All categories

3 years ago

Need help with this problem

Mathematics

1 answer:

Viefleur [7K]3 years ago

4 0

Answer:

h(x) = -x² + 11 x + 2

Step-by-step explanation:

Explanation:-

Given that the functions are

f(x) = 2 x² - 5x -3

g(x) = x² + 6x -1

h(x) = g(x) - f(x)

= x² + 6x -1 - (2 x² - 5x -3)

= - x² + 6 x +5x -1+3

= -x² + 11 x + 2

h(x) = -x² + 11 x + 2

Final answer:-

h(x) = -x² + 11 x + 2

You might be interested in

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

AnnZ [28]

Answer:

$\textsf{Factored form}: \quad f(x)=2x(x-4)$

$\textsf{Vertex form}: \quad f(x)=2(x-2)^2-8$

Step-by-step explanation:

Factored form of a quadratic function

$f(x)=a(x-p)(x-q)$

where:

p and q are the x-intercepts
a is some constant

Given x-intercepts:

(0, 0)
(4, 0)

Therefore:

$\implies f(x)=a(x-0)(x-4)$

$\implies f(x)=ax(x-4)$

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

$\implies 2a(2-4)=-8$

$\implies -4a=-8$

$\implies a=2$

Therefore, the function's equation in factored form is:

$f(x)=2x(x-4)$

Vertex form of a quadratic equation

$f(x)=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given:

vertex = (2, -8)

Therefore:

$\implies f(x)=a(x-2)^2-8$

To find the constant a, substitute one of the x-intercepts into the equation and solve for a:

$\implies a(0-2)^2-8=0$

$\implies 4a-8=0$

$\implies a=2$

Therefore, the function's equation in vertex form is:

$f(x)=2(x-2)^2-8$

4 0

2 years ago

Read 2 more answers

Two angles of a triangle are 47 and 32 degrees. Select all angles that could represent exterior angles of a triangle.

notsponge [240]

Answer:

133, 79, 148 are ALL possible, so select 133 and 79

Step-by-step explanation:

Subtract 47 and 32 from 180 to find the third angle of the triangle (it is 101).

Then do 180-101 = 79

180-32=148

180-47=133

That tells you the exterior angle of each. Only two possible choices on your list.

3 0

2 years ago

What is the volume of a rectangular prism with a height of 8in, width of 13in, and a length of 2ft? Give your answer in cubic in

Agata [3.3K]

Volume of rectangular prism
=length*width*height
=8" * 13" * 2'
=8" * 13" * 2*12"
=8*13*2*12 cubic inches
=2496 cubic inches.

7 0

3 years ago

Read 2 more answers

A machine produces 75 widgets an hour. How many widgets does it produce in 6 minutes.

AVprozaik [17]

Greetings!

"A machine produces 75 widgets an hour. How many widgets does it produce in 6 minutes?"...

An hour/60 minutes is ten times more than 6.
Therefore, we divide the amount per hour by ten:
75/10
=7.5

The machine produced 7.5 widgets /7 full widgets every six minutes.

Hope this helps.
-Benjamin

3 0

4 years ago

Steven is moving to another city next weekend and wants to rent a moving truck. The rental rates for two companies in his area a

ASHA 777 [7]

Answer:

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Company (2) is $7.4 cheaper.

Step-by-step explanation:

From the tables given in the picture,

Let the equation representing the rental 'y' and distance traveled 'x' is represented by,

y = mx + b

For company (1),

Here m = per mile rental charges = Slope of the graph

b = Initial charges

Since slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,

m = $\frac{87.15-53.55}{60-30}$ = $1.12 per mile

So the equation will be,

y = 1.12x + b

Since this line passes through (30, 53.55),

53.55 = 1.12(30) + b

b = 53.55 - 33.6

b = 19.95

So the expression representing charges for the company (1) will be,

y = 1.12x + 19.95

For company (2),

Per mile charges = slope of the line

m = $\frac{78-56.75}{50-25}$

m = $0.85 per mile

Equation for the charges will be,

y = 0.85x + b

Since this line passes through (25, 56.75),

56.75 = 0.85(25) + b

b = 56.75 - 21.25

b = 35.5

Therefore, equation representing total charges for company (2) will be,

y = 0.85x + 35.5

By comparing per mile charges,

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Steven plans to drive 85 km in rental truck.

Charges for company (1),

y = 1.12x + 19.95

y = 1.12(85) + 19.95

y = $115.15

Charges for company (2),

y = 0.85x + 35.5

y = 0.85(85) + 35.5

y = $107.75

Difference in charges of both the companies = 115.15 - 107.75 = $7.4

Therefore, company (2) is $7.4 cheaper.

6 0

3 years ago

Need help with this problem ​

Need help with this problem