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2 years ago

Construct a linear equation for the table. What is the slope of the line

Mathematics

1 answer:

Klio2033 [76]2 years ago

3 0

We have points (-3, 4), (-1, 2), (4, -3) and (6,-5)

Let's verify it's a line by calculating the slopes between successive points.

Slope is change in y over change in x.

(2 - 4)/(-1 - -3) = -2/2 = -1

(-3 - 2)/(4 - -1) = -5/5 = -1

(-5 - -3)/(6 - 4) = -2/2 =-1

Yup. We have a line of slope -1 through point (-1, 2)

y - 2 = -1(x - -1)

y = -x - 1 + 2

y = -x + 1

That's the linear equation for the table.

Answer: Linear equation: y = -x + 1 slope = -1

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PLEASE ANSWER ASAP! THANK YOU! SUPER EASY! Mrs. Davis is planning to put a circular rug in her living room. The circumference of

netineya [11]

Answer:

Part A) The diameter of the rug is $10\ ft$

Part B) The radius of the rug is $r=5\ ft$

Part C) The area of the rug is $78.5\ ft^{2}$

Step-by-step explanation:

Part A) Find the diameter of the rug

we know that

The circumference of a circle (circular rug) is equal to

$C=\pi D$

where

D is the diameter

we have

$C=31.4\ ft$

$\pi=3.14$

substitute the values and solve for D

$31.4=(3.14)D$

$D=31.4/(3.14)=10\ ft$

Part B) Find the radius of the rug

we know that

The radius of a circle (circular rug) is half the diameter

we have

$D=10\ ft$

$r=D/2$

substitute

$r=10/2=5\ ft$

part C) What is the area the rug is covering?

The area of the circle (circular rug) is equal to

$A=\pi r^{2}$

we have

$r=5\ ft$

$\pi=3.14$

substitute

$A=(3.14)(5)^{2}$

$A=78.5\ ft^{2}$

7 0

3 years ago

PLEASE HELP ME WITH THIS<br><br>

Vladimir [108]

Answer:

A. (0, 60)

B. 15x

Step-by-step explanation:

The initial value is the same as the y-intercept, which is 60 or (0, 60).

The rate of change would be the same as the slope. To find the slope, you do rise/run. You move 15 units up, and 1 to the right. That would be 15x.

Hope this helps!

5 0

3 years ago

Evaluate and simplify the following complex fraction.:6/7 ÷ 3/11

inna [77]

Answer:

3 7/50

Step-by-step explanation:

so you need them to become common denominators

a common multiple they both have would be is 77

6/7 becomes 66/77 and 3/11 becomes 21/77

now we divide

keep the 66/77 as is and flip 21/77 (keep, change, flip)

so now our equation looks like this: 66/77 x 77/21

and your answer is 3.14

but as a fraction it is 157/50 and to simplified it would be 3 7/50 (mixed fraction)

3 0

2 years ago

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

2 years ago

The nth term of a sequence is 25-3n

Komok [63]

Answer:

22, 19, 16 and - 5

Step-by-step explanation:

To evaluate any term from the n th term formula substitute the terms position value for n

given $a_{n}$ = 25 - 3n, then

(a)

$a_{1}$ = 25 - (3 × 1) = 25 - 3 = 22

$a_{2}$ = 25 - (3 × 2) = 25 - 6 = 19

$a_{3}$ = 25 - (3 × 3) = 25 - 9 = 16

(b)

$a_{10}$ = 25 - (3 × 10) = 25 - 30 = - 5

5 0

3 years ago

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