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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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Evaluate the numerical expression. −8.1 – 3.5 ÷ (−0.5)

beks73 [17]

The answer is -1.1
Hope you get it right

5 0

2 years ago

Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷

tester [92]

Answer: a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

$1\ ton=32000\ oz\\\\1\ lb=16\ oz$

so, it becomes,

$8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz$

8 T. 1,398 lb. 14 oz. × 6 becomes

$278382\times 6\\\\=1670292\ oz$

b) 349 lb. 6 oz. ÷ 130

It becomes,

$349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz$

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

$6\times 32000+294\times 16\ oz\\\\=196704\ oz$

At last it becomes,

$\frac{196704}{3071}\\\\=64.1\ oz$

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

6 0

2 years ago

Read 2 more answers

A carnival has two payment options. Plan A, you pay $10 admission plus $3 for each ride. Plan B, you pay a $20 admission plus $1

stiks02 [169]

<span>Let x = # of rides

Plan A: 10 + 3x

Plan B: 20 + x

if x < 5 rides then plan A is better buy
if x = 5 both plans are the same
if x > 5 then plan B is the best buy

Prove:
x = 6 (rides)

plan A: </span>10 + 3x = 10 + 3(6) = 10+18 = $28
plan B: 20 + x = 20 + 6 = $26

3 0

2 years ago

Read 2 more answers

Serena wants to determinethe area of the lawn the grass part of her front yard using the information given in the diagram below

vivado [14]

Answer:

The answer is 295 square yards.

Step-by-step explanation:

[48(72-12)-15^2] divide by 9

3456-576-225 divide by 9

Subtract 3456 by 576

2880-255

2655 divide by 9

=295 square yards.

Hope this helped!

7 0

2 years ago

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago