Can someone answer these 3 trig questions using sum and difference identities formula and show work ty very much

The vertex is (4,1), and the parabola opens b since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to one of its sides. It is a type of quadratic function, which can be expressed in the form of y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.

f(x) = x²+8x-3

To complete the square, we need to add and subtract the square of half the coefficient of x:

f(x) = (x²+8x+16) - 19 --> (x+4)² - 19

So, the equation in vertex form is: f(x) = (x+4)² - 19.

The vertex is (-4,-19), and the parabola opens upwards since the coefficient of the squared term is positive. The axis of symmetry is x=-4, and the domain is all real numbers. The range is [-19, ∞), since the minimum value is -19.

f(x)=-2x² + 16x-31

To complete the square, we need to factor out the leading coefficient of -2, and then add and subtract the square of half the coefficient of x:

f(x) = -2(x² - 8x + 16) - 31 + 32 --> -2(x-4)² + 1

So, the equation in vertex form is: f(x) = -2(x-4)² + 1.

The vertex is (4,1), and the parabola opens downwards since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

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Answer: $5.40

Step-by-step explanation:

First, let's calculate the tax for each purchase and then find the total amount paid by Dave and James.

For Dave:

Basketball cost = $15

Tax = 8% of $15 = 0.08 * 15 = $1.20

Total amount paid by Dave = Cost + Tax = $15 + $1.20 = $16.20

For James:

Football cost = $20

Tax = 8% of $20 = 0.08 * 20 = $1.60

Total amount paid by James = Cost + Tax = $20 + $1.60 = $21.60

Now, let's find the difference between the amounts paid by Dave and James.

Difference = Amount paid by James - Amount paid by Dave = $21.60 - $16.20 = $5.40

So, the difference in the amounts paid by Dave and James, including tax, is $5.40.

Answer:

2x^2+8x-4

Step-by-step explanation:

The quadratic function that models the height h of the ball after t seconds in flight is h(t) = -16t² + 70t + 3.5

A quadratic function is a type of function in algebra that involves a variable raised to the power of 2, or squared. The general form of a quadratic function is:

f(x) = ax² + bx + c

where f(x) represents the output of the function for a given input x, a, b, and c are constants that determine the shape and position of the function, and x is the input variable.

The graph of a quadratic function is a parabola, which is a curved shape that opens upwards if the coefficient a is positive, and downwards if the coefficient a is negative. The vertex of the parabola is the point at which the function reaches its minimum or maximum value, depending on the direction of the opening of the parabola. The x-coordinate of the vertex is given by:

x = -b/2a

The height h of the ball after t seconds in flight can be modeled by the quadratic function:

h(t) = -16t² + vt + s

where v is the initial velocity of the ball, s is the initial height of the ball, and -16 is the acceleration due to gravity in feet per second squared.

In this case, we know that the ball is hit with an initial velocity of 70 ft/s and is 3.5 ft off the ground, so we can substitute these values into the equation:

h(t) = -16t² + 70t + 3.5

Therefore, the quadratic function that models the height h of the ball after t seconds in flight is:

h(t) = -16t² + 70t + 3.5

Note that this function is only valid until the ball reaches its maximum height and starts falling back down to the ground.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]

Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.

Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).

Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.

The nature of Erin's capital gains and losses are as follows:

Answer:

B: y ≥ 2r-4.

Step-by-step explanation:

To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:

2x - y ≤ 4

Then, we can subtract 2x from both sides to get:

-y ≤ -2x + 4

Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:

y ≥ 2x - 4

Now we can see that the equivalent inequality is option B: y ≥ 2r-4.

Answer:

55% of the whole wall is covered in paint of any color.

Step-by-step explanation:

To determine what percentage of the wall is covered in paint, we need to add the fractions of the wall covered by each color of paint and then convert the result into a percentage.

Red paint: 1/5

Blue paint: 1/10

Green paint: 1/4

First, we need to find a common denominator, which is the least common multiple (LCM) of the denominators 5, 10, and 4. The LCM of 5, 10, and 4 is 20. Now, we can convert the fractions to equivalent fractions with a denominator of 20:

Red paint: (1/5) * (4/4) = 4/20

Blue paint: (1/10) * (2/2) = 2/20

Green paint: (1/4) * (5/5) = 5/20

Now, add the fractions:

Total paint coverage = 4/20 + 2/20 + 5/20 = (4 + 2 + 5)/20 = 11/20

To convert this fraction to a percentage, we can divide 11 by 20 and multiply the result by 100:

(11/20) * 100 = 0.55 * 100 = 55%

Thus, 55% of the whole wall is covered in paint of any color.

