Complete the equation of the graphed linear function in point-slope form.y – (–2) = ? (x – ?)

Answers

Answer 1

Answer: The point-slope form:
$y-y_1=m(x-x_1)$
m - slope
x₁, y₁ - the coordinates of a point

It passes through the points (1,-2) and (2,2).
$(1,-2) \nx_1=1 \n y_1=-2 \n \n(2,2) \nx_2=2 \n y_2=2 \n \nm=(y_2-y_1)/(x_2-x_1)=(2-(-2))/(2-1)=(2+2)/(1)=4$

$\boxed{y-(-2)=4(x-1)}$

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Why does the amount of water that flows in a river change during the year?

Answers

because of the rain. It can either increase or decrease

What is the result of isolating y2 in the equation below?(x + 4)2 + y2 = 22

A.
y2 = x2 - 8x + 6

B.
y2 = 22 - x2

C.
y2 = -x2 - 8x + 16

D.
y2 = -x2 - 8x + 6

ALL y2 are y^2

Answers

STEP-BY-STEP SOLUTION:

( x + 4 )^2 + y^2 = 22

x^2 + 2 × x × 4 + 4^2 + y^2 = 22

x^2 + 8x + 16 + y^2 = 22

y^2 = 22 - x^2 - 8x - 16

y^2 = - x^2 - 8x + 6

FINAL ANSWER:

Therefore, the answer is:

D. y^2 = - x^2 - 8x + 6

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Can someone show me how to solve this step by step?

Answers

9514 1404 393

Answer:

x = -15

Step-by-step explanation:

It appears the drawing is showing two representations for the distance LK. Of course, they both have the same value.

10 = LK = x+25

Subtracting 25 from the equation, we have ...

-15 = x

(This value of x makes KJ = (2(-15)+27) = -3, a nonsense value.)

_____

Alternate (more sensible) interpretation

If the bottom line is intended to represent LJ, then we have ...

10 +(2x+27) = (x +25) . . . . LK +KJ = LJ

x +37 = 25 . . . . subtract x

x = -12 . . . . . . . subtract 37

With this value of x, the length of KJ is 2(-12)+27 = 3, and the overall length LJ is (-12)+25 = 13. This is consistent: LK=10, KJ = 3, LJ = 13.

Triangle PQR has vertices P(0, 0), Q(3, 4), and R(3, 0). If triangle PQR is rotated 180° about the origin, what is the length of side P'Q'?

Answers

Answer:

The length of P'Q' is 4 units

The length of P'R' is 3 units

Step-by-step explanation:

If you rotate the figure 180° then the vertex would be R, and from P to Q is 3 units left and 4 units down

Final answer:

To find the length of side P'Q' after rotating triangle PQR 180° about the origin, we need to find the distance between the points P'(0,0) and Q'. When you rotate a point (x, y) 180° about the origin, the new coordinates are (-x, -y). Using the distance formula, we can find the length of side P'Q': d = sqrt((-3-0)^2 + (-4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5. Therefore, the length of side P'Q' is 5 units.

Explanation:

To find the length of side P'Q' after rotating triangle PQR 180° about the origin, we need to find the distance between the points P'(0,0) and Q'.

When you rotate a point (x, y) 180° about the origin, the new coordinates are (-x, -y).

So, the coordinates of point Q' would be (3, 4) rotated 180°, which is (-3, -4).

Using the distance formula, we can find the length of side P'Q':

d = sqrt((-3-0)^2 + (-4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5.

Therefore, the length of side P'Q' is 5 units.

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Identify the domain and range of each function.y = 3 • 5x
The domain of this function is ?
negative infinity to zero
0 to infinity
negative infinity to infinity

The range of this function is?
0 to infinity
3 to infinity
negative infinity to infinity

Answers

The domain of this function is:

C.) Negative infinity to infinity

The range of this function is:

A.) 0 to infinity

Y=4^x-5+3

The domain of this function is:

C.) Negative infinity to infinity

The range of this function is:

B.) 3 to infinity

Final answer:

For the function y = 3 • 5x, the domain is all real numbers (negative infinity to infinity) and the range is all real numbers from zero to infinity.

Explanation:

In mathematics, the domain of a function is the complete set of possible values of the independent variable. In the case of the function y = 3 • 5x, the independent variable is 'x' which can take any real number. Therefore, the domain of this function is from negative infinity to infinity.

The range of a function is the complete set of possible values of the dependent variable. In this function, the dependent variable is 'y', which increases as 'x' increases. Because the lowest value y can take is 0 (when x is 0), the range is from 0 to infinity.

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Which statement best applies to the slope of the line below?A.
the slope is negative
B.
the slope is zero
C.
the slope is positive
D.
the line has no slope

Answers

A vertical line has an undefined slope... AKA has no slope. So your answer would be D

Answer:

the line has no slope

Step-by-step explanation:

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