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3 years ago

Solve the equation for x. show each step of the solution. name the justifications for each step of the solutions.

1 answer:

5 0

9/2{8-x}+36=102-5/2{3x+24}
you first use 9/2 to open brackets
9/2*8=36,
9/2*x=9/2x
36-9/2x=102-5/2{3x+24}
5/2*3x=15/2x+60
36-9/2x=-15/2x-60
36+60=15/2x+9/2x
96=12x you then divide and the answer obtained will be 8.
x=8

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How did you determine which value to use for the constant and which value to use for the coefficient?

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3 years ago

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What is AE ? Enter your answer in the box. units Two segments A D and B C intersect at point E to form two triangles A B E and D

spin [16.1K]

Answer:

The length of AE is 20 units.

Step-by-step explanation:

Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.

we have to find the length of AE

AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD

In ΔABE and ΔDCE

∠EAB=∠EDC (∵Alternate angles)

∠EBA=∠ECD (∵Alternate angles)

By AA similarity, ΔABE ≈ ΔDCE

therefore, $\frac{AE}{ED}=\frac{AB}{CD}$

⇒ $\frac{2x+10}{x+3}=\frac{10}{4}$

⇒ $8x+40=10x+30$

⇒ $x=5$

Hence, AE=2x+10=2(5)+10=20 units

The length of AE is 20 units.

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3 years ago

A plane travels 3,625.26 miles in 6.9 hours. What is the plane’s unit rate?

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Answer:

The correct answers are:

a) $\frac{3625.26 miles}{6.9hours}$

b)36252.6 tenths miles÷ 69 tenths hours

c) $\frac{3500miles}{7hours}= 500\frac{miles}{hour}$

d) $\frac{3625.26miles}{6.9hours} \frac{10}{10} =\frac{36252.6miles}{69hours}$

e) 525.4 miles/h

Step-by-step explanation:

The division is solved by using the division algorithm in the attached picture.

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3 years ago

A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received wit

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Answer:

The probability that the message will be wrong when decoded is 0.05792

Step-by-step explanation:

Consider the provided information.

To reduce the chance or error, we transmit 00000 instead of 0 and 11111 instead of 1.

We have 5 bits, message will be corrupt if at least 3 bits are incorrect for the same block.

The digit transmitted is incorrectly received with probability p = 0.2

The probability of receiving a digit correctly is q = 1 - 0.2 = 0.8

We want the probability that the message will be wrong when decoded.

This can be written as:

$P(X\geq3) =P(X=3)+P(X=4)+P(X=5)\\P(X\geq3) =\frac{5!}{3!2!}(0.2)^3(0.8)^{2}+\frac{5!}{4!1!}(0.2)^4(0.8)^{1}+\frac{5!}{5!}(0.2)^5(0.8)^0\\P(X\geq3) =0.05792$

Hence, the probability that the message will be wrong when decoded is 0.05792

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2 years ago