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3 years ago

Write the slope intercept form of the equation for the line that is described in the following function table.

Mathematics

1 answer:

Elenna [48]3 years ago

7 0

Answer:

y=mx+b

m = slope

b = y-intercept

To find slope we use the equation, change in y divided by the change in x. Let's use points (2, 2) and (3, 1).

(2-1) / (2-3) = -1

Meaning our slope is -1 and it will be going down.

Next, we have to find the y-intercept which is the value of y when x=0. When x is 0 y will be 4.

y=-1x+4

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3 years ago

Verify the identity. cot(x - pi/2) = -tan(x)

gizmo_the_mogwai [7]

Answer:

See below.

Step-by-step explanation:

$\cot(x-\frac{\pi}{2})=-\tan(x)$

Convert the cotangent to cosine over sine:

$\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)$

Use the cofunction identities. The cofunction identities are:

$\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)$

To convert this, factor out a negative one from the cosine and sine.

$\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)$

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

$\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)$

8 0

3 years ago

Solve for x 8-2x = 5( x4)

MissTica

4/11 because when you multiply 5x4x you get 20x , so 8-2x=20x. Then you move the terms with variables and get -2x-20x=-8. This gives you the answer that -22x=8 and when u divide by 22 to both sides, you get 4/11.

5 0

3 years ago

The sum of 2 consecutive numbers is 37. Find the numbers. If x represents the smaller integer, then the larger integer is

NARA [144]

Answer:

x + 1

Step-by-step explanation:

There are a few ways this problem could be solved. The easiest route is to note that the first part of the question says "2 consecutive numbers". If the numbers are next to each other on a number line (consecutive) and x is the smaller number, the larger number is x + 1.

To check, let's find the two numbers. We know the numbers are next to each other on a number line and that together, they equal 37. Let's begin with 15 and 16.

15 + 16 = 31

These numbers are too low, as they should add to 37. Let's try 18 and 19.

18 + 19 = 37

There are the two correct numbers. If x = the smaller number, x = 18.

18 + 1 = 19

Since this is correct, we know for sure that the answer is x + 1.

6 0

3 years ago

A single story house is to be built on a rectangular lot 70 feet wide by 100 feet deep. The shorter side of the lot is along the

dedylja [7]

Answer:

250 sq ft

Step-by-step explanation:

Since the shorter side is along the street and the setback is 10ft from each side, the house is 50 ft wide

and 100 -20 -30 = 50 ft long

50 x 50 = 250 sq ft

3 0

3 years ago