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3 years ago

Michelle went shopping for some clothes and found a pair of slacks that cost

Mathematics

1 answer:

rjkz [21]3 years ago

7 0

Answer:

The sirt cost $7.5 before tax.

Step-by-step explanation:

Since the pair of slacks cost twice as much as the shirt, we have:

slacks = 2*shirt

And the total purchase was $22.5, so we have:

slacks + shirt = 22.5

We can create a system of equations such as:

slacks = 2*shirt

slacks + shirt = 22.5

If we apply the first formula on the second we can solve for the value of the shirt, we have:

2*shirt + shirt = 22.5

3*shirt = 22.5

shirt = 22.5/3 = 7.5

So the slacks cost:

slacks = 2*7.5 = 15

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Garret has already biked 75 kilometers

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3 years ago

What is the answer to the question

Mazyrski [523]

$134 is how much she spends
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4 years ago

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The graph represents the feasible region for the system:

morpeh [17]

We have been given a system of inequalities and an objective function.

The inequalities are given as:

$y\leq 2x\\
x+y\leq 45\\
x\leq 30\\$

And the objective function is given as:

$P=25x+20y$

In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.

The graph of the region is shown below:

From the graph, we can see that corner points of the feasible region are:

(x,y) = (15,30),(30,15) and (30,60).

Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.

$\text{At (15,30)}\Leftrightarrow P=25\cdot 15+20\cdot 30=975\\
\text{At (30,15)}\Leftrightarrow P=25\cdot 30+20\cdot 15=1050\\
\text{At (30,60)}\Leftrightarrow P=25\cdot 30+20\cdot 60=1950\\$

Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30

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4 years ago

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If 25 is added to 5 times a certain number, the result is 7 times the number minus 35. Find the number.

Blizzard [7]

Step-by-step explanation:

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

Let the certain number =x

According to the question

${:}\longrightarrow$ $\sf 5x+25=7x-35$

Simplify

${:}\longrightarrow$ $\sf 7x-35=5x+25$

${:}\longrightarrow$ $\sf 7x-5x=25+35$

${:}\longrightarrow$ $\sf 2x=60$

${:}\longrightarrow$ $\sf x={\dfrac {60}{2}}$

${:}\longrightarrow$ $\sf x=30$

$\therefore$ The number is 30.

3 0

3 years ago

The vertex form of the equation of a vertical parabola is given by y= 1/4p(x-h)^2 , where (h, k) is the vertex of the parabola a

matrenka [14]

Answer:

A. y = -2

B. A(6, -2)

C. use the midpoint tool to locate the vertex B(6, 1) halfway between F and A

D. up

E. divide 6 by 2; positive

F. 3

G. y = (1/12)(x -6)² +1

H. see attached

Step-by-step explanation:

A. The horizontal line 6 units below a point with y-coordinate 4 will be at ...

y = 4 -6

y = -2

B. The point of intersection will have the same x-coordinate as the focus (6) and the same y-coordinate as the line (-2). That point is A(6, -2).

C. As with every other point on the parabola, the vertex is the same distance from the focus as it is from the directrix. It will be the midpoint of segment FA. The vertex is B(6, 1).

D. The focus is "inside" the parabola. The focus is above the directrix, so the parabola opens upward, away from the directrix.

E, F. We're told to locate the directrix 6 units below the focus. The value of p is half that distance, 3 units. It can also be found by using GeoGebra to measure the length of segment FB.

G. Using the vertex form equation with p=3, (h, k) = (6, 1), the equation of the parabola is ...

$y=\dfrac{1}{4p}(x-h)^2+k=\dfrac{1}{4\cdot 3}(x -6)^2+1\\\\\boxed{y=\dfrac{1}{12}(x-6)^2+1}$

H. see the attachment

I. Multiplying the above equation by 12 and eliminating parentheses, we have ...

12y = x^2 -12x +36 +12

-48 = x^2 -12x -12y . . . . . . . subtract 48+12y

This is the same equation as shown by GeoGebra.

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3 years ago