Caleb solved this equation and recorded his work. 7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6 1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6 2. 15.6x − 16.4 = −2.3x + 35.4 3. 17.9x − 16.4 = 35.4 4. 17.9x = 51.8 5. X ≈ 2.89 When Caleb verified his solution, it didn't work. What mistake did he make? In step 1, the distributive property was not used properly on the right side of the equation. In step 2, the like terms were not combined properly on the right side of the equation. In step 3, the addition property of equality was not used properly to isolate the variable term. In step 5, the division property of equality was not used properly to solve for x.

Answer:

Step-by-step explanation:

Answer:

≈ 20.11 m²

Step-by-step explanation:

Area of lawn covered by one full rotation:

Area covered by 20 rotations of the roller:

Answer:

Graph D.

Step-by-step explanation:

Hey there!

A coefficient is the number being multiplied by the variable,

Example: 5x - 5 is a coefficient

Graph d has a negative slope meaning the slope would be,

-1, -2, -3, -4, -5, ect.

So graph D is correct.

Hope this helps :)

Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

  -32 -2 ?? -2

  -34 < -2 . . . . . . not greater than

The question is incomplete, the complete question is as follows:

What do Steven Hawking and Thomas Edison have in common

- Both men made mathematics discoveries

- Both men made discoveries that were well-received

- both men created technological inventions

- Both men used observations in their field of study

Answer:

- Both men made discoveries that were well-received

Step-by-step explanation:

Stephen Hawking and Thomas Edison were two great physicist or scientists, whose discoveries were well-recieved by all over the world.

Stephen Hawking gave theories in cosmology such as black holes that includes the second law, that states that black hole will never reduce its shape.

Thomas Edison was one of the great inventors in the history in different feilds such as mass communication, electric power generation, motion pictures, and sound recording. some of the inventions include Automatic Telegraph and tin foil phonograph.

They both have given scientific research and logics for their discoveries and so people accepted them.

Hence, the correct answer is " Both men made discoveries that were well-received ".

The answer is:

Answer:

Step-by-step explanation:

a. 4/7 + 3/8 = 32/56 + 21/56 = 53/56

b. 2/5 + 5/8 = 16/40 + 25/40 = 41/40 = 1  1/40

c.  3/8 + 2/10 = 15/40 + 8/40 = 23/40

d. 4/5 + 2/6 = 24/30 + 10/30 = 34/30 = 1 4/30 = 1 2/15

e. 5/6 + 2/9 = 15/18 + 4/18 = 19/18= 1 1/18

f. 2/15 + 5/12 = 8/60 + 25/60 = 33/60 = 11/20

Answer:

[tex]0[/tex]

Step-by-step explanation:

[tex] \frac{8 - m}{n + p {}^{2} } = \frac{8 - 8}{2 + 49} = \frac{0}{51} = 0[/tex]

Answer:

the value of the printer is going down over the years because it is getting older. all you need to do for this is label the x and y axis with the nbers on the graph and then fill it in

has ur teacher gone over how to fill in graphs yet?

Answer:

what is your fav movie or show on netfix

Step-by-step explanation:

Answer:

[tex] \boxed{\sf Time \ taken \ (t) = 100 \ s} [/tex]

Given:

Distance (d) = 48 km = 4800 m/s

Speed (s) = 48 m/s

To Find:

Time taken (t)

Step-by-step explanation:

Formula:

[tex]\boxed{ \bold{ Speed \ (s) = \frac{Distance \ (d)}{Time \ (t)}}}[/tex]

Substituting value of s & d in the equation:

[tex] \sf \implies 48 = \frac{4800}{t} \\ \\ \sf \implies t = \frac{4800}{48} \\ \\ \sf \implies t = 100 \: s[/tex]

[tex] \therefore[/tex]

Time taken (t) = 100 s

Answer:

The Elegant Home Architects charges are less than Rock the House Digital Designs charges for hours worked more than 2.

If the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Step-by-step explanation:

Let ℎ represent the number of hours for which the Johnson family hires the design firm.

Suppose the  Johnson family hires the design firm for ten hours so h= 10

Then the charges by the Rock the House Digital Designs will be

$ 500 + 50(10)= $ 500+ $500= $1000

And the charges for the services by Elegant Home Architects will be

$75.00(10) = $ 750

Therefore the Elegant Home Architects charges are less than Rock the House Digital Designs charges.

But if the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Rock the House Digital Designs

For 2 hours

$ 500 + 50(2)= $300

For 1 Hour

$500 + 50 (1)= $ 550

Elegant Home Architects

For 2 hours

$75.00(2) = $ 300

For 1 Hour

$75.00(1) = $ 75

Answer:

r = 2a + k

Step-by-step explanation:

Hope this helps :D

Answer: 1/8 of 48 is 6.

