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
Can someone please tell me how to find the value of x.
Answers
Answer:
2.547 = x
Step-by-step explanation:
tan 23 = x/6 Use this equation to find the value of x
0.4245 = x/6 Multiply both sides by 6
2.547 = x
Lance bought a used car for $5500. He sold it two years later for $2475. What is the percent change of the price?
Answers
Answer: 55%
Step-by-step explanation:
2475/5500 = .45
He sold it for 45% of the price, so it went down by 55%
Compare the given dimensions of four triangles. Which triangle is possible to construct?
side lengths of 6 m, 8 m, and 9 m
side lengths of 4 m, 5 m, and 12 m
side lengths of 2 m, 5 m, and 8 m
side lengths of 4 m, 7m, and 13 m
Answers
The triangle with side lengths of 6 m, 8 m, and 9 m is possible to construct.
What is the condition to construct a triangle with given dimensions?
In a triangle, the sum of the two smaller sides must be greater than the larger side of the triangle. If this condition satisfies, then the triangle could be possible to construct.
Given,
1. A triangle with side lengths of 6 m, 8 m, and 9 m. Here, (6 + 8) > 9. Therefore, the triangle is possible to construct.
2. A triangle with side lengths of 4 m, 5 m, and 12 m. Here, (4 + 5) < 12. Therefore, the triangle is not possible to construct.
3. A triangle with side lengths of 2 m, 5 m, and 8 m. Here, (2 + 5) < 8. Therefore, the triangle is not possible to construct.
4. A triangle with side lengths of 4 m, 7 m, and 13 m. Here, (4 + 7) < 13. Therefore, the triangle is not possible to construct.
Learn more about the condition to construct a triangle here: https://brainly.com/question/1299079
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Which of the following is the measure of an acute angle?
A. 126
B. 86°
C. 90°
Answers
Answer:
b
Step-by-step explanation:
an acute angle is an angle that is smaller than 90 degrees.
if the angle is exactly 90 degrees, then it is a right angle.
anything larger than 90 degrees is considered to be an obtuse angle.
Hope this helps for other questions like this as well!
Angle 86° is less than 90°. Then the angle of 86° will be an acute angle. Then the correct option is B.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The types of angles are as follows:
If the measure of the angle is less than 90°, then the angle is an acute angle.
If the measure of the angle is equal to 90°, then the angle is a right angle.
If the measure of the angle is greater than 90°, then the angle is an obtuse angle.
Angle 86° is less than 90°. Then the angle of 86° will be an acute angle. Then the correct option is B.
More about the angled link is given below.
https://brainly.com/question/15767203
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Two similar cylinder have radii 3 cm and 4 cm. If the first cylinder has a volume of 270cm³ , find the volume of the second cylinder.
Please help me , i need help.
Answers
Answer: 480 cu. cm
Step-by-step explanation:
Height of first cylinder: h = V/pi r^
= 9.55 cm
Volume of second cylinder = pi r^2 h
= 480
Answer:
360
Step-by-step explanation:
Find the relativeness: If 3 is to 270 then 4 is to ?
270/3 = 90
90 times 4 = 360
Therefore if
3 is to 270
then
4 is to 360
What addition expression is shown on the
number line?
8
+
?
15
Answers
12.
What is the solution of the equation x2 + 2x - 7 = 0?
Answers
Answer:
cancel out as much of the equation as possible by doing inverse operations so add the 7 to both sides
x2 + 2x = 7
Divide by 2
x2 = 3.5
divide by 2 again
x = 1.75
now change x with 1.75 to check
1.75 x 2 = 3.5
3.5 + 3.5 - 7 = 0 so 1.75 is correct
Hope this helps
Step-by-step explanation:
equation of the line that passes through (2, -1) and has a slope of
-5
Answers
A car manufacturer announced that next year the price of a certain model car would increase by 5.5 %. This year the price is $17,635. Find the increase and the new price. The increase in the price of the car is $? (Round to the nearest cent as needed.) The new price of the car is $? (Round to the nearest cent as needed.)
