How many different roots does the polynomial function,
y = (x − 2)(x + 3)² have?
-
A. 1
B. 3
C. 2
D. 4

The SAS congruency is applied here.

Hence,

[tex] \frac{TR}{JK} = \frac{RS}{JL} = \frac{TS}{KL} \\ \frac{24}{x} = \frac{12}{6} = \frac{y}{15} \\ \frac{24}{x} = 2 \\ x = 48 = JK[/tex]

[tex] \frac{y}{15} = 2 \\ y = 30[/tex]

Perimeter =

[tex]6 + 30 + 48 \\ 36 + 48 \\ = 84[/tex]

Answer:

Step-by-step explanation:

ham 3.45x

The total 7 two-player games and 6 six-player games were played.  

Here the total games = 13

And the total number of athletes participated = 50

Let us assume that x represents the total 2-player games played and y represents the total 6-player games played.

The neighborhood holds 13 total games.

So, we get an equation,

x + y = 13                    ................(1)

There are 50 athletes signed up for a neighborhood basketball competition.

So, we get an equation,

2x + 6y = 50                 .............(2)

From equation (1)

x = 13 - y                   ..........(3)

substitute above value of x in equation (2)

2(13 - y) + 6y = 50

26 - 2y + 6y = 50

4y = 24

y = 6

Substitute above value of y in equation (3)

x = 13 - 6

x = 7      

Thus, we can conclude that the total 7 two-player games and 6 six-player games were played.  

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The acute angle formed by the hands of a clock at 4:20a.m is 10°.

For the minute hand, we can compute that, for its every move, it covers 6 degrees. And for the hour hand, each move covers 30 degrees.

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

The angle between the hour's hand and the minute hand when the clock shows 4:20 pm can be calculated by using the formula:

Angle=|11/2 M-30H|

where M= minute H= hour's

Here M=20 H=4

Therefore we get the angle |11/2(20)- 30*4|=|110-120|=|-10°|=10°

Hence, 10° is the correct answer.

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The probability that Andre, Olivia, and Zach all win gift cards that are at least $25 is 0.

Since the value of the gift cards is determined by chance, it is impossible to calculate the probability of this exact outcome. Instead, we can calculate the probability of any one person winning a gift card that is at least $25, which is 0.5.

The probability of them all winning would be the product of the individual probabilities, which is 0.5 x 0.5 x 0.5 = 0.125. However, since this is impossible, the probability of this exact outcome is 0.

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Answer:

  D)  500(1 +.03/4)^(4(5))

Step-by-step explanation:

You want to know the expression you would input to a calculator to find the money Joe will have in his account from a $500 deposit earning 3% interest compounded quarterly for 5 years.

The value of the account is given by the formula ...

  A = P(1 +r/n)^(n·t)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, you would want your calculator to evaluate ...

  500(1 +.03/4)^(4(5)) . . . . . . . matches choice D

__

Additional comment

The attachment shows a couple of different calculator inputs that could be used to find the account value. Note that the product (4)(5) is the exponent of the base (1 +.03/4). This calculator uses the caret (^) key to open the exponent expression.

The calculator also has a "future value" function that will compute the same result.

The value in the account will be $580.59.

<95141404393>

Using division we know that each person will have 1/4 pound of Skittles.

In mathematics, the division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

The division sign, "," or occasionally "/," is used in computer code.

So, we know that:

Lauren and Shayla have 1/2 pound of Skittles

They will share it with 2 more people.

Then, each will have:

(1/2)/2

1/2 / 2

1/2 * 1/2

1/4

Therefore, using division we know that each person will have 1/4 pound of Skittles.

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30 different combinations can be made among six people.

The total number of arrangements is called Permutations.

According to the question,

There are 6 members to choose from.

And there are 2 posts to be filled. i.e, President, Vice-President.

Let's assume each position is a blank. Here each blank represents a placeholder.

The first position can be filled in 6 ways (because any one of the students can get that position)

The second position can be filled in 5 ways (as one person already got the first position, he can't get the second position).

The total number of ways all three positions can be filled in

= 6 * 5 = 30

So, the total number of ways in the combination = 30.

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x = 1

Answer:

-----------

3x + 1 = 4x

4x = 3x + 1

4x - 3x = + 1

x = 1

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of the same size.

The frequency (or absolute frequency) of an event in statistics is the number of times the event occurred in an experiment or research. Histograms are frequently used to graphically show these frequencies.

The absolute frequency of an occurrence normalized by the total number of events is referred to as its relative frequency (or empirical probability). A frequency distribution can be created by plotting the values of all events.

A histogram is a graphical representation of tabulated frequencies that is displayed as consecutive rectangles erected at discrete intervals (bins) with an area equal to the frequency of the observations in the interval.

The frequency density of the interval, i.e. the frequency divided by the width of the interval, is also equal to the height of a rectangle.

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The eigenvectors of AAH are called the left-singular vectors of A and the eigenvectors of AHA are the right-singular vectors of A . They are called this way because of their use in singular value decomposition. Say A=UΣVH , then the columns of U are the left-singular vectors and the columns of V are right-singular vectors.

We know that the non-zero eigenvalues of AAH  and AHA are the same, they are the squares of the singular values of A . A singular of value of A is a value σ such that Av=σu   AHu=σv where u is a left-singular vector and vs a right-singular vector. This can be taken as the definition of singular value, left-singular vector (which is an eigenvector of AAH) and right-singular vector (which is an eigenvector of AHA).the left-singular and right-singular vector pair works with AAH and AHA

AAHu=σAv=σ2u

AHAv=σAHu=σ2v

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Q: What is the relationship between the eigenvectors of AAT and ATA?

As per the statement the data are qualitative because they don't measure or count anything.

The term measurement in math is known as the process of associating numbers with physical quantities and phenomena.

Here we have the statement the types of food served by restaurants Italian, Chinese, fast, etc.

As we looking into the statement we have identified that the statement is defines the characteristics of the restaurant which is also defines that there is no value for counting in it.

So, this refers the quality of the product instead of quantity.

Which also defined that there is no measurement value in it.

Therefore, the correct option is (c).

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W = 6 is a solution to the inequality.

In mathematics, Inequality is an unequal comparison between two or more algebraic terms or expressions. The solution of an inequality is a numerical value that will satisfy the given expression.

The signs that we use in Inequality expression are  

'>' - greater than

'<' - less than

'≥' - greater than or equal to

'≤' - less than or equal to

Here we have

Inequality 8 > W

Where the symbol '>' less than indicates 8 is greater than W

or the value of W is less than 8  

As we can see that 6 < 8

Therefore,

W = 6 is a solution to the inequality.

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Complete the pyramid with the corresponding values

Since each number is the product of the two numbers directly below it. Then the pyramid can be completed as follows:

Check the attached image for labeling.

j = -1 × -1 = 1

h = -2 × j = -2 × 1 = -2

y = h × -1 = -2 × -1 = 2

j × n = -1

1 × n = -1

n = -1

n × m = 2

-1 × m = 2

m = -2

w = -1 × 2 = -2

t = y × w = 2 × -2 = -4

-1 × k = n

-1 × k = -1

k = 1

k × l = m

1 × l = -2

l = -2

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She should use the equation k = P/x². The correct answer would be an option (D).

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

The potential energy, P, in spring is represented using the formula, as follows:

P = kx²

Solve for variable k and we get the equation:

k = P/x²

When we compare this equation to the provided possibilities, we can easily see that it corresponds to the last option.

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Answer:

Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function is the set of values that we are allowed to plug into our function. While a functions range, is the set of values that the function can take.

To be more precise, he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

A relation's domain can also be discussed, where one element in the domain may be mapped to more than one element in the range.

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Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave with a frequency of 4.11×10⁴ Hz is 7299.27 m.

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).

Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) using the following equation:

v = f×λ

In this case, you know:

v= 3×10⁸ m/s

f= 4.11×10⁴ Hz

λ= ?

Replacing:

3×10⁸ m/s= 4.11×10⁴ Hz× λ

Solving:

λ= 3×10⁸ m/s ÷ 4.11×10⁴ Hz

λ=7299.27 m

In summary, the wavelength of the wave is 7299.27 m.

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If the force is changed to 50N, the acceleration of the object becomes 10m/s²

From the information given, we have that force is directly varies as the acceleration.

Given that;

This is represented as;

F ∝ a

Then, the constant is

F= ka

Now, make 'k' the subject of the formula, we get;

k = F/a

substitute the values to determine the value of k

k = 40/8 = 5

If the value of the force, F of the object changes to 50N, then the acceleration is given as;

a = F/k

Substitute the values into the formula

a = 50/5

Divide the values

a = 10m/s²

Hence, the value is a = 10m/s²

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The class midpoint of the first class in the case of table of quantitative data is 0-4 and the second class is 5-9 is 2.5

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(x - h)^2 + (y - k)^2 = r^2 is the equation for a circle with center (h, k) and radius (r).

What exactly is a math equation?

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

So, an equation that represents a circle with center (5, -1) and radius of 16 units is:

(x - 5)^2 + (y + 1)^2 = 16^2

or

(x - 5)^2 + (y + 1)^2 = 256

The graph of this equation will be a circle centered at the point (5,-1) with a radius of 16 units.

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An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - (-4))

y - 3 = 3(x + 4)

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Answer: A: what would be population equal 100 years from now?

Step-by-step explanation: I hope this helps!

The approach used to solve equations with integer coefficients & constants can also be used to solve equations with fractional / decimal coefficients and constants.

An equation is a mathematical statement that expresses the equality of two expressions. It is a relationship between two or more variables, such as x + y = z. Equations are used to solve a wide variety of problems in mathematics, physics, chemistry, engineering and other scientific fields.

The main difference is that when solving equations with fractional or decimal coefficients and constants. For example, if you have an equation with a decimal coefficient, divide both sides by the coefficient to make the coefficient 1 before you can use the same steps to solve the equation.

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Answer:

48×14 in.

Step-by-step explanation:

[tex]50^{2} =48^{2} +14^{2}[/tex]

[tex]2500=2304+196[/tex]

[tex]2500=2500[/tex]

The TV screen is 48 inches long and 14 inches high.

Hope this helps.

Answer:

Hi, my name is Za'Riah! I will gladly help you with your problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out with this problem.

60% of 150 is 90

150 + 90 = 240 inches

The truck is 240 inches long.

Answer:

240

The two rational numbers that result in the lowest product are given as follows:

18.5 and -12.4.

For the product of two rational numbers, we have that their signal is given as follows:

For the lowest product, we want a negative number, with the highest absolute value, hence we take the lowest negative and highest positive, as follows:

18.5 and -12.4.

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With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are performed on variables and constants. Let's imagine that while playing with matchsticks, James and Natalie came up with the idea to arrange the sticks into patterns that represented numbers.

James drew a four in the air with four matchsticks. Natalie was able to make a pattern with two 4s by putting three more matchsticks on the board. They realised they could proceed to add three matchsticks each round until they had a total of four. This led them to the conclusion that, in general, 4+ 3(n-1) sticks are needed to make a pattern with n numbers of 4s. This sentence makes reference to the algebraic expression 4+ 3(n-1).

The total no. of tables are 32

Let x be the no. of Small tables = 2x

And y be the no. of Large tables = 4y

Total no. of tables = 12

2x + 4y = 32

And

x + y = 12

x = 12 - y

Putting the value of x in first equation

2(12 - y) + 4y = 32

24 - 2y + 4y = 32

4y - 2y = 32 - 24

2y = 8

y = 4

And Putting the value of y in 2nd equation

x = 12 - (4)

x = 8

Thus, With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

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Using the similarity rectangle theorem, the value of FG is approx 23.

We determine the value of FG using the using the similar rectangle theorem.

Two rectangles must have proportional sides in order for them to be identical (form equal ratios). The two shorter sides should be proportionately equal to the two longer sides.

The rectangle ABCD and FGEH are both have same shape.

As we know that the rectangle same two sides equal. So

FG/EF = AD/DC

FG/15 = 18/12

Multiply by 15 on both side, we get

FG = 18/12 * 15

FG = 3/2 * 15

FG = 22.5

FG = 23 (approx)

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The complete question is:

Square 1 ABDC square 2 FGEH. AD= 18 DC=12 FE= 15. How do I find the square factor FG?

The horizontal distance that the jet has traveled in 10 seconds will be 3000feet and the jet’s altitude at this time is 6.44 minutes

Given: A plane flies off at a 15-degree angle and 350 feet per second.

Find The time needed to ascend to a height of 35,000 feet.

Imagine a right triangle with a 15-degree angle at the origin at Q1.

The plane's flight route is the hypotenuse.

speed = distance/time

speed * time = distance

distance = 300*10 = 3000feet

Sin(15) = opposite / hypotenuse

Sin(15) = 35000 / (350*t)

350*t  =  35000 / Sin(15)

t  =  35000 / (350 * Sin(15)

t  =  100 / Sin(15)

t   = 100 / .25882

t   =  386.37 seconds

t = (386.37 sec) * (1 min. / 60 sec)  = 6.44 minutes

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