The graph of f(x) = 2x³+x² - 4x-2 is shown.
How many of the roots of f(x) are rational?
O 0
O 1
O2
O3
DONE

The value is 3/2 (a)

The given function is , f(x)= 2x 3 where x = value of this function .

Here , we will put the value 1/4 ( here x = 1/4 ) into the given function. if , f(1/4) = 2 . 1/4 . 3 = 3/2

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On solving for x, we get x = -1

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. Decimal system is the most commonly used number system with base 10.

Given is the following expression -

3 base x + 34 base x - 40 base x = 0

The given expression can be solved by converting the above expression in decimal form. Therefore -

3 base x in decimal = (3 x⁰) base 10 = 3

34 base x in decimal = (3 x¹ + 4 x⁰) base 10 = 3x + 4

40 base x = (4 x¹ + 0 x⁰) base 10 = 4x

Substituting the decimal values in the expression given -

3 + (3x + 4) + 4x = 0

7x + 7 = 0

7x = -7

x = - 1

Therefore, on solving for x, we get x = -1

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If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.

To determine the rate or speed of each train, an algebraic expression can be used.

As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,

6x + 6(x + 21) = 978

Here, (x + 21) represents the speed of the faster train

6x + 6x + 126 = 978

12x = 978 - 126

12x = 852

x = 852 ÷ 12

x = 71

x + 21 = 71 + 21 = 92

Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.

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If AC = 4x - 3, DC = 2x + 9, m ∠ ECA = 15x + 2, and EC is a median of ΔAED then EC is not an altitude of ΔAED because of m ∠ ECA = 92.

In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.

Given: AC = DC

4x - 3 = 2x + 9

4x - 2x - 3 = 2x - 2x + 9

simplifying the above equation, we get

2x - 3 = 9

2x - 3 + 3 = 9+3

2 x = 12

x = 6

Substitute the value of x in m ∠ ECA, then we get

m ∠ ECA = 15x + 2

= 15(6) + 2

m ∠ ECA = 92

EC is not an altitude of ΔAED because of m ∠ ECA = 92.

Therefore, EC is not an altitude of ΔAED.

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The height of the lighthouse to the nearest tenth of a foot is 137.8 feet.

This is a question of heights and distances.

It is given in the question that the passing boat is 310 feet from the base of a lighthouse. Also, the angle of depression from the top of the lighthouse is 24°.

We have to find the height of the lighthouse to the nearest tenth of a foot.

As you can see in the figure, using trigonometry we can write,

cot 24 = 310/Height of the lighthouse

Hence,

Height of the lighthouse = 310/cot 24

We know that,

cot 24 ≈ 2.25

Hence,

Height of the lighthouse = 310/2.25 ≈ 137.77778 ≈ 137.8 feet.

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Answer:

21.9 is a possible value

Step-by-step explanation:

I just wrote the equation below have a very small but positive value on the right side and solved for x

x - 21.8 = 0.1

x = 21.9

The expression at the end of the third year would be:  500x³ + 200x² + 600x

We have the rate at x = 1 + r

This is the rate of the interest that is earned per year.

In the first year.

initial deposit = $500

deposit at the end of the year = 500 * x = 500x

In the second year

The initial balance = 500x + 200

The balance at the end of the year = (500x + 200)x

= 500x² + 200x

In the third year

Initial balance = 500x² + 200x + 600

Then the year end balance would be (500x² + 200x + 600)x

= 500x³ + 200x² + 600x

Hence the expression that can be used to show the polynomial is given as 500x³ + 200x² + 600x

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Answer:

A. s+7726>=12,600

Step-by-step explanation:

s is the number of steps left to reach her goal of at least 12,600 steps.

7726 is the number of steps already taken.

12,600 is her goal.

s+7726>=12,600

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Answer:

The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.

The solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².

According to the given question.

We have a formula.

s = (1/2)gt²

Since, we have to solve this given formula s = (1/2)gt² for the variable g.

Which means we have to write separate variable g to one side from the other variables which are in the given formual s = (1/2)gt² .

Thereofre, the solution of the given formula for the variable g is given by

s = (1/2)gt²

⇒ 2s = gt²               (multipling both the sides by 2)

⇒2s/t² = g               (dividing both the sides by t²)

⇒ g = 2s/t²

Hence, the solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².

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3) a) The domain of the rational function is x ≥ 1.

b) The domain of the rational function is all the real numbers except x = 3 and x = - 4.

4) a) The root of the rational function is 6.

b) The roots of the rational function are 4 and 1.

Rational functions are algebraic expressions of the form P(x) / Q(x), where P(x) is the numerator and Q(x) is the denominator. 3) The domain of rational functions are the x-values that comprises P(x) except all values such that Q(x) = 0. Then, we proceed to find the domain of each function:

Case 1

The domain of P(x) = √(x - 1) is x ≥ 1 and the indetermination values of Q(x) = 2 · x is x = 0. Then, the domain of the rational function is x ≥ 1.

Case 2

The domain of P(x) = 3 is all the real numbers and the indetermination values of Q(x) = (x - 3) · (x + 4) are x = 3 and x = - 4. Then, the domain of the rational function is all the real numbers except x = 3 and x = - 4.

4) The roots of a function are all the values at which the function is evaluated such that is equal to zero.

Case 1

1 - 2 / (x - 4) = 0

[(x - 4) - 2] / (x - 4) = 0

x - 6 = 0

x = 6

The root of the rational function is 6.

Case 2

(x² - 5 · x + 4) / 5 = 0

x² - 5 · x + 4 = 0

(x - 4) · (x + 1) = 0

The roots of the rational function are 4 and 1.

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Answer:

195.86

Step-by-step explanation:

Answer: 195.86. Yw.

Step-by-step explanation: Pls add me Brainliest >3

The shuttle is 34.03 miles high.

In this question,

Anna is watching a space shuttle launch 6 miles from Cape Canaveral in Florida.

The angle of elevation from her viewing point to the shuttle is 80°

If the space shuttle is going straight up, we need to how high the shuttle is.

Let x be the unknown value.

Consider tangent of angle 80°

So, tan(80°) = x/6

⇒ x = 6 × tan(80°)

⇒ x = 6 × 5.6713

⇒ x = 34.03 miles

Therefore, the shuttle is 34.03 miles high.

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Answer: 70 days

Step-by-step explanation:

According to the given statement The total far distance = 88.2cm

A lens equation, sometimes known as a lens formula, is an equation that connects focal length, image distance, as well as object distance. . where v is the distance between the picture and the lens, u is the object distance, and f is the focal length

A lens's power is defined as both the reciprocal of its focal length. It is symbolized by that the letter P. P=1f gives the power P of something like a lens with a focal length of f (in m). The SI unit of lens power is a 'diopter.'

P = -1.16

The expression of the focal length is represented as:

f = 1/p

p is the power.

so,

f = 1/-1.16

 = -0.862

 = -86.2 cm

the expression for the lens formula is:

1/f = 1/v - 1/u

1/(-86.2) = 1/v - 0

v = -86.2

The total distance is represent as:

d = v + s

so,

d = 86.2 + 2

  = 88.2 cm

The total far distance = 88.2cm.

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Answer: DB=6.5 units

Step-by-step explanation:

DB=BD

AB+BD=AD

AB=BD ==> Bisectors divide a segment into two equal parts

BD+BD=13

2*BD=13

BD=13/2

BD=

DB=6.5 units

The probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.

Probability:

Probability defines the possibility of the event across the total event.

Given,

Point A is chosen at random on [tex]\bar{BE}[/tex].

Here we need to find the the probability of the following event.

P(A is on [tex]\bar{CE}[/tex]).

Let us consider the following image, in order to solve this.

Based on the image we have identified that the probability of the event  P(A is on [tex]\bar{CE}[/tex]) is calculated by dividing the length of CE by the length of BE.

So, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is,

P(A is on [tex]\bar{CE}[/tex]) =  (length of CE) / (length of BE)

Then, length of CE is calculated by adding the distance,

=> CD + DE

=> 12 + 9

=> 21

Now,

Apply the values then we get,

P(A is on [tex]\bar{CE}[/tex]) = 21 / ( 5 + 12 + 9)

P(A is on [tex]\bar{CE}[/tex]) = 21 / 26

Therefore, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.

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Step-by-step explanation:

[tex] = \lim \limits_{x \to0}x \cot(2x) [/tex]

[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } [/tex]

[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \times \frac{2x}{2x} [/tex]

[tex] = \lim \limits_{x \to0} \frac{2x}{ \tan(2x) } \times \lim \limits_{x \to0} \frac{x}{2x} [/tex]

[tex] = \lim \limits_{u \to0} \frac{u}{ \tan(u) } \times \frac{1}{2} [/tex]

[tex] = \frac{1}{2} [/tex]

The equation of the line 4x + 6y = 12 expressed in slope-intercept form is y = -2/3 x + 2 with a slope equal to -2/3.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 4x + 6y = 12, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.

4x + 6y = 12

6y = -4x + 12

Dividing both sides by 6,

y = -4/6 x + 2

y = -2/3 x + 2

Hence, the equation of the line in slope-intercept form is y = -2/3 x + 2 where the slope, m, is equal to -2/3.

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Answer:

hi

Step-by-step explanation:

Answer:

FITNESS Laura wants to go to a fitness class

tomorrow. She can choose a 5:00 or a 7:30 class and

spin or water aerobics. Represent the sample space

for the situation by making an organized list, a table,

and a tree diagram.

Step-by-step explanation:

Step-by-step explanation:

222-6=216

216÷4=54

so 54 students per bus

Answer:

54 students

Step-by-step explanation:

222 - 6 (students that had to travel in cars) = 216

216 / 4 (4 buses) = x

x = number of students on each bus

216 / 4 = 54

x = 54

54 students on each bus

216 students rode the bus, 6 students rode in cars

The 32th term of the arithmetic sequence AP is estimated to be 0.3.

In math, an arithmetic progression (AP) is a list or sequence of numbers in which each term is obtained by adding a finite number to the term before it.

Now for the answer to the question;

The numbers in the given sequence are-

-9,-8.7,-8.4, ...........

There are 32 terms with in series for that we need to find the 32nd number.

Let's say the first term is 'a₁' = -9.

Let 'a₂' = -8.7 be the second term.

Let 'a₃' = -8.4 be the third term.

The common difference between two consecutive terms that are equal of an AP is 'd.'

d = a₂ - a₁  

Substitute the values in the preceding equation; the 32nd term is

d = -8.7 - (-9)

d = -8.7 + 9

d = 0.3

Now calculated using the nth term formula.

Substitute all of the values in the formula now.

a₃₂ = a + (n - 1) d

a₃₂ = -9 + (32 - 1)(0.3)

a₃₂ = -9 + 9.6 - 0.3

a₃₂ = 0.3

As a result, the arithmetic sequence's 32nd term is estimated to be 0.3.

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Answer:

(a): 26.1

(b): 27.9

Please see below for the steps.

Step-by-step explanation:

(a):

Use points (0,0) and (3, 78.3)

Use slope formula. The slope formula is also used to find average rate of change (just so you know).

y2-y1/x2-x1

78.3-0/3-0=78.3/3=26.1

Answer for (a) is 26.1

(b):

Use points (4, 147.6) and (9, 287.1)

Use slope formula.

y2-y1/x2-x1

287.1-147.6/9-4=139.5/5=27.9

The answer for (b) is 27.9

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If linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.

Let Vera's age be v

Let Linda's age be 2v

Let Tanya's age be 8v- 4

Let the total age be 9v + 2

Hence,

v + 2v + 8v- 4 = 9v + 2

11v - 4 = 9v + 2

Collect like terms

2v = 6

Divide both side by 2v

v=6/3

v = 3

So,

Tanya's age = 8v - 4

Tanya's age= 8(3) - 4

Tanya's age=24-4

Tanya's age = 20 years

Therefore if linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.

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The constant percent rate of change of f(x) with respect to x is (d) 25% decay

The function is given as

f(x) = 46(0.75)^x

The above function is an exponential function

The growth/decay factor is

b = 0.75

The constant rate is then calculated as

Rate = 1 - b

This is because b is less than 1 (i.e. an exponential decay)

So, we have

Rate = 1 - 0.75

Evaluate

Rate = 25%

Hence, the constant percent rate of change of f(x) with respect to x is (d) 25% decay

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Answer: D

Hope this helps :)

Answer:Substitute the value of the variable into the equation and simplify.

84

Step-by-step explanation:

The set of items that exist as part of both sets A and B exists at the intersection of the two sets.

If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

It exists given that the Probability of two independent event A and B exists given by P(A)  and P(B).

The intersection of event A and B is given by P( A∩B).

The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.

The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).

Given: P(a|b) = 0.40

P(A) = 1 - 0.40 = 0.6

P(B) = 1 - 0.74 = 0.26

P(A∪B) = P(A) + P(B) − P(A∩B)

substitute the values in the above equation, we get

0.40 = 0.6 + 0.26 - P(A∩B)

- P(A∩B) = 0.40 -  0.6 - 0.26

P(A∩B) = 0.46

Therefore, the independent events of A and B exists 0.46.

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The situation can be solved by determining the probability of the selecting a certain color marble.

Probability is the ratio of a favorable outcome x to the total number of outcomes n of an event. In the give case, if the prediction is correct, you get a dollar.

Probability=x/n

On the first draw, the chance that predicted color is drawn is:

Probability=2/4=1/2

Amount you may get is ½*1=1/2

On the second draw, the chance the color with two left balls is predicted and come out:

Probability=2/3

Amount you may get is 2/3*1=2/3

On the third draw, you predicted a color with no same color balls left:

Probability=1/3

Amount you may get is 1/3*1=1/3

Or you predicted a color with two different color balls left

Probability=2/3*1/2=2/6=1/3

Amount you may get is 1/3*1=1/3

On the fourth draw, the probability of correct predicted ball is 1

Amount you may get is 1=1

If you played the game optimally, summing up the amount=1/2+2/3+1/3+1/3+1=17/6≈2.88

Hence, by playing the game optimally, the expected value of the game is $2.88.

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Answer:

C.)-200

Step-by-step explanation:

Each week if you take away $40 for 5 weeks, you would take away $220. -40*5=200.