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3 years ago

6. slope = -1; y-intercept = 8 Write the linear equation in slope intercept form

Mathematics

1 answer:

Mice21 [21]3 years ago

8 0

Answer: y = -1x + 8

Step-by-step explanation: linear equations must be written in the format

y = mx + b from.

m represents the slope which it -1

b represents the y-intercept which is 8.

Just substitute the slope and y-intercept in the m and b places and that is a linear equation.

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3 years ago

the volume of a cube is increasing at a constant rate of 824 cubic centimeters per minute. At the instant when the volume of the

Maurinko [17]

Answer:

DA/dt = 75.27 cm²

Step-by-step explanation:

Cube Volume = V(c) = 683 cm³

DV(c) /dt = 824 cm³

V(c,x) = x³

Then

DV(c,x)/ dt = 3x² Dx/dt

( DV(c,x)/ dt )/ 3x² = Dx/dt (1)

Now as V(c,x) = x³ when V(c,x) = 683 cm³ x = ∛683

x = 8.806 ( from excel)

And by subtitution of this value in equation (1)

Dx/dt = ( DV(c,x)/ dt )/ 3x² ⇒ Dx/dt = 824 / 3*x²

Dx/dt = 824 /3*77.55

Dx/dt = 824/232,64

Dx/dt = 3,542

Then we got Dx/dt where x is cube edge. The area of the face is x² then

the rate of change of the suface area is

DA/dt = ( Dx/dt )²*6 ( 6 faces of a cube)

DA/dt = (3.542)²*6

DA/dt = 75.27 cm²

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2 years ago

Each year the seventh graders who study life science participate in a special field trip to the city zoo in 2010 the school paid

juin [17]

Answer:

Yes, the price the school pays each year in entrance fees is proportional to the number of students entering the zoo

Step-by-step explanation:

Relationships between two variables is proportional if their ratios are equivalent.

In 2010, the school paid $1,260 for 84 students to enter the zoo.

Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = $1260:84=15:1$

In 2011, the school paid $1,050 for 70 students to enter the zoo.

Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = $1050:70=15:1$

In 2012, the school paid $1,395 for 93 students to enter the zoo.

Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = $1,395:93=15:1$

As $1260:84=1260:84=1,395:93=15:1$ ,

the price the school pays each year in entrance fees is proportional to the number of students entering the zoo.

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3 years ago

What is the opposite of factoring

ASHA 777 [7]

Answer:

simplifying

Step-by-step explanation:

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3 years ago

Read 2 more answers

An acrobat is on a platform that is 25 feet in the air. She jumps down in the initial velocity of 4 feet/seconds . Write the qua

Alenkasestr [34]

Answer:

a) h(t) = -16t²+ 4t + 25

b) Therefore it would take her 1.25 seconds to land safely in the net.

Step-by-step explanation:

The equation to be used is given as

h(t) = –gt²+ vt + S(t)

where g = force of gravity and because our question is in feet's = 16

V= Initial velocity

h = height

S = distance

a) The quadratic function for the above question

Using the formula

v = Initial velocity in the question = 4ft/s

S(t) = 25ft in the air

Hence the Quadratic function is

h(t) = –gt²+ vt + S(t)

h(t) = -16t²+ 4t + 25

b) If the safety net is placed 5 feet above the ground, how long will it take her to land safely in the net?

We are to find the time(t)

We can calculate this by using the quadratic function we derived in question (a)

The quadratic function is

h(t) = -16t²+ 4t + 25

Where, the height (h) = 5 feet above the ground

5= -16t² + 4t + 25

-16t² + 4t + 25 -5 = 0

-16t² + 4t + 20 = 0

Using the quadratic equation formula of

x = -b ± √b² -4ac /2a

where the quadratic equation =

ax² + bx + c = 0

a = -16 , b = 4 , c = 20

x = -16 ± √4² - 4×-16×20 / 2×-16

x = -1 or ,1.25

Therefore it would take her 1.25 seconds to land safely in the net

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3 years ago