Answer:
x = 9,-21
Step-by-step explanation:
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Cancel absolute sign and add plus-minus to 15:
[tex]\displaystyle \large{x+6=\pm 15}[/tex]
Transport 6 to subtract ±15:
[tex]\displaystyle \large{x=\pm 15-6}[/tex]
Consider:
[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Second Method
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Absolute Function Property:
[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]
Consider both intervals:
When x ≥ a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]
Transport 6 to subtract 15:
[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]
When x < a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]
Transport -6 to add 15:
[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]
Transport negative sign to 21:
[tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
A group of researchers wants to estimate the difference in time it takes to heal enough to return to work after knee replacement surgery using two different physical therapy plans. They plan to use the data in the following table to construct a two-sample t interval.
Therapy plan A B
Mean healing time (weeks) 8.2 6.8
Standard deviation (weeks) 1.5 0.9
Number of participants 45 60
Which of the following are conditions for this type of interval?
Choose all answers that apply:
A. The times for each participant are independent of each other.
B. The distributions of times in the population are approximately normal.
C. Each sample includes equal numbers of men and women.
Answer:
A
Step-by-step explanation:
Got it right on Khan Academy.
Hope this helps!
Please mark as brainliest!
can someone help me with this I already answered half of all of them but I need to make sure It's right?
Answer:
of 34.576:
34.576 = (3 * 101) + (4 * 100) + (5 * 1/101) + (7 * 1/102) + (6 * 1/103)
34.576 = (3 * 10) + (4 * 1) + (5 * 1/10) + (7 * 1/100) + (6 * 1/1,000)
34.576 = 30 + 4 + 5/10 + 7/100 + 6/1,000
34.576 = 30 + 4 + 0.5 + 0.07 + 0.006
Step-by-step explanation:
That is 34.576 in expanded form, so know you can know which is correct
A right rectanular prism has a length of 2 a width of 4 and a height of 5. How many unit cubes can fit in the prism
Answer:
40
Step-by-step explanation:
4 x 2 = 8 x 5
l x w x h
or
Bxh
If 10% of your paycheck was withheld for federal income taxes and another 6% for state income taxes, how much would your net (or take-home) pay be?
Your net income/take-home would be 84.6 percent of the gross amount.
What is net income?Your net income is the amount of money left after payroll deductions in the form of taxes and other charges on the gross amount of your paycheck.
If we deduct federal and state taxes, 10 percent and 6 percent respectively, we would charge 10 percent and 6 percent of 100 and have 84.6 percent of your original(gross) income left.
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A Triangle has a perimeter of 80 feet. If the three sides of the triangle are, n, 3n + 7, and 3n + 3, what is the length of each side?
Answer:
Step-by-step explanation:
Givens
Perimeter = 80 feet
side 1 = n
side 2 = 3n + 7
side 3 = 3n + 3
Formula
Side 1 + side 2 + side 3 = 80
Solution
Substitute the length for each side into the equation
n + 3n + 7 + 3n + 3 = 80
7n +10 = 80 Subtract 10 from both sides
7n + 10 - 10 = 80 - 10 Combine
7x = 70 Divide by 7
7x/7 = 70/7 Combine
x = 10
Answer
Side 1 = n = 10
Side 2 = 3n + 7 = 3*10 + 7 = 37
Side 3 = 3n + 3 = 30 + 3 = 33
PLEASE HELP I WILL GIVE BRAINLIEST
Step-by-step explanation:
37×2=74
360-74 = 286
286 ÷ 2=143
Of course, if AD and BC , and also BA and CD are even.
The frequency table shows the number of students selecting each type of
food.
Nachos Popcorn Smoothies Total
Boys
5
6
4
15
Girls
6
8
4
18
Total
11
14
8
33
What proportion of students chose popcorn?
The proportion of students who chose popcorn will be 14/33.
How to calculate the proportion?From the information, the frequency table shows the number of students selecting each type of
food.
The number of people who choose popcorn = 14
Total number of people = 33
Therefore, the proportion of students chose popcorn will be:
= 14/33
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Answer:
0.42
Step-by-step explanation:
help. will give brainliest. please hurry!!! <3
also, please explain how to get my answer. need to show work.
An investor just purchased a rectangular 1-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?
If you bought 28 shares of stock at $30/sh and sold them at $25/sh. And How much did you net after selling the shares? Was it a profit or a loss?
Answer:
selling price$840
it's a loss.
Step-by-step explanation:
cost price = 28× 30 = $840
selling prince =25×28=$700
since cost price is bigger than selling price, it's a loss.
8) Which table shows a proportional relationship between x and y?
1
y
1
4
2
3
4
8
4
6
10
с
12
8
А
9
16
14
16
12
22
20
20
15
28
x
3
.
y
5
1
12
6
10
2
14
12
D
w N
B
15
16
18
18
4
24
20
20
30
25
5
9 Danielle constructs a scale model of a building with a rectangular base. Her model
Answer:
D
Step-by-step explanation:
A table shows a proportional relationship if all of the y/x ratios are the same.
A: 4/3 ≠ 10/6 . . . . not proportional
B: 6/12 ≠ 12/14 . . . . not proportional
C: 2/4 ≠ 20/20 . . . . not proportional
D: 1/5 = 2/10 = ... = 5/25 . . . . proportional relationship
Answer:
D
Step-by-step explanation:
1*5=5
2*5=10
3*5=15
4*5=20
5*5=25
What are the x-intercepts of this conic section?
no x-intercepts
(−1, 0) and (1, 0)
(0, −2) and (0, 2)
(0, −1) and (0, 1)
Using it's concept, it is found that the conic section has no x-intercepts.
What is a x-intercept of a function?
A x-intercept of a function is given by the value of x when y = 0. On a graph, it is the value of x when the function crosses the x-axis.
In this problem, the conic section given in the graph does not cross the x-axis, hence it has no x-intercepts.
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How do I find the volume?
Answer:
150m^3
Step-by-step explanation:
The formula for the volume a triangular prism, like the one you have, is 1/2 base x height. For your prism the volume would be 1/2 (30 x 10) which equals 150. Now just add the measurment m (meters) and you're set.
please help brainliest included for honest attempt
Think of two different technological innovations that occurred in the last 50 years: one that relied largely on innovations within a specific technology (for example, the upgrades that smartphones have seen over the years) and one that relied largely on knowledge or skills that came from a field of technology that was distinct from the main field that innovation deals with (for example, video games that use technology originally designed for navigation). Briefly describe each innovation and what inspired it, then compare the innovations: for example, which innovation seems more of an incremental improvement versus a paradigm-shift in its field? Which one do you think was more widely used in the five years after it was invented? Which one most inspired other innovations?
Answer:
The Electric Car
The Cell Phone
The GPS
DNA Testing
3D Printing
(10) The population of bacteria an experiment can be modeled by d p(d)= 400(1.56)^d , where d is the number of days the population has been growing.
(a) Find the average rate the population has been growing over the interval 0≤d≤7.
Round to the nearest integer and include appropriate units.
(b) If the population of bacteria was modeled as a function of the number of hours, h,
such that h p(h)= 400b^h then what would be the value of b to the nearest thousandth?
Show or explain how you found your answer.
The average rate at which the population is growing over the interval 0≤d≤7 is 1228, while the exponential function as a function of hours is [tex]p(h)=400(1.56)^{\frac{h}{24} }[/tex]
What is an exponential function?An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Let p represent the population of the bacteria after d days.
[tex]P(d)=400(1.56)^d\\\\P(7)=400(1.56)^7=8994\\\\P(0)=400\\\\\\Average\ rate\ of\ change=\frac{P(7)-P(0)}{7-0}=\frac{8994-400}{7-0} =1228[/tex]
b) 24 hours = 1 day, hence:
[tex]p(h)=400(1.56)^{\frac{h}{24} }[/tex]
The average rate at which the population is growing over the interval 0≤d≤7 is 1228, while the exponential function as a function of hours is [tex]p(h)=400(1.56)^{\frac{h}{24} }[/tex]
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Latoya just bought a refrigerator for $931. She paid $139.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$197.80
Step-by-step explanation:
$931.00 - $139.80 = $791.20
$791.20 / 4 equal installments = $197.80
Some pens are shared among three students anne,lucy, and John.Anne gets 5 times many pens as lucy, and lucy gets 2 pens less than john. Suppose John gets x pens, how many pens does anne get in terms of x
Using a system of equations, it is found that Anne gets 5x - 10 pens.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, we consider that John gets x pens.
Lucy gets 2 pens less than john, hence:
L = x - 2.
Anne gets 5 times many pens as lucy, hence:
A = 5L = 5(x - 2) = 5x - 10.
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The numbers 4 through 14 are placed in a bowl and drawn at random then replaced after being drawn.What is the probability that you will choose an even number
Answer:
The probability is probably about 55%
Step-by-step explanation:
— I just need help,
look at picture for information .
Answer:
a = √28
Step-by-step explanation:
The Pythagorean theorem tells you the area of the large square is the sum of the areas of the smaller two squares.