Answers
Answer:
Increase: $969.93 New Price: $18,604
Step-by-step explanation:
I got this answer by finding out how much of the initial price 5.5% was, it ended being 969.925 so I rounded that to 969.23 so that I may found how much the price increased, then I added the increase price to the initial price so that I may find out how much the car would cost next year which is, $18,604.
Martina read that approximately 10% of all people are left-handed. She wants to design a
simulation to approximate the probability of selecting exactly 2 right-handed people when 3
people are randomly selected.
Part A
In the simulation, Martina has a spinner with sections of equal size. One section is labeled "L"
(left) and the rest of the sections are labeled "R" (right).
For this simulation to be as accurate as possible, what is the total number of
sections that the spinner should have?
Answers
Answer:
15%
Step-by-step explanation:
Which inequality is true?
A. 6 - pi > 3
B. pi + 3 < 6
C. 8 pi > 24
D. 12/pi > 4
Answers
Answer:
C.
Step-by-step explanation:
Round pi to 3.14 to get a rough estimate.
6 - 3.14 > 3 FALSE
3.14 + 3 < 6 FALSE
8 * 3.14 > 24 TRUE
12 ÷ 3.14 > 4 FALSE
(x+y)^2 (x2+2xy+y2) pleas show all work
Answers
Answer:
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
Step-by-step explanation:
1 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)
2
=a
2
+2ab+b
2
.
({x}^{2}+2xy+{y}^{2})({x}^{2}+2xy+{y}^{2})(x
2
+2xy+y
2
)(x
2
+2xy+y
2
)
2 Expand by distributing sum groups.
{x}^{2}({x}^{2}+2xy+{y}^{2})+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
2
(x
2
+2xy+y
2
)+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
3 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
4 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
(x
2
+2xy+y
2
)
5 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}{x}^{2}+2{y}^{3}x+{y}^{4}x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
x
2
+2y
3
x+y
4
6 Collect like terms.
{x}^{4}+(2{x}^{3}y+2{x}^{3}y)+({x}^{2}{y}^{2}+4{x}^{2}{y}^{2}+{x}^{2}{y}^{2})+(2x{y}^{3}+2x{y}^{3})+{y}^{4}x
4
+(2x
3
y+2x
3
y)+(x
2
y
2
+4x
2
y
2
+x
2
y
2
)+(2xy
3
+2xy
3
)+y
4
7 Simplify.
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
answer: x^4+4x^3 y+6x^2 y^2+4xy^3+y^4
1.) Edge Fitness charges $18 a month for a gym membership and a $30 start-up fee. How much would you spend after 1 year at the gym?
Equation:
Answers
Answer:
$246
Step-by-step explanation:
30 + 18(12)=
30 + 216
246
Answer:
30+12*18=246
Step-by-step explanation:
İf the bill 18 dollars for month, it's equals 216 from 12*18.
And the start-fee is 30 dollars. Then 216+30=246
Santana went for a hike on the 21 mile South Boundary Trail. If she can hike2 miles
in 60 minutes, how long will it take her to hike the entire trail?
Draw a diagram to support your thinking and demonstrate your understanding. Be sure
to show all of your work.
Answers
Answer:
It will take santana 630 minutes or 10.5 hours to complete the 21 miles.
Step-by-step explanation:
[tex]\frac{2}{60\\}[/tex] [tex]\frac{21}{y}[/tex] y is what you are trying to find multiple her miles by the number of minutes and then divided by how many miles in 60 min.please help i’ll give brainliest !
Answers
Answer:
1: (ab)^3
2: 3m^2n^5
3: 15y^3x^7
4: 8s^5r^7
5: 6q^3p^5
Step-by-step explanation:
sorry but fot the explanation, it would take me 10 years to write but you can trust me with these answers
2.) 3m^2 n^5
3.)15x^7 y^3
4.) 8s^5 r^7
5.) 6p^5 q^3
Explanation:
For all the questions multiply the base numbers, if there are any. And add the exponent numbers. For example if the question is, (x^2)(x^4) add 2 and 4 to get 6. If there is more than one letter only add the like exponents with the same letter. For example, (x^2 y^2)(x^4 y^3) add 2+4=6 and 2+3=5, which means the final answer would be x^6 y^5
Write y + 1 = –2x – 3 in standard form.
Question 15 options:
a)
x + 12y = −2
b)
-2x-y = 4
c)
2x + y = -4
d)
y = -2x-4
Answers
Answer:
d
Step-by-step explanation:
isolate y and evaluate
Answer:
B
Step-by-step explanation:
move the y to the other side and the three to its opposite side
A triangle has angle measurements of 36°, 90°, and 54°. What kind of triangle is it?
A. acute B. right C. obtuse
Answers
Answer:
Right
Step-by-step explanation:
when a triangle has a 90 degree angle it is always right
Answer:
right angle triangle
Step-by-step explanation:
triangle consists of 90° causing it to be right angledA sloth is climbing down a tree at a constant speed. The sloths height changes by -55 feet in 11 minutes. Which expression represents change in the sloths height each minute?
-55•(-11)
-55•11
-55 divided by 11
-55 divided by (-11)
Answers
-55 divided by (-11)
Because you can have a negative minute after dividing
the table below represents the function f
Answers
Answer:
1
Step-by-step explanation:
I belive its one because 3^2 is 9 and 9+1 = 10
to make sure it not just once 3^3 is 27 and 27+1=28
If it is on sale for 20% OFF and the sale price is $68; what was the original price?
Answers
Answer:
85
Step-by-step explanation:
The discount is original price times the percent off
The sale price is the original price minus the discount
original price - original price * 20 % = 68
Factor out the original price and change the percent to a decimal
original price ( 1 - .20) = 68
original price ( .80) = 68
Divide each side by .80
original price = 68/.80
original price = 85
Answer:
$13.60
Step-by-step explanation:
($68 x 20%) / 100
1360 / 100 = 13.6
solve for x and y
help please!!
need step by step explanation.
will give the brainliest!!
Answers
Answer:
x=4, y=10
Step-by-step explanation:
(x+2)/3= (y-2)/4= (y-x)/3
x+2= y-x ⇒ y= 2x+2(x+2)/3= (2x+2-2)/4 ⇒ (x+2)/3= x/2 ⇒ 2x+4= 3x ⇒ x=4y=2*4+2= 10Answer:
The value of x is 2 and y is 10.
Step-by-step explanation:
First, you have to do cross multiplications of any 2 fractions :
1st equation,
[tex] \frac{x + 2}{3} = \frac{y - 2}{4} [/tex]
[tex]4(x - 3) = 3(y - 2)[/tex]
[tex]4x + 8 = 3y - 6[/tex]
2nd equation,
[tex] \frac{y - 2}{4} = \frac{y - x}{3} [/tex]
[tex]4(y - x) = 3(y - 2)[/tex]
[tex]4y - 4x = 3y - 6[/tex]
Next, you have to solve the simultaneous equation by elimination :
[tex]4x - 3y = - 14 - - - (1)[/tex]
[tex] - 4x + y = - 6 - - - (2)[/tex]
[tex](1) + (2)[/tex]
[tex]4x - 3y + ( - 4x) + y = - 14 + ( - 6)[/tex]
[tex] - 2y = - 20[/tex]
[tex]y = 10[/tex]
[tex]substitute \: y = 10 \: into \: (1)[/tex]
[tex]4x - 3(10) = - 14[/tex]
[tex]4x - 30 = - 14[/tex]
[tex]4x = - 14 + 30[/tex]
[tex]4x = 16[/tex]
[tex]x = 4[/tex]
pls help on this question
*image
Answers
Answer:
216 2/3
Step-by-step explanation:
yoys : frents
6 : 13
We have 100 yoys
100/6 =50/3
Multiply by 50/3
yoys : frents
6 *50/3 : 13*50/3
100 : 650/3
As a mixed number
650/3 frents
216 2/3
The concentration determined for an unknown sample of hydrochloric acid by a student is 0.1354 M.According to the instructor’s information, the true molarity (M) of this solution is 0.1364 M. What is the percent error in this experiment? Round your answer to the nearest tenth.
Answers
Answer:
≈ 0.7% error
Step-by-step explanation:
To solve for percent error, first you have to do 0.1354-0.1364 and take the absolute value, which is 0.001.
Then, divide 0.001 by 0.1364, and then multiply by 100, and the answer is 0.007331378299.
The percent error is approximately 0.7%
1 GEOMETRY - 1206310)
. An angle expression in an equilateral triangle is 3x + 12. What is the value of X?
Answers
Answer:
16
Step-by-step explanation:
The angle in an equilateral triangle is given as:
3x + 12
The angle is an equilateral triangle is 60°. Therefore:
3x + 12 = 60
=> 3x = 60 - 12 = 48
x = 48 / 3 = 16
x is 16
Can anyone help out with this one?
Answers
Answer:
the answer is 32
Step-by-step explanation:
8 x 4 = 32
tip: division is backwards multiplication with different signs
hope this helps :)
mark as brainliest?
4−2(x−5)=x−19? Help
Answers
Answer:
x=11
Step-by-step explanation:
Start by distributing:
4-2(x-5)= x-19
4-2x+10= x-19
Add 19 and 2x to both sides (the -19 and -2x will turn into 0)
4+10+19= 2x+x
Add 4+10+19
33= 3x
Divide by 3
x=11
If f(x) = 2x2 + 3 and g(x) = x2 - 7, find (f-9)(x).
O A. 3x2 - 10
O B. 3x2 - 4
O c. x2 + 10
O D. x² - 4
Plzzz helpp
Answers
Answer:
x^2 + 10
Step-by-step explanation:
f(x) = 2x^2 + 3
g(x) = x^2 - 7,
(f-g)(x) = 2x^2 +3 - ( x^2 -7)
Distribute the minus sign
= 2x^2 +3 -x^2 +7
Combine like terms
= x^2 +10
The last time Andy went bowling he had a mean score of 158
per game.
After three games Andy has a total score of 473. He thinks he
needs to score over 160 in game four to get a mean score
greater than 158.
(a) Is Andy correct?
Show why you think this.
Show a check of your working.
Your answer:
Answers
Answer:
no
Step-by-step explanation:
suppose he will get exactly the score of 160 in the game four, the mean score this time will be (473+160)/4=158.25
which has already reached the mean score 158 and even higher than it
therefore, his statement is wrong
write a function rule that relates r and t.
Input r: -2, 0, 2, 4, 6
Output t: 0, -1, -2, -3, 1
Answers
Answer: [tex]t=-\frac{1}{2}r- 1[/tex]
Step-by-step explanation:
For a lineal equation [tex]t=mr+n[/tex]
For r=0 and t=-1
[tex]-1=m(0)+n\\n=-1[/tex]
For r=-2 and t=0
[tex]0=m(-2)-1\\m(-2)=1\\m=-\frac{1}{2}[/tex]
Them [tex]t=-\frac{1}{2}r- 1[/tex]
???? The output for 6 is 1????
the points scored per game by a professional basketball player are represented by the box plot below if the player scores 9 points and 35 points in the next two games how is the median of the data set affected
Answers
Answer:
The median points per game is not affected.
Step-by-step explanation:
Compare the points scored in the two most recent games to the values given in the box plot to determine how the new values affect the median of the original data set.
The box plot for points scored indicates that the minimum points per game is 11, the maximum is 26 points, and the median is 21 points.
Since the median of 21 is between the two new values of 9 and 35, the median points per game is not affected by the new values.
