Question 8 of 10
What is the sum of the roots of the polynomial shown below?
f(x) = x3 + 2x2 – 118 - 12
Answer here

Answer:

Part A)

The slope is two.

Part B)

[tex]\displaystyle y = 2x - 7[/tex]

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

[tex]\displaystyle y = x^2 - 2x - 3[/tex]

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]

Since we want to find the slope of the curve at P(2, -3), x = 2.

Substitute:

[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]

Simplify. Note that f(2) = -3. Hence:

[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]

Substitute. m = 2. Therefore, our equation is:

[tex]\displaystyle y + 3 = 2(x-2)[/tex]

We can rewrite this into slope-intercept if desired:

[tex]\displaystyle y = 2x - 7[/tex]

We can verify this by graphing. This is shown below:

Answer:

64 km per hour

Step-by-step explanation:

544/8.5=64

Answer: x = 1

Step-by-step explanation:

Given

3/2 + (1/2)x = 2x

Multiply 2 on both sides to cancel out the denominator

2 · [3/2 + (1/2)x] = 2 · 2x

3 + x = 4x

Subtract x on both sides

3 + x - x = 4x - x

3 = 3x

Divide 3 on both sides

3 / 3 = 3x / 3

[tex]\boxed {x=1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Area is the total surface covered by the shape and perimeter is the total length of the shape.

Answer:

-5/4

Step-by-step explanation:

C is at the point (2,3) and D is at the point (6,-2)

-2-3 = -5 which would be the top part and 6-2=4 and that's the bottom part.

Answer:

1992

Step-by-step explanation:

Let x be the amount invested at 12%.

Then the rest amount is (21360-x) dollars.

The 12% stock earning is 0.12x dollars.

The rest amount loss  is 0.05*(21360-x) dollars.

Your equation is

interest - loss            = total interest,    or

0.12x     - 0.05*(21360-x) = 1992    dollars.

Simplify and solve for x.

Answer:

It'll be the same figure- an acute isoceles triange

Step-by-step explanation:

Reflection is just copying the same shape across the x-axis (the main horizontal line on graphs) or the y-axis (the main vertical line on graphs). It's like looking at yourself in the mirror, like a reflection!

Answer:

the difference between the temperatures is -50.9. f=-50.9

Step-by-step explanation:

33.6°F+17.3°F=50.9

33.6°F+F= -17.3°F

33.6°F+(-50.9°F= -17.3°F

so, F=-50.9°F

Step-by-step explanation:

d=T2-T1=(-17.3-33.6)=-50.9°F

(a) X has a probabiliity density of

[tex]f_X(x) = \begin{cases}\dfrac1{b-a}&\text{if }a<x<b\\0&\text{otherwise}\end{cases}[/tex]

If the lower quartile is 5 and the upper quartile is 9, then

[tex]\displaystyle \int_a^5 f_X(x)\,\mathrm dx = 0.25 \text{ and } \int_9^b f_X(x)\,\mathrm dx = 0.25[/tex]

Computing the integrals gives the following system of equations:

[tex]\displaystyle \int_a^5\frac{\mathrm dx}{b-a} = \frac{5-a}{b-a} = 0.25 \\\\ \int_9^b \frac{\mathrm dx}{b-a} = \frac{b-9}{b-a} = 0.25[/tex]

5 - a = 0.25 (b - a)   ==>   0.75a + 0.25b = 5   ==>   3a + b = 20

b - 9 = 0.25 (b - a)   ==>   0.25a + 0.75b = 9   ==>   a + 3b = 36

Eliminate a :

(3a + b) - 3 (a + 3b) = 20 - 3×36

-8b = -88

==>   b = 11   ==>   a = 3

and so P(X = x) = 1/(11 - 3) = 1/8 for all 3 < x < 11.

(b)

[tex]\displaystyle P(6<X<7) = \int_6^7f_X(x)\,\mathrm dx = \int_6^7\frac{\mathrm dx}8 = \boxed{\frac18}[/tex]

(c) The distribution function is then

[tex]\displaystyle F_X(x) = \int_{-\infty}^x f_X(t)\,\mathrm dt = \begin{cases}0&\text{if }x\le3 \\ \dfrac x8 &\text{if }3<x<11 \\ 1&\text{if }x\ge11\end{cases}[/tex]

Answer:

f(x) = [tex]-2^{x+1}-1[/tex]

Step-by-step explanation:

I. If you see (0, -3) point on the green line

II. Perform x = 0, if y = -3 means the statement is true

    = [tex]-2^{0+1} - 1[/tex]

    = [tex]-2^{1}[/tex] - 1

    = -2 - 1

  y = -3

Got more question or somethin to discuss? Leave comment below

Answer:

c part is correct answer

Answer: D) 240 cm^3

Step-by-step explanation:

On edge

Answer:

exponent is -3 and coefficient is 4

Answer:

c

Step-by-step explanation:

thats the anser

9514 1404 393

Explanation:

Add sin(θ)

  cos(θ) = sin(θ)

Divide by cos(θ)

  1 = sin(θ)/cos(θ) = tan(θ)

Square both sides

  1 = tan²(θ)

Add 1

  2 = tan²(θ) = sec²(θ)

Take the square root

  √2 = sec(θ) . . . . for 0 < θ < π

_____

Additional comment

The equation cos(θ) -sin(θ) = 0 has two solutions: θ = π/4 and θ = 5π/4. For the first-quadrant solution, sec(θ) = √2. For the third-quadrant solution, sec(θ) = -√2.

Answer:

13.6122

Step-by-step explanation:

(x-18.6)/15.3=-0.326

x-18.6=-0.326*15.3

x-18.6=-4.9878

x=-4.9878+18.6

x=13.6122

Answer:

B

I just did it and got it right

Step-by-step explanation:

a²=b²

since a=b, therefore we can write a in place of b or b in place of a,

a²=a² or b²=b²

Hence, it is proved.

I hope it helped U

I hope it helped Ustay safe stay happy

Answer:

B

Step-by-step explanation:

It just is

let length be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]

[tex]\\ \sf\longmapsto x=4(28)[/tex]

[tex]\\ \sf\longmapsto x=112[/tex]

Answer:

Step-by-step explanation:

There are 420 students.

41% are first year students.

41% = 41/100

420 * 41/100 = 172.4

What do you do about the 0.4? I would just round to the nearest whole number which is 172.

There are 420 - 172 = 248 who are not first year students.

Answer: B

Step-by-step explanation:

The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

From the given patterns

Figure 1 has 5 lines and it is blue in color.

Figure 2 has 4 lines and it is red in color.

Figure 3 has 3 lines and it is blue in color.

So, Figure 4 must has 2 lines and red in color.

Therefore, option B is the correct answer.

Learn more about the pattern here:

https://brainly.com/question/23136125.

#SPJ7

Answer:

(m - 43)/2m

Step-by-step explanation:

Step-by-step explanation:

Hahahaha this is math.lol

9514 1404 393

Answer:

  x = -4

Step-by-step explanation:

Put the given point in the equation and solve for x.

  4x = 5(-3) -1

  4x = -16 . . . . . . simplify

  x = -4

B

if it is not correct sory

Diagram B is a proper demonstration of an angle bisector.

Letter A is wrong because they are a set of intersecting ines.

Letter C is wrong because they are a set of parallel lines.

Letter D is wrong because they are also a set of perpendicular lines.

So, now, we know that Letter B is the correct answer. The reason for this is also because ∠ACD is bisected by line B.

I hope that this helped answer your question. Have a good day!