Consider the line 4x-8y= -6.

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line​

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

Explanation:

x = width of the walkway in feet

This is some positive real number.

The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x

Refer to the diagram below.

The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft

The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.

-----------

Area = length*width

1056 = (20+2x)*(40+2x)

1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule

1056 = 800 + 40x + 80x + 4x^2

0 = 4x^2 + 40x + 80x + 800 - 1056

0 = 4x^2 + 120x - 256

4x^2 + 120x -  256 = 0

4(x^2 + 30x - 64) = 0

x^2 + 30x - 64 = 0

Let's use the quadratic formula to finish solving for x.

Plug in a = 1, b = 30, c = -64

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]

Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.

The only practical solution is x = 2

Therefore, the walkway is 2 feet wide

The complete statements are mathematically given as

Generally,  The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."

In conclusion, the amount borrowed= 88000

the annual interest rate= 6%

the number of payments per year= 12

The loan term= 18

the payment amount.=667*12

the payment amount.=8004

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Answer:

width = 10 cm

Step-by-step explanation:

the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )

the perimeter (P) of a rectangle is calculated as

P = 2 × width + 2 × length

given P = 70 then

2(2x) + 2(5x) = 70

4x + 10x = 70

14x = 70 ( divide both sides by 14 )

x = 5

Then

width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm

The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²

Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

We need to form a polynomial expression with the following properties;

fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;

y = 2(x - 3)³(x + 4)²

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Answer:  (5/1, -3)

Hope this helps :)

Answer:

Look at the attachment.

Step-by-step explanation:

Look at the attachment.

Answer:

Step-by-step explanation:

To rotate any figure we have to have the CENTER of rotation!!!!

You did not provide us (your helpers) with that point, so I chose point on the horizontal mirror.

The angles are: A =24.7° ; B = 40.6° ; C =114.7°.

The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.

Cosine Law

a² = b²+c²-2bc cos A

b² = c²+a² -2ca cos B

Sum of three angles of a triangle is 180°.

a = 34 ; b= 53; c = 74

Substituting the given values in the cosine law, we have

34² = 53² + 74² - 2*53 *74 * cos A

7844 cos A = 2809 + 5476 - 1156 = 7129

cos A = 7129/7844 = 0.9088

A = cos⁻¹ (0.9088) = 24.6600° = 24.7°

53² = 74² + 34² - 2 (74)(34) cos B

5032 cos B = 5476 + 1156 - 2809 = 3823

cos B = 3823/5032 = 0.7597

B = cos⁻¹ (0.7597) = 40.5622° = 40.6°

Also, A + B + C = 180°

24.7 + 40.6 + C =180

C =180 -  65.3 = 114.7°

Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°

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Answer:

6.34 min to empty

Step-by-step explanation:

80 cm x 40 cm x 30 cm = 96000 cm^3

  this volume represents  25.36 gallons of water (US)

25.36 gal / 4 gal/min = 6.34 min  to empty

Answer:

h=-2

Step-by-step explanation:

the graph was shifted 2 units left

The perimeter of the following rectilinear figure is 54 units.

Perimeter of a figure is the distance covered when a person walk one round across its edges .

The given figure is in the form of a rectangle ,

The perimeter is equal to the sum of all sides ,

The bottom base is 13 includes (base of the small extended figure )

The left side is 14(includes left side of the small extended figure)

The right side is 10+5+4 (includes right side of the small extended figure)

The top is 8

Therefore the perimeter is 13+14+10+5+4+8 = 54 units

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Answer:

1.  "a"  [tex]u'=6x[/tex]

2.  "d"  [tex]v'=15x^2[/tex]

3.  "b"  [tex]y'=75x^4+30x^2+6x[/tex]

Step-by-step explanation:

Part 1.

Given [tex]u=3x^2+2[/tex], find [tex]\frac{du}{dx} \text{ or } u'[/tex].

[tex]u=3x^2+2[/tex]

Apply a derivative to both sides...

[tex]u'=(3x^2+2)'[/tex]

Derivatives of a sum are the sum of derivatives...

[tex]u'=(3x^2)'+(2)'[/tex]

Scalars factor out of derivatives...

[tex]u'=3(x^2)'+(2)'[/tex]

Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...

[tex]u'=3(2x)+0[/tex]

Simplify...

[tex]u'=6x[/tex]

So, option "a"

Part 2.

Given [tex]v=5x^3+1[/tex], find [tex]\frac{dv}{dx} \text{ or } v'[/tex].

[tex]v=5x^3+1[/tex]

Apply a derivative to both sides...

[tex]v'=(5x^3+1)'[/tex]

Derivatives of a sum are the sum of derivatives...

[tex]v'=(5x^3)'+(1)'[/tex]

Scalars factor out of derivatives...

[tex]v'=5(x^3)'+(1)'[/tex]

Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...

[tex]v'=5(3x^2)+0[/tex]

Simplify...

[tex]v'=15x^2[/tex]

So, option "d"

Part 3.

Given [tex]y=(3x^2+2)(5x^3+1)[/tex]

[tex]\text{Then if } u=3x^2+2 \text{ and } v=5x^3+1, y=u*v[/tex]

To find [tex]\frac{dy}{dx} \text{ or } y'[/tex], recall the product rule:  [tex]y'=uv'+u'v[/tex]

[tex]y'=uv'+u'v[/tex]

Substituting the expressions found from above...

[tex]y'=(3x^2+2)(15x^2)+(6x)(5x^3+1)[/tex]

Apply the distributive property...

[tex]y'=(45x^4+30x^2)+(30x^4+6x)[/tex]

Use the associative and commutative property of addition to combine like terms, and rewrite in descending order:

[tex]y'=75x^4+30x^2+6x[/tex]

So, option "b"

The value of y is -8 if the x  -24 and y varies directly with x, and If y = 4 when x = 12.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

The question is incomplete.

The complete question is:

If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?

y ∝ x  (given)

y = kx

k is the constant of proportionality.

4 = 12k  (y = 4, and x = 12)

k = 1/3

y = x/3

Plug x = -24

y = -24/3

y = -8

Thus, the value of y is -8 if the x  -24 and y varies directly with x, and If y = 4 when x = 12.

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Answer:

x < 8

Step-by-step explanation:

9x + 3 > 10x - 5

9x - 10x > -5 - 3

-x > -8

x < 8

Use the definitions of expectation and variance.

[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]

Integrate by parts,

[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]

with

[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]

[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]

(since the integral of the PDF is 1, and this integral is 4 times that)

[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]

Compute the so-called second moment.

[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]

Integrate by parts, with

[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]

[tex]E(X^2) = 8 E(X) = 32[/tex]

and the variance is

[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]

Answer:

bro nobody can figure this out you need to word the entire question with numbers and all. and proper English pls

Answer:

−135z

2

−2z
The 2 is representing Square

Step-by-step explanation:

(3z)
2

−4z+11−(12z)
2

+2z−11

Expand (3z)

2

.

3

2

z

2

−4z+11−(12z)

2

+2z−11

Calculate 3 to the power of 2 and get 9.

9z

2

−4z+11−(12z)

2

+2z−11

Expand (12z)

2

.

9z

2

−4z+11−12

2

z

2

+2z−11

Calculate 12 to the power of 2 and get 144.

9z

2

−4z+11−144z

2

+2z−11

Combine 9z

2

 and −144z

2

 to get −135z

2

.

−135z

2

−4z+11+2z−11

Combine −4z and 2z to get −2z.

−135z

2

−2z+11−11

Subtract 11 from 11 to get 0.

−135z

2

−2z

0.072 is the margin of error.

The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.

According to the question,

In a random sample of 250 students,

p= 0.98 (or 98%) were in favor of longer hours at the school library.

The standard error of p(the sample proportion) is (approximately)

The standard error of p =   [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

p = 0.98

1 - p = 1 - 0.98 = 0.02

Here,

n = 250

The standard error of p =   [tex]\sqrt{ \frac{0.98 (0.02) }{250}[/tex]

The standard error of p ≈   0.072

Therefore,

The margin of error is 0.072.

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a)The probability that all 10 will arrive within two days is 0.3486.

b)  P(x = 8) = 0.1937

c)  P(x=5)= 0.0014

d)  mean = 9

e) Standard deviation = √0.90 = 0.9486

The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times and the outcome for a given patient is either a success or a failure.

Given:

p = 90/100 = 0.90

q(probability of success) = 1 - p = 1 - 0.90 = 0.10

n = 10

a)The probability that all 10 will arrive within two days

P(x = 10) = 0.3486

b) P(x = 8) = 0.1937

c) P(x=5)= 0.0014

d) mean = np = 10 × 0.90 = 9

e) Variance = npq = 10 × 0.90 × 0.10 = 0.90

Standard deviation = √0.90 = 0.9486

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The value of x is calculated with the help of a similar triangle is 24.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.

Then we have

x / 12 = 32 / 16

     x = 24

Then the value of x is 24.

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Answer:

(-2,7)

Step-by-step explanation:

x=7-3y

2(7-3y)+4y=8

14-6y +4y=8

14-2y=8

-2y = -6

y=3

x + 3(3) = 7

x + 9 = 7

x = -2

(-2,7)

Answer: -2,3

Step-by-step explanation:

The graph is attached and all the sub parts have been answered.

A function is  away of relating a dependent variable to an independent variable .

It is given that

Current weight of Rex at 2 months =6 pounds

Let x represents the age in months of Rex

then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is

Let y be the current weight of Rex

then

y = 6 + 9(x -2)

The table  that represents Rex’s current weight, in pounds, as a function of his age, in months

2              6

3              15              

4              24

5              33

6              42

7              51

8              59

The graph is plotted for the given data and attached .

If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old

6 + 9*(12-2)

96 pounds.

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The maximum number of turns for the graph given by the function is; 2.

It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.

This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.

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Answer:

15

Step-by-step explanation:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

Answer:

(6,4)

Step-by-step explanation:

^^^

Answer:

converges

Step-by-step explanation:

well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0  and k = 8. Since 0 < (8-1)

0 < 7 the series converges

Answer:

28.26 feet squared

Explanation:

Area of circle is determined by : π(radius)²

Here given:

Solve for area:

Answer:

28.26 feet squared

Step-by-step explanation:

Radius of the watering pattern = 3 feet

Area = π r²

= 3.14 × 3²

= 28.26 feet squared

Answer: There is no mode.

Step-by-step explanation:

The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.

I hope this helped!! :)

Answer:

1, 2, 3, 4

or none

Step-by-step explanation:

Mode is the value or values in the data set that occurs most frequently.

example:

For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.

in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode

hope this helps:)

Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9.  This labeled is correct.

According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.

So Option C is correct after all assumptions.

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