Answers
Answer: x = 10
Step-by-step explanation:
The Pythagorean's theorem says that for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:
A^2 + B^2 = H^2
In this case, we have:
A = (x - 4)
B = (x - 2)
H = x
Then we have the equation:
(x - 4)^2 + (x - 2)^2 = x^2
Now we need to solve this for x, first let's simplify it.
(x^2 - 2*x*4 + 16) + (x^2 - 2*2*x + 4) = x^2
2*x^2 - 12*x + 20 = x^2
2*x^2 - 12*x + 20 - x^2 = 0
x^2 - 12*x + 20 = 0
The solutions of this equation are given by the Bhaskara's equation, such that for an equation like:
a*x^2 + b*x + c = 0
The solutions are:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
Then the solutions for our equation are:
[tex]x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4*1*20} }{2*1} = \frac{12 \pm 8 }{2}[/tex]
Then the two possible solutions are:
x = (12 - 8)/2 = 4/2 = 2
Notice that if x = 2, then the length of the catheti will be:
A = 2 - 4 = -2
B = 2 - 2 = 0
This has no sense, so we can discard this solution.
The other solution for x is:
x = (12 + 8)/2 = 10
x = 10
Then:
H = 10
A = 10 - 4 = 6
B = 10 - 2 = 8
This solution makes sense, then x = 10.
Related Questions
I need to know the answer to the question
Answers
Answer:
X=4
Step-by-step explanation:
Answer and Step-by-step explanation:
To get x, we need to put everything on the right. We start off by multiplying each side by 3.
3 × [tex](\frac{7+2x}{3} ) =[/tex] 5 × 3
7 + 2x = 15
Now, we subtract 7 from each side.
(7 + 2x) - 7 = 15 - 7
2x = 8
Finally, we divide each side by 2.
2x ÷ 2 = 8 ÷ 2
x = 4
The answer to this equation is x = 4.
I hope this helps!
A thanks and 5 stars + brainliests are appreciated, but I help to help!
#teamtrees #PAW (Plant And Water)
Someone Please Help Me!
Answers
9514 1404 393
Answer:
discrete
Step-by-step explanation:
"The number of (anything)" means the possible values are counting numbers. The random variable involved is necessarily discrete.
Find the area of four walls of a room (Assume that there are no doors or windows) if its length 12 m., breadth 10 m. and height 7.5 m. ?
Answers
Answer:
Refer to the attached file
Hope it helps..
Have a great day : )
Answer:
Hopefully u will satisfy with my answer..!!SOLVE: 3/4 x 4/5 = *
Answers
3
4
×
4
5
=
3
5
Result in decimals: 0.6
Calculation steps:
3
4
×
4
5
=
3 × 4
4 × 5
=
12
20
=
12 ÷ 4
20 ÷ 4
=
3
5
1.6 × 10^6 ÷ 4.8 × 10^5. Give your answer as a mixed number
Answers
Answer:
(10^11)/3
10^6 x 10^5 = 10^11
8/5 x 5/24 = 1/3
so multiply 10^11 and 1/3 together
Tina's gross pay is $2860. How much of her gross pay will be deducted for FICA taxes? (The Social Security tax is 6.2% of gross pay. The Medicare tax is 1.45% of gross pay.)
$218.79
$205.02
$177.32
$41.47
Answers
-3(d + -2) + -4 = 5
solve for d
Answers
Answer:
d=−1
Step-by-step explanation:
−3(d−2)−4=5
Step 1: Simplify both sides of the equation.
−3(d−2)−4=5
(−3)(d)+(−3)(−2)+−4=5(Distribute)
−3d+6+−4=5
(−3d)+(6+−4)=5(Combine Like Terms)
−3d+2=5
−3d+2=5
Step 2: Subtract 2 from both sides.
−3d+2−2=5−2
−3d=3
Step 3: Divide both sides by -3.
−3d
−3
=
3
−3
d=−1
[tex]-3(d+(-2))+(-4)=5[/tex]
[tex]-3d-6+(-4)=5\\-3d-10=-5\\-3d=5\\3d=-5\\d=-\frac{5}{3}[/tex]
help ASAP please! ill mark u brainliest
Answers
Answer:
box and whisker
Step-by-step explanation:
A florist used 18 flowers to make a bouquet, including 8 lilies.
What is the probability that a randomly selected flower will be a lily?
Write your answer as a fraction or whole number.
Answers
Answer:
4/9 will be the probability.
Hope it helps you!!
a.f(a)=22
b.f(a)=37
c.f(a)=32
d.f(a)=42
Answers
Answer:
with no question asked the answer could be anyone of the options
Step-by-step explanation:
Find the Slope-intercept equation of the line which passes through (3, -4) and (-3, 8).
