factor the trinomial or state that the trinomial is prime 3a^2 -10a-32

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Answer:

  1,000,000

Step-by-step explanation:

The attached place value chart shows the power of ten associated with each number place in a decimal number.

You have ...

  1 × 10⁶ = 1,000,000

(Put the multiplier digit in the appropriate number place, and fill the remaining spaces with zeros. The digits 32,465 on the chart can be ignored.)

__

Additional comment

For powers of 10, the exponent (6 in this case) tells you the number of zeros to the right of the digit 1. That is, 10^6 is 1 followed by 6 zeros:

  1,000,000

Answer: 3

Step-by-step explanation:

3x8 = 24

24x2= 48!

8x12= 96!

Answers must be divisible by both numbers, and achievable by both inputs.

Hope This Helped

Answer:

Step-by-step explanation:

Area = 30 x 15 - 10 x 5

Area = 450 - 50

Area = 400 m^2

Hope that helps! :)

-Aphrodite

Answer:

400 m^2

Step-by-step explanation:

the figure is composed by a square and a rectangle

Area of the square = side^2 = 10^2 = 100 m^2

area of the rectangle = base x height = 20 x 15 = 300 m^2

total area = 300 + 100 = 400m^2

light stand for knowledge in the poem

Answer:

light stand for knowledge in the poem

Step-by-step explanation:

The equivalent equatiοn x² + 16x = 22 will be (x + 8)² = 86. Then the cοrrect οptiοn is A.

The equivalent is the expressiοns that are in different fοrms but are equal tο the same value. Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value(s) fοr the variable(s).

The equatiοn is given belοw.

x² + 16x = 22

Add bοth side 64.

x² + 16x + 64 = 22 + 64

        (x + 8)² = 86

Then the cοrrect οptiοn is A.

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Complete question:

Which equation is equivalent to the given equation? x² + 16x = 22

a. (x+8)² = 86

b. (x+8)² = 38

c. (x+16)² = 278

d. (x+4)² = 22

Answer:

when we add all the angles.

=58+94+15=167

so it's a 180..

180_167

=13

round to nearest tenth.

=10..

Answer:

the variance of X is 0.126.

Step-by-step explanation:

The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:

P(X = k) = (nCk)(N-nCk) / (NCk)

where C denotes the combination function.

(a) Expectation of X:

E(X) = np = nK/N = (4/20) * 4 = 0.8

Therefore, the expected number of white balls drawn is 0.8.

(b) Variance of X:

Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126

Therefore, the variance of X is 0.126.

Answer:

The expected number of white balls drawn is 0.4 and the variance of X is 0.24.

Step-by-step explanation:

The proof is shown below:

The tangent is defined as a line touching circles or an ellipse at only one point.

As, tangent line is perpendicular to radius of the circle.

So,

AR ⊥ RS

BS ⊥ RS

Thus, AR and BS ⊥ to same line RS.

Now, either AR or BS are in same line or parallel.

since, they are the radius of different circles.

Hence, AR ║BS.

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The Guy above me is correct

The new coordinates of the reflected point will be (2, 2).

In mathematics, reflection is a transformation that "flips" an object over a line or plane. Reflection is a type of symmetry, where an object appears exactly the same after being reflected as it did before.  

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.  

Here we have

The point (-2, 2) is reflected across the y-axis

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.

The new coordinate of the point = (-(-2), 2) = (2, 2)

Therefore,

The new coordinates of the reflected point will be (2, 2).

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Check the picture below.

so the quadrilateral is really two triangles, each with a base of 3 and a height of 6

\(\stackrel{\textit{area of the two triangles}}{2\left[ \cfrac{1}{2}(\underset{b}{3})(\underset{h}{6}) \right]\implies 2(9)\implies} \text{\LARGE 18}\)

The test scores 78,90,94,72,80,68,72,88,94,98,86,96 for students in Mr.Garcia's study group arranged as box-whisker-plot in option D is the correct form.

What is box-whisker-plot?

It is a type of data representation which is also known as box plot. It shows the main 5 pointed data which includes maximum value of given data, minimum value of the given data, median of the data, upper quartile and the lower quartile. The upper and lower extremes are indicated using end point of the lines. The box indicates the inter quartile range and the whisker inside the box indicates the median of the data.

