Answers
Since two sides and one included angle is equal in △PQS and △PRS, we can conclude that they are congruent under the SAS congruence criterion.
Which means :
▪︎Angle S = Angle S
▪︎PS = PS
▪︎QS = RS
Given :
Measure of segment QS = 6n+3
Measure of segment RS = 4n+11
Thus :
[tex] = \tt6n + 3 = 4n + 11[/tex]
[tex] = \tt6n + 3 - 4n = 11[/tex]
[tex] =\tt 2n + 3 = 11[/tex]
[tex] = \tt2n = 11 - 3[/tex]
[tex] = \tt2n = 8[/tex]
[tex] =\tt n = \frac{8}{2} [/tex]
[tex]\hookrightarrow\color{plum}\tt n = 4[/tex]
Thus, the value of n = 4
Measure of segment QS :
[tex] =\tt 6n + 3[/tex]
[tex] = \tt6 \times 4 + 3[/tex]
[tex] = \tt24 + 3[/tex]
[tex]\color{plum}\tt \: \bold{QS = 6n + 3 = \tt\bold{27}}[/tex]
Thus, measure of QS = 27
Measure of RS :
[tex] =\tt 4n + 11[/tex]
[tex] =\tt 4 × 4 + 11 [/tex]
[tex] =\tt 16+11 [/tex]
[tex]\color{plum}\tt \: \bold{RS = 4n + 11 = \tt\bold{27}}[/tex]
Measure of QR :
[tex] =\tt 27+27[/tex]
[tex]\color{plum}\tt \: \bold{QR = 27+27 \tt\bold{=54}}[/tex]
Thus :
▪︎QS = 27
▪︎RS = 27
▪︎QR = 54
Therefore, the correct options are :
▪︎(C) SR = 27
▪︎(D) QR = 54
Related Questions
!! 100 points for anyone who answers this problem !!
1,673,581,437 x 9,852,463,267 =__________
NO CALCULATORS!
lets see how smart you are >:)
Answers
Answer:
1,673,581,437 x 9,852,463,267 = 1.6488899E19.
Answer:
16488899632375574679
Step-by-step explanation:
So you have to multiply 1,673,581,437 x 9,852,463,267
Your answer is 16488899632375574679
Segment AB measures 3 cm. Point O is the center of dilation. How long is the image of AB after a dilation with . . .
Use decimal notation if necessary.
a. scale factor 5?
Answers
Answer:
The image of AB will be 15 cm long after dilation by a scale factor of 5.
Step-by-step explanation:
We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.
If the scale factor > 1, the image is enlarged If the scale factor is between 0 and 1, it gets shrunk If the scale factor = 1, the object and the image are congruentRule to calculate the mage of the segment AB after dilation of the segment AB by a scale factor 5 centered at the origin
AB = length → A'B' = 5(length)
It means the length of the image of the segment AB can be determined by multiplying the length of the original segment AB by 5.
so
AB = 3 cm
Thus, the length of image A'B' will be:
A'B' = 5(3) = 15 cm
Therefore, the image of AB will be 15 cm long after dilation by a scale factor of 5.
What is the range of the function y-e*+1 graphed below?
5
4
3
2
1 +
--5
-4
-2-11
1 2 3
4 5
9 9 9 9
y > 0
Ny CD
yal
Answers
Answer:
2
Step-by-step explanation:
Determine whether each pair of angles is conguent or not congruent. Select the correct answer for each lettered part.
a. <A and <B O Congruent O Not congruent
b. <A and <C O Congruent O Not congruent
c. <B and <C O Congruent O Not congruent
d. <B and <D O Congruent O Not congruent
e. <C and <D O Congruent O Not congruent
Answers
Answer:
a. congruent
b. not congruent
c. not congruent
d. congruent
e. not congruent
Step-by-step explanation:
a, b, & d are 45 degrees each.
c >45 degrees
a map is drawn in the scale of 1:500000. the area of a pond on the actual ground is 100km^2. find the area on the map in square centimetres that represents the pond
Answers
Answer:
2 000 000 [tex]cm^{2}[/tex]
Step-by-step explanation:
100 [tex]km^{2}[/tex] = 1 000 000 000 000 [tex]cm^{2}[/tex]
the scale of 1:500000 means that 1 cm in the map represents 500000 cm in reality
So on the map this pond's area would be
[tex]\frac{1 000 000 000 000}{500000}[/tex] = 2 000 000 [tex]cm^{2}[/tex]
I need help on this question I’m in the middle of a quiz please answer if you know the answer.
Answers
Answer:
y-2=0
Step-by-step explanation:
okk
simple
y-2=0
okk
Answer:
second one
Step-by-step explanation:
help! How many square feet of outdoor carpet will we need for this hole
Answers
Try to find the area of the brown spots, which filled in as green, would make one big rectangle.
1. Take the whole area of the rectangle (use the area of the brown rectangle around the green, and the area of the brown triangle towards the top left).
The area for the brown rectangle
A = b*h becomes A = 2*3 = 6 ft^2
Area for brown triangle (upper-left) is found by the length of the whole figure shown. The whole length is 12ft at the bottom; at the top, we know 6ft and 2ft. Therefore, the missing measurement there is 12ft - (6ft + 2ft) = 4ft
Area for the triangle (I will include some trigonometry; don’t be afraid to use it!:)
Find the long side of the triangle:
Pythagorean Theorem: a^2 + b^2 = c^2
which becomes:
3^2 + 4^2 = c^2
9 + 16 = c^2
c^2 = 25
sqrt(c^2) = sqrt(25)
c = 5
Next,
I know there are easier formulas and processes for the following, but they will work.
S (semiperimeter)= 1/2(a+b+c)
Counting up the sides of the triangle, then dividing by two will give you your semiperimeter.
Then,
A= sqrt [(S)(S-a)(S-b)(S-c)] = 6
I believe that the S value and a value are the same because that brown triangle made earlier is a 3-4-5 triangle (the sides).
Finally, now that we know the area of the brown rectangle and the brown triangle, we can subtract them from the big rectangle!
1. The big rectangle: A= b*h becomes A = 12*5 = 60 ft^2
2. Take the 60 ft^2 and set up the following:
60 ft^2 - (6ft^2+6ft^2) = 60ft^2 - 12ft^2 = 48ft^2, as the final answer.
Point A has coordinates (5,3). If Point A is reflected across the x-axis, what are the coordinates of its image?
(-5, -3)
(-5, 3)
(3, -5)
(5, -3)
Answers
Answer:
(5, -3)
Step-by-step explanation:
when you reflect across x axis the y changes symbols.
Given the equation 2x − 5 = 8, which order of operations completely solves for x? (1 point)
Answers
Answer:
x=11 please correct me if i'm wrong. I hope I helped.
Step-by-step explanation:
2x-5=8
add 2 to both sides
so the 2 on the left cancels out, and now on the right it is 6
now add 5 to both sides, so x is by its self and on the right of the equation sign it is 11
so x=11
Question 3 of 10
What is the measure of _XYZ shown in the diagram below?
Possible answers 69, 67 ,68,66
Answers
I've seen the graph, the answer is A
Name
Date
8. The graph below represents the number of containers and liters of water
contained in the containers. What is the constant of proportionality?
60
Water (liters)
10 15 20
Number of Containers
25
I
I
9. The graph below represents the number of mennte that
Answers
equation to find original price if sale price of $429 is a 34% discount
Answers
Answer:
The original price is $650
Step-by-step explanation:
There's an actual algebra method for this, but this is my method because I find it way easier to remember.
Since the most you can discount out of an item is 100% (well, it's considered free then) let's subtract 100 - 34, which is 66.
Now, turn it into a decimal because it makes the numbers easier- 0.66.
Since when you're finding the discount of an original price, you multiply the original price by the discount- instead for finding the original price for a discounted item we divide $429 by 0.66 instead, since when you divide a number by another number that's under 1 the quotient is a larger number.
So, 429 ÷ 0.66 = 650.
Therefore, the original price of the $429 sale price for a 34% discount is $650.
Given the following two points, find the Rate of Change for the function.
(-2,-1) and (4,5)
Answers
Answer:
(6, 6)
Step-by-step explanation:
(x) 4-(-2) = 6
(y) 5-(-1)= 6
Rectangle HYGT has a perimeter of 170 inches. If the length is 10x - 7
and the width is 6x + 12, how wide is the rectangle?
Answers
Answer:
The wide of the rectangle = 42 inches
The length of the rectangle = 43 inches
Step-by-step explanation:
Step(i):-
Given that the length of the rectangle = 10x-7
Given that the width of the rectangle = 6x +12
The perimeter of the rectangle = 2(length + width)
Given that the perimeter of the rectangle = 170
Step(ii):-
2(length + width) = 170
length + width = 85
10x-7 +6x +12 =85
16x +5 = 85
16x = 85-5 = 80
x = [tex]\frac{80}{16}[/tex]
x = 5
Final answer:-
The length of the rectangle = 10(5)-7 = 50-7 = 43
The wide of the rectangle = 6x +12 = 6(5) + 12 = 30+12 =42
The perimeter is the sum of its all sides. The rectangle is 42 inches wide.
What is the perimeter of the rectangle?The perimeter is the sum of its all sides. The perimeter of the rectangle is twice the sum of its length and its width.
[tex]\rm \text{Perimeter of rectanle}=2(Length +Breadth)[/tex]
As it is given to us that the length of the rectangle is (10x-7), while the width of the rectangle is (6x+12). Also, the perimeter of the rectangle is 170 inches. Therefore, using the formula of the perimeter of the rectangle we will get,
[tex]\rm Perimeter=2(Length +Breadth)\\\\170=2[(10x-7)+(6x+12)]\\\\170=2{10x-7+6x+12}\\\\170=2(16x+5)\\\\170=32x+10\\\\32x=160\\\\x=\dfrac{160}{32} = 5[/tex]
Now, substitute the value of x,
The width of the rectangle = 6x + 12 = 6(5)+12 = 30+12 = 42 inches.
Thus, the width of the rectangle is 42 inches.
Learn more about the Perimeter of Rectangle:
https://brainly.com/question/15287805
A magazine costs $3 and a book cost $7 if you want to spend exactly $45 on reading this month and you need to buy eight magazines how many books can you buy write an equation in standard form modeling the situation then see how many books you can buy let em represent the number of magazines you buy and B represents the number of books you buy.
Answers
Answer:
m = 8 and b = 3 OR m = 15 and b = 0
Step-by-step explanation:
Note that the conditions on this problem could be contradictory (they are likely not, but could be)
let m be the number of magazines bought
let b be the number of books, then
3m is the cost of the magazines bought and
7b is the cost of the books bought, since $45 exactly must be spent then
3m + 7b = 45
Let us assume m = 8 and see what happens
3(8)+7b = 45
24+7b=45
7b=21
b=3, this meets the requirements and results in an integer (whole) number of books, if b had ended up as a fraction, then m=8 would have to be wrong and we would have tried m=9 , then 10, 11, 12, up to 15 if necessary until we got a whole number of books. Notice that 15 magazines and 0 books also works
17. The expression x2 - 12x + 36 represents the
area of a rectangular chalkboard. What is the factored
form of the expression? If each factor represents the
height and width of the chalkboard, what is the most
specic description of its shape?
A.(x-6), square
c B. (X - 5)(x + 6); rectangle
C. (x + 5)2: square
D. (x - 12): square
Answers
Find two numbers that multiply to 36 and add to -12. Those two numbers are -6 and -6, making the factored form (x-6)(x-6) or (x-6)^2
Sarah and Brian went shopping and spent a total of $47.5 Brian spent $15.5 less than Sarris me how much she Brian spend
Answers
Answer:
32
Step-by-step explanation:
The rectangle below has an area of 35x^3 square meters and a width of 5x meters.
What is the length of the rectangle?
Answers
[tex]a = lw[/tex]
[tex]35 {x}^{3} = l(5x)[/tex]
[tex] \frac{35 {x}^{3} }{5x} = l[/tex]
[tex]7 {x }^{2} = l[/tex]
The length is 7x²
The area of a rectangular outdoor stage has been extended on one side. The entire new area in square meters can be written as 216+12x. Factor the expression to find the dimensions of the extended stage.
PLZ HELP
Answers
Answer:
Dimension of the extended stage is; length = 6 m and width = 2x m
Step-by-step explanation:
Area of the rectangular outdoor = length x width
New area = area of the outdoor + area of the extended stage
= 216 + 12x
= 6(36 + 2x)
New area = 6 (36 + 2x)
So that;
The dimension of the rectangular outdoor = 36 x 6
i.e length = 36 m and width = 6 m
So that the dimension of the extended stage = length x width
= (6 x 2x) m
i.e length = 6 m and width = 2x m
Which question is best for gathering statistics?
A) What ethnic groups make up the population of your state?
B) Where were you born?
Answers
Answer: A
Step-by-step explanation:
A $170.00 item is marked down by 10%.
Answers
Answer:
The new price is $153
Step-by-step explanation:
10% 0f 170 is 17
170-17=153
13r=3/7 what is r?
R=91/3. R=39/7
R=7/39. R= 3/91
Answers
Answer:
r=3/91
Step-by-step explanation:
look at the picture ............
All trapezoid are ______________________.
Answers
Answer:
quadrilaterals:))))))))))))
Step-by-step explanation:
hope it helped:))))))))))
Answer:
Quadrilaterals
Step-by-step explanation:
All trapezoids have 4 sides, quadtrilaterals are 4-sided polygons.
Hope this helped :)
Ask me anything I’ll answer you
Answers
Answer:
uhh......weirdest dream you've had?
Harleigh bought new wrestling shoes for $45. Last
week they were on sale for $35, what is the percent of
increase?
Answers
Answer:
28.57
Step-by-step explanation:
35-45 would be a 28.57 percent increase
What is the final elevation if a. A bird starts at 20 m and changes 16m? b. A butterfly starts at 20 m and changes -16m? c. A diver starts at 5 m and changes -16m? d. A whale starts at -9 m and changes 11 m? e. A fish starts at -9 meters and changes -11 meters?
Answers
Answer:
A.36m
C.-11m
D.2m
E.20m
Step-by-step explanation:
Sorry I forgot b
The final elevation of the given animals is as follows 1)Bird = 36m 2) butterfly = 4m 3) diver = -11m below sea level 4) whale = 2m 5) fish= -20 m
What is the rule for summing positive and negative numbers?To get the sum of a negative and a positive number, use the sign of the larger number and subtract. For example: (–7) + 4 = –3. 6 + (–9) = –3.
Given here,1) A bird starts at 20 m and changes 16m in a positive direction therefore net elevation is 20 + 16 = 36m
2) A butterfly starts at 20 m and changes -16m, thus again net elevation is
20-16 = 4m
3) A diver starts at 5 m and changes -16m, the net depth of the diver below sea level is 5+(-16) = -11m
4) A whale starts at -9 m and changes 11 m in the positive direction then net depth is -9+11 = 2m
5) A fish starts at -9 meters and changes -11 meters in the negative direction thus net depth is = 9-11= -20m below sea level
Hence these are the final answers.
Learn more about the BODMAS rule here:
https://brainly.com/question/29795897
#SPJ5
Pls help me and answer the question and not take my points pls and thank you.
Answers
Answer:
1/9 of 18 is 2
5/9 of 18 is 10
9 rows
1.Write 0.50 as a fraction
2.Is 7.199 greater than or less than 7.104
3.Solve: 3x (4+1) - 5 =
Answers
Answer:
1) 50/100
2)greater
3)10
Answer:
Step-by-step explanation:
1) 0.50=50/100=5/10=1/2
2) 7.199>7.104 (greater than)
3) 3x(4+1)-5=3(5)-5=15-5=10
The price of concert ticket dropped from $177 to $91. What was the precent of decrease in price of tickets? PLEASE HELP ASAP
Answers
Answer:
The percent of decrease can be calculated with this formula:
(Original value - New Value)/(Original Value)
In this case, the original value is 117 and the new value is 91.
So the percent of decrease is 26/117, or about 22%.
Hope this helps!
The radius of the Ferris wheel is 125ft. Which is the circumference of the Ferris wheel, rounded to the nearest foot?
Answers
Answer: 786 ft
Step-by-step explanation:
The Ferris wheel is circular in shape so this can be treated as a circle.
If the radius is 125 ft, the circumference can be calculated with the formula:
= 2 * π * radius
= 2 * 22/7 * 125
= 785.71 ft
= 786 ft