Answers
Answer:
a) x = 14
b) The perimeter of △QRS is 77 units.
Step-by-step explanation:
a) Due to the question asking for a solution using the Triangle Proportionality Theorem, it is assumed that △RQS is similar to the smaller triangle inside it.
Let us define the point at which the line inside △RQS meets line RQ as T, and the point at which that same line meets line RS as V.
Hence, △RTV ~ △RQS.
According to the Triangle Proportionality Theorem:
[tex]\frac{RT}{RQ} = \frac{TV}{QS} = \frac{VR}{SR}[/tex]
Hence, we can substitute all values that we know from the diagram:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{TV}{17} = \frac{21 - 7}{21}[/tex]
After getting this information, all we have to do is simplify and solve the equation:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{21 - 7}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{14}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{2}{3}[/tex]
[tex]3(2x - 2) = 2(2x + 11)[/tex]
[tex]6x - 6 = 4x + 22[/tex]
[tex]6x - 4x = 22 + 6[/tex]
[tex]2x = 28[/tex]
[tex]x = 14[/tex]
To verify this answer, we can plug in the value of x into the equation:
[tex]\frac{2(14) - 2}{2(14) - 2 + 13} = \frac{2}{3}[/tex]
[tex]\frac{26}{39} = \frac{2}{3}[/tex]
[tex]\frac{2}{3} = \frac{2}{3}[/tex]
Hence, after verification, we can get the answer: x = 14.
--------------------------------------------------------------------------------------------------------------
b) To find the perimeter of △QRS, all we have to do is to add all the lengths of the sides of △QRS together.
Hence, 2(14) - 2 + 13 + 17 + 21
= 28 - 2 + 13 + 17 + 21
= 77 units
Therefore, the perimeter of △QRS is 77 units.
Hope this helped!
Related Questions
The area of a rectangle is 36 square meters. If the length of the rectangle is 3, what is the width?
a
12
b
15
c
108
d
9
Answers
So, 36/3 = 12
Width is 12
At a bake sale, as student spent $11.00 buying 3 brownies and 5 cookies. His friend spent $3.95 buying 1 brownie and 2 cookies. What is the price of a brownie?
Answers
Answer:
$[tex]$2.25[/tex]
Step-by-step explanation:
Let [tex]b =[/tex] the cost of one brownie, [tex]c =[/tex] cost of one cookie
[tex]3b + 5c = 11[/tex]
[tex]b+2c = 3.95[/tex]
Times [tex]3[/tex] on both sides on the second equation above to get the following:
[tex]3b + 6c = 11.85[/tex]
[tex]3b+6c - (3b+5c) = 11.85-11[/tex]
[tex]3b+6c-3b-5c = 0.85[/tex]
[tex]c = 0.85[/tex]
To find the value of [tex]b[/tex], use substitution:
[tex]b+2c = 3.95[/tex]
[tex]b = 3.95-2c[/tex]
[tex]= 3.95 - 2\times0.85[/tex]
[tex]= 2.25[/tex]
[tex]\therefore[/tex] the cost of a brownie is $[tex]$2.25[/tex]
Hope this helps :)
Write the slope-intercept form of the equation of the line through the given point and slope.
Point: (1, -3)
Slope: -4
Answers
Answer:
y=-4x+1
Step-by-step explanation:
Graph (1,-3)
Go down 4 over one/ up left one
Get y-intercept
Then BOOM you got it
Answer:
y = -4x + 1
Step-by-step explanation:
We are given that a line has a slope of -4 and a point (1, -3).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept.
As we are already given the slope, we can immediately plug its value into the equation.
Substitute -4 as m in the equation.
y = -4x + b
Now we need to find b.
As the equation passes through the point (1, -3), we can use its values to help solve for b.
Substitute 1 as x and -3 as y.
-3 = -4(1) + b
Multiply.
-3 = -4 + b
Add 4 to both sides
1 = b
Substitute 1 as b in the equation.
y = -4x + 1
Topic: writing the equation of the line (slope-intercept form)
See more: https://brainly.com/question/22448557
HELP URGENT !!!!!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
Which of the following represents an inequality statement with a solution of
Please help out I’ll give you brainliest
Answers
Answer:
the second to last one
Step-by-step explanation:
Sorry if it is incorrect!
GIVING BRAINLIEST AND STARS
13)
Using a map scale of 1/2 inch = 10 miles, what would be the distance on the map between two cities that are actually 120 miles
apart?
A)
6 inches
B)
8 inches
C)
10 inches
D)
12 inches
Answers
Answer:
A) 6 Inches
Step-by-step explanation:
1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.
Conversion rate is 120 ÷ 10 which equals 12.
Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.
i'd appreciate a brainliest :)
Carrie has 18 pens. Carrie has 2 more than 4
times the number of pens that Patricia has.
Exactly how many pens does Patricia have?
Answers
Answer: ( sorry I misread the problem)
I'm not sure what I'm supposed to be multiplying with
but I'll try my best
subtract 2 with 18 and divide 4 with the remaining
18 -2 = 16
then it is 16/4= 4
Pat has a total of 4pens
Round 33,500 to the nearest 1000.
Answers
Answer: 34,000 (Since it's 500, it rounds up)
I hope this helps, and Happy Holidays! :)
Use a power-reducing formula to rewrite the given expression in terms of the first power of the cosine:
tan^2(8x)
Answers
tan²(8x) = sin²(8x) / cos²(8x)
… = (1 - cos²(8x)) / cos²(8x)
… = 1 / cos²(8x) - 1
… = 2 / (1 + cos(16x)) - 1
where the last equality follows from the half-angle identity for cosine,
cos²(x) = (1 + cos(2x)) / 2
Can someone help me with 3 and 4
Answers
Answer:
x÷3+10 (if x=15)
15÷3+10
5+10
15
what is the correct factorization of x^2 - 2x - 15?
Answers
Answer:
Step-by-step explanation:
x2 - 2x - 15
x2 - 5x + 3x - 15
x(x - 5) + 3(x - 5)
(x - 5) and (x + 3) are the factors
if this needs to be solved further, you will need to set both of these equations equal to 0.
x-5=0 and x+3=0
this will give you x=5 and x=-3
i hope this helped :)
Will give brainliest please help
Answers
Answer:
49
Step-by-step explanation:
In the middle of the figure , there's a square whose each side length is 7. So area of the square will be [tex] {7}^{2} = 49 \: {unit}^{2} [/tex]
What’s three more than seventeen?
Answers
hope this helps :)
which statement is true regarding the graphed functions?
Answers
Answer:
if -2 refers to the y-intercept "f(-2)=g(-2)" would be correct
y = 230x + 100
Is this proportional or non proportional?
Answers
Proportional equations are of the form y = kx, for some fixed constant k. The k value is the constant of proportionality.
The +100 at the end is why we don't have a proportional equation.
Visually all proportional equations go through the origin, meaning the lines have y intercept of 0. For y = 230x+100, the y intercept is 100.
Dkendbdjdbebdbdbdjdnd
Answers
Answer:
5/2
Step-by-step explanation:
The 5^-3 and 5^6 cancel out to be 5^3. Then the 5^3 cancels out with the 5^2 in the denominator and leaves you with just a 5. The 2^2 makes the 2^3 in the denominator just 2. So, you are left with 5/2! Hope this helps.
Which of the following is equivalent to 75/100? A 2/3 B 10/15 C 25/50 D 15/20
Answers
Answer:
D. 15/20
Step-by-step explanation: Because if it is 100 divide by 5 then it equals 20 and since 75% is 3/4 then 15/20 is your answer.
Answer:
D 15/20
Step-by-step explanation:
A quiche took 101 minutes to make and 175 minutes to bake. Estimate the combined time it took to prepare the quiche by rounding to the nearest ten first and then adding the rounded numbers.
Answers
Answer:
1233
Step-by-step explanation:
kieley
Answer:
80
Step-by-step explanation:
180-100+80.
A man travels 320 miles in 8 hours. If he continues at the same rate, how many miles will he
travel in the next 2 hours?
Answers
Answer: 80 miles
Step-by-step explanation:
320miles/8hours= 40mph
40mph=xmiles/2hrs
40*2= 80 miles
HELP GIVEING BRAINLIST What is the solution set of -11 > 1 + a?
a > -10
a -12
a < -10
a < - 12
Answers
Answer:
the solution set is -11 > 1 + a?
a > -10
a -12
a < -10
What is the quotient of 228 ÷ 12?
Answers
Answer:
19
Step-by-step explanation:
228/12=19
Help me pleaseeeeeeeeeeeeeeeeee
Answers
Which of these tables represents a function?
Answers
Answer:
W
Step-by-step explanation:
The table that will represent a function is the table where every x-value (domain) has exactly one y-value (range).
Table W represents a function because each x-value has exactly only one y-value.
The other tables have two y-values assigned to a one x-value.
Answer:
W
Step-by-step explanation:
Please help me 20 points!!!!!
Answers
Answer:
A. 0.4 km
B. 48 fruits to 12 vegetables
C. 72 hours
60%
Step-by-step explanation:
1 km = 1000 m
You have 400 m
1000m/1km = 400m/1000m
400/1000
0.4km
4:1
Ok so an easy way to do this one is multiplication.
you need the number of fruits to be 4 times more than the number of vegetables.
A would be 2:1 because 16 is 2 times more than 8
B would be 4:1 because 48 is 4 times more than 12
C would be 8:1 because 24 is 8 times more than 3
D would be 3:1 because 60 is 3 times more than 20
B would be the correct answer
If they traveled 216 miles in 3 hours, to find average you have to divide miles by hours.
216/3
72 hours
The tigers won 12 of their last 20 games.
12/20
0.6
Percent is 100 times the decimal.
0.6*100
60%
Don't be afraid to reach out with any more questions! I hope this helps!
************************
Answers
Answer: I think i my be wrong but i thing its B
Step-by-step explanation:
21. Which property is used to simplify the expression 5(3x + 18) to 152 + 90?
Can you answer this?
Answers
find the area of each trapezoid 32 ft x 16 ft 18 ft
Answers
Answer:
A = 432 ft^2
Step-by-step explanation:
[tex]A=\frac{a+b}{2} *h[/tex]
A = (32+16)/2 * 18
A = 48/2 * 18
A = 24*18
A = 432 ft^2
15 people are expected for a dinner. Three ounces of corn serves one person. A can of corn is nine ounces. How many cans of corn should be bought for the dinner?
Answers
Answer:
there should be 5 cans of corn! hope This Helps
Step-by-step explanation:
Answer:
The answer is 5
Step-by-step explanation: You have to multiply the amount of people by the servings a person gets (15*3), you then divide that by the amount of ounces a can has (45/9) the result is 5.
Write the following ratio in simplest form 8 to 12
Answers
Answer:
2/3 or 2 to 3
Step-by-step explanation:
Good luck!
Hurry please
I need the answer to this one in 2 minutes
Answers
Answer:
125
Step-by-step explanation:
45 ÷9=5
5² or 5×5=25
25×5=125
Hope this helps!
Answer:
I THINK ITS
Step-by-step explanation:
5x(2025 ÷81)
5x25
125