Given f(x)= 3(2−x), what is the value of f(−4)?

Answer: x=-15

Step-by-step explanation:

-1 = 4 + x/3

-1-4=4-4+x/3

-5=x/3

-5*3=x*3/3

-15=x*1

x=-15

[tex]-1=4+\frac{x}{3}\\ \\-1(-4)=4+\frac{x}{3}-4\ \ \ \ \ \ \ \ \ \ justify:subtract\ by\ 4\ on\ both\ sides\\\\(3)-5=x/3(3)\ \ \ \ \ \ \ \ \ justify:\ multiply\ by\ 3\ on both sides\\\boxed{x=-15}[/tex]

Answer:

a score of 100 is required

Step-by-step explanation:

the average is calculated as

average = [tex]\frac{sum}{count}[/tex]

given her average for 4 subjects is 80 , then

[tex]\frac{sum}{4}[/tex] = 80 ( multiply both sides by 4 to clear the fraction )

sum = 320

let x be the score required to raise average to 84 , then

[tex]\frac{320+x}{5}[/tex] = 84 ( multiply both sides by 5 )

320 + x = 420 ( subtract 320 from both sides )

x = 100

she requires to score 100 in her fifth subject

Answer: she needs score 100 in the fifth subject.

Step-by-step explanation:

Let a subject is nₓ

Hence,

[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4}{4} =80\\[/tex]

Multiply both parts of the equation by 4:

[tex]n_1+n_2+n_3+n_4=(80)(4)\\n_1+n_2+n_3+n_4=320[/tex]

[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4+n_5}{5}=84[/tex]

Multiply both parts of the equation by 5:

[tex]n_1+n_2+n_3+n_4+n_5=(84)(5)\\(n_1+n_2+n_3+n_4)+n_5=420\\320+n_5=420\\320+n_5-320=420-320\\n_5=100[/tex]

The equation for the vertical translation of y=f(x). 4 units up is y=f(x)+4.

Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications/transformations to change it to the desired function.

A point on the graph of y=f(x) has the shape (x,f(x)).

The points on the graph of y=f(x)+4 are of the form (x,f(x)+4).

So, the graph for y=f(x) +4 is the same as the graph for y=f(x) shifted up by 4 units.

The new equation is:

y=f(x)+4

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The equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)

Given,

The slope m= 0

The points =(-2,6)

We know the point-slope form,

[tex]y-y_{1}=m(x-x_{1} )[/tex]

Substitute the values in the equation

y-6=0(x-(-2))

y-6=0(x+2)

Hence, the equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)

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Answer:

123 people

Step-by-step explanation:

60 + 36x ≤ 4500  x is  the number of people

36x ≤ 4440  Subtract 60 from both sides of the equation

x ≤ 123.333...  Divide both sides  by 36.

We cannot have a portion of a person, so we would round down to the next person which would be 123.

The measure of m (arc ACD) is 180°

Here,

AD and CG are diameter of circle B.

We have to find the measure of m ACD.

What is Diameter of a circle?

A line that passes through the center and meets the circumference at opposite ends is called diameter of a circle.

Now,

Since, AD is a diameter.

Therefore, ACD is a semicircle.

The measure of a semicircle is 180.

So, The measure of m (arc ACD) is 180°.

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The arithmetic mean a n of the given terms. a n₋₁ =-2 x, a n₊₁=2 x

[tex]a_{n}[/tex] = x/2

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.

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Answer:

What is the maximum rectangular area that can be enclosed by 460 ft of fencing?

Step-by-step explanation:

What is the maximum rectangular area that can be enclosed by 460 ft of fencing?What is the maximum rectangular area that can be enclosed by 460 ft of fencing?

Answer:

first to get a 60 sided figure we know there if 360 degrees in a full rotation so let's simply divide it by 60

360÷60= 60 degrees

Answer:

y= -4

Step-by-step explanation:

3-4y=19

-3      -3

-4y=16/-4

y=-4

At 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.

Total amount invested = $ 10, 000

interest earned = $ 290

Let amount invested for 2 % annual interest = x

Let amount invested for 5 % annual interest = 10,000 - x

so, we get that:

2 % x + 5 % (10,000 - x) = 290

0.02 x + 500 - 0.05 x = 290

500 - 0.03 x = 290

0.03 x = 500 - 290

0.03 x = 210

3 x = 21000

x = 21000 / 3

x = 7,000

10,000 - x = 3,000

Therefore, at 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.

