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2 years ago

Line m passes through point (5,- 8) and has a slope - 3. What is the equation for the line point slope form

Mathematics

1 answer:

skad [1K]2 years ago

7 0

Answer:

$y + 8 = -3(x-5)$

Step-by-step explanation:

Point Slope form is:

$y - y_1 = m(x-x_1)\\\rule{150}{0.5}\\\text{ m - slope}\\(x_1,y_1) \text{ - point}\\\rule{150}{0.5}$

We are given the point (5, -8) and the slope of -3.

$y-y_1=m(x-x_1)\rightarrow y - (-8) - -3(x-5)\rightarrow \boxed{y+8=-3(x-5)}$

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A number is less than 20 units away from 7 on the number line. What numbers are within these parameters? Choose the inequality t

Alex787 [66]

Answer:

For the pull out menu it was B

Step-by-step explanation:

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2 years ago

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The graph of the piecewise function f(x) is shown.

NeTakaya

Answer:

{f(x) | -∞ < f(x) ≤ 4 }

Step-by-step explanation:

The range is made up of the y values. Remember f(x) = y

In this graph the least value of y is -∞ and the greatest value of y is 4

So, the range is {f(x) | -∞ < f(x) ≤ 4 } which is the 2nd choice

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2 years ago

On a coordinate plane, triangle A B C has points (negative 3, negative 1), (negative 2, negative 3), (1, negative 1) and is refl

andreev551 [17]

Answer:

A' = (-3, 3)

Step-by-step explanation:

If the points are as follows:

A = (-3, -1)

B = (-2, -3)

C = (1, -1)

When reflecting across a y axis the x values remain the same.

When reflecting across y = 1 the y values will remain equal distant from y = 1.

A' = (-3, 3) y value = |-1 - 1| = 2 + 1 = 3

B' = (-2, 5) y value = |-3 - 1| = 4 + 1 = 5

C' = (1, 3) y value = |-1 - 1| = 2 + 1 = 3

7 0

2 years ago

A series of equal quarterly payments of $10,000 for 15 years is equivalent to what future worth amount at an interest rate of 6%

kogti [31]

Answer:

$976,578.71

Step-by-step explanation:

We assume the deposits are made at the <em>beginning</em> of each quarter. The quarterly interest rate is 6%/4 = 1.5%. The number of quarterly payments is 15×4 = 60. The future value of an annuity due is ...

A = P(1+r)((1+r)^n -1)/r

where r is the quarterly interest rate, n is the number of payments, and P is the payment amount.

A = $10000(1.015)(1.015^60 -1)/.015 ≈ $976,578.71

The future value is $976,578.71.

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3 years ago

(3) Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and t

Gekata [30.6K]

Answer:

The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Step-by-step explanation:

Here, we note the following

Let the person walking way fom the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X, 2 ft/sec × 15 s = 30 ft away from the elevator

For Y, 7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

= 30² +105² = 11925 ft²

d = √11925 ft² = 109.202 ft

The rate of change of the distance between the two peopl, X and Y is given as

$\frac{dd^2}{dt} = \frac{dx^2}{dt} + \frac{dy^2}{dt}$

Therefore, $2d\frac{dd}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}$ or $d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}$

Since $\frac{dx}{dt}$ is given as 2 ft/sec and $\frac{dy}{dt}$ = 7 ft/sec

Then $d\frac{dd}{dt} = 30 \times 2 + 105 \times 7 = 795\\$

$\frac{dd}{dt} = \frac{795}{109.202 } =7.28 ft/sec$

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2 years ago

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