What is the simplest form of the expression 2x(x â’ 6) â’ 7x2 â’ (13x â’ 3)? A. 5x2 â’ 25x 3 B. -5x2 â’ 25x 3 C. -5x2 x 3 D. -5x2 â’ 25x â’ 3.

In the given function, the value of f(4) is 9

A function is a process or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

To find the value of f(4), we need to evaluate the function f(x) at x = 4. Let's substitute x = 4 into the appropriate piece of the function:

f(4) = x² - 7

f(4) = 4² - 7

f(4) = 16 - 7

f(4) = 9

Therefore, the value of f(4) is 9.

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Answer:

Volume = 261.8 cm³

Surface area = 254.2 cm²

Step-by-step explanation:

To calculate the volume of the cone, we have to use the following formula:

\(\boxed{V = \frac{1}{3} \pi r^2 h}\),

where:

V ⇒ volume

r ⇒ radius = 5 cm

h ⇒ height = 10 cm

Using the above formula and the provided measures, we get:

V = \(\frac{1}{3}\) × π × (5)² × 10

    = \(\frac{1}{3}\) × π × 25 × 10

      = 261.8 cm³

In order to calculate the surface area of the cone, we have to use the following formula:

\(\boxed{SA = \pi r^2 + \pi r l}\)

where:

SA ⇒ surface area

r ⇒ radius = 5 cm

l ⇒ slant length = \(\sqrt{r^2+h^2}\) = \(\sqrt{5^2+10^2}\) = 5√5 cm

Using the formula,

SA = π × (5)² + π × 5 × 5√5

     = π × 25 + π × 25√5

     = 254.2 cm²

Answer:

50+10x=140

so.......

week one 60$

week two 70$

week three 80$

week four 90$

week five 100$

week six 110$

week seven 120$

week eight 130$

week nine 140$

Step-by-step explanation:

so in nine weeks you will have enough money to buy the shoes

Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

The given categorical propositions and their forms are as follows:

(1) Some cats like turkey - Form: I:

Subject class: Cats,

Predicate class: Turkey

(2) There are burglars coming in the window - Form: E:

Subject class: Burglars,

Predicate class: Not coming in the window

(3) Everyone will be robbed - Form: A:

Subject class: Everyone,

Predicate class: Being robbed

In the first statement:

Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.

In the second statement:

There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.

In the third statement:

Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

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Answer:

12x=-1

Step-by-step explanation:

if q(x)=4, plug -4 because that equals -4.

-4=12x-3

add -3 to each side

-1=12x

In the equation 4y-12x=36 the solution of y is 9+3x

The given equation is 4y-12x=36

Four times of y minus twelve times of x equal to thirty six

We have to solve for y

Add 12x on both sides

4y=36+12x

Four times of y equal to thirty six plus twelve times of x

Divide both sides by four

y=36/4 +12x/4

y=9+3x

Hence, the solution of y is 9+3x in the equation 4y-12x=36

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Answer:

124

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180:

m<R + m<S + m<T = 180

11x + 3 + x + 15 + 2x + 8 = 180 add like terms

14x + 26 = 180 subtract 26 from both sides

14x = 154 divide both sides by 14

x = 11 to find m<R replace x with 11

11*11 + 3 = 124

Apply angle sum property

\(\\ \rm\rightarrowtail 11x+3+x+15+2x+8=180\)

\(\\ \rm\rightarrowtail 14x+26=180\)

\(\\ \rm\rightarrowtail 14x=154\)

\(\\ \rm\rightarrowtail x=11\)

a) The given relation is function.

b) The function is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he original amount of her loan is 6000.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, no two outputs have same input.

b) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                        = 18.5

So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.

c)  Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+  x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The modeled function. P(m) = 6000 - 300m.

so, the original amount of her loan is 6000.

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Answer:

Step-by-step explanation:

You want an inequality to determine how many miles eddie can travel if he has $15 to spend on a taxicab that charges $1.75 for the flat fee and $0.25 for each mile.

The mileage charge is the per-mile charge ($0.25) multiplied by the number of miles (m). It will be $0.25m.

The total charge is the mileage charge plus the flat fee. Eddie wants that to be no greater than $15.

  1.75 +0.25m ≤ 15

We can solve this inequality in 2 steps.

  0.25m = 13.25 . . . . . subtract 1.75

  m = 53 . . . . . . . . . . . divide by 0.25 (or multiply by 4)

Eddie can travel 53 miles if he has $15 to spend.

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hope this answer helps you dear....may u have a great day ahead!

Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer: Mean ≈ 105.81

Mode = No mode

Range = 87

Median = 104

Variance ≈ 924.35

Standard Deviation ≈ 30.40

Step-by-step explanation:

To find the mean, mode, range, median, variance, and standard deviation of the given data, let's calculate each one step by step:

Mean:

To find the mean, we sum up all the values and divide by the total number of values.

Mean = (153 + 104 + 118 + 166 + 89 + 104 + 100 + 79 + 93 + 96 + 116 + 94 + 140 + 84 + 81 + 86 + 108 + 111 + 87 + 126 + 101 + 111 + 122 + 108 + 126 + 93 + 108 + 87 + 103 + 95 + 129 + 93) / 31

Mean = 3,280 / 31

Mean ≈ 105.81

Mode:

The mode is the value(s) that appears most frequently in the data.

In this case, there is no value that appears more than once. Therefore, there is no mode.

Range:

The range is the difference between the maximum and minimum values in the data.

Range = Maximum value - Minimum value

Range = 166 - 79

Range = 87

Median:

To find the median, we arrange the data in ascending order and find the middle value.

Arranging the data in ascending order: 79, 81, 84, 86, 87, 87, 89, 93, 93, 94, 95, 96, 100, 101, 103, 104, 104, 108, 108, 111, 111, 116, 118, 122, 126, 126, 129, 140, 153, 166

Since the data set has 31 values, the median will be the 16th value.

Median = 104

Variance:

To find the variance, we need to calculate the squared difference between each data point and the mean, sum up those squared differences, and divide by the total number of values.

Variance = Σ((x - mean)²) / n

where Σ represents the sum, x represents each data point, mean is the mean value, and n is the total number of values.

Calculating the variance:

Variance = ((153 - 105.81)² + (104 - 105.81)² + ... + (93 - 105.81)²) / 31

Variance ≈ 924.35

Standard Deviation:

The standard deviation is the square root of the variance.

Standard Deviation ≈ √924.35

Standard Deviation ≈ 30.40

The value of x that satisfies the equation is determined as 16.

The value of x that satisfies the equation is calculated as follows;

The given equation is;

√ (4x) - 6 = 2

Simplify the equation by collecting similar terms as follows;

"6" "2" are similar terms, so we will add them together as follows;

√ (4x)  = 2 + 6

√ (4x) = 8

Square both sides of the equation as follows;

[ √ (4x)  ]² = 8²

4x = 64

Divide both sides of the equation and solve for x;

4x/4 = 64/4

x = 16

Thus, the solution of the equation is, x = 16.

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The complete question is bellow:

\(\sqrt{4x} - 6 = 2\). Find the value of x that satisfy the equation above.

Answer:

2x+4 is the correct answer

Answer:

0.5, 0.15, 0.115, 0.005

Step-by-step explanation:

A number can be written from the greatest to the and the lowest to the highest when given a series of number. This series of number can be in mixed fraction forms, improper fraction or decimal. When a number is said to be written from the greatest to the lowest, it is called descending order but from the lowest to the greatest it is called ascending order.

From the list of the series of the decimal numbers given, writing the numbers in order from the greatest to the least number will choose the form:

0.5, 0.15, 0.115, 0.005

Answer:

2 + y > 16

Step-by-step explanation:

the sum of 2 and y is greater than 16

                   2 + y           >                   16

2 + y > 16

The rule that can also model the function is f(x)= 4 + 3x.

The initial population of fruit flies = 4 and the population of fruit flies triple every week

Let x represent number of weeks

Therefore function can be modelled as:

f(x)= 4 + 3x

Now assume population grows for two weeks, using the function:

f(x)= 4 + 3x

f(2)= 4+3×2

f(2)= 10

Therefore population grows to 10 fruit flies in 2 weeks based on our function

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Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?

Angle UTV is given: 68°

Since the triangle is isoceles, the other two angles measure the same.

