Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.

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:

(4x + 3)(2x + 5)

4x(2x + 5) +3(2x + 5)

8x^2 +20x +6x + 15

8x^2 +26x + 15

so, g(h(x))=8x^2 +26x +15

again

(4x + 3)(2x +5).0

0

so, g(h(0))=0

Answer:

3x2-11x-4

Step-by-step explanation:

The equivalent expressions when y = 2 and y = 5 are the expressions that have the same numeric value when y = 2 and when y = 5.

Equivalent expressions are expressions that have the same numeric value.

Hence, the equivalent expressions when y = 2 and y = 5 have the same value when y = 2 and y = 5.

This numeric value is calculated replacing each instance of y by 2 when y = 2 and each instance of y by 5 when y = 5.

For example:

Different numeric values, hence not equivalent, just an example as to how you should proceed.

You will do this for all expressions, and when you find equal values for y = 2 and for y = 5, then they will be equivalent.

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The probability that this person choosen only visited one of the two places is 9/20

What is Probability?

Probability is a measure of the possibility that an event to occur.

 The probability for an event to occur= Possible outcome /Total outcome

to get the possible out come we must Know the number of people that visited ET and NDC only.

using set theory;

if x is the no of people that visited both places then,

8-x =ET only

13-x= NDC only

5= none visited ET and NDC

x+13-x+8-x+5=20

collect like terms

26-x= 20

x =6

therefore ET only= 2

NDC only= 7

probability of ET = 2/20

probability of NDC= 7/20

therefore probability that the person chosen only visited one place = p(ET)+P(NDC)= 7/20+2/20

= 9/20

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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

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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Answer

The height of the child in a year time = 124.8 cm

Explanation

The child is currently 120 cm tall.

The child grows 4% bigger in 1 year.

We now need to calculate how tall the child is in that 1 year.

New height for the child = (Current height) + (Increase in height)

Current height = 120 cm

Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm

New height for the child = (Current height) + (Increase in height)

= 120 + 4.8

= 124.8 cm

Hope this Helps!!!

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.

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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Answer:

Please comment if it is wrong.

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: 3, 9, and 9

Step-by-step explanation:

X+3x+3x=217x=21x=33, 9, 9=21

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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Answer:

1.)|4x-2|=-6

This eguation has not solution.

Answer:

the first one; absolute value cannot be negative

Step-by-step explanation:

|4x-2| = -6

add 2

|4x| = -4

divide 4 on both sides

x = -1

|4x-2| = 6

repeat the same steps

x = 2

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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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

The slope of the line that is perpendicular 6y=−7x+4 is: 6/7.

If one line has a slope of a/b, the slope of the line that is perpendicular to the line would be the negative reciprocal of a/b, which is -b/a.

If the slopes of perpendicular lines are multiplied together, for example (a/b)(-b/a), we would always have a result of -1.

Rewrite the equation 6y = −7x + 4 in slope-intercept form as y = mx + b, in other to determine the value of m = slope.

6y/6 = −7x/6 + 4/6

y = −7/6x + 2/3

The slope of 6y = −7x + 4 is -7/6. 6/7 is the negative reciprocal of -7/6. Therefore, the slope of the perpendicular line is: 6/7.

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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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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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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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Answer: (5x - 1)(x + 9)

Step-by-step explanation:

    Please note the method of factoring may differ per class, but this is how I was taught.

    First, we will multiply the coefficient of x² by the constant.

5 * -9 = -45

   Next, we will find two numbers that add up to 44 (coefficient of x) and multiply to -45 (the number we got above).

-1 * 45 = 45

-1 + 45 = 44

       -1 and 45 ✓

   Now, we can start to factor. First, we will rewrite 44x.

5x² + 45x - 1x - 9

   Then, we will factor by grouping.

5x(x + 9) -1(x + 9) ➜ (5x - 1)(x + 9)

      The completely factored form is:

                    (5x - 1)(x + 9)

Answer: I don't know why I'm here

Step-by-step explanation: help

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.

Answer:

x = -2

Step-by-step explanation:

If m(x) = 4x + 15 and m(x) = 7, the we can substitute and get the equation:

4x + 15 = 7

x = -2

Answer :- 60 cm^2

Step-by-Step Solution :-

Let ABCD be the Rectangle.

Given :

AD = 12 cm

BD = 13 cm

To Find : Area of ABCD

Solution :

In ∆ADB,

AD = 12 cm and BD = 13 cm

By Pythagoras Theorem,

(BD)^2 = (AD)^2 + (AB)^2

13^2 = 12^2 + (AB)^2

169 = 144 + (AB)^2

AB^2 = 169 - 144 = 25

AB = √25

Therefore, AB = 5 cm

Now, to find the Area,

Area of Rectangle = length × breadth

Area of ABCD = 12 × 5

Therefore, Area of ABCD = 60 cm^2

After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

As given in the question,

Given expression is equal to :

-4r -2r + 5

Now combine the like terms to get the equivalent expression we have,

Like terms of the given expression -4r -2r + 5 are -4r and -2r

( -4r -2r) +5

= -r (4+2) +5

= -6r +5

Equivalent expression of the given expression -4r -2r + 5  is -6r +5.

Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

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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