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2 years ago

In the diagram, triangle RST is congruent to triangle XYZ. Find x.

Mathematics

2 answers:

vova2212 [387]2 years ago

5 0

In the diagram where as the triangle RST is cognruent to triangle XYZ and ask to calculate the value of X. Base on my calculation and through step by step procedure and with the guidance of the theories and by the use of formulas, I came up with an answer of 35.

svlad2 [7]2 years ago

3 0

Answer: (c) 35 is the correct option.

Step-by-step explanation: Given that triangles RST and XYZ are congruent to each other.

We are to find the value of x.

From the figure, we note that

RT = (x +21) units and XZ = (2x - 14) units.

Since RT and XZ are corresponding parts of the congruent triangles, so we must have

$RT=XZ\\\\\Rightarrow x+21=2x-14\\\\\Rightarrow 2x-x=21+14\\\\\Rightarrow x=35.$

Thus, the value of x is 35.

Option (c) is CORRECT.

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a motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in

tangare [24]

Answer:

rate of the boat in still water = 6.5 miles / hour

rate of the current = 2.5 miles / hour.

Explanation:

1) Name the two variables:

c: rate of the current

b: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

down the river: b + c

upstream: b - c

2) Now set the equations for the distance as a function of the times and the rates:

distance = rate × time

downstream: 18 miles = (b + c) × 2 hours

upstream: 18 miles = (b - c) × 4.5 hours

3) Set the system of equations:

18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)

18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

4) Solve the system by elimination:

Add equations (1) and (2): 9 + 4 = 2b

Divide both sides by 2: 13/2 = b

Simplify: b = 6.5

Replace b with 6.5 in equation (2) and solve:

4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

5) Results:

b = rate of the boat in still water = 6.5 miles / hour

c = rate of the current = 2.5 miles / hour.

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1 year ago

Read 2 more answers

jake makes 9 loaves of olive bread. he uses 30 grams of olives in each loaf.he started with 1 kilogram of olives.how many grams

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2 years ago

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Answer:

Step-by-step explanation:

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The accompanying data are lengths (inches) of bears. Find the percentile corresponding to 65.5 in.

Jlenok [28]

Complete question is missing, so i have attached it.

Answer:

Percentile is 74th percentile

Step-by-step explanation:

All the lengths given are;

Bear Lengths 36.5 37.5 39.5 40.5 41.5 42.5 43.0 46.0 46.5 46.5 48.5 48.5 48.5 49.5 51.5 52.5 53.0 53.0 54.5 56.8 57.5 58.5 58.5 58.5 59.0 60.5 60.5 61.0 61.0 61.5 62.0 62.5 63.5 63.5 63.5 64.0 64.0 64.5 64.5 65.5 66.5 67.0 67.5 69.0 69.5 70.5 72.0 72.5 72.5 72.5 72.5 73.0 76.0 77.5

The number of lengths (inches) of bears given are 54 in number.

We are looking for the percentile corresponding to 65.5 in.

Looking at the lengths given, since they are already arranged from smallest to highest, let's locate the position of 65.5 in.

The position of 65.5 in is the 40th among 54 lengths given.

If the percentile is P, then;

P% x 54 = 40

P = (40 × 100)/54

P ≈ 74

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