[tex]|x-7|=5[/tex]
ExplanationWe know that we need to write our absolute value equation as [tex]|x-b|=c[/tex]. We also know that the solutions must be [tex]x=2[/tex] and [tex]x=12[/tex]. We need to replace those values for [tex]x[/tex] in our absolute value equation, so we can create a system of equations and find the values of [tex]b[/tex] and [tex]c[/tex].
- For [tex]x=2[/tex]
[tex]|x-b|=c[/tex]
[tex]|2-b|=c[/tex] equation (1)
- For [tex]x=12[/tex]
[tex]|x-b|=c[/tex]
[tex]|12-b|=c[/tex] equation (2)
Now we can solve our system of equations step-by-step:
Step 1. Replace equation (1) in equation (2)
[tex]|12-b|=|2-b|[/tex]
Step 2. Square both sides of the equation to get rid of the absolute values
[tex]|12-b|=|2-b|[/tex]
[tex](12-b)^2=(2-b)^2[/tex]
Step 3. Use the square of a binomial formula: [tex](a-b)^2=a^2-2ab+b^2[/tex] and solve the equation.
For our first binomial, [tex](12-b)^2[/tex], [tex]a=12[/tex] and [tex]b=b[/tex]; for our second binomial, [tex](2-b)^2[/tex], [tex]a=2[/tex] and [tex]b=b[/tex]
[tex](12-b)^2=(2-b)^2[/tex]
[tex]12^2-(2)(12)(b)+b^2=2^2-(2)(2)(b)+b^2[/tex]
[tex]144-24b+b^2=4-4b+b^2[/tex]
[tex]144-24b=4-4b[/tex]
[tex]140=20b[/tex]
[tex]b=\frac{140}{20}[/tex]
[tex]b=7[/tex] equation (3)
Step 4. Replace equation (3) in equation (2) to find the value of [tex]c[/tex]
[tex]|12-b|=c[/tex]
[tex]|12-5|=c[/tex]
[tex]|7|=c[/tex]
[tex]c=7[/tex]
Putting it all together we can conclude that our absolute value equation is [tex]|x-7|=5[/tex]
Answer:Ix-7I=5
Hope this helps lol
2. Delia and Beto left for school at the same time.
Delia lives 3/4 mile from school and walks at a pace of
16 minutes per mile. Beto lives 3 1/2 miles from school
and bikes at a pace of 3 minutes per mile. Who will get to
school first?
Answer:
Beto will get to the school first.
Step-by-step explanation:
We are given that Delia lives 3/4 mile from school and walks at a pace of
16 minutes per mile.
So Delia takes [tex] \frac{3}{4} \times 16 = [/tex] 12 minutes to reach school.
While Beto lives 3 1/2 miles from school and bikes at a pace of 3 minutes per mile.
So Beto takes [tex] \frac{7}{2} \times 3 = [/tex] 10.5 minutes to reach school.
Therefore, Beto will get to the school first.
Kylie saved $550 from babysitting. She used 32% of her money for a down payment on summer camp and 3/20 of her savings for two new video games. She deposited the rest into a college savings account. Expressed as a decimal, what part of her money did Kylie deposit into her college savings account?
Answer: %53
Step-by-step explanation:
3/20=%15
15+32=%47 for both video games and camp
100-47= %53 left over for college
Answer: .53
Step-by-step explanation: Of Kylies $550, 32% was for a down payment for summer camp. This is calculated with the formula 550 x .32 = $176 down payment.
She used 3/20 for two video games. 3/20 = .15, so the video games cost .15 x $550 = $82.50.
Kylie spent $176 + $82.50 = $258.50.
$550 savings - $258.50 = $291.50 is the amount that she put into her savings account. Expressed as as decimal, it is 291.50/550 = .53, so she put .53 of her babysitting money into her college savings account.
how do i graph y = 2x - 1
Answer:
Step-by-step explanation:
Make a table that has (x) on the left and (y) on the right. There should be a slash between them. After that, you should place the numbers (1,2,3,4,5...) on the x column or on the left. Then times the x in y = 2x - 1 with the numbers on the left and that would give the numbers on the right. Once you are done with that, then pair the numbers from the left to the right. Then simply graph it.
