Answer:
(b) ΔRST ~ ΔRUS ~ ΔSUT(a) a = 400/21; b = 580/21Step-by-step explanation:
1.Similarity statements are written with corresponding vertices in the same order. So, there are two tasks involved: (1) identifying corresponding vertices; (2) making sure they are written in the same order in the similarity statement.
Here, we could go to the trouble to identify all pairs of corresponding vertices. Then we could write our own similarity statements and see which answer choice corresponds. However, it is sufficient to do just enough work to allow elimination of bad answer choices.
Sometimes in figures like this, it is difficult to tell the short side of the right triangle from the long side. (This figure is pretty helpful.) However, it is always possible to identify the hypotenuse of each triangle. They are ...
RT, RS, ST
What this means is that these letters should appear in the same spots in each part of the similarity statement.
(a) RT are in the 1st and 3rd spots of the first triangle name. In the second triangle name, those spots are occupied by SU--not a hypotenuse. (rejected)
(b) The 1st and 3rd spots of each statement are occupied by RT, RS, ST, so this is a viable candidate.
(c) The 1st and 3rd spots of the first triangle name are occupied by ST, but those spots of the second triangle name are SU--not a hypotenuse. (rejected)
(d) The 1st and 2nd spots of the first triangle name are occupied by RT, and those spots in the second triangle name are RS. However, those spots in the third triangle name are TU--not a hypotenuse (rejected).
The only viable choice for similarity statement is the second choice:
ΔRST ~ ΔRUS ~ ΔSUT
__
2.We can find segment 'a' by writing a proportion between sides of the largest and medium-size triangles:
hypotenuse/long side = (21 +a)/29 = 29/21
21(21 +a) = 29² . . . . . multiply by 29·21
441 +21a = 841 . . . . simplify
21a = 400 . . . . . . . subtract 441
a = 400/21 . . . . . . . . . . . divide by 21. (eliminates choices C and D)
At this point, we can solve for b in similar fashion. However, it is sufficient to use "triangle sense" to eliminate the remaining bad choice. We know the hypotenuse of any right triangle is the longest side. Here, that means ...
b > 20 . . . . . (eliminates choice B)
The only viable answer choice is A:
a = 400/21, b = 580/21
__
Additional comments
For multiple-choice questions, you can arrive at a solution just as effectively by eliminating bad choices as you can by working the problem in detail to develop the correct choice. Here, we try to use "common sense" to simplify the work as much as possible. This saves time, which is what you want when you're working a timed assignment.
__
This geometry has several interesting features. If you start at the right angle and write side lengths in order clockwise, the two "inside triangles" have the order {longest side, hypotenuse, shortest side}. The overall outside triangle has the order {shortest side, hypotenuse, longest side}. That is, the order of the outside triangle vertices is counterclockwise for the same order of corresponding sides. Realizing/remembering this can immensely simplify the process of writing similarity statements for these triangles.
Another feature is one we demonstrated in the solution for 'a' in the second problem: the length of a segment touching the longest hypotenuse is the geometric mean of the lengths of the hypotenuse segments it touches. In the case in point: 29 = √((21)(21 +a)). We could also write the relationship: 20 = √((21)(a)), perhaps getting there more directly: a=400/21. And finally, b = √((a(a+21)). These geometric mean relationships all derive from the proportions you can write using triangle similarity.
(The geometric mean of two numbers is the square root of their product. For n numbers, it is the n-th root of their product.)
+2+1+6 this is confusing what is the answer and explanation
Answer:
9
Step-by-step explanation:
hi I'm pretty sure this is really wrong but just kinda guessing
+2 is just a positive 2 so it's just known as 2
2+1+6 = 9
Answer: 9
Step-by-step explanation:because if its 2+1+6 then u get 2 and 6 add thats 8 then your 1 and its 9.
PLEASE HELP!
subtract [tex]\frac{3p}{5}[/tex] - [tex]\frac{1}{6}[/tex]
Answer:
Your answer is: 18p-5/30
To subtract fractions, find the LCD and then combine.
Step-by-step explanation:
Hope this helped : )
Answer:
---------------------------------answer will be (18p-5)/30_____________________Prove that the difference between a two-digit number and the product of its digits will always be a 2 digit number.
Solution:
Let's take the greatest two-digit number as an example.
=> 99Proving...
99 - (9 x 9) = Two-digit number=> 99 - 81 = Two-digit number=> 18 = Two-digit numberSince the difference between the greatest two-digit number and the product of its digits is a two-digit number, the difference between the other two-digit numbers '10, 11, 12.... 97, 98' and the product of its digits will always be a two-digit number, as the product of its digit is less than the two-digit number.
Hence proved. ✔✔
Step-by-step explanation:
Let the two-digit number is [tex]xy[/tex]
This can be written as:
10x + y, where 1 ≤ x ≤ 9 and 0 ≤ y ≤ 9The difference between the number and product of its digits is:
d = 10x + y - xyRewrite this as below:
d = 10x - xy + y - 10 + 10 =
x(10 - y) - (10 - y) + 10 =
(x - 1)(10 - y) + 10
We see that:
0 ≤ x - 1 ≤ 8 according to the condition given above1 ≤ 10 - y ≤ 10 again according to the condition given aboveThe value of d is then:
0 + 10 ≤ d ≤ 8*10 + 1010 ≤ d ≤ 90Proved50 points pls help!!
Answer:
p = 23
q = 18
Step-by-step explanation:
The four interior angles of a square are all 90° each
4p - 2 = 90
⇒ 4p = 92
⇒ p = 92 ÷ 4
⇒ p = 23
5q = 90
⇒ q = 90 ÷ 5
⇒ q = 18
Answer:
p=23; q=18.
Step-by-step explanation:
1) m∠(XWZ)=90, then 4p-2=90 and p=23°;
2) m∠(WZY)=90, then 5q=90 and q=18°.
Which of the following are solutions to the equation below?
Check all that apply.
4x2 + 12x + 9 = 25
V5-3
O A. x=
16.
O B. x= -1
Answer:
see below
B.
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 and -4
Sofie claims to be a tasting expert. To test her abilities, someone bakes Sofie a cake using 3 of the following
ingredients:
Coffee
Nutmeg
Vanilla
Cinnamon
Sea salt
Ginger
Sofie's challenge is to identify which set of 3 ingredients was used in the cake. Suppose that Sofie is just
randomly guessing.
What is the probability that Sofie correctly identifies the set of 3 ingredients in the cake?
Summing all the ingredients to get the total sample size, we applied the formula for obtaining the probability which is
Pr(3) = 0.5
ProbabilityGiven Data
Sample Space
CoffeeNutmegVanillaCinnamonSea saltGingerTotal Sample size = 6
Probability of identifying 3 ingredient used is
Pr(3) = 3/6
Pr(3) = 1/2
Hence the Probability is 0.5
Learn more about probability here:
https://brainly.com/question/25870256
Answer:
1/20
Step-by-step explanation:
From Kahn
Identify whether each equation has one solution, infinitely many solutions, or no solution.
2.3x - 7 = -7
3x = 5 + 3x
4(10 - x) = 40 - 4x
-7 + x = - (x + 7)
Answer:
1 solution
No solution
Infinitely many solutions
1 solution
Step-by-step explanation:
2.3x - 7 = -7
2.3x = 0
x = 0
1 solution
3x = 5 + 3x
0 = 5
No solution
4(10 - x) = 40 - 4x
40 - 4x = 40 - 4x
Infinitely many solutions
-7 + x = -(x + 7)
-7 + x = -x - 7
2x = 0
x = 0
1 solution
Answer:
he is right
Step-by-step explanation:
isosceles and equilateral
Answer:
I think it is 60°
Step-by-step explanation:
b/c angle of triangle is 180° and when we divide 180° by 3 it will be 60°
87.125 is it rational or irrational? Explain how.
Answer:
87.125 is rational
Step-by-step explanation:
it is a rational number because it can be represented as a fraction
A kite flying in the air has an 11-ft line attached to it. Its line pulled taut and casts a 9 -ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
All we have to do is apply the Pythagorean theorem which states that a²+b²=c²
where c is the hypotenuse of the triangle or the side facing the 90° angle.
Moreover a & b are the other two sides of the triangle.
[tex]11 {}^{2} = {9}^{2} + h {}^{2} [/tex]
where h is the height from the ground
[tex]121 = 81 + {h}^{2} [/tex]
[tex]h {}^{2} = 121 - 81[/tex]
[tex]h {}^{2} = 40[/tex]
[tex]h = \sqrt{40} = 6.324[/tex]
Rounding to the nearest tenth,
[tex]h = 6.3[/tex]
4Gopal is paid 20 000 rupees each month.
Jamuna is paid 19 200 rupees each month
Gopal and Jamuna are both given an increase in their monthly pay.
After the increase, they are both paid the same amount each month.
Gopal was given an increase of 8%
Work out the percentage increase that Jamuna was given.
Desperately need help
[tex]\begin{cases} x=-5\implies &x+5=0\\ x=3\implies &x-3=0 \end{cases}\qquad \implies \underline{a(x+5)(x-3)~~ = ~~\stackrel{0}{y}} \\\\\\ \stackrel{\textit{we also know that}}{P(0)=-30}\implies \begin{cases} x=0\\ y=-30 \end{cases}\implies a(0+5)(0-3)~~ = ~~-30 \\\\\\ a(5)(-3)=-30\implies -15a=-30\implies a=\cfrac{-30}{-15}\implies \boxed{a=2} \\\\[-0.35em] ~\dotfill\\\\ 2(x+5)(x-3)=y\implies 2(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \underline{2x^2+4x-30=y}[/tex]
Check the picture below.
Solve for all possible values of x : |x-3|+4=1
A: 6
B: 0
C: 6 or 0
D: no real solutions
Answer:
D: no real solutions
Step-by-step explanation:
Enola has a toy car collection. She keeps some in a display case and the rest on the wall. 155 of her toy cars are on the wall, and 69% of her toy cars are in the display case. What is the total number of toy cars in Enola's collection?
Give me brainliest if right: 106.95
The total number of toy cars in Enola's collection is 500 if 155 of her toy cars are on the wall, and 69% of her toy cars are in the display case.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
She keeps some in a display case and the rest on the wall. 155 of her toy cars are on the wall, and 69% of her toy cars are in the display case.
Let x be the total number of toy cars in Enola's collection:
69% of x = x - 155
0.69x = x - 155
0.31x = 155
x = 500
Thus, the total number of toy cars in Enola's collection is 500 if 155 of her toy cars are on the wall, and 69% of her toy cars are in the display case.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ5
factorise 3-x^2 can’t do it
Answer:
(√3 - x)(√3 + x)
Step-by-step explanation:
Use difference of two square formula:
a² - b² = (a - b)(a + b)
So a² = 3 ⇒ a = √3
and b² = x² ⇒ b = x
Therefore, 3 - x² = (√3 - x)(√3 + x)
I need help on 12 lol
Answer:
68.58m
Step-by-step explanation:
hope it helps!!!
Find the value of y and find m∠C and m∠D in the triangle given below.
y =
m∠C =
m∠D
Answer:
Step-by-step explanation:
(3c-5d)²EXPAND IT PLEASE
Answer:
9c^2 - 30cd + 25d^2
Step-by-step explanation:
(3c - 5d)^2
= (3c - 5d) (3c - 5d)
= [3c * 3c] + [3c * -5d] + [-5d * 3c] + [-5d * -5d]
= 9c^2 - 30cd + 25d^2
I need help with this question
Answer:
It's the second answer, hope this helps!
Lena pays $8.96 for every 3 ounces of coffee. If she were to
graph the relationship between the number of ounces of
coffee and the total cost, what would be the meaning of the
slope of this graph?
