($20/hour)

If the equation is: [tex]y = 10x + 5[/tex]

Then the rate is 10 ($10/hr)

Next, is to compare the rates;

For Edge landscaping, we have:

[tex]m = 12.0[/tex]

For Gatewood, we have:

[tex]m = 10[/tex] ------------ assume the equation is: [tex]y = 10x + 5[/tex]

Compare the rates:

[tex]12 > 10[/tex]

Hence, Edge landscaping has a greater hourly rate

1. 45 is what percent of 82?
2. What percent of 5 is 26?
3. 22% of what number is 84?
Answer This Question In A Row.

Answers

Answer:

45 is 54.9 percent of 82.

26 is 520% of 5.

84 is 22% of 381.8.

Name the property : (-1/2) x [(-3/4) + 4/7] = (-1/2) x (-3/5) + (-1/2) x (4/7) ​

answer fast

Answers

Answer:

this is a DISTRIBUTIVE property

Gabriela makes a profit of $0.80 for every cup of coffee that she sells at her coffee shop. She wanted to make a profit of at least $75 today on coffee. If she sold 90 cups today, which statement is correct? She met her goal, because she made less than $75 on coffee today. She met her goal, because she made more than $75 on coffee today. She missed her goal, because she made less than $75 on coffee today. She missed her goal, because she made more than $75 on coffee today.What is the value of the expression below?

(9.5 minus 3 times 1 and one-half) divided by 0.5
0.5
5
10
19.5

Answers

Answer:

She missed her goal, because she made less than $75 on coffee today.

10

Step-by-step explanation:

Target profit = $75

Profit per cup = $0.80

Number of cups sold = 90

Profit made today = Profit per cup * Number of cups sold

= $0.80 * 90

= $72

She missed her goal, because she made less than $75 on coffee today.

2. (9.5 minus 3 times 1 and one-half) divided by 0.5

(9.5 - 3 * 1 1/2) ÷ 0.5

= 9.5 - 3 * 3/2 ÷ 0.5

= 9.5 - 9/2 ÷ 0.5

= (9.5 - 4.5) ÷ 0.5

= 5 ÷ 0.5

= 10

Which of the following points lies on the graph of the function y = 3 Superscript x?
a. (1, 0)
c. (3, 1)
b. (2, 9)
d. (0, 3)



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer:

(2,9)

Step-by-step explanation:

I am assuming that you mean: [tex]y= 3^x[/tex]

I have graphed the function given along the points given. When they are graphed, only the point (2,9) lie on the line.

This means that Option B is the correct answer.

See graph below.

Hope this helps.

I NEED HELP PLZZ.... WHATS 9+10? ill give brainliest

Answers

Answer:

WHAT IT'S 19??? HELP HAHAHAHAHA

Step-by-step explanation:

deez  njuts

Answer:

19

Step-by-step explanation:

because its 19

Please help!!!! Anyone!!

Answers

9514 1404 393

Answer:

  g(x) = |x -7|

Step-by-step explanation:

The form given for your answer has parameters 'a', 'h', and 'k'. The parameter 'a' is the vertical scale factor. Since g(x) is a translation only, that factor is 1. The parameters (h, k) identify the translation (right, up). The translation is 7 units right and 0 units up, so (h, k) = (7, 0).

Filling in these values of the parameters, your g(x) is ...

  g(x) = |x -7|

please help step by step, please

Answers

9514 1404 393

Answer:

title: 300%payday: 650%check cashing: 214%

Step-by-step explanation:

The formula for simple interest is ...

  I = Prt

where P is the principal amount loaned, r is the annual rate, and t is the time in years. Solving for interest rate, we get ...

  r = I/(Pt)

We assume 12 months or 52 weeks in a year.

__

Car title loan

  r = 125/(500×1/12) = 3 × 100% = 300%

The APR is 300%.

__

Payday loan

  r = 125/(500×2/52) = 6.5 × 100% = 650%

The APR is 650%.

__

Check cashing

  r = 19.66/(478.41×1/52) ≈ 2.1369 × 100% ≈ 214%

The APR is about 214%.

If RT is 10 centimeters long, what is ST?

Answers

Answer:

Answer: a

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

First, find x

RT = 2x + 3x

10 = 2x+3x

10 = 5x

10/5 = 2

Now place 2 in place of x in the line ST

ST = 3x

ST = 3 * 2

ST = 6

Solve x2+y3 = 1 for x.