But always remember, left is (x) and right is (y)
If 70 is increased by 30%, what is the new amount?
Answer:
91
Step-by-step explanation:
70 * .30 = 21
21 + 70 = 91
A supersonic jet was flying at a constant velocity starting 8,400 kilometers west of U.S. airspace. It
flew one-third of the way to U.S. airspace in 2 hours. What was the jet's velocity?
Write your answer as a whole number.
Answer:
1,400 km/hr
Step-by-step explanation:
One third of the distance 8,400 km is 2,800 km.
The unit rate (speed) of the jet is therefore
2,800 km
--------------- = 1,400 km/hr
2 hr
I have no idea what to do on this someone plzzzzz help :)
Answer:
Step-by-step explanation:
Term: 3x,10
Coefficients:3
Constant: 10
a rectangle with a perimeter of 32 inches has whole-number side lengths. what is the difference between the greatest and the least areas of the rectangle?
Answer:
49
Step-by-step explanation:
Let x represent the length and y represent the width of the given rectangle. The perimeter of the rectangle will be:
Perimeter = 2(x + y)
32 = 2(x + y)
16= x + y
This means, the sum of length and width of the rectangle can be 16. Since only whole number side lengths are allowed, following are the possibilities:
Side Lengths: 15, 1 Area = 15Side Lengths: 14, 2 Area = 28Side Lengths: 13, 3 Area = 39Side Lengths: 12, 4 Area = 48Side Lengths: 11, 5 Area = 55Side Lengths: 10, 6 Area = 60Side Lengths: 9, 7 Area = 63Side Lengths: 8, 8 Area = 64Hence the largest possible value of Area is 64 and the least possible value is 15. The difference is 64 - 15 = 49
6. In a survey, 10 students and 10 teachers were asked how many hours of sleep they get each night. Here are the results.
Students: 7,6,8,9,8,9,10,10,10
Teachers: 6,6,4,5,7,8,7,8,8,8,
What is the mean of each data set? What do the means tell you about each data set?
The mean of the students' data set is approximately 8.56 hours of sleep per night, while the mean of the teachers' data set is approximately 6.7 hours of sleep per night. This suggests that, on average, students get more sleep than teachers.
Explanation:To find the mean of a data set, you need to add up all the values and then divide the sum by the total number of values. Let's start by finding the mean of the students' data set. Summing up the values: 7 + 6 + 8 + 9 + 8 + 9 + 10 + 10 + 10 = 77. Since there are 9 values in the data set, we can calculate the mean by dividing the sum by 9: 77 / 9 = 8.56 (rounded to two decimal places). Therefore, the mean of the students' data set is approximately 8.56 hours of sleep per night.
Next, let's find the mean of the teachers' data set. Summing up the values: 6 + 6 + 4 + 5 + 7 + 8 + 7 + 8 + 8 + 8 = 67. Since there are 10 values in the data set, we can calculate the mean by dividing the sum by 10: 67 / 10 = 6.7 (rounded to one decimal place). Therefore, the mean of the teachers' data set is approximately 6.7 hours of sleep per night.
The means tell us the average amount of sleep that students and teachers get each night. The mean of the students' data set (8.56) suggests that, on average, students get more sleep than the mean of the teachers' data set (6.7). This indicates that, based on this survey, students tend to get more sleep than teachers.
What is the least common multiple of 10, 20, and 14?
Answer:
140
Step-by-step explanation:
The multiples of 10 are : 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, ...
The multiples of 20 are : 20, 40, 60, 80, 100, 120, 140, ....
The multiples of 14 are : 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, .....
The least common multiple of 10, 20 and 14 is 140
What is the volume of the prism given below?
Answer: the answer is c. 420
Step-by-step explanation:
this is because
V= L*W*H
SO
V= 12*14*5
But since there is a triangle as the base you divide by 2 or multiply by 1/2
1/2( 12*14*5)= to 420
so the answer is 420
Hoped it helped
make me brainlist
PLLLLLL HELP!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
We can use the "vertical line test" to determine whether a given graph represents a function or not.
If your vertical line intersects the graph in more than one place, the graph does NOT represent a function. Thus, D does not represent a function, as a line drawn vertically thru this graph intersects the graph multiple times.
Graph A: Note that if you draw a vertical line thru x = -2, your line will intersect the BLACK dot (-1 3/4, 0) and the EMPTY circle (-1 3/4, 3 1/4). This is OK; this graph represents a function.
Anybody got an easy question for me to answer in any subject?
Answer: Reshma is making a necklace using green beads and purple beads in a ratio represented on the following double number line. Fill in the missing values on the diagram.
If Reshma uses 20 green beads, how many purple beads will she use?
there are 28 other students in Tiana's class,not including her self. her teacher is going to randomly choose one student's name for a prize how many outcomes are possible.
I’m not sure what you mean but I will say that the probability of Tiana getting chosen is 1/29z
Evaluate h(d) =4/9d+6 2/3 for d=3
A. 8
B. 7
C.7 1/3
D. 2 2/3
For this case we have a function of the form [tex]y = h (d)[/tex]. Where:
[tex]h (d) = \frac {4} {9} d + 6 \frac {2} {3}[/tex]
Rewriting the mixed number as a fraction:
[tex]h (d) = \frac {4} {9} d + \frac {3 * 6 + 2} {3}\\h (d) = \frac {4} {9} d + \frac {20} {3}[/tex]
Substituting [tex]d = 3[/tex]:
[tex]h (3) = \frac {4} {9} (3) + \frac {20} {3}\\h (3) = \frac {4} {3} + \frac {20} {3}\\h (3) = \frac {24} {3}\\h (3) = 8[/tex]
ANswer:
Option A
Helpppppp I don’t understand Anwsers welcome
Answer:
Just substitute values for x in such as 1,2,3,4 and 5 for the both the equations
Step-by-step explanation:
1) Intersection point is at (-1, 2)
3) Intersection point is at (-2,3)
Good luck ^-^
By the way just for the future I'll teach you how to to the problem because it'll be 10x easier for you!
Let's say you have the equation y = -4x - 2
You go 2 down on the y-axis. So place a point on (0, -2)
After that we have -4x which is actually -4/1 which means +1 for the x-axis and -4 on the y-axis!
Which determines our new point to be on (1, -6)
And you just make the lines now or to make it even easier flip (1, -6) to (-1, 6)
That'll make drawing your lines way easier! Good luck ^-^
Plz help!!!!!!!!!!!!
Answer: b) x = -3, x = 3
Step-by-step explanation:
[tex]g(x) = \dfrac{x-4}{x^2-9}[/tex]
The vertical asymptotes are the restrictions on x, which can be found by finding the x-values that make the denominator equal to zero.
x² - 9 = 0
x² = 9
x = ± 3
The perimeter of a square is 36 inches. Find the length of a diagonal. Round your answer to the nearest tenth.
Answer:
12.7
Step-by-step explanation:
The diagonal formula is x*sqrt(2) with x being one side length.
To find the side length divide the perimeter by 4.
That gives us 9.
Then, all you have to do is multiply that by the square root of 2 and then round.
To find the diagonal of a square with a perimeter of 36 inches, calculate the side length as 9 inches and apply the Pythagorean theorem, resulting in a diagonal length of approximately 12.7 inches.
Explanation:The perimeter of a square is given as 36 inches, so to find the length of one side, we divide the perimeter by 4, since a square has four equal sides. Therefore, each side of the square is 36 inches ÷ 4 = 9 inches. To determine the length of the diagonal, we can apply the Pythagorean theorem in the square. The square's diagonal splits it into two right triangles, each with legs equal to the side of the square. If we denote the length of the diagonal as d and one side as s, the formula d² = s² + s² applies.
With both sides being 9 inches, this becomes d² = 9² + 9², leading to d² = 81 + 81 = 162. Taking the square root to find d, we get d = √162, which is approximately 12.7 inches when rounded to the nearest tenth.
What is the answer to question 17
Answer:
It is 1/1536
Step-by-step explanation:
You divide 1/512 by three since it is a cube.
Camden gets paid every 2 weeks. Federal withholding is 15.6% of his gross pay, Social Security is 6.2% of his gross pay, and Medicare is 1.45%. Find Camden net pay after 2 weeks. Show your work.
