Answers
If we're dealing with a right triangle, then the sum of the squares of the 2 shorter sides of the triangle is equal to the square of the hypotenuse:
a^2 + b^2 = c^2
In your particular problem, a = x+6, b= x+3, and c = x+9.
Then (x+6)^2 + (x+3)^2 = (x+9)^2
so: x^2 + 12x + 36 + x^2 + 6x + 9 = x^2 + 18x + 81
Cancel x^2 from both sides. Then you have
12x + 36 + x^2 + 6x + 9 = 18x + 81
Now group all the x terms together on the left side:
12x + x^2 + 6x - 18x + 36 + 9 - 81 = 0
Combine all the x terms. Combine all the constants.
x^2 - 36 = 0 Factor this: (x-6)(x+6) = 0
Then x=6 and x=-6. We must check whether one or both of these results is correct before calling it a "solution."
Example: (-6+6)^2 + (-6+3)^2 = (-6+9)^2 True or false?
0 + 9 = 9 True! so x = -6 is a solution.
You MUST also check to determine whether or not 6 is also a solution.
Related Questions
what is 5/9-2/3×5/2=
Answers
5/9-5/3=
-10/9
Answer:
5/9-2/3×5/2=
5/9-5/3=
-10/9
Step-by-step explanation:
Which answer shows these decimals written in order from greatest to least? 23.697 23.72 22.8
Answers
23.72
23.697
22.8
The more decimal numbers, the smaller the number gets.
BJ's Game Store buys video games for $30. They charge the customers $50 for the games. What is the percent markup ?
Answers
The markup percentage for the video games is 66.67%.
Markup Percentage Calculation:
Calculate the markup by subtracting the cost price from the selling price: $50 - $30 = $20.To find the markup percentage, divide the markup by the cost price and multiply by 100: ($20 / $30) * 100 = 66.67%.What scientific value for n will make this equation true?
(4.8 × 10–3)(n) = 9.6 × 109
Answers
To make the equation (4.8 × 10^–3)(n) = 9.6 × 10^9 true, the value of n is 2 × 10^12.
Explanation:To make the equation (4.8 × 10–3)(n) = 9.6 × 109 true, we need to find the value of n. Let's solve the equation:
First, divide both sides of the equation by (4.8 × 10–3). This simplifies the equation to n = (9.6 × 109) / (4.8 × 10–3).
Next, simplify the right side of the equation by dividing the numbers and subtracting the exponents: n = (9.6 / 4.8) × 109-(-3) = 2 × 1012.
Therefore, the scientific value for n that makes the equation true is 2 × 1012.
Final answer:
To solve for n in the equation (4.8 × 10–3)(n) = 9.6 × 10⁹, divide both sides by 4.8 × 10–3. After dividing the coefficients and subtracting the exponents, the scientific value for n is 2 × 10².
Explanation:
To find the scientific value for n that makes the equation (4.8 × 10–3)(n) = 9.6 × 10⁹ true, we need to isolate n by dividing both sides of the equation by 4.8 × 10–3.
Divide each side by 4.8 × 10–3 to get:
n = (9.6 × 10⁹) / (4.8 × 10–3)
Now, we divide the coefficients (9.6/4.8) and subtract the exponents of 10 (9 - (-3)) to find n:
n = 2 × 10²
So, the scientific value for n is 2 × 10².
Write the following phrase as an algebraic expression. Use n for “a number.” three increased by the quotient of a number and two
Answers
The phrase 'three increased by the quotient of a number and two' translated into an algebraic expression is '3 + n/2'.
Explanation:To convert the given phrase 'three increased by the quotient of a number and two' into an algebraic expression, we first need to understand the mathematical operations involved in the phrase. 'increased by' is typically addition, 'the quotient of a number and two' signifies division. Using 'n' to represent 'a number', 'the quotient of a number and two' can be represented as 'n/2'. Now, 'three increased by the quotient of a number and two' can be written as '3 + n/2'. So, the algebraic expression for 'three increased by the quotient of a number and two' is '3 + n/2'.
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A boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.25 he saved. How much money did he have originally?
Answers
So, [tex] \frac{x}{2} [/tex] + [tex] \frac{x}{3} [/tex] + 2.25 = x
or, [tex] \frac{3x+2x+(6*2.25)}{6} = x [/tex]
or, 5x + 13.5 = 6x
or, x = 13.5
So, he had $13.5 originaly.
Thanks!
The required money that the boy has is $13.50 initially.
Given that,
A boy spent one-half of his money on a book and one-third of his money on a pen. The remaining $2.25 he saved, how much money he had originally to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the money boy has to be x,
According to the question,
x - x/2 -x /3 = 2.25
x(1 / 6) = 2.25
x = 2.25 × 6
x = $13.50
Thus, the required money that the boy has is $13.50 initially.
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A truck with a heavy load drove from Boston to New York at 45 mph. After unloading, it returned from New York to Boston at a speed of 65 mph. What was its average speed for the whole trip?
Answers
Answer:
Average speed: 585/11 or 53 2/11
Step-by-step explanation:
Let distance from New York to Boston, and vice-versa, be D
Then, time taken to travel from Boston to New York is: D/45
Also, time taken to travel from New York to Boston is: D/65
Total time taken for entire trip: D/45+D/65
Average speed: total distance/total time
Average speed: 2D/22D/585
Average speed: 53 2/11 or 585/11 mph
ac and bd are perpendicular bisectors of each other. find the perimeter of ADE
Answers
AC and BD are perpendicular bisectors of each other.
=> ABCD is rhombus.
AD = 13
AE = √(13^2 - 12^2) = 5
the perimeter of triangle ADE = 13+12+5 = 30A small fruit smoothie is 18 ounces while a large fruit smoothie is 21.96 ounces. The large fruit smoothie is _% larger
Answers
3.96 divided by 18 = 0.22
Move .22 to a %
22 % increase
if it takes 3 hours for 8 workers to paint a fence, how long would it take for 6 workers.
SHOW WORKING
Answers
Final answer:
It would take 6 workers 4 hours to paint the fence, as the total amount of work, 24 worker-hours, divided by 6 workers, gives 4 hours.
Explanation:
Let's tackle the problem by first determining the total amount of work done when 8 workers paint a fence in 3 hours. This work can be considered as 24 worker-hours (since 8 workers * 3 hours = 24 worker-hours). This total amount of work would stay the same regardless of the number of workers. So if 6 workers are going to do the same job, we'd divide the total work by the number of workers to find out how many hours it would take for 6 workers to complete the task.
Dividing the 24 worker-hours by 6 workers, we get:
24 worker-hours / 6 workers = 4 hours
Therefore, it would take 6 workers 4 hours to paint the fence.
What is the value of b? −7.5(x−3)=3.75 Enter your answer in the box.
Answers
Answer:
premium answer :D
Step-by-step explanation:
I don't get this at all and it's confusing me
Answers
• Destiny’s time (1 lap) = 1 1/2 minutes (1 minute 30 seconds)
• Thelma’s time (1 lap) = 2 minutes
Now, we have to find the combination to find the amount t time it takes to run the number of laps that was given. In this case, we have to multiply Destiny’s time per lap by 5 and Thelma’s time per lap by 3. If you do this correctly, your answer should be:
• Destiny’s total time (5 laps) = 7 1/2 minutes (7 minutes 30 seconds)
• Thelma’s total time (3 laps) = 6 minutes
Describe how you would use Distributive Property to simplify (39 x 5).
Answers
PL has endpoints P(4, −6) and L(−2, 1). The segment is translated using the mapping (x, y) → (x + 5, y). What are the coordinates of P’ and L’? P’(9, -6), L’(-2, 1) P’(4, -6), L’(3, 1) P’(9, -6), L’(3, 1) P’(9, -1), L’(3, 6)
Answers
Answer: C P’(9,-6), L’(3,1)
The coordinates of P' and L' after the translation are (9, -6) and (3, 1) respectively.
Explanation:A translation rule in mathematics describes the process of moving a geometric figure from one location to another without changing its shape or orientation. It involves shifting the figure horizontally or vertically by a certain distance. Translation rules are essential in geometry and are used to analyze and manipulate shapes on a coordinate plane.
The segment PL has endpoints P(4, -6) and L(-2, 1). To find the coordinates of P' and L' after being translated using the mapping (x, y) → (x + 5, y), we simply add 5 to the x-coordinates of P and L. Therefore, the coordinates of P' are (4 + 5, -6) which is equal to (9, -6), and the coordinates of L' are (-2 + 5, 1) which is equal to (3, 1).
Please help me with #1
Answers
let apple juice = x
milk = 2x
fruit punch = 3x
3x + 2x + x = 660
6x = 660
x = 660/6
x = 110 apple juices
2*110 = 220 milks
3*110 = 330 fruit punches
Melissa's employer purchased a health insurance plan that costs $475 per month and requires that Melissa pay $85 toward the plan. What is the annual value of the employer's contribution
Answers
So, the employer's monthly contribution to the total cost of the plan is $475-$85=$390.
Therefore, over the course of one year, the employer would contribute $390*12=$4680.
Answer:
4680 is correct
Step-by-step explanation:
math question down below
Answers
Leon bought a dozen daisies for $3.75. What is the amount he paid per daisy (round to the nearest hundredth place)?
Answers
The amount he paid for per dairy is (rounded to the nearest hundredth would be) $0.31 (31 cents)
What is division?Division is the process of splitting a number or an amount into equal parts.
