Mathematics College

Which values of x will make the absolute value equation true? |x – 3| = 40
A. {–43, –37}
B. {43, –37}
C. {40, –40}
D. {43, 37}

Answers

Answer 1
Final answer:

The values of x that satisfy the absolute value equation |x – 3| = 40 are 43 and -37. These are derived from solving the two possible scenarios for absolute value equations, resulting in a positive and a negative solution.

Explanation:

To find which values of x will make the absolute value equation |x – 3| = 40 true, we need to consider both the positive and negative scenarios that can result from the absolute value. The absolute value of a number equals the number itself if it is positive or zero, and it equals the negative of the number if it is negative.

So, we set up two equations:

x - 3 = 40 (when x – 3 is non-negative)x - 3 = -40 (when x – 3 is negative)

Solving the first equation for x, we add 3 to both sides:

x = 40 + 3

x = 43

Solving the second equation for x, we add 3 to both sides:

x = -40 + 3

x = -37

Therefore, the values of x that will satisfy the equation are 43 and -37. Option D is the correct answer.

Answer 2

Final answer:

The values of x that make the absolute value equation true are 43 and -37.

Explanation:

To solve the equation |x-3| = 40, we need to consider two cases:

1. x-3 = 40: In this case, we add 3 to both sides to isolate x and get x = 43.

2. -(x-3) = 40: In this case, we distribute the negative sign and add 3 to both sides to isolate x, which gives x = -37.

Therefore, the values of x that make the absolute value equation true are {43, -37}.

Related Questions

Janice has car insurance that she must pay four times a year. If each payment is $156, how much money should she set aside each month to cover her car insurance? $13 $26 $39 $52

Answers

she has to set $52 every month so by the third month she will have exactly 156

[tex]\left[\begin{array}{ccc}A&13&-\\B&26&-\\C&39&-\\D&52&Correct\end{array}\right][/tex]


Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 1515 in. by 99 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.

Answers

Hello,
Please, see the attached files.
Thanks

because his goal is to bike 65 miles over the four days what equation can be used to find the number of miles he should bike on the first day

Answers

His first day
Answer: 16.25

[tex]y = 65 \div 4[/tex]

x+2y=6
2x+4y=12

I need to use substitution to solve, may anybody help?

Answers


[tex]x + 2y = 6[/tex]

[tex]x = - 2y + 6[/tex]
[tex]2( - 2y + 6) + 4y = 12[/tex]
then find y and plug that y value into one of the original equations to find x

Hope this helps!

A trucker traveled an average of 48.6 miles each hour on a 583.2-mile trip. For how many hours did the trucker travel?

Answers

Divide 583.2 by 48.6 to get your answer, 12 hours.

Answer: The trucker traveled for 12 hours.

Step-by-step explanation:

Given : A trucker traveled an average of 48.6 miles each hour on a 583.2-mile trip.

i.e. Total distance =  583.2 miles

Average speed =  48.6 miles per hour

Using Formula , [tex]\text{Total Time}=\dfrac{\text{Total Distance}}{\text{Average speed}}[/tex]

We have

[tex]\text{Total Time}=\dfrac{583.2}{48.6}\\\\=\dfrac{5832}{486}\\\\=12\text{ hours}[/tex]

Hence, the trucker traveled for 12 hours.

you have a piggy bank containing a total of 93 coins in dimes and quarters. If the piggy bank contains $14.85, how many dimes are there in piggy bank

Answers

Let d = number of dimes.
Let q = number of quarters.

The total number of coins is 93, so the first equation is

d + q = 93

The value of 1 dime is $0.10. The value of 1 quarter is $0.25.
d dimes are worth 0.1d, and q quarters are worth 0.25q.
The total value of the coins is $14.85, so that gives us our second equation.

0.1d + 0.25q = 14.85

Now we have a system of two equations in two unknowns.

d + q = 93
0.1d + 0.25q = 14.85

Rewrite the first equation. Then multiply both sides of the second equation by -10, and write it underneath. Then add the equations.

 d +     q =     93
-d - 2.5q = -148.5
------------------------
      -1.5q = -55.5

Divide both sides by -1.5.

q = 37

Now substitute 37 for q in the first original equation and solve for d.

d + q = 93

d + 37 = 93

Subtract 37 from both sides.

d = 56

Answer: There are 56 dimes in the piggy bank.

Help me with this question pleaseeee!!!

Answers

we have that
the measure of angle ∅=7*pi/6
the measure of its reference angle is?
remember that pi=180°
then 
7*pi/6=7*180/6=210°------------> III Quadrant
Part A) its reference angle is 210°-180°=30°
Part B) sin(30°)=-0.5--------> negative because  belongs III quadrant

the answer ............

