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3 years ago

Which equation has a slope of -2 and a y-intercept of 4?

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

3 0

Answer:

y=-2x+4 (c)

Step-by-step explanation:

y=mx+b

m=slope

b= y-intercept

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The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec.

Andrej [43]

The ladder, the ground and the wall form a right triangle; the ladder length (L) is the longest side of this triangle. L^2 = h^2 + x^2, where h represents the height of the point on the wall where the ladder touches the wall, and x represents the distance of the base of the ladder from the wall.

We need dh/dt, which will be negative because the top of the ladder is sliding down the wall.

Starting with h^2 + x^2 = L^2, we differentiate (and subst. known values such as x = 5 feet and 4 ft/sec to find dh/dt. Note that since the ladder length does not change, dL/dt = 0. This leaves us with

dh dx
2h ---- + 2x ----- = 0.
dt dt

Since x^2 + h^2 = 15^2 = 225, h^2 = 225 - (5 ft)^2 = 200, or
200 ft^2 = h^2. Then h = + sqrt(200 ft^2)

Substituting this into the differential equation, above:

2[sqrt(200)] (dh/dt) + 2 (5) (4 ft/sec) = 0. Solve this for the desired quantity, dh/dt:

[sqrt(200)] (dh/dt) + (5)(4) = 0, or

dh/dt = -20 / sqrt(200) = (-1.41 ft / sec) (answer)

This result is negative because the top of the ladder is moving downward.

4 0

4 years ago

A type of fish for your aquarium costs $9 each. You can spend at most $45. How many

Alenkinab [10]

U can buy 5 fish hope it’s right
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3 years ago

A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded.

Angelina_Jolie [31]

Answer:

Part 1) The lateral area is $LA=88\ units^2$

Part 2) The area of the two bases together is $2B=60\ units^2$

Part 3) The surface area is $SA=148\ units^2$

Step-by-step explanation:

Part 1) Find the lateral area

we know that

The lateral area of a prism is given by

$LA=Ph$

where

P is the perimeter of the base

h is the height of the prism

$P=2(6+5)=22\ units$ ----> perimeter of rectangle

$h=4\ units$ ---> given

substitute

$LA=22(4)=88\ units^2$

Part 2) The area of the two bases together is?

The area of the rectangular base B is equal to

$B=(6)(5)=30\ units^2$

therefore

The area of the two bases together is

$2B=2(30)=60\ units^2$

Part 3) The total surface area is

we know that

The surface area is equal to

$SA=2B+LA$

substitute

$SA=60+88=148\ units^2$

4 0

3 years ago

Read 2 more answers

Find the equation of a line through (2,-4) and (-7,-4)

steposvetlana [31]

---------------------------------------------
Find slope :
---------------------------------------------
$\text {Slope = } \dfrac{-4 - (-4)}{-7-2} = \dfrac{0}{-9} = 0$

When the slope is 0, the graph is a horizontal line.

Equation of the graph is y = -4

------------------------------------------------------
Answer: y = -4
------------------------------------------------------

3 0

3 years ago

Can someone help? 25 points

tigry1 [53]

Answer:

Triangle A: acute

Triangle B: acute

Triangle C: obtuse

Triangle D: right

Step-by-step explanation:

acute= less than 90 degrees each angle

obtuse=more than 90 degrees for one angle

right=equal exactly 90 degrees for one angle

5 0

3 years ago

Read 2 more answers