Here, given that,
Leon bought a dozen dairies for $3.75
i.e. cost of 12 dairies = $3.75
Then, cost of per dairy = $3.75÷12
=$0.3125
(The answer would be $3.75/12 which equals to $0.3125. )
Hence, The amount he paid for per dairy is $0.31.
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A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
Answers
A culture of 6.25×10^15 bacteria is in petri dish B
so
1.75×10^18 / 6.25×10^15 = 0.28 x 10^3 = 280
answer
280 <------------ in standard notation
Helpp pls Whwt does this mean
Answers
162 water bottles in 9 cases, write each ratio as a unit rate
Answers
I dont really see why ur answer was marked " no " because all u did was reduce the fraction instead of simply dividing 162 by 9.....but the way u did it resulted in the same answer....because ratios are basically just equivalent fractions
In which quadrant does the point (-16, 13) lie?
A. Quadrant III
B. Quadrant I
C. Quadrant II
D. Quadrant IV
Answers
you have 12 cups of granola and 8 1/2 cups of peanuts to make trail mix. what is the greatest number of full batches of trail mix can you make?
Answers
To determine the greatest number of full batches of trail mix that can be made, divide the total quantity of each ingredient by the required amount per batch.
Explanation:To determine the greatest number of full batches of trail mix that can be made, we need to compare the quantities of granola and peanuts. First, we calculate the number of full batches we can make using granola. Since each batch requires 12 cups of granola, we divide the total quantity of granola (12 cups) by the required amount per batch (12 cups). The result is 1 full batch.
Next, we determine how many batches we can make using the peanuts. Since each batch requires 8 1/2 cups of peanuts, we divide the total quantity of peanuts (8 1/2 cups) by the required amount per batch (8 1/2 cups). The result is 1 full batch.
Therefore, the greatest number of full batches of trail mix that can be made is 1 batch.
how do I solve this problem
Answers
to convert a fraction to a decimal, divide the top number by the bottom number
2 divided by 7 = 0.2857
rounded to the nearest thousandth = 0.286
Two plans for reaching a goal are given below. Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour. Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour. Which of the following is a true statement?
Answers
Both plans will work for achieving the goal.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Two plans for reaching a goal are given below.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
Then the total amount after 8th weeks will be
⇒ 8 x 9 x 7.20
⇒ $518.4
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
Then the total amount after 8th weeks will be
⇒ 6 x 15 x 6.5
⇒ $585
Both plans will work for achieving the goal.
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The volume of a baseball is about 13.39 cubic inches. What is the diameter? Round to the nearest tenth.
Answers
a number decreased by 12 is 24
Answers
x - 12 = 24
x = 24 + 12 =
36
Find m <ABC (7x-1) (3x-9
Answers
10x-10=180
Add 10 to both sides
10x=170
Divide both sides by 10
X=17 degrees
3x-9
3(17)-9
51-9
=48
Answer:
Therefore, [tex] \angle ABC = 48\degree[/tex]
Step-by-step explanation:
We need to find the [tex] \angle ABC[/tex]
Since, [tex] \angle DBC = 180\degree[/tex] ( since DBC is straight line )
[tex](7x-1)+(3x-9)=180\degree[/tex]
[tex]10x-10=180 \degree[/tex]
Add both the sides by 10 in above expression
[tex]10x-10+10=180\degree+10[/tex]
[tex]10x=180 \degree+10[/tex]
[tex]10x=190 \degree[/tex]
divide both the sides by 10 in above expression
[tex]x=\frac{190}{10}[/tex]
[tex]x=19 [/tex]
Hence, the value of x is 19.
Now, we will calculate [tex] \angle ABC[/tex]
[tex] \angle ABC = 3x-9[/tex]
Put x = 19 in above
[tex] \angle ABC = 3(19)-9[/tex]
[tex] \angle ABC = 57-9[/tex]
[tex] \angle ABC = 48[/tex]
Therefore, [tex] \angle ABC = 48[/tex].
A teacher let her students grade their math quizzes. •Jon wrote 13 out of 18 •Jim wrote .7 (repeated .7) •Joe reduced his to 5/6 who had the higher grade?
Answers
Answer:
Joe
Step-by-step explanation:
Jon wrote 13 out of 18
Dividing 13 by 18 we get, decimal form
[tex]\frac{13}{18}=0.722........[/tex]
Jim wrote .7 (repeated .7)
0.777..........
Joe reduced his to 5/6
Dividing 5 by 6 we get, decimal form
[tex]\frac{5}{6}=0.833........[/tex]
These numbers are irrational numbers
0.833......>0.777........>0.722......
So, Joe had the higher grade.
The volume of a cone is 1004.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.) 64 32 8 4
Answers
[tex]V=\frac{1}{3} \pi r^{2}h[/tex]
[tex]1004.8=\frac{1}{3}(3.14)(15)r^2[/tex]
[tex]64=r^2[/tex]
[tex]r=8[/tex]
Answer:
r=8 8 is the answer
Step-by-step explanation: