Given f(x) = 2x^2 - 3x -12, find f(7).

For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1             2

Cost in dollars      :    $11.50      $23

As given in the question,

Given equation to represents the total cost to watch a movie related to number of tickets of movie.

c = 11.5t

Where t is the number of tickets to watch movie and c is the total cost to watch movie.

Table which represents the given situation is given by:

Option A:

Number of tickets cannot be in decimals that is 0.09 and 0.17.

Incorrect.

Option B.

Number of ticket  = 1

cost 'c' = 11.5(1)

          = $11.5

when t = 2

c = 11.5(2)

  = $23

Correct.

Option C:

Number of tickets cannot be in decimals that is 11.5.

Option D:

when t = 1

c = $0.09 is incorrect.

Therefore, For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1               2

Cost in dollars      :    $11.50      $23

Learn more about equation here

brainly.com/question/10413253

#SPJ1

The simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

The expression is given in the question

4(3x + 2) −2

Apply the distributive property of multiplication,

4×3x + 4 × 2 −2

12x + 8 - 2

Apply subtraction operation,

12x + 6

The expression is given in the question

20b − 16

To determine the factor of the expression

20b − 16

5 × 4 × b - 4 × 4

Factor out 4 in the above expression

4 (5b - 4)

Thus, the simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

The number of terms in the arithmetic sequence {-8, 1, 10, 19, 28, ..., 469} is 54 terms

The number of terms in the sequence { -8, 1, 10, 19, 28, ..., 469 } is calculated from the formula

Un = a1 + (n - 1) d

where a1 = first term

d = common difference

n = number of terms

a = -8

d = second term -  first term

= 1 - -8

= 9

solving for n

Un = a1 + (n - 1) d

469 = -8 + (n - 1)9

469 + 8 = (n - 1)9

collecting like terms

(n - 1) = 477 / 9

n - 1 = 53

n = 54

Learn more about arithmetic sequence:

https://brainly.com/question/28354530

#SPJ1

The double angle results are;

sin 2x = 62/64

cos 2x = 14/64

tan 2x = 384/83

We can see that it is possible for an angle to be given in the double angle format and we need to obtain the angles from it.

We know that sin x = 5/8

Using the Pythagoras theorem;

c^2 = a^2 + b^2

c = 8

a= 5

b= √c^2 - a^2

b = √ 8^2 - 5^2

b = √ 64 -25

b= 6.2

cos x = 6.2/8

Tan x = 5/6.2

Then;

sin2x = 2 sinxcosx

sin 2x = 2(5/8 × 6.2/8)

sin2x = 2(31/64)

sin2x = 62/64

cos 2x = 1 - 2sin^2x

cos 2x = 1 - 2(5/8)^2

cos 2x = 1 - 2(25/64)

cos 2x = 1 - 50/64

cos 2x = 14/64

Tan 2x = 2tan x/1 - tan^2 x

tan 2x = 2 (5/6.2)/1 - (5/6.2)^2

tan 2x = 10/6.2/1 - 25/38.4

tan2x = 10/6.2/13.4/38.4

tan2x = 10/6.2 * 38.4/13.4

tan 2x = 384/83

Learn more about double angle:https://brainly.com/question/19143742

#SPJ1

Answer:

y = 4/3 x + 4/3

Step-by-step explanation:

y - (-4) = 4/3(x-(-4)

y+4 = 4/3 (x +4)

y + 4 = 4/3 x + 16/3

y = 4/3 x +16/3 -4

y = 4/3 x + (16- 12)/3

y = 4/3 x + 4/3

y = 4/3 x + 4/3

Answer:

y=4/3x+4/3

Step-by-step explanation:

-4=4/3(-4)+9

-4=-16/3+9

-4=-5 1/3+9

-4= 4 1/3

4+4 1/3=8 1/3

9-8 1/3=2/3

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

-4=-16/3+2/3

-4=-14/3

-4=-4 2/3

2/3+2/3=4/3

-4=4/3(-4)+4/3

-4=-16/3+4/3

-4=-12/3

-4=-4

The shape of units you would get that has a perimeter of 22 and an area of 30 is a rectangle, which is shown in the image below.

A rectangle is a quadrilateral that has two opposite sides that are equal and are longer than the other two opposite sides that are equal and parallel to each other.

