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3 years ago

Determine if x + 2 is a factor of p(x) = x 4 + 3x 3 + 4x 2 - 8 and explain why.

1 answer:

3 0

The Factor Theorem says (x - a) is a factor of function p(x) if p(a)=0

so check for p(-2)

= -2^4 +3(-2)^3 + 4(-2)^2 - 8

= 16 - 24 +16 -8

= 0

so (x + 2) is a factor

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$34.98 with 8.2 tax

Paraphin [41]

Answer:

$37.85

Step-by-step explanation:

Here the price is $34.98 and there's an 8.2% tax on that. To obtain the after-tax amount due, multiply $34.98 by (1 + 0.082), or 1.082, obtaining:

1.082($34.98) = $37.85 (rounded to the nearest cent)

7 0

3 years ago

Given segments AB and CD intersect at E.

nata0808 [166]

The length of a segment is the distance between its endpoints.

$\mathbf{AB = 3\sqrt{2}}$
AB and CD are not congruent
AB does not bisect CD
CD does not bisect AB

<u>(a) Length of AB</u>

We have:

$\mathbf{A = (1,2)}$

$\mathbf{B = (4,5)}$

The length of AB is calculated using the following distance formula

$\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}$

$\mathbf{AB = \sqrt{18}}$

Simplify

$\mathbf{AB = 3\sqrt{2}}$

<u>(b) Are AB and CD congruent</u>

First, we calculate the length of CD using:

$\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Where:

$\mathbf{C = (2, 4)}$

$\mathbf{D = (2, 1)}$

So, we have:

$\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}$

$\mathbf{CD = \sqrt{9}}$

$\mathbf{CD = 3}$

By comparison

$\mathbf{CD \ne AB}$

Hence, AB and CD are not congruent

<u>(c) AB bisects CD or not?</u>

If AB bisects CD, then:

$\mathbf{AB = \frac 12 \times CD}$

The above equation is not true, because:

$\mathbf{3\sqrt 2 \ne \frac 12 \times 3}$

Hence, AB does not bisect CD

<u>(d) CD bisects AB or not?</u>

If CD bisects AB, then:

$\mathbf{CD = \frac 12 \times AB}$

The above equation is not true, because:

$\mathbf{3 \ne \frac 12 \times 3\sqrt 2}$

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

7 0

3 years ago

The event of walking your dog is A and the event of electing a female as class president is B. If these events are independent e

KengaRu [80]

The value of the probability is 0.54

<h3>How to determine the probability?</h3>

The given parameters are:

P(A) = 0.35

P(B) = 0.54

From the question, we understand that the events are independent.

This means that

P(B|A) = P(B)

Substitute P(B) = 0.54

P(B|A) = 0.54

Hence, the value of the probability is 0.54

Read more about probability at:

brainly.com/question/11234923

#SPJ1

3 0

2 years ago

A bakery uses 8 table spoons of honey for every 10 cups of flour to make bread dough some days they bake bigger batches and some

Arada [10]

Answer:

The ratio would be, 4 tablespoons of honey: 5 cups of flour

Step-by-step explanation:

4/5 is the simplified version of 8/10, which is what we were first given

6 0

2 years ago

An expression to convert 50 miles per hour to miles per minute is shown. 50 miles Over 1 hour into 1 hour Over blank minutes

Darina [25.2K]

Answer:

$\frac{50 miles}{1 hour} * \frac{1 hour}{60 minutes}$

Step-by-step explanation:

Since 1 hour contains 60 minutes, So 1 hour would by divided by 60

So, the required expression is,

=> $\frac{50 miles}{1 hour} * \frac{1 hour}{60 minutes}$

7 0

3 years ago

Read 2 more answers