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2 years ago

13

Write an equation of the line in slope-intercept form.

1 answer:

Tasya [4]2 years ago

6 0

Answer:

y = x + 4

Step-by-step explanation:

From point (-1, 3) to point (0, 4), go up 1 (rise = 1) and go right 1 (run = 1).

slope = m = rise/run = 1/1 = 1

The y-intercept is b = 4

y = mx + b

y = x + 4

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What two numbers add up to -20 and multiply to -1125

Oliga [24]

I don't have my calculator handy just now. But just looking at that problem, why don't you try +20 and -45 and see if they do the job.

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2 years ago

X^2-14x+49 as a graph

Vaselesa [24]

<span> -x^2 + -14x = 49
-(x^2 +14) = 49
-[(x+7)^2 -49] = 49
</span>

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3 years ago

Futhe Mathematics<br><img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

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We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago

Find the missing angle.

Sphinxa [80]

Answer:

$m\angle XYV=135^{\circ}$

Step-by-step explanation:

Notice that $m\angle XYV=m\angle XYW+m\angle VYW$ .

The diagram already marks $m\angle VYW=80^{\circ}$ , so we just need to find $m\angle XYW$ .

$\angle TYU$ and $\angle XYW$ are vertical angles, which means they are equal in measure.

Therefore,

$m\angle TYU=m\angle XYW=6x+7$

Since there are $180^{\circ}$ on each side of a line, we have the following equation:

$m\angle XYW+m\angle VYW+m\angle UYV=180^{\circ},\\6x+7+13+4x+80=180,\\10x+20=100,\\10x=80,\\x=8$ .

Plugging in $x=8$ , we have:

$m\angle XYW=6(8)+7=55^{\circ}$ .

Therefore,

$m\angle XYV=55^{\circ}+80^{\circ},\\m\angle XYV=\fbox{$135^{\circ}$}$ .

5 0

3 years ago

Tim and Luke start a lawn-mowing business and buy a lawnmower for $325. They plan to charge $25 to mow one lawn. Which inequalit

bonufazy [111]

lawnmower = 325 USD

lawn mowing = 25 / lawn

total profit >= 1000 USD

x = number of lawns

25x - 325 = 1000

25x = 1000 + 325

x = 1325 / 25

x >= 53 lawns

25(53) >= 325 + 1000

The answer is D.

5 0

3 years ago

Read 2 more answers