Assuming that the shape being referred to is a rectangle that has an area of 30 units² and a perimeter of 22 units, therefore, the dimensions of the rectangle is shown in the image attached below, and they are:

Length of rectangle = 6 units

Width of rectangle = 5 units

Therefore:

Area of the rectangle = 6 × 5 = 30 units².

Perimeter of the rectangle = 2(6 + 5) = 2(11) = 22 units.

This implies that the shape of units with an area of 30 units² and a perimeter of 22 units is most likely a rectangle.

Learn more about rectangle on:

https://brainly.com/question/25292087

#SPJ1

There are numerous reasons to use number lines to teach positive and negative numbers. But the following which is not used number line is B) Number lines match several familiar situations, like altitude, temperature, and football.

What is number line?

   A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6). Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers on the left are smaller than the integers on the right. For instance, 0 is lower than 1 and -1

Here the reasons we use number line for to teach positive and negative numbers is ,

=> Children are taught the fundamentals of addition and subtraction in mathematics using number lines with negative and positive numbers. It can also be used to multiply by skipping counts. The use of positive or negative signs makes it challenging to solve equations involving negative integers on a number line.

=> Number lines can be utilised in a variety of various ways, despite the fact that it may seem like addition, subtraction, and multiplication principles are best taught to children using number lines. The negative number line and positive number line are used by people to compute and measure specifics. These lines display the values' substantial increases and decreases.

Therefore the correct option is B)Number lines match several familiar situations, like altitude, temperature, and football.

To learn more about number line refer the below link

https://brainly.com/question/24644930

#SPJ9

By using natural logarithm properties we will see that the solutions of the two equations are:

17) x = 3.11

19) p = 2.02

Here we will use the property of natural logarithms:

Ln( a^x) = x*ln(a)

17) We have the exponential equation:

5^(x - 2) = 6

If we apply the natural logarithm in both sides, we will get:

ln( 5^(x - 2)) = ln(6)

(x - 2)*ln(5) = ln(6)

(x - 2) = ln(6)/ln(5)

x = ln(6)/ln(5) + 2

x = 3.11

19) Now the exponential equation is:

7^p = 51

We will do the exact same thing, apply the natural logarithm in both sides:

ln(7^p) = ln(51)

p*ln(7) = ln(51)

p = ln(51)/ln(7) = 2.02

Learn more about exponential equations:

https://brainly.com/question/11832081

#SPJ1

The amount of calling for which the two plans cost the same will be 525 minutes.

The cost when two plans cost the same amount is $68.25.

Answer:

C

Step-by-step explanation:

to find the unit rate divide miles travelled by petrol used , that is

60 [tex]\frac{2}{3}[/tex] ÷ 4 [tex]\frac{2}{3}[/tex] ← change mixed numbers to improper fractions

= [tex]\frac{182}{3}[/tex] ÷ [tex]\frac{14}{3}[/tex]

• leave first fraction, change ÷ to × , turn second fraction ' upside down'

= [tex]\frac{182}{3}[/tex] × [tex]\frac{3}{14}[/tex] ( cancel 3 on numerator/ denominator )

= 182 × [tex]\frac{1}{14}[/tex]

= [tex]\frac{182}{14}[/tex]

= 13

the car travels 13 miles per gallon of petrol

Answer:

64 marbles

Step-by-step explanation:

hope it helped :)

The answer is,

Yes, the residual plot lacks a recognizable pattern.

So, the correct option is c

A simple random sample, in which each participant has an equal chance of being chosen, chooses a small, random portion of the whole population to represent the entire data set.

Researchers may produce an uncomplicated random sample by using methods like lotteries or random draws.

A sampling error may have occurred if the sample does not accurately reflect the population it is supposed to represent.

By selecting values at random from a population and giving each item a series of values, simple random samples are produced.

Simple random sampling is a sample design option to systematic, stratified, or cluster sampling.

To know more about simple random sampling, visit:

https://brainly.com/question/13219833

#SPJ13

The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

Two or more expressions with an equal sign are defined as an equation.

The given equation is Three-fifths(30x -  15) = 72.

Simplify the equation as follows:
Three-fifths(30x -  15) = 72

3/5(30x - 15) = 72

18x - 9 = 72

Which is equivalent to "18x minus 9 = 72".

Solve for the  value of x:

18x -9 = 72

18x = 72 + 9

18x = 81

x = 81/18

x = 27/6

x = 4.5

Now, solve the equation in the first option:

18x - 15 = 72

18x = 87

x = 4.83

Solve the equation in the second option:

50x - 25 = 72

50x = 97

x = 1.94

The third equation is already shown to be equivalent to the given equation.

The solution to the fourth equation is:

3(6x - 3) = 72

18x -9 =72

Which is the same as the given equation.

The last equation is x = 4.5

Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

Learn more about equations here:

https://brainly.com/question/10413253

#SPJ1

Answer:

it can be 100 because percentages are out of 100

The number of hours at which both companies' rental costs will be the same is nearly 6 hours.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions displayed on the left and right sides have an equal connection. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Let the number of hours = h The deposit price at the first canoe rental company = $10

Cost per hour to rent a canoe = $8.25/h

The total cost for rental for the first company is given by

C(A) = 10 + 8.25h

The deposit price at the second canoe rental company = $12.50

Cost per hour to rent a canoe = $7.85/h

The total cost for rental for the second company is given by

C(B) = 12.50 + 7.85h

The number of hours at which both company's rental costs will be the same is given as

C(A) = C(B)

10 + 8.25h = 12.50 + 7.85h

8.25h - 7.85h = 12.50 - 10

0.4h = 2.5

h = 2.5/0.4

h = 6.25

h ≈ 6 hours

To know more about equations, visit:

https://brainly.com/question/1529522

#SPJ13

The correct option is C.

The statement best describes the solution set to the inequality as the solution set includes all values of x greater than -8 and less than 9.

Inequality: An inequality is an expression that shows an unequal comparison of two or more numbers and variables.

Given that:

Inequality

0 < 8 + x < 17

Adding on both sides by -8.

=> 0 - 8 < 8 + x - 8 < 17 - 8

=> -8 < x < 9

The solution set is (-8,9).

Therefore, the solution set includes the value of x greater than -8 and less than 9.

Hence, the correct statement that best describes the solution is option C.

To learn more about inequality visit: brainly.com/question/24210947

#SPJ1

Answer:

15 eggs

5 bananas

Step-by-step explanation:

6/4=x/10

6(10)=4x

60=4x

/4.  /4

15=x

We need 15 eggs

2/4=x/10

2(10)=4x

20=4x

5=x

We need 5 bananas

Or

6/4=1 1/2

Now we make 1 and 1/2 have a denominator of 10

1 5/10=15/10

Meaning 15 eggs

2/4=1/2=5/10

Meaning 5 bananas

Hopes this helps please mark brainliest

Answer:you would need 15 eggs and 5 bananas for 10 people

Step-by-step explanation:multiply the 6 eggs and 2 bannanas by 2 then add half more of each

sorry if this confuses you im not a good explainer

The value of ab=6.

What is [tex](a-b)^2[/tex] formula ?

    To find the square of a binomial, use the [tex](a-b)^2[/tex] formula. One of the most common algebraic identities is the a minus b Whole Square Formula. This formula is also known as the difference between two terms squared formula. To factorise some special types of trinomials, the [tex](a-b)^2[/tex] formula is used.

Here [tex](a-b)^2 = a^2+b^2-2ab[/tex] then,

=> [tex](a-b)^2 = a^2+b^2-2ab[/tex]

Here a-b=5 and [tex]a^2+b^2[/tex] = 37.

=> [tex]5^2[/tex] = 37-2ab

=> 25 = 37-2ab

=> 2ab=37-25

=> 2ab = 12

=> ab=6.

Hence the value of ab=6.

To learn more about    [tex](a-b)^2[/tex] formula

https://brainly.com/question/28658646

#SPJ13

Answer:

the answer is 100...........

y=−1/2x+1/2

Step-by-step explanation:

Answer: x=16

Step-by-step explanation:

log₇(3x²+x)-log₇x=2

Domian:

1)

3x²+x>0

x(3x+1)>0

-∞__+__-1/3__-__0__+__∞

x∈(-∞,-1/3)U(0,∞)

2)

x>0

Hence, x∈(0,∞)

Thus x∈(0,∞)

In this problem we use the following formula:

                       [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}[/tex]

[tex]\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\Hence,\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\ Divide\ both\ parts \ of\ the \ equation\ by\ 3:\\\\x=16[/tex]

The extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2 is x= 4.

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

We have Logarithmic expression as

log7 (3x³ + x)-log7(x)=2

we know, [tex]log_ax - log_a y= log_a (x/y)[/tex]

Using the above property as

log7 (3x³ + x)-log7(x)=2

[tex]log_7[/tex] (3x³ + x) - [tex]log_7[/tex] x =2

[tex]log_7[/tex] x(3x² +1) / x = 2

[tex]log_7[/tex] (3x²+1) = 2(1)

[tex]log_7[/tex] (3x²+1) = 2(1)[tex]log_7 (7)[/tex]

[tex]log_7[/tex] (3x²+1) = [tex]log_7[/tex]7²

Now, comparing we get

3x² +1 = 7²

3x² = 48

x² = 16

x = 4

Learn more about Logarithm here:

https://brainly.com/question/30085872

#SPJ5

Answer:

[tex] \huge{ \bold{y = - 2x - 5}}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is represented by

y = mx + c

where

m is the slope

c is the y-intercept

First of all we have to find the slope from the two points given by using the formula

[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question the points are (-3,1) and (4, -13)

We have

[tex]m = \frac{ - 13 - 1}{4 - - 3} = \frac{ - 13 - 1}{4 + 3} = - \frac{14}{7} = - 2 \\ [/tex]

Next we find the y-intercept 'c' by placing one of the points and the slope into the slope-intercept form equation

Using point (-3,1) and m = -2

We have

[tex]1 = ( - 2)( - 3) + c \\ 1 = 6 +c \\ c = 1 - 6 = - 5[/tex]

Since we have both m and c we can place it into the main equation to find the equation

Using point and m = -2 c= -5

We have the final answer as

[tex] \bold{y = - 2x - 5}[/tex]

Hope this helps you

Answer:

x = 78

Step-by-step explanation:

[tex]\frac{8}{24} =\frac{26}{x}[/tex]

==> cross multiply

26 x 24 = 8 x "x"

==> simplify

624 = 8x

==> divide both sides by 8

78 = x

Answer: x = 78

Step-by-step explanation:

It is 78 because if you cross-multiply, you get 624 = 8x. Then if you divide by 8 on both sides, you get x = 78.

The equation 36-7p=-7p-35 has no solution.

What is equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

Here the given equation is

=> 36-7p=-7p-35

=>-7p+7p=-35-36

=>0=71

Then the statement is false for any value of p.

Hence the given equation has no solution.

To learn more about equation refer the below link

https://brainly.com/question/18831322

#SPJ9

Answer:

5n + 12p + 12m

Step-by-step explanation:

Perimeter means you are adding up all three sides.

4m + 3n + 8m + 10p + 2p + 2n

= 2n+3n + 10p+2p + 4m+8m

Combine like terms.

= 5n + 12p + 12m

In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

coordinate geometry:

It establishes a connection between geometry and algebra using curves and line graphs.

A point's x and y coordinates are also referred to as abscissa and ordinate, respectively.

the abscissa is the x–coordinate of any point A(x, y).

so,

abscissa of the point ( 8,7 ) is 8.

In coordinate system, the number that is the abscissa of the point ( 8,7 ) is 8.

To know more about abscissa

https://brainly.com/question/1214621

#SPJ1

The minimum number of nickels that Jaxson could have is 9.

Given that, Jaxson has some pennies and some nickels.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of pennies be P and the number of nickels be N.

So, P + N > 13

Therefore

P×0.01 + N×0.05 ≥ 0.33

Because he has at most, $0.33

If  P = 4

4×0.01 + N0.05 ≥ 0.33

∵ $0.33 - $0.04 = $0.29

N×0.05≥ 0.29

N = 0.29/0.05 = 5.8

The number of nickels that he might have is 9.6, but because he cannot have 0.6 of a nickel, we have to round the figure down to 9.

Now that we also know that he had at least 15 coins in total, we can use that equation to get the smallest possible number for N.

4 +  N  > 13

N > 13 - 4

N> 9

So we have the range:

9 < N ≤ 5.8

Therefore, the minimum number of nickels that Jaxson could have is 9.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

The function F(x) = -3x² + 18x + 3 has a maximum value of 30 at x = 3

From the question, we have the following equation that can be used in our computation:

F(x) = -3x² + 18x + 3

A quadratic function is represented as

F(x) = ax² + bx + 3

By comparison, we have

a = -3

For a quadratic function to have a maximum value, the value of a must be less than 0

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

Read more about quadratic functions at

brainly.com/question/1214333

#SPJ1