Answers

Answer:

x = 3 + 2y

Step-by-step explanation:

x - 2y = 3 ( Isolate x on the left side by adding 2y to both sides )

x = 3 + 2y

Step-by-step explanation:

Step 1: Add -y^3 to both sides.

y3+x2+−y3=1+−y3

x2=−y3+1

Step 2: Take square root.

x=√−y3+1 or x=−√−y3+1

Answer:

x=√−y3+1  or  x=−√−y3+1

(I think this is right) (tell me if im right plz and thx)

Solve the following question algebraically please

Answers

Answer:

c. x = ± 7

Step-by-step explanation:

2x^2 = 98

x^2 = 98 / 2

x^2 = 49

x^2 = ± 7

Answer:

c

Step-by-step explanation:

x2= 98/2

=49

x2=49

x= +_7

Ariana invested $400 in an account paying an interest rate of 3.8% compounded
monthly. Assuming no deposits or withdrawals are made, how much money, to the
nearest ten dollars, would be in the account after 11 years?

Answers

$54970

11 years = 132 months so the balance will compound 132 times.
Adding 3.8% is the same as multiplying by 1.038
400 x 1.038^132 = 54968.09

Of course the 3.8% interest per month is an effective rate of 56.4% per annum
Ariana should have invested a lot more at this amazing rate of interest.

A more reasonable question would have said the annual rate of 3.8% was compounding monthly
3.8% pa = 0.31666...% per month
400 x 1.0031667^132 = $607.17
Depending on the level of your course this answer makes more sense

Which equation can be used to solve for c?

Answers

Please provide more information on this question.

Find the dicontinuities of the function.
f(x) =
x2 + 12x + 27
x2 + 4x + 3
.
There is a removable discontinuity at
(
,
).

Answers

Answer:

Step-by-step explanation:

I'm assuming you meant to type in

[tex]f(x)=\frac{x^2+12x+27}{x^2+4x+3}[/tex] because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to

[tex]f(x)=\frac{(x+3)(x+9)}{(x+1)(x+3)}[/tex] and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.

The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!

The figure is made up of 2 rectangles and 2 right triangles. What is the area of the figure? 132 units2 156 units2 168 units2 216 units2

Answers

132 units2

Just find the area of each shape:
Big triangle- 1/2 x 8 x 9 = 36 units2
Small triangle- 1/2 x 4 x 6 = 12 units2
Big rectangle: 15 x 4 = 60 units2
Small rectangle: 6 x 4 = 24 units2

Add them all up together:
36 + 12 + 60 + 24 = 132 units2

Trust me this is the answer.
COM.MENT ME IF U HAVE ANY QUESTIONS
(Pls say if im right)

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is y=2x an inverse variation

Answers

Answer:

ha ha ha... yesno

Step-by-step wrong explanation:

becoause it is the dilemma of the miniyamma

y=2x is a direct variation. For example, doubling the value of x will double the value of y.

Therefore, it is not an inverse variation.

Nelda drove 315 kilometers and used 35 liters of gasoline. Her car averaged how many kilometers per liter of gas?​

Answers

Going 315 km uses up 35 liters of gasoline

On average, 1 liter of gasoline can travel the number of kilometers:

315 : 35 = 9 liters of gasoline

The population of a town is 1000. This is 125% of the population four years
ago. What was the population four years ago?

NO LINK

Answers

Answer:

800

Step-by-step explanation:

I think it is 1000/1.25 0r 800

Answer:

800

Step-by-step explanation:

if f(x) =g(x) + 10 and g(x) = 3(x) - 18

Answers

Step-by-step explanation:

This is called a nested function. Remember, math is a language.

We define a function where x is whatever we want it to be, f(x) = g(x) +10

but we have yet another function inside and itvs defined as g(x) = 3x - 18

if we were to write it out, it woukd be

f(x) = (3x - 18) + 10

Solve 3|x - 61 = 12.

Answers

Last option
-2 is ur answer

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
6
4
B
х
.
O x-4
O x-2

Answers

Answer:

Step-by-step explanation:

x+2

A factor of the polynomial function f(x) graphed on the coordinate plane below is,

⇒ x + 2

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The polynomial function f(x) graphed on the coordinate plane below.

Now, We have;

The vertex of the function is,

⇒ x = - 2

⇒ x + 2

Thus, A factor of the polynomial function f(x) graphed on the coordinate plane below is,

⇒ x + 2

Learn more about the function visit:

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