Select the correct answer.
Function g is a transformation of the parent cosine function such that g(x) = 3 cos (x + 2) + 1. Which graph represents function g?

The average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25  .

In the question ,

it is given that

the position of the particle that travels along the x-axis at time t is given by the function

x(t)=2t²+t

the average speed of the particle can be calculated by using the formula

average speed = (change is distance)/(change in time)

particle position at t=2

x(2) = 2(2)²+2 = 2*4+2 = 10

particle position at t=10

x(10) = 2(10)²+(10)

= 2*100+10

= 200+10

= 210

So, change in distance = 210-10= 200

change in time = 10-2 = 8

Putting the values in the average speed formula we get

average speed = 200/8

= 100/4

=25

Therefore , the average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25  .

The given question is incomplete , the complete question is

A particle travels along the x-axis such that its position at time t is given by the function x(t)=2t²+t . What is the average speed of this particle over the interval 2 ≤ t ≤ 10?

(a) 4

(b) 25

(c) 32

(d) 200

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Solution:

Given the absolute value parent function below

If the function is vertically compressed by a factor of 4, the function becomes

Where

Hence, the answer is

Option A

See explanation below

An ellipse has a standard equation formula written as:

When the sign between the x^2 and y^2 terms is positive, then it is a ellipse

An hyperbola has a standard equation written as:

when the sign between the parenthesis of x^2 and y^2 terms is minus, then it is an hyperbola

A circle has a general formula written as:

The terms x^2 and y^2 are not divided by a constant. Also the left side of the equation represents the square of the radius

Parabola has a vertex form of equation written as:

Here, we only have term x^2, no y^2. y has an exponent of 1. Also a constant of a

Answer:

Please comment if it is wrong.

Yes, the number of scoops proportional.

Define Proportional

A linear relationship between two amounts or variables is indicated by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

Hence, It is proportional. This is because as the number of people increases, the number of scoops also increase.

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Answer:

Step-by-step explanation:

no

Each bird would receive 1/9 cup of bird food.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.

The dividend would be

⇒ 2/3

The divisor would be

⇒ 6

The division expression would be

⇒ 2/3

Divided by 6

Rewrite the division expression to get

⇒ 2/3 × 1/6

⇒ 2 / 18

⇒ 1/9

Therefore, each bird would receive 1/9 cup of bird food.

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Answer: -4

Step-by-step explanation:

Let the integer be x.

[tex]8(x+1)-x=-20\\\\8x+8-x=-20\\\\7x+8=-20\\\\7x=-28\\\\x=-4[/tex]

So, the integers are -4 and -3.

The determinant of the given matrix is [tex]2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]

Determinant of the matrix:

Determinant of the matrix is defined as a scalar value which is associated with the square matrix.

Given,

Here we have the matrix show in the question.

Now, we need to find the determinant of the matrix.

To find the determinant of the matrix we have to do the following steps:

1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.

2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.

This process can be elaborated in the following steps:

[tex]=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)[/tex]

When we expand the equation then we get,

[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)[/tex]

Group the similar terms and arrange them in order,

[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)[/tex]

Again we have to expand it and then we get,

[tex]= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4[/tex]

After the simplification, the resulting determinant is

[tex]=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]

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Answer:

5+5 5-5=0 is not a solution

Step-by-step explanation:

The equation that have same solution to 3x-12=24 is 4x - 30 = 18.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation given is illustrated as:

3x - 12 = 24

Collect like terms

3x = 24 + 12

3x = 36

Divide through by 3.

3x / 3 = 36 / 3

x = 12

In this case, 4x - 30 = 18 will be:

4x - 30 = 18.

Collect like terms

4x = 18 + 30.

4x = 48

Divide

x = 48/4

x = 12

Therefore, 4x - 30 = 18 has same solution.

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The polynomial is x⁹ - 23x⁷ - 6x³ + 2x² + 10 in the standard form, the degree of the polynomial is nine, and its leading coefficient is 1.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The polynomial below which is given in the question

-23x⁷ + x⁹ -6x³ + 10 + 2x²

To determine the polynomial in the standard form.

⇒ -23x⁷ + x⁹ -6x³ + 10 + 2x²

Rearrange the terms in the descending order of the degree of variables

⇒ x⁹ - 23x⁷ - 6x³ + 2x² + 10

This is the polynomial in the standard form

Here the degree of the polynomial is nine because nine is the highest degree in the above expression and its leading coefficient is 1.

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The question seems to be incomplete the correct question would be:

Write the polynomial in the standard form, and then identify the degree and leading coefficient

-23x⁷ + x⁹ -6x³ + 10 + 2x²

We have to find how the interval (1-α) affects the width of the confidence interval.

The interval (1-α) represents the confidence required for the interval.

The greater the confidence required, the wider will be the interval.

This means also that when we decrease the confidence required, the interval width decrease too, as we are less strict with the number of sample means that have to fall within that interval.

Then, when (1-α) decreases, the width of the confidence interval also decreases.

Answer: A. Decreased,

The mixed fraction of the given improper fraction is [tex]1\frac{2}{5}[/tex].

According to the question,

We have the following improper fraction:

7/5

Now, to convert this into mixed fraction we will divide the numerator by the denominator and add the quotient before the fraction and the remainder will form the numerator and the denominator will remain same as that of this improper fraction.

(More to know: there are three kinds of fraction: proper fraction (in proper fraction, we have denominator larger than numerator), improper fraction and mixed fraction.

So, we will divide 7 by 5:

[tex]1\frac{2}{5}[/tex]

Hence, the mixed fraction of 7/5 is [tex]1\frac{2}{5}[/tex].

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If a survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books. The  percent of the youths surveyed prefer reading electronic books is: 54%

Given data:

Youth book preference

Print = 34

Electronic = 40

Now let determine the percentage using this formula

Total = Print + Electronic book

Total = 34 +40

Total = 74

Now let determine the percentage of youth that preferred reading electronic book which  is calculated as :

Percentage = 40 / 74

Percentage = 0.54 × 100

Percentage = 54 %

Therefore we can conclude that 54% like to read electronic book.

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The side of the square of each block = 2 feet

Given,

Shelly sews a square blanket that has an area of 144 square feet.

and,  it has 36 square blocks, each the same size.

To find the approximate length of each side of a block

Now, According to the question:

36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks

= 144/ 36

= 4

The area of each square = 4 square feet

We know that

Area of square = side ^2

Side ^2 = 4

side = [tex]\sqrt{4}[/tex]

Side = 2

Hence, The side of the square of each block = 2 feet

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The coordinates of the point on the directed line segment are (-4, 4).

What is partitions of the segment?

Finding a position that is an equal distance from A and b equal distance from B is necessary for partitioning a line segment, AB, into a ratio of a/b.

Trying to find the coordinates of point that splits the line between (-7, -2) to (-2, 8) at a ratio of 3:2.

Since the ratio is 3:2 we are going o find the point that is 3/5 of the distance from (-7, -2) to (-2, 8).

For the x coordinate, find the distance between x coordinates (-2-(-7)) = 5.

Take 3/5 of 5 equals to 3 and add that to the first x coordinate (-7) to get the x - coordinate of interest -4.

For the y - coordinate, find the distance between y coordinates (8-(-2)) = 10.

Take 3/5 of 10 equals to 6 and add that to to the first y coordinate (-2) to get the y coordinate of interest 4.

The coordinates of the point on the directed line segment  from (-7, -2) to (-2, 8) that partitions the segment into a ratio of 3:2 are (-4, 4).

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Answer:

To create a perfect square of given expression,

On solving the above expression we get,

we have that,

To create a perfect square: add ( half the coefficient of the x- term )²

Coefficient of x term is 3

half the coefficient of the x- term is 1.5

( half the coefficient of the x- term )² is 2.25

Add 2.25 to the quadratic expression inside the bracket, we get,

In general, we adding 11.25 (that is, 2.25x5=11.25) to the given expression.

we get,

Multiply 5 to the above equation, we get

Based on the above calculation, we adding 11.25 and multiplying the expression by 5 in order to create a perfect square.

Adding 11.25 and multiplying the expression by 5 in order to create a perfect square.

