Find the distance between the points (3, 8) and (-1, 9).
Square root 15
Square root 15
Square root 17

Answer:

  {-1/2, 1}

Step-by-step explanation:

You can divide the given polynomial by the factor (x +2) to find the remaining quadratic. That can be factored in the usual way to find the remaining zeros, or other means can be used. Such "other means" include graphing and the use of the quadratic formula.

The first attachment shows the synthetic division of f(x) by (x+2). The quotient is 2x^2 -x -1, which factors as ...

  2x^2 -x -1 = (2x +1)(x -1)

The zeros are the values of x that make these factors zero: -1/2, +1.

_____

My favorite way to find the roots of any higher degree polynomial is to use a graphing calculator. The second attachment shows that method.

We can find other zeros for the given polynomial by polynomial factoring or polynomial division. Upon dividing the given polynomial by (x+2), we get another polynomial. The zeros of this second polynomial can be found using the quadratic formula; getting the two zeros as x = 1 and x = -0.5.

Given a polynomial  [tex]f(x) = 2x^3 + 3x^2 - 3x - 2[/tex]and one of its zeros is -2; we can find the other zeros by polynomial factoring or polynomial division. First, divide the entire polynomial by (x+2) because -2 is one of the zeros. So we end up with 2x^2 - x - 1 = 0.

Now use the quadratic formula to find the remaining zeros: [tex]x = [-b\±\sqrt(b^2 - 4ac)] / (2a).[/tex]By substituting the constants from the factored polynomial equation, we will get [tex]x = [-(-1)\±\sqrt((-1)^2 - 4*2*(-1))] / (2*2) = [1\±\sqrt(1 + 8)] / 4.[/tex]This simplifies to  [tex]x = [1\±\sqrt(9)] / 4 = [1\±3] /4.[/tex] Hence our two more zeros are x = 1 and x = -0.5.

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Answer:

[7, 13/3]

Step-by-step explanation:

Answer: 15 lines of symmetry.

Step-by-step explanation:

There are 15 lines of symmetry does a 15 sided polygon have.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Number of lines of symmetry does a 15 sided polygon have

Since, We know that;

Number or line of symmetry is equal to number of sides of polygon.

Here, Number of side = 15

Hence, There are 15 lines of symmetry does a 15 sided polygon have.

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Answer:

Step-by-step explanation:

Look at the picture.

The correct equivalent expression is D. [tex]\log_2{256}[/tex].

The given expression is:
[tex]\log_2{16} + \log_2{16}[/tex]

First, we need to simplify the given expression using properties of logarithms.

Using the property:
[tex]\log_b{m} + \log_b{n} = \log_b(m \times n)[/tex]

We can rewrite the given expression as:
[tex]\log_2{16} + \log_2{16} = \log_2{(16 \times 16)} = \log_2{256}[/tex]

Now we can analyze the options given:

A. [tex]\log_2{28}[/tex]: This is not equivalent because 28 is not the same as 256.

B. 8: This is not in logarithmic form and not equivalent to the simplified expression.

C. [tex]\log{256}[/tex]: This is not equivalent because the base here is 10 (common logarithm), while the given expression has a base of 2.

D. [tex]\log_2{256}[/tex]: This is correct because our simplified form is exactly [tex]\log_2{256}[/tex].

Answer:

x^9

Step-by-step explanation:

The rule of exponents that applies is ...

(a^b)^c = a^(b·c)

For your problem, you have a=x, b=(3/2), c=6, so ...

(x^(3/2))^6 = x^(3/2·6) = x^9

Answer:

[tex]x^9[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\left\{(x)^{\frac{3}{2}\right\}^6[/tex]

We have to simplify the given expression

In order to simplify the expression we will use given below rule

We know that [tex](a^b)^c= a^{b\cdot c}[/tex]

Using this rule

[tex](x)^{\frac{3}{2}\cdot 6}[/tex]

[tex](x)^{3\cdot 3}[/tex]

[tex]x^9[/tex]

[tex]\left\{(x)^{\frac{3}{2}\right\}^6=x^9[/tex]

The answer is:

[tex]t_1=3.60s\\t_2=7.94s[/tex]

Time equal to 3.30 seconds when the arrow was going up.

Time time equal to 7.94 seconds when the arrow was going down.

To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.

Also, we are given some information, we need to substitute it and then use the quadratic equation.

The equation is:

[tex]h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0[/tex]

Substituting the given information we have:

[tex]-16t^{2}+vot-h=0[/tex]

[tex]-16t^{2}+180\frac{ft}{s} t-420=0[/tex]

We have a quadratic equation where:

[tex]a=-16\\b=180\\c=-420[/tex]

Now, using the quadratic equation to find the value or values of "t", we have:

[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94[/tex]

Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:

[tex]t_1=3.60s\\t_2=7.94s[/tex]

Time equal to 3.30 seconds when the arrow was going up.

Time equal to 7.94 seconds when the arrow was going down.

Have a nice day!

Answer:

3.3secs, 7.9secs

Step-by-step explanation:

We are looking for the number of seconds it takes the arrow to reach a height of 420ft. We are given the projectile formula h=−16t2+v0t, where h is the height, in feet, and t is the time, in seconds. We can substitute the initial velocity v0=180 and desired height h=420 to find

420=−16t2+180t

Rewriting this quadratic equation in standard form, we have

16t2−180t+420=0

Now that the equation is in standard form, at2+bt+c=0, we can identify the coefficients a=16, b=−180, and c=420. Substituting these into the quadratic formula, we have

t=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−180)±(−180)2−4(16)(420)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(16)=180±5520‾‾‾‾‾√32

The approximate values for t are

t=≈180+5520‾‾‾‾‾√327.9andt=≈180−5520‾‾‾‾‾√323.3

The arrow will go up and then fall down. As the arrow goes up, it will reach 420ft after approximately 3.3s. It will also pass that height on the way down at approximately 7.9s.

Answer: The answer is D

Step-by-step explanation:

Factor and set each set equal to zero to get x=0,2,-1,1

Answer:

D

Step-by-step explanation:

x¹³ - 2x¹² - x¹¹ + 2x¹⁰ = 0

x¹⁰(x³ - 2x² - x + 2) = 0

x¹⁰ [x²(x - 2) - (x - 2)] = 0

x¹⁰(x² - 1)(x - 2) = 0

x = 0 (multiplicity 10)

x = 1

x = -1

x = 2

Answer:

Option A is correct.

Step-by-step explanation:

No of white cars: 25

No of blue cars : 17

Total number of white and blue cars = 25 + 17 = 42

No of silvers cars: 21

No of red cars: 9

Total number of silver and red cars = 21+9 = 30

No of white and blue cars more than silver and red cars

=Total number of white and blue cars - Total number of silver and red cars

=42 - 30

= 12 cars

So, Option A is correct.

Answer:

-6s-c+1

Step-by-step explanation:

(-3s-4c+1)+(-3s+3c)

We have been given the above expression. To find the sum, we simply collect the like terms and combine them;

(-3s-4c+1)+(-3s+3c) = -3s + -3s -4c + 3c + 1

-3s + -3s -4c + 3c + 1 = -3s - 3s + 3c - 4c + 1

-3s - 3s + 3c - 4c + 1 = -6s - c + 1

Therefore;

(-3s-4c+1)+(-3s+3c) = -6s-c+1

Answer:

[tex]W=839.464\ ft*lbf[/tex]

Step-by-step explanation:

The work done is the product of the magnitude of the force applied to the object by the magnitude of the displacement of the object by the cosine of the angle between the force and direction of the displacement. This is:

[tex]W=|F|*|r|cos(\theta)[/tex]

In this case

[tex]\theta=30\°[/tex]

|F|=180 pound force

The magnitude of vector AB is:

[tex]|r|= \sqrt{5^2 + 2^2}\\\\|r|= \sqrt{29}\ fr[/tex]

Finally the work is:

[tex]W=180*\sqrt{29}*cos(30\°)[/tex]

[tex]W=839.464\ ft*lbf[/tex]

Answer:

the answer is option 1, A

Step-by-step explanation:

Using the continuous compounding formula A = Pe^rt, Katie's account balance after 10 years will be approximately $103,204, with her initial investment of $33,750 at an annual interest rate of 11.17%.

