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3 years ago

Sketch the graph of each line. 2x-5y=25

Mathematics

1 answer:

ki77a [65]3 years ago

3 0

Well, you transform the standard form equation into slope-intercept form (y=mx+b), since you can only graph it using this form.

First of all, the layout of the equation is $Ax+By=C$

So, in this case, A is 2, B is 5, and C is 25.

Now, to put it into slope intercept form, you either use the formula to change it and solve it:

$y= \frac{-A}{B}x+ \frac{C}{B} \\ y= \frac{-2}{-5}x+ \frac{25}{-5} \\ \\ y= \frac{2}{5}x-5$

Or you can just solve for y:

$2x-5y=25 \\ 2x-5y-2x=25-2x \\ -5y=-2x+25 \\ \frac{-5y}{-5}= \frac{-2x+25}{-5} \\ \\ y= \frac{2}{5}x-5$

In addition, I attached what the graph looks like.

Hope this helps!

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3(x+1)+11 = -2(x+13)<br> Thank you for the help

iVinArrow [24]

Answer:

x = -8

Step-by-step explanation:

3(x+1)+11=-2(x+13)

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3x+14=-2x-26

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3 years ago

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Use the rules of exponents to evaluate or simplify. Write without negative exponents. (-243)^3/5=___________?

stepladder [879]

The answer would be -27 but since you aren't using negatives, A trick I use is cross the line change the sign. So it would be 1/27 I believe

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3 years ago

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The sales record of a real estate company for the month of May shows the following house prices (rounded to the nearest $1,000).

Semenov [28]

Answer:

see below

Step-by-step explanation:

minimum = 45

first quartile = 55

median = 75

third quartile = 85

maximum = 95

lower fence = Q1 - 1.5 x IQR = 10

upper fence = Q3 + 1.5 x IQR = 130

Therefore, one outlier = 140

b) mean = sum of all numbers ÷ n = 760 ÷ 10 = 76 ($76,000)

There is an outlier (140). Outliers don't affect the median as much as they affect the mean.

c) see attached

d) negative skew

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2 years ago

Which statements are true for the functions g(x) = x^2 and h(x)= -x^2? Check all that apply.

kogti [31]

Answer:

A, C, E & F are true

Step-by-step explanation:

We are given the functions;

g(x) = x² and h(x)= -x²

Let's analyze the options;

A) For any value of x,g(x) will always be greater than h(x);

Let's put x = 1 in both functions;

g(x) = 1² = 1

h(x) = - (1)² = - 1

Let's try a negative number say -1:

g(x) = (-1)² = 1

h(x) = -(-1)² = -1

In both cases, we see that g(x) > h(x) and so the statement is true.

B) For any value of x,h(x) will always be greater than g(x); As seen in A above, for any value of x, h(x) will always be greater than g(x). And so this statement here is wrong.

C) g(x) > h(x) for x = -1;

As seen in A above, at x = -1, g(x) > h(x).

Thus, this statement is true

D) g(x) < h(x) for x = 3;

g(x) = (3)² = 9

h(x) = -(3)² = -9

g(x) is not less than h(x) and so the statement is not correct.

E) For positive values of x, g(x) > h(x).

We have tried positive numbers at x = 1 and x = 3 in previous answers above and in both cases, g(x) > h(x).

Thus, statement is true.

F) For negative values of x, g(x) > h(x).

We have seen earlier that at a negative value of x = -1, g(x) > h(x)

Let's try x = -2

g(x) = (-2)² = 4

h(x) = -(-2)² = -4

Still seeing that g(x) > h(x).

Thus the statement is true.

6 0

2 years ago

Find the amplitude, phase shift, and period of the function. Give the exact values, not decimal approximations.y= -1+3cos(2x+pi/

antiseptic1488 [7]

The parts of a trigonometric function are:

$y=A\sin(Bx+C)+D$

Where:

A= Amplitude

2PI/B= Period

C= Phase

D= Shift

You have:

$y=3\cos(2x+\frac{\pi}{3})-1$

Amplitude= 3

Phase= π/3

Shift= -1

And the period:

$P=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi$

The period = pi

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1 year ago