In the right triangle below, an altitude is drawn to the hypotenuse. Solve
for x.
Answers
Answer:
x = 4
Step-by-step explanation:
Right Triangles
In right triangles, where one of the internal angles is 90°, the Pythagora's Theorem is satisfied:
If m is the hypotenuse of a right triangle, and p, q are the shorter sides or legs, then:
[tex]m^2=p^2+q^2[/tex]
If we need to calculate any of the legs, say, p:
[tex]p^2=m^2-q^2[/tex]
The figure below shows two additional variables z and h which will help us to find the value of x.
The triangle with sides 12, 36, z can be solved for z, being 36 the hypotenuse:
[tex]z^2=36^2-12^2=1296-144=1152[/tex]
The base of the triangle to the left is (36-x), the height is h, and the hypotenuse is z, thus:
[tex]h^2=z^2-(36-x)^2[/tex]
Substituting z:
[tex]h^2=1152-(36-x)^2[/tex]
The triangle to the right has dimensions x, h, and 12, and:
[tex]h^2=12^2-x^2[/tex]
Equating both expressions for h:
[tex]1152-(36-x)^2=12^2-x^2[/tex]
Expanding the squares:
[tex]1152-1296+72x-x^2=144-x^2[/tex]
Simplifying the x squared and operating:
-144+72x=144
Adding 144:
72x = 288
Solving:
x = 288 / 72 =4
x = 4
Related Questions
How many hours would someone who earns $7.50 per hour have to work to earn $116.25?
15.5
123.75
6.45
108.75
Answers
Answer:
15.5 hours
Step-by-step explanation:
cause i know
Write and evaluate the expression. Then, complete the statements.
A 1-column table with 5 rows. Column 1 is labeled Multiplication Words with entries double, multiply, product, twice, times.
Yuna ran three times as many kilometers.
Evaluate when k = 12.2.
Answers
Answer:
Write and evaluate the expression. Then, complete the statements.
A 1-column table with 5 rows. Column 1 is labeled Multiplication Words with entries double, multiply, product, twice, times.
Yuna ran three times as many kilometers.
Evaluate when k = 12.2.
First, write the expression as
✔ 3k
.
Second,
✔ substitute
12.2 in for the variable, k.
Third,
✔ simplify
by
✔ multiplying
3 and 12.2.
The answer is
✔ 36.6
Since Yuna ran three times as many kilometers so here expression should be 3k and the answer is 36.6
The writing and evaluating the expression:Expressions are considered to be mathematical statements that have at least of two terms comprised of numbers or variables that should be linked. It could be of addition, subtraction, multiplication, or division.
First, write the expression as 3k
Second, substitute 12.2 in for the variable, k.
Third, simplify by ✔ multiplying 3 and 12.2.
And, finally, The answer is 36.6
Learn more about expression here: https://brainly.com/question/11656147
A small business borrows $50,000 to get started. Some of the money is borrowed at 9%, some at 7%, and some at 10% simple interest. The total of the annual interest they are charged is $4340, and the amount borrowed at 7% is two times the amount borrowed at 9%. Set up a system of equations to represent the situation, then find the amounts of money (x, y, and z) borrowed at each interest rate.
Answers
Answer: Amount borrowed at 9% = 9,428.57
Amount borrowed at 7% = $18,857.14
Amount borrowed at 10% = $ 21,714.29
Step-by-step explanation:
Formula for simple interest :
I = PRT,
P= Principal, R =rate , T= time
Let x = amount borrowed at 9%.
y = amount borrowed at 7%.
z = amount borrowed at 10%.
