Find the missing side. Be sure to show all of your work. Round to the nearest tenth
if necessary
Answers
Answer:
x=3.9 approximately
Step-by-step explanation:
Using Pythagorean theorem:
[tex]x^{2} + (5x)^{2} = 20^{2}[/tex]
[tex]x^{2} + 25x^{2} = 400[/tex]
26x^2 =400
x^2 = 15.3846
x=3.9
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityGeometry[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a legb is another legc is the hypotenuseApplicationStep 1: DefineLet's define what the problem gives us:
We are given a right triangle, indicated by the square box inside the triangle, with side lengths 5x and x and a hypotenuse of 20.We can set these measurements equal to our variables defined above in our Pythagorean Theorem equation:
a = 5xb = xc = 20Step 2: WorkNow, we can substitute our variables and solve for x, which will help us find the side lengths as well:
[Pythagorean Theorem] Substitute in variables:[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\\end{aligned}[/tex][Order of Operations] Simplify:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\\end{aligned}[/tex][Simplify] Combine like terms:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\\end{aligned}[/tex][Equality Properties] Divide both sides by 26:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\\end{aligned}[/tex][Equality Properties] Square root both sides:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\\end{aligned}[/tex][Simplify] Evaluate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13}\end{aligned}[/tex][Evaluate] Approximate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13} \\& \approx \boxed{3.9} \\\end{aligned}[/tex]
∴ our x approximately equals 3.9.
Now we can use our value of x to solve for the missing triangle lengths:
Length of 5x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\\end{aligned}[/tex]Evaluate:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\& = \boxed{19.5}\end{aligned}[/tex]
∴ this particular side length has a length of 19.5.
Length of x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = x \\& = \boxed{3.9}\end{aligned}[/tex]
∴ this particular side length has a length of 3.9.
Answer∴ the side lengths of this particular triangle are 19.5 and 3.9, respective to their variables 5x and x.
___
Learn more about Triangles: https://brainly.com/question/20094559
Learn more about Geometry: https://brainly.com/question/16909531
___
Topic: Geometry
Unit: Triangles
Related Questions
whats 2+2 ? ( This is worth 60 points go get them )
Answers
2+2 = 4
Very easy, just add them lol gotem
Answer:
4
Step-by-step explanation:
2 + 2
Add the numbers.
= 4
the sum of two numbers is 90 .the larger number is 14 more than 3 times the smaller number.
Answers
Answer:
The numbers are 19 and 71.
Step-by-step explanation:
Let x and y represent the two numbers. Then x + y = 90.
Also, if we assume that the larger number is y, then y = 3x + 14.
We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:
x + y = 90 becomes x + 3x + 14 = 90, or:
4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.
The numbers are 19 and 71.
Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.
What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1
Answers
Answer:
Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (… ... Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1 ... To get the sum to infinity of the geometric series, we need to get its first term
Step-by-step explanation:
Which took place in 1853?
O The US made the Gadsden Purchase.
The US received payment from Mexico for Texas.
Mexico won the Mexican-American War.
Mexico paid the US for the Mexican Cession.
Answers
Answer:
The answer is a
Step-by-step explanation:
I hoped i helped
which phrase best describes a theorem in an axiomatic system?
Answers
Answer:
The best phrase that describes a theorem in axiomatic system is :
A statement proven to be true using logic
Axiomatic system is a set of axiom in which the axioms are derived from logic
hope this helps
Answer:
A statement proven to be true using logic
Axiomatic system is a set of axiom in which the axioms are derived from logic
A.3/4
B.4/3
C.-4/3
D.-3/4
I need help so bad pls
Answers
Evaluate 4 ÷ 5/6 Give your answer as a mixed number in its simplest form.
Answers
Answer:
4 ÷ 5/6
= 4 × 6/5
= 24/5
= 4 4/5
Hope this helps.
25 POINTS!!!!Which of the following statements are true? Select all that apply.
The product of B and D is negative.
The quotient of A and C is positive.
= A ∙
The quotient of 0 and F is undefined.
A ∙ D = -E ∙ D
Answers
Answer:
then 0 and f have to be positive.
Step-by-step explanation:
Mark me brainlest.
Answer:
Its A and C and F
Step-by-step explanation:
I need help on this 10j< – 10
Answers
Answer:
j<-1
Step-by-step explanation:
10j<-10
divide both sides by 10 and get
j<-1
Answer:
[tex]j < - 1[/tex]
Step-by-step explanation:
[tex]10j < - 10 \\ \frac{10j}{10} < \frac{ - 10}{10} \\ = j < - 1[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
PLEASE PLEASE PLEASE HELP
Answers
Step-by-step explanation:
I rectangle measures⅛(width)by 1/5(length). You have been asked to shade whose area is 3/5(w
length)by ⅞(width)
1)width=⅞÷1/8=7rectangles
2)length=3 /5÷1/5=3rectangles
thus shade 7rectangles along the width(sideways) and 3 rectangles along the length(downwards)
Express x^2+4x-7 in the form (x+a)^2-b where a and b are integers
Answers
Answer:
(x + 2)^2 - 11.
