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2 years ago

Explain why the polynomial 100x^2 + 150x + 49 is not a perfect square.

1 answer:

4 0

Answer: The correct answer is Choice C.

For this polynomial to be a perfect square, it would need to be:
(10x + 7)^2

This will ensure that the first terms and the last terms will be 100x^ and 49. However, if you use foil to multiply the factors, you will not get 150x for the center term. Choice C also states that 150x will not be the middle term.

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A student has some $1 and $5 bills in his wallet. he has a total of 15 bills that are worth $51. How much of each type of bill d

snow_tiger [21]

Answer:

# of 5 dollar bills: 9

# of 1 dollar bills: 6

Step-by-step explanation:

9•5 = 45

1•6 = 6

To Check: 45 + 6=51

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a line segment has one endpoint at the origin (0,0) and one endpoint at (0,6). how long is this segment?

tiny-mole [99]

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2 years ago

What value of x makes the equation true? 3(4x-5)-4x+1=-6 Please show work

V125BC [204]

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3(4x - 5) - 4x + 1 = -6

Step 2: Solve for x

Distribute 3: 12x - 15 - 4x + 1 = -6
Combine like terms: 8x - 14 = -6
Isolate x term: 8x = 8
Isolate x: x = 1

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 3(4(1) - 5) - 4(1) + 1 = -6
Multiply: 3(4 - 5) - 4 + 1 = -6
Subtract: 3(-1) - 4 + 1 = -6
Multiply: -3 - 4 + 1 = -6
Subtract: -7 + 1 = -6
Add: -6 = -6

Here we see that -6 does indeed equal -6.

∴ x = 1 is the solution to the equation.

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2 years ago

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that

zimovet [89]

Answer:

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

Step-by-step explanation:

Given : We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

To find : How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?

Solution :

At 95% confidence the z-value is z=1.96

The sample mean is within 3 minutes of the population mean i.e. margin of error is E=3 minutes

The population standard deviation is s=12 minutes

n is the number of sample

The formula of margin of error is given by,

$E=\frac{s\times z}{\sqrt{n}}$