8² = a² +6²
a² = 8² -6² = 64 -36 = 28
Taking the square root, we find ...
a = √28
make r the subject of this formula t=2r/r-1
[tex]t= \dfrac{2r}{r-1}\\\\\implies tr-t= 2r\\\\\implies tr -2r = t\\\\\implies r(t-2) = t\\\\\implies r = \dfrac{t}{t-2}[/tex]
The formula of r is t/t-2 for equation t=2r/r-1.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is t = 2r/r-1
t equal to two times of r divided by r minus one
We need to find the formula for r
t = 2r/r-1
Apply cross multiplication
t(r-1)=2r
Apply distributive property on left side
tr-t=2r
Subtract 2r on both sides
tr-2r=t
r(t-2)=t
Divide both sides by t-2
r=t/t-2
Hence, the formula of r is t/t-2 for equation t=2r/r-1.
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What the value of w?
Answer:
56 degree
Step-by-step explanation:
90 - 34 = 56
Answer:
w = 56
Step-by-step explanation:
w + 34 = 90 (the angle is a right angle)
w = 90-34 = 56
Write an equation of a parabola with the given vertex and focus. Vertex (3,-2); focus (3,-3). Y=
Answer:
help mee
Step-by-step explanation:
i neddd heplp with my mathh thankyou
Find the lateral surface area of the rectangular prism in centimeters
Answer:
180 cm2 is the answer you can multiply all sides
Answer:
Step-by-step explanation:
length = l = 9 cm
Width = w= 3 cm
height = h = 4 cm
Lateral surface area = 2 *( lh+ lw)
= 2*( 9*4 + 9*3)
= 2 * (36 + 27)
= 2 * 63
= 126 square cm
Help help help math math
Answer:
>
Step-by-step explanation:
Negative is that amount below zero. For example -3 is 0 - 3. This means that since -3 is 3 less than 0, -3 < 0. This can also be said as 0 > -3.
Answer:
Answer: 0 (> )-3
Step-by-step explanation:
Hope it helps
A cup contains 438 grams of sand. A bucket contains 2,120 grams of sand.
How many more grams of sand are in the bucket than the cup?
The bucket that contains 2120 grams of sand and a cup that contains 438 grams of sand , the bucket of sand has 1682 grams of sand than the cup of sand in the cup.
How to calculate difference in mass?A cup contains 438 grams of sand. A bucket contains 2120 grams of sand.
Therefore, the number of more grams of sand in the bucket than the cup is as follows:
mass of sand in cups = 438 grams
mass of sand in the bucket = 2120 grams
Therefore,
difference in mass = 2120 - 438
difference in mass = 1682 grams
Therefore, they are 1682 grams of sands in the bucket than the cup.
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PLEASE HELP ME PLEASE
Answer
true
Step-by-step explanation:
Answer:
I think true because that's the only star that is closest to the earth
This practice contains 15 questions. If you get 3 incorrect, what will your percent grade be? Hint: Grades are based on correct questions/total questions.
A. 30%
B. 0.8%
C. 20%
D. 80%
Answer:
D. 80%
Step-by-step explanation:
15-3 = 12
12/15 = 4/5 = .8
80%
Write a money problem you can solve using sharing, joining, or separating
Answer:
Jonny have 100 dollars and he gave his 2 friend's $20 how much does he have left?
Step-by-step explanation:
100-40=60
Jonny has 60 dollars left
Please help I'll mark brainliest.
Answer:
I believe the answer is class 3 because each number of boys and girls goes into class 3.
Answer: Class 3.
Step-by-step explanation: Answers with a 1 to 2 ratio have ratios like 4 to 8, or 5 to 10. Class 3 is the only one with a 1 to 2 ratio, which is 7 to 14, with 7 being the number of girls in that class and 14 being the number of boys in that class. Class 1 has a 1 to 1 ratio, class 2 has a 2 to 1 ratio, and class 4 has a different ratio than all the rest, so that's why all of those are wrong. Therefore, class 3 is your answer.
Have a great day! :)
an office manager purchased 39 boxes of pens for the staff. each box contains 6 black pens and 4 blacks pens. Use the distribute property to write an equivalent expression for the total number of pens. them, simplify the expression
Answer:
390 pens in total
Step-by-step explanation:
Each box has 6 black and 4 black
so the total amount of pens per box should be 10 because 6+4=10
Since we have to use distributive property you can write the equation (6+4)*39 because you need to figure out the total amount of pens in all the boxes.
6+4 is 10
and 10 * 39 is 390
therefore the answer is 390 pens in total