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What is the equation of the line in point-slope form?
4
= {(x + 4)
Oy+4=;
O y-4 = 2(x + 4)
N
Oy - 0 = 2(x-4)
Oy - 4 = 2(x -0)
4
-2.
2.

Answers

Answer 1

Answer:

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

What is the Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

m = (0 - (-4)) / (4 - (-4))

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the givenpoints on the line. Let's use the point (-4, -4):

y = mx + b

-4 = (1/2)(-4) + b

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

Learn more about Linear equations here:

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Answer 2

Answer:

Answer:

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4). You can use these points to find the slope. Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2. This cancels out choices C and D.

With the point (-4, -4), A is the answer.

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Solve the following equation for X.
2x - 18y = - 8

Answers

Answer:

x = 9y - 4

Step-by-step explanation:

2x - 18y = - 8 /: 2

x - 9y = - 4

x = 9y - 4

The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select all of the constraints for this situation. a) y>13x b)340x+670y≤5650 c)y>0 340x+670y<5650 d) x>13y x>0

Answers

Answer:

c and d

Step-by-step explanation:

The cost inequalities tell you that x corresponds to bicycles, so answer (a) is incorrect. The cost constraint is strictly less than, so answer (b) is incorrect.

(d) correctly expresses the relationship between bicycles (x) and treadmills (y).

_____

The only integer solution is y=0 and 0 < x ≤ 15.

Answer: c. $y>0\ ;\ 340x+670y<5650$

d. $x>13y ; x>0$

Step-by-step explanation:

Let x be the number of new bicycles and y be the number of new treadmills.

Given : The number of new bicycles must be more than 13 times the number of new treadmills.

i.e. $x>13y$

Each bicycle costs $340 and each treadmill costs $670.

He must spend less than $5,650.

i.e. $340x+670y<5650$ '

Hence, the constraints for this situation will be :

$x>13y ; x>0$

$340x+670y<5650$

Hence, c and d are the correct options.

Write each decimal in figures.1) five hundred forty-four and four-tenths
2) three and twenty-five hundreds
3) twenty-five and one-tenth
4) fifty-two and seventy-six hundred
5) eight hundred seventy-two and one tenths

Answers

Step-by-step explanation:

1 544.4

2. 3.025

3. 25.1

4. 52.076

5. 872.1

for your information

1 tenth is equal to 0.1

1 hundredth is equal to 0.01

1 thousandth is equal to 0.001

The length of a rectangle is 12 m.Its width is 15 m.
Find the area and perimeter of this rectangle.

Answers

Answer:

for perimeter you add all sides. so Lenth x2 + width x2 is 24+30 which would equal 54

for area it's Lenth times width so 12 times 15 equals 156

Solve the equation by completing the square. X^2+10x+24=0

Answers

Answer:

x = -4

x = -6

Step-by-step explanation:

X^2+10x+24=0

(b/2)^2 = (10/2)^2 = 25

X^2+10x+25=-24+25

(x+5)^2 = 1

(x+5) = ± 1

x = +1 -5 = -4

x = -1 -5 = -6

Find the first partial derivatives of the function. f(x, t) = e−9t cos(πx)

Answers

Answer:

$f_(x)(x,t) = -\pi e^(-9t) sin((\pi x))$

$f_(t)(x,t) = -9cos((\pi x)) e^(-9t)$

Step-by-step explanation:

We are given the following function:

$f(x,t) = e^(-9t) cos((\pi x))$

First derivatives:

We find the first derivatives in function of x and of t.

Function of x:

The exponential is only a function of t, so it is treated as a constant.

$f_(x)(x,t) = e^(-9t) \frac{d}{dx](cos((\pi x))) = -e^(-9t) sin((\pi x)) (d)/(dx)(\pi x) = -\pi e^(-9t) sin((\pi x))$

Function of t:

Same logic as above, the cosine as treated as a constant.

$f_(t)(x,t) = cos((\pi x)) (d)/(dt)(e^(-9t)) = cos((\pi x)) e^(-9t) (d)/(dt)(-9t) = -9cos((\pi x)) e^(-9t)$

Final answer:

To find the first partial derivatives of the function e^(-9t) cos(πx), we differentiate the function with respect to x and t separately, treating the other variable as a constant. The partial derivative with respect to x is 9t sin(πx), while the partial derivative with respect to t is -e^(-9t) cos(πx).

Explanation:

To find the first partial derivatives of the function, we will differentiate the function with respect to each variable separately while treating the other variable as a constant.

For the partial derivative with respect to x, we can treat t as a constant. Differentiating e-9t cos(πx) with respect to x gives us -9t * (-sin(πx)) = 9t sin(πx).

For the partial derivative with respect to t, we can treat x as a constant. Differentiating e-9t cos(πx) with respect to t gives us -(e-9t) * cos(πx) = -e-9t cos(πx).