Answers

f(0) = 2
g(0) = 2

1. f(g(0)) = f(2) = 0

2. h(f(0)) = h(2) = 2² -3 = 1

3. h(g(0) +1) = h(2 +1) = h(3) = 3² -3 = 6

you sure answer for number 9 to calculate how much money mr. and mrs. J make per week there 52 weeks per year the answer I came up with for the first one was $82,796

Answers

Assuming there on the ($40.798) there is a decimal instead of a comma. So that states Mrs. Jay with ($41,998) Plus Mr. Jay with ($40.798) Just simply add these two numbers together and you get the answer of 

How much do they make together? Correct answer equals - (42038.798) is how much money Mr. and Mrs. Jay make together! 

Hope this helps. 
Have a great day! 

Draw three dimes 1 nickel and 2 pennies. Describe how to count on to find the total value of this group of coins

Answers

Total Value: $0.37

The total value of this group of coins can be found by first counting the value of each type of coin, and then adding them all together. The value of a dime is 10 cents, so if there are three dimes, the total value is 30 cents. The value of a nickel is 5 cents, so if there is one nickel, the total value is 5 cents. The value of a penny is 1 cent so if there are two pennies, the total value is 2 cents. After adding 30 + 5 + 2, the total comes to $0.37. 

15+w+(-12)=15-12+w what is the answer

Answers

Hi there!

To solve this problem, we need to simplify.

15 + w - 12 = 15 - 12 + w
3 + w = 3 + w

w = w

So, the answer is undefined, since w is not given.

Hope this helps!

how do you change 87/9 into a mixed number

Answers

Divide 87 by 9 ! You'll get 9, with a remainder of 6/9 or 2/3. So the mixed number is 9 2/3.
Divide 87 by 9 and put remainder in fraction form - 9 6/9 which reduces to 9 2/3

whats (-2,8) and (-22,8) finding the slope from points

Answers

Since y is a constant, the slope is zero.

t=sqrt(2h-40t/g) I'm not sure where to even start on this one.

Answers

[tex]\bf T=\sqrt{\cfrac{2h-40t}{g}}\impliedby \textit{then we square both sides} \\\\\\ T^2=\left( \sqrt{\cfrac{2h-40t}{g}} \right)^2\implies T^2=\cfrac{2h-40t}{g}\implies gT^2=20h-40t \\\\\\ gT^2+40t=20h\implies \cfrac{gT^2+40t}{20}=h[/tex]

The circumference of a circle is 25.12 miles. What is the circle's diameter? C=25.12 mi Use 3.14 for ​pi

Answers

The answer to your question is 8mi. I just divide the circumference by pi to find your diameter.
Circumference=2pi*r or 
and diameter=2r
in your case, the circumference is 25.12 miles, so we plug it in to the first formula:
25.12=2pi*r
12.56=3.14*r
4=r
and since 2r=diameter, the diameter is 8

HELP PLEASE!! A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining. Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.

Answers

Let's first define the variables:
 x = number of weeks.
 y = number of boxes after x weeks.
 We write the inequation that adapts to the problem
 y> -65x + 460
 For a number less than 100 boxes we have:
 100> -65x + 460
 We clear x:
 65x> -100 + 460
 65x> 360
 x> (360/65)
 x> 5.54
 Answer: 
 it will take more than 5.54 weeks for the warehouse to have less than 100 boxes
Final answer:

To determine how many weeks it will take for the warehouse to have less than 100 boxes, we can use the inequality 460 - 65w < 100. Solving this inequality gives w > (460 - 100) / 65, meaning it will take more than 6 weeks.

Explanation:

To determine how many weeks it will take for the warehouse to have less than 100 boxes, we can use the inequality:

460 - 65w < 100

Where 'w' represents the number of weeks. To solve this inequality, we can subtract 460 from both sides and then divide by -65, remembering to reverse the inequality symbol when dividing by a negative number. This gives us:

w > (460 - 100) / 65

So, it will take more than 6 weeks for the warehouse to have less than 100 boxes remaining.

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A brother and sister split the $990,000 from the sale of their parent's house. According to the will, the sister was to receive 25% more than her brother, for having managed the property. How much money did the sister receive?

Answers

The ratio of inheritance is
.. sister : brother = 1.25 : 1 = 5 : 4

Then the sister receives 5/(5+4) = 5/9 of the total, $550,000.

It costs $7.00 to play a very simple game in which a dealer gives you one card from a deck of 52 cards. if the card is a heart, spade, or diamond, you lose. if the card is a club other than the queen of clubs, you win $11.50. if the card is the queen of clubs, you win $50.00. the random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. what is the mean of x, rounded to the nearest penny?
a. $3.38
b. −$3.62
c. −$3.38
d. $3.62

Answers

It costs $7.00 to play a straightforward game in which a dealer gives you one card from a deck of 52 cards. 

If the card is a heart, spade, or diamond, you lose. 

If the card is a club other than the queen of clubs, you win $11.50. 

If the card is the queen of clubs, you win $50.00. 

The random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. What is the mean of x, rounded to the nearest penny?

------
Random "winnings"::.....-7.......4.50......43

Probabilities::........ 39/52....12/52....1/52 

------------------------------------------------------

u(x) = [39*-7 + 12*4.5 + 43]/52 = -$3.38

If the Federal Reserve decreases the reserve rate from 5% to 2.5%, how does this affect the amount of money that would result because of fractional-reserve banking from an initial deposit into a bank of $35,000? A. It incraeses the amount by 1,400,000 B.It decreases the amount by 1,400,000 C.It decreases the amount by 700,000 D. It increases the amount by 700,000

Answers

The money in circulation is inversely proportional to the reserve rate, so changes from
.. 35000/5% = 700,000
to
.. 35000/2.5% = 1,400,000.

It increases the amount by 700,000, corresponding to the 4th selection.

What are the roots of the polynomial equation?

x^2−14x−32=0

Enter your answers in the boxes.

Answers

the roots are ; 16, - 2

true or false one quart is greater than 40 fluid ounces

Answers

True. 
One quart is equal to 32 standard US fluid ounces
there is 32 ounces in one quart.
So, 40 fluid ounces is greater than one quart.

rose rode the roller coaster 9 times. Leila rode the roller 6 less times than Rose. Joseph rose roller coaster 5 times as many as Leila. how many times did Joseph ride the roller coaster?

Answers

Joseph rode the roller coaster 15 times.
Because - 9 - 6 = 3 x 5 = 15
he rode the roller coaster 15 times because 9-6=3 and 3×5=15.

The volume of a cone varies jointly with the area of the base and the height. When the area of the base is 27 cm2 and the height is 6 cm, the volume is 54 cm3. Therefore, the area of the base is _____ cm2 when the height is 12 cm and the volume is 124 cm3.

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \textit{\underline{V} varies jointly with \underline{B} and \underline{h}}\qquad V=kBh \\\\\\ \textit{we also know that } \begin{cases} B=27\\ h=6\\ V=54 \end{cases}\implies 54=k(27)(6)\implies \cfrac{54}{(27)(6)}=k \\\\\\ \cfrac{1}{3}=k\qquad therefore\qquad \boxed{V=\cfrac{1}{3}Bh} \\\\\\ \textit{when h = 12, and V = 124, what is \underline{B}?}\qquad 124=\cfrac{1}{3}B(12)[/tex]
Final answer:

The area of the base of a cone can be calculated by using the volume, height, and a constant derived from given values. Applying this formula to the specified conditions, the area of the base when the height is 12 cm and the volume is 124 cm3 is 31 cm2.

Explanation:

The volume V of a cone can be represented using the formula V = k * B * h, where 'V' is the volume, 'B' is the area of the base, 'h' is the height, and 'k' is a constant proportionality factor. In this case, you are given that the area of the base is 27 cm2, the height is 6 cm, and the volume is 54 cm3. From these values, you can calculate that the constant 'k' is (54/(27*6)) = 0.333. Now, given a volume of 124 cm3 and a height of 12 cm, you can rearrange the equation to solve for the area of the base 'B': B = V/(k*h) = (124/(0.333*12)) =  31 cm2. Therefore, the area of the base when the height is 12 cm and the volume is 124 cm3 is 31 cm2.

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please help me with another problem

Answers

"one" will fill both blanks.

what is the volume of a cube with a side length of 5/6 cm

Answers

(5/6) * 3 = 2.5 cm

hope this helps! :)

three lots of three make

Answers

3 lots of 3 make 9 use a calculator

The radius of a circle is 4 millimeters. What is the circle's circumference? r=4 mm Use 3.14 for ​.

Answers

The circumference of the circle is: 25.12 mm.

The Circumference of a CircleCircumference of a circle = 2πr

Given:

radius of circle = 4 mm

π = 3.14

Required:

Circumference of the circle

Thus:

Circumference of the circle = 2×3.14×4

Circumference = 25.12 mm

Therefore, the circumference of the circle is: 25.12 mm.

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The correct answer is the circle's circumference is approximately 25.12 millimeters.

To find the circumference of a circle, one can use the formula:

[tex]\[ C = 2\pi r \][/tex]

where [tex]\( C \)[/tex] is the circumference, [tex]\( \pi \) (pi)[/tex] is a mathematical constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius of the circle.

Given that the radius [tex]\( r \)[/tex] is 4 millimeters, we can substitute the values into the formula:

[tex]\[ C = 2 \times 3.14 \times 4 \text{ mm} \][/tex]

Now, we perform the multiplication:

[tex]\[ C = 2 \times 3.14 \times 4 = 25.12 \][/tex]

find rhe volume of a cylinder with a diameter of 10 inches and a height of 20 inches

Answers

since the diameter of the cylinder is 10, its radius is half that, or 5, thus

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=5\\ h=20 \end{cases}\implies V=\pi (5)^2(20)[/tex]

Which of the following statements contain a variable?all that apply
A.there are 60 second in a minute
B.he is year old
C.double the number of pages in the book
D.the age of my friend

Answers

B. and C. 
Gotta write more for the 20 characters limit

ten less than triple a number is 21

Answers

3x-10=21 is the answer
3n -10 = 21

Hope this helps
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