MATHEMATICS HIGH SCHOOL

(x-5) divided by (x^2+3x-40)

Answers

Answer 1

Answer:

Answer:

1/ x +8

*The 1 over x + 8

Answer 2

Answer:

Answer:

$(1)/(x+8)$

Step-by-step explanation:

Here is your original equation:

$(x-5)/(x^(2) +3x-40)$

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to $x-5$ later):

$x^(2) +3x-40$

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that $x^(2)$ has an exponent of 2. When variables are multiplied, the exponents are added, meaning that $x*x=x^(2)$ . (Or $x^(1) + x^(1) =x^(2)$ , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

$x^(2) +3x-40 = (x+)(x-)$

Next, let's look at the factors of 40:

1 and 40 2 and 20 4 and 10 5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

$8-5=3$

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in $3x$ . Therefore, $8(-5)=-40$ .

$x^(2) +3x-40 = (x+8)(x-5)$

Now let's go back to our original equation and substitute our old expression with the new one:

$(x-5)/((x+8)(x-5))$

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a $(1)/(1)$ .

$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$

Therefore, your simplified answer is $(1)/(x+8)$ !

Here's the whole process:

$(x-5)/(x^(2) +3x-40) \n\n(x+?)(x-?)\n\n40:\n1, 40\n2, 20\n4, 10\n5, 8\n\n8-5=3 \n(8x-5x=3x)\n\n(x+8)(x-5)\n\n(x-5)/((x+8)(x-5))=(1)/(x+8) \n\n(1)/(x+8)$

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

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The equation of a line is 2(y + 1) = 10x + 3. The y-intercept of the line is ______ , and the slope of the line is ______.

Answers

Answer:

The y-intercept of the line is $(1)/(2)$ , and the slope of the line is 5.

Step-by-step explanation:

The equation of a line is 2 (y + 1 ) = 10x + 3

We have to find y-intercept and slope of the given line.

We will convert this equation into the standard form of the equation of a line.

2(y+1) = 10x + 3

2y + 2 = 10x + 3

2y = 10x + 3 - 2

2y = 10x + 1

y = $(1)/(2)$ (10x + 1)

y = 5x + $(1)/(2)$

Now the slope of the line is 5 and y-intercept will be $(1)/(2)$ .

2(y+1) = 10x + 3
2y + 2 = 10x + 3
2y = 10x +1
y = 10/2x + 1/2

y = 5x + 1/2

Y-intercept is 1/2
Slope/m is 5

The graph shows the amount of money paid when purchasing bags of peanuts at the zoo:I REALLY NEED HELP!!!

A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 13. Four points are shown on the graph on ordered pairs 0, 0 and 1, 4 and 2, 8 and 3, 12. These points are joined by a line. The label on the x-axis is Bags of peanuts. The title on the y-axis is Total cost in dollars.

What does the point (0, 0) on the graph represent? (4 points)
a
The cost of one bag of peanuts

b
The cost of zero bags of peanuts

c
The cost of two bags of peanuts

d
The cost of three bags of peanuts

Answers

Answer:

B, the cost of 0 bags

Step-by-step explanation:

Answer:

b) The cost of zero bags of peanuts

Explanation:

Because it is at (0,0), that means it's at $0 and 0 bags of peanuts based on the labels for the x and y axis.

I am confused on number 15, the instructions are at the top.

Answers

You don't have #15 included. If you meant to put #25, I already answered that. Here is the solution again though.

#25 is fairly simple. Plug in -4 and 3 into the equation, and the extraneous root will be the one that does not work.
$√(12-(-4)) = √(16) = \frac{+}{}4$
Extraneous root in this case is positive four since +4≠-4
$√(12-3) = √(9) = \frac{+}{}3$
In this case it's negative 3, since -3≠3

What is the union of the two sets A={2,3,6,11,16} and B={6,11}? A. {2,3,6,11,16} B. {2,3,16} C. {6,11} D. {16}