Answer:
A: the cost per pund of coffee
Step-by-step explanation:
You need x and y- values. So one would be the pound (x) and the other would be the cost (y)
Pls answer i will mark u brainlist
Hello!
75,000 - 10% of 75,000
= 75,000 -(10*75,000)/100
= 75,000 -7,5 => 67,500
67,500 - 10% of 67,500
= 67,500- ( 10*67,500)/100
=67,500 - 6,75 = 60,750
60,750 -10% of 60,750
= 60,750-( 10*60,750)/100
= 60,750 - 6,075 => 54,675
A package contains 4 cups of trail mix. He wants to divide the trail mix into 1/3 cup servings. How many 1/3 cup servings are there in 4 cups? Explain how you found your answer.
Answer: 12
Step-by-step explanation:
to find this, divide 4 by 1/3:
4/(1/3) = 4x3 = 12
there are 12 1/3 cup servings in 4 cups
Answer:
Hey there!
Contains 4 cups of trail mix
He wants 1/3 go cup servings
=> 4 ÷ 1/3
=> 4×3/1
=> 12
Therefore, there are 12 of 1/3 in 4 cups
Eric runs every day. He can run 5 miles in 50
minutes. What is the unit rate that Eric runs in
one minute?
Answer:
10
Step-by-step explanation:
If he runs 50 minutes 50 divided by 5 is 10
In the following pictograph, how many total books have the four groups read?
a. 27
b. 90
c. 54
d. 9
Best answer gets brainliest!
Answer:
c; 54
Step-by-step explanation:
to find the answer you can first add all the books together
this can be represented by
3 + 2 + 2.5 + 1.5
this answer is 9
then multiply it by 6
9 * 6 = 54
is is c
Given that ¹/x=²/y+¹/z. express y interms of x and z. if x=5 and z=10. find the value of y leaving your answer as a mixed fraction
Answer:
[tex]y=\dfrac{2xz}{(z-x)}[/tex]
Step-by-step explanation:
Given:
[tex]\dfrac{1}{x}=\dfrac{2}{y}+\dfrac{1}{z}[/tex]
[tex]\implies \dfrac{2}{y}=\dfrac{1}{x}-\dfrac{1}{z}[/tex]
[tex]\implies \dfrac{2}{y}=\dfrac{z-x}{xz}[/tex]
[tex]\implies 2xz=y(z-x)[/tex]
[tex]\implies y=\dfrac{2xz}{(z-x)}[/tex]
When x = 5 and z = 10:
[tex]\implies y=\dfrac{2(5)(10)}{(10-5)}[/tex]
[tex]\implies y=\dfrac{100}{5}[/tex]
[tex]\implies y=20[/tex]
multiply 8/2a^5 • 6/12a^2
Answer:
2/a^7
Step-by-step explanation:
how do you simplify 24+3x=3x+2(3•4)
Answer:
all rational numbers
Step-by-step explanation:
24+3x=3x+2(3*4) shows that there can only be two possible answer, all integers or no solution. As you can see 2*3*4 is 24, making the answer all rational numbers.
Solve for missing angle
Hello!! Your answer would be 55''. If the other side is the same length, the this side is 55'' too.
Hope this helps!
Answer:
135!!!
Step-by-step explanation:
Maddie has 18 flowers plants to put in her garden. she wants to plant them on 3 rows with an equal number on each row. how many rows will she plant
Answer:
6
Step-by-step explanation:
18 ÷ 3 = 6
3+3+3+3+3+3=18
Answer:
6 per row
Step-by-step explanation:
If Maddie has to spread out a total number of flowers (18) over a set number of sections (3) you would be able to solve this by dividing the total into the sections, which would look something like 18/3.
Pls answer the question attached.
I WILL MARK U BRAINLIST
Area of figure = area of trapezoid + area of rectangle
A(rectangle) = 18 x 5 = 90 cm2
A(trapezoid) = (10+18) x (13-5) : 2 = 112 cm2
A(figure) = 112 + 90 = 202 cm2