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____ [38]
3 years ago
7

If f(x)= 3x^2+1 and g(x)= 1-x, what is the value of (f-g)(2)?

Mathematics
1 answer:
enyata [817]3 years ago
3 0

Answer:

14

Step-by-step explanation:

note that (f - g) = f(x) - g(x)

f(x) - g(x) = 3x² + 1 - (1 - x) = 3x² + 1 - 1 + x = 3x² + x

To evaluate (f - g)(2) substitute x = 2 into f(x) - g(x)

(f - g)(2) = 3(2)² + 2 = (3 × 4) + 2 = 12 + 2 = 14

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Solve the system of equations
rewona [7]

Answer:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

Here we have a system of 3 equations with 3 variables:

4*x + 2*y + 1 = 1

2*x - y = 1

x + 3*y + z = 1

The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:

2*x - y = 1

2*x - 1 = y

Now that we have an expression equivalent to "y", we can replace this in the other two equations:

4*x + 2*(2*x - 1) + 1 = 1

x + 3*(2*x - 1) + z = 1

Now let's simplify these two equations:

8*x - 1 = 1

7*x - 3 + z = 1

Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:

8*x - 1 = 1

8*x = 1 + 1 = 2

x = 2/8 = 1/4

Now that we know the value of x, we can replace this in the other equation to find the value of z.

7*(1/4) -3 + z = 1

7/4 - 3 + z = 1

z = 1 + 3 - 7/4

z = 4 - 7/4

z = 16/4 - 7/4 = 9/4

z = 9/4

Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:

y = 2*(1/4) - 1

y = 2/4 - 1

y = 1/2 - 1

y = -1/2

Then the solution is:

x = 1/4

y = -1/2

z = 9/4

7 0
3 years ago
Find the slope of the line passing through the two points: (1, -2) and (-3, -7)
GarryVolchara [31]

Answer:

5/4

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Determine the value of x
KATRIN_1 [288]

Answer:

The value of x is 12 feet

Step-by-step explanation:

The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.

To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.

Area of rectangle = length X breadth

Area of triangle = 1/2 base X height.

However, to calculate the area of the triangle, we need to find its height first.

The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.

Height of triangle = 16 ft - 10 ft = 6 ft

recall area = 156 square feet.

We now have most of our missing dimensions

We can now set up an equation as follows:

(10 \times x) +0.5 \times x \times 6 = 156

10x +3x=156\\13x=156\\x=12 feet

Therefore the value of x is 12 feet

8 0
3 years ago
An office supply company sells two types of fax
Phantasy [73]

14 of the machine that cost $150 was sold and 8 of the machine that cost $225 was sold.

To solve this problem, we would write a system of linear equations.

  • Let x represent the machine that cost $150
  • Let y represent the machine that cost $225

We can proceed to write our equations now.

x + y = 22...equation(i)\\150x + 225y = 3900...equation(ii)

From equation 1

x+ y = 22\\x = 22 - y...equation (iii)

<h3>The Value of Y</h3>

put equation (iii) into (ii)

150x + 225y =3900\\x = 22-y\\150(22-y)+225y=3900\\3300-150y+225y=3900\\3300+75y=3900\\75y=3900-3300\\75y=600\\75y/75=600/75\\y=8

<h3>The Value of X</h3>

Since we know the number of y, we can simply substitute it into equation (i) and solve.

x + y = 22\\x + 8 = 22\\x = 22-8\\x = 14

From the calculations above, 14 of the machine that cost $150 was sold and 8 of the machine that cost $255 was sold.

Learn more about system of equations here;

brainly.com/question/13729904

3 0
3 years ago
What is the measure of the angle x?​
navik [9.2K]
AOB = 2 . x
2x = 60°
x = 30°
4 0
3 years ago
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