i.e. x+y+z= 50000 (i) [Given : amount invested = 50000]
Interest on x = x (0.09)(1) [as P=x, T=1 year, r= 0.09]
= 0.09x
Similarly
Interest on y = y(0.07)(1) = 0.07y
Interest on z = z(0.1)(1)=0.1z
Total interest = 0.09x+0.07y+0.1z = 4340 (ii)
Also, y=2x [given] (iii)
Put y=2x in (i) and (ii), we get
x+2x+z= 50000 ⇒ 3x+z=50000 (iv)
0.09x+0.07(2x)+0.1z=4340 ⇒ 0.09x+0.14x+0.1z=4340
⇒ 0.23x+0.1z=4340 (v)
Multiply 10 on both sides of (v)
2.3x+z=43400 (vi)
Eliminate (vi) from (v)
0.7x=6600
⇒ x= 9,428.57
From (iii), y= 2(9428.57) =18,857.14
From (vi),
2.3(9428.57)+z=43400
⇒ 21685.71+z=43400
⇒ z= 43400-21685.71
⇒ z=21714.29
Hence, Amount borrowed at 9% = 9,428.57
Amount borrowed at 7% = $18,857.14
Amount borrowed at 10% = $ 21,714.29
Mary has $267 in her checking account . She writes checks for $33,$65 and 112. What is the balance in her account now ?
Answers
Answer:
57
Step-by-step explanation:
f (x) = 2x^2 - 4x + 1
Answers
Answer:
tinanong ko rin po yang tanong nyo at ito po ang sagot nilaMike spent $32.86 on 15.5 pounds of grass seed for his yard. What is the price per pound of the grass seed?
Answers
Step-by-step explanation:
the price per pound of grass is $2.12
Jim is baking chocolate chip muffins. He has a total of 7 1/3 cups of chocolate chips. If each batch of muffins uses 2/3 of a cup of chocolate chips, enter the most number of batches of muffins Jim can bake
Answers
Answer:
16
Step-by-step explanation:
The first step to answering a question like this is to turn it into an improper fraction so 7 1/3=24/3. Then divide the numerator by the denominator so 24 divided by 3=8 so 8=1/3. Their is 2/3 so do 8 times 2 which equals 16
Roman solved the equation 5 a + 2 b = 10 for a. His steps are shown below.
1. Subtract 2b: 5 a + 2 b minus 2 b = 10 minus 2 b. 5 a = 10 minus 2 b.
2. Multiply by 5: a = 50 minus 10 b.
Which statement about Roman’s work is true?
I need a quick answer pls!
Answers
Answer:
In step 2, he needed to divide both sides of the equation by 5
Step-by-step explanation:
I'm very positive about this
Hope this helps!!!!!!
Answer:
step 2
Step-by-step explanation:
The point (1,0) is rotated (5π/4) about the origin. Find the coordinates of its image correct to three decimal places.
Answers
Answer:
The result can be shown in multiple forms.
(1,0),3.92699081 ...
which of these situations does not have quantities that combine to make 0.
A. In the morning, the temperature rises 30 degrees. in the evening, it falls by 30 degrees
B. Hikroko earns $20 working concessions at the football game. she earns $20 as as babysitter
C. A dolphin swims 20 feet straight down from the surface. it then rise 20 feet to reture to the surface
D. A hot air balloon rises 40 feet. it then drops 40 feet to the ground
Hurry please
Answers
Answer:
B. Hikroko earns $20 working concessions at the football game. she earns $20 as as babysitter
Step-by-step explanation:
also the person who keeps deleting all my answers i hope u break your back
Can somebody help pleaseIf a number is a whole number, then it cannot be an
A. irrational number
B. a natural number
C. an integer
D. national number
Answers
Answer:
the answer is A - An irrational number
Pls help I will brainlest u
Find the sum without using a number line.
Answers
Answer:
- 1 1/4
Step-by-step explanation:
-9 1/4 + 8 = -1 1/4
PLEASE HELP I'M QUITE SURE WITH THIS QUESTION
Answers
The answer is ( D ), y ≤ 6
The range begins from minimum value to maximum value.
However, in the graph. There's no minimum value as it's heading toward negative infinity.
So we use y ≤ 6 instead.
So the clear answer is y ≤ 6 or ( D )
What is 9 - 3 ÷ 1/3 + 1 Please show work
Answers
Answer:
answer
Step-by-step explanation:
9-3 = 6
6 divided by 1/3 is (3x6) = 18
18 + 1 = 19
Answer:
the answer is 19
Step-by-step explanation:
El peso promedio de 500 árboles de un vivero es de 70kg y la desviación estándar de 3kg. Suponiendo que los pesos se distribuyen normalmente, encontrar CUANTOS arboles pesan: a) Entre 60 y 75 kg b) Más de 90kg c) Menos de 64kg. D) 64 Kg
Answers
Answer:
Step-by-step explanation:
Resolvemos usando la fórmula de puntuación z
z = (x-μ) / σ, donde
x es la puntuación bruta
μ es la media poblacional = 70 kg
σ es la desviación estándar de la población = 3 kg
a) Entre 60 y 75 kg
Para x= 60kg
z = 60 - 70/3 kg
=-3.33333
Valor de probabilidad de la tabla Z:
P(x = 60) = 0.00042906
Para x = 75 kg
z = 75 - 70/3 kg
= 1.66667
Valor de probabilidad de la tabla Z:
P(x = 75) = 0.95221
P(x = 75) - P(60)
0.95221 - 0.00042906
b) Más de 90 kg
Para x> 90 kg
z = 90 - 70/3
= 6.66667
Valor de probabilidad de la tabla Z:
P (x <90) = 1
P (x> 90) = 1 - P (x <90) = 0
Número de árboles = 500
Por tanto, 500 × 0 = 0 árboles
c) Menos de 64 kg
x <64 kg
z = 64 - 70/3 kg
= -2
Valor de probabilidad de Z-Table:
P (x <64) = 0,02275
Hay 500 arboles
= 500 × 0.02275
= 11.375 árboles
D) 64 kilogramos
x = 64 kg
z = 64 - 70/3 kg
= -2
Valor de probabilidad de Z-Table:
P (x = 64) = 0,02275
Hay 500 arboles
= 500 × 0.02275
= 11.375 árboles
Simplify -7 1/8 - 9 1/2
A. - 2 3/8
B. - 16 5/8
C. 16 5/8
D. 2 3/8
Answers
Answer:
d
Step-by-step explanation:
Greta is taking a road trip from Cincinnati to San Francisco. On the first day, she drove 650 miles in 10 hours. On the second day, she got a later start and drove 540 miles in 8 hours. How many miles per hour faster was her average speed the second day?
Answers
Answer:
2.5 miles per hour fasterStep-by-step explanation:
Step one:
the first day
distance= 650miles
time taken= 10 hours
speed= distance/time
speed= 650/10
speed= 65miles per hour
Step two:
the second day
distance= 540mile
time taken= 8 hours
speed= distance/time
speed= 540/8
speed= 67.5miles per hour
Step three:
the difference between the two speeds is =67.5-65= 2.5
therefore on the second day, the speed is 2.5 miles per hour faster
A rectangular room is 19.7 m by 7.0 m. What is the side length of a square room with the same area as the room?
Answers
Answer:
68.95
Step-by-step explanation:
A postage box should weigh 1.0 pound. If there is a 5% error on the weight, what is the range of acceptable weight?
Answers
Answer: 0.95
Step-by-step explanation: 1.0 and 10% is 0.10 so 5% is 0.5 and if u take 0.5 away from 1.0 it’s 0.95
The area of Canada is approximately 1×10^7 square kilometers, and the area of Mexico is approximately 2×10^6 square kilometers. The area of Canada is approximately how many times the area of Mexico?
Answers
Answer:
5 times
Step-by-step explanation:
Given that,
The area of Canada is approximately 1×10⁷ square kilometers, and the area of Mexico is approximately 2×10⁶ square kilometers.
We need to find the area of Canada is approximately how many times the area of Mexico.
Dividing both areas as follows :
[tex]\dfrac{A_c}{A_m}=\dfrac{10^7}{2\times 10^6}\\\\\dfrac{A_c}{A_m}=5\\\\A_c=5A_m[/tex]
So, the area of Canada is approximately 5 times the area of Mexico.
What is the ordered pair for point A
Answers
Answer:
(-1.5, 2.5)
Step-by-step explanation:
look at x-value and y-value
find difference between -1 and -2 which is 0.5 same goes with y-axia
The 2020 Election is shaping up to be the largest one yet! They estimate that there are 240,000,000 eligible voters in the United States this year. So far, 70,000,000 have voted, and experts estimate that upwards of 150,000,000 people will vote in total this year. What percentage of eligible voters will participate in this year's election?
