For the polynomial P(x) = 4x + 7x + 8 and c = 1, find P(c) by (a) direct substitution and (b) the remainder theorem

From the given figure , we will use the Sine function in order to find segment x .

Sin 70 ° = opposite /hypotaneus

Sin 70 ° =x /7

∴x = 7* Sin 70°

x = 6.5778

x ≈6.6 ...( rounded to the nearest 10 )

Simplifying:

Answer

(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1

Explanation

The question simply wants us to simplify the expression

(8m + 1)^2

= (8m + 1)²

= (8m + 1) (8m + 1)

= 8m (8m + 1) + 1 (8m + 1)

= 64m² + 8m + 8m + 1

= 64m² + 16m + 1

Hope this Helps!!!

The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:

Then, if we apply this theorem to the figure shown we can say that

This means that:

The area formula of a circle is :

From the problem, the diameter is 8 inches.

The area will be :

The answer is 50.27 in^2

By definition, the of a line written in Standard form is:

Where "A", "B" and "C" are Integers ("A" is positive).

The Slope-Intercept form of the equation of a line is:

Where "m" is the slope and "b" is the y-intercept.

You know that this line passes through these points:

By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:

Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":

Then, the slope of the line is:

Therefore, the equation of this line in Slope-Intercept form is:

To write it in Standard form, you can follow these steps:

- Subtract 2 from both sides of the equation:

- Subtract "y" from both sides of the equation:

The answer is:

Answer:

2x-y =-2

Step-by-step explanation:

To find the equation of the line in standard form, first, we need to find the slope

m = ( y2-y1)/(x2-x1)

m = (10-2)/(4-0)

   = 8/4 = 2

Then we can use the slope intercept form

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

y = 2x +b

Using the y-intercept ( 0,2)

y = 2x +2

The standard form is Ax +By =C  where A is a positive integer and B is an integer

Subtract 2x from each side

-2x +y = 2

Multiply each side by -1

2x-y =-2

1. The probability that they win both contract will be 23.4%.

It should be noted that probability simply means the likelihood that an event will occur.

The probability of winning the contract will be:

= Probability of A winning × Probability of B winning

= 45% × 52%

= 0.45 × 0.52

= 0.234

= 23.4%

The probability is 23.4%

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Defining:

Number of messages of Lashonda = L

Number of messages of Josh = J

Number of messages of Brian = B

We know that:

L+J+B=90 (Equation 1)

We also know:

L = J+10 (Equation 2)

B=2J (Equation 3)

Now, we can substitue the values for L and B in the first equation

L+J+B=90

J+10 + J + 2J = 90

4J=90-10

4J=80

J=80/4

J=20

Since you found how many messages Josh sent, we can return to Equation 2 and 3:

L = J+10

L = 20 + 10

L = 30

B=2J

B=2*20

B=40

ANSWER:

Number of text messages Lashonda sent: 30

Number of text messages Josh sent: 20

Number of text messages Brian sent: 40

System A

solve the first equation for x

replace in the second equation

The system has infinitely many solutions, They must satisfy the following equation

System B

solve for x for the first equation

replace in the second equation

The system has no solution.

Range of a Data Set :

The range of a set of data is the difference between the highest and lowest values in the set

MEAN :

The mean is the mathematical average of a set of two or more numbers

Set A: 2, 10, 8, 19, 23

Arrange the data of set A in ascending order;

Set A : 2, 8, 10, 19, 23

For range; the highest term is 23, lowers term is 2

Range = highest - lowest

Range = 23 - 2

Range = 21

for Mean; the sum of all entries divided by the total number of entries in data set.

In data A, total number of entries are : 5

Thus, mean of set A is 12.4

Now, for set B;

Set B : 14 16 15 17 16

Arrange the elements of set B in the ascending order;

Set B : 14, 15, 16, 16, 17

For range; the highest term is 17, lowers term is 14

Range = highest - lowest

Range = 17-14

Range = 3

Thus, range of set B is 3

for mean of set B;

The sum of all entries divided by the total number of entries in data set.

In data B, total number of entries are : 5

Thus, the mean for set B is 15.6

Answer : The mean of set A is 12.4 and range is 21

The mean of set B is 15.6 and range is 3

The numbers represented by the word problems are 33 and 6

The statements in the question are:

Let the numbers in the expressions be x and y

So, we have

x + y = 39

x = 7y - 9

Substitute x = 7y - 9 in the equation x + y = 39

So, we have

7y - 9 + y = 39

Evaluate the like terms

8y = 48

Divide both sides by y

y = 6

Substitute y = 6 in x + y = 39

x + 6 = 39

Evaluate the like terms

So, we have

x = 33

Hence, the numbers are 33 and 6

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Answer:

1) Given

2) Subtraction Property of Inequalities

3) Division Property of Inequalities

Check the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]

Answer:

Sure

Step-by-step explanation:

Let me know what you want by making me brainliest

Given the system of equations:

8x - 6y = 3

-3y + 4x = 4

To find how many times the lines will intersect. let's solve the system of equation using substitution method.

8x - 6y = 3 ........................................1

-3y + 4x = 4 ......................................2

From equation 1, make x the subject:

8x - 6y = 3

8x = 3 + 6y

We have:

Multiply through by 2 to eliminate the fraction:

Since we have 0 = 5, it means the system of equations has no solution.

Therefore, the lines will not intersect, because this system has no solution.

ANSWER:

A. The lines will not intersect, because this system has no solution.

The number of couches manufactured and sold in order to maximise the profit is 1560.