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Answer:

$300

Step-by-step explanation:

subtract $200 by $50= $150, then $150 to $100.

Using substitution method, the solution of the given system of equations is (-9, -26)

A system of equation can be solved using:

The given system of equations:

y = 3x+1   ............   (1)

2x - y = 8  .............. (2)

Notice the y variable is already isolated on the left side. Therefore, we can immediately use the substitution method.

Substitute y = 3x+1 into equation (2):

2x - y = 8

2x - (3x + 1) = 8

-x -1 = 8

-x = 9

Multiply by (-1)

x = -9

Substitute back x = -9 into equation (1)

y = 3x + 1

   = 3.(-9) + 1

   = -27 + 1 = -26

Hence, the solution is (-9, -26)

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The number of kilometers are 1,3.5,0.5,0.075,0.001.

Meters are 1000,3500,500,75,1.

The number of meters is x.

The number of kilometers is y.

kilometer = 1/1000×meter

y = 1/1000×x

The units of length and distance are meters and kilometers, respectively. The kilometer, or 1,000 meters, serves as the unit of distance measurement in the metric system. Therefore, one meter is equivalent to a thousandth of a kilometer.

A meter is denoted by the letter m, whereas a kilometer is denoted by the letter km. The default unit of length measurement in the metric system. Between the length of a ruler and the spacing between objects in a room, meters are used to measure everything.

Therefore the number of kilometers are 1,3.5,0.5,0.075,0.001.

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Answer: Scale factor = 5/4 and this is a fraction number.

Step-by-step explanation:

Given Data,

find the question in the attachment.

Scale factor = (Dimensions of image) / (corresponding dimensions of preimage)

Let us assume,

         Dimensions of image = B

       corresponding dimensions of preimage = A

So,

we can write,

             Length of rectangle B = 45/2

             Length of rectangle A =18

Then,

                Scale factor = B/A

                                     = (45/2) / (18)

                                     =  22.5 / 18

                                     = 5/4

                                     = 1.25

Therefore, image rectangle A is dilated with by a scale factor of  1.25

In order to express 1.25 as a fraction, we will first try to remove the decimal.

As 1.25 has 2 numbers after the decimal point, we will divide it by 100 in order to remove the decimal.

Hence, we get: 1.25 = 125/100

Now, dividing both sides by a common factor of 25, we will get:

125/100 = 5/4

Thus, 1.25 a as a fraction is 5/4.

Therefore,

Scale factor = 5/4 and this is a fraction number.

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The equation x = 2

is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

It is given that, the line is passing through two points (2, -1) and (2, 6)

The formula to find the equation of a line in two point form is

(y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

where m = [tex]\frac{y2 - y1}{x2 - x1 }[/tex] is the slope of the line

Slope is the measurement of the level of steepness of the line

We need to find the Two- Point form of the line

Using the above formula we get, where

x1 = 2 , x2 = 2, y1 = -1, y2 = 6

m = [tex]\frac{(6-(-1))}{(2-2)}[/tex]= [tex]\frac{7}{0}[/tex]

The equation of the line = (y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

[y - (-1)] = [tex]\frac{7}{0}[/tex] (x - 2)

0. [y - (-1)] = 7(x-2)

7x - 14 = 0

x = 2

Hence, x =2 is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

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yes,  the set of points at which the function f(x, y, z) = p 2x 7y 3z .

Describe the equation of continuity with an example?

given , f( x,y,z) = [tex]\sqrt{4x + 7y + z}[/tex]

clearly ( 4x + 7y+ z ) is a polymial  function

So, differentiable & continuous on R

So, [tex]\sqrt{4x + 7y + z }[/tex]  is coutinuous on every point  with 4x + 7y+ z≥ 0

       i.e.  with z ≥ ( -4x - 7y)

∴ the set points at which  f is continuous is

D = { X , Y,Z } Z ≥  ( 4x - 7y)

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Answer:

im pretty sure it's

Step-by-step explanation:

all the angles added should be 180, so you subtract 62 and 94 from 180 to get 24.

The cost of each video is found to be $0.99.

Two-variable linear equations If a, b, and r are all real numbers (and a and b are not both equal to 0), ax+by = r is known as a linear equation in two variables.

(The x and y are the "two variables.") The coefficients of a equation ax+by = r are the numbers a and b.

Now, as per the stated question;

Let the number of video be denoted by 'x'.

Let the number of songs be denoted by 'y'.

