Graph the linear equation.
4x+6y=-12

Answer:

Rose bought 14 packages of granola bars.

Step-by-step explanation:

Total bill = 1 bag of potatoes + x amount of packages of granola bars

Total bill = $74.25

1 bag of potatoes = $6.00

1 package of granola bar = 5.25

We set the equation to:

74.25 = 6.00 + 5.25x

Subtract 6.00 from both sides:

68.25 = 5.25x

Divide both sides by 5.25 to leave x by itself

68.25/5.25 = 5.25x/5.25

13 = x

This means Rose bought 13 packages of granola bars.

Let's recheck our work by inputting x = 13 into the equation:

74.25 = 6.00 + 5.25(13)

74.25 = 6.00 + 68.25

74.25 = 74.25

The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).

In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).

We must check if the proposition is true for every ordered pair. Let analyze each case:

Case I

[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]

Case II

[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]

Thus, the proposition is false.

To learn more on propositions: https://brainly.com/question/14789062

#SPJ1

The algebraic expression that is a polynomial is -6x³ + x² - √5

Polynomials are algebraic expressions that consist of variables and coefficients.

In a simpler term a polynomial can have constants, variables and exponents, but never division by a variable.

Therefore, the polynomial among the options is as follows:

-6x³ + x² - √5

learn more on polynomial here: https://brainly.com/question/12401404

#SPJ1

Answer:

2/11

Step-by-step explanation:

A reciprocal is a number or fraction flipped. So, 5 1/2=11/2. 11/2 flipped is 2/11.

Answer:

1) Radius of the cone = 9.5 cm

2) BA = 90.25 π cm²

3) SA = 384.7 π cm²

Step-by-step explanation:

1) Radius of the cone = 9.5 cm

2) Base Area of the cone =

BA = (π)(9.5)²

BA = 90.25 π cm²

3) Surface Area of Cone =

SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)

SA = 9.5π(9.5 + 31)

SA = 9.5π(40.5)

SA = 384.7 π cm²

Edge 2022

Pile Y has the greater mean number of pages per book because it is 5 books less than pile W.

From the complete information, we can deduce that the number of each pile of book is given as follows:

For pile W;

Red books = 10 × 5 = 50 red books.

Blue books = 5 × 5 = 25 blue books.

Therefore, total books in pile W = 50 + 25 = 75 books.

Mathematically, the mean for each pile can be calculated by using the following formula:

Mean = [F(x)]/n

Mean = 75/10

Mean = 7.5.

For pile Y;

Red books = 10 × 5 = 50 red books.

Mean = [F(x)]/n

Mean = 50/5

Mean = 10.

In conclusion, pile Y has the greater mean number of pages per book because it is 5 books less than pile W.

Read more on mean here: https://brainly.com/question/9550536

#SPJ1

Answer: -8

Step-by-step explanation:

[tex]\frac{5w+4}{3}=\frac{3w}{2}[/tex]

Cross-multiplying,

[tex]2(5w+4)=9w\\10w+8=9w\\w+8=0\\w=\boxed{-8}[/tex]

Answer:

square root = not polynomial

Answer:

alright well

from what I got x is 29.444 , y is 34 and angle b is 60 degrees

the correct answer is A.

Step-by-step explanation:

Answer:

hi,

Step-by-step explanation:

A consistent system of equations has at least one solution, and an inconsistent system has no solution.

Here the system has one solution.

Answer:

C

Step-by-step explanation:

Two negatives cancel out and turn into a positive.

In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8

So the answer is C

Answer:

1) 8

2) the median of the scores is 81

3) So, 8 students scored in the 70s, and the median score is 81

Step-by-step explanation:

1) the number of numbers listed is how many numbers there are

2) the median is the middle number! when you list all of the numbers, the one in the middle is the median!

let me know if any of this is confusing and i'll try to explain it further :)

Answer:

step 2: 8x-4=2(6+x+6)

Step-by-step explanation:

[tex]4(2x - 4) = 8 + 2x + 8 \\ 8x - 16 = 16 + 2x here \\ 8x - 2x = 16 + 16 \\ 6x = 32 \\ \frac{6x}{6} = \frac{32}{6} \\ x = 5[/tex]

Answer:

4(2x-4)=8+2x+8

8x-16=16+2x

8x-2x=16+16

6xboth sides over 6

x=5.3repiting

The statement which describes how the data should be plotted on a coordinate grid is: C. from the origin, go 9 units to the right and 12 units up.

A coordinate grid can be defined as a two-dimensional plane which comprises a horizontal line (x-axis) and a vertical line (y-axis) that are perpendicular to one another.

For this coordinate grid, the number of letters in the data for word 2 should be plotted on the x-axis and the percentage of students who spelled the word correctly on the y-axis.

Based on the table, the number of letters for word 2 is equal to 9 while the percentage of students who spelt it correctly is 12.

In conclusion, to plot the data on a coordinate grid, from the origin, go 9 units to the right and 12 units up.

Read more on coordinate grid here: https://brainly.com/question/22235711

#SPJ1

Complete Question:

The table of values below shows data for a five-word spelling test. Number of Letters vs. Percentage who Spelled Correctly Word Number of letters in the word Percentage of students who spelled the word correctly. Which describes how the data for word 2 should be plotted on a coordinate grid?

Step-by-step explanation:

x = number of small boxes

y = number of large boxes

these equations model the situation :

x + y = 8

12x + 45y = 195

FYI - the solution :

from the first equation we get

x = 8 - y

we use that in the second equation

12(8 - y) + 45y = 195

96 - 12y + 45y = 195

33y = 99

y = 3

x = 8 - y = 8 - 3 = 5

The thing that can be deduced from Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic.

It should be noted that elasticity of demand simply means the responsiveness to demand when there's a change in price.

Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic. This is when the percentage change in quantity demanded is infinite due to the price change.

Learn more about demand on:

brainly.com/question/1245771

#SPJ1

Answer:

a_n = n^2 − 1

Step-by-step explanation:

The numbers can be described as a polynomial with the following formula:

a1 = 1^2 − 1 = 1 - 1 = 0

a2 = 2^2 − 1 = 4 - 1 = 3

a3 = 3^2 − 1 = 9 - 1 = 8

a4 = 4^2 − 1 = 16 - 1 = 15

a5 = 5^2 − 1 = 25 - 1 = 24

Answer:

= -1.2 + 3.28d

Step-by-step explanation:

0.4 * -3 + 0.4 * 8.2d

= -1.2 + 3.28d

Answer:

Step-by-step explanation:

NOTE :

the sum of the 4 interior angles of a quadrilateral is 360°.

…………………………………………

Then

h + h + 2h + 2h = 360

Then

6h = 360

Then

h = 360 ÷ 6 = 60

Then

2h = 2 × 60 = 120

Answer:

XIV - VI = VIII

Step-by-step explanation:

14 - 6 = 8

Hope this helps

The solution of the inequality are (iii) and (iv)

The solution of the equality is x = 8.

The solution of the equality is x = 0.

The solutions of the inequalities can be found as follows:

x³ + 3(5 - 2) ≥ 20 - 4

x³+ 3(3) ≥ 16

x³+ 9 ≥ 16

x³ ≥ 16 - 9

x³ ≥  7

x ≥ ∛7

x ≥ 1.9

Therefore, (iii) and (iv) are solution.

4(72 - x²) = 3.12 - 4

288 - 4x² = 36  - 4

288 - 4x²= 32

-4x² = -256

x²=  256 / 4

x²=64

x= √64

x= 8

7(x + 12) = 7.12

7x + 84 = 84

7x= 84 - 84

7x= 0

x = 0

learn more on inequality here: https://brainly.com/question/20383699

#SPJ1

Answer:

all real numbers

Step-by-step explanation:

When you factor in the .2 on the left side you are left with 1.4 + .4t which is equal to the other side. And so, no matter what value for t you plug in, they will always be equal to eachother.

The perimeter and area of the square are 16√5 mm and 80 mm²

Perimeter of a square = 4L

where

Therefore,

Perimeter of a square = 4 × 4√5

Perimeter of a square = 16√5 mm

Area of a square = l²

Area of a square = (4√5)²

Area of a square = 16 × 5

Area of a square = 80 mm²

learn more on square here: https://brainly.com/question/14090908

#SPJ1

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

To learn more on quadratic functions: https://brainly.com/question/17177510

#SPJ1

The number of ways to check off one answer to each question is; 20ways.

The number of ways to check off one answer to each question and get it wrong is; 15ways.

a) Since each question has four possible answers, it therefore follows that the student can choose any of 4 options in each question and consequently, the number of different ways is; 4 × 5 = 20.

b) Since only one option is correct, it follows that there are 3 wrong choices in each question case and hence, the number of ways to pick one wrong answer is; 3 × 5 = 15.

Read more on combinations;

https://brainly.com/question/4658834

#SPJ1

Answer:

y,3y,4y,5y,6y,7y,8y,9y,10y ----------

Step-by-step explanation:

because if the variable is similar with y it is like term of 2y

Answer:

y,3y,4y,5y,6y,7y,8y,9y,10y ----------

Step-by-step explanation:

because if the variable is similar with y it is like term of 2y

A function assigns the values. The function of the given graph is y=3(4)ˣ, thus, the correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

If the parent function is y = 4ˣ, which is the function of the graph?

y = −2(4)ˣ

y = −3(4)ˣ

y = 3(4)ˣ

y = 2(4)ˣ

Since the graph intersect the y-axis at 3, and the parent function of the function is y=4ˣ, therefore, we can write,

y = A(4)ˣ

3 = A(4)⁰

3 = A × 1

A = 3

Hence, the function of the given graph is y=3(4)ˣ, thus, the correct option is C.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

The conclusions that can be drawn about f–1(x) are:

Given:

[tex]f(x) = \frac{-2}{3}x - 24[/tex]

[tex]f(x) + 24 = \frac{-2}{3}x[/tex]

To find x, we would multiply both sides by -2/3

= [tex]x= \frac{-3}{2} (f(x) + 24)[/tex]

[tex]f^-^1(x) = -\frac{3}{2} (0) - 36[/tex]

[tex]f^-^1(x) = -36[/tex]

Therefore, [tex]f^-^1(x)[/tex]  has an x-intercept of (-36, 0)

Furthermore, [tex]f^-^1(x)[/tex] has a range of all real numbers.

Read more about real numbers here:

https://brainly.com/question/17020343

#SPJ1