I PART B: Which quote from the text best supports the answer to Part

what is the equation in point-slope form of a line that passes through the points parentheses( 3, -5) and (-8, 4)

viva [34]

slope = (y2-y1)/(x2-x1)

m = (4--5)/(-8-3)

m=(4+5)/(-8-3)

m=9/-11

point slope form

y-y1 =m(x-x1)

y--5 =-9/11 (x-3)

y+5 = -9/11(x-3)

8 0

3 years ago

A The length of a rectangle is 4 m more

Lady bird [3.3K]

Given :

The length of a rectangle is 4m more than the width.
The area of the rectangle is 45m²

⠀

To Find :

The length and width of the rectangle.

⠀

Solution :

We know that,

$\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:$

So,

Let's assume the length of the rectangle as x and the width will be (x – 4).

⠀

Now, Substituting the given values in the formula :

$\qquad \sf \: { \dashrightarrow x \times (x - 4) = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 9x+ 5 x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow x(x - 9) + 5(x - 9) = 0 }$

$\qquad \sf \: { \dashrightarrow (x - 9) (x + 5) = 0 }$

$\qquad \sf \: { \dashrightarrow x = 9, \: \: x = - 5}$

⠀

Since, The length can't be negative, so the length will be 9 which is positive.

⠀

$\qquad { \pmb{ \bf{ Length _{(rectangle)} = 9\:m}}}\:$

$\qquad { \pmb{ \bf{ Width _{(rectangle)} = 9 - 4=5\: m}}}\:$

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8 0

2 years ago

Ramona went to a theme park during spring break. She was there for 7 hours and rode 14 rides. At what rate did Ramona ride rides

Tanzania [10]

Answer:

2 rides per hour

Step-by-step explanation:

This is a division problem since we would need to divide in order to answer the question.

Divide the amount of rides she rode to the number of hours she was there.

Input the numbers below:

amount of rides she rode/number of hours there

14/7=2

At this rate, Ramona rode 2 rides per hour.

8 0

3 years ago

What's the solution please its urgent<br> -7w+8(w+1)=w-7

Dahasolnce [82]

Uhm i don't understand ;(!!

4 0

3 years ago

Evaluate the following limit, if it exists : limx→0 (12xe^x−12x) / (cos(5x)−1)

Amanda [17]

Answer:

$\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}$

Step-by-step explanation:

Notice that $\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}$ , which is in indeterminate form, so we must use L'Hôpital's rule which states that $\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}$ . Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:

$\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}$

Now, plug in the limit and evaluate:

$\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}$

Thus, $\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}$

3 0

2 years ago