Consider the equation 2x+1=16
a. Does the equation have a solution in the set of integers? ____
b. Does the equation have a solution in the set of rational numbers? ____

Answers

Answer 1

Step-by-step explanation:

2x + 1 = 16

2x = 15 (subtract 1 on both sides)

x = 7.5 (divide 2 om both sides)

Since 7.5 is not an integer, (a) is No.

However 7.5 is rational, therefore (b) is Yes.

Answer 2

Answer:

[tex]2x + 1 = 16 \\ 2x = 15 \\ x =\frac{15}{2} \\ \boxed{x = 7.5 }[/tex]

a. Does the equation have a solution in the set of integers? ____

→As 7.5 is not a integer, the right answer is No.

b. Does the equation have a solution in the set of rational numbers? ____

→7.5 is a rational number, the right answer is Yes.


Related Questions

Can anybody answer this??

Answers

Answer:

(x, y) represent coordinates, m represents slope, and b represents the y-intercept

(7x2 – 4) - (3x2 – 5x + 1)

Answers

Step-by-step explanation:

[tex]( {7x}^{2} - 4) - ( {3x}^{2} - 5x + 1)[/tex]

[tex] {7x}^{2} - 4 - {x}^{2} + 5x - 1[/tex]

[tex] {4x}^{2} + 5x - 5[/tex]

Which statement describes a unit rate? Group of answer choices Sara is reading 97 words in 1 minute. Sara ate 3 crackers and 1 apple. Sara ate 1 cookie. Sara is driving 16 miles.

Answers

Answer:

97 words in 1 minute

Step-by-step explanation:

A unit measure is so many somethings done usually per unit time. Examples

1 orange in 1 minute.10 tomatoes per tomato plant50 miles in one hour10 cookies per week

3 crackers and 1 apple is not. For ever apple, she ate 3 crackers would be

1 cookie is not. It is not per anything.

Driving 16 miles is not. Again, it is not per anything.

The answer is 97 words in 1 minute.

if the length of AC equals 84, what is the length of the mid-segment DE?​

Answers

Answer:

dang I forgot how to solve this but it has something to do with 360

Step-by-step explanation:

The mid-segment theorem says that the mid-segment is half the length of the third leg, so the length of DE is 84/2=42.

Solve using the quadratic equation. Round your solution to the nearest hundredth of 2x^2-3x+4

Answers

Answer:

2x2+3x−4=0 is a quadratic equation in the form ax2+bx+c, where a = 2, b = 3, and c = − 4.

Step-by-step explanation:

Hope this helps

PLEASE ANSWER I NEED HELP


Kayla gets paid $15 to rake the lawn. Kayla gets paid 3 times as
much to rake the lawn as she does to mow the lawn. How much
does Kayla get paid to mow the lawn?

Answers

Answer:

$5

Step-by-step explanation:

The opposite of multiplication is division.

$15/Raking = 3 times more pay than mowing the lawn.

Divide $15/Raking by 3 and you'll get the pay for mowing the lawn.

15/3 = 5

Answer:

5

Step-by-step explanation:

Jude is 1.44 meters tall. Elijah is 1 3/10 meters tall. What is the combined height of Jude and Elijah? Select one:
O2.75 meters
O 2.57 meters
O2.14 meters
O2.74 meters​

Answers

Answer:

D

Step-by-step explanation:

1.44 + 1.30 = 2.74

Answer: 2.74 meters

Step-by-step explanation:

1 3/10 meters can be converted into 1.30 meters

1.30+1.44=2.74

Please help me I just can’t figure this out. I’ll mark you brainiest if you know it but ONLY if you know it

Answers

Answer:

Step-by-step explanation:

All square angles are 90° exactly 90° so we can use that to your advantage. since "7x + 3" is one of the square's angles, that means 7x + 3 must equal 90°. (7x + 3)° = 90°.

7x + 3 = 90

7x = 90 - 3

7x = 87

7x/7 = 87/7

x = 87/7

Write in slope-intercept form an equation of the line that passes through the points (−4, 2) and (6,−3).

Answers

Answer:

        y = -0.5x

Step-by-step explanation:

[tex]\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

(−4, 2)    ⇒     x₁ = −4,  y₁ = 2

(6,−3)     ⇒     x₂ = 6,  y₂ = −3

So the slope:

[tex]\bold{m=\dfrac{-3-2}{6+4}=\dfrac{-5}{10}=-0.5}[/tex]

The point-slope form of the equation of the line passing through point (x₀,y₀) and with slope m is:  y - y₀ = m(x - x₀)

m = -0.5

(−4, 2)    ⇒     x₀ = −4,  y₀ = 2

Therefore:

               y - 2 = -0.5(x - (-4))

               y - 2 = -0.5x - 2               {add 2 to both sides}

               y = -0.5x          ←  the slope-intercept form of the equation (b=0)

-1/5x≤8

what is the aswer

Answers

Hey there!

“-1/5x ≤ 8”

MULTIPLY both sides by -5

-1/5x × -5 ≤ 8 × 5

CANCEL out: -1/5 × -5 because that gives you 1

KEEP: 8 × 5 because that helps us solve for your given equation

NEW EQUATION: x ≥ 8 × 5

8 × 5 = 40

Answer: x ≥ 40

It is a CLOSED circle SHADED to the RIGHT

The answer would be

Hope this helps

3x²+17x²+21x-9+ (x+3)

Answers

Answer:

22x^2 + 22x - 6

Step-by-step explanation:

Answer:

It is 22x^2 + 22x - 6

Step-by-step explanation:

Hope this helped have an amazing day/month/year!

A $30 shirt is marked, "Get 25% off." What is the sale price of the shirt?

Answers

Answer : $22.50
Explanation: .30•25=7.5 30-7.5=22.5

Answer:

$22.50

Step-by-step explanation:

First, we find how much we need to take off so our equation is:

30 x 0.25 = 7.5

So, we take 7.5 off of 30 which is:

30 - 7.5 = 22.5

So, the shirt is selling for $22.50

Hope this helps:)

5. The Clearance Center sold a dress for $32
The original cost of the dress was $40.
What was the percent of decrease ? ?

Answers

8%. shsjsjdjnddhdhjdnndndnsnsnsns

The speed of light is about 300,000 kilometers per second. The Sun is about 93 million miles from Earth. How many minutes does it take for the sunlight to reach Earth? Round to the nearest tenth if necessary.

Answers

Answer: 8.3 minutes

Step-by-step explanation:

1 mile is to 1.60934km so 93 million miles is:

= 93 * 1.609

= ‭149,637,000‬ km

Travelling at 300,000 km per second, the number of seconds it takes is:

= ‭149,637,000‬/300,000

= ‭498.79‬ secs

In minutes this is:

= ‭498.79‬/60

= 8.3 minutes

From the expressions below, select the one that results in a negative difference.

Answers

uhm..

what expressions?

help me plz i’ll give u extra points

Answers

i think 16 is the slope t=16x+96
16 is the slope i’m pretty sure

pls help, urgent!!!!! Will try to give brainliest

Answers

Answer:

1: 86 inches is the width

2: -20

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

-2 x 4 = -8

-2 x -2 = 4

-8 - (-4) = -4

(keep change flip)

-4 - -4(3) 4x4x4= -64

-4 - (-64)

60

There are 8 green marbles, 6 blue marbles, and 6 yellow marbles. What is the probability that you pick a marble out of the bag that is yellow, then you put the marble back in the bag, choose a second marble and it is green?

Answers

Answer3/10

Step-by-step explanation:

Answer:

green

Step-by-step explanation:

there's mostly green marbles

10-2b^2
when b=3
pls help me

Answers

Answer:

= -8

Step-by-step explanation:

plug in 3 for b

10 - 2 (3)^2

10 -2 (9)

10 - 18

-8

Answer: -8

Step-by-step explanation: just substitute the 3 in for b

a piece of wood is cut in the ratio 3:7 if the shorter piece is 45 cm long,how long is the whole piece of wood?

