Which expressions are polynomials?

Select each correct answer.

x – 1
5x²-√x
6+p
8x-z³

Answer:

111/190

Step-by-step explanation:i know you dont want to see explanation so yeah...

Probabilities are used to determine the chances of an event.

The probability that the two selected sweet will not be of the same type is [tex]\frac{111}{190}[/tex]

The given parameters are:

[tex]n = 20[/tex] --- number of sweet

[tex]L = 12[/tex]

[tex]M = 5[/tex]

[tex]H = 3[/tex]

First, we calculate the probability that the two selected sweet will be of the same type.

This is calculated as:

[tex]P(Same) =P(L\ and\ L) + P(M\ and\ M) + P(H\ and\ H)[/tex]

Because the selection is without replacement, the equation becomes

[tex]P(Same) = \frac{12 \times 11}{20 \times 19} +\frac{5 \times 4}{20 \times 19} + \frac{3 \times 2}{20 \times 19}[/tex]

[tex]P(Same) = \frac{132}{380} +\frac{20}{380} + \frac{6}{380}[/tex]

Add fractions

[tex]P(Same) = \frac{132+20+6}{380}[/tex]

[tex]P(Same) = \frac{158}{380}[/tex]

Using the complement rule, the probability that the two selected sweet will not be of the same type is:

[tex]P(Not\ same) = 1 - P(Same)[/tex]

This gives

[tex]P(Not\ same) = 1 - \frac{158}{380}[/tex]

Take LCM

[tex]P(Not\ same) = \frac{380 - 158}{380}[/tex]

[tex]P(Not\ same) = \frac{222}{380}[/tex]

Simplify

[tex]P(Not\ same) = \frac{111}{190}[/tex]

Hence, the required probability is: [tex]\frac{111}{190}[/tex]

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The x value for point C is not one of the given options.

To find the x value for point C such that AC and BC form a 2:3 ratio, we first need to find the coordinates of point C. The given components are Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21, we get:

C = sqrt((-2/3)² + (-4/3)² + (7/3)²) = sqrt(23/3)

Therefore, the x value for point C is not one of the options given. None of the options (A) 6, (B) -0.6, (C) 4, or (D) -2.4 are correct.

Final answer:

To find the x value for point C such that AC and BC form a 2:3 ratio, substitute the coordinates of point C into the equation and solve for C.

Explanation:

To find the x value for point C such that AC and BC form a 2:3 ratio, we can use the coordinates of points A, B, and C. We have Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21 gives:

C = √((-2/3)² + (-4/3)² + (7/3)²) = √(4/9 + 16/9 + 49/9) = √(69/9).

So the x value for point C is √(69/9).

The total distance of the trail is 100/7 km, which simplifies to approximately 14.29 km.

To find the total distance of the trail, let's break down the information provided step by step.

First day: They hiked 1/8 of the trail.

Second day: They hiked 4/7 of the remaining trail after the first day. So, on the second day, they covered (1 - 1/8) × (4/7) of the total trail.

Third day: They hiked 1/3 of the remaining trail after the second day, plus the last 8 km.

Now, we can set up an equation to solve for the total distance:

1/8 + (1 - 1/8)× (4/7) + (1 - 1/8 - (1 - 1/8)× (4/7)) × (1/3) + 8 = Total Distance.

Let's calculate each part:

First day: 1/8 of the total trail.

Second day: (1 - 1/8)× (4/7) = 28/56 - 7/56 = 21/56 of the total trail.

Third day: (1 - 1/8 - 21/56)× (1/3) = (56/56 - 7/56 - 21/56) × (1/3) = 28/56× (1/3) = 28/168 = 1/6 of the total trail.

Now, let's add all these parts together:

1/8 + 21/56 + 1/6 + 8 = Total Distance.

To simplify, let's find a common denominator:

1/8 + 3/8 + 14/56 + 8/8 = Total Distance.

Now, add the fractions:

16/56 + 14/56 + 14/56 + 56/56 = Total Distance.

Combine:

100/56 = Total Distance.

Now, simplify:

Total Distance = 100/56×8/8 = 800/56 km.

Divide both numerator and denominator by the greatest common divisor, which is 8:

Total Distance = 100/7 km.

So, the whole trail is approximately 14.29 km.

r² + r - 2 R -4r+8 just got this wrong on quiz so i know this is the right answer now

The simplified expression of  (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r

An expression is combination of variables, numbers and operators.

The given expression is  (r⁴ - r² + 4) ÷ (r² - r + 2)

r power four minus r square plus four divided by r square minus r plus two.

The expression can not be simplified further as the denominator (r^2 - r + 2) cannot be factored into linear factors

The expression is a rational function and can only be simplified by partial fraction decomposition which involves writing it as a sum of simpler fractional terms.

r (r³ -r+ 4/r) ÷ r(r - 1 + 2/r)

r³ -r+ 4/r ÷ r - 1 + 2/r

Hence, the simplified expression of  (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r

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Answer:

The correct answer is D.

Step-by-step explanation:

Recall that when we make a dilation with center at the origin, the only needed operation is to multiply the coordinates of each point by the factor of dilation. In this particular case the dilation factor is 0.5 so we must do the following operations:

So, the vertices of the triangle after the dilation are those who appear in D.

The 3rd Image defines a piecewise function because for it to be a function, every input must match to exactly one and only one output. In Images 1, 2, and 4, there are certain inputs that have two outputs or stated otherwise, have two y-values for the same x-value. Only the 3rd Image matches 1 x-value to every 1 y-value. So, that's your answer.

Answer: C! The 3rd graph

Step-by-step explanation: Why does your equations have f(x)= and g(x)= ? Mine is only y= for every graph shown. All same numbers though.

Answer:

Sample response: Julio divided 6 whole parts into groups of 2 instead of dividing them into groups of  

1

2

which would make the quotient 12, not 3.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

6(4 - 3y)

Step-by-step explanation:

Factor the expression 24−18y

The first thing to check is the common factor to be able to factorize the expression. Take for instance where we have

xa - xb  = x ( a - b)

The common factor is x which is outside the bracket

24−18y

The greatest common factor between 24 and 18 is 6.

Therefore,

24−18y  = 6(4 - 3y)

24−18y  = 6(4) - 6(3y)

Answer:

maybe 2,800,000

The complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:

h(t) = 25 · sin((π / 3) t) + 4

To model Amare's height above the ground, use the equation of a sinusoidal function.

In this case, since the Ferris wheel has a diameter of 50 meters, the amplitude of the function is half of the diameter, which is 25 meters. The Ferris wheel completes three revolutions in six minutes, so the period of the function is 6 minutes.

The equation for the height function is given by:

h(t) = A · sin((2π / T) t + φ) + h0

Where:

A is the amplitude (25 meters)

T is the period (6 minutes)

φ is the phase shift (0 radians, since Amare enters at the low point)

h0 is the vertical shift (4 meters, since the Ferris wheel sits four meters above the ground)

Substitute the given values into the equation

h(t) = 25 · sin((2π / 6) t + 0) + 4

Simplifying further:

h(t) = 25 · sin((π / 3) t) + 4

Therefore, the complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:

h(t) = 25 · sin((π / 3) t) + 4

Complete question

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.

h(t)=--- ·sin----  πt+---- π )+ ----

Answer:

The area added to the office according to the new blueprint

Step-by-step explanation:

you're welcome

Chumani's bill represents 85% of the original bill after a 15% discount is applied. The discounted amount can be found by multiplying the original bill by 0.85.

If the discount on an item is 15%, and Chumani is paying after this discount has been applied, we want to find out what percent of the original bill Chumani's bill is. To do this, we subtract the discount rate from 100%. So, 100% - 15% = 85%. Thus, Chumani's bill is 85% of the original bill.

To calculate the discounted bill, you multiply the original bill amount by 0.85 (which represents 85%). If the original bill was, for example, $100, the calculation would be $100 x 0.85 = $85. So, Chumani would pay $85, which is 85% of the original bill amount.

To rewrite[tex]\(2x^2 - 7x + 5\) by completing the square, first factor out the coefficient of \(x^2\), then add and subtract \(\frac{49}{16}\) inside the parentheses, rewrite as a perfect square trinomial, and simplify. The result is \(2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\).[/tex]

To rewrite the quadratic function[tex]\(2x^2 - 7x + 5\)[/tex]by completing the square, follow these steps:

1. Factor out the coefficient of[tex]\(x^2\):\[2x^2 - 7x + 5 = 2(x^2 - \frac{7}{2}x) + 5\][/tex]

2. Take half of the coefficient of [tex]\(x\)[/tex]and square it:

[tex]\[\left(\frac{-7}{2} \div 2\right)^2 = \left(\frac{-7}{4}\right)^2 = \frac{49}{16}\][/tex]

3. Add and subtract this value inside the parentheses:

[tex]\[2\left(x^2 - \frac{7}{2}x + \frac{49}{16} - \frac{49}{16}\right) + 5\][/tex]

4. Rewrite the expression inside the parentheses as a perfect square trinomial:

[tex]\[2\left[\left(x - \frac{7}{4}\right)^2 - \frac{49}{16}\right] + 5\][/tex]

5. Distribute and simplify:

[tex]\[2\left(x - \frac{7}{4}\right)^2 - 2 \times \frac{49}{16} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + \frac{40}{8}\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\]So, the quadratic function \(2x^2 - 7x + 5\) rewritten by completing the square is \(\boxed{2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}}\).[/tex]

Answer:

Option 2nd , 4th and 6th correct

[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Given the expression:

[tex]\frac{5}{6}a-2b-16.3+\frac{b}{12}+c-0.9b[/tex]

Combine like terms;

[tex]\frac{5}{6}a+b(-2+\frac{1}{12}-0.9}-16.3+c[/tex]

Simplify:

[tex]\frac{5}{6}a-2.81666667b-16.3+c[/tex]

Therefore, the  term can be combined in the given expression is,

[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]