Answers
Answer:
y = -2x + 2
Step-by-step explanation:
8 + 4/ -6
= -2
y = -2x + b
8 = -2(-3) + b
8 = 6 + b
2 = b
check work
-4 = -2(3) + 2
-4 = -6 + 2
-4 = -4
it is correct
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y - x = -12.
Answers
Answer:
3y=x-12
y=x/3-4
m=1/3
At (18,2)
y-2=1/3(x-18)
y-2=x/3 - 6
y=x/3 - 4
The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of ANB. Compute the whole number value of 2021 squared -2022The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of A and B. Compute the whole number value of 2021 squared -2020 squared
Answers
Question:
The identity [tex]A^2 - B^2 = (A + B) (A - B)[/tex] is true for all values of A and B. Compute the whole number value of [tex]2021^2 -2022^2[/tex]
Answer:
[tex]2021^2 - 2022^2 = -4043[/tex]
Step-by-step explanation:
Given
[tex]A^2 - B^2 = (A + B) (A - B)[/tex]
Required
Solve: [tex]2021^2 -2022^2[/tex]
In: [tex]2021^2 -2022^2[/tex]
[tex]A = 2021; B = 2022[/tex]
[tex]A^2 - B^2 = (A + B) (A - B)[/tex] becomes
[tex]2021^2 - 2022^2 = (2021 + 2022)(2021 - 2022)[/tex]
[tex]2021^2 - 2022^2 = (4043)(-1)[/tex]
[tex]2021^2 - 2022^2 = -4043[/tex]
PLEASE HELP ME PLEASE PLEASE PLEASE
Answers
Answer:
Step-by-step explanation:
l/100 km means liters per 100 Kilometre. How many liters a car need for traveling 100 km.
Km/l means liter per km
Help meeeee pweaassee!!
Answers
Answer:
7. divide both sides by 18.
8. subtract 4 from both sides.
9. add 3 on both sides.
10. multiply by 6 on both sides
Hope that helps! :3
Step-by-step explanation:
Can I have some help please
Answers
Answer:
I think it's trapezium .
Please help and explain please. would appreciate it!
Answers
Answer:
area of ΔAPQ = 8 units²
Step-by-step explanation:
since the dimensions are 1/3 size, the area scale factor will be 1/9.
72/9 = 8 units²
Answer:
Step-by-step explanation:
A/4=72/12
A=4(72)/12
A=24 u^2
Tools
Question 11
The table shows the relationship between y, the cost to rent a boat, and the amount of time the boat is rented,
Boat Rental Costs
Time, X Cost, v
(hours) (dollars)
1
3
5
80
7
104
Which graph best represents the relationship between x and y shown in the table
Answers
A local hotel has 158 rooms. Due to a scouting event, the entire hotel booked except for two rooms. If the girls scouts are using three times as many rooms as the boy scouts, how many rooms are the boy scouts using?
Answers
Answer:
39
Step-by-step explanation:
Let, total rooms girls booked be x and total rooms girls booked be y.
entire hotel was booked except two rooms.
so, total = 158-2 = 156
x+ y = 156
this is equation 1.
also, girls are using three times more room than boys.
so, y=3x
substituting y=3x in 1st equation,
x+ 3x = 156
or, 4x = 156
or, x= 156/4
x= 39
need help please 9× > 108
Answers
Answer:
x > 12
Step-by-step explanation:
9x>108
x> 108/9
x > 12
Answer:
[tex] \boxed{ \tt{x > 12}}[/tex]
Step-by-step explanation:
[tex]9x > 108 \\ x > \frac{108}{9} \\ x > 12[/tex]
A cube has a total surface area of 150 inches squared. Considering every side length is
congruent, and every face equivalent on a cube, what is the side length?
Answers
Answer:25.0
Step-by-step explanation: 5.0 times 5.0
Ian paints /8 of a fence. Anna paints 3/4 of another fence. Draw a number line to show that Ian and Anna have painted the same amount of each fence.
Answers
Answer:
See attachment for number line
Step-by-step explanation:
Given
[tex]Ian = \frac{6}{8}[/tex]
[tex]Anna = \frac{3}{4}[/tex]
Required
Number line to represent both amounts
The interval on the number line is 16.
So, we need to calculate the position of both as thus.
[tex]Ian = \frac{6}{8} * 16 = \frac{96}{8} = 12[/tex]
[tex]Anna = \frac{3}{4} * 16 = \frac{48}{4} = 12[/tex]
So, both will be positioned on the 12th position.
The yellow dot represents Anna while the blue dot represents Ian
See attachment for their position on the number line
. A soccer ball manufacturer claims the diameters of their ball have a standard deviation of 2 mm when properly inflated. Based on a random sample of 10 balls you find a standard deviation of 3.2 mm. Does the sample suggest the standard deviation is higher than that claimed by the manufacturer?
Answers
Answer:
Yes, there is significant evidence to support the claim that sample standard deviation is higher than that claimed by the manufacturer
Step-by-step explanation:
Sample standard deviation, s = 3.2
Population standard deviation, σ = 2
Defining the Null and alternative hypothesis :
H0 : σ = 2
H1 : σ > 2
The test statistic :
Use the Relation :.
[(n - 1)*s²] ÷ σ²
[(10 - 1) * 3.2²] ÷ 2²
(9 * 10.24) ÷ 4
92.16 ÷ 4
= 23.04
We obtain the Pvalue for the distribution :
Using the Pvalue from Chisquare distribution calculator :
Pvalue(Chisquare score, df)
df = n - 1 = 10 - 1 = 9
Pvalue(23.04, 9) = 0.006107
Decision :
If Pvalue is < α ; Reject H0 ; α = 0.05
0.006107 < 0.05 ; We reject H0
WILL GIVE BRAINLIEST
Answers
36 + 64 = 100
100 = 100
so yes because 6² + 8² = 10²
Option B
Find an equation for the line below
Answers
Hope this helps!
y=mx+b
first do rise over run so it goes down 3 units and to the right 6 units then you simplify 3/6 to the smallest fraction which would be 1/2 and since the line is going down horizontally the slope(1/2) would be negative then you simply see where the line crosses the y-axis and that is the "b"(4.5) for the equation now all you gotta do is plug in the numbers and you get
y=-1/2x+4.5
PLEASE HELP!!
Question 1 of 5
Solve the following equation for x using a table of values (nearest fourth of a unit), graphing technology, and successive
approximation (three iterations). The solution lies between x = -2 and x = -1.
x + 3 = 2 (- x - 1)
Select the correct order that shows the least accurate to most accurate method of approximation.
Lowest Accuracy: Table of values: x= -1.5
Intermediate Accuracy: Successive approximations: x-1.5625
Highest Accuracy: Graphing technology: x-1.543
O
Lowest Accuracy: Table of values: X~ -1.5
Intermediate Accuracy: Graphing technology: x -1.543
Highest Accuracy: Successive approximations: x-1.5625
O
Lowest Accuracy: Successive approximations: x= -1.5625
Intermediate Accuracy: Table of values: x-1.5
Highest Accuracy: Graphing technology: x -1.543
o
Lowest Accuracy: Graphing technology: x-1.543
Intermediate Accuracy: Successive approximations: x= -1.5625
Highest Accuracy: Table of values: x-1.5
Answers
Answer:
lowest accuracy: Table of values:x=-1.5
intermediate accuracy: successive approximate: x=-1.5625
Highest accuracy: Graphing technology: x=1.543
Step-by-step explanation:
i just did this question
does the volume method length x width x height apply to all volume finding questions
Answers
Answer:
No.
Step-by-step explanation:
This only applies to solids like cubes and some prisms.
It does not apply to such solids are cylinders, pyramids, cones and triangular prisms. It will apply to a prism whose cross-section is a rectangle.
IM MARKING BRAINLIEST
Valerie replaces one car alternator every 1.75 hours. She takes a 1-hour lunch break.
Which equation can be used to determine how many alternators she replaces in 8 hours?
Multiple choice question.
A)
1.75w−1=8
B)
1.75w+1=8
C)
18w−1=8
D)
18w+1=8
Answers
Answer:
A)
1.75w−1=8
Step-by-step explanation:
20 feet. The builder asks him to give the measurements in yards. What will be the length in yards?Immersive Reader
Answers
Answer:
6.67 yards
Step-by-step explanation:
20 feet. The builder asks him to give the measurements in yards. What will be the length in yards?
Please note that:
1 foot = 0.333 yard
20 feet = x yards
Cross Multiply
1 foot × x yards = 20 feet × 0.333 yards
x yards = 20 feet × 0.333 yards/1 foot
x yards = 6.66667 yards
Approximately = 6.67 yards
Therefore, the measurements in yards is 6.67 yards.
Amy works at an orange juice stand on Monday she used 1 2/5 bags of oranges on Tuesday she used 1 1/4 times as many oranges as on Monday how many bags did she use on tuesday do you know???
Answers
You multiply them and get 7/4 which equals 1 3/5 bags.
