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3 years ago

6

Mr. Sanchez is grading papers. Yesterday he graded 3 papers in 10 minutes. Today, he graded 2 papers in 8 minutes. What was the

difference between todays and yesterdays grating rate, in papers per hours?

1 answer:

siniylev [52]3 years ago

3 0

Answer:

The difference is 3 papers per hour

Step-by-step explanation:

First, you make turn the 10 minutes to 60 minutes by multiplied by 6 and the same to three and you would get 18 paper per hour. Next, you simplify the 8 minute rate to 1 paper in 4 minutes then multiply the 4 by 15 = 60 minutes then the same to the 1 equal to 15 paper per hour. Finally, you subtract 18 - 15 = 3 paper.

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If the square of twice a number is 81, what is the number? I tried doing 2x^2=81 but that did not come out to the answer 4.5,-4.

Vlada [557]

If the number is n then

square of 2 times a number
square of 2n
(2n)²
that was your mistake, because (2n)²=4n², not 2n²

the result is 81
(2n)²=81
square root both sides
remember positive and negative roots
2n=+/-9
divide by 2
n=+/-4.5

n=4.5 or -4.5

4 0

4 years ago

Find an equation of the circle that has center (-1,6) and passes through (-6,1)

horsena [70]

Answer:

(x + 1)² + (y - 6)² = 50

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

The radius is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (- 1, 6) and (x₂, y₂ ) = (- 6, 1)

r = $\sqrt{(-6+1)^2+(1-6)^2}$

= $\sqrt{(-5)^2+(-5)^2}$

= $\sqrt{25+25}$

= $\sqrt{50}$

(h, k ) = (- 1, 6 ), then

(x - (- 1))² + (y - 6)² = ( $\sqrt{50}$ )² , that is

(x + 1)² + (y - 6)² = 50 ← equation of circle

3 0

3 years ago

What is the next number in the sequence 2 7 8 3 12 9

Illusion [34]

<span>2 7 8 3 12 9... 14. the next number would be 14</span>

8 0

3 years ago

The radius of a circle is 4.3 inches. Using the formula A ≈ 3r2, what is the approximate area of the circle?

xz_007 [3.2K]

Please, use the symbol " ^ " to denote exponentiation. At first I had no idea what you meant by 3r2.

You are using the approx. formula A = 3 r^2 to find the area.
The given radius is 4.3 inches. Subst. this value for r in the above equation.
Find A (keeping in mind that it's an approximation).

6 0

3 years ago

Please help with these partial fractions!!!

VARVARA [1.3K]

a. Factorize the denominator:

$\dfrac{x+14}{x^2-2x-8}=\dfrac{x+14}{(x-4)(x+2)}$

Then we're looking for $a,b$ such that

$\dfrac{x+14}{x^2-2x-8}=\dfrac a{x-4}+\dfrac b{x+2}$

$\implies x+14=a(x+2)+b(x-4)$

If $x=4$ , then $18=6a\implies a=3$ ; if $x=-2$ , then $12=-6b\implies b=-2$ . So we have

$\dfrac{x+14}{x^2-2x-8}=\dfrac3{x-4}-\dfrac2{x+2}$

as required.

b. Same setup as in (a):

$\dfrac{-3x^2+5x+6}{x^3+x^2}=\dfrac{-3x^2+5x+6}{x^2(x+1)}$

We want to find $a,b,c$ such that

$\dfrac{-3x^2+5x+6}{x^2(x+1)}=\dfrac ax+\dfrac b{x^2}+\dfrac c{x+1}$

Quick aside: for the second term, since the denominator has degree 2, we should be looking for another constant $b'$ such that the numerator of the second term is $b'x+b$ . We always want the polynomial in the numerator to have degree 1 less than the degree of the denominator. But we would end up determining $b'=0$ anyway.

$\implies-3x^2+5x+6=ax(x+1)+b(x+1)+cx^2$

If $x=0$ , then $b=6$ ; if $x=-1$ , then $c=-2$ . Expanding everything on the right then gives

$-3x^2+5x+6=ax^2+ax+bx+b+cx^2=(a-2)x^2+(a+6)x+6$

which tells us $a-2=-3$ and $a+6=5$ ; in both cases, we get $a=-1$ . Then

$\dfrac{-3x^2+5x+6}{x^2(x+1)}=-\dfrac1x+\dfrac6{x^2}-\dfrac2{x+1}$

as required.

5 0

4 years ago