4. In the following diagram, STU, RTP and
RUQ are straight lines, SU is parallel to P2.
RPQ = 90°, SR = SP=9 cm, TU = 5 cm and
RU = 7 cm.
(a) Identify two triangles which are
congruent.
(b) Calculate the lengths of UQ and PQ,
Answers
a) The two triangles that are congruent are △RUQ and △SPR. b) The length of UQ is 7√2 cm. The length of PQ is 2√30 cm.
(a) The two triangles that are congruent are △RUQ and △SPR. This is because they have the same side lengths: RU=RP=7 cm, SU=SP=9 cm, and ∠RPQ=∠SPR=90°.
(b) To calculate the length of UQ, we can use the Pythagorean Theorem on △RUQ. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is UQ, and the other two sides are RU and RP.
[tex]UQ^2[/tex] = [tex]RU^2[/tex] + [tex]RP^2[/tex]
[tex]UQ^2[/tex] = [tex]7^2[/tex] + [tex]7^2[/tex] = 98
UQ = √98 = 7√2
Therefore, the length of UQ is 7√2 cm.
To calculate the length of PQ, we can use the Pythagorean Theorem on △PQR. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is PQ, and the other two sides are RP and QR.
[tex]PQ^2[/tex] = [tex]RP^2[/tex] + [tex]QR^2[/tex]
[tex]PQ^2[/tex] = [tex]7^2[/tex] + [tex]9^2[/tex] = 120
PQ = √120 = 2√30
Therefore, the length of PQ is 2 30 cm.
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Related Questions
Help me with this question please ;(
Answers
Answer:
I wish I could help but i did not learn this yet
Step-by-step explanation:
Please answer this below Question # 15
Answers
Answer:
[tex]c. \: 5x - 2y = 10 \\ \: \: \: \: \: 10x - 4y = 20 \\ [/tex]
Sam receives $50,000 for his monthly salary. If he pays $8,000 for electricity bill, $2,000bfor water bill and $10,000 for grocery. What percentage does he have left?
Answers
Answer:
60%
Step-by-step explanation:
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2. An Evergreen Eagle flies about 13 meters in one second. How many kilometers could it fly in 20 minutes? *
Answers
Answer:
Evergreen Eagle can will fly 1.56 km in 20 minutes.
Step-by-step explanation:
Speed of Evergreen Eagle = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
= [tex]\frac{13}{1}[/tex]
= 13 meters per second
With this speed Eagle can fly the distance in 20 minutes Or 120 seconds
= Speed × Time
= 13 × 120
= 1560 meters
Since, 1000 meters = 1 Km
1 meter = [tex]\frac{1}{1000}[/tex] km
Therefore, 1560 meters = [tex]\frac{1560}{1000}[/tex]
= 1.56 km
Therefore, Evergreen Eagle can will fly 1.56 km in 20 minutes.
Can you help me plz right answer only
Answers
Answer:
20
Step-by-step explanation:
To solve this problem use proportions. The tree's proportion is equal to [tex]\frac{30}{40}[/tex] and the shed's proportion is [tex]\frac{15}{x}[/tex]. These proportions are made by putting the height of the object over the length of the shadow. Then, cross multiply to find x. Do this by multiplying [tex]30 *x[/tex] and [tex]40*15[/tex]. Next set these equal to each other, [tex]30x=600[/tex]. Finally, divide both sides by 30 to find x. This equals 20 feet.
Jivesh brought his Model B rocket on a camping trip near the top of a mountain. He wants to model how it descends down the mountain. Here, he uses the equation h = −640t^2. When has the rocket descended 1,690 centimeters? Round your answers to the nearest hundredth. After t ≈ seconds, the rocket will have descended a distance of 1,690 centimeters. The negative time (can, cannot) be used in this context.
Answers
Answer:
i. 1.63 s
ii. The negative time cannot be used in this context
Step-by-step explanation:
i. Since h = −640t² and the rocket descends 1,690 m, h = -1,690 m (since there is a drop in height).
So, h = -640t²
t² = h/-640
t = √(- h/640)
Substituting h into the equation, we have
t = √(- h/640)
t = √[-(-1,690)/640]
t = √2.640625
t = 1.625
t ≈ 1.63 s
ii. So, the negative time cannot be used in this context because, the height drop is negative.
A species of bacteria is 10 micrometers long. A virus is 10,000 times smaller than bacteria. a. Using the table above, find the length of the virus in meters. Write the answer as a power. The virus is meter long
Answers
Answer:
[tex]10^{-4}[/tex] times 10 micrometers (or [tex]10^{-5}[/tex]) is [tex]10^{-9}[/tex]
Answer:
It's as long as the centimeter
Step-by-step explanation:
doing 0.000001x10,000 gives you .01
If I'm wrong flame me
After two years, the ash tree grew 51 inches. What is the unit rate? Use a ratio table to find the vertical growth after five years.
Answers
Answer:
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Step-by-step explanation:
Nina buys a small rug in the shape of a kite. The width of the rug is half its height. What are the width and the area of the rug
Answers
Answer:
Width = 1/2h
Area = 1/4h²
Step-by-step explanation:
This is quite a vague question from you. Being asked to find the width and area of a particular shape, without being given dimensions.
However, I would try to solve it nonetheless.
From your question, you stated that the width of the rug is half its height, if so, then,
w = 1/2h
Again, you're being asked to find the area. Area of a kite is given as
Area = 1/2 * Width * Height and as such, we have
Area = 1/2 * 1/2h * h
Area = 1/4 * h²
All that you need to do now is substitute the value of h
doughnuts are sold in bags and cartons a bag holds 4 doughnuts and a carton holds 10 doughnuts tom buys b bags of doughnuts and c cartons of doughnuts he buys a total of t doughnuts write down a formula for t in terms of b and c
Answers
Answer:
t = 4b + 10c
Step-by-step explanation:
t = total of doughnuts
b = bags of doughnuts which hold 4 each
c = cartons of doughnuts which hold 10 each
The 1st 3 terms of an A.P., a, a+d, and a+2d, are the same as the 1st 3 terms of a G.P.( a is not equal to 0). Show that this is only possible if r=1 and d=0
Answers
Answer:
See Below.
Step-by-step explanation:
The first three terms of an A.P is equivalent to the first three terms of a G.P.
We want to show that this is only possible if r = 1 and d = 0.
If a is the initial term and d is the common difference, the A.P. will be:
[tex]a, a+d, \text{ and } a+2d[/tex]
Likewise, for the G.P., if a is the initial term (and it does not equal 0) and r is the common ratio, then our sequence is:
[tex]a, ar,\text{ and } ar^2[/tex]
The second and third terms must be equivalent. Thus:
[tex]a+d=ar\text{ and } a+2d=ar^2[/tex]
We can cancel the d. Multiply the first equation by -2:
[tex]-2a-2d=-2ar[/tex]
We can now add this to the second equation:
[tex](a+2d)+(-2a-2d)=(ar^2)+(-2ar)[/tex]
Simplify:
[tex]-a=ar^2-2ar[/tex]
Now, we can divide both sides by a (we can do this since a is not 0):
[tex]-1=r^2-2r[/tex]
So:
[tex]r^2-2r+1=0[/tex]
Factor:
[tex](r-1)^2=0[/tex]
Thus:
[tex]r=1[/tex]
The first equation tells us that:
[tex]a+d=ar[/tex]
Therefore:
[tex]a+d=a(1)\Rightarrow a+d=a[/tex]
Hence:
[tex]d=0[/tex]
Q.E.D.
You are planning to retile the walls around your bathtub. You measure the dimensions of the wall and find that the length of the tub is 7 feet, the width of the tub is 2 feet and the height of the wall is 5 feet. You go to the hardware store to pick out some tile. You find ones that you like. There are 4 sizes of tile and are priced differently. The prices are 1 square inch tile is 10 cents, 6 square inch tile is 25 cents, 8 square inch tile is 75 cents and 18 square inch tile is $1.50. Find the best deal (price) for tile in order to tile your bathroom. How much will you spend? Why is this the best deal? Show ALL OF YOUR WORK and explain how you found the answer.
Answers
Answer:
it is the best deal cause i said
Step-by-step explanation:
3. Convert this rate (80km/hr) to a rate measured in m/s
Answers
Draw three line segments
P(4, 2) to H(4, 8)
G(4, 6) to J(7, 6)
H(4, 8) to K(8, 8)
Answers
A cut is made to the shape shown below at an angle from the top of the shape to the base of the shape. What is the shape of the cross
section that results from the cut?
A square
B. parallelogram
C. rectangle
D. triangle
Answers
Answer:
square
Step-by-step explanation:
why is this labeled high school this is so simple
Drag each graph to the correct location on the table.
The points on the graphs represent relations. Classify these relations according to whether or not they are functions
Answers
Answer:
Functions: Second Graph
Not functions: first and third graph
Step-by-step explanation:
The first and third graph are not functions and the second graph is a function. Use the vertical line test. I'm 100% sure.
By the vertical line test, it's clear that graph first will not be a function, second will be a function and third will also not be a function.
What is the e-test?A vertical line test is a test to determine whether a given function is a function or not.
In the vertical line test, we draw a vertical line on every x's point if the line intersects with only a single value of corresponding y then it will be a function otherwise not.
In the first given function if we draw a vertical line at x = 2 then it gave different values corresponding to y hence, it will not a graph.
In the second given function by drawing a vertical line, it gave a single unique value so it will be a function.
In the third given function if we draw a vertical line at x = 1 and 2 then it gives different values corresponding to y hence, it will not be a graph.
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A major credit card company requires monthly payments equal to or greater than 8% of the total balance.A consumer has a credit card balance of $320. Write an inequality that represents acceptable payment amounts.
Answers
Answer:
320 x 0.08 = X
In the case, a payment equal to or greater than $ 25.60 would be considered acceptable by the company.
Step-by-step explanation:
Given that a major credit card company requires monthly payments equal to or greater than 8% of the total balance, and a consumer has a credit card balance of $ 320, the following calculations must be performed to determine an inequality that represents acceptable payment amounts:
320 x 0.08 = X
25.6 = X
Thus, in the case, a payment equal to or greater than $ 25.60 would be considered acceptable by the company.
What is the cosine equation of the function shown?
Answers
Answer: f(x)=5cos(x+pi/3)+4
Step-by-step explanation: I just tool the quiz
0.7x − 0.2 = 8.3x + 7.2
Answers
Answer: -37/38
Step-by-step explanation:
What is this? -1 - ( -8 )
Answers
Answer:
Since you are subtracting a negative, you must add instead. -1+8 = 7.
Answer:
7
Step-by-step explanation:
-1--8 or -1+8
-1+8
7
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can the equation ( y1 - y2 and x1- x2) ALSO go (y2-y1 and x2- x1)
why?
Answers
I took a picture of the problem.
Answers
Step-by-step explanation:
[tex] - {3}^{2} m {n}^{5} m {n}^{2} {m}^{6} = \\ = - 9 {m}^{8} {n}^{7} [/tex]
Factor out the GCF:
-9n^5 + 3n
Answers
Answer:
3n or -3n([tex]3n^{4}[/tex]-1)
Step-by-step explanation:
i hope its correct!!!
^^
Answer: 3n(-3n^3 + 1)
Step-by-step explanation:
A Fish tank can hold 75 gallons of water. There is a crack in the fish tank letting out 5 gallons per minute. How long will it take for
the fish tank to lose 20 gallons?
How long will the fish tank take to be completely empty?
Answers
Answer:
It will take 4 minutes for 20 gals, 15 for the whole thing.
Step-by-step explanation:
Answer:
4 minutes to lose 20 gallons, and 15 minutes to empty the tank.
Step-by-step explanation:
20 divided by 5, and 75 divided by 5
HELP!! I WILL GIVE BRAINLIEST
Answers
Number one: Just plot down on the number like the numbers you have. Just took the test for this.
What's the equation
Answers
Given:
The graph of a parabola.
To find:
The equation for the parabola.
Solution:
The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex.
From the given graph it is clear that the vertex of the parabola is at point (-1,6). So, h=-1 and k=6.
Putting h=-1 and k=6 in (i), we get
[tex]y=a(x-(-1))^2+(6)[/tex]
[tex]y=a(x+1)^2+6[/tex] ...(ii)
The y-intercept of the graph is at point (0,3). Putting x=0 and y=3 in (ii), we get
[tex]3=a(0+1)^2+6[/tex]
[tex]3-6=a[/tex]
[tex]-3=a[/tex]
Putting a=-3 in (ii), we get
[tex]y=-3(x+1)^2+6[/tex]
Therefore, the equation of the parabola is [tex]y=-3(x+1)^2+6[/tex].
ABC is dilated by a factor of 1/2 to produce AA'B'C!
helpppppp
Answers
Answer:
abc
Step-by-step explanation:
abc
Answer:
B
Step-by-step explanation:
A P E X
The value of the expression 2x²+ 3x for x = 2 is:
Answers
Answer:
Step-by-step explanation:
lets replace x with 2
2(2^2)+3(2)=2*4+6=8+6=14
v) Find the perimeter of the rectangle whose length is 60m and breadth is 55m
vi) Find the perimeter of a square room with side equal to 8m each.
Answers
Answer:
Step-by-step explanation:
l = length
b = breadth
We know the length is twice the breadth, therefore l = 2b
We also know that the perimeter p = 60m and can also be expressed as a sum of its sides where p = l + l + b + b = 60 which simplified is:
60 = 2l + 2b
Now we have 2 variables, but thankfully we were given a ratio (l = 2b) relating the two. Substituting 2b in for l gives us:
60 = 2(2b) + 2b = 4b + 2b = 6b
60 = 6b
b = 10 m
Now that we know the breadth we can find the length:
l = 2b → l = 2(10) = 20 → l = 20 m
With a breadth of 10 m and a length of 20 m
I need help with this geometry question. Please show work:)