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Law Incorporation [45]
3 years ago
10

the function f(x)= x+3 represents the length of a rectangle. the function g(x)=12x-5 represents the width of the rectangle. use

(f • g)(3) to determine the area of the rectangle.
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
6 0

Answer:

(f • g)(3) = 186

Step-by-step explanation:

The area of a rectangle is (length)(width).

Here, (length) = x + 3 and (width) = 12x - 5, and so the area as a function of x is

(f • g)(x) = (x + 3)(12x - 5) = 12x^2 - 5x + 36x - 15.

This simplifies to:

(f • g)(x) = (x + 3)(12x - 5) = 12x^2 + 31x - 15.

Evaluating this function at x = 3, as instructed, we get:

 (f • g)(3) = (12)( - 5) = 12(3)^2 + 31(3) - 15.

Carrying out the indicated operations, we get:  108 + 93 - 15, or

(f • g)(3) = 186

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the straight line L has the equation 4y=5x+3. Point A has the coordinates (3,-2) Find the equation of the line straight line tha
Aleonysh [2.5K]

Answer:

y = - \frac{4}{5} x + \frac{2}{5}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4

y = \frac{5}{4} x + \frac{3}{4} ← in slope- intercept form

with slope m = \frac{5}{4}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{5}{4} } = - \frac{4}{5} , thus

y = - \frac{4}{5} x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = - \frac{12}{5} + c ⇒ c = - 2 + \frac{12}{5} = \frac{2}{5}

y = - \frac{4}{5} x + \frac{2}{5} ← equation of perpendicular line

4 0
2 years ago
A fuel tank contains 1 3/4 gallons of gasoline. Casey adds 33 1/3 gallons of gasoline to the tank. How many gallons of gas does
krek1111 [17]

Answer:

35 1/12 gallons of gasoline

Step-by-step explanation:

so what you're going to do is take both of the fractions (3/4 and 1/3) and convert them into two fractions with the same denominator so you can add them easily. the closest number that you can convert them to would be a denominator of 12, so we would turn 3/4 into its equivalent of 9/12 and 1/3 would now be 4/12. now we add them and get 13/12, which is an improper fraction, so we would change that to 1 and 1/12. and finally, we add 1 1/12 + 1 + 33 and we would get 35 and 1/12 as our final answer :)

6 0
3 years ago
Cos (A+B) =1/5<br>COS (A-B) = 3/5<br>Then find tan (A-B)​
Soloha48 [4]

Answer:

tan (A-B)​ = ± 4/3

Step-by-step explanation:

COS (A-B) = 3/5

COS² (A-B) = (3/5)² = 9/25 = 1 - sin² (A-B)

sin² (A-B) = 1 - 9/25 = 16/25

sin (A-B) = ± 4/5

tan (A-B) = sin (A-B) / cos (A-B) = (± 4/5) / (3/5) = ± 4/3

4 0
3 years ago
hey, can someone please double check these questions for me / or help me solve them if they are incorrect? thank you U-U ​
zzz [600]

Question 11

The directrix is a horizontal line, which means the parabola opens either upward or downward. In this case, it opens downward. This is because all answer choices have a negative leading coefficient. Also, it's because the focus is below the directrix.

For vertically opening parabolas, we use this form

4p(y-k) = (x-h)^2

where (h,k) is the vertex and p is the focal distance, aka the distance from the vertex the focus. To find (h,k), we start at the focus (0,-4) and move directly up until we reach the directrix y = 4. We'll arrive at (0,4). The midpoint of (0,-4) and (0,4) is (0,0) which is the vertex's location. So (h,k) = (0,0).

Note that in moving from (0,-4) to (0,4) is a span of 4 units. So this is the value of p.

Plug h = 0, k = 0, p = 4 into the equation mentioned and solve for y

4p(y-k) = (x-h)^2

4*4(y-0) = (x-0)^2

16y = x^2

y = (1/16)x^2

The only adjustment we need to make is to change the 1/16 to -1/16 so that the parabola opens downward.

<h3>Answer:  Choice D.  y = -(1/16)x^2</h3>

===============================================

Question 3

The given equation is in the form y = ax^2+bx+c

In this case,

  • a = 2
  • b = 4
  • c = 3

Let's compute the x coordinate of the vertex h

h = -b/(2a)

h = -4/(2*2)

h = -1

This h value is plugged into the original function to find k

f(x) = 2x^2+4x+3

f(-1) = 2(-1)^2+4(-1)+3

f(-1) = 1

We find that h = -1 and k = 1 pair up together. In short, (h,k) = (-1,1) is the vertex.

<h3>Answer: Choice B.  (-1,1)</h3>
8 0
2 years ago
Fifty balls are numbered 1 to 50 and a red dot is painted on those balls that are a multiple of 6. The balls are mixed into a ba
djyliett [7]

Answer:

the answer is 1350

Step-by-step explanation:

i got it right

7 0
3 years ago
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