Answer:

338262.124

Step-by-step explanation:

127.6/10 = 12.76 (depending on how many zero is how much you'll move the decimal to the left)

12.76^5 = 338262.124 because it's 12.76x12.76x12.76x12.76x12.76

Step-by-step explanation:

In order to find the f(x) or y value, you have to replace x with the given one in the table:

x = -1,

[tex]y = \sqrt[3]{ - 1 - 7} = \sqrt[3]{ - 8} = - 2[/tex]

.

x = 6,

[tex]y = \sqrt[3]{ 6 - 7} = \sqrt[3]{ - 1} = - 1[/tex]

.

x = 7,

[tex]y = \sqrt[3]{7 - 7} = \sqrt[3]{0} = 0 [/tex]

.

x = 8,

[tex]y = \sqrt[3]{8 - 7} = \sqrt[3]{1} = 1 [/tex]

.

x = 15,

[tex]y = \sqrt[3]{15 - 7} = \sqrt[3]{8} = 2[/tex]

Also, the correct graph is in the 2nd photo, where the root is (7; 0)

The radius οf the rain barrels is apprοximately 40.03 cm.

A value knοwn as the square rοοt οf a number is οne that, when multiplied by itself, yields the οriginal number. An alternative tο square rοοting a number is tο use it. Therefοre, the cοncepts οf squares and square rοοts are cοnnected. The οriginal number is equal tο the square rοοt οf any integer, which is equivalent tο a number.

The tοtal surface area is given as 40,212 square centimeters. Therefοre, we can write the equatiοn:

[tex]2\pi r^2 +\pir^2 + 4\pi r^2 + \pi r^2 = 40212[/tex]

Simplifying this equatiοn, we get:

[tex]8\pi r^2 = 40212[/tex]

Dividing bοth sides by 8π, we get:

[tex]r^2 = 1602.62[/tex]

Taking the square rοοt οf bοth sides, we get:

r ≈ 40.03 cm

Therefοre, the radius οf the rain barrels is apprοximately 40.03 cm.

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The three true statements are

Step-by-step explanation:

Standard form for a circle is  ( x -h)^2 + ( y-k)^2 = r^2

     h, k   is the center      r is the radius

x^2 -2x + y^2 = 8     arrange into standard form ( complete the square for 'x')

(x-1)^2 + y^2 = 8+1

(x-1)^2 + y^2 = 9        shows center is at   1, 0

                                   radius = 3

 So

The radius of the circle is 3 units.

The center of the circle lies on the x-axis    (1,0 is on the x axis)

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The lowest odd integer is [tex]35[/tex] followed by the next two odd integers in a row,[tex]37[/tex] and [tex]39[/tex] Thus, these are three consecutive odd integers.

Numbers that can be positive, negative, or zero but are not fractions are said to be integers. All mathematical operations, such as addition, subtraction, multiplication, and division, can be performed on integers. There are integer occurrences of [tex]1, 2, 5, 8, -9[/tex], and so on. [tex]Z[/tex] represents a number.

The variable for the lowest odd integer should be defined first. Assume that [tex]x[/tex] is the lowest odd number.

Since there is always a [tex]2[/tex] difference between two successive odd integers, the following two would be [tex]x+2[/tex] and [tex]x + 4[/tex]

The problem statement states that twice the smallest number [tex](2x)[/tex] is [tex]45[/tex]less than the total of twice the largest number  [tex]2(x+4)[/tex] and twice the middle number [tex](x+2).[/tex]

[tex]2x = (x+2) + 2 (x+4) ) - 45[/tex]

When we simplify and find x, we obtain:

[tex]2x = x + 2 + 4x + 8 - 45[/tex]

[tex]2x = 3x - 35[/tex]

[tex]x = 35[/tex]

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Answer:

34

Step-by-step explanation:

5+5+2=12

12+6+3=21

21+8+5=34

Answer:45

Step-by-step explanation:

5+5(8)=45

Answer:

7.38%

Step-by-step explanation:

If TV cable company has 2400 subscribers who are each paying ​$16 per month, charging $52 per month will yield a maximum revenue of $98,304.

To find the rate that will yield the maximum revenue, we can use the formula:

r = -b / 2a

where r is the rate, a is the coefficient of the quadratic term, and b is the coefficient of the linear term in the revenue equation.

The revenue equation is:

R = (2400 + 120x)(16 - 0.5x)

Expanding and simplifying, we get:

R = -0.5x^2 + 52x + 38400

So, a = -0.5 and b = 52. Plugging these values into the formula, we get:

r = -52 / 2(-0.5) = 52

This means that the company should charge $52 per month to maximize revenue. To find the maximum revenue, we can plug this value into the revenue equation:

R = (2400 + 120(52))(16 - 0.5(52)) = $98,304

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Answer: X= -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of rectangle+area of triangle

hope the picture helps

Using factors, we can conclude that the new product will be 48 time more than the old product.

In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.

Let the product be P.

Let the numbers be a and b.

Now,

P = a × b

According to the question.

Let a is increased by a factor of 12 and b by 4:

P = 12a × 4b

P = 48 × a × b

Hence, we can conclude that the product will increase by a factor of 48.

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Answer:

Because you are spending your time doing other things

Step-by-step explanation:

most of the time people waste time in school because they are busy doing other things and they probably don't think school is important.

a way to stop wasting time in school is to pay attention more in class and start developing a desire to learn.

:) i hope this helps lol

Answer:

For more opportunities to go to college, graduating college gets you a degree, the better degree the better job opportunities, the better job opportunities the more money earned. Your in school for money, the best end goal.

In the excerpt from "The City Lost in the Snow," the statement that best reflects how the cultural setting influences Sigismondo's attitude is: C.

The scarcity of jobs makes Sigismondo appreciate the temporary employment the snow provides. T

his statement reflects the importance of the cultural setting, as it shows that Sigismondo values the opportunity to work and earn money, even if it's temporary, due to the scarcity of jobs in the city.

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The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.

Answer:

The correct answers for this question are:

A. Diagonals bisect each other.

C. Opposite angles are congruent.

D. Opposite sides are parallel.

E. Consecutive angles are supplementary. Those are the statements that describe properties of parallelograms. They are also belong to the family of quadrilateral.

Step-by-step explanation:

The only equivalent expression is option (a) [tex]7^x[/tex].

What is expression ?

An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.

To find equivalent expressions for[tex]21^x/3^x[/tex], we can try to simplify the expression using exponent rules.

21 can be factored as 7*3, so we can write:

[tex]21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x[/tex]

Therefore, we can see that option (a) 7^x is equivalent to the given expression.

To check the other options:

b) [tex](7/3)^x[/tex] = [tex](7^x)/(3^x)[/tex] which is not equivalent to the given expression.

c) [tex]3^(2x+1)[/tex] can be written as [tex]3^(2x)[/tex] × [tex]3^1[/tex] = [tex](3^2)^x[/tex] × 3 = [tex]9^x[/tex] × 3 which is not equivalent to the given expression.

d) [tex]7^(x-1)[/tex] can be written as [tex]7^x/7[/tex] which is not equivalent to the given expression.

e) [tex](3/7)^x[/tex] is not equivalent to the given expression.

Therefore, the only equivalent expression is option (a) [tex]7^x[/tex].

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The complete question is:

Which expressions are equivalent to [tex]21^x/3^x[/tex]? Check all that apply.

a) [tex]7^x[/tex]

b) [tex](7/3)^x[/tex]

c) [tex]3^(2x+1)[/tex]

d) [tex]7^(x-1)[/tex]

e) [tex](3/7)^x[/tex]

Answer:

soln

6+r =2r+3

6-3=2r-r

3=r

The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.

Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:

Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]

Here, Principal = $160,000

APR = 4.57%,

Number of Months = 30 years ÷ 12 months/year = 360 months.

First, we need to convert the APR to a monthly interest rate by dividing it by 12:

Monthly Interest Rate = 4.57% × 12

Monthly Interest Rate = 0.3808%

Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]

Monthly Yield = $637.71

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The probabilities that select an incorrect choice are

a) P(correct) = 1/6 b) P(incorrect) = 5/6 c) P(correct) = 1/3 d) P(incorrect) = 2/3.

What is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It is a way of quantifying uncertainty, and is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain.

What are events in probability?

In probability, an event refers to an outcome or a set of outcomes of a random experiment or a process. A random experiment is an experiment or a process that has multiple possible outcomes, and the outcome of the experiment is uncertain or unpredictable.

a) The probability of selecting the correct choice from six possible choices is 1 out of 6, or 1/6, since there is only one correct answer among the six options.

b) The probability of selecting an incorrect choice from six possible choices is 5 out of 6, or 5/6, since there are five incorrect answers among the six options.

c) If three choices can be eliminated, then there are only three options left, with one correct answer among them. Therefore, the probability of selecting the correct choice from the remaining options is 1 out of 3, or 1/3.

d) Similarly, if three choices can be eliminated, then there are three options left, with two incorrect answers among them. Therefore, the probability of selecting an incorrect choice from the remaining options is 2 out of 3, or 2/3.

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Answer: (x+2)(x-8)

Step-by-step explanation:

x^2-6x-16
x^2-8x+2x-16
x(x-8)+2(x-8)
(x+2)(x-8)

Answer:

Yes, Alexa is correct.

Step-by-step explanation:

Counting by 8 means adding 8 repeatedly. The first multiple of 8 is 8 (1 x 8), the second multiple is 16 (2 x 8), the third multiple is 24 (3 x 8), the fourth multiple is 32 (4 x 8), and the fifth multiple is 40 (5 x 8). So, by counting by 8 five times, Alexa can find the fifth multiple of 8 which is 40.