Answers

Answer:

150 cm

Step-by-step explanation:

45/3  * 10 = 15 * 10 =150

check: 150 * 0.3 = 45

           150 * 0.7 = 105

105+45 = 150

Which expression will have the same value as 3(4x + 9 ) - 6x for all values of x?

Answers

an equal expression would be: 6x+27

All I did was just distribute and then subtract

5/11 :Terminate or repeat
Terminate or repeat

7/8 :Terminate or repeat

Answers

Answer:

5/11=repeat

7/8=terminate

Sorry the quality is bad- I’ll mark brainlist

Answers

Answer: A and C

Step-by-step explanation:

Melissa is a software saleswoman. Her base salary is $2100, and she makes an additional $80 for every copy of History is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this
equation to find her total pay if she sells 27 coples of History is Fun.

Answers

P = 2100 + 80(N)
P = 2100 + (80 x 27)
P = 2100 + 2160
P = 4260

Write the number 5267 correct to
the nearest hundred.

Answers

Answer:

5300.

If you're rounding to the nearest hundred you look at the tens place. If its 5 or over you go up. So in this case we'll raise the 2 to a 5 because 6 is above 5.

Harper knows he is 50 yards from school. The map on his phone shows that the school is 3/4 inch from his current location. How far is Harper from home, if the map shows the distance as 3 inches? Enter your answer in the box.

Answers

Answer:

Harper is 200 yards away from her home if the map shows 3 inches

Step-by-step explanation:

50 yards = 3/4 inch

3 inches = 3/1

3/1 x 4/4 = 12/4

12/4 = 3 inches

50 x 4 = 200

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

3. An annual pass to the Super Fun theme
park is $400 and includes parking. The
daily pass is $80 but requires a $20 daily
parking pass. How many times of buying
the daily pass and parking would it take to
equal the annual pass?

Answers

Answer:

i think it would be 25

Step-by-step explanation:

cause, 400÷ 80+ 20 is 25

but i might be wrong

How does the graph of the function f(x) = 2x4− 3 differ from the graph of its parent function? Select all the transformations.
◻A.The graphs are the same.
◻B.Subtracting 3 translates the graph down 3 units.
◻C.The leading coefficient, 2, stretches the graph vertically.
◻D.Subtracting 3 translates the graph up 3 units.
◻E.Subtracting 3 translates the graph right 3 units.

Answers

Answer:

B and C are the correct options

Step-by-step explanation:

The parent function here will be ;

f(x) = x^4

Multiplying x^4 by 2 means that we are having a vertical stretching

What this means is that the leading coefficient 2 stretches the graph vertically by 2 units

Subtracting -3 means that we are translating the graph down by a value of 3 units

So the correct options are;

B and C

In pedros town 42% of the houses have both internet service and a home phone. If 82% of all the houses in his town have internet service, what is the probability that a house has a home phone if it has internet service?

Answers

Answer: 0.51

Step-by-step explanation:

We know that:

For a random selection, we have a probability of 0.42 where the house has both services and a probability of 0.82 that the house has only internet service.

Let's suppose that the percentage of houses the houses with internet service (the 82% of the total) that also have a home phone is X

Then we must have that, (X/100%) times the 0.82, must be equal to 0.42

(X/100%)*0.82 = 0.42

X = (0.42/0.82)*100% = 51%

This means that 51% of the houses with internet service, also have a home phone.

Then the probability that a house has a home phone given that it has internet service, is equal to:

51%/100% = 0.51

The probability is 0.51

a successful music app tracked the number of downloads each day for 4 artists, represented by lines l, j, m and d over the course of a month. which lines represent an artist whose download remained consistent

Answers

Answer:

l

Step-by-step explanation:

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