1 point
What is the slope of a line perpendicular to 3x + 4y = -2?

Answer:

b + 5; when b = 3.4 the distance Sandra rode is 17 miles.

Step-by-step explanation:

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Explanation:

area of rectangle = L*W = 129

L*W = 129

x*(2x-9) = 129

2x^2-9x = 129

2x^2-9x-129 = 0

Apply the quadratic formula. We'll use a = 2, b = -9, c = -129.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-129)}}{2(2)}\\\\x = \frac{9\pm\sqrt{1113}}{4}\\\\x \approx \frac{9\pm33.36165464}{4}\\\\x \approx \frac{9+33.36165464}{4}\ \text{ or } \ x \approx \frac{9-33.36165464}{4}\\\\x \approx \frac{42.36165464}{4}\ \text{ or } \ x \approx \frac{-24.36165462}{4}\\\\x \approx 10.59041366\ \text{ or } \ x \approx -6.09041364\\\\[/tex]

We ignore the negative solution because a negative length makes no sense.

The length is approximately L = 10.5904 cm.

The width is 2L-9 = 2*10.5904-9 = 12.1808 cm approximately.

As a quick check,

L*W = 10.5904*12.1808 = 128.99954432

which isn't too far off from 129. We have rounding error which is why we don't perfectly land on the target area value. If you wanted to get closer to the value 129, then use more decimal digits in the approximations of L and W.

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If you draw a diagonal in the rectangle, then you form two identical or congruent right triangles.

Focusing on one of those triangles, we have

Apply the pythagorean theorem

a^2+b^2 = c^2

c = sqrt( a^2 + b^2 )

c = sqrt( (10.5904)^2 + (12.1808)^2 )

c = 16.1408940520653

c = 16.14

The diagonal is roughly 16.14 cm long.

Answer:

see below

Step-by-step explanation:

amount of water w

l liter of pure alcohol = 100% alcohol

solution is 45 % percent alcohol

total amount of fluid is w+l

(w+l)( .45) = l*.100

Distribute

.45w  + .45 l = 1l

.45 w = 1l - .45l

.45 w = .55l

w = .55l / .45

w =11/9 l

Answer:

[tex]y=4x[/tex]

Answer:

y = -4x

hope that helped.........

Answer:

x = 14

y = -7

z = -3

but this is none of the provided answer options !

Step-by-step explanation:

it's really easy by principle. it's just some work to do.

we try to find equations to express one variable in terms of the others.

but one thing there is : your teacher made a mistake.

the right solution is x = 14, y = -7, z = -3

your teacher made a typo at d.

but the right answer should be d.

just to give you an idea how this can be done (and also to prove that there is a mistake by the teacher):

we can directly try to transform one expression into one that describes x by y and z.

and then another to describe e.g. z by y. and then solve the third one just for y. and then we get the other 2 by these other expressions.

or we can e.g. add or subtract one equation to/from another. this is one of these cases, because we can find really simple expressions that way :

we do

5x + 6y + 7z = 7

- (3x + 4y + 3z = 5)

- (2x + 2y + 3z = 5)

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

0x + 0y + z = -3

=> z = -3

3x + 4y - 3×3 = 5

3x = -4y + 14

x = (-4y + 14)/3

2×(-4y + 14)/3 + 2y - 9 = 5

(-8y + 28)/3 + 2y = 14

-8y + 28 + 6y = 42

-2y = 14

y = -7

x = (-4×-7 + 14)/3 = (28+14)/3 = 42/3 = 14

Answer:

the answer is 30 percent.

Step-by-step explanation:

i did it on acellus.

9514 1404 393

Answer:

  1

Step-by-step explanation:

The slope is given by the formula ...

  slope = (y2 -y1)/(x2 -x1)

  slope = (5 -4)/(3 -2) = 1/1 = 1

The slope of MN is 1.

__

Dilation does not change the slope.

Answer:

A

Step-by-step explanation:

I guess that is it may be

9514 1404 393

Answer:

  a) $164,413.47

  b) $96,000

  c) $68,413.47

Step-by-step explanation:

a) The account value is given by the annuity formula:

  A = P(12/r)((1 +r/12)^(12·t) -1)

where monthly payment P earns interest at annual rate r compounded monthly for t years.

  A = $400(12/0.05)((1 +0.05/12)^(12·20) -1) = $400(240)(1.712640285)

  A ≈ $164,412.47

You will have $164,413.47 in the account after 20 years.

__

b) You put $400 in the account each month for 240 months, for a total of ...

  $400 × 240 = $96,000 . . . . total of your deposits

__

c) The account balance in excess of your deposits is the amount of interest you earned:

  $164,413.47 -96,000 = $68,413.47 . . . . interest earned

In this question, the variance of the population is tested. From the data given in the exercise, we build the hypothesis, then we find the value of  test statistic and it's respective p-value, to conclude the test. From this, it is found that the conclusion is:

The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.

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Claimed variance of 0.19:

This means that at the null hypothesis, it is tested if the variance is of 0.19, that is:

[tex]H_0: \sigma^2 = 0.19[/tex]

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Test if the variance of the share price of the bond fund is different than claimed at α = 0.05.

At the alternative hypothesis, it is tested if the variance is different of the claimed value of 0.19, that is:

[tex]H_1: \sigma^2 \neq 0.19[/tex]

The test statistic for the population standard deviation/variance is:[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

In which n is the sample size,  is the value tested for the variance and s is the sample standard deviation.

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0.19 is tested at the null hypothesis, as the variance:

This means that [tex]\sigma_0^2 = 0.19[/tex]

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He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2517.