Step-by-step explanation:
F=0.156g
S=0.062g
M=0.0145g
N=g-(F+S+M)
N=g-(0.156g+0.062g+0.0145g)
N=g-0.2325g
N=0.7675g
Camden's net pay is 76.75% of his gross pay
Alternative:
100%-15.6%-6.2%-1.45%=76.75%
Final answer:
To calculate Camden's net pay, you subtract federal withholding, Social Security, and Medicare deductions from his gross pay based on provided percentages. By applying these calculations to an example, Camden's net pay from a $2,000 gross salary over two weeks would be $1,535, after deductions totaling $465.
Explanation:
The calculation of Camden's net pay involves subtracting federal withholding, Social Security, and Medicare deductions from his gross pay. Assuming Camden's gross pay is a certain amount, we'll illustrate how to find the net pay. Let's not forget to account for the percentages provided for each deduction category: 15.6% for federal withholding, 6.2% for Social Security, and 1.45% for Medicare.
Calculate Federal Withholding: Gross Pay * 15.6%.
Calculate Social Security Deduction: Gross Pay * 6.2%.
Calculate Medicare Deduction: Gross Pay * 1.45%.
Add all deductions together: Federal Withholding + Social Security + Medicare.
Subtract the total deductions from the Gross Pay to get the Net Pay.
For example, if Camden's gross pay is $2,000 for two weeks, his deductions would be:
Federal Withholding: $2,000 * 15.6% = $312
Social Security: $2,000 * 6.2% = $124
Medicare: $2,000 * 1.45% = $29
Total Deductions: $312 + $124 + $29 = $465
Net Pay: $2,000 - $465 = $1,535
r-23 for r= 32 what is the answer
Answer:
The answer is 9.
Step-by-step explanation:
If r=32, all you do is plug 32 where the r is
32-23=9 as your answer.
find the height of a right rectangular prism with surface area 286 m^2, length 10 m, and width 8 m.
I need this ASAP
Answer: The height of the right rectangular prism is 3.5 meters.
Step-by-step explanation:
To find the height of the right rectangular prism, you need to use the formula of the surface area of a rectangular prism, where [tex]l[/tex] is the lenght, [tex]w[/tex] is the width and the height is [tex]h[/tex]:
[tex]SA=2wh+2lw+2lh[/tex]
Substitute [tex]SA=286[/tex], [tex]l=10[/tex] and [tex]w=8[/tex] into the formula and solve for the height of the right rectangular prism:
[tex]SA=2wh+2lw+2lh\\\\286=2(8)h+2(10)(8)+2(10)h\\\\286=16h+160+20h\\\\286=160+36h\\\\286-160=36h\\\\126=36h\\\\\frac{126}{36}=h\\\\h=3.5\ m[/tex]
Final answer:
Using the surface area formula for a right rectangular prism, the height is calculated to be 3.5 meters after setting up the equation with given surface area, length, and width.
Explanation:
To find the height of a right rectangular prism with a given surface area, length, and width, we can use the surface area formula for a prism: SA = 2lw + 2lh + 2wh, where SA is the surface area, l is the length, w is the width, and h is the height.
Given that the surface area is 286 m2, the length is 10 m, and the width is 8 m, we can set up the equation 286 = 2(10)(8) + 2(10)h + 2(8)h.
Simplify this to 286 = 160 + 20h + 16h, which further simplifies to 286 = 160 + 36h. Subtracting 160 from both sides, we get 126 = 36h. Dividing both sides by 36 gives us h = 3.5 m.
Therefore, the height of the prism is 3.5 meters.
-0.06 as a mixed number is what
Answer:
-3/50
Step-by-step explanation:
-0.06 = -6/100
-6/100 = -3/50
What is the sum of the first 5 prime numbers
Final answer:
The sum of the first 5 prime numbers, which are 2, 3, 5, 7, and 11, is 28.
Explanation:
The sum of the first 5 prime numbers can be calculated by identifying those numbers and adding them together. The first 5 prime numbers are 2, 3, 5, 7, and 11. When we add these numbers, the sum is calculated as follows:
2 (the first prime number)
3 (the second prime number)
5 (the third prime number)
7 (the fourth prime number)
11 (the fifth prime number)
So, the sum would be 2 + 3 + 5 + 7 + 11 = 28.
Write the standard form of the equation of the circle with its center at (-5,0) and a radius of 8 what is the equation of the circle in standard form
Answer:
[tex]\large\boxed{(x+5)^2+y^2=64}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (-5, 0) and the radius r = 8. Substitute:
[tex](x-(-5))^2+(y-0)^2=8^2\\\\(x+5)^2+y^2=64[/tex]
7,,,,,,,,,,,,,,,,,,,,please help
Answer:
1
Step-by-step explanation:
The given expression is
[tex]\frac{2^{\frac{11}{2} }\times 2^{-7}\times 2^{-5}}{2^3\times 2^{\frac{1}{2} }\times 2^{-10}}[/tex]
Recall and use
[tex]a^m\times a^n=a^{m+n}[/tex]
[tex]\frac{2^{\frac{11}{2} -7-5}}{ 2^{3+\frac{1}{2} -10}}[/tex]
[tex]\frac{2^{-\frac{13}{2}}}{ 2^{-\frac{13}{2}}}[/tex]
Same bases are dividing, so we write one base and subtract the exponent.
[tex]2^{-\frac{13}{2}+\frac{13}{2}}[/tex]
[tex]2^0=1[/tex]
You roll a 6-Sided fair die What is the P that you get a number less then 4
Answer:
The answer is 66.6%
Step-by-step explanation:
All you have to do to solve this question is 6÷4
Answer:
66.6
Step-by-step explanation:
Jason and Shawn both begin riding their bikes from different points away from the ranger station. They both ride their bikes in the direction away from the station along the same trail.
Jason starts biking 1 mile away from the station. Jason rides at a constant speed of 20 miles per hour.
Shawn starts biking 2 miles away from the station. Shawn rides at the same constant speed as Jason.
Let y represent the total miles away from the station.
At how many hours, x, will it take Shawn to catch up with Jason?
Based on the information provided, complete each expression below and determine the number of solutions.
Answer:
No Solution
Step-by-step explanation:
Jason starts riding a bike 1 mile from the station.
Shawn starts biking 2 miles from the station.
For Jason to reach Shawn, he needs to go at a higher speed. However we know that they are going at the same constant speed. Then they will never meet.
To prove it we propose the following system of equations. Where x is the hours and y is the distance in miles.
For Jason we have:
[tex]y = 20x + 1[/tex]
For Shawn
[tex]y = 20x + 2[/tex].
We want to know when Jason and Shawn are at the same distance.
Then we write the following eqution and clear x:
[tex]20x + 1 = 20x + 2\\20x -20x + 1 = 2\\1 = 2[/tex]
Equality is not satisfied. Therefore, it has no solution.
I mean Jason and Shawn will never be the same distance
Erik spends $680 for cable television service. The cable company offers a deal that promises Erik 3 free months of cable if he signs a contract with them for $40 per month.
complete the equation below to find th number of months that Erik will have cable television service with his deal. use m to represent the number of months.
Answer:
20
Step-by-step explanation:
Sales tax is an every day example of where________ are used.
Answer:
Sales tax is an every day example of where percents are used
Step-by-step explanation:
" Percentages " are used for sales tax.
What is sales tax ?It is a tax which is a consumption tax required to pay to government for every goods.
Formula to calculate sales tax,
Sales tax = Cost of an item × Rate of sales tax
What is percentage ?Percentage is defined as the quantity in whole quntity, where the whole quantity is always 100.
It is denoted by the symbol "%"
Example - If someone gets 80% in an exam, this means that he scored 80 out of 100.
What is the required answer ?Sales tax is an everyday example of where percentages are used.
Learn more about Percentage here :
https://brainly.com/question/24304697
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please help me can anyone solve this what is x^2+5x-7?
Answer:
x = (-5+-sqrt(53))/2
Step-by-step explanation:
Apply the quadratic formula to this equation with a = 1, b = 5, and c = -7.
Plug it in then simplify.
Quadratic formula is x = (-b+-sqrt(b^2-4ac))/2a