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Marianna [84]
3 years ago
8

Last month you spent ​$40 on clothing. This month you spent ​120% of what you spent last month. Set up a proportion to model thi

s situation. How much did you spend this​ month?
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0

Answer:

$48

Step-by-step explanation:

Given that:

Money spent on clothing last month = $40

Money spent this month is 120% of the spending of the last month.

To find:

A proportion to model this situation.

And the spending done this month?

Solution:

Let us have a look at 120% first.

120\%= \dfrac{120}{100} = \dfrac{6}{5}

\frac{6}{5} of x can be found by comparing x with 5, then we have to find the equivalent of 6.

Here, x is 40.

5 parts are equivalent to 40

1 part is equivalent to \frac{40}{5} = 8

6 parts are equivalent to 8\times 6 = 48

OR

simply:

40 \times \dfrac{120}{100} = 48

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What is the equation of the quadratic graph with a focus of (4,3) and a directrix of y=-6
Rufina [12.5K]

Answer:

f(x) = (1/18)x^2 - (4/9)x - 65/18

Step-by-step explanation:

Since the focus (4,3) is higher up than is the directrix y = -6, the vertex is between y = -6 and y = 3, halfway between these values, to be exact:  y = -3/2.  Thus, the y-coordinate of the vertex is (-6 + 3/2), or -4.5.  The x-coordinate of the vertex is 4, which comes from that 4 in (4,3).  Thus, the vertex is (4, -4.5) or (4, -4 1/2).

The standard equation for a vertical parabola with vertex at (h,k) is:

4p(y-k) = (x-h)^2, where p is the distance between vertex and focus or between vertex and directrix.  In this case p = 4.5.  Thus, the equation of this quadratic is 4(4.5)(y - [-4.5]) = (x - 4)^2, or

18(y+4.5) = (x-4)^2, or y+4.5 = (1/18)(x-4)^2.

Let's expand this and rewrite the result as a quadratic equation in standard form y = ax^2 + bx + c:

y + 4.5 = (1/18)(x^2 - 8x + 16).  Multiplying all terms by 18 to remove both fractions, we get:

18y + 81 = x^2 - 8x + 16.  Rearranging these terms, we get:

18y = x^2 - 8x + 16 - 81, or

18y = x^2 - 8x - 65, or

y = f(x) = (1/18)x^2 - (4/9)x - 65/18.

5 0
3 years ago
Read 2 more answers
Which expressions are equivalent??
Brilliant_brown [7]

<u>Given</u>:

The given expression is 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)

We need to determine the equivalent expression.

<u>Option A:</u> -1

Solving the expression, we get;

\frac{3}{2} x+14-\frac{3}{2} x+15

Simplifying, we get;

14+15=29

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is not equivalent to -1.

Hence, Option A is not the correct answer.

<u>Option B</u>: 29

Solving the expression, we get;

\frac{3}{2} x+14-\frac{3}{2} x+15

Simplifying, we get;

14+15=29

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 29.

Hence, Option B is the correct answer.

<u>Option C</u>: 2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Let us rewrite the given expression.

2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Thus, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Thus, Option C is the correct answer.

<u>Option D</u>: 2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)

Rewriting the expression, we get;

2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]

Hence, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent not to 2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)

Thus, Option D is not the correct answer.

<u>Option E:</u> 2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Multiplying the terms within the bracket, we get;

2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Hence, the expression 2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right) is equivalent to 2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)

Thus, Option E is the correct answer.

4 0
3 years ago
In a baseball card collection, 40% of the cards are worth more than 100$. If 12 cards in the collection are worth more than $100
Helen [10]

Answer:

30

Step-by-step explanation:

12 is 40% of the total number of cards.

12 = 0.4x, where x is total number of cards

/0.4 /0.4

30 = x

30 cards

5 0
3 years ago
Read 2 more answers
Find m angle Y
LiRa [457]
I think it is A 54 because I did it already and I got a 100
6 0
3 years ago
Wal-Mart is selling 12 highligters for $5.47. What is the unit price of the highlighters? (round the price to the nearest hundre
BaLLatris [955]

To be able to quickly solve this, we can temporarily make 5.47 into 547

Now, we can divide 547 by 12.

547 / 12 = 45.5

Now, we can round up from 45.5 to get 46.

However, we originally moved our decimal 2 places over, so now we must move it 2 places again.

46 ⇒ 0.46

The correct answer is $0.46

4 0
3 years ago
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