Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks,
costing a total of $97.50. Jacob went into the same movie theater and bought
5 bags of popcorn and 4 drinks, costing a total of $51.50. Determine the price
of each bag of popcorn and the price of each drink.
Each bag of popcorn costs $
and each drink costs $

Answer:

Solutions below.

Step-by-step explanation:

This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.

To find the x-intercept, we know that y = 0.

Therefore we can substitute y = 0 into the line equation:

[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]

Therefore the point of the x-intercept is (8,0).

Likewise to find the y-intercept, we know x = 0.

Therefore we can substitute x = 0 into the line equation:

[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]

Therefore the point of the y-intercept is (0,2).

Answer:

x-intercept:  (8, 0)

y-intercept:  (0, 2)

Step-by-step explanation:

Given equation:

[tex]y=-\dfrac{1}{4}x+2[/tex]

The graph intersects the y-axis when x = 0.  

To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:

[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the y-axis are:

The graph intersects the x-axis when y = 0.  

To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:

[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]

Therefore, the coordinates of the point of intersection with the x-axis are:

Step-by-step explanation:

a)

(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)

[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]

[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]

[tex] = \frac{ - 5175}{58}[/tex]

4x^2 - 7 + 1/(2x + 3 - 7x - 11)

[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]

[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]

[tex] = \sf \frac{22793}{58}[/tex]

Since we have that y = 10, then:

Then

In the first part, we need to sum 15 to both sides of the equation.

In the second part, we divide both sides by 5.

Then, x = 19.

Answer:

[tex]f(x) = - 2x - 1 \\ h(x) = - x + 5 \\ \\ The \: \: value \: \: of \: \: \: f(6) = ( - 2) \times 6 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ as \: we \: know ,\: \\➪(hf)(x) = h(f(x)) \\ so \:➪( hf)(6) = h(f(6)) \\ \\ put \: the \: value \: \: of \: f(6) \: we \: \: get \\ \\➪ (hf)(6) \: = h( - 13) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - ( - 13) + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13 + 5 \\ \: \: \: \: \: \: \: = 18[/tex]

Given:

Ethan is 23 years older than Evan

So, let Ethan is (x) years old

And Evan is (y) years old

So, the difference between them is 23 years old

so, x - y = 23

And the sum of Ethan and Evan's age is 43

so, x + y = 43

So, we have the following system of equations:

add the equations to eliminate (y):

Now, substitute with (x) into the second equation to find (y):

So, the answer will be:

Ethan's age = x = 33

Evan's age = y = 10

The values of x and y are 26° and 54° respectively.

Consider the triangle with x is triangle 1

Triangle with y is triangle 2

In triangle 1

Since it is a right angled triangle one angle is already known

Another angle is 64°

We know the sum of interior angles of a triangle is equal to 180

Hence 90 + 64 +x = 180°

154 + x = 180°

x= 180 - 154

x = 26°

From triangle 2 it is evident that x and y are complementary angles which means they sum up to 90°

Hence  x + y = 90°

26 + y = 90

y = 90 - 26

y = 54°

Hence the value of x and y are 26° and 54° respectively

Learn more about Triangles at

https://brainly.com/question/2773823?referrer=searchResults

#SPJ1

The apple that costs the least per pound is Apple B.

The cost per pound for each apple will be calculated as:

= Cost / Weight

Apple A:

= Cost / Weight

= 4.90 / 4

= $1.25 per pound

Apple B:

= Cost / Weight

= $1 / 10

= $0.1 per pound

Apple C:

Cost / Weight

= $0.45 / 0.5

= $0.9 per pound

Therefore, apple B is the cheapest

Learn more about cost on:

brainly.com/question/25109150

#SPJ1

Multiplication:

Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?

--> 3 * 3 = 9 carts in total

Division:

Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.

--> 9 / 3 = 3 carts per person

what the??????????????

2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.

Given the expression in the question;

( 2a² + 7a - 10 )( a - 5 )

To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.

( 2a² + 7a - 10 )( a - 5 )

a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )

a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 2a²

2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 7a

2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10

Multiply a and -10

2a³ + 7a² - 10a -5×2a² -5×7a -5×-10

Multiply -5 and 2a²

2a³ + 7a² - 10a - 10a² -5×7a -5×-10

Multiply -5 and 7a

2a³ + 7a² - 10a - 10a² - 35a -5×-10

Multiply -5 and -10

2a³ + 7a² - 10a - 10a² - 35a + 50

Collect and add like terms

2a³ + 7a² - 10a² - 10a  - 35a + 50

2a³ - 3a² - 45a + 50

Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.

Learn more about FOIL Method here: https://brainly.com/question/2092062

#SPJ1

We have to do a diagram with the following characteristics.

• VX has to intersect UW at V.

• VX is perpendicular to UW.

• U, V, and W are collinear.

Based on the given information, we have the following diagram

The image above shows the answer.

To determine the arc length of the shaded area you have to use the following formula:

"θ" represents the measure of the central angle, in degrees

"r" represents the radius of the circle

We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º

The radius of the circle is r=15cm

The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

From the table given, we have

The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.

The avergae daily balance was

=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]

= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]

=[tex]\frac{48550}{31}[/tex]

=1566.13

So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

To learn more about average visit :

brainly.com/question/24057012

#SPJ9

Out of $205000, the total commission earned by the agent will be $12300.

A commission is a fee paid to a salesperson in exchange for services in facilitating or completing a sale transaction. Mathematically -

Commission [C] = Sales revenue [R] x commission rate [rc]

Given is an agent who lists a sellers house for 6% commission. The final agreed sales price is $205,000.

The total sales price = [P] = $205000

The commission on house = [C] = 6%

Now, the money agent gets as a commission will be = [M] -

[M] = 6% of 205000

[M] = (6/100) x 205000

[M] = 6 x 2050

[M] = 12300

Therefore, out of $205000, the total commission of the agent will be $12300.

To solve more questions on percentage, visit the link below-

https://brainly.com/question/12220476

#SPJ1

Reflection:

A reflection is a transformation that flips a figure across a line.

Properties of reflection:

• The length remains the same, the angles remain the same.

• This means that the image and the pre-image have the same size and shape only the orientation changes.

• The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.

• The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.

Following is an example of a reflection

This is called a horizontal reflection since the image and the pre-image is flipped across the x-axis. The line of reflection is the vertical line.

Answer:

3 1/13

Step-by-step explanation:

rate(time) of one pipe + rate(time) of the other pipe = 1 job

The rate would be the the number of jobs over the time

The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.

Together:

1/5t + 1/8t = I job

t(1/5 + 1/8) = 1

t(8/40 + 5/40) = 1

t(13/40) = 1  multiply each side by 40/13

t(40/13)(13/40) = 1(40/13)

t = 40/13

t = 3 1/13

Solve the system using substitutions:

x has a value of 1. Use this value to find the value of y.

y has a value of 1.

x=1

y=1

The smallest whole number is 750,000, while the largest whole number is 849,999.

Consider the facts offered.

We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000

Rounding a numerical rule

If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.

If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.

Consider the number 800,000 for a moment.

Because we want the smallest number possible, the number at the hundred thousand place should be 7.

As a result, the smallest whole number is 750,000.

We now want the largest whole number that rounds to 800,000

Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.

As a result, the biggest whole number is 849,999.

Learn more about rounding at

https://brainly.com/question/683956

#SPJ1

To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:

We used the distributive property for -5 (1 + 5).

Then, we have:

Adding like terms:

In summary, therefore, the equivalent expression is:

The value of the function f(7/3)-h(-2) is 30

Functions are simply defined as theorems, laws, equation or rules that holds true for the relationship between two variables in a given expression.

The variables are known as;

Given the functions as;

To determine f(73), substitute the value as x in the function, we have;

f(7/3) = 3(7/3) - 1

expand the bracket

f(7/3) = 7 -1

f(7/3) = 6

For h(-2), substitute the value as x in the function, we have;

h(-2) = -2(-2)² + 3(-2) - 9

expand the bracket

h(-2) = -8 -6 - 9

Subtract the values

h(-2) = -23

Now, f(7/3)-h(-2) = 7 --23

f(7/3)-h(-2) = 30

Hence, the value is 30

Learn more about functions here:

https://brainly.com/question/2328150

#SPJ1

To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.

Let's start with Point A.

The post image coordinate of A is at (-4, 8).

Moving on to Point B.

The post image coordinate of B is at (-10, 0).

Lastly to Point C.

The post image coordinate of C is at (-12, 12).

The total cost with taxes included is given by

which is equal to

which gives

then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36

The solutions to the quadratic trigonometric equation are given as follows:

x = kπ, k = ± 1, ± 3, ± 5, ± 7.

The quadratic trigonometric equation is defined as follows:

cos²(x) + cos(x) = 4cos(x) + 4.

Then the following transformation is applied to solve the equation:

y = cos(x).

Hence:

y² + y = 4y + 4

y² - 3y - 4 = 0

(y - 4)(y + 1) = 0.

Applying the Factor Theorem, the solutions are given as follows:

However, we want the solutions for x, hence they are obtained as follows:

cos(x) = 4.

x = arccos(4), which has no solution, as there are no angles with a cosine of four.

cos(x) = -1.

x = arccos(-1)

x = kπ, k = ± 1, ± 3, ± 5, ± 7

More can be learned about quadratic equations at https://brainly.com/question/24737967

#SPJ1

A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.

To know more about quadrilateral refer to https://brainly.com/question/23935806

#SPJ9

At an animal shelter, 3/8 of the animals are dogs, of the dogs, 2/5 have spots, 3/20 portion of the animals at shelter are dogs that have spots. A fraction, which derives from Latin word fractus, which means "broken," is a portion of whole or, more broadly, any number of equal pieces.

A fraction, which derives from Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) line on which the numerator is shown. Compound fractions, complicated fractions, and mixed numeral fractions are the examples of uncommon fractions that use numerators and denominators.

The numerator and the denominator of positive common fractions are both natural integers. The denominator shows how many of numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, denominator cannot be zero. For instance, numerator 3 in the fraction 3/4 denotes that the fraction is made up of 3 equal parts, while denominator 4 denotes that the fraction is made up of 4 parts altogether.

Let, [tex]\frac{3}{8} x[/tex] animals are dogs,

[tex]\frac{2}{5} * \frac{3}{8}x = \frac{3}{20}x[/tex]

Therefore, [tex]\frac{3}{20}[/tex] of the animals at shelter are dogs that have spots.

To know more about fraction visit: https://brainly.com/question/10354322

#SPJ9

(a) Option B, 30

(b) 60, Option A

We need to find the average termperature change per hour during January 2008.

We have the information that Minnesota fell from 41 degrees to -13 degrees over 24 hours.

Then, 41 degrees to -13 degrees, there is a difference of 41+13 = 54 degrees over 24 hours.

If the difference is over 24 hours, then:

54 degrees / 24 hours =2.25 F is the rate of change.

However, the termperature is decreasing, so the rate of change must be negative.

Hence, the rate of change = -2.25 F.

The correct answer is the third option.