Step-by-step explanation: working this on a calculator helps as well! I hope that makes everything make sense

Answer:

6

Step-by-step explanation:

of means multiplication

Answer:

70 pints per day

Step-by-step explanation:

1 cubic meter is 2113.38 pints

on average, there is 30 days in a month

2113.38 divided by 30 is 70.44600

70.44600 is about 70

Answer:

91590

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, I will compute twice the sum so I need to compute,

[tex]\begin{aligned}1&+2&+...+&(n-1)&+n\\\\n&+(n-1)&+...+&2&+1\\\\-&-----&---&---&---\\\\(n+1)&+(n+1)&+...+&(n+1)&+(n+1)\end{aligned}[/tex]

1+n = n+1

2 + n-1=n+1

...

n-1+2=n+1

n+1=n+1

So, this is n times n+1 so it is n*(n+1)

[tex]2(1+2+3...+n)=n(n+1)\\\\1+2+3...+n=\dfrac{n(n+1)}{2}[/tex]

Answer:

4 gallons of gasoline the car has left after it has traveled 330 miles.

Step-by-step explanation:

We are given with the following data of Distance Traveled and Gas Left in Tank below;

   Distance Traveled (in miles)       Amount of Gas Left in Tank (in gallons)

                 0                                                            15

                90                                                           12

               180                                                            9

               270                                                           6

               330                                                           ?

As we can see from the table that for every 90 miles of distance traveled, there has been a reduction of 3 gallons of gas which is left in the tank, i.e;

From 90 to 180 - Gas reduced from 12 to 9

This means that in 1 gallon of gas, the distance traveled is =  [tex]\frac{90}{3}[/tex] = 30 miles

So, from distance 270 to 300, the amount of Gas Left in Tank = 6 - 1 = 5 gallons

From distance 300 to 330 miles, the amount of Gas Left in Tank = 5 - 1 = 4 gallons

Hence, 4 gallons of gasoline is left after the car has traveled 330 miles.

Answer:

1 4 3 4 4 = ilyvm

1 4 3 3 = ilyt

Step-by-step explanation:

Question:

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26.

What is the solution set of this problem?

Answer:

[tex]x \leq -21[/tex]

Step-by-step explanation:

Given

Represent the number with x

So:

[tex]5 * (x + 27) \geq 6 * (x + 26)[/tex]

Required

Determine the solution set

[tex]5 * (x + 27) \geq 6 * (x + 26)[/tex]

Open Both Brackets

[tex]5 * x + 5 * 27 \geq 6 *x + 6 * 26[/tex]

[tex]5x + 135 \geq 6x + 156[/tex]

Collect Like Terms

[tex]5x - 6x \geq 156-135[/tex]

[tex]- x \geq 21[/tex]

Multiply both sides by -1

[tex]x \leq -21[/tex]

Hence, the solution set is [tex]x \leq -21[/tex]

Answer:

[tex]x\leq -21[/tex]

Step-by-step explanation:

Answer:

I believe it would be "mean".

Step-by-step explanation:

Mean is an average of a set of numbers.

Answer:

21

Step-by-step explanation:

the reason it is 21 is because u have 20 then u add 1 so it is 21 20+1=21

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

John already has 20 apples. If John gets 1 more apple, he would have 21 apples in total.

The word gets means addition. 20 plus 1 equals 21.

John has 21 apples after he gets another apple.

Ok technically I would have 0 apples since I didn't receive any only John did.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer: Rational

Step-by-step explanation: 12 is a rational number because it can be expressed as the quotient of two integers: 12÷ 1

Answer:

3

Step-by-step explanation:

[tex]2x^{2} = 18\\ => x^{2} = \frac{18}{2} =9\\ => x = \sqrt{9} = 3[/tex]

Hope u'll like it.....

Step-by-step explanation:

2x²=18

x²=18/2

x²=9

squaring both sides

and we get

x=3

Answer:

x = 4/3

Step-by-step explanation:

Answer:

work is pictured and shown

Answer:

19.25

Step-by-step explanation:

if it sells per pound you would just multiply by 7 because thats what your looking for

have a great day :)

Answer:

$19.25

Step-by-step explanation:

One lb of granola sells for $2.75. You are trying to find how much 7 pound costs. Multiply 2.75 with 7:

($2.75/1 lb of granola) x (7/7) = (2.75 * 7/7 lb of granola)

Simplify:

2.75 * 7 = 19.25

7 lbs of granola costs $19.25

~

Answer:

s^-13

Step-by-step explanation:

you subtract when it is division

s^-10 / s^3

-10 - 3 = -13

s^-13

Answer:

s^0.03333333333

Step-by-step explanation:

s^1/10 divided by s^3

Answer:

West

10 cm

The first one

Answer:

About $0.2708 per unit ' each can '.

Answer:

$.27

Step-by-step explanation:

$3.25 / 12 = 27

Answer:

(11/3, 4)

Step-by-step explanation:

To calculate the coordinates of the point that partitions the line segment in the given ratio, we shall be using the internal division formula.

Mathematically, that is ;

= {(mx2 + nx1/(m+n), (my2 + ny1)/(m + n)}

m and n represents the ratios 1:2

(x1, y1) represents the coordinates of A

(x2,y2) represents the coordinates of B

From the question, let’s list out the individual values;

m = 2

n = 1

x1 = 3

x2 = 4

y1 = 6

y2 = 3

Substituting these values in the equation, we have;

(2(4) + 1(3)/(1+2) , (2(3) + 1(6)/(1 + 2))

= (8 + 3)/3 , (6 + 6)/3)

= (11/3, 12/3)

= (11/3 , 4)