Answer:

yes

Step-by-step explanation:

Answer:

1 and 3 makes linear pair

1 and 4 vertically opposite angle

1 and 5 are corresponding angle

1 and 8 alternate exterior angle

Answer:

12.5 hours

Step-by-step explanation:

The flat rate is the base, in which no matter how long you rent it for, they'll still charge you that much. You have 200 dollars, and negative 75 is 125 dollars, which you can spend on the hours. Assuming you can rent the jet ski for half an hour, you can divide 125 by 10 for the amount of hours, and the answer is 12.5 hours. However, if you can't rent the jet skis for half an hour, the answer is 12 hours.

Given the graph in the attached image.

The red line represents f(x) and the blue line represents g(x);

From the graph;

The intercept, b, of f(x) is

and the slope, m, of f(x) is;

So, f(x) is;

For g(x)

The y-intercept, b, of g(x) is;

and the slope, m, of g(x) is;

So, g(x) is;

To derive the solution, let us equate the two equations;

Answer:

x =(8-√204)/2=4-√ 51 = -3.141

x =(8+√204)/2=4+√ 51 = 11.141

Step-by-step explanation:

Factoring  x2-8x-35

The first term is,  x2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -35

Step-1 : Multiply the coefficient of the first term by the constant   1 • -35 = -35

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   -8 .

     -35    +    1    =    -34

     -7    +    5    =    -2

     -5    +    7    =    2

     -1    +    35    =    34

The remainder when  2 to the 100th power is divided by 5 is 8.

The remainder when 2 to the 100th power is divided by 5 is 8. We can achieve the accurate result by using the exponential formula where:

a^mn = a^m(n)

So, applying this here, we will have

2^10 (10)/5

Recall that multiplying 10 by 10 will give us 100. What was done in this case is simply splitting the figures up to make the division simpler. The exponential law was applied here.

Now, 2^10/5

204.8

The remainder as we can see from this result is 8. Thus we arrive at the answer 8.

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The approximate volume of the pyramid when it's 75% full is 303.75 inches³.

The volume of a square base pyramid can be represented as follows:

volume of the square base pyramid = 1 / 3 Bh

where

Therefore, the square bas pyramid has a base side of 9 inches and height of 15 inches. Let's find the volume when it's 75% full.

B = 9² = 81 inches²

h = 15 inches

Therefore,

volume of the square base pyramid = 1 / 3 × 81 × 15

volume of the square base pyramid = 81 × 5

volume of the square base pyramid = 405 inches³

Therefore, when it's 75% full

volume  = 75% of 405

volume = 75 / 100 × 405

volume = 30375 / 100

volume = 303.75 inches³

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First, let's edit the equation of the given line.

We were asked to identify three points. Let us give the value of [tex]x[/tex] as [tex]2,4[/tex] and [tex]6[/tex] respectively.

Why did we give consecutive even numbers? Because our unknown is preceded by an odd number. We applied this to find the integer in the rational expression.

Finally, you will mark the three points we found on the coordinate plane. In the photo below, I have marked them for you.

to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ 20 }{ 5 } \implies \text{\LARGE 4}[/tex]

The expression of the mathematical statement given as the difference of t and five multiplied by six is four is 6(t - 5)  = 4

From the question, the mathematical statement is given as

the difference of t and five multiplied by six is four

The difference of numbers means that we subtract the numbers

i.e. difference means subtraction

So, we have

the difference of t and five multiplied by six is four ⇒ (t - five) multiplied by six is four

The multiplication of numbers means that we take the product of the numbers

i.e. multiply means product

So, we have

the difference of t and five multiplied by six is four ⇒ (t - five) x six is four

Lastly, we have

(t - five) x six = four

Express as numbers

(t - 5) x 6 = 4

This becomes

6(t - 5)  = 4

Hence, the expression represented by the statement is 6(t - 5)  = 4

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The y-intercept of the line passes through (12,-4) and (-6,10) is 32/6

Let (x1, y1) = (12, -4)

and (x2, y2) = (-6, 10)

Using the formula of the two-point form of equation of line,

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

(y + 4)/(10 + 4) = (x - 12)/(-6 - 12)

(y + 4)/14 = (x - 12)/(-18)

-18y -72= 14x - 168

-18y = 14x - 168 + 72

-18y = 14x - 96

y = -(14/18)x + 96/18

y = -7/9 x + 32/6

Comparing with slope-intercept form of line y = mx + b

y-intercept(b) = 32/6

Therefore, the y-intercept of the line passes through (12,-4) and (-6,10) is 32/6

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