Then,

Tameron downloaded 2 videos and 7 songs $10.91 .

2x + 7y = 10.91   ......(equation 1)

Jake downloaded 3 videos and 4 songs for $ 9.93.

3x + 4y = 9.93   ......(equation 2)

Solving equation 1 and 2 by elimination method, we get

x = 1.956 and y = 0.99

Therefore, the cost of each video is $0.99.

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The slope of the line 5y + 3 = (2/5)x is 2 .

The equation of a straight line can be written as follows,

y = mx + c                                         equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 5y + 3 = (2/5)x .

To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1.

So, now we will rearrange the given equation as,

 5y + 3 = (2/5)x

⇒ 5y = (2/5)x - 3

Now on dividing this equation by 5 on both sides, we will get

⇒ y = 2x + (-3/5)                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 2

Intercept = c = (-3/5)

The slope of the line 5y + 3 = (2/5)x  is 2 .

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Step-by-step explanation:

that is the solution above

Answer:

it might be 3.8169 to the 6th power or 9.6296 to the 2nd power.

Step-by-step explanation:

but I might be

The equation be I = √W/R  

Where I is the current.

W stands for electrical power.

R stands for resistance in ohms then the value of I = 0.5.

A circuit's ability to transport electrical energy is referred to as its electric power. One joule per second, or one watt, is the SI unit of power. Similar to other SI units, watts have standard suffixes that refer to thousands, millions, and billions of watts as kilowatts, megawatts, and gigawatts, respectively.

Let the equation be I = √W/R

Where, I is the current.

W stands for electrical power.

R stands for resistance in ohms.

Simply enter the values of W and R into the equation, i.e.,

When W = 50, R = 200, to solve for the value of I for each set.

I = √50/ 200

The square root of I = √0.25

W = 50, R = 200, I = 0.5.

I = √50/ 200

The square root of I = √0.25

I = 0.5

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The property of real numbers illustrated by the equation is commutative property of multiplication.

The basic properties of real numbers are used to determine the sequence of simplifying mathematical expressions.

Commutative property of multiplication states that change order of factors does not change the product. i.e. a*b=b*a.

In the given equation, to determine if the property is applicable, we need to rewrite the equation:

97(7)=100(7)-3(7)

Taking the common factor out on the right side:

97(7)=7(100-3)

Simplifying,

97(7)=7(97)

Both sides of the equation will give the same answer of 679.

Hence, in this form it is evident that commutative property of multiplication is illustrated by the equation 97(7)=100(7)-3(7)

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Answer:

x = -1

Step-by-step explanation:

The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.

Some of the Translation are,

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.

Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

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The complete question image is attached.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's your solution :

[tex] \qquad \sf  \dashrightarrow \: \cfrac{r + 6}{3r - 6} + \dfrac{r + 1}{3r - 6} [/tex]

[ since the denominator is same, we can just add the numerators ]

[tex] \qquad \sf  \dashrightarrow \: \cfrac{r + 6 + r + 1}{3r - 6} [/tex]

[tex] \qquad \sf  \dashrightarrow \: \cfrac{2r + 7}{3r - 6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x - 1} - \dfrac{5x}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6(4) - 5x(x - 1)}{4(x - 1)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{24- 5x {}^{2} + 5x}{4x - 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x}{5x + 4} + \dfrac{6x}{2x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x(2x + 3) + 6x(5x + 4)}{(5x + 4)(2x + 3)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{4 {x}^{2} + 6x+ 30 {x}^{2} + 24x}{10 {x}^{2} + 15x + 8x + 12} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{34 {x}^{2} + 30x}{10 {x}^{2} + 23 {x}^{} +12 }[/tex]

The given statement exists true. If the measures of the base angles of an isosceles triangle are integers, then the sum of those angles is 2 times that integer, so the sum is an even number. The three angles added together must add to 180.

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

The characteristics of an isosceles triangle are as follows: There is an agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

If the measures of the base angles of an isosceles triangle are integers, then the sum of those angles is 2 times that integer, so the sum is an even number. The three angles added together must add to 180.

An even number plus an odd number will be an odd number, and 180 exists always even.

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The fractions in the simplest form is: = -73/24.

Given the expression involving fractions, -7/8 + (-2⅙), we would solve as shown below:

-7/8 + (-2⅙)

Convert the mixed fraction to improper fraction

= -7/8 + (-13/6)

Distribute to eliminate the parentheses

= -7/8 - 13/6

= (-21 - 52)/24

= -73/24

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