All categories

2 years ago

Find f (-2) f(x)= 3x^2 - 8x + 7

Mathematics

1 answer:

Maslowich2 years ago

8 0

Answer: Solving for f. Want to solve for x instead?

1 Remove parentheses.

f\times -2fx=3{x}^{2}-8x+7f×−2fx=3x

 −8x+7

2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

 x

 =x

a+b

 .

-{f}^{2}\times 2x=3{x}^{2}-8x+7−f

 ×2x=3x

 −8x+7

3 Regroup terms.

-2{f}^{2}x=3{x}^{2}-8x+7−2f

 x=3x

 −8x+7

4 Divide both sides by -2−2.

{f}^{2}x=-\frac{3{x}^{2}-8x+7}{2}f

 x=−

3x

 −8x+7

5 Divide both sides by xx.

{f}^{2}=-\frac{\frac{3{x}^{2}-8x+7}{2}}{x}f

 =−

3x

 −8x+7

6 Simplify \frac{\frac{3{x}^{2}-8x+7}{2}}{x}

3x

 −8x+7

 to \frac{3{x}^{2}-8x+7}{2x}

2x

3x

 −8x+7

 .

{f}^{2}=-\frac{3{x}^{2}-8x+7}{2x}f

 =−

2x

3x

 −8x+7

7 Take the square root of both sides.

f=\pm \sqrt{-\frac{3{x}^{2}-8x+7}{2x}}f=±√

−

2x

3x

 −8x+7

8 Simplify \sqrt{-\frac{3{x}^{2}-8x+7}{2x}}√

−

2x

3x

 −8x+7

 to \sqrt{\frac{3{x}^{2}-8x+7}{2x}}\imath√

2x

3x

 −8x+7

 ı.

f=\pm \sqrt{\frac{3{x}^{2}-8x+7}{2x}}\imathf=±√

2x

3x

 −8x+7

 ı

9 Regroup terms.

f=\pm \imath \sqrt{\frac{3{x}^{2}-8x+7}{2x}}f=±ı√

2x

3x

 −8x+7

Done- :)

f=±ı√ 2x 3x 2 −8x+7

Step-by-step explanation

You might be interested in

{HIGH PAYOUT} Can someone help by showing work on how to get to answer?

Gala2k [10]

Let's assume each line is one toothpick.

In figure 1, there is a square made out of the 4 toothpicks.

In figure 2, there are four squares made. However, the 4 four toothpicks were already used, so we don't count them twice. That gives 4 (that were used) + 3 (the new ones on the left) + 3 (new ones on top) + 3 (new ones on right). We sum them up: 4 + 3 + 3 + 3 = 13.

In figure 3 there are nine squares made. We have the 13 squares made, plus 3 on the left column, 2 on the left center column, 3, on the center column, 2 on the right center, and 3 on the right. We total them up. 13 + 3 + 2 + 3 + 2+ 3 = 26.

Let's look at the pattern.

Figure # # Toothpicks

1 4

2 13

3 26

From figure 1 to 2, we added 9. From 2 to 3 we added 13. If we draw figure 4, we would add (from left to right) 3, 2, 2, 3, 2, 2, 3. That would be 17 toothpicks added, and 39 total. Let's go back to the table.

Figure # # Toothpick

1 4

2 13

3 26

4 39

Now let's look at the sequence happening. As we add more, we increase by 9, then 13, then 17. For each row, we add the same number as the previous row and then add 4. Drawing Figure 5 would be too much, but we can conclude based on the pattern that 21 squares would be added. We can take this sequence as far as we need to. We want the 10th figure or term, so we apply the pattern and keep going until we get there.

Figure # # Toothpick

1 4

2 13 <--- add 9

3 26 <--- add 13, the same 9 and 4 more

4 39 <--- add 17, the same 13 and 4 more

5 60 <--- add 21, the same 17 and 4 more

6 85 <-- add 25, the same 21 and 4 more

7 114 <-- add 29, the same 25 and 4 more

8 147 <-- add 33

9 184 <---- add 37

10 225 <-- add 41

Thus the 10th figure has 225 toothpicks.

5 0

3 years ago

Please help!! Geometry, will mark brainliest!

melisa1 [442]

Answer:

n = 36

Step-by-step explanation:

The opposite sides of a parallelogram are congruent , that is

AB = DC , substitute values

$\frac{2}{3}$ n - 5 = $\frac{1}{3}$ n + 7 ( multiply through by 3 to clear the fractions )

2n - 15 = n + 21 ( subtract n from both sides )

n - 15 = 21 ( add 15 to both sides )

n = 36

8 0

3 years ago

Read 2 more answers

A triangle has sides with lengths of 8 inches, 15 inches, and 17 inches. Is it a right triangle?

In-s [12.5K]

Answer:

Yes

Step-by-step explanation:

A square plus b square equal c square

3 0

3 years ago

Read 2 more answers

write the equation of the parabola and a vertex form and standard form given the following information

beks73 [17]

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

(9)

Here (h, k) = (3, - 2), thus

y = a(x - 3)² - 2

To find a substitute (2, 3) into the equation

3 = a(2 - 3)² - 2 ( add 2 to both sides )

5 = a(- 1)² = a , then

y = 5(x - 3)² - 2 ← in vertex form

y = 5(x² - 6x + 9) - 2

= 5x² - 30x + 45 - 2

y = 5x² - 30x + 43 ← in standard form

(10)

Here (h, k) = (2, - 5), thus

y = a(x - 2)² - 5

To find a substitute (5, 4) into the equation

4 = a(5 - 2)² - 5 ( add 5 to both sides )

9 = a(- 3)² = 9a ( divide both sides by 9 )

a = 1

y = (x - 2)² - 5 ← in vertex form

y = x² - 4x + 4 - 5

y = x² - 4x - 1 ← in standard form

4 0

3 years ago

Read 2 more answers

7. License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we con

sergejj [24]

Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.

Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.

let $p_{1}$ be the probability that commercial cars have rear license plates and $p_{2}$ be the probability that connected trucks have rear license plates.

Cars Trucks Total

Total 2049 334 2383

x 239 45 284

p 0.1166 0.1347 0.1191

α=0.05

Hypothesis will be :

$H_{0}:p_{1} =p_{2}$

$H_{1} :p_{1} < p_{2}$

It is a left tailed test at 0.05 significance.

Standard errors of p= $\sqrt{p(1-p)/n}$

= $\sqrt{(0.1191*0.8809)/2383}$

= $\sqrt{0.1049/2383}$

=0.0066

Test statistic Z=p difference/standard error

=(0.1166-0.1347)/0.0066

=-0.0181/0.0061

=-2.967

p value=0.001505<5%

Since p is less than 5% we reject null hypothesis.

We cannot calculate standard deviation so we cannot calculate confidence interval.

Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

Learn more about z test at brainly.com/question/14453510

#SPJ4

5 0

2 years ago