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
Find the modes of this data set.
Answers
Answer:
1, 2
Step-by-step explanation:
the mode is the ones that appear the most in a data set, so since 1 and 2 appear 4 times each, they are the two modes.
Find the verb in the sentence below and decide whether it is action (AV) or linking (LV).
It was a warrant.
verb:
action
linking
Answers
Answer:
was
And it's a linking verb
A line passes through the point (8, -7) and has a slope of -3/2 Write an equation in slope-intercept form for this line
Answers
Answer:
y=mx+b
-7=34 (8)+b
-7=272+b
-280=b
y=34x-280
i might be absolutely wrong
Is 2/3 bigger that 4/7?
Answers
First, convert. Least common multiple of 3 and 7 is 21.
2x7=14 3x7=21.
4x3=12 7x3=21.
The new fractions are 14/21 and 12/21.
Which is bigger?
---
hope it helps
Together Mike and Sara ran 42 laps on the
track. Sara ran twice as many laps as
Mike did. Write a system of equations and
solve it to see how many laps they each ran.
Answers
Answer:
i dont know the system of equations since i only calculated it until i got the right answer but sara did 28 laps and mike did 14
Which two are congruent?
Answers
Answer:
A and E
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth
Answers
Answer:
64.01
Step-by-step explanation:
tan∅= p/b
tan58= x/40
or, x= 40×tan58
x = 64.01
Pets In a group of 150 people, each person has Complete the table.
a dog, a cat, or a bird. The frequency table
shows how many people have each kind of pet. Total Relative Frequency
Complete a relative frequency table to show the
Table
distribution of the data with respect to all
Pets Men Women Total
150 people.
% % %
Cat % % %
Frequency Table
Pets Men Women Total
Bird % % %
Dog 30 38 68
Total % % 100%
Cat 30 19 49
(Round to the nearest tenth as needed.)
Bird 17 16 33
Total 77 73 150
Answers
Explanation is in the file
tinyurl.com/wpazsebu
A block of marble is in the shape of a rectangular prism. The block is 2 feet long. 3 feet wide, and 90 inches high. What is the volume of the block? The volume of the block is cubic feet
Answers
Answer:
Volume of a rectangular prism can be found with the equation
v = length × width × height
They are trying to trip you up a little bit here because they give 2 measurements in feet then the last in inches. So for your prism...
18 inches = 1.5 ft
v = l×w×h
v = 3×2×1.5
v = 9 ft^3
Volume=length*width*height, so first you would have to change the units of the inches to feet, which would be 90/12=7.5, so now you can fit that into the equation, 2*3*7.5=45 ft cubed!
I would appreciate it if someone helped me:)
Answers
Answer:
24 more chocolotae chip cookies are sold
Step-by-step explanation:
CCC 7(15)+6 105+6=111
SC 6(15)-3 90-3 = 87
111-87 = 24
how do you find the indivisuil of 4 divided by 6
Answers
Answer:
6
Step-by-step explanation:
Answer:
u use like 4/6=2/3=0.6
Alexander is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he flips a coin and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?
Answers
Answer:
its 24
Step-by-step explanation:
delta math said it was right
Answer is 12.
Possible Outcomes:
It is a list of all the resulting possibilities from an event.
(Here),
when he flips the coin, there are 2 outcomes = {front, back}
When he rolls a die, there are 6 outcomes = {1, 2, 3, 4, 5, 6)
For every outcomes of coin there are 6 outcomes of a die.
So, Possible outcomes = 2 * 6 = 12.
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#SPJ2
find the value of given expression
=》
[tex] \sqrt[3]{65 - 1} [/tex]
Answers
Answer:
Answer is 4 I hope this help you
Answer:
4
Step-by-step explanation:
[tex] \sqrt[3]{65 - 1} \\ \\ = \sqrt[3]{64} \\ = 4[/tex]
What is the y-intercept of a line through (2, 7) and perpendicular to the
graph of y=-3/2x+6
Answers
Answer:
it is y=-3/2x+6 and then you subtract it by 2 and then add 7 and then u get 49
Step-by-step explanation:
Find the radius given the circumference is equal to 50.24 ft (hint: π = 3.14)
Answers
Answer:
Check pdf
Step-by-step explanation:
Answer:
4ft
Step-by-step explanation:
circumference of circle = π r^2
=> circumference = 50.25 ft
=> πr^2 = 50.25 ft
=> r^2 = 50.25/3.14 = 16 ft
=> r = √16
=> r = 4 ft
hope it helps
Need some help with this one!!!
Answers
Answer:
210
Step-by-step explanation:
2 x 3 x 5 x 7 = 210
4. Phil bought a block of cheese in the shape of a triangular prism measuring 8 inches by 4 inches by 2 inches. What is the volume of the block of cheese?
Answers
Answer:
32 inches^3
Step-by-step explanation:
Volume = 1/2 ( base x height x length)
0.5 ( 4 x 2 x 8) = 32 inches^3
please help!!! will mark brainliest
Answers
Answer:
2nd one I believe
Step-by-step explanation:
All points of a sphere are ______ equal distances to its center.
Always
Never
Sometimes
Answers
A) Always
In a perfect sphere the centre is an equal distance from any point from the surface.
THANK YOU!!
∝ Sidhdi
Convert 0.3 to a percentage.
Answers
[tex] \sqrt{ {4 a}^{2} + {12a}^{2} } [/tex]
Answers
Answer:
The answer is 4a
Step-by-step explanation:
1) Simplify 4a² + 12a² to 16a².
[tex] \sqrt{ {16a}^{2} } [/tex]
2) Use this rule:
[tex] \sqrt{ab} = \sqrt{a} \sqrt{b} [/tex]
[tex] \sqrt{16} \sqrt{ {a}^{2} } [/tex]
3) Since 4 × 4 is 16, the square root of 16 is 4.
[tex]4 \sqrt{ {a}^{2} } [/tex]
4) Simplify.
[tex]4a[/tex]
Therefor, the answer is 4a.
Choose the solution to this inequality.
Answers
It’s B
Have a good day and here is a bobcat
The answer is c because 8-4is 4 and 3 (dominator) stays the same
The average baby giraffe weighs 150 pounds and is 6 feet tall.
Question 1
Part A
How many kilograms does a baby giraffe weigh?
Answers
Answer:
68 kilograms
Step-by-step explanation:
Find the values of the missing angles
HELP PLEASE DO ANY! I’ll give you brilliance
Answers
Answer:
1) x = 42 ; y = 42
2) x = 72 ; y = 48 ; z = 60
Step-by-step explanation:
1)
x + 42 + 96 = 180
x + 138 = 180
x = 42
y + 42 + 96 = 180
y + 138 = 180
y = 42
2)
x + 108 = 180
x = 72
y + 132 = 180
y = 48
z + x + y = 180
z + 72 + 48 = 180
z + 120 = 180
z = 60
Simplify the expression.
30 - 7m + 5 + 16m
Answers
Answer:
[tex]35 + 9m[/tex]
Step-by-step explanation:
1) Collect like terms.
[tex](30 + 5) + ( - 7m + 16m)[/tex]
2) Simplify.
[tex]35 + 9m[/tex]
Therefor, the answer is 35 + 9m.
A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park the opening day ticket sales for the park including pre-sales is represented by this function where T(h) is the number of tickets sold H hours after opening at 7:00.am.
What is the approximate rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m?
HELP PLEASE I WILL MARK BRAINLIEST!!♥️
Answers
Answer:
-21 tickets per hour
Step-by-step explanation:
I think it's right
Answer:
Therefore, the correct answer is option C. 21 tickets per hour.
Step-by-step explanation:
Given: the opening day ticket sales for the park is given by the function[tex]T(h)=\frac{386+110h}{h}[/tex] where [tex]T(h)[/tex] represents the number of tickets sold [tex]h[/tex] hours after opening at 7:00 a.m.
To find: the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m.
For 10 a.m., [tex]h=3[/tex]
So the number of tickets sold upto 10 a.m. are,
[tex]T(3)=\frac{386+110 (3)}{3}[/tex]
[tex]T(3)=238.67[/tex]
Similarly, for 1 p.m., [tex]h=6[/tex] hours
So, the number of tickets sold in 6 hours are,
[tex]T(6)=\frac{386+110(6)}{6}[/tex]
[tex]T(6)=174.33[/tex]
Now, the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m is,
[tex]\frac{T(6)-T(3)}{6-3}[/tex]
[tex]=\frac{174.33-238.67}{3}[/tex]
[tex]=-21.445[/tex]
which is approximately [tex]-21[/tex] tickets per hour.
Hence, the rate of change in the number of tickets sold between 10:00 a.m and 1:00 p.m is -21 tickets per hour.
The correct answer is option C.
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I need help please if you will
Answers
Answer: 4
Step-by-step explanation:
Sorry for the wait, I am busy verifying my work.
please help me!!! I’ll give you Brainly
Answers
Write a proportion to find how many
points a student needs to score on the
test to get the given score.
1. Test worth 60 points; test score of
60%.
Answers
Answer:
59 and umm... I dont know
Someone help and plz make sure it’s right plz! :)
Answers
Answer:
-21/4
Step-by-step explanation:
slope = y2-y1/ x2-x1
-18 - 3 / 17-13 = -21/4