To calculate what Katie's account balance will be in 10 years, with an investment of $33,750 at 11.17% compounded continuously, we use the formula for continuous compounding:

A = Pert

Where:

Plugging in the values we get:

A = $33,750 * e(0.1117 * 10)

Calculating the exponent:

A = $33,750 * e1.117

Calculating the future value:

A = $33,750 * 3.0579 (approximate value of e1.117)

A = $103,204

Katie's account balance after 10 years will be approximately $103,204.

Answer:

  D.  -|0.35t -14| +14

Step-by-step explanation:

The problem statement is asking for an expression for distance in miles, so the constants in the expression will be miles. In the time it takes to get to point B (40 minutes), the ferry has gone (0.35 mi/min)×(40 min) = 14 mi. Hence the maximum value of the function must be 14. The only function with that characteristic is the one of selection D.

[tex]4x^2 - 25=(2x-5)(2x+5)[/tex]

17 pieces. She had two and she had to have 15 to give to the children. If each child got 3 and there is 5. This turns into 3*5=15. Then you would add 15+2 to get 17

Sara initially had 17 candies. This computation is based on the 2 pieces she kept for herself and the three pieces of candy each of her five children received.

The subject of this question is mathematics, specifically it deals with basic arithmetic and problem solving. According to the problem, Sara kept 2 pieces of candy for herself and then gave each of her 5 children 3 pieces. In mathematical terms, this can be represented as an equation: 2 (pieces Sara kept) + 5 (children) * 3 (pieces each child received) = Total pieces of candy Sara had initially.

To solve this equation, first multiply the number of children by the pieces each received: 5 * 3 = 15. Then add the pieces Sara kept: 2 + 15 = 17. Therefore, Sara initially had 17 pieces of candy.

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Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle

Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.

The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.

Answer:

Unusual

Step-by-step explanation:

we know that

The z-score is a measure of how close the given data point is to the mean of the values given with the standard deviation

so

if its z-score is greater than or equal to -2, or less than or equal to 2., then the data value is considered ordinary

if its z-score is less than -2 or greater than 2, then the data value is considered unusual

A data value is considered an outlier if its z-score is less than -2 or greater than 2.

Z-scores are a statistical measure that standardizes data, enabling comparisons across different datasets.

A z-score tells us how many standard deviations a data point is from the mean.

When a z-score is below -2 or above 2, it suggests that the data point is significantly distant from the mean of the dataset.

This indicates that the data point is an extreme observation, differing substantially from the rest of the data.

Outliers can be caused by various factors, such as measurement errors, data entry mistakes, or genuine anomalies in the underlying data. Identifying and handling outliers is crucial for robust statistical analysis and modeling.

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Answer:

Ans1.

Outlier

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.

Cluster

When data seems to be "gathered" around a particular value.

For example: for the values 2, 6, 7, 8, 8.5, 10, 15, there is a cluster around the value 8.

Ans.2

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot.  

This line may pass through some of the points, none of the points, or all of the points.

i will explain through an example

1.  Prepare a scatter plot of the data on graph paper.

2.  Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3.  Find two points that you think will be on the "best-fit" line.  

4.  We are choosing the points (9, 260) and (30, 530).  

You may choose different points.  

5.  Calculate the slope of the line through your two points (rounded to three decimal places).

6.  Write the equation of the line.  

7.  This equation can now be used to predict information that was not plotted in the scatter plot.

Question: Predict the total calories based upon 22 grams of fat. ANS: 427.141 calories

Ans.3

1.Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated.

2.Frequency can easily be determined by conducting a simple experiment and noting how many times the event in question occurs; no calculations are needed. On the other hand, relative frequency is determined by using simple division.

ANSWER

[tex]3 \: radians[/tex]

EXPLANATION

The formula for the calculating the length of an arc is

[tex]l = r \theta[/tex]

where theta is in radians.

From the diagram

[tex]l = 12cm[/tex]

[tex]r = 4cm[/tex]

We substitute the values to obtain;

[tex]4\theta = 12[/tex]

Divide both sides by 4 to get;

[tex]\theta = \frac{12}{4} [/tex]

[tex]\theta = 3 \: radians[/tex]

Answer:

1.40

Step-by-step explanation:

Last week, the price of oranges at the farmers market was 1.75

This week, the price has reduced by 20%

20% of 1.75 = 0.2 × 1.75 = 0.35

The price of the oranges this week is 1.75 - 0.35 = 1.40

Answer:

The correct answer to this problem is the second option: YZ is the longest side.

Step-by-step explanation:

In order to solve this problem, we need to understand the relationship between angle measure and side lengths in a triangle.  

In a triangle, the longest side is located across from the largest angle measure, the smallest side is located across from the smallest angle, and the middle length side is located across from the medium sized angle.

Using this knowledge, we can conclude that since XYZ is the smallest angle, XZ must be the smallest side.  We can also state that since YXZ is the largest angle, YZ is the longest side.  

Looking at the answer options, the only choice that aligns with this information is the second option: YZ is the longest side, and thus we can conclude that this is the correct answer.

Hope this helps!

YZ is the longest side

Step-by-step explanation:

Answer:

[tex]1^2[/tex]

Step-by-step explanation:

The number 1 is called the base.  When we multiply like bases, we add the exponents.  So in order to get 1^9, we will multiply 1^7 by 1^2 because 7+2=9.

Answer:

The answer is [tex]1^{2}[/tex]

Step-by-step explanation:

Using the formula: [tex]a^{m}+a^{n}= a^{m+n}[/tex]

[tex]1^{9}=1^{7}*1^{2}=1^{7+2=9} =1^{9}[/tex]

Answer:

complementary angles

Step-by-step explanation:

∠1 and ∠2 form a right angle and are complementary, that is they sum to 90°

Answer:

  D. x to the power of nine

Step-by-step explanation:

The applicable rule of exponents is ...

  (x^a)^b = x^(ab)

You have a=3/2, b=6, so ab = 3/2·6 = 9.

  (x^(3/2))^6 = x^(3/2·6) = x^9

Answer:

4.25 yards

Step-by-step explanation:

Area of rectangle = Base x Height

or

Height = Area of Rectangle ÷ Base

In this case, Area =38.25 sq yards and Base = 9 yards

Height = 38.25 ÷ 9 = 4.25 yards

Answer:

Step-by-step explanation:

x ≥ 0 means x is non-negative, but it does not mean x is an integer. An additional restriction would need to be applied for x to be a non-negative integer.

Step-by-step explanation:

f(x) = (3/2)ˣ

g(x) = (2/3)ˣ

These are examples of exponential equations:

y = a bˣ

If b > 1, the equation is exponential growth.

If 0 < b < 1, the equation is exponential decay.

So f(x) is an example of exponential growth, and g(x) is an example of exponential decay.

Also, 2/3 is the inverse of 3/2, so:

g(x) = (3/2)^(-x)

So more specifically, f(x) and g(x) are reflections of each other across the y-axis.

Answer:

  64 cm²

Step-by-step explanation:

Suppose the original paper was x cm on a side. Then the original perimeter was 4x.

When the square is folded in half, two of the sides are now x/2, so the perimeter is ...

  x + x/2 + x + x/2 = 3x

If 3x = 24 cm, then x = 8 cm.

The area of the original paper is ...

  A = x² = (8 cm)² = 64 cm²

Answer:

The maximum number of days is 5

Step-by-step explanation:

Let

x ----> the number of days

y ---> the total cost to rent a car in dollars

we know that

The fixed rental fee plus the daily fee multiplied by the number of days must be less than or equal to Pasion's budget

so

The inequality that represent this situation is

[tex]25+10x\leq 75[/tex]

Solve the inequality  for x    

Subtract 25 both sides      

[tex]10x\leq 75-25[/tex]                  

[tex]10x\leq 50[/tex]        

Divide by 10 both sides          

[tex]x\leq 5\ days[/tex]

therefore

The maximum number of days is 5