The observations given are:78,90,94,72,80,68,72,88,94,98,86,96

On arranging the data in ascending order, we get:

68, 72, 72, 78, 80, 86, 88, 90, 94, 94, 96, and 98

As the number of observations are even, the median will be the average of \(\frac{N}{2} and \frac{N}{2}+1\) terms{where N=number of observations}

Median= mean of \(\frac{12}{2} and \frac{12}{2} + 1\) terms

           =mean of 6th and 7th term of the sequence

           =mean of 86 and 88   {6th term=86 and 7th term=88}

Median =87

First quartile Q1: Median of all terms before median{68, 72, 72, 78, 80, 86}

Quartile 1= mean of 3rd and 4th term { \(\frac{N}{2} and \frac{N}{2}+1\) }

               =mean of 72 and 78  {3rd term=72 and 4th term=78}

               =75

Quartile 3=Median of all terms after median{88, 90, 94, 94, 96, 98}

Quartile 3= median of terms {88, 90, 94, 94, 96, 98}

               = mean of 3rd and 4th term { \(\frac{N}{2} and \frac{N}{2}+1\) }

               =mean of 94 and 94  {3rd term=94 and 4th term=94}

               =94

Inter quartile range=quartile 3 - quartile1

                               =94 - 75

                                =19

The 5 points to check the correct box-whisker-plot are:

Minimum observation=68

Lower quartile=75

Median=87

Upper quartile=94

Maximum observation=98

The correct option is D.

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Refer to the figure attached below for options.

The area of the triangle given as in the attached image to the task content is; 1 ft².

It follows from the task comtent that the area of the triangle given be determined.

Since the area of a triangle is given by the formula; Area = (1/2) × base × height.

Since the base of the triangle in discuss is 3 ft and it's height (altitude) as given in the task content is; (2/3) feet.

It follows that the area is;

Area = (1/2) × 3 × (2/3).

Area = 1 ft².

Ultimately, the area of the triangle is; 1 ft².

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Answer:  geometric series

Step-by-step explanation:

If it is arithmetic, the difference from each term to the next will always be the same.

4096 - 1024 = 3072; 1024 - 256 = 768

3072 ≠ 768. so not arithmetic

If it is geometric, the ratio of each term to the next will always be the same.

4096/1024 = 4

1024/256 = 4

256/64 = 4

64/16 = 4

This is a geometric series. Each term (after the first) is (1/4) of the term before.

Hope this helps.

Answer:

-24r + 56

Step-by-step explanation:

To find the area of this rectangle we multiply width and length

8 × (-3r + 7) = -24r + 56

Answer:

x=9.6

Step-by-step explanation:

The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.

The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.

Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:

\(a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6\)

a. Luke's age can be expressed as z - 4.

b. Mischa's age can be expressed as (z - 4)/2.

c. If Zoe is 16 years old, Luke is 12 years old, and Mischa is 6 years old.

Expressions are often used to simplify complex ideas or calculations and can be used in a variety of contexts.

a. Luke's age can be expressed as z - 4, where z is Zoe's age.

b. Mischa's age can be expressed as (z - 4)/2, where z is Zoe's age.

c. If Zoe is 16 years old, Luke is 16 - 4 = 12 years old, and Mischa is

(16 - 4)/2 = 6 years old.

To demonstrate, let's plug in Zoe's age of 16 into the expressions:

a. Luke's age = z - 4

= 16 - 4

= 12

b. Mischa's age = (z - 4)/2

= (16 - 4)/2

= 6

Therefore, if Zoe is 16 years old, Luke is 12 years old and Mischa is 6 years old.

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Answer:

The cost of one ticket will be £8.20

The answer is:

(x - 3)(2x + 9)

Work/explanation:

Since (x-3) appears in both terms, we move it to the first place:

(x - 3)

We need to have another term; for that other term, we take what's left, and put that as our other term.

As a result, we have:

(x - 3)(2x + 9)

Hence, this is the answer.

The use of internal rhyme affect the poem by: C. It helps create and maintain the poem's playful tone

Internal rhyme tend to occurs when words that are in the same line of a poem rhyme with one another.

The use of internal rhyme can tend to  add  more musical quality to a poem and it as well help to create cohesion within a line or stanza. Internal rhyme also help to a sense of playfulness in the poem.

Therefore we can conclude that the correct option is C.

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Answer: 2

Step-by-step explanation:

See attached image

For the population to double, it takes around 7.07 hours.

The continuous exponential growth model is given by:

\(N(t) = N0 * e^{rt}\)

Where:

N(t) is the population size at time t

N is the initial population size (at t = 0)

r is the growth rate parameter

t is the time elapsed

We want to find the time t it takes for the population size to double, which means N(t) = 2N. Substituting into the growth model, we get:

\(2N = N * e^{rt}\)

Dividing both sides by N, we get:

\(2 = e^{rt}\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting r = 0.098 (9.8% as a decimal), we get:

t = ln(2)/0.098

t ≈ 7.07 hours

Therefore, it takes approximately 7.07 hours for the population size to double.

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Answer:a A. 4x-7/2x(x-2)

got it right on the test

Step-by-step explanation: