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3 years ago

Factor completely: 3x2 − 17x − 28

Mathematics

1 answer:

Olin [163]3 years ago

8 0

Hello,

3x²-17x-28=3x²-21x+4x-28=3x(x-7)+4(x-7)=(x-7)(3x+4)

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Find the solution of this system of equations. -x - 5y= 30, 10x + 5y= -75

madreJ [45]

Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

------------------

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

7 0

3 years ago

Use the Distributive Property to expand 4(x+3)

Serga [27]

Answer:

4x+12

Step-by-step explanation:

4(x+3)=4x+12.

You use the distributive property by multiplying both numbers in the parentheses by 4

6 0

2 years ago

Read 2 more answers

A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000

Vinil7 [7]

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

$p_1=X_1/n_1=494/1000=0.494$

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

$p_2=X_2/n_2=552/1000=0.552$

The difference between proportions is (p1-p2)=-0.058.

$p_d=p_1-p_2=0.494-0.552=-0.058$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022$

Then, the margin of error is:

$MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014$

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

7 0

3 years ago

Transform the following polar equation into an equation in rectangular coordinates: r=2 cos theta A. x + y = 2 B. y = 2x C. x =

Mila [183]

$r=2\cos\theta$
$r^2=2r\cos\theta$
$\implies x^2+y^2=2x$
$x^2-2x+y^2=0$
$x^2-2x+1+y^2=1$
$(x-1)^2+y^2=1$

8 0

3 years ago

Read 2 more answers

What is the sum of the difference?

Alona [7]

Answer:

A. 9x^4 and 3x^5y

Step-by-step explanation:

there are two ways to solve this:

first way:

You can solve this my substituting numbers for x and y in this case i used 2 for x and 3 for y and see which one is equal to the original equations

the second way is the regular way

when you add or subtract numbers with variables and exponents you want to add the constants and add the exponents in this case $5x^{4} +4x^2$ is the same as $(5x+4x)^(4+4)$ = $9x^4$ and you can do the same process for subtraction

$12x^{5}y-9x^5 y\\(12x-9x)^(5+5)*y$ = $3x^5y$

8 0

3 years ago