This way,

Thereby,

Notice that

Because UW is tangent to the circle

Therefore,

Answer:

Answer:

Represents a direct variation

Step-by-step explanation:

y = 2/7x

To find x-intercept/zero, substitute

y = 0

0 = 2/7x

Multiply both sides of the equation by 7/2

0 = x

Swap the sides of the equation

x = 0

Solution

x = 0

This is a direct variation because when x = 0. Y has to = 0 as well and it is so that makes this equation a direct variation.

direct variation - mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

Answer:

P(-5) = 109

Step-by-step explanation:

     If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).

   Dividend = divisor * quotient + remainder.

   p(x) = (x-a) * q(x) + p(a)

Here, q(x) is the quotient and p(a) is the remainder.

      P(x) = 4x² - x + 4

     P(-5) = 4*(-5)² - 1*(-5) + 4

              = 4*25 + 5 + 4

              = 100 + 5 + 4

              = 109

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

X = 2

Y=7

Step-by-step explanation:

The explanation is in the pictures

Answer:

x=2, y = 7.

As an ordered pair the solution is (2, 7).

Step-by-step explanation:

5x - 6y = -32

3x + 6y = 48​

Adding the 2 equations, we eliminate the terms in y:

8x +0 = 16

x = 16/8 = 2.

Now substitute x = 2 in the first equation:

5(2) - 6y = -32

10 + 32 = 6y

6y = 42

y = 7.

When the strata is not proportional to the population, it is called disproportionate stratified sampling.

The sampling method used in this case is a stratified sampling method. What is Stratified Sampling? Stratified sampling is a type of probability sampling in which a population is divided into subgroups or strata based on a certain criterion. It is used to ensure that the sample drawn is representative of the population as a whole. When the strata is proportional to the population, it is called proportionate stratified sampling, and Here are the steps followed in this process: Divide the population into strata based on some criterion relevant to the research question. Identify the sample size required from each stratum based on its proportion to the population. Draw a random sample from each stratum to arrive at the final sample.

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The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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The rate of change of the balance with respect to deposits is $100 per deposit

An equation is an expression that shows the relationship between numbers and variables.

The slope intercept form of linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants.

From the graph, using the points (0, 50) and (1, 150):

Slope = (150 - 50) / (1 - 0) = 100

The rate of change is 100

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Answer:

A = 4

B = 5

C = 9

ABC + ACB = CBA is then

459 + 495 = 954

Step-by-step explanation:

Working with

ABC + ACB = BCA,

There seems to be no feasible solution, but upon checking online, the correct question was obtained to be

ABC + ACB = CBA,

where A, B and C represent different digits

A B C +

A C B

C B A

So, for the units column

C + B = A

or

C + B = 10 + A

For the tens column

There are four possibilities

B + C = B

OR

1 + B + C = B

OR

B + C = 10 + B

OR

1 + B + C = 10 + B

Checking the equations one at a time

- If B + C = B, then C = 0

If C = 0, then units column equation 1, C + B = A, will not work because A, B, and C must stand for three different digits and B ≠ A.

If C = 0, then units column equation 2, C + B = 10 + A, will not work because B must stand for a single digit, B ≠ 10 + A

Therefore, tens column equation 1, B + C = B is not valid.

- If 1 + B + C = B, then C = -1

C must be a positive integer.

Therefore, tens column equation 2, 1 + B + C = B is not valid.

- If B + C = 10 + B

C cannot be equal to 10, as it is given that C is a single digit number.

Therefore, tens column equation 3, B + C = 10 + B, is not valid.

- If 1 + B + C = 10 + B

C = 9

Hence, this is the valid equation.

Our equation becomes

A B 9 +

A 9 B

9 B A

For the hundred's column, there is only one possibility.

Hundred's column equation 1:

since C is an odd number, the equation for the hundred's column is:

1 + A + A = C

1 + A + A = 9

therefore, A = 4

Our equation becomes

4 B 9 +

4 9 B

9 B 4

Solve for B using units column equation 2:

C + B = 10 + A

9 + B = 10 + 4

B = 5

Our final equation is then

4 5 9 +

4 9 5

9 5 4

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