All categories

3 years ago

Find f(0), if not supplied, and then find the equation of the given linear function.

Mathematics

1 answer:

My name is Ann [436]3 years ago

3 0

Answer:

Part 1) $f(0)=2$

Part 2) $f(x)=3x+2$

Step-by-step explanation:

Part 1) Find f(0)

we know that

Looking at the data in the table

When the value of x increases by 1 unit, the value of y increases by 3 units

therefore

When the value of x decreases by 1 unit from 1 to 0, the value of y would decreases 3 units from 5 to 2

thus

$f(0)=2$

This value represent the y-intercept

Part 2) Find the equation of the given linear

Find the slope

take the points (1,5) and (2,8)

$m=(8-5)/(2-1)=3$

The equation of the line in slope intercept form is equal to

$f(x)=mx+b$

we have

$m=3\\b=2$

substitute

$f(x)=3x+2$

You might be interested in

posledela

Answer:

The bakery will bake 600 butterscotch bread, 550 chocolate bread, and 1,000 coconut bread

Step-by-step explanation:

In order to answer the word problem question, we list the parameters as follows;

The number of bread types the bakery takes = 3 types of bread

The monthly cost of the bakery for baking the bread, C = RM 6,850

The number of bread loaves baked = 2,150

The cost of baking a loaf of butterscotch bread = Rm 2

The cost of baking a loaf of chocolate bread = Rm 3

The cost of baking a loaf of coconut bread = Rm 4

The sale price of a butterscotch bread = Rm 3

The sale price of a chocolate bread = Rm 4.50

The sale price of a coconut bread = Rm 5

The amount of monthly profit the bakery makes, P = Rm 2,975

Therefore, the total revenue of the company, R = C + P

∴ R = Rm 6,850 + Rm 2,975 = Rm 9,825

Let 'x', 'y', and 'z', represent the number of loaves of butterscotch, chocolate, and coconut bread the company bakes respectively

Then we get;

x + y + z = 2,150...(1)

2·x + 3·y + 4·z = 6,850...(2)

3·x + 4.5·y + 5·z = 9,825...(3)

Multiplying equation (1) by 2 and subtracting from equation (2) gives;

2·x + 3·y + 4·z - 2×(x + y + z) = 6,850 - 2 × 2,150 = 2,550

2·x - 2·x + 3·y - 2·y + 4·z - 2·z = 2,550

∴ y + 2·z = 2,550...(4)

Adding equation (1) to (2) and subtracting from (3) gives;

3·x - 3·x + 4.5·y - 4·y + 5·z - 5·z = 9,825 - (6,850 + 2,150) = 825

1.5·y = 825

y = 825/1.5 = 550

The number of loaves of chocolate bread baked, y = 550

From equation (4), we get;

550 + 2·z = 2,550

2·z = 2,550 - 550 = 2,000

z = 2,000/2 = 1,000

The number of loaves of coconut bread baked, z = 1,000

∴ From equation (1) x = 2,150 - (550 + 1,000) = 600

The number of loaves of butterscotch bread baked, x = 600.

3 0

2 years ago

Area=<br> Help me please!! Thanks :)

Savatey [412]

Answer:

80π

Step-by-step explanation:

Circle O with radius IO:

large radius = IO = 12 = R

Circle O with diameter JK

IJ = JK = KL = 2 × IO = 24

IJ = JK = KL = 24/3 = 8

small radius = 8/2 = 4 = r

The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.

That is the same as

1 semicircle of radius 12 plus 1 semicircle of radius 4

A = πR²/2 + πr²/2

A = π(12² + 4²)/2

A = 160π/2

A = 80π

8 0

2 years ago

Solve the following inequality. <br> 2P-3>P+6

MakcuM [25]

The answer is P>9 The number line (if needed is)

8 0

2 years ago

Read 2 more answers

-6 = u/ -1 +-4 what's u

yuradex [85]

Answer:

the answer to your question is U=2

Step-by-step explanation:

6 0

2 years ago

Help please 1. Describe the transformations necessary to transform the graph of

natta225 [31]

Here are all the steps, and what they do:

STEP 1: HORIZONTAL TRANSLATION

We transform

$x^2\mapsto (x-1)^2$

The general transformation is

$f(x)\mapsto f(x+k)$

These transformations translate the graph horizontally, k units to the left if k>0, k units to the right if k<0.

In this case, k = -1, so we translate the original graph 1 unit to the right.

STEP 2: VERTICAL STRETCH

We transform

$(x-1)^2\mapsto 3(x-1)^2$

The general transformation is

$f(x)\mapsto kf(x)$

These transformations stretch the graph vertically. The graph expands if |k|>1, while it shrinks if 0<|k|<1. If k is negative, we also reflect the graph with respect to the x axis.

In this case, k = 3, so we stretch the graph vertically by a factor 3.

STEP 3: VERTICAL TRANSLATION

We transform

$3(x-1)^2\mapsto 3(x-1)^2+4$

The general transformation is

$f(x)\mapsto f(x)+k$

These transformations translate the graph vertically, k units up if k>0, k units down if k<0.

In this case, k = 4, so we translate the graph 4 units up.

So, we start from the original graph of $f(x)=x^2$ and we:

Translate it 1 unit to the right
Stretch it vertically by a factor 3
Translate it 4 units up

(the order is important!)

to get the graph of $g(x)=3(x-1)^2+4$

4 0

2 years ago