Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.
To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.
First, let's isolate the absolute value term on one side of the equation:
|3x + 3| = -3
Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.
To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:
3x + 3 = -3
-(3x + 3) = -3
Solving equation 1:
3x + 3 = -3
3x = -6
x = -2
Solving equation 2:
-(3x + 3) = -3
-3x - 3 = -3
-3x = 0
x = 0
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The Bureau of Economic Analysis estimates that in 2015, personal consumption expenditures of American totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion: for example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion: for example, food, clothing, fuel), and services ($8.3 trillion: for example, health care, education, transportation).
a. What was the approximate annual per capita spending on personal consumption? Assume a population of 321 million.
B. What was the approximate daily per capita spending on personal consumption?
c. On average, about what percentage of personal consumption spending was devoted to services? Is this figure consistent with your own spending ?
d. Spending on health care was estimated to be $2.1 trillion. About what percentage of all personal consumption spending was devoted to health care?
e. In 2000, the total spending on personal consumption was $6.8 trillion, while health care spending was $918 billion. Compare the percentage increase in total spending and health care spending between 2000 and 2015.
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
a. The approximate annual per capita spending on personal consumption in 2015 was $38,218. This figure was calculated by dividing the estimated total personal consumption expenditure of $12.3 trillion by the population of 321 million.
b. The approximate daily per capita spending on personal consumption in 2015 was $104.89. This figure was calculated by dividing the approximate annual per capita spending of $38,218 by 365 days.
c. Services accounted for approximately 67.2% of personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on services of $8.3 trillion by the total personal consumption expenditure of $12.3 trillion. This figure is consistent with my own spending, as the majority of my expenditure is devoted to services such as transportation, food delivery, and entertainment.
d. Health care accounted for approximately 17.1% of all personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on health care of $2.1 trillion by the total personal consumption expenditure of $12.3 trillion.
e. The percentage increase in total spending between 2000 and 2015 was 77.5%, while the percentage increase in health care spending between 2000 and 2015 was 129.9%. This was calculated by first subtracting the total spending on personal consumption in 2000 of $6.8 trillion from the total spending on personal consumption in 2015 of $12.3 trillion, and then dividing the result by the total spending in 2000. This was done for both total spending and health care spending, and the results were then multiplied by 100 to get the percentage increase.
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
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How smart am I from a scale of 1-10?
Answer:
if you are asking us then probably a... hmmm -_- 3 yes
3 out of 10
Step-by-step explanation:
Answer: we’ll first to find how “smart” you are, we have to verify the level of unsmartness and see if there is any given number. Since the is no given number we will use x as our unknown number. Then we will subtract 1 from 10, therefore giving us the number 9 that we will use in our equation to determine the level of “smart”.
Now we will put 9 and x together:
9x
Now we will find the next part of our equation which will find by looking at how we got the number 9, which is: 10-1
Now we group the parts of this equation which will be:
9x÷10-1
First we will solve one side of our equation
10-1=9
Then we will insert the solved side of the equation
9x÷9
Now we will divide
9/9x
we are left with 1
x=1
Now we insert our solved number back into our previous equation with 1 replacing x
9⋅1÷10-1
Now after we have solved the equation
The answer is: -0.1 will be your level of “smart”
. On Mary’s MP3 player for everly 3 pop songs Maria had she also had 4 country songs. If she has 15 pop songs on her MP3 player, how many country songs does she have? ________________
Answer:
20
Step-by-step explanation:
every three pop add 4 country you will get 4 8 12 16 20 making 20 your answer
Ashley is making cookies. The recipe calls for ¾ of a cup of sugar. She needs to make five batches of cookies. How many cups of sugar does Ashley need?
Answer:
3 3/4
Step-by-step explanation:
3/4×5
15/4
simplify
3 3/4
Answer:
Ashley needs \(3\frac{3}{4}\) cups of sugar
Step-by-step explanation: 3/4 multiplied by 5 is 3.75 or 3 3/4
PLEASE HELP !!!!!!!!!!!!
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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LU 1
- 2x + 3 < 5 and - 4x – 3 > 9
Answer: x>-1
x<-3
Step-by-step explanation:
\(-2x+3<5\)
subtract 3 on both sides
\(-2x<2\)
divide -2 on both sides
\(x>-1\)
The sign changed because I divided by a negative.
\(-4x-3>9\)
add 3 on both sides
\(-4x>12\)
multiply -1 on both sides
\(4x<-12\)
divide 4 on both sides
\(x<-3\)
Brainlist please
Answer:
x > -1
x < -3
Step-by-step explanation:
-2x + 3 < 5
Subtract 3 on both sides.
-2x < 5 - 3
-2x < 2
Divide -2 into both sides.
x < 2/-2
x > -1
-4x - 3 > 9
Add 3 on both sides.
-4x > 9+3
-4x > 12
Divide -4 into both sides.
x > 12/-4
x < -3
Which function shows a greater rate of change?
Function A
y (Output)
28
24
20
16
12
00
8
4
1 2 3 4 5
Function B
x (input)
y (output)
0
1
10 14
2
18
3
22
4
26
5
30
Step-by-step explanation:
the rate of change (or slope for a line function) is the rate
y coordinate change / x coordinate change
for function A we see that x needs to change by 2 units, so that y changes by 1 unit.
that rate of change or slope is
1/2
for function B we see that when x changes by 1 unit, y changes by 4 units.
that rate of change or slope is
4/1 = 4
so, because 4 > 1/2, function B has the greater rate of change.
Find the 89th term of the arithmetic sequence 25, 35, 45, ...25,35,45,...
Answer:
895
Step-by-step explanation:
There's a repetitive pattern of adding +10 each time.
The distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres. What percent of the journey did he run?
A student ran 6% of the journey.
In this question, we have been given the distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres.
We know that 1 km = 1000 meters
So, 8 km = 8000 meters
So, the percent of the journey he ran,
480/8000 * 100
= 6%
Therefore, A student ran 6% of the journey.
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a school has 900 students. 1/6 of the students in the school are in year 7. 2/5 of the year 7 students are going on a trip to the castle. how many year 7 students are going on the trip?
Answer: 12 students
Step-by-step explanation:
1/6 of 900 is 30 kids. and 2/5 of the 30 kids is 12
(x-y)(x-y+1)² -2(x-y)(x-y+1)+x-y
help ASAP pleasee!!
Step-by-step explanation:
If u are looking for factorization this is the way
(x-y)(x-y+1)² -2(x-y)(x-y+1)+(x-y)=
(x-y)[(x-y+1)^2-2(x-y+1)+1]=
(x-y)[(x-y+1)^2-2(x-y+1)+1^2]=
(x-y)[(x-y+1)-1]^2=(x-y)(x-y+1-1)^2
(x-y)(x-y)^2=
(x-y)^3
Point D (-5, 3) and point E (6, -2) are located on a coordinate grid.
Which measurement is the best representation of the distance between point D and point E in units?
Answer:
Rounding to the nearest number, the answer would be 12 units
Step-by-step explanation:
I hope this helped! Please mark me as brainliest if you can!
Help please, will mark you as brainliest !!!
Answer: Question 7 is 38
1/28x
Step-by-step explanation:
A child walks 3/10 of a mile in 1/5 hour. At this rate, how far will the child walk in 1 hours ?
Answer:
1.5 miles
Step-by-step explanation:
.3 miles/12 minutes x 5/5 = 1.5 miles/ 1 hour
-2x + 9y=-41 and -2x -5y =1
plase help 50 points
Match to the correct one
Answer:
1. b_ 2. a_ 3. c_ 4. d
Step-by-step explanation:
1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.
Un coche tarda 12 minutos en dar la vuelta a un circuito si va a una velocidad de 80 km/h. Cuánto tiempo tardara en recorrer el mismo circuito si va a una velocidad de 100 km/h?
A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.
What theory directly contradicts concept of absolute zero?
All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).
Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.
Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.
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What is the formula forfinding the area of a circle using its radius or diameter.
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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Divide. round your answer to the nearest hundredeth: 1 divided by 3 = the steps are decimals?
Answer: 1/3 or 1 divided by 3 is equivalent to 0.333333
Answer:
0,33
Step-by-step explanation:
this for sure.......
How many degrees are there in 5/8 of a circle
Answer:
Step-by-step explanation:
First the max degree is 360
Then multiply by 5/8
360 x 5/8 = 1800/8
1800/8 = 225
Answer: 225
The numbers of trading cards owned by 8 middle-school students are given below. (Note that these are already ordered from least to greatest.)
306, 416, 437, 463, 547, 555, 574, 686
Send data to calculator
Suppose that the number 686 from this list changes to 582. Answer the following.
(a) What happens to the median?
It decreases by O
It increases by
It stays the same.
(b) What happens to the mean?
It decreases by
It increases by
It stays the same.
Answer:
Step-by-step explanation:
736.5
What is this!!! I need to know quick
Answer:
x<3
Step-by-step explanation:
the dot is not black so it means that its not equal to three but bigger than three
((1/3)x^2))-((1/9)x)-(2/9)=0
The solution of the quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
Any equation that can be written in the standard form where x stands for an unknown and a, b, and c are known quantities, with a 0, is said to be quadratic.
An assignment of values to the unknown variables that establish the equality in the equation is referred to as a solution.
Consider the expression,
(1/3)x² - (1/9)x - 2/9 = 0
Multiplying each side of the quadratic equation by 9,
9 × [ (1/3)x² - (1/9)x - 2/9 = 0 ]
3x² - x - 2 = 0
Using the quadratic formula,
\(x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}\)
\(x = \frac{1 \pm \sqrt{1+24} }{6}\\ x = \frac{1 \pm \sqrt{25} }{6}\)
x = 1 and x = - 2/3
Hence, the solution of quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
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What is the distance between the points(-4,-1) and (-6,8) in simplest radical form.
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6 - (-4)]^2 + [8 - (-1)]^2}\implies d=\sqrt{(-6+4)^2+(8+1)^2} \\\\\\ d=\sqrt{(-2)^2 + 9^2}\implies d=\sqrt{85}\)
11 out of the 22 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?
Answer:
50% of the employees work part time.
Step-by-step explanation:
11/22=0.5
0.5 *100=50
2. How do you know if a number is
divisible by 9 without dividing?
Answer:
Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.
Decide how many solutions this equation has:
x2 - 2x + 1 = 0
In the diagram below, GPK = 18x + 5 and KPH = 14x + 15. Solve for the measure of angleGPK.PH
We can say that the two triangles are identical, then, the angle GPK is equal to the angle KPH, then we write the following equation:
\(\begin{gathered} \angle GPK=\angle KPH \\ \\ 18x+5=14x+15 \\ \\ 4x=10 \\ \\ x=\frac{10}{4}=\frac{5}{2}=2.5 \end{gathered}\)Now we know the value of x, we can return to the equation and find the value of the angle GPK
\(\begin{gathered} \angle GPK=18x+5 \\ \\ \operatorname{\angle}GPK=18\cdot\frac{5}{2}+5 \\ \\ \operatorname{\angle}GPK=9\cdot5+5 \\ \\ \operatorname{\angle}GPK=45+5 \\ \\ \angle GPK=50 \end{gathered}\)Therefore, the measure of the angle GPK is equal to 50 degrees