What is the equation of a line in slope-intercept form with a slope of -3/4 and a y-intercept of -2

1. Divide: x+3x+2 x +4x+4 x+1 x + 5x+4

Margarita [4]

Answer:

x

4

−5x

2

+4

To factor the expression, solve the equation where it equals to 0.

x

4

−5x

2

+4=0

By Rational Root Theorem, all rational roots of a polynomial are in the form

q

p

, where p divides the constant term 4 and q divides the leading coefficient 1. List all candidates

q

p

.

±4,±2,±1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=1

By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x

4

−5x

2

+4 by x−1 to get x

3

+x

2

−4x−4. To factor the result, solve the equation where it equals to 0.

x

3

+x

2

−4x−4=0

By Rational Root Theorem, all rational roots of a polynomial are in the form

q

p

, where p divides the constant term −4 and q divides the leading coefficient 1. List all candidates

q

p

.

±4,±2,±1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=−1

By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x

3

+x

2

−4x−4 by x+1 to get x

2

−4. To factor the result, solve the equation where it equals to 0.

x

2

−4=0

All equations of the form ax

2

+bx+c=0 can be solved using the quadratic formula:

2a

−b±

b

2

−4ac

. Substitute 1 for a, 0 for b, and −4 for c in the quadratic formula.

x=

2

0±

0

2

−4×1(−4)

Do the calculations.

x=

2

0±4

Solve the equation x

2

−4=0 when ± is plus and when ± is minus.

x=−2

x=2

Rewrite the factored expression using the obtained roots.

(x−2)(x−1)(x+1)(x+2)

5 0

3 years ago

Statement: If 3x = 6, then x = 2. What is the contrapositive of the statement? Emeans not equal

nikitadnepr [17]

Answer:

x=2

Step-by-step explanation:

you are correct for x=2 because 6 divided by 3 is 2

5 0

3 years ago

the shadow of a statue is 20 feet long while the shadow of a student is 4ft long. if the student is 6ft tall how tall is the sta

zaharov [31]

Answer:

Step-by-step explanation:

ratio and proportion:

20 ft. long = 4 ft. long

x tall 6 ft. tall

4 (x) = 20 (6)

x = 120 / 4

x = 30 ft. tall

3 0

3 years ago

Jack has some marbles. He has ten more red marbles than blue marbles. He has fewer yellow marbles than blue marbles.

kap26 [50]

Answer:

Jack has at least 15 marbles: 12 red, 2 blue and 1 yellow.

Step-by-step explanation:

1. Let's review the information given to us to solve the problem correctly:

Number of red marbles = 10 more than blue marbles

Number of yellow marbles fewer than blue marbles

2. How many of each color marble could Jack have?

r = Number of red marbles

b = Number of blue marbles

y = Number of yellow marbles

r = b + 10

y < b

If y = 1, then b ≥ 2, and r = b + 10,

fulfilling the three conditions, we have:

y = 1, b = 2, and r = 12

5 0

3 years ago

You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a r

SIZIF [17.4K]

Answer:

The critical value that corresponds to a confidence level of 99% is, 2.58.

Step-by-step explanation:

Consider a random variable X that follows a Binomial distribution with parameters, sample size n and probability of success p.

It is provided that the distribution of proportion of random variable X, $\hat p$ , can be approximated by the Normal distribution.

The mean of the distribution of proportion is, $\mu_{\hat p}=\hat p$

The standard deviation of the distribution of proportion is, $\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$ .

Then the confidence interval for the population proportion p is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }$

The confidence level is 99%.

The significance level is:

$\alpha =1-\frac{Confidence\ level}{100}=1-\frac{99}{100}=1-0.99=0.01$

Compute the critical value as follows:

$z_{\alpha /2}=z_{0.01/2}=z_{0.005}$

That is:

$P(Z>z)=0.005\\P(Z$

Use the z-table for the z-value.

For z = 2.58 the P (Z < z) = 0.995.

And for z = -2.58 the P (Z > z) = 0.005.

Thus, the critical value is, 2.58.

7 0

4 years ago