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3 years ago

Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

Mathematics

2 answers:

NISA [10]3 years ago

7 0

The answer is p= Q .

TiliK225 [7]3 years ago

4 0

Pq= 1 because dollars for every item would make more sense then items for every dollar.

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May I please have the answers to this problem

sp2606 [1]

Answer:

6x+5

Step-by-step explanation:

2x+4x =6x

10-5=5

6x+5

6 0

3 years ago

15 is what percent of 20

Lera25 [3.4K]

100%/x%=20/15
(100/X)*x=20/15*x --I multiply both sides of the equation by X
100=1.33333333333*x --I divided both sides of the equation by .........................................(1.33333333333) to get X
100/1.33333333333=x
75=x
x=75

15 is 75% of 20

6 0

3 years ago

Find the value of r so that the line through (8,r) and (4,5) has a slope of -4

Ratling [72]

Answer:

r = - 11

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 4

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (8, r)

m = $\frac{r-5}{8-4}$ = $\frac{r-5}{4}$ = - 4 ( multiply both sides by 4 )

r - 5 = - 16 ( add 5 to both sides )

r = - 11

7 0

2 years ago

Which of these tables is a ratio table? A 2-column table has 3 rows. Column 1 is labeled A with entries 2, 4, 5. Column 2 is lab

makkiz [27]

Answer:

its b

Step-by-step explanation:

7 0

2 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago