What is the domain and range of this function

Answers

Answer 1

Answer:

The domain is all real numbers. The range is also all real numbers.

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Please solve equations by completing square
5q+4 -11/2= 2q + 3/2(2q-1)
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With the 20% off coupon, Alexis received a discount of $15 on her shoes. What was the regular price of her shoes before the 20% off coupon was applied? Justify your answer using equations, models, and/or words to explain your mathematical reasoning.Please answer so a middle school kid can understand

Answers

Answer: 75

regular price ---- x

it said the 20% discount came to $15

so,

.2x = 15

x = 15/.2 = 75

Hope this helps :)

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the sum of two numbers is 9. if one number is subtracted from the other, the result is 3. find the numbers

Answers

x, y - the numbers

The sum of the two numbers is 9.
$x+y=9$

If one number is subtracted from the other, the result is 3.
$x-y=3$

Solve the system of equations:
$x+y=9 \n\underline{x-y=3} \nx+x=9+3 \n2x=12 \ \ \ |/ 2 \nx=6 \n \nx+y=9 \n6+y=9 \ \ \ |-6 \ny=3$

The numbers are 6 and 3.

Let's say x to the first number and y to the second one.
We add them : $x+y=9$
Then we substract them : $x-y=3$
Now we add the equations:

$(x+y)+(x-y)=9+3\n x+x+y-y=12\n 2x=12\n \n x=\frac { 12 }{ 2 } \n \n x=6$

and finally rewrite the equation:

$6+y=9\n y=9-6\n y=3\n \n x=6\quad and\quad y=3$

Factoring
3xsquared + 14x +20

Answers

The equation (3xsquared+ 14x + 20 = 0) has no real roots, so there are no factors made of only real numbers.

The factors are [ -7 plus and minus ( i x square root of 11 ) ]

" i " is the square root of -1 .

An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin. How many pounds of the second alloy must be added to the first to get a 12% mixture? 30 lb 40 lb 60 lb

Answers

so, they alloy is hmmm some piece of metal.

it has tin, among other metals, regardless of what other metals it may have, we know that for the first one, 15% is tin, the rest something else, and we also know that the alloy itself, weights 20 lbs.

now, how much is just the weight of the tin metal in it alone? well, is 15% of 20 lbs, or (15/100) * 20, or 3 lbs, so of all those 20 lbs, only 3 lbs or 15% is tin.

for the second alloy, let's say we'll add "x" lbs, we know the second alloy is 10% tin, how much of that weight is tin? well 10% of x, or (10/100) * x, or 0.10x lbs.

now, we're looking for a mixture, say the resulting lbs of mix will be "y" lbs, and we know the mixture will be 12% of tin, how much is 12% of y? (12/100) * y, or 0.12y.

now, regardless of what "x" and "y" is, we know that 20 + x = y, and that 3 + 0.10x = 0.12y, thus

$\bf \begin{array}{lccclll} &\stackrel{lbs}{amount}&\stackrel{tin~\%}{quantity}&\stackrel{tin~lbs}{quantity}\n &------&------&------\n \textit{15\% alloy}&20&0.15&3\n \textit{10\% alloy}&x&0.10&0.10x\n ------&------&------&------\n mixture&y&0.12&0.12y \end{array} \n\n\n \begin{cases} 20+x=\boxed{y}\n 3+0.10x=0.12y\n ----------\n 3+0.10x=0.12\left( \boxed{20+x} \right) \end{cases} \n\n\n 3+0.10x=2.4+0.12x\implies 3-2.4=0.12x-0.10x \n\n\n 0.6=0.02x\implies \cfrac{0.6}{0.02}=x\implies 30=x$

Answer:

30 lb

Step-by-step explanation:

Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-100x2+350x-150 Choose the inequality that shows the business will make a positive profit.

Answers

The first question's answer is:

0<-100x^2+350x-150

The second question "Look at the factorization shown below.

0 < –100x2 + 350x – 150

0 < –50(2x2 – 7x + 3)

0 < –50(2x – 1)(x – 3)

Select the range that Mario can choose from to price his muffins and make a positive profit.

The answer is:

$0.50 < x < $3.00

Figure WXYZ is a rectangle with a semicircle added to its base.What is the perimeter of figure WXYZ? Use 3.14 to approximate pi.

Answers

Figure WXYZ is a rectangle that has a semicircle added to its base. The rectangle has a length of sixteen inches and a width of seven inches. The semicircle has a diameter equal to the length of the rectangle.

Given:
Rectangle: Length = 16 inches ; width = 7 inches
Semicirle added to its base, the length of the rectangle. Only one length.

We need to get the circumference of the semi circle and add the length and 2 widths of the rectangle.

Circumference of a circle = 2πr ⇒ 2 * 3.14 * 8 inches = 50.24
Circumference of a semicircle = 50.24/2 = 25.12 inches
Widths of the rectangle = 2 * 7 inches = 14 inches

Perimeter of the figure = 25.12 in + 14 in + 16 in = 55.12 inches.

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