9/10( -2/3) ( symplify )

A line passes through (−1, 7) and (2, 10).

Pachacha [2.7K]

The slope m of a line through points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by :

$\displaystyle{m = \frac{y_2-y_1}{x_2-x_1}
$

Thus, the slope of the line passing through points (−1, 7) and (2, 10) is

 $\displaystyle{m= \frac{10-7}{2-(-1)}= \frac{3}{3}=1$


The equation of a line with slope m passing through a point P(a, b) is given by
(y-b)=m(x-a).

We can consider any of the points (-1, 7), or (2, 10). Let's choose (2, 10):

y-10=1(x-2)
y-10=x-2
y-x=-2+10
y-x=8

Answer: C. −x+y=8

7 0

3 years ago

If x^2=y^2+z^2 what does x equal?

Zepler [3.9K]

Answer:

$\displaystyle x = \sqrt{y^2 + z^2}$

General Formulas and Concepts:

Pre-Algebra

Equality Property

Algebra i

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle x^2 = y^2 + z^2$

Step 2: Solve for x

[Equality Property] Square root both sides: $\displaystyle x = \sqrt{y^2 + z^2}$

3 0

2 years ago

triangle ABC above is isosceles with AB=AC and BC =48. the ratio of DE is 5:7. what is the length of DC

marshall27 [118]

Answer:

28

Step-by-step explanation:

Question Image is attached.

Triangle BED and Triangle CFD are similar.

We can let the length of BD be 5x and DC 7x

We also know BC = 48, thus we can write:

5x + 7x = 48

12x = 48

x = 4

Now, Since DC = 7x, we plug in x = 4 into it.

DC = 7x

DC = 7(4)

DC = 28

Length of DC is 28

6 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%5Ctiny%5Cint_%7Be%7D%5E%7B%7Be%7D%5E%7B2%7D%7D%20%5Cleft%28%20%5Csqrt%7Bx%20%2B%20%5Cfrac%

dlinn [17]

We have the identity

$\left(\sqrt x + \dfrac1{2^n}\right)^2 = x + \dfrac1{2^{n-1}} \sqrt x + \dfrac1{2^{2n}}$

Take the square root of both sides and rearrange terms on the right to get

$\sqrt x + \dfrac1{2^n} = \sqrt{x + \dfrac1{2^{n-1}} \left(\sqrt{x} + \dfrac1{2^{n+1}}\right)}$

Decrementing n gives

$\sqrt x + \dfrac1{2^{n-1}} = \sqrt{x + \dfrac1{2^{n-2}} \left(\sqrt{x} + \dfrac1{2^{n}}\right)}$

and substituting the previous expression into this, we have

$\sqrt x + \dfrac1{2^{n-1}} = \sqrt{x + \dfrac1{2^{n-2}} \sqrt{x + \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right) } }$

Continuing in this fashion, after k steps we would have

$\sqrt x + \dfrac1{2^{n-k}} = \sqrt{x + \dfrac1{2^{n-(k+1)}} \sqrt{x + \dfrac1{2^{n-k}} \sqrt{x + \dfrac1{2^{n-(k-1)}} \sqrt{\cdots \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right)}}}}$

After a total of n - 2 steps, we arrive at

$\sqrt x + \dfrac14 = \sqrt{x + \dfrac12 \sqrt{x + \dfrac1{2^2} \sqrt{x + \dfrac1{2^3} \sqrt{\cdots \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right)}}}}$

Then as n goes to infinity, the first nested radical converges to √x + 1/4. Similar reasoning can be used to show the other nested radical converges to √x - 1/4. Then the integral reduces to

$\displaystyle \int_e^{e^2} \left(\sqrt x - \frac14\right) + \left(\sqrt x + \frac14\right) \, dx = 2 \int_e^{e^2} \sqrt x \, dx = \boxed{\frac43 \left(e^3 - e^{\frac32}\right)}$

5 0

2 years ago

How long is 5 inches and 20 centimeters in pints

DochEvi [55]

Answer:

the answer is 0.067628

Step-by-step explanation:

7 0

2 years ago