Step-by-step explanation:
f(x) = x^2 + 4x - 7
Now x^2 + 4x = (x + 2)^2 - 4 so we have:
f(x) = (x + 2)^2 - 4 - 7
f(x) = (x + 2)^2 - 11.
Here, we are required to express x² + 4x - 7 in the form (x+a)² - b and determine the values of a and b.
The values of a and b are 2 and 11 respectively.By completing the square method;
a = (4/2) = 2.
Therefore, by expanding (x+a)² i.e (x+2)²
We therefore have; x² + 4x + 4
However, the question is given as x²+4x-7
Therefore, by comparison between;
x² + 4x + 4 and x²+4x-7; we have;
4 - b = -7, b = 7+4
Ultimately, b = 11
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Find the measure of an exterior angle of a regular hexagon
Answers
Answer: 60 degree angle
Step-by-step explanation:
The rule for polygons is that the sum of the exterior angles adds up to 360. Since there are 6 exterior angles on a 6 sided polygon (hexagon), then we can divide 360 by 6 to find the measure of an exterior angle. This means that one exterior angle of a hexagon is equal to 60 degrees.
Find the difference quotient of f; that is, find StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction comma h not equals 0 comma for the following function. f left parenthesis x right parenthesis equals negative 4 x plus 6
Answers
Answer:
-4
Step-by-step explanation:
Given the following function:
f(x) = -4x + 6
We have to find the difference quotient of f(x); that is,
[f(x + h) - f(x)]/h
So, we ned to compute f(x + h) as follows:
f(x+h) = -4(x+h) + 6 = -4x - 4h + 6
Replacing into the difference quotient, we get:
[f(x + h) - f(x)]/h = [-4x - 4h + 6 - (-4x + 6)]/h
[f(x + h) - f(x)]/h = [-4x - 4h + 6 + 4x - 6)]/h
[f(x + h) - f(x)]/h = [- 4h)]/h
[f(x + h) - f(x)]/h = -4
what is the standard form of 7+3i/2-5i
Answers
Answer:
-1/29+41/29*i
Step-by-step explanation:
(7+3i)/(2-5i)=(7+3i)(2+5i)/(2-5i)(2+5i)=(14+35i+6i+15i^2)/(4-25i^2)=
(14+41i-15)/(4+25)=(-1+41i)/29=-1/29+41/29*i
Allie and Samuel are rock climbing
*Allie climbs 5 1/2 meters in the first 1/4 hour.
*Samual climbs 14 1/4 meters in the first 3/4 hour.
each person's rate stays the same for the first hour they climb.
Part A
Which statements are true?
Select all that are Correct.
A. Samuel climbs at a rate of 19 hours per hour
B. Allie takes 1/22 of an hour to climb one meter.
C. Allie climbs at a rate of 1/22 meter per hour
D. Samuel climbs at a rate of 1/19 meter per hour
E. Samuel takes 1/19 of an hour to climb one meter
Answers
Answer:
A and E
Step-by-step explanation: I done this before
The statements that are true are:
Allie takes 1/22 of an hour to climb one meter.
Samuel takes 1/19 of an hour to climb one meter.
Options B and E are correct.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numberator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
For Allie.
She climbs 5(1/2) meters in 1/4 hour.
This means,
11/2 meters = 1/4 hour
22 meters = one hour
Rate = 22 meters per hour.
We can also say,
To climb one meter, she takes 1/22 of an hour.
For Samuel.
He climbs 14(1/4) meters in 3/4 hour,
This means,
57/4 meters = 3/4 hour
19 meters = one hour
Rate = 19 meters per hour.
We can also say,
To climb one meter, he takes 1/19 of an hour.
Thus,
Allie takes 1/22 of an hour to climb one meter is true.
Samuel takes 1/19 of an hour to climb one meter is true.
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can someone help me??????
Answers
Answer:
25.2
Step-by-step explanation:
Volume of container: 2x3x5=30
0.84x30=25.2
Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
Answers
Answer:
Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64 ---4 67x54 5xe4t4 6x
select the two valuse of x that are roots of this equation. x^2+2x-5=0
Answers
Answer:
1 + sqrt(6)
You can't factor this by itself so you have to use the quadratic formula
Step-by-step explanation:
Jake took a handful of M&Ms from the candy dish on the coffee table.
gave half of them to his little sister. He sorted the M & Ms he had left and
put one third of them back in the dish because they were read and he do
not like red M & Ms. That left Jake with 6 M & Ms. How many did Jake hav
in his original handful?
Answers
Answer:
36
I want brainliest
Step-by-step explanation:
6 x 3/1 or 6 x 3 = 18
put the reds back in
18 x 2 = 36
take the ones from his sister
Answer = 36
Step-by-step explanation:
6 x 3/1 or 6 x 3 = 18
reds go back in
18 x 2 = 36
take ones from the sister and there u go
Plz help ASAP will give brainliest if answered correctly!!
Answers
Answer:
C
Step-by-step explanation:
Multiply 5/8 by 4 in which you get 2.5 which is 5/2 and simplify, then you get answer C
A hemisphere has a radius of 8 centimeters. If a cone whose diameter is the same and whose height is equal
to the radius of the hemisphere removed, what volume remains of the hemisphere?
(1) 483 cubic centimeters
(2) 536 cubic centimeters
(3) 589 cubic centimeter
(4) 614 cubic centimeters
Answers
Answer:
The volume remaining is approximately 536 cm³
Step-by-step explanation:
The volume of a hemisphere is the volume of the sphere divided by two, therefore it's formula is:
[tex]\text{volume hemisphere} = \frac{4}{6}*pi*r^3\\\text{volume hemisphere} = \frac{4}{6}*pi*8^3 = 1072.33 \text{ } cm^3[/tex]
While the volume of the cone is:
[tex]\text{volume cone} = \frac{\pi*r^2*h}{3}\\\text{volume cone} = \frac{\pi*(8)^2*8}{3}\\\text{volume cone} = \frac{\pi*512}{3} = 536.1651 \text{ } cm^3[/tex]
What remains on the hemisphere is the difference between these volumes, therefore:
[tex]\text{remaining volume} = 1072.33 - 536.17 = 536.16 \text{ } cm^3[/tex]
The volume remaining is approximately 536 cm³
pls answer as quick as possible for brainliest!!
Answers
Answer:
15
Step-by-step explanation:
(2 1/2 + 1 1/2 + 3 1/2) = 7 1/2 * 2 = 15
Answer:
15
Step-by-step explanation:
2.5+1.5+3.5 = 7.5
7.5*2 = 15
Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible.
(8,1); y=-8x-1
Answers
Answer:
y= ⅛x
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the gradient and c is the y-intercept.
Let's find the value of m first.
The product if the gradients of 2 perpendicular lines is -1.
Gradient of given line= -8
m(-8)= -1
m= -1 ÷(-8)
m= ⅛
y=⅛x +c
To find the value of c, substitute a coordinate.
When x=8, y=1,
1= ⅛(8) +c
1= 1 +c
c= 1 -1
c= 0
Thus, the equation if the line is y= ⅛x.
Two times a number is equal to the absolute value of the quantity "sixty-three less than five times that number." What could the number be?
Answers
Answer:
The number is 21.
Step-by-step explanation:
First you need to solve for n.
So the equation would be 2n = |5n-63|
First you'd subtract 5n from each side, that would give you -3n=|-63|
Then you need to divide each side by -3 to get n=21.
~~~~~
To check, you can just plug 21 back into the equation.
2(21) = |5(21) - 63|
42 = |105-63|
42 = |42|
42 = 42
Gregory spins the spinner once. What is P(vowel)?
PLEASE HELP ME!!!
Answers
Answer:
There is two vowels and 6 sections in total
2 wanted sections / 6 total sections = 1/3
1/3 chance or 33.33333%
Step-by-step explanation:
PLEASE HELP! FIRST CORRECT ANSWER WILL MARK BRAINLIEST!
A grocer wishes to blend two different coffee brands in order to make a blend of 400 pounds to sell at $3.00 a pound. If he uses a brand of coffee worth $2.70 a pound with another brand worth $3.20 a pound, how many pounds of each does he use?
Answers
Answer:
160 pounds at 2.70
240 pounds at 3.20
Step-by-step explanation:
Let x be the pounds and 2.70 per pound
400-x is the pounds and 3.20 per pound
there will be 400 pounds and 3.00 per pound
2.70 x + (400-x) *3.20 = 400 *3
Distribute
2.70x +1280-3.20x = 1200
Combine like terms
-.5x +1280 = 1200
Subtract 1280 from each side
-.5x = -80
Divide each side by -.5
x = -80/-/5
x =160
160 pounds at 2.70
400-160 = 240 pounds at 3.20
I don’t need you to explain just answer.
Answers
Y-intercept:
To find the y-intercept, where the line crosses the y-axis, you need to find the value of y when x is 0.
Slope:
To find the slope of the line, use the equation:
(y₂ - y₁)/(x₂ - x₁)
where (x₁, y₁) is one point on the line and (x₂, y₂) is a different point on the line.
Equation:
y = (y-intercept) + x(slope)
Which statement about this figure is true?
a. it has rotational symmetry with an angle of rotation of 90°
b. it has no reflectional symmetry
c. it has reflectional symmetry with two lines of symmetry
d. it does not have symmetry point
Answers
Answer:
a. it has rotational symmetry with an angle of rotation of 90°
Step-by-step explanation:
Mr.Brown is planting trees in a field that is one mile long and 2 miles wide. How much is his field.
Answers
Answer:
Step-by-step explanation:
Wtwtettete
Answer:
2 miles squared.
Step-by-step explanation:
A= length times width
A= 1 mile times 2 miles
A= 2 miles squared
which inequality is represented by this graph ?
Answers
Answer:
D
Step-by-step explanation:
The point is on 4 so it cannot be A or B, and it is a closed circle not an open circle so it cannot be C.
Answer:
x≥4
Step-by-step explanation:
There is a closed circle at 4 which means there is an equal to sign and the lines goes to the right which means greater than
x≥4
