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3 years ago

Find the equation of the line that passes through points A and B

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

4 0

Answer:

y= 2x - 1

Step-by-step explanation:

find the slope of the two points using the slope formula. then use one point with the slope to find b in y= mx + b

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Write an algebraic rule to describe the translation P(–8, 6)

yKpoI14uk [10]

T_(-8,6): (x,y) -> (x-8, y+6)

5 0

3 years ago

Based on the data table, which equation accurately represents the situation?

8090 [49]

Answer:

The equation of the line is:

$y = 28x$

Hence, option C is correct.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

Given the table

Gallons Miles Driven

8 224

10 280

4 112

Finding the slope between any two points, let say (8, 224) and (10, 280)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(8,\:224\right),\:\left(x_2,\:y_2\right)=\left(10,\:280\right)$

$m=\frac{280-224}{10-8}$

$m=28$

now substituting (8, 224) and m = 28 in the slope-intercept form of line equation

$y = mx+b$

224 = 28(8) + b

224 = 224 + b

b = 0

Thus, the y-intercept b = 0

now substituting b = 0 and m = 28 in the slope-intercept form of line equation

$y = mx+b$

$y = 28x+0$

$y = 28x$

Therefore, the equation of the line is:

$y = 28x$

Hence, option C is correct.

7 0

3 years ago

Solve the matrix and prove that it is equal 0

Art [367]

Step-by-step explanation:

$\underline{ \underline{ \text{Given}}} :$

$\tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}$

$\underline{ \underline { \text{To \: Find}}} :$

$\sf{ {A}^{2} - 5A+ 22I= 0}$

$\underline{ \underline{ \text{Solution}}} :$

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by $\sf{ {A}^{T}}$ . Again , Interchange it's rows and columns in order to find ' A '.

$\tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}$

Now , LEFT HAND SIDE ( L.H.S )

$\tt{ {A}^{2} - 5A+ 22I}$

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ $\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}$

⟼ $\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}$

⟼ $\sf{0}$

RIGHT HAND SIDE ( R.H.S ) : 0

L.H.S = R.H.S [ Hence , proved ! ]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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4 0

3 years ago

What is the answer? 236,272 round to the nearest ten thousand

mr_godi [17]

The answer is just 236,000 I hope it helps and is right

8 0

3 years ago

There are 875 members in an astronomy club. 350 of the members are female. What percentage of the members are males?

zaharov [31]

875: 100% = 350: x%
875x = 350 * 100
875x = 35000
x = 35000/875
x= 40% - that is the percentage of female members
Which means that the percentage of the members who are male is 60%.

3 0

4 years ago