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3 years ago

Joe and Brody order some food for their families. Joe orders 2 chicken dinners and 3 sides for $34.50. Brody

Mathematics

1 answer:

Lerok [7]3 years ago

8 0

Answer: D

Step-by-step explanation:

If Joe orders 2 chicken dinners and 3 sides for $34.50, then you have to multiply 3.50 by 3 to get the ammount that the dinners cost.

3.50x3 = 10.50

Next, you have to subtract 10.50 from 34.50 to get the cost of just the 2 dinners.

34.50 - 10.50 = 24.00

Now, divide 24 by 2 to get the cost for 1 dinner.

24/2 = 12

Since Brody ordered 2 sides, you have to subtract 3.50x2 = 7 from 43 to get the total of his dinners.

43 - 7 = 36.

Now we can check our answer. Since 1 dinner costs $12, we can multiply 12 by 3 to get 36, which is the exact same number as the one we just figured out. So, each side costs 3.50.

(You can also multiply 12 by 3.50 to get 43, which was the total cost of Brody's order.)

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What is the y intercept of y=60(1+0.04)x^

Kobotan [32]

60(1+.04)x^2 goes through the origin

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3 years ago

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.

PolarNik [594]

Answer:

one point

Step-by-step explanation:

A system of two linear equations will have one point in the solution set if the slopes of the lines are different.

When the equations are written in the same form, the ratio of x-coefficient to y-coefficient is related to the slope. It will be different if there is one solution.

ratio for first equation: 1/1 = 1
ratio for second equation: 1/-1 = -1

These lines have different slopes, so there is one solution to the system of equations.

_____

Additional comment

When the equations are in slope-intercept form with the y-coefficient equal to 1, the x-coefficient is the slope.

y = mx +b . . . . . slope = m

When the equations are in standard form (as in this problem), the ratio of x- to y-coefficient is the opposite of the slope.

ax +by = c . . . . . slope = -a/b

As long as the equations are in the same form, the slopes can be compared by comparing the ratios of coefficients.

If the slopes are the same, the lines may be either parallel (empty solution set) or coincident (infinite solution set). When the equations are in the same form with reduced coefficients, the lines will be coincident if they are the same equation.

8 0

2 years ago

ronaldo delivers the papers at the rate of 6 papers in 24 minutes. how much longer would it take him to deliver 56 papers than 4

UkoKoshka [18]

We are given

Ronaldo delivers the papers at the rate of 6 papers in 24 minutes

so, number of papers =6 in time =24 minutes

so, firstly we can find rate

rate = ( number of papers)/( time taken)

$r=\frac{6}{24} =\frac{1}{4}$

now, we can find times

Time for 56 papers:

we are given

number of papers =56

rate is

$r=\frac{1}{4}$

now, we can find time

$t_1=\frac{56}{r}$

$t_1=\frac{56}{\frac{1}{4}}$

$t_1=224min$

Time for 41 papers:

we are given

number of papers =41

rate is

$r=\frac{1}{4}$

now, we can find time

$t_2=\frac{41}{r}$

$t_2=\frac{41}{\frac{1}{4}}$

$t_2=164min$

now, we can find time difference

$t=t_1-t_2$

so, we can plug values

$t=224-164$

$t=60 min$ ..............Answer

8 0

3 years ago

Read 2 more answers

Plssssssssssssssssssss Answer this is Major?

julsineya [31]

Answer:

See below because there are 9 parts (A through I)

Explanation:

Part A: write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y = ax2 + bx + c.

The figure shows a rectangular table with these dimensions:

Length: - x + 64
Witdth: x + 4

The area of a rectangle is width × length:

$(x + 4)\times (-x+64)$

Use distributive property:

$x\cdot (-x)+x\cdot(64)+4\cdot (-x)+4\cdot (64)=-x^2+64x-4x+256$

Simplify:

$-x^2+64x-4x+256=-x^2+60x+256$

Part B. Graph the equation you wrote in part A. Adjust the zoom of the graphing window so the vertex, x-intercepts, and y-intercept can be seen.

1. Factor the equation:

Common factor - 1:

$-x^2+60x+256=-(x^2-60x-256)$

Find two numbers that add - 60 and whose product is -256. Theyb are -64 and + 4

$-(x-64)(x+4)$

2. Find the roots:

Equal the expression to zero:

$-(x-64)(x+4)=0\\ \\ x-64=0\implies x=64\\ \\ x+4=0\implies x=-4$

Those are the x-intercepts: (-4,0) and (64,0)

3. Find the symmetry axis:

The simmetry axis is the line x = the middle value between the two roots:

$x=(64-4)/2=60/2=30$

4. Find the vertex

The vertex has x-coordinate equal to the x axis (30 in this case).

Substitute in the equation of find the y-coordinate:

$y=-(30-64)(30+4)=-(-34)(34)=1,156$

Hence, the vertex is (30, 1,156)

5. Find the y-intercept

Make x = 0

$y=-(x^2-60x-256)=-(0-256)=256$

Hence, the y-intercept is (0, 256)

With the x-incercepts, the y-intercept, the axis of symmetry, and the vertex, you can sketch the graph.

You can see now the graph in the attached figure

Part C. Extreme location of the graph

The graph shows that the parabola opens downward. That is due to the fact that the coefficient of the leading term (x²) is negative.

The parabola starts in the second quadrant. starts growing, crosses the x-axis at (-4,0), crosses the y-axis at (0,256), reaches the maximum value at (30, 1156), and then decreases toward the fouth quadrant, crossing the x-axis at (64,0).

Thus the vertex is a maximun, and the coordinates of the maximum are (30, 1156).

Part D. According to the graph, what is the maximum possible area of the game board? Give your answer to the nearest whole number. (Assume that the maximum area is not reduced by the open hole in the game board.)

The maximum possible area of the game is the maximum value of the function y = -x² + 60x + 256.

This value was calculated as y = 1156.

Part E. Use the original expressions for the length and width, and substitute the x-coordinate from the extreme location. What are the length and width of the game board at the extreme location?

The length is:

length = - x + 64 inches

x = 30

length = - 30 + 64 = 34 inches

The width is:

width = x + 4

x = 30

width = 30 + 4 = 34 inches

Part F. What type of quadrilateral will be formed when the game board covers the maximum possible area?

Since the length and the width are equal, the quadrilateral is a square.

Part G. Suppose the carnival director asks you to create a game board that is 1,120 square inches. Find the dimensions that would meet this request by setting the area equation equal to 1,120, solving for x, and substituting x into the expressions for the length and width.

$y=-x^2+60x+256\\ \\ 1,120=-x^2+60x+256\\ \\ x^2-60x-256+1120=0\\ \\ x^2-60x+864=0$

Factor:

Find two numbers whose sum is - 60 and the product os 864. They are -24 and - 34:

$x^2-60x+864=(x-24)(x-36)$

Use the zero product rule:

$(x-24)(x-36)=0\\ \\ x-24=0\implies x=24\\ \\ x-36=0\implies x=36$

Now substitute to find the dimensions:

x = 36

length = - x + 64

length = - 36 + 64 = 28

width = x + 4 = 36 + 4 = 40

Hence, legth = 28, width = 40

x = 24

length = - x + 64 = -24 + 64 = 40

width = x + 4 = 24 + 4 = 28

Part H. When you solved the area equation for x, did any extraneous solutions result? Describe how an extraneous solution would arise in this situation.

The two solutions are valid (non extraneous) because both leads to positive real dimensions for which the areas can be 1,120 in².

28×40 = 1,120

40×28 = 1,120

An extraneous solution could arise if you try to find areas for which x is greater than or equal to 64, because in that case - x + 64 would be zero or negative and dimensions must be positive.

For the same reason, also an extraneous solution would arise if you try to fix areas for which x is less than or equal to - 4.

So, the domain of your function has to be - 4 < x < 64.

Part I. What method of solving quadratics did you use to solve the equation set equal to 1,120? Why did you choose this method?

The method use was factoring.

Discuss the usefulness of other methods of solving quadratics as they pertain to this scenario.

The other importants methods are graphical and the quadratic equation.

For graphical method you graph your parabola and find the values of x that sitisfies the area searched (value of y).

The quadratic equation gives the y-values (areas) without factoring:

$\frac{-b+/-\sqrt{b^2-4(a)(c)} }{2(a)}$

8 0

3 years ago

The graph of f(x)=√x is reflected over the y-axis. Use the graphing calculator to graph this reflection. Which list

Basile [38]

The list contains three points that lie on the graph of the reflection is (-49, 7), (-18, 9), (-1, 1).

<h3>What is graph reflection?</h3>

The graph of any function when mirrored on the same plane.

Given the graph of f(x)=√x is reflected over the y-axis. Use the graphing calculator to graph this reflection.

The points which can satisfy the reflection of the graph is (-49, 7), (-18, 9), (-1, 1).

Thus, the fourth option is correct.

Learn more about graph reflection

brainly.com/question/18765560

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4 0

2 years ago