Which statement is true for all real values of θ? sin2θ − cos2θ = 1 cos2θ − sin2θ = 1 cos2θ = sin2θ − 1 cos2θ = 1 − sin2θ

Given:

Calculate the values for f(x),

The graph of given function is,

The average of a set is computed as follows:

In this case,

tan (Q) = opposite/ adjacent

tan (55º) = PR/ 4.9

________________________

1.43 = PR/ 4.9

PR= 1.4* 4.9 = 6.9

Answer

6.9

______________________________________

Can you see the updates?

Do you have any questions regarding the solution?

____________________

PR= tan (55)* 4.9 = 6.997925 ≅ 7

_________________________________

The arc length can be found through the formula:

then, we can say that r is equal to 4 and the angle is 30°

Answer:

The arc length is approximately equal to 2.09

TheseGiven the set: {-18, -16, -14, -12, -10, -8, -6}

This is 7 numbers

Multiplies of -6 are:

This is 3 numbers

Therefore, the probability is given by:

So:

Answer: 3/7

Answer:

Kaitlin bought 48 yards of ribbon.

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's start by figuring out what we know and what we need to figure out. First of all, we started with $15 and ended with $4.92. We also know that the price of the ribbon is $0.21 per yard and we need to figure out how many yards of ribbon she purchased.

In order to figure this out, we first want to know the difference in the price between what we started and what we ended up with. So, we can subtract! It would look like this:

[tex]15-4.92=10.08[/tex]

So, we figured out that the difference in the price is $10.08, but how do we find out how many yards of ribbon Kaitlin bought? Well, since we know that it is $0.21 cents for a yard of ribbon, we can just take the difference in price and divide it by how much a ribbon cost for a yard of it. So it would look like this:

[tex]10.08/0.21=48[/tex]

We have a nice whole number and that's our answer! Therefore, Kaitlin bought 48 yards of ribbon.

Mathematical Way:

To do it in a more mathematical way, we can put it in the form of a formula. We know that the end total is $4.92 and the initial is $15. We also know that it's $0.21 cents per yard of ribbon but we don't know how many yards she bought. We can let the number of yards she bought represent x in the formula, so we have:

[tex]15=0.21x + 4.92[/tex]

This formula makes sense because we start with $15 at the beginning, so we want to add $4.92 from 0.21x because the end total is the remainder of how many yards Kaitlin bought. The process is essentially the same as the method above. If we were to solve the formula, it would give us the same answer:

[tex]15=0.21x+4.92[/tex]

[tex]15-4.92=0.21x[/tex] - Moving the 4.92 over to the left side, beginning to isolate x.

[tex]10.08=0.21x[/tex]  - Subtracting $4.92 from $15.

[tex]\frac{10.08}{0.21} =\frac{0.21x}{0.21}[/tex] - We divide by $0.21 to solve for x.

[tex]48=x[/tex]

And here, we get the exact same answer, 48 yards of ribbon.

The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.

Since the length is labeled 2 inches, the real length of the room is:

Since the width is labeled 4.5 inches, the real with of the room is:

1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:

Multiply the width and the length to find the area of the room:

Therefore, to the nearest whole number, the area of the game room is 56ft^2.

Answer: B=3

Step-by-step explanation:

Because we have the same denominator we can do the subtraction

Paul did well the representation of the fractions in the diagram, but the operation that he made as we can see is wrong because the result is 9/10

Okay, here we heve this:

We need to combine like terms in the following equation:

Here, we want to complete the table

To do this, we consider points on the plot

From what we have;

We are told that a graph of an exponential function does not cross the x-axis and thus, y cannot be zero

When x =0, y = 1

When x = 1, y = 2

when x = 2, y = 4

The y-intercept is the value of y when x = 0; it is the point at which the graph crosses the y-axis

What we have here is that wehn x = 0, y = 1

Hence, 1 is the y-intercept

Now, let us take a look at the end behavior

We can obtain this from the graph;

As x moves towards infinity, the y value moves towards infinity too as evident from the upward curve of the graph

As x moves toward negative infinity, y moves closer to zero

Since the equation is y=3/8x and x is equal to 44/3, we have

We know that give any pair of real numbers A and B, the following statement will be true:

if, and only if

Now, if we factor a quadratic equation into two factors A and B, and use the fact we've just mentioned, we can then equal each factor to zero, solve for x and get the solutions to said quadratic equation.

First, you have to locate the point (1,3)

Next, from that point, you have to locate the next one. To do that, you need the slope, which in this case is 3. So, from (1,3) you have to move 1 unit to the right and 3 units up, reaching the point (2, 6). Finally, you draw the line that passes through these two points

The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

[tex]p(x)=x^3-5x^2+16x-30[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z = a+bi[/tex] , the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

[tex]p(x)=a(x-3)(x-(1-3i))(x-(1+3i))[/tex]

As the leading coefficient is 1, then a = 1:

[tex]p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

Expand the polynomial:

[tex]\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

[tex]\implies p(x)=(x-3)(x-1+3i)(x-1-3i)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+1-9(-1))[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+10)[/tex]

[tex]\implies p(x)=x^3-2x^2+10x-3x^2+6x-30[/tex]

[tex]\implies p(x)=x^3-2x^2-3x^2+10x+6x-30[/tex]

[tex]\implies p(x)=x^3-5x^2+16x-30[/tex]

The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.

To determine the total distance he traveled you have to add both distances:

To solve this sum, add the fractions first and then add the result to the whole number:

- Add both fractions:

To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:

The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:

- Solve the division:

The mixed number will have the whole number "1".

- To express the decimal value as a fraction, multiply it by 12

The result is the numerator of the fraction, and the denominator will be 12, so:

And the resulting mixed number is:

Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:

The distance he traveled from home to school is 2 1/12 km.

Given:

The equation is given as,

The interval is given as,

The objective is to find the average rate of change.

Explanation:

The general formula to find the average rate of change is,

On plugging the function in the equation (1),

On further solving the above equation,

Hence, the average rate of change is 3.

The x-intercept happens when:

Therefore, the x-intercepts for that functions are:

Answ

Explanation:

To know how much ice pop mixture can each mold hold, we need to calculate the volume of the mold.

The volume of a cone is equal to

Where r is the radius and h is the height of the cone. Replacing r = 2 cm and h = 15 cm, we get:

Therefore, the answer is

A. 20

The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.

Given that:-

Amount invested in life insurance = $ 255

Number of payments in life insurance = 4

Amount invested in real estate taxes = $ 455.35

Number of payments in real estate taxes  = 2

Amount invested in auto insurance = $ 66.21

Number of payments in auto insurance = 6

We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.

Hence,

Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96

Amount put by Rebecca in a month = 2327.96/12 =  $ 193.997 ≈ $ 194

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The speed of the boat is given by the gradient of the line.

Given two points (x1,y1) and (x2,y2) on a graph, the gradient of the line that passes through the two points is given by

In this case,

the line passes through the points (0,0) and (2,2).

We can set (x1,x2) = (0,0) and (y1,y2) = (2,2)

Therefore,

Given that a body travels with speed, s, and in time, t, the distance travelled, d, is given by

In this case,

s = 1km/h, and t = 15hours

Therefore,

Therefore, the boat travelled a distance of 15km

The percent of increase in the cost of the perfume is 29.86%

What is percentage and how can it be calculated?
A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it. No dimension exists for percentages. Thus, it is referred to as a dimensionless number.
Mathematically,
Percent of increase = [(Final value - Initial value)/(Initial value)]×100

Given, the final value of the perfume at purchase = $41.49
Also, the initial value of the perfume as assessed = $31.95
Therefore using the formula established in the literature above,
Percentage increase = [(41.49 - 31.95)/31.95]×100 = 29.86%
Thus, the percent of increase in the cost of the perfume is 29.86%

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Answer:

x = - [tex]\frac{5}{2}[/tex] , x = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

6x² + 23x + 20 = 0 ( factorise the left side )

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × 20 = 120 and sum = 23

the factors are + 8 and + 15

use these factors to split the x- term

6x² + 8x + 15x + 20 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 4) + 5(3x + 4) = 0 ← factor out (3x + 4) from each term

(3x + 4)(2x + 5) = 0

equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = - [tex]\frac{4}{3}[/tex]

To find the area of an obtuse triangle you have to multiply the base of the triangle by the vertical height and divide the result by 2 following the formula:

The base of the triangle is b= 7 miles and the height is h= 8 miles, using these lengths calculate the area as follows:

The area of the triangle is 28 square miles.

The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.

Let the numbers be represented as a and b.

Therefore a + b = -4 .....i

a × b = 53 ........... ii

From equation I, a = -4 - b

Put this into equation ii

ab = 53

(-4 - b)b = 53

-b² - 4b = 53

Equate to 0

-b² - 4b - 53 = 0

The value can be found using the Almighty formula

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In the given right angle triangle BCA : BC = 5, CA = 3 and BA = root 34

From the trignometric ratio of right angle triangle :

The tangent of angle is the ratio of the Adjacent side to the opposite side

In the given triangle, the side opposite to angle A = BC and adjacent side CB

Substitute the value :

The value of tanA = 5/3 or 1.66

Given

P(A) = 0.52

Find

complement of P(A)

Explanation

As we know sum of probabilities is equal to one,

so ,

Final Answer

Therefore, the complement of P(A) = 0.48

• Given that Martha baked 332 muffins,

• 332 / 12 = 27.67 boxes

• If she sold each box for $ 6 ; it will be

27*6 = $162

0.67 * 6 = 4.02

Total 162+4.02 = 166.02≈ $166

• She will make $166, ,

We need the formula that gives us the values of the sequence

where n is the value of the position

using the formula

as we can see the formula is the correct formula because we obtain the values of the sequence