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Romashka-Z-Leto [24]
3 years ago
11

Given the following functions f(x) and g(x), solve (f + g)(3) and select the correct answer below:

Mathematics
2 answers:
kati45 [8]3 years ago
8 0
(f+g)(3) = f(3) + g(3) = 6(3) + 3 + 3 -7 = 18 +6 -7 = 17.

Answer: 17
Ann [662]3 years ago
3 0

Answer:

Option B is correct

(f+g)(3) = 17

Step-by-step explanation:

Given the functions:

f(x) = 6x+3

g(x) = x-7

Solve: (f+g)(3)

First do:

(f+g)(x) = f(x)+g(x)

Substitute the given values we have;

(f+g)(x) = 6x+3+x-7 = 7x-4

Put x = 3 above we have;

(f+g)(3) = 7(3)-4 = 21-4=17

Therefore, the value of (f+g)(3) is 17

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3 Simplify the expression: 5! 2:3! 4. Simplify the expression:​
vredina [299]

Answer:

10

Step-by-step explanation:

5! 2:3! 4  \\  \\ =  \frac{5! \:  .2}{3! \: . 4}  \\  \\  =  \frac{5.4. \cancel{3!} \: . 2}{\cancel{3!} \:  .4}  \\  \\  =  \frac{40}{4}  \\  \\  = 10

6 0
3 years ago
Find the total number of outcomes from rolling a number cube with sides labeled 1-6 and choosing a letter from the word "NUMBERS
Irina18 [472]

Answer:

........................................................................................

Step-by-step explanation:

4 0
3 years ago
Write the slope-intercept form of the equation of the line through the given points:
vredina [299]

Answer:

equation of line

x-2y=8

Step-by-step explanation:

equation of line in slope intercept form

(y-y1)={(y2-y1)/(x2-x1)}(x-x1)

 or,(y+3)={(-5+3)/(-2-2)}(x-2)

 or,(y+3)=(1/2)(x-2)

  or,2y+6=x-2

   or,6+2    =x-2y  

or,x-2y=8

3 0
2 years ago
Answer each question below.
HACTEHA [7]

Answer:

\huge\boxed{\sf L = 78\°}

Step-by-step explanation:

<h3><u>Given that:</u></h3>

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

<h3><u>Statement:</u></h3>
  • Exterior angle is equal to the sum of non-adjacent interior angles.

So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.

Here,

Exterior angle of L = M + N

5x + 12 = 3x - 2 + 50

5x + 12 = 3x + 48

Subtract 12 to both sides

5x = 3x + 48 - 12

5x - 3x = 36

2x = 36

Divide 2 to both sides

x = 18

So,

<h3><u>Measure of angle M:</u></h3>

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

<h3><u>Measure of angle L:</u></h3>

<u>We know that,</u>

  • Sum of all the interior angles of triangle is 180 degrees.

L + M + N = 180°

L + 52 + 50 = 180

L + 102 = 180

Subtract 102 to both sides

L = 180 - 102

L = 78°

\rule[225]{225}{2}

7 0
2 years ago
Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,
MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

       $=0-0+6$

       $=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

   It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴  x coordinate = $\frac{-(-7)}{2 \times 1} $

                         $\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

         = -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get   $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts  are the points where the parabola crosses the x-axis, which is the height $h(x)=0$. The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$.

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0
2 years ago
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