The demand function will be

p = 2700 - 0.75x

Here p = price per couch and x = number of couch

Total Fixed cost = $760000

Variable cost per couch = $360

Total cost = Fixed cost + variable cost

T(x) = 760000 + 360x

Revenue function will be

R(x) = Px

(2700 - 0.75x)x

2700x - 0.75x²

Since profit function = Pr(x)

Pr(x) = R(x) - T(x)

= 2700x - 0.75x² -760000 -360x

- 0.75x² + 2700x - 360x - 760000

For maximum profit

[tex]\frac{d}{dx}(Pr(x)) = 0[/tex]

[tex]\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0[/tex]

-1.5x + 2340 = 0

x = 2340/1.5

x = 1560

The couches sold for maximum profit = 1560

Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.

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We have that in 70 minutes 120 players of an orchestra play Beethoven's 9th symphony because it always lasts 70 minutes.

The lenght of a musical piece does not depend in the number of musicians playing it. The orchestra could have 2 violinists more or less and they still will play the same 70 minutes musical piece.

Then, an orchestra of 60 players would take the same 70 minutes to play Beethoven's 9th symphony.

...................

- Area of First Carousel:

diameter = 13 m

- Area of Second Carousel:

diameter = 19 m

- The difference between the two areas is:

Answer:

The platform area of the larger carousel is 150.7 m^2 larger than the platform area of the smaller carousel.

Marco bought 12 roses for $48. Each rose was originally $4 before the discount, and Super Saver Get $2 off each rose when you buy 12 or more roses each rose is $6.

Therefore,

Marco bought 12 roses for $48. Each rose was originally $4 before the discount.

∴ 48/12 = $4   and,

Super Saver Get $2 off each rose when you buy 12 or more roses

each rose is $6.

∴ 12/2 = $6

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Given the area of the triangle:

You can identify in the figure provided in the exercise that the height of the triangle is:

The area of a triangle can be calculated using this formula:

Where "A" is the area, "b" is the base, and "h" is the height.

If you solve for "b", you obtain this formula:

Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:

Hence, the answer is:

First we have to take a look at the expression f(x + 1). This represents an horizontal translation. So this is the first transformation:

1. Horizontal translation

Now we can see that we have to multiply f(x + 1) by -1. This represents a reflexion on the y-axis

2. Reflection on y-axis

Finally we can see that -f(x + 1) is added by 3 units. This represents a vertical translation:

3. Vertical translation

Answer:

1. Horizontal translation

2. Reflection on y-axis

3. Vertical translation

Now let's see the final function:

f(x) = 2x - 5

f(x+1) = 2(x + 1) - 5

f(x+1) = 2x + 2 - 5

f(x+1) = 2x - 3

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

g(x) = -2x + 6

So let's plot f and g on the same reference system:

MATHEMATICALLY we say

[tex]0 \leqslant x \leqslant 4[/tex]

THAT IS THE DOMAIN OF THE GRAPH

THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.

Answer:

Correct answer:

a. The Savannah River

After we evaluate the function f at the indicated values the results are

a. (4) −11, (5) −52, (6) 0

b. (4) -1, (5) −17, (6) -5

c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a

d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a

A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.

Lets evaluate the function a. f(-3)

4. f(-3) = 2(-3)-5

          = −11

5. f(-3) = −5(-3)²+2(-3)−1

          = −52

6.  f(-3) = -3-1-(-3)+1

            = 0

Lets evaluate the function b. f(2)

4. f(2) = 2(2)-5

          = −1

5. f(2) = −5(2)²+2(2)−1

          = −17

6.  f(2) = -3-1-(2)+1

            = −5

Lets evaluate the function c. f(-a)

4. f(-a) = 2(-a)-5

          = −2a−5

5. f(-a) = −5(-a)²+2(-a)−1

          = −5a² −2a−1

6.  f(-a) = -3-1-(-a)+1

            = −3+a

Lets evaluate the function d. -f(a)

4. -f(a) = -(2(a)-5)

          = −2a+5

5. -f(a) = -(−5(a)²+2(a)−1)

          = 5a² −2a+1

6.  -f(a) = -(-3-1-(a)+1)

            = 3+a

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The given temperature is 63 F

The formula for convert temperature into Degree C from Degree F.

Substitute all the value in the above equation.

The nearest tenth is 17degree C.

Matching the following function

What is a Function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The function of f^(-1)(x) = 5x is:

f(x)= x / 5

The function of f^(-1)(x) = x^3 / 2 is:

f(x)=3√2x

The function of f^(-1)(x) = x+10 is:

x - 10

The function of f^(-1)(x) = 3(x + 17) / 2 is:

(2x / 3) - 17

Hence, These are the Match of one-to-one functions with their inverse functions.

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we have

Find the unit rate in each case

so

718/5.95=120.67 miles per hour ---------> greater than 100 miles per hour

45.8/4=11.45 miles per hour ------> between 10 and 96 miles per hour

2,865/24.8=115.52 miles per hour -------> greater than 100 miles per hour

419.72/80.6=5.21 miles per hour ------------> less than 10 miles per hour

935.47/22.75=41.12 miles per hour ------> between 10 and 96 miles per hour

Given the following equation:

You need to solve for the variable "w" in order to find its value. To do this, you can follow the steps shown below:

1. You can apply the Subtraction property of equality by subtracting 29.7 from both sides of the equation. Then:

2. Finally, you need to apply the Division property of equality by dividing both sides of the equation by -0.2. Then, you get:

The answer is: