What is the slope of a line perpendicular to the line whose equation is
3x+18y=-486

By evaluating the function graphically ,  f (4) = -4

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).

According to the Given information

f( x ) = y

where x is an input and y is an output

We need to find the value for f(4)

f( 4 ) = y

For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant

f (4) = -4

By evaluating the function graphically ,  f (4) = -4

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Each person ate 21/2 pounds of nut

First of all, we have 7 friends who are going to share 2/3 pound bag of pistachios

This will mean that we will have to divide equally the two-thirds-pound bag of pistachios among the seven people that we have so that we get the share that each person will get

There are 7 friends that share a 2/3-pound bag.

The first step will be: 7÷2/3

7÷0.6666

we will get 21/2 or 10.5

This will imply or mean that each of the friends will get an equal share of 21/2 of the  a two-thirds pound bag of pistachios

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The given function is  x² - 7x + 5 and the most general antiderivative of the function  is F(x) = x³/3 - 7x²/2 + 5x + c.

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = ∫f(x)dx

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = ∫x² - 7x + 5

F(x) = x³/3 - 7x²/2 + 5x + c

Where c is the constant of the integration (antiderivative).

The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.

Therefore,  F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.

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The whole numbers are closed under subtraction only by distributive property else they are not closed under subtraction.

Whole numbers constitute natural numbers including zero. The subset is given by {0, 1, 2, 3, 4, 5, …}, the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}

To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two whole numbers say 5 and 2.

now 5-2=3, but 2-5= -3 which is not a whole number.

Thus, whole numbers are not closed under subtraction by closure property.

2. The commutative property-

let's take two whole numbers say 5 and 2.

now 5-2=3 and 2-5=-3

hence, we get 2-5 ≠ 5-2.

Thus, whole numbers are not closed under subtraction by commutative property.

3. The associative property-

let's take three whole numbers say 5, 3, and 2.

now (5-3)-2 = 0 and 5-(3-2)= 4

hence, we get (5-3)-2 ≠ 5-(3-2).

Thus, whole numbers are not closed under subtraction by associative property.

4. The distributive property-

let's take three whole numbers say 20, 6, and 5.

now, 20 × ( 6 – 5 ) =  20 × 6 – 20 × 5  = 20

         and 20 × ( 6 – 5 ) = 20 × 1 = 20

Hence, 20=20.

Thus, whole numbers are closed under subtraction only by distributive property.

Hence, we can conclude that whole numbers are closed under subtraction only by distributive property.

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The value of all the given expression are as follow:

a. Absolute value of -3 / 2 is equal to 3 /2.

b. The value of 32^4 is equal to 1048576.

c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.

d. Value of 4^2 is 16

As given in the question,

Simplification of the given expressions are :

a. The absolute value of ( -3 / 2 )is

| - 3 / 2 | = ( 3/2 )

b. The value of the expression 32^4  is:

32^4

= 32 × 32 × 32 × 32

=  1048576

c. The value of the given expression ( 32 ) ^ 1/4 :

( 32 ) ^ 1/4

= ( 2⁵) ^ 1/4

= 2^(5/4)

d. Value of 4^2 is

4^2

= 4 × 4

= 16

Therefore, the value of the given expression is given by :

a. Absolute value of -3 / 2 is equal to 3 /2.

b. The value of 32^4 is equal to 1048576.

c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.

d. Value of 4^2 is 16

The complete question is:

What is the absolute value of -3/2 ?

what is the value of 32^4?

what is the value of 32 to the one - fourth power?

what is the value of 4^2?

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The percentage of all customers prefer port drink and tea is 17.55%. The result is obtained by multiplying the two percentages of the data.

We have a number of customers.

Of all customers, find the percentage that they prefer port drink and tea!

If 55% prefer soda over port drink, then the ones who prefer port drink is

100% - 55% = 45%

Of the customers who prefer port drink, 61% prefer coffee over tea. So, the ones who prefer tea is

100% - 61% = 39%

From that information, we can get the ones who prefer port drink and tea. Let's say pt = port drink and tea.

pt = 39% × 45%

pt = 0.39 × 0.45

pt = 0.1755

pt = 17.55%

Hence, of all customers, the percentage who prefer port drink and tea is 17.55%.

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f(x) = Area = (length)(width)

width = x

The length is 16 yards greater than 3 times x

length = 3x+16

f(x) = (3x+16)(x) = 3x^2 + 16x

Answer:

Step-by-step explanation:

We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards

Length of parking lot is 16 + 3x

Width of parking lot is x

We have to write the function f(x) that describes the area, in square yards, as a function of the width, x

Area of rectangle is Length × width

[tex] \sf Area = f(x) [/tex]

put value of length and width here,

[tex] \sf f(x) = (16 + 3x)(x )[/tex]

[tex] \sf f(x) = 3x^2 + 16x [/tex]

Therefore, f(x) = 3x² + 16x

Answer:

D

Step-by-step explanation:

Answer:

Here

Step-by-step explanation:

The vertex of the parabola is at (0.5, 8.5).

Answer: 248

Step-by-step explanation: First, you add 4 + 6 to get 10, then you multiply that by 5 to get 50. Then you multiply 50 by 5 to get 250, so 250-2 = 248. I hoped this solved your problem.

Answer:

248

Step-by-step explanation:

(4+6)x5x5-2

10x5x5-2

50x5-2

250-2

248

(if wrong sorry)

Answer: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `

Step-by-step explanation: Straight lines `2x + y = 5` and `x-2y = 3` intersect at point `A`. Points `B` and `C` are chosen on these two lines such that `AB = AC`. Then the equation of a line `BC` passing through the point `(2.3)` is: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `

I hope this helps :)

The function x^2 +10x +15 in vertex form is (x+5)^2 - 10 and the vertex is a minimum at (-5, -10)

The vertex of a parabola is a point at which the parabola makes its sharpest turn. A parabolic function has either a maximum value (if it is of the shape '∩') or a minimum value (if it is of the shape 'U"). The vertex of a parabola is also the point of intersection of the parabola and its axis of symmetry.

y = x^2 + 10x +15

making x^2 + 10x +15 a perfect square expression we square the half of the coefficient of x on both sides which is (5)^2

y + (5)^2 = x^2 + 10x + (5)^2 + 15

y + 25 = x^2 + 10x + (5)^2 + 15

x^2 + 10x + (5)^2  can be written as (x+5)^2 since iti is now a perfect square expression

y + 25 = (x+5)^2 + 15

y = (x+5)^2 + 15 - 25

y = (x+5)^2 -10

Equation of parabola in vertex form is  y = a (x - h)2 + k

where k is the minimum or maximum point of vertex and h is the x coordinate of vertex.

comparing both equations, the coordinate of vertex (h, k) is (-5, -10) which is a minimum point.

In conclusion the vertex is a minimum at (-5, -10) and the equation in vertex form is  (x+5)^2 -10

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The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.

The slope-intercept form is expressed as;

y  = mx + b

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the line q using the slope intercept-form.

y = mx + b

3x + 5y = 10

5y = -3x + 10

y = (-3/5)x + 10/5

y = (-3/5)x + 2

Hence;

Slope of line q m = -3/5

Since, line r is parallel to line q, they both have the same slope.

Therefore, slope of line r will be m  = -3/5

Now, plug the point  (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - (-4) = (-3/5)( x - 5 )

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

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

y = (-3/5)x - 1

Therefore, the equation of line r is  y = (-3/5)x - 1.

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Answer:

30 ft

Step-by-step explanation:

Answer:

122 ft

Step-by-step explanation:

The 100 ft and the 70 ft are two legs of a right triangle....their distance apart is the hypotenuse of this triangle ....use Pythagorean theorem

d^2 = 100^2 + 70 ^2

  d = 122 ft

Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

ABC refers to a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

So, the triangles PRE and POC appear to be comparable triangles in the diagram.

Utilizing the similarity theorem:

PR/RE = PR+RO/OC

x/135 = (x+140)/230

By cross-multiply:
230x = 135(x+ 140)

230x = 135x + 18,900

230x - 135x = 18,900

95x = 18900

x =18900/95

x = 198.94

Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

The method that he chooses to select his sample is Stratified Sampling.

In Stratified, the population is divided into subpopulations and then the same sampling is applied to each region or subpopulation.

The ability to obtain a sample population that most accurately represents the overall population being investigated while ensuring that each subgroup of interest is represented makes stratified random sampling one popular technique employed by researchers. Researchers use stratified sampling to ensure that specific subgroups are represented in the sample. It also helps in the precise evaluation of each group's characteristics. This technique is often used in surveys to better understand disparities between subpopulations.

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Answer: 50 teams

Step-by-step explanation:

       We will set up a proportion to solve.

[tex]\displaystyle \frac{30\%}{15\;\;\text{teams}} =\frac{100\%}{x\;\;\text{teams}}[/tex]

       A percent divided by 100 becomes a decimal.

[tex]\displaystyle \frac{0.3}{15\;\;\text{teams}} =\frac{1}{x\;\;\text{teams}}[/tex]

       Next, we will cross-multiply:

0.3x = 15

       Lastly, we will divide.

x = 50

The triangle ABC is a Dilation of triangle DEF.

A dilation is a transformation that produces an image that is the same shape as the original one but in a different size. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. So, the shape of triangles ABC and DEF are the same.

Since they have similar shapes, their angles will be the same. The largest angle measured in triangle DEF = The largest angle measured in triangle ABC.

Dilation can reduce the shape of an object. The dilation can also enlarge a shape proportionally resulting in a giant monster version of itself.

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The number which is less than that of -2.67 are -2.8, -2.9, -3.0.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Which numbers are less than –8/3 = -2.67

So given in the option which is less than -2.67

Numberless -2.7 are

-2.8, -2.9, -3.0.

Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.

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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2

This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

Given that,

The statement is a confidence interval is the rejection region of a two-sided test.

We have to say if the statement is true or false.

We know that,

In statistics, a confidence interval describes the probability that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.

Therefore, This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

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Answer:

The probability for the green one is 6/10

and for the next one, it is 4/10  

Step-by-step explanation:

Answer: x^2 + 1

Step-by-step explanation:

-x²+2-1+ 6x² - 4x²

We combine the x^2 and the numbers and we have the equation

x^2 + 1

the solution to the equation is x=12

The distributive property is defined as

Let us now solve the equation.

5(x - 6) = 2(x + 3)

Using the distributive property, simplify the parentheses on both sides.

5(x - 6) = 2(x + 3)

5x - 30 = 2x + 6

The parenthesis was simplified. However, we have one x term on one side and another x term on the other.

5x - 30 - 2x = 2x + 6 - 2x

3x - 30 = 6

We only have an x term on one side of the equation now.

To begin, reverse the subtraction by adding 30 to either side of the equation.

To keep an equation balanced or true, we do the identical operation on both sides.

3x - 30 + 30 = 6 + 30

3x = 36

We're getting close to an answer. Only one more step.

The x term is multiplied by 3.

We can undo the multiplication operation by dividing both sides by 3.

3x / 3 = 36 / 3

x = 12

So, x is equal to 12.

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The area of a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola   [tex]y=c-x^2[/tex]   is   [tex]4(\frac{c}{3})^\frac{3}{2}[/tex].

A rectangle has a width  [tex]2x[/tex] ⇒ w= [tex]2x[/tex]

height of the rectangle is   [tex]c-x^2[/tex] ⇒    [tex]y=c-x^2[/tex]

Area=width multiplied by the height

                                       ⇒[tex]area=width*height[/tex]

we maximize Area by setting   [tex]\frac{dA}{dx} =0[/tex] .

                                     [tex]\frac{d(2c-2x^3)}{dx} =0\\\\2c-6x^2=0\\\\x^2=\frac{1}{3}c\\ \\x=\sqrt{\frac{c}{3} }[/tex]

substituting back the value of x in the formula of the area we get  

                                  [tex]area=2\sqrt{\frac{c}{3} } *2\frac{c}{3} \\\\area=4(\frac{c}{3})^\frac{3}{2}[/tex]

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The rule of reflection for the triangle △JKL to △J'K'L' is x = -4.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the vertices of △JKL are J(1, 0), K(-5, 2), L(4, -4).

The vertices of △J'K'L' are J'(-9, 0), K'(-3, 2), L'(-12, -4).

The formula of midpoint of (x₁, y₁) and (x₂, y₂) is

((x₁+x₂)/2,  (y₁+y₂)/2)

The midpoint of J(1, 0) and J'(-9, 0) is ((1+(-9)/2,(0+0)/2) = (-8/2,0) = (-4,0)

The midpoint of K(-5, 2) and K'(-3, 2) is ((-5+(-3)/2,(2+2)/2) = (-8/2,4/2) = (-4,2)

The midpoint of L(4, -4) and L'(-12, -4) is ((4+(-12)/2,(-4+(-4))/2) = (-8/2,-8/2) = (-4,-4)

Thus the x-coordinate of the midpoint is the same.

Thus the line of reflection is x = -4.

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By using algebra (5, 4) is not a solution of the inequality.

Boundary does not contain in the given graph this is the error was made when graphed.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

x + 2y ≤ 12

Here the inequality contain ≤ .

Since, if there is ≤  sign then graph must contain boundary line.

The boundary line is solid line need to use in the graph.

But in the given graph the boundary line is dotted.

Boundary does not contain in the graph.

Hence, this is the error was made when graphed.

Also from graph we can see that the point (5, 4) is not contain in the graph.

Hence, (5, 4) is not a solution of the inequality.

Now prove by using algebra.

Plug x = 5, y = 4 in the given inequality

⇒  5 + 2(4) ≤ 12

         5 + 8 ≤  12

             13 ≤  12

It is not possible that 13 ≤  12.

Hence, (5, 4) is not a solution of the inequality.

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Answer:

l and lll

Step-by-step explanation:

228.32 + 48.16 - 28.16 = 248.32

The maximum volume of the rectangular solid in cubic units in terms of the width, w is [tex]-3w^{3}-6w^{2}+105w[/tex].

Information from the question is known as follows :

width = w

length = w+7

height = 15-3w

The maximum volume of a rectangular solid can be found by the formula :

Volume = length x width x height

Volume  = (w+7) x w x (15-3w)

Volume  = [tex](w+7)(15w-3w^{2} )[/tex]

Volume  = [tex]15w^{2}-3w^{3} +105w-21w^{2}[/tex]

Volume  = [tex]-3w^{3}-6w^{2}+105w[/tex]

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The slope (m) of the line that passes through the points (0, 4) and (8, 0) is -1/2 and the y-Intercept is (0, 4).  

What is the slop of the line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the points (0, 4) and (8, 0)

Slop (m) = ?

The slope formula is:

m =  (y₂-y₁) ÷ (x₂-x₁)

so here,

m = (0 - 4) ÷ (8 - 0)

m = -4 ÷ 8

m = -1/2

Hence, the slope (m) of the line that passes through the points (0, 4) and (8, 0) is -1/2 and the y-Intercept is (0, 4).  

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If Jesus borrowed $1,000 for 1 week at an APR of 350%, the interest he has to pay at the end of the week is B. $67.31.

The interest represents the cost of borrowing.

The interest is computed as the principal multiplied by the annual percentage rate (APR) and time (period).

The interest formula used here is the simple interest instead of the compound interest, which charges interest on accumulated interest and the principal every period.

Principal borrowed for 1 week = $1,000

Annual percentage rate (APR) = 350%

Loan period = 1 week

52 weeks = 1 year

Interest = Principal x APR x Time

= $1,000 x 350% x 1/52

= $67.31.

Thus, the interest that the borrower pays for $1,000 for 1 week at 350% APR is not $52.70, $78.42, or $86.21, but $67.31.

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