Lines c and d are perpendicular. The slope of line c is −1/3. What is the slope of line d?

Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:

D The function has one real zero and two nonreal zeros.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the function is given by:

f(x) = x³ - 3x² + 16x + 48.

Using a calculator, the roots are given by:

[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]

The first root is real, while the second and third are complex(nonreal), hence option D is correct.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

#SPJ1

The arithmetic sequence has a common difference, and a first term and the 17th term in the arithmetic sequence is -21

The given parameters are:

The nth term of an arithmetic progression is:

Tn = a + (n - 1)d

So, we have:

T17 = a + 16d

Substitute the given values

T17 = 11 - 16 * 2

Evaluate

T17 = -21

Hence, the 17th term in the arithmetic sequence is -21

Read more about arithmetic sequence at:

https://brainly.com/question/6561461

#SPJ1

Answer:

250

Step-by-step explanation:

Bulb box and carton both are of cuboidal shape.

For bulb box the dimensions are:

For Carton the dimensions are:

To find the number of bulbs packed in the carton, divide the [tex]V_{Carton}[/tex] by [tex] V_{Bulb\: box}[/tex]

So, 250 bulbs will be packed in one carton.

Answer:

Gretta would be 2500 meters tall

Step-by-step explanation:

2km=2000 and the 1/2 would be 1/2=500 so the answer it 2500

Pls mark brainliest!!!!

Answer:

x= 27.71281 = 16√3

y= 13.85641 = 8√3

Step-by-step explanation:

hope it helps :)

Answer:

6m + 10

Step-by-step explanation:

Distributive Property

Solving

The measure of angle ACB for circle centered at point O is 21°

An equation is an expression that shows the relationship between two or more numbers and variables.

∠AOB = 2 * ∠ACB (angle at center is twice the angle at circumference)

42 = 2 * ∠ACB

∠ACB = 21°

The measure of angle ACB for circle centered at point O is 21°

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

23/5

Step-by-step explanation:

* means multiply

4 3/5

5 * 4 = 20

20 + 3 = 23

23/5

Answer:

[tex]\frac{23}{5}[/tex]

Step-by-step explanation:

The type of fraction we are dealing with is called a mixed fraction

In order to convert this fraction into a fraction greater than 1, we will have to convert it into an improper fraction

So we keep the denominator

Multiply the whole number by the denominator and add that to the numerator

root*324=18

441=21

529=23

hope it helps

please mark as brainliest

Step-by-step explanation:

there are some pieces of information missing like the price of apples and flour. or the selling prices. or any restrictions like a fixed budget to buy ingredients or how many pies and cobblers he can make in a certain available time.

all we can say based on the given information :

one pie = 4a + 3f (a = apples, f = flour)

one cobbler = 2a + 3f

P(x, y) = 3x + 2y =

= x(selling price - 4a - 3f) + y(selling price - 2a - 3f)

the max. of P(x, y) is the maximum profit by selling pies and cobblers, which is without any further information +infinity.

the more pies and cobblers he sells, the bigger the profit - no limit.

The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

For a right angle triangle, the trigonometry ratios can be given as,

[tex]\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}[/tex]

Here, a is base side, b is perpendicular side and c is the hypotenuse side of the triangle.

In the given triangle, the length of base side is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.

[tex]a=8\\b=6\\c=10[/tex]

Thus, the  tangent, cosine and sine ratios of angles X & Y are,

[tex]\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}[/tex]

Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

Learn more about the trigonometry angles here;

https://brainly.com/question/20519838

#SPJ1

Answer:

B

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

Given:

[tex]\implies \sf PMT=\dfrac{195000(0.066)(1+0.066)^{360}}{(1+0.066)^{360-1}}[/tex]

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-4,7)\qquad B(5,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-4,7)=1(5,1)[/tex]

[tex](\stackrel{x}{-8}~~,~~ \stackrel{y}{14})=(\stackrel{x}{5}~~,~~ \stackrel{y}{1})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8 +5}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{14 +1}}{1+2} \right)} \\\\\\ P=\left(\cfrac{-3}{3}~~,~~\cfrac{15}{3} \right)\implies P=(-1~~,~~5)[/tex]

now, the segment AB cut by P in a 1:2 ratio, makes 3 thirds, so the ratio AP/AB is

[tex]\cfrac{AP}{AB}\implies \cfrac{1}{1+2}\implies \cfrac{1}{3}[/tex]

Hi!!

