How many and of which kind of roots does the equation f(x) = x³ + 2x² + 4x + 8 have?A. 3 realOB. 2 real; 1 complexOC. 2 real; 2 complexOD. 1 real; 2 complexReset Selection

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer

$266.66

Step-by-step explanation:

We have here ,

We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .

⇒ SI = P × R × T / 100

⇒ SI = $ 200 × 16 × 10 / 12 × 100

⇒ SI = $ 26.66

Now Calculate amount as ,

⇒ A = SI + P

⇒ A = $ 200 + $ 26.66

⇒ A = $ 226.66

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Testing the hypothesis in this problem which is a two-tailed test, we can conclude that there is not sufficient evidence to conclude that the mean time of installation has changed, since the p-value of the test is 0.0364 > 0.01,

At the null hypothesis, we test if the mean is of 25 minutes, that is:

\(H_0: \mu = 25\)

At the alternative hypothesis, we test if the mean has changed, that is, if it is different than 25 minutes.

\(H_1: \mu \neq 25\)

We have the standard deviation for the sample, thus, the t-distribution is used. The value of the test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which:

In this problem:

The value of the test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{26.2 - 25}{\frac{4}{\sqrt{51}}}\)

\(t = 2.14\)

Since the p-value of the test is 0.0364 > 0.01, there is not sufficient evidence to conclude that the mean time of installation has changed.

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

Step-by-step explanation:

35.26    rounded to  35.3

8.32   rounded to        8.3

6.78    rounded to       6.8

35.3 + 8.3 = 43.6

43.6 + 6.8 = 50.4

The answer is 50.4.

39.26 rounds to 35.3

8.32 rounds to 8.3

6.78 rounds to 6.8

When you add them together, you get 50.4.

The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.

The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.

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2  Answers:

Choice C) It will use a closed circle

Choice D) The ray will move to the left

=========================================================

Explanation:

The inequality \(x \le -8\) means that x = -8 or x < -8. Since we're including -8 itself, which is the endpoint, we'll use a closed circle. In contrast, an open circle would be used if the inequality was \(x < -8\) to exclude the endpoint -8.

The ray is to the left because we're visually describing all values smaller than -8. Such example values are -10 and -22 as these values are to the left of -8 on the number line.

In short, the graph consists of a closed circle at the endpoint -8 and the arrow is to the left. We can say the shading is to the left.

Answer:

Step-by-step explanation:

[3x-2]÷4=2x-8

3x-2 = 4·(2x-8)

3x-2 = 8x-32

-2 = 5x-32

30 = 5x

x = 6

Answer:

(3x-2)/4= 2x-8  x=6

Step-by-step explanation:

(3x-2)/4 times 4= 2x-8

Multiply both sides by 4

3x-2/4 times 4= 2x  times 4-8 time 4

Simplify

3x= 8x = 8x-30-8x

Subtract 8x from both sides

3x-8x=8x-30-8x

Simplify

-5x=-30

Divide both sides by -5

-5x/-5 = -30/-5

Simplify so you get x=6

1. The trigonometric ratios are given as follows:

2. The equation to solve for x is given as follows: sin(52º) = x/13.

3. Two equations to solve for m are given as follows:

4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.

5. The lengths are given as follows:

The three trigonometric ratios are given as follows:

In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:

sin(52º) = x/13.

In item 3, the Pythagorean Theorem is used to solve for m, as follows:

n² + m² = l².

m² = l² - n²

m = square root (l² - n²).

In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:

sin(62º) = 7/h

h = 7/sin(62º)

h = 7.9 inches.

The length BD in item 5 is obtained as follows:

cos(30º) = BD/5

BD = 5 x cos (30º)

BD = 4.3 cm.

Then the length BC is calculated as follows:

sin(22º) = 4.3/BC

BC = 4.3/sin(22º)

BC = 11.5 cm.

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Answer:

I need Help on this one too.

Step-by-step explanation:

please help

Answer: Its b

Step-by-step explanation:

Answer:

6:5

Step-by-step explanation:

This is because its asking for clocks (6) to tables (5).

Hope this helps!

Answer:

  rectangular table

Step-by-step explanation:

You want to know the largest area of tables that are ...

The formulas for the areas of the various shapes are ...

The area of the square table is ...

  A = (36 in)² = 1296 in²

The area of the rectangular table is ...

  A = (20 in)(73 in) = 1460 in²

The area of the round table is ...

  A = π(21 in)² ≈ 1385 in²

The rectangular table has the largest area.

__

Additional comment

You can eliminate the square table right away by realizing the rectangular table is more than twice as long, and more than half as wide. If the rectangle were 18 in by 72 in, it would have the same area as the square.

Answer:

x=70

Step-by-step explanation:

Due to the law of alternate interior angles, we can see that one of the angles in the triangle is equal to 35 degrees as well (please see the picture attached).

We're given that one of the exterior angles of the triangle is equal to 105. The exterior angle of a triangle will always be equal to the sum of the two opposite interior angles. Knowing this, we can write:

x+35=105

Subtract both sides by 35

x+35-35=105-35

x=70

Therefore, the value of x is 70 degrees.

I hope this helps!

Answer:

X=11 trust me on my mom

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.

Given that:

Perimeter = sum of all sides

Perimeter = AB + BC + CA

Estimate each distance using the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

AB = √(1 - 5)² + (5 - 3)²

AB = √(-4)² + (-2)²

AB = √(16 + 4)

AB = √20

BC = √(3 - 1)² + (0 - 5)²

BC = √(2)² + (-5)²

BC = √(4 + 25)

BC = √29

CA = √(5 - 3)² + (3 - 0)²

CA = √(2)² + (3)²

CA =  √(4 + 9)

CA = √13

Perimeter = AB + BC + CA

Perimeter = √20 + √29 + √13

Perimeter = 4.47 + 5.38 + 3.60

Perimeter = 13.45 units.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

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The solution set for the system of two inequalities is x < - 1.

In this question we have a system formed by two linear expressions with a single variable, x, whose solution set has to be found by algebraic procedures:

x / 2 < - 2 or - 3 > x - 2            Given

x < - 4 or - 1 > x                        Compatibility with addition / Compatibility with multiplication / Existence of additive inverse / Existence of multiplicative inverse / Modulative property / Trichotomy

x < - 4 or x < - 1                        Tricothomy

x < - 1                                        Definition of disjunction / Result

The solution set for the system of two inequalities is x < - 1.

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Answer:

20,442,240 possible account numbers.

Step-by-step explanation:

First character has 10 possibilities.

Next 2 has 26 x 26=676 possible combinations.

The last 4 has 9x8x7x6 = 3024 possible combinations.

The answer would be 10 x 676 x 3024

= 20,442,24.

Hope this helps.

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

Step-by-step explanation:

Let the speed of the current be c km/h.

When the ship sails with the current, its effective speed is (50 + c) km/h.

When the ship sails against the current, its effective speed is (50 - c) km/h.

We know that the distance traveled is the same in both cases, which is 60 km.

Let's use the formula:

time = distance / speed

When sailing with the current, the time taken is:

60 / (50 + c)

When sailing against the current, the time taken is:

60 / (50 - c)

We know that when sailing against the current, it takes 0.5 hours more time than when sailing with the current:

60 / (50 - c) = 60 / (50 + c) + 0.5

Simplifying the equation, we get:

60(50 + c) = 60(50 - c) + 0.5(50^2 - c^2)

3000 + 60c = 3000 - 60c + 1250 - 0.5c^2

Simplifying further,

120c = 1250 - 0.5c^2

0.5c^2 + 120c - 1250 = 0

Solving the quadratic equation by factoring or using the quadratic formula, we get:

c = 10 km/h (ignoring the negative root)

Therefore, the speed of the current is 10 km/h.

Answer: 50km/h, 60km, 0.5 hr

Step-by-step explanation:

Let's begin by listing out the information given to us:

The ball travels in a straight line

Batter: (x, y) = (1, 1)

Shortstop: (x, y) = (5, 10)

The distance between the two-point is given by:

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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Answer:

D

Step-by-step explanation:

Lines d and e are parallel by the corresponding angles theorem (since the 123° angle will form a linear pair with the 57° angle).

Answer:

f1 ( x ) valid pdf . f2 ( x ) is invalid pdf

k = 1 / 18 , i ) 0.6133 , ii ) 0.84792

Step-by-step explanation:

Solution:-

A) The two pdfs ( f1 ( x ) and f2 ( x ) ) are given as follows:

- To check the legitimacy of a continuous probability density function the area under the curve over the domain must be equal to 1. In other words the following:

- We will perform integration of each given pdf as follows:

Answer: f1 ( x ) is a valid pdf; however, f2 ( x ) is not a valid pdf.

B)

- A random variable ( X ) denotes the resistance of a randomly chosen resistor, and the pdf is given as follows:

                       if  8 ≤ x ≤ 10

                               0  otherwise.

- To determine the value of ( k ) we will impose the condition of validity of a probability function as follows:

- Evaluate the integral as follows:

                     ... Answer

- To determine the CDF of the given probability distribution we will integrate the pdf from the initial point ( 8 ) to a respective value ( x ) as follows:

To determine the probability p ( 8.6 ≤ x ≤ 9.8 ) we will utilize the cdf as follows:

                   p ( 8.6 ≤ x ≤ 9.8 ) = F ( 9.8 ) - F ( 8.6 )

                   p ( 8.6 ≤ x ≤ 9.8 ) =

ii) To determine the conditional probability we will utilize the basic formula as follows:

               p ( x ≤ 9.8  | x ≥ 8.6 ) = p ( 8.6 ≤ x ≤ 9.8 ) / p ( x ≥ 8.6 )

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 1 - p ( x ≤ 8.6 ) ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 1 - 0.27666 ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 0.72333 ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.84792 ... answer

Hope it helps! ;)

Answer:

Im just doing this for points .,.

Step-by-step explanation:

There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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