The binomial x + 7 is a factor of polynomial p.

Use this information to complete the equation.

Value for (f⁰g)(-2) = -6/3

Given :

             g(x) = 3x + 2

              f(x) =  (x-2)/3        

Now,

(f⁰g)(x) = f(g(x))

(f⁰g)(-2) = f(g(-2))

substitute x = -2

g(-2) = 3(-2) + 2 = -4

f(g(-2)) = f(-4)

(f⁰g)(-2) = f(-4) =  -6/3

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Step-by-step explanation:

(0.5-2)-1 = -1.5 - 1

= -2

(3+4) -2 = 7 - 2

= 5

(-8+5)+3 = -3+3

= 0

-(0.5-2)+1 = -(-1.5)+1

= +1.5 + 1

= 2.5

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

= -5

-(-8-5) -3 = -(-13) -3

= +13 -3

= 10

Answer:

-7>x

Step-by-step explanation:

-2x-7>5x+14

-7>3x+14

-21>3x

-7>x

The bag that has the lowest unit price per pound is the 5 pound bag.

Unit price is the value of a single unit of measure.

A 3-pound bag of apples costs $3.94, and a 5-pound bag costs $5.92.

Let's find the unit price per pounds of each products to know the lowest.

Therefore,

unit price per pound  for the 3 pound bag = 3.94 / 3

unit price per pound  for the 3 pound bag = 1.31333333333

unit price per pound  for the 3 pound bag = $1.313 per pound

unit price per pound  for the 5 pound bag = 5.92 / 5

unit price per pound  for the 5 pound bag = 1.184

unit price per pound  for the 5 pound bag = $1.184 per pound

Therefore, the apple bag of 5 pound has the lowest unit price.

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Answer:

[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

Factor out a [tex]\sqrt{5}[/tex] from the [tex]\sqrt{80}[/tex], and you will get [tex]\sqrt{5} * \sqrt{16}[/tex]

Then you get: [tex]4\sqrt{5}[/tex], since the square root of 16 is just 4. Then we have this expression:

[tex]4\sqrt{5} -\sqrt{5}[/tex], which gives us [tex]3\sqrt{5}[/tex].

Hope this helps

According to  the solving the estimated sum of the numbers:

To estimate implies to come up with a solution that is close but not accurate. It's a reasonable solution to a problem. A sum is the solution to an addition issue. A difference is a solution to a subtraction issue.

To get the total, we round each number to the closest tenth and then add the rounded figures. Let us calculate 38 + 23. 38 is more like 40 than 30. As a result, 38 is rounded up to 40.

1 435 + 678 + 925 =  2,038

on round of  = 2040

2.359 + 814 + 207 = 1,380

on round of  = 1380

3. 6428 + 7154 + 9345 = 22,927

on round of  = 22930

4. 2987 + 6873 + 4555 = 14,415

on round of  = 14420

5. 6759 + 8210 + 7642 = 22,611

on round of  = 22610

2,040

1,380

22,930

14,420

22,610

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I understand that the question you are looking for is:

Estimate the sum:

1 435 + 678 + 925 =

2.359 + 814 + 207 =

3. 6428 + 7154 + 9345 =

4. 2987 + 6873 + 4555 =

5. 6759 + 8210 + 7642 =

The width of the rectangle is: 3 meters.

Perimeter of a rectangle is determined using the formula:

Perimeter = 2(length + width)

Given the parameters below:

Width of the rectangle = w meters

Length of the rectangle = 2w - 3 meters

Perimeter of the rectangle = 24 meters

Therefore:

2((2w - 3) + w) = 24

Solve for w (width of the rectangle)

2((2w - 3 + w) = 24

2(3w - 3) = 24

6w - 6 = 24

6w = 24 - 6

6w = 18

6w/6 = 18/6

w = 3

Therefore, the width of the rectangle is: 3 meters.

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Answer: Positive ÷ positive = positive.

Negative ÷ negative = positive.

Negative ÷ positive = negative.

Step-by-step explanation: The division of two positive integers results positive integer.

Positive (+) ÷ Positive (+) = Positive (+)

The division of two negative integers results positive integer.

Negative (+) ÷ Negative (+) = Positive (+)

The division of two different sign integers results negative integer.

The division of f (x) and g (x) is x - 1 and the domain is  [ 1 , ∞ ].

Given,

f (x) = x - 2

g (x) = x ² - 3 x + 2

The question states to find the division of the function f, that is, f (x) = x - 2, and function g, that is, g (x) = x ² - 3 x + 2

Performing the division operation on these functions is just like simple division.

This implies, dividing the two functions f (x) and g (x), we get

g (x) / f (x) = x² - 3x + 2 / x - 2

            x - 1

        ___________

x - 2 |   x² - 3x + 2

           x² - 2x

         ____________

                   -x + 2

                   -x + 2

         ____________

                           0

=> g (x) / f (x) = x - 1

This implies that the division of the two functions f (x) and g (x) gives x - 1

To find the domain :

y =  x - 1

=> x ≥ 1

=> Domain = [ 1 , ∞ ]  

Therefore, we get the division of f (x) and g (x) as x - 1 and the domain as  [ 1 , ∞ ].

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The range of the function f(x) = | x + 2| - 2 for all x belongs to real is [-2,∞].

Closed interval includes the points and we denote it by third brackets and open interval do not include the points and denoted by first brackets.

According to the given question we have to determine the range of the function y = |x + 2| - 2 where domain of x ∈ R.

We know, |x + 2| ≥ = 0.

∴  | x + 2 | - 2 ≥ -2  and f(x) = | x + 2 | - 2 so, f (x) ≥ - 2, ∀ x ∈ R.

There fore the range of the function f(x) is [ -2, ∞ ].

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Answer:

The value behind a decimal point isn't increased by zeros, zeros are actually just placeholders

Step-by-step explanation:

Answer:

answers is 26.3%.

Step-by-step explanation:

you will say ( NEW price-OLD price)

95.99-75.99=20

20/75.99*100%

=26.3%

The single transformation which takes shape A to shape B is given by the vector [tex](^{-5}_{-5})[/tex]

Transformation is the movement of a point from its initial location to a new location. Types of transformations are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The single transformation which takes shape A to shape B is given by the vector [tex](^{-5}_{-5})[/tex]

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Answer:

We would predict 177 girls

Step-by-step explanation:

We can set up a proportion

[tex]\frac{Girls}{Boys}[/tex] = [tex]\frac{Girls}{Boys}[/tex]  Put in the number that I know and solve for the number that I do not know.

[tex]\frac{3}{4}[/tex] = [tex]\frac{g}{236}[/tex]  I can cross multiply to solve for x

4g = 3(236)

4g = 708  Divide both sides by 4

g = 177

The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)

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The equation of the line shown in the reference graph, attached hereby, that passes through the points (-6, 0) and (0, 4) is  [3y = (2x + 12)].

As per the question statement, we are provided with a straight line, drawn on the cartesian quadrants that pass through two points, (-6, 0) and (0, 4).

We are required to determine the equation of the line.

To solve this question, we need to know the formula to determine the linear equation of a line passing through two points, (x₁, y₁) and (x₂, y₂), which goes as [tex][(y-y_{1})=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}) (x-x_{1})][/tex].

Here, let us consider, (-6, 0) to be (x₁, y₁), and (0, 4) to be (x₂, y₂). Therefore, using these values in the above mentioned equation, we get

[tex](y-0)=[\frac{4-0}{0-(-6)}][x-(-6)]\\ or, y=(\frac{4}{6})(x+6)\\ or, y=(\frac{2}{3})(x+6)\\or, 3y=2x+12[/tex]

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Answer:

A.

Step-by-step explanation:

D: there is no square root

for both C and B there is no decimal.

A should end up being y=-8x+5 which is in y=mx+b form

12 x 5 = 60

10x 6= 60

so 5 packs of pencils and 6 packs of erasers.

The only one that is not  part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.

The steps for constructing a copy of an angle using only a compass and a straightedge are as follows;

Step 1: Mark the point that will be the vertex of the new angle, and label it P.

Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.

Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.

Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.

Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.

Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.

Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.

Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.

Looking at the given options, the only one that is not  part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.

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Answer:

d

Step-by-step explanation:

Answer:

b = [tex]\frac{a}{c}[/tex]

Step-by-step explanation:

[tex]\frac{a}{b}[/tex] = c ( multiply both sides by b )

a = bc ( isolate b by dividing both sides by c )

[tex]\frac{a}{c}[/tex] = b

Using a linear function, it is found that 1466 gallons of water were in the tank when jabria began adding water.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

A linear function is modeled by: y = mx + b

where,

In this problem, we have given that in 12 minutes, the amount of water increased by 3456 gallons, hence the slope is given by :

m = 3456/12 = 288.

In 7 minutes, the tank contained 3,482 gallons of water, hence the initial amount was given by :

3482 - 7 x 288 = 1466

1466 gallons of water were in the tank when jabria began adding water.

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The correct option for the end behaviour of function is option C. As x approaches positive infinity, g(x) approaches positive infinity.

We have been assigned the following function:

g(x) = 1/2|x - 3| - 7

Behavior at the end:  As x approaches negative and positive infinity, the limit of g(x) is reached.

Infinity minus one:

lim g(x) =   lim      1/2|x - 3| - 7

x → -∞          x → -∞

lim g(x) =  1/2|-∞ - 3| - 7   = | -∞ |  = ∞

x → -∞        

Thus, the negative end behaviour is ∞ .

Infinity plus one:

lim g(x) =   lim      1/2|x - 3| - 7

x → ∞          x → ∞

lim g(x) =  1/2|∞ - 3| - 7   = | ∞ |  = ∞

Thus, positive end behaviour is also  ∞ .

As a result, it approaches positive infinity in both cases, and the correct option is C.

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The correct question is-

Which statement describes the end behavior of this function?

g(x) = 1/2|x - 3| - 7

A. As x approaches positive infinity, g(x) approaches negative infinity.

B. As x approaches negative infinity, g(x) approaches negative infinity.

C. As x approaches positive infinity, g(x) approaches positive infinity.

D. As x approaches negative infinity, g(x) is no longer continuous.

let's first of all, convert all the mixed fractions to improper fractions and then proceed.

[tex]\stackrel{mixed}{3\frac{4}{15}}\implies \cfrac{3\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{49}{15}} ~\hfill \stackrel{mixed}{6\frac{3}{10}}\implies \cfrac{6\cdot 10+3}{10}\implies \stackrel{improper}{\cfrac{63}{10}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{3\frac{4}{15}}{ ~~ 8\cdot 6\frac{3}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ 8\cdot \frac{63}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ \frac{252}{5} ~~ }\implies \cfrac{49}{15}\cdot \cfrac{5}{252}\implies \cfrac{49}{252}\cdot \cfrac{5}{15} \\\\\\ \cfrac{7}{36}\cdot \cfrac{1}{3}\implies \cfrac{7}{108}[/tex]

The fraction that's left to read in the book is 3/8.

From the information given, it should be noted that Tim has 5/10 of a book left to read for school. Tim read 1/8 of a book on Monday.

Therefore, the fraction that will be left to read will be:

= 5/10 - (1/8)

= 20/40 - 5/40

= 15/40

= 3/8.

The fraction that is left will be 3/8.

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Answer:

Hope this helps!

Data of different sizes can be easily arranged with histograms, but not with stem-and-leaf diagrams. This is a drawback.

Stem-and-leaf charts often include the original data values while histograms do not. This is a crucial advantage the former has over the latter.

The primary benefit of stem-and-leaf charts over histograms is that they display the original data values.

In contrast to stem-and-leaf charts, which lack this capability, histograms make it straightforward to organize data of various sizes. This is a serious disadvantage.

In conclusion, a stem-and-leaf display, sometimes referred to as a stem-and-leaf plot, is a tool that shows quantitative data graphically to assist visualize the form of a distribution.

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Answer:

18=49

Step-by-step explanation: