proving lines parallel!!! please help

Answer:

3rd option (top right)

Step-by-step explanation:

3rd option represents a linear equation

y = -2x-1

Answered by GAUTHMATH

9514 1404 393

Answer:

  -1/2

Step-by-step explanation:

The factor outside parentheses multiplies each term inside.

  5/2(-8/5 +7/5)

  = (5/2)(-8/5) +(5/2)(7/5)

  = -8/2 +7/2 = -1/2

Answer:

Ok I'm assuming that know what??

Step-by-step explanation:

9514 1404 393

Answer:

  false

Step-by-step explanation:

The statement is nonsense (false). Regardless of the sign of a product, subtraction plays no part in anything related to it.

Answer:

x=27

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

90 + x+15 + 2x-6 = 180

Combine like terms

3x+99=180

Subtract 99 from each side

3x+99-99=180-99

3x =81

Divide each side by 3

3x/3 = 81/3

x=27

Answer:

Carlos

Step-by-step explanation:

Hope this helps

Here we have the quadratic function:

f(x) = -16*x^2 + 60*x + 16

We can see that it is in standard form:

y = a*x^2 + b*x + c

a) First we want to completely factorize the function f(x).

To do it, we first need to find the roots of f(x).

Remember that for a generic quadratic equation:

a*x^2 + b*x + c = 0

whit roots x₁ and x₂, the factorized form is:

a*(x - x₁)*(x - x₂)

And the roots are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:

[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]

So the two roots are:

x₁ = (-60 + 68)/-32 = -0.25

x₂ = (-60 - 68)/-32 = 4

Then the factorized form is:

f(x) = -16*(x - 4)*(x + 0.25)

B) We already found the roots, which are:

x₁ =  -0.25

x₂ =  4

These are the x-intercepts:

(-0.25, 0) and (4, 0)

C) We can see that the leading coefficient is negative.

This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.

D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.

If you want to learn more about this topic, you can read:

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Answer:

False

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

West University:

15 out of 100, so:

[tex]p_W = \frac{15}{100} = 0.15[/tex]

[tex]s_W = \sqrt{\frac{0.15*0.85}{100}} = 0.0357[/tex]

East University:

12 out of 100, so:

[tex]p_E = \frac{12}{100} = 0.12[/tex]

[tex]s_E = \sqrt{\frac{0.12*0.88}{100}} = 0.0325[/tex]

Test the difference in driving abilities at the two universities:

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0, so:

[tex]H_0: p_W - p_E = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, if the subtraction of the proportions is different of 0. So

[tex]H_1: p_W - p_E \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_W - p_E = 0.15 - 0.12 = 0.03[/tex]

[tex]s = \sqrt{s_W^2+s_E^2} = \sqrt{0.0357^2+0.0325^2} = 0.0483[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.03 - 0}{0.0483}[/tex]

[tex]z = 0.62[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the proportions differ by at least 0.03, which is P(|z| > 0.62), that is, 2 multiplied by the p-value of z = -0.62.

Looking at the z-table, z = -0.62 has a p-value of 0.2676.

2*0.2676 = 0.5352.

The p-value of the test is 0.5352 > 0.05, which means that the difference in driving is not statistically significant at the .05 significance level, and thus the answer is False.

Answer:

55°

Step-by-step explanation:

Vertical angles are similar

Answered by GAUTHMATH

Answer:

2500 mg

Step-by-step explanation:

Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.

Since r(t) =  50 (e^-01t - e^-0.20t)

m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)

= 50∫₀⁰⁰(e^-01t - e^-0.20t)

= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]

= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)

= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})

= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})

= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})

= 50(1/-0.01[- 1] - {1/-0.02[- 1]})

= 50(1/0.01 - 1/0.02)

= 50(100 - 50)

= 50(50)

= 2500 mg

Answer:

67.98,68.11, 68.6

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Answer:

Step-by-step explanation:

Reflection over the line x=a is the transformation ...

  (x, y) ⇒ (2a -x, y)

Then the double reflection over x=a and x=b is the transformation ...

  (x, y) ⇒ (2b -(2a -x), y) = (2(b-a) +x, y)

That is, the result is translation by twice the distance between the lines. For a=1 and b=3, the transformation is ...

  (x, y) ⇒ (x +4, y) . . . . . . . translation to the right by 4 units.

  A(-5, 2) ⇒ A''(-1, 2)

  B(-1, 5) ⇒ B''(3, 5)

  C(0, 3) ⇒ C''(4, 3)

Problem 1

The idea here is to follow PEMDAS in reverse to undo what is happening to the variable b, so we can isolate it.

-11b + 7 = 40

-11b = 40-7

-11b = 33

b = 33/(-11)

b = -3

To check this value, plug it back into the original equation. You should get 40 on each side to help confirm the answer.

=====================================================

Problem 2

There are two ways we can solve. One method is to use the hint your teacher gave you. So we'll distribute first and then follow the same idea as problem 1

9(p-4) = -18

9p-36 = -18

9p = -18+36

9p = 18

p = 18/9

p = 2

Another method you can use is to follow these steps

9(p-4) = -18

p-4 = -18/9

p-4 = -2

p = -2+4

p = 2

Either way, we get the same result. To check the answer, replace every p with 2 in the original equation. You should get -18 on the left side after simplifying.

Answer:

The remainder is -2.

Step-by-step explanation:

According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (x - a), then the remainder of the operation will be given by P(a).

Our polynomial is:

[tex]P(x) = x^3-4x^2-6x-3[/tex]

And we want to find the remainder when it's divided by the binomial:

[tex]x+1[/tex]

We can rewrite our divisor as (x - (-1)). Hence, a = -1.

Then by the PRT, the remainder will be:

[tex]\displaystyle\begin{aligned} R &= P(-1)\\ &=(-1)^3-4(-1)^2-6(-1)-3 \\ &= (-1)-4(1)+(6)-3 \\ &= -2 \end{aligned}[/tex]

The remainder is -2.

Answer:

6

Step-by-step explanation:

|-6| = 6

|6| = 6

- -6 = +6

so, we have

6 - 6 + 6 = 6

Answer:

$48

Explanation:

> 50 x .20 = $10

$50 + $10= $60

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

> 60 x .20 = $12

$60 - $12= $48

Answer:

606.6 and 233.3 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3

Answer: A

Step-by-step explanation:

(tangent is opposite over adjacent)

[tex]tan(40)=\frac{x}{3.8}\\x=3.8*tan(40)[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...

  (x, y) ⇒ (x, y -4)

  A(3, 3) ⇒ A"(3, -1)

  B(2, 5) ⇒ B"(2, 1)

  C(4,3) ⇒ C"(4, -1)

Answer:

D

Step-by-step explanation:

Y => - 3 that is {−3, −2, −1, 0, . . .}

Answer:

A the input x=3 goes to two different output values

Step-by-step explanation:

This is not a function

x = 3 goes to two different y values

x = 3 goes to t = 10 and y = 5

Answer:

m<GEF = 66°

Step-by-step explanation:

(72+60)/2

= 132/2

= 66

Answered by GAUTHMATH

Answer:

The answer is "1900"

Step-by-step explanation:

It takes 500 fewer calories per day for her to lose 1 lb of weight every week.

[tex]\to (15 \times 160)-500 =(2400)-500 =2400-500=1900[/tex]

Answer:

Answer:

Point T,R,P not seen how I don't understand your question.

The length of arc APD is: [tex]\frac{\pi r}{2}[/tex]

A square when inscribed in a circle will fit the circle such that, the 4 edges of the square touches the sides of the circle. The radius of the circle can be drawn from any of the 4 edges.

Given that ABCD is a square:

This means that:

[tex]AB = BC = CD = DA[/tex] --- equal side lengths

To calculate the length of arc APD, we make use of the following arc length formula

[tex]APD = \frac{\theta}{360} * 2\pi r[/tex]

Where

[tex]\theta = \angle ADO[/tex] and O is circle center

Since ABCD is a square, then:

[tex]\theta = \angle ADO = 90^o[/tex]

So, we have:

[tex]APD = \frac{90}{360} * 2\pi r[/tex]

[tex]APD = \frac{1}{4} * 2\pi r[/tex]

[tex]APD = \frac{\pi r}{2}[/tex]

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Answer:

+∞.

Step-by-step explanation:

That would be positive infinity.

The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.

The following steps which are required to find the extreme value of polynomial are:

According to the given question.

We have a polynomial

[tex]f(x) = x^{2} -4[/tex]

Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.

Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Find out more information about extreme value of a polynomial here:

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