Answers
Answer:
Percentage = 91.67%
Step-by-step explanation:
Number of eligible voters = 240,000,000
Number of voters so far = 70,000,000
Number of estimated voters = 150,000,000
Total number of participants (voters) = 70,000,000 + 150,000,000 = 220,000,000
To find the percentage;
[tex] Percentage = \frac {220,000,000}{240,000,000} * 100 [/tex]
[tex] Percentage = \frac {11}{12} * 100 [/tex]
[tex] Percentage = 0.9167 * 100 [/tex]
Percentage = 91.67%
Therefore, the percentage of eligible voters that will participate in this year's election is 91.67%
Answer:
91.67%
Step-by-step explanation:
SoMebOdY oNcE
ToLd mE iTS
YOur pOweR
ToDo
rOKi-
Select all equations that have graphs with the same y-intercept.
Group of answer choices
y=3x - 8
y=3x - 9
y=3x + 8
y= 5x-8
y=2x -8
y=1/3x -8
Answers
help plz its about proportionality
Answers
Answer:7
Step-by-step explanation:no need to explain
The area of a rectangle is 26.88 square centimeters. The length of the rectangle is 9.6 centimeters. What is the width of the rectangle in centimeters?
Answers
Answer:
26.88 divided by 9.6 is 2.8
Meaning that the width is 2.8 cm
Lucy can spend no more than $125 on props for a school play. She has already phurchased costume fabrics that cost $49. Write and solve an inequality to show how much more she spend on props.
Answers
Answer: 49+x≤ 125, where x = Amount she can spend more on props.
Now she can spend no more than $76 on props.
Step-by-step explanation:
Given: Lucy can spend no more than $125 on props for a school play.
I.e. Total money she can spend ≤ $ 125
She already purchased costume fabrics that cost $49.
Let x = Amount she can spend more on props.
Required inequality: 49+x≤ 125
Subtract 49 from both sides, we get
x≤ 76
Hence, now she can spend no more than $76 on props.
What is the solution to n/4 = -12.4?
n = 3.1
n = -3.1
n = 49.6
n = -49.6
Answers
Answer:
n= -49.6
Step-by-step explanation:
49.6 i did this test and got it right
Y’all please helppp it says (ax + by)/c = d solve for x
Answers
Answer:
[tex]x=\frac{dc-by}{a}[/tex]
Step-by-step explanation:
[tex]\frac{ax+by}{c}=d\\\\ax+by=dc\\\\ax=dc-by\\\\x=\frac{dc-by}{a}[/tex]
URGENT HELP!!
The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. If MD = 9 and NF = 5, find:
Answers
Answer:
NK = 7, MK = 2, MF = 9.9, Area = 42Step-by-step explanation:
Refer to attached
To find:
NK , MK, MF, Area of trapezoidSolution
The trapezoid is isosceles and NK is its height, therefore
MD - NF = 2MKMK = (9 -5)/2 = 2Since ∠KDN = 45°, the triangle NKD is isosceles and so
NK = KD = MD - MK = 9 - 2 = 7MF = ND as trapezoid is isosceles and therefore diagonals are equal
ND = NK√2 = 7√2 = 9.9 So MF = 9.9Area of trapezoid
A = 1/2(b1 + b2)h A = 1/2(9+5)(7) = 6*7 = 42Thirty more than one half of the students at at canyon middle school are in band.Five less than three fifths of the students are in athletics.If the number of students who are in band is equal to the number of students in athletics how many students are enrolled in canyon middle school
Answers
Answer:
Students at canyon middle school = 350
Step-by-step explanation:
Students at canyon middle school = x
Band = 1/2x + 30
Athletics = 3/5x - 5
athletics.If the number of students who are in band is equal to the number of students in athletics
1/2x + 30 = 3/5x - 5
1/2x - 3/5x = -5 - 30
5x-6x/10 = -35
-x/10 = -35
= -x(1/10)= -35
x = -35 ÷ -1/10
= -35 × -10/1
= 350
x = 350
Students at canyon middle school = 350