This means that [tex]n = 22, s^2 = (0.2517)^2 = 0.0634[/tex]

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Value of the test statistic:

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

[tex]\chi^2 = \frac{21*0.0634}{0.19}[/tex]

[tex]\chi^2 = 7[/tex]

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P-value of the test and decision:

The p-value of the test is found using a chi-square for the variance calculator, considering a test statistic of [tex]\chi^2 = 7[/tex] and 22 - 1 = 21 degrees of freedom, and a two-tailed test(test if the mean is different of a value).

Using the calculator, the p-value of the test is 0.0038.

The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.

For more on hypothesis tests using variances/standard deviation, you can check https://brainly.com/question/13993951

Answer:

x=4

y=7

Step-by-step explanation:

12=3x

x=4

6=y-1

y=6+1

y=7

Answer:

x=4

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

multiply 2 and get 2x^2+18-4=0

combine like terms

2x^2+14=0

subtract 14

2x^2=-14

there can't be a square root of a negative number so there's no solution

Answer:

x = ±i sqrt(7)

Step-by-step explanation:

2(x^2+9)-4=0

Add 4 to each side

2(x^2+9)-4+4=0+4

2(x^2+9)=4

Divide by 2

2(x^2+9)/2=4/2

(x^2+9)=2

Subtract 9 from each side

x^2 +9-9 = 2-9

x^2 = -7

Taking the square root of each side

sqrt(x^2) =sqrt(-7)

x = sqrt(-1 *7)

x = ±i sqrt(7)

Answer:

a. 9 students

b. 20 students

c. 4 students

Answer:

i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one

and there you go thats your graph

Step-by-step explanation:

Answer:

x > 8

Step-by-step explanation:

You can start y multiplying both sides by 4 to cancel out the division by 4:

x/4 > 2

*4      *4

x > 8

Answer:

x > 8

Step-by-step explanation:

x/4 > 2

=> x > 2 × 4

=> x > 8

Complete question is;

The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?

Answer:

dC/dt = 49.45

Step-by-step explanation:

Since C(x) = ⅔x² + 6x + 45

And x(t) = 0.3t² + 0.04t

This means that;

C(x) = C(x(t))

The rate at what cost is changing with respect to time is given as;

dC/dt

Thus, from chain rule;

dC/dt = (dC/dx) × (dx/dt)

dC/dx = (4/3)x + 6

dx/dt = 0.6t + 0.04

Now, when t = 5, then;

x(5) = 0.3(5)² + 0.04(5)

x = 7.7

Thus;

dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267

At 5 hours,

dx/dt = 0.6(5) + 0.04 = 3.04

Thus;

dC/dt = 16.267 × 3.04

dC/dt = 49.45

9514 1404 393

Answer:

  (x, y') = (-13, 13)

Step-by-step explanation:

At the given value of x, f(x) = 2. Then 9f(x)-5 = 9(2) -5 = 13.

The point on the scaled, translated graph will be ...

  (x, y') = (-13, 13)

_____

The graph shows a function f(x) with a distinct feature (vertex) at (-13, 2). It also shows where that distinct feature moves to when the function is scaled and translated.

Answer:

3rd option

Step-by-step explanation:

(1/2)^-2t

= (2^-1)^-2t

= 2^2t

= (2^2)^t

Answered by GAUTHMATH

5(2x^2-x-2)(x-2)

Step-by-step

Answer:  [tex]5(\frac{10x^3}{5}+\frac{-25x^2}{5}+\frac{20}{5}) \\\\5(2x^3-5x^2+4)\\\\5(2x^2-x-2)(x-2)[/tex]

Answer:

y= 1/2x-3/2

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 1/2x+b

Using the point for x and y we can find b

-3 = 1/2(-3)+b

-3 = -3/2 +b

-6/2 = -3/2+b

Add 3/2 to each side

-6/2 +3/2 = b

-3/2 = b

y= 1/2x-3/2

Answer:

Step-by-step explanation:

y + 3 = 1/2(x + 3)

y + 3 = 1/2x + 3/2

y + 6/2 = 1/2x + 3/2

y = 1/2x - 3/2

The centroid and center of mass need not be the same point. They are the same only when a body's mass is uniformly distributed.

The length of CV is 5 units

The length of C’V’ is 7.5 units

The scale factor is 7.5 / 5 = 1.5

Answer: 1.5

Answer:

Determination of type of error arising from the situations

Situation       Type of Error

1.                    Nonresponse

2.                   Bad sampling method

3.                   Question wording

4.                   Undercoverage

Step-by-step explanation:

Types of errors:

a. question wording means that the manner a question is worded elicits some particular responses, which may not accurately reflect reality.

b. undercoverage occurs when some elements of the target population is not represented on the survey frame.

c. processing error arises from data processing

d. bad sampling method is caused by the voluntariness of those who choose to respond.

e. response error is caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.

f. nonresponse error arises as a result of incomplete information or partial response.

g. random sampling error arises from the limited sample size when compared with the population size.

Answer:

a) 25/35

b) 30/42

Step-by-step explanation:

a)

Variable x = denominator if numerator is 25

5/7 = 25/x

5 × x = 7 × 25

5x = 175

x = 35

b)

Variable y = numerator if denominator is 42

5/7 = y/42

5 × 42 = 7 × y

210 = 7y

30 = y

25/35

30/42

To get 25/35 multiply by 5

To get 30/42 multiply by 6

Answer:

Let us check these out one at a time:

1. x + y is odd.  FALSE.  The sum of 2 odd numbers is even.

2. xy is odd.  TRUE.  The product of 2 odd numbers is odd.

3. x/y is odd.  TRUE.  The ratio of 2 odd numbers is odd, if the ratio is an integer.

4. x - y is odd.  FALSE.  The difference of 2 odd numbers is even.

Only statements 2 and 3 are TRUE, so that makes (C) the correct answer.