Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6

Answers

Answer 1

Answer:

[tex]\{a[/tex][tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex][tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]


Related Questions

Which two shapes make up the digital camera below?

Answers

Rectangular prism and cylinder

Rectangular prism and cylinder make up a camera.

What is rectangular prism and cylinder?

A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.

A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.

Hence, Rectangular prism and cylinder make up a camera.

To learn more about rectangular prisms and cylinders refer to:

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PLEASE HELP AND BE CORRECT

Answers

(b⁷/4⁵)⁻³

= (4⁵/b⁷)³

= 4¹⁵/b²¹

Therefore answer is option b

Must click thanks and mark brainliest

how many pieces each 31/6 metres long can be cut fram a cloth 155/2 metres long ?​

Answers

Answer:

?

Step-by-step explanation

my 4th person to ask a question

Please I need the answer according to steps

Answers

Answer:

Factorise out x and y terms:

[tex]{ \tt{ = \frac{ {x}^{2} {y}^{4} (5x - 3y)}{45} }} \\ [/tex]

This graph represents which of these expressions?

Answers

Answer:

x > 43

Step-by-step explanation:

Open circle at 43, which means it is not equal to 43

Line goes to the right, which means x is greater than

x > 43

Answer:

B

Step-by-step explanation:

I HAVE ANOTHER ONE MY MOM THINKS I AM SMART TO GET THIS BUT I CANT HEEEELLLLLLPPPP PLZ I WILL THANK EVERYONE WITH THE RIGHT ANSWER HELLLLLPPPPPP FAST

Answers

Answer:

-4 + -6 = 10

Step-by-step explanation:

The first point is 4 units below zero, so -4

The next point shows that it is 10 points below zero, so -10

-4 + blank = -10

-10 - (-4) = -10 + 4 = -6

blank = -6

Check:

-4 + (-6) = -10

-4 - 6 = -10

correct

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

For spring break you and some friends plan a road trip to a sunny destination that is 2215 miles away. If you drive a car that gets 38 miles per gallon and gas costs $3.119/gal, about how much will it cost to get to your destination

Answers

9514 1404 393

Answer:

  $181.81

Step-by-step explanation:

  (2215 mi)/(38 mi/gal)×($3.119/gal) = $181.8048

We round this up so that we have enough gas to get there. We don't want to have to walk the last 309 feet to the destination.

  It will cost $181.81 to get to the destination.

Simplify the following expression

Answers

Answer:

[tex]\frac{98p^{6}}{q}[/tex]

Step-by-step explanation:

Distribute the exponents

[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]

[tex](\frac{q}{98p^{6}} )^{-1}[/tex]

Distribute the -1

[tex]\frac{98p^{6}}{q}[/tex]

Jack’s backpack weighs 15 pounds. Fernando’s backpack weighs less than Jack’s. Which graph shows how much Fernando’s backpack can weigh?

Answers

Answer:

A

Step-by-step explanation:

c and d out of the question

b has its circle filled in meaning it could be 15lbs, which it's not

A correct answer by default

Answer:b

Step-by-step explanation: it has a filled in diamond which mean it's that...

please can anyone help me with this question what is the probability of the spinner landing on an even number.​

Answers

1/2 chance it will land on an even number


Explanation there is 4 even numbers and 4 odd numbers meaning it’s a 50/50 chance

Describe domain and range of the graph.

Answers

Domain: the set of possible values of the independent variable or variables of a function.
Range of graph: The range is the set of possible output values, which are shown on the y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

find the sum of all multiples of 9 between 0 and 200​

Answers

Answer:

I thick the answer is 2277

URGENT! WILL GIVE BRAINLIEST (PICTURE INCLUDED)

Answers

9514 1404 393

Answer:

  x > -1 and x ≠ 3

Step-by-step explanation:

The function value will be positive when there are an even number of negative factors. The factors change sign at x = -1, are zero at x = 3. The expression is positive for ...

  x > -1 and x ≠ 3

1106.666667 to the nearest whole number

Answers

Answer:

1106.666667 to the nearest whole number

1107

Answer:

1106.666667 rounds to 1107

Step-by-step explanation:

We look at the whole number, 6

Then look at the tenths place .6

Since 6 is greater than or equal to 5, we round the whole number up one place to 7

1106.666667 rounds to 1107

What is the volume of the cone

Answers

Answer:

The volume of this cone would be approximately equal to 2787.64 [tex]yd.^2[/tex].

Step-by-step explanation:

The formula used to calculate the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex] where [tex]r[/tex] represents the radius of the circle at the base of the cone, and [tex]h[/tex] represents the vertical height of the cone. In this case, [tex]r[/tex] equals the diameter of the base divided by two, which is [tex]\frac{22}{2}[/tex] or 11 yards; and [tex]h[/tex] is equivalent to 22 yards. Insert these values into the formula and you'll get that the volume of this cone is equal to [tex]11^2*\pi*\frac{22}{3} = 121\pi * \frac{22}{3}[/tex] ≈ 2787.64 [tex]yd.^2[/tex], so that is the correct answer.

How to make my answer for 0.70 a fraction

Answers

Answer:

0.70 = 7/10

Step-by-step explanation:

Answer:

70/100 or 7/10 (Simplified)

Step-by-step explanation:

0.70 is basically .70 of 1. You can wrote this as a fraction, 70/100. If you divide 70 by 100, it gives you .70.

If you want to simplify it, it becomes 7/10, and if you divide 7 by 10, it also gives you 0.70.

Depends if you want your fraction simplified or not.

have a great day.

Find the length of X

Answers

Answer:

[tex] x = 8\sqrt{2} [/tex]

Step-by-step explanation:

Leg = x

Hypotenuse = 16

[tex] x\sqrt{2} = 16 [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]

[tex] x = 8\sqrt{2} [/tex]

Can someone help me solve this problem ?

Answers

Answer:

B

Step-by-step explanation:

Since x= 3/4

To take the fraction on left hand side, inverse 4/3

Take π as denominator

Then cube root the entire equation on the left hand side.

Answer:

Step-by-step explanation:

what is the constant proportionality in the equation y=2.5x

Answers

Answer:

Step-by-step explanation:

According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17

Answers

Answer:

15/8

Step-by-step explanation:

tan(62)=P/B

tan(62)=15/8

Pls if anyone knows the answer with work included/steps that will be greatly appreciated :) for 6 just want to know is it w y x or z

Answers

Answer:

Step-by-step explanation:

Let's begin calculating the MPH for Fran.: Joanne's MPH is 250 / 2.5 = 100 MPH.

Now I'm going to subtract the 100 MPH by Fran. going 10 MPH less: 100 - 10 = 90.

I can't see the bottom part of the graph, so based on the MPH, it might be X, if you could put a better picture it would be better!

Which of the symbols correctly relates the two numbers below? Check all that
apply.
45 ? 45
A. >
B. 2
DC.s
D. =
DEZ
OF. <

Answers

Answer:

D. =

Step-by-step explanation:

Because 45 and 45 are the same number so they equal the same value

Answer:

Step-by-step explanation:

Answer  B C D

Use the drop-down menu to create true statements,
If the graph of an inverse passes the
, you know that the inverse is
a function,
The composition of a function and its inverse is
always
DONE
DOWE
The range values of an inverse are the
values of the original function,
The graph of an inverse is the reflection of the
graph of the function over the line
DONE
DOWE

Answers

Answer:

A) Vertical test

B) y=x

C) x

D) domain

If the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

What is Inverse Function?

Inverse functions are functions which can be reversed in to another function.

Then the function is said to be the inverse of the second function.

The test which is used to know whether an inverse is a function or not is Vertical line Test.

So, if the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

Composition of a function and it's inverse is always x.

Let y = f(x) be a function. Then x = f⁻¹ (y)

(f⁻¹of)(x) = f⁻¹ (f(x)) = f⁻¹ (y) = x

The graph of an inverse is the reflection of the graph of the function over the line y = x.

The range values of the inverse function are the domain values of the original function.

Hence the blank terms are found.

Learn more about Inverse of Functions here :

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A 90% confidence interval is (35 45). What is the margin of error?
A. 5
B.4.5
C.9
D.10

Answers

Answer:

option A 5

I hope it's correct

.....

5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?​

Answers

Answer:

5 a) Total = 20.83 hrs = 20 hrs and 50 mins  (1250mins total)

5 b) Total = 96 meters. = 0.096km in 8 hrs.

Step-by-step explanation:

1km = 1000 meters

5 mins = 4 meters

1000/4 = 250 multiplier

250 x 5mins = 1250 minutes

1250/60 = 20hrs + 50 minutes

50 / 60 =  0.83 = 20.83hrs

b)  8 hrs = 8 x 60 = 480 minutes

480/5 = 24 multiplier of 4 meters

24 x 4 = 96 meters

Jean drove 67 miles per hour for a total of 469 miles on a trip. She used the equation below to calculate the time, t, it would take her to complete the trip.



469 = 67t


What is the constant of proportionality in the equation?
A.
7
B.
67
C.
469
D.
t

Answers

9514 1404 393

Answer:

  B.  67

Step-by-step explanation:

Miles are proportional to time at some speed. The constant of proportionality is the speed, 67 (miles per hour).

Can someone do #4 and #5

Answers

Answer:

First, find two points on the graph:

(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]

16 + (-3) = 16 - 3 = 13

Trish's punch recipe calls for 8 liters of lemon-lime soda and 4 liters of cranberry juice, Jenny's punch recipe requires 7
liters of lemon-lime soda and 6 liters of cranberry juice. Which recipe has a higher ratio of lemon-lime soda to cranberry
juice?
( A, neither, the ratios are equivalent
B. Trish's recipe
c. Jenny's recipe
D. not enough information

Answers

B because it’s shows that 8-4=4 and 7-6=1 so there’s your answer

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
4L TO 7.2 L

Answers

9514 1404 393

Answer:

  5/9

Step-by-step explanation:

  [tex]\dfrac{4\text{ L}}{7.2\text{ L}}=\dfrac{40}{72}=\dfrac{5\cdot8}{9\cdot8}=\boxed{\dfrac{5}{9}}[/tex]

A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year

Answers

Answer:

[tex]P(x \le 3) = 0.9920[/tex]

Step-by-step explanation:

Given

[tex]p = 6\%[/tex] --- proportion of drivers that had accident

[tex]n = 14[/tex] -- selected drivers

Required

[tex]P(x \le 3)[/tex]

The question is an illustration of binomial probability, and it is calculated using:

[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]

[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]

[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]

[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]

[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]

So, we have:

[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]

[tex]P(x \le 3) = 0.99202855611[/tex]

[tex]P(x \le 3) = 0.9920[/tex] -- approximated

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