Let x^{3}-5 x^{2}-17 x+21=0x
3
−5x
2
−17x+21=0​ be a polynomial equation.

a) Find all potential rational solution(s) using the Rational Root Theorem. Separate multiple solutions with commas if necessary.
Preview
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b) Find all the distinct,​ actual rational solution(s). Separate multiple solutions with commas if necessary. If no solutions exist, enter \text{None}None​.

Step-by-step explanation:

The answer is in the pic above

When checking alignment angles in a vehicle, a technician should look for several factors to ensure proper alignment:

a. All angles within factory specifications: The technician should check if all the alignment angles, including camber, caster, and toe, fall within the specified range provided by the vehicle manufacturer.

b. The camber on the left and right should be within 0.5 degrees of each other: Camber refers to the inward or outward tilt of the wheels when viewed from the front of the vehicle.

c. The caster on the left and right should be within 0.5 degrees of each other: Caster refers to the angle of the steering axis when viewed from the side of the vehicle. It helps provide stability and steering control.

By checking these factors and ensuring they meet the specified criteria, the technician can ensure that the vehicle's alignment is correct, promoting optimal tire wear, handling, and overall performance.

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Answer:

9

Step-by-step explanation:

There are nine angles in a nonagon.

Answer: x = 0, 20

Step-by-step explanation:

The equation would be 100p-5p^2=0

Then factor 100 and -5 by 5

Answer:

9/4

Step-by-step explanation:

Answer:

A. is the correct answer

Step-by-step explanation:

the answer is 27

Answer:

A. 25

Step-by-step explanation:

f(x)= 8x - 7

f(4)= 8*4 - 7= 25

f(4)= 25

Answer:

work is shown and pictured

The solutions to the equation -3sin^2θ = 1.5 in the interval from 0 to 2π are approximately θ = 0.74 and θ = 5.50.

To solve the equation -3sin^2θ = 1.5 in the interval from 0 to 2π, we can first isolate sin^2θ by dividing both sides of the equation by -3:

sin^2θ = -1.5/3

sin^2θ = -0.5

Taking the square root of both sides gives us:

sinθ = ±√(-0.5)

Since the interval is from 0 to 2π, we're looking for values of θ within this range that satisfy the equation.

Using a calculator or reference table, we find that the principal values of sin^-1(√(-0.5)) are approximately 0.74 and 2.36.

However, we need to consider the signs and adjust the values based on the quadrant in which the solutions lie.

In the first quadrant (0 to π/2), sinθ is positive, so θ = 0.74 is a valid solution.

In the second quadrant (π/2 to π), sinθ is positive, but sinθ = √(-0.5) is not possible since it's negative. Hence, there are no solutions in this quadrant.

In the third quadrant (π to 3π/2), sinθ is negative, so we need to find sin^-1(-√(-0.5)) which is approximately 4.08.

In the fourth quadrant (3π/2 to 2π), sinθ is negative, but sinθ = -√(-0.5) is not possible since it's positive. Hence, there are no solutions in this quadrant.

Therefore, the solutions in the given interval are approximately θ = 0.74 and θ = 5.50.

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The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

Given data;

Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.

To get the probability of the sequence W, W, L, L, W.

Now,

As the results are probabilistically independent,

The probability of the sequence is;

→ [(P(W)]³ + [(P(L)]²

→ (0.4)³ + (0.6)²

Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

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choose any 2 points on the graph

To calculate the slope use the formula:

slope = y (point 2)-y (point 1)/x (point 2)-x (point1)

substitute the choses points in

calculate your awnser

Answer:

b,c,d

Step-by-step explanation:

We have to simplify the given expression given (5x + 3y + (-x) + 6z).

We will use the process as given below.

1) We will identify the like terms, we have to add or subtract.

2) Like terms are those, which have the same variable of the same degree.

3) We get the simplified expression by combining the same terms.

5x + 3y + (-x) + 6z = 4x + 3y + 6z

Therefore, Options B, C and D will be the correct options.

43³/₄% can be expressed as a decimal to give 43.75%, which can be pronounced as forty-three point seventy-five percent.

A decimal value is a number that contains a whole and a fractional part.

Mathematically, decimal values are expressed using the decimal sign (.).

43³/₄%, which is a fractional value that can be changed into a decimal value thus:

= 43% + ³/₄%

= 43% + 0.75%

= 43.75%

Thus, 43³/₄%, which is forty-three-three-fourth percent, can be expressed as a decimal to give 43.75%.

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Answer:

31.2 pounds

Step-by-step explanation:

159 x 0.196 = 31.164

Step-by-step explanation:    

       The question gives us two points, (9,-6) and (-8,7), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)    

                                         =  (7 - (- 6)) ÷ (-8 - 9)  

                                         =   - ¹³/₁₇  

Checking my answer:

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

                                 ⇒  y - (-6) =  - ¹³/₁₇ (x - 9)

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

The graph of the given functions is (see in attachments).

From the question, we have

g(x) = 0.44√3.2x−4.1

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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We want to find the value of cot(θ) given that sin(θ) = 3/8 and θ is an angle in a right triangle, we will get:

cot(θ) = (√55)/3

So we know that θ is an acute angle in a right triangle, and we get:

sin(θ) = 3/8

Remember that:

Then we have:

opposite cathetus = 3

hypotenuse = 8 = √(3^2 +  (adjacent cathetus)^2)

Now we can solve this for the adjacent cathetus, so we get:

adjacent cathetus = √(8^2 - 3^2) = √55

And we know that:

cot(θ) = (adjacent cathetus)/(opposite cathetus)

Then we get:

cot(θ) = (√55)/3

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Correct question :

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Answer:

Total number of marbles = 36

Step-by-step explanation:

Marbles in bag: Red and Blue only

Probability of randomly choosing a red marble = 7/9

Number of red marbles = 28

Total number of marbles in the bag =?

Probability = required outcome / Total possible outcomes

P(red marble) = required outcome (number of red marbles) / Total possible outcomes(total number of marbles

7/9 = 28 / total number of marbles

Total number of marbles * 7/9 = 28

Total number of marbles = 28 ÷ 7/9

Total number of marbles = 28 * (9/7)

= 252 / 7

Total number of marbles = 36

Answer:

The person is 14 years old

Step-by-step explanation:

1. Multiply 6 times 18 which is 108

2. Add all numbers together in list which is 94

3. Subtract 94 from 108 which is 14

4. To check answer add 94 plus 14 and divide by 6 and you will get the median which is 18, now you know this answer is correct.

One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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The interval forms of the inequations are: a) x ∈ (20.5, + ∞), b) t ∈ (- ∞, 102], c) y ∈ (- ∞, - 8) ∪ (6, + ∞).

The simplified forms of the radical expressions are: a) m³ · n⁴, b) - 2√(2 · a), c) 3∛ 2 / 20.

In the first part of this question we must transform inequalities into interval notation:

a) x > 20.5, inequalities of the form x > a are equivalent to x ∈ (a, + ∞). Thus, x > 20.5 is equivalent to x ∈ (20.5, + ∞).

b) t ≤ 102, inequalities of the form t ≤ a are equivalent to t ∈ (- ∞, a]. Thus, t ≤ 102 is equivalent to t ∈ (- ∞, 102].

c) y ≥ 6 or y ≤ - 8, the conditional "or" used in logics is equivalent to the operator ∪ used in set theory. Thus, y ≥ 6 or y ≤ - 8 is equivalent to y ∈ (- ∞, - 8) ∪ (6, + ∞).

The second part of this questions consists in simplifying radical expressions by algebraic handling:

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Answer:

y=12

Step-by-step explanation:

y=2x ,so 2x=8x-x^2

x^2=8x-2x

x^2=6x

x^2/x=6x/x

x=6

y=2x ,2(6)

y=12

x=5.....................

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

now, going either way the boat travelled the same 18 miles.

\(\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&18&b-c&4.5\\ Downstream&18&b+c&2 \end{array}\hspace{5em} \begin{cases} 18=(b-c)4.5\\\\ 18=(b+c)2 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{18=(b-c)4.5}\implies \cfrac{18}{4.5}=b-c\implies 4=b-c\implies \boxed{4+c=b} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{18=[~(4+c)+c~]2}\implies \cfrac{18}{2}=4+2c\implies 9=4+2c \\\\\\ 5=2c\implies \blacksquare~~ \cfrac{5}{2}=c ~~\blacksquare\hspace{5em}4+\left( \cfrac{5}{2} \right)=b\implies \blacksquare~~ \cfrac{13}{2}=b ~~\blacksquare\)

Answer:

x = 5√3

Step-by-step explanation:

We will use the Pythagorean theorem with a and b as the lengths of the legs, and c as the length of the hypotenuse.

a² + b² = c²

We need two of the three lengths of a, b, and c, so we can find the third length.

The height divides the equilateral triangle into two right triangles.

Look at one of the right triangles.

One leg is half the side of the triangle.

a = 10/2 = 5

One leg is the height.

b = x

The hypotenuse is the side of the equilateral triangle.

c = 10

a² + b² = c²

5² + x² = 10²

25 + x² = 100

x² = 75

x = √75

x = 5√3

Answer: b

Step-by-step explanation:

I think three might be the correct answer

No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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