All categories

2 years ago

F(x)=3x+2 and g(x)=-2x-4, find h(x) = f(x)-g(x)

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

6 0

Answer:

5x-2

Step-by-step explanation:

Since f(x)-g(x) you take 3x+2 and subtract -2x-4.

3x+2+2x-4

5x-2

You might be interested in

Help how do you do this help fast please

GalinKa [24]

Answer:

x= 50°

Hope it helps!

Step-by-step explanation:

The sum of the exterior angles of a polygon is always 360°

So, x+40+x+20+2x+2x = 360

6x + 60= 360

6x = 360-60 = 300

6x= 300

x= 300/6

= 50

7 0

2 years ago

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

pochemuha

Answer:

The quadratic function whose graph contains these points is $y=-x^{2}-2x-2$

Step-by-step explanation:

We know that a quadratic function is a function of the form $y=ax^{2}+bx+c$ . The first step is use the 3 points given to write 3 equations to find the values of the constants a,b, and c.

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

$-2=a*0^{2}+b*0+c\\c=-2$

$-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17$

$-17=a*3^{2}+b*3+c\\ c=-9a-3b-17$

We can solve these system of equations by substitution

Substitute $c=-9a-3b-17$

$-9a-3b-17=25a+5b-17\\-9a-3b-17=-2$

Isolate a for the first equation

$-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}$

Substitute $a=\frac{b}{2}$ into the second equation

$-9\left(-\frac{b}{2}\right)-3b-17=-2$

Find the value of b

$-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2$

Find the value of a

$a=\frac{b}{2}\\ a=-1$

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

$y=-x^{2}-2x-2$

As you can corroborate with the graph of this function.

8 0

2 years ago

Can an area of a polygon be zero? true or false

Nata [24]

False. If the area is 0 that means there is nothing there, therefore the area of a polygon cannot be zero.

4 0

2 years ago

Read 2 more answers

Aaron was offered a job that paid a salary of \$57,000$57,000 in its first year. The salary was set to increase by 1% per year e

Jobisdone [24]

Answer:

The total amount received is: $1906650

Step-by-step explanation:

Given

$a = \$57000$ --- initial

$b = 1\%$ --- rate

$n = 29$ --- time

Required

Determine the total amount at the end of 29 years

The given question is an illustration of geometric progression, and we are to solve for the sum of the first n terms

Where $n = 29$

$r = 1 + b$

$r = 1 + 1\%$

Express percentage as decimal

$r = 1 + 0.01$

$r = 1.01$

The required is the calculated using:

$S_n = \frac{a(r^n - 1)}{r - 1}$

So, we have:

$S_n = \frac{57000 * (1.01^{29} - 1)}{1.01 - 1}$

$S_n = \frac{57000 * (1.3345- 1)}{0.01}$

$S_n = \frac{57000 * 0.3345}{0.01}$

$S_n = \frac{19066.5}{0.01}$

$S_n = 1906650$

The total amount received is: $1906650

8 0

2 years ago

The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 85% p

djyliett [7]

Let x = amount of 70% juice we use.

Then 60-x = amount of 85% juice we'll use.

We'll set up an equation that is based on how much pure juice comes from each component and how much we need in the final mixture.

So 70% of x plus 85% of (60-x) must equal 80% of 60, or...

0.7x + 0.85(60-x) = 0.8(60)

0.7x + 51 - 0.85x = 48

-0.15x + 51 = 48

-0.15x = -3

x = 20

Then 60 - x = 60 - 20 = 40

Check: 70% of 20 pints = 14 pints of pure juice.

85% of 40 pints = 34 pints of pure juice

That's 48 pints of pure juice in the mix, which matche 80% 0f 60 pints.

You'd need 20 pints of the 70% juice and 40 pints of the 85% juice.

4 0

2 years ago