Answer:

I'm not 100% sure, but I think it's 3.1.

Step-by-step explanation:

I took your volume, which is 125[tex]\pi[/tex], then a formula, which is

V=[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex], then I just plugged in the 125 and I got 3.1. I'm so sorry if it's wrong! <3

Answer:

x =6

Step-by-step explanation:

17x + 8 + 66 + 74 +110 = 360

17x + 258 =360

17x = 360 -258

17x =102

x =6

Apply angle sum property

Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.

Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.

Alex buys 30 shares of Walmart at the close price of $48.80.

His broker charges him 3% of each share.

Purchasing of 30 shares =48.80 *30

                                         =$1464

Now we have to find the 3% of total purchasing of shares.

So,

Broker's fees =[tex]\frac{3}{100}*1464[/tex]

                      = 0.03 * 1464

                      = 43.92

So, total cost of stock= 1464+43.92

                                   = 1507.92

Hence, Alex spend $1507.92 in total to buy this stock.

Learn more about shares here:

https://brainly.com/question/2120956

#SPJ1

Step-by-step explanation:

length × width = 24

2×length + 2×width = 22

length + width = 11

length = 11 - width

this we use in the first equation again :

(11 - width) × width = 24

11×width - width² = 24

width² - 11×width + 24 = 0

the general solution to an quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = -11

c = 24

and so we get

width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =

= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =

= (11 ± sqrt(25))/2 = (11 ± 5)/2

width1 = (11 + 5)/2 = 16/2 = 8 cm

width2 = (11 - 5)/2 = 6/2 = 3 cm

and teenaged to this is then

length1 = 11 - width1 = 11 - 8 = 3 cm

length2 = 11 - width2 = 11 - 3 = 8 cm

so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.

Answer:

2.5777

Step-by-step explanation:

Answer: 2.5777

Step-by-step explanation:

Given:

2.577681

Find the fourth decimal place:

2.577681

Round:

2.5777

Rounding:

Is the place to the right greater than or less than 5?

If greater than or equal to, round up. If less than, it stays the same.

    In this case, 8 > 5

Answer:

90 in²

Step-by-step explanation:

First,check the figure I provided .

Area of the figure = area1 + area2 + area3 + area4

= (3×2) + (7×7) + (7×2) + (7×6)÷2

= 6 + 49 + 14 + 21

= 90

Answer:

B. 3.114 > 3.112

D. 0.541 > 0.145

E. 0.141 < 0.19

Step-by-step explanation:

In order to determine which decimal is greater or less than another, compare the place values from left to right. First, compare the whole numbers to the left of the decimal point. If they are not the same, the smaller decimal number is the one with the smaller whole number. This applies to the rest of the places.

----------------------------------------------------

32.3 has a greater tenths value than 32.03, so 32.03 < 32.3. Option A is false.

----------------------------------------------------

3.114 has a greater thousandths value than 3.112, so 3.114 > 3.112. Option B is true.

----------------------------------------------------

4.003 has a greater whole number than 3.996, so 4.003 > 3.996. Option C is false.

----------------------------------------------------

0.541 has a greater tenths value than 0.145, so 0.541 > 0.145. Option D is true.

----------------------------------------------------

0.19 has a greater hundredths value than 0.141, so 0.141 < 0.19. Option E is true.

hope this helps!

The inequalities which are truly compared are B, D and E.

Given certain inequalities.

We have to find the true comparisons.

We have to look at the corresponding digits of numbers which are compared from left to right. Greater numbers on the left will be the greater number.

A. 32. 03 > 32. 3

This is false since 32.3 is greater. In 32.03, 0 is in the tenth place, while 3 is in the tenth place for 32.3.

B. 3. 114 > 3. 112

This is true since in the thousandths place, 4 is greater than 2.

C. 4. 003 < 3. 996

This is clearly false, since in the whole part, 4 is greater than 3.

D. 0. 541 > 0. 145

This is true, since in the tenths place, 5 is greater than 1.

E. 0. 141 < 0. 19

This is also true, since in the hundredths place, 9 is greater than 4.

Hence the true comparisons are B, D and E.

Learn more about Inequalities here :

https://brainly.com/question/28823603

#SPJ2

The expected value of the assumed probability density function is 3/4 and the variance is 3/80

The probability density function is not properly stated.

So, I will provide a general explanation on how to determine E(x) and V(x) of a probability density function

Assume that the probability density function is given as:

[tex]f(x)= \left[\begin{array}{ccc}3x^2 &0 \le x \le 1\\0&Otherwise\end{array}\right[/tex]

The expression E(x) is calculated using:

[tex]E(x) = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]

So, we have:

[tex]E(x) = \int\limits^1_0 {x \cdot 3x^2 \ d(x)[/tex]

Evaluate the product

[tex]E(x) = \int\limits^1_0 { 3x^3 \ d(x)[/tex]

Integrate

[tex]E(x) = \frac34x^4 |\limits^1_0[/tex]

Expand

[tex]E(x) = \frac34(1-0)^4[/tex]

Evaluate

[tex]E(x) = \frac34[/tex]

The variance is then calculated using:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Calculate [tex]E(x^2)[/tex] using:

[tex]E(x^2) = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]

This gives

[tex]E(x^2) = \int\limits^1_0 {x^2 \cdot 3x^2} \, dx[/tex]

Expand

[tex]E(x^2) = \int\limits^1_0 {3x^4} \, dx[/tex]

Integrate

[tex]E(x^2) = \frac{3}{5}x^5|\limits^1_0[/tex]

Expand

[tex]E(x^2) = \frac{3}{5}(1 - 0)^5[/tex]

Evaluate

[tex]E(x^2) = \frac{3}{5}[/tex]

Substitute [tex]E(x^2) = \frac{3}{5}[/tex] and [tex]E(x) = \frac34[/tex] in [tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = \frac 35 - (\frac{3}{4})^2[/tex]

Evaluate the exponent

[tex]Var(x) = \frac 35 - \frac{9}{16}[/tex]

Evaluate the difference

[tex]Var(x) = \frac{3}{80}[/tex]

Hence, the variance of the probability density function is 3/80

Read more about expected value and variance at:

https://brainly.com/question/15858152

#SPJ1

Answer:

x=90°

Step-by-step explanation:

Too much work............. ....

Answer:

I believe the answer is 0.7813

Step-by-step explanation:

Find the difference between 400 and 200, as they are first and second terms. This is going to be 0.5 since it is being divided.

The formula is: a∨n=a∨1(r)^(n-1)

n= the number of the sequence you are looking for

r=0.5

a∨1=400

a∨2=200

400(0.5)^(10-1)

Answer:

D one is the answer

Step-by-step explanation:

Answer:

If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)

Answer:

For each of the following equations determine the output values Corresponding to the input value

(-2;-1;0;1;2;3)

Answer:

  x = -2

Step-by-step explanation:

The function is decreasing where the first derivative is negative.

That is, the function is decreasing on the interval (-2, 5), except at x=2, where there is a flat spot. That means the maximum value is found at the left end of that interval, at x=-2.

__

The maximum value might be found at x = 6, at the right end of the interval (5, 6) on which the function is increasing. However, we judge the area under the first derivative curve between x=5 and x=6 to be less than the total area under the curve between x=-2 and x=5. That means the function does not increase enough from its minimum at x=5 to make up for the decrease over the longer interval.

__

The attachment shows an approximation of the derivative function given in the problem statement (dashed line) and its integral (solid line). Not all of the curvature of f'(x) is accounted for in the approximation, but the overall result is consistent with the above analysis.

Answer:

∠ B = 85°

Step-by-step explanation:

the inscribed angle B is half the measure of its intercepted arc AC , then

∠ B = [tex]\frac{1}{2}[/tex] × 170° = 85°

Answer:

1/3 or 33.33%

Step-by-step explanation:

30000000/90000000