Find g(f(x))

f(x) = -2x^2
g(x) = 3x -1

SHOW YOUR WORK

Step-by-step explanation:

Let x represent theta.

\( \sin( \frac{\pi}{4} - x ) \)

Using the angle addition trig formula,

\( \sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y) \)

\( \sin( \frac{\pi}{4} ) \cos(x) - \cos( \frac{\pi}{4} ) \sin(x) \)

\(( \frac{ \sqrt{2} }{2}) \cos(x) - (\frac{ \sqrt{2} }{2} )\sin(x) \)

Multiply one side at a time

Replace theta with x , the answer is

\( \frac{ \sqrt{2} \cos(x) }{2} - \frac{ \sin(x) \sqrt{2} }{2} \)

2. Convert 30 degrees into radian

\( \frac{30}{1} \times \frac{\pi}{180} = \frac{\pi}{6} \)

Using tangent formula,

\( \tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) } \)

\( \frac{ \tan(x) + \tan( \frac{\pi}{6} ) }{1 - \tan(x) \tan( \frac{\pi}{6} ) } \)

Tan if pi/6 is sqr root of 3/3

\( \frac{ \tan(x) + ( \frac{ \sqrt{3} }{3} ) }{1 - \tan(x) (\frac{ \sqrt{3} }{3} ) } \)

Since my phone about to die if you later simplify that,

you'll get

\( \frac{(3 \tan(x) + \sqrt{3} )(3 + \sqrt{3} \tan(x) }{3(3 - \tan {}^{2} (x) } \)

Replace theta with X.

The positive difference between the two solutions of the quadratic equation \(2x^{2}\) + 5x + 12 = 19 -7x is \(\frac{\sqrt{200} }{4}\).

We are required to determine the positive difference between the two solutions of the given quadratic equation: \(2x^{2}\) + 5x + 12 = 19 -7x

1. Move all terms to the left side of the equation to form a standard quadratic equation:

\(2x^{2}\) + 5x + 12 + 7x - 19 = 0

2. Simplify the equation: \(2x^{2}\) + 12x - 7=0.

3. Use the quadratic formula to find the solutions for x:

\(x = \frac{-b \pm \sqrt{b^{2} -4ac}}{2a}\)

where a=2, b=12, and c=-7.

4. Substitute the values:

\(x = \frac{-12 \pm \sqrt{12^{2} -4(2)(-7)}}{2(2)}\)

5. Simplify the expression:

\(x = \frac{-12 \pm \sqrt{144 + 56}}{4}\)

6. Calculate the value under the square root:

\(x = \frac{-12 \pm \sqrt{200}}{4}\)

7. Now, we have two solutions:

\(x_{1} = \frac{-12 + \sqrt{200}}{4}x_{2} = \frac{-12 - \sqrt{200}}{4}\)

8. Find the difference between the solutions:

\(x_{1} - x_{2}\) = \(\frac{\sqrt{200} }{4}\)

The positive difference between the two solutions is\(\frac{\sqrt{200} }{4}\).

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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Answer:

  $900

Step-by-step explanation:

Kyle's commission on an extra $5000 in sales was ...

  $1575 -1350 = $225

So, his commission on $10000 in sales would be ...

  $225 × 2 = $450

Since $450 of Kyle's first month's sales was commission, his base salary was ...

  $1350 -450 = $900 . . . . Kyle's fixed monthly salary

52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Answer:

The rate of change can be expressed with the formula x = Rise/Run And in this graph it rises 1 and runs 1 meaning you have a slope of 1/1 or 1 :)

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

13.4 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Now lets solve!!

12^2 + b^2 = 18^2

144 + b^2 = 324

Now we subtract!!

324 - 144 = b^2

180 = b^2

Now we need to find the square root!!

\(\sqrt{180}\) = 13.4

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

$13.25

Step-by-step explanation:

Given data

Cost of game = $25

Markup= 6%

Let us find the total cost of the game

First, the markup cost

=6/100*25

=0.06*25

=$1.5

Now the total cost is

=25+1.5

=$26.5

So, each is expected to pay

=26.5/2

=$13.25

Answer:

Diagonals linse

Step-by-step explanation:

Answer:

0.68

Step-by-step explanation:

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the derivatives.

Hence, y = 3 sin(-4x), we use the chain rule here.

dy/dx =3 ( cos(-4x).-4)

====> dy/dx = -12 cos(-4x)

The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.

To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.

In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].

However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.

Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].

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Answer:

\( 4\sqrt{10} \)

Step-by-step explanation:

Perimeter of the rhombus, STAR, is the sum of the length of all it's 4 sides.

The coordinates of its vertices are given as,

S(-1, 2)

T(2, 3)

A(3, 0)

R(0, -1)

Length of each side can be calculated using the distance formula given as \( d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Find the length of each side ST, TA, AR, RS, using the above formula by plugging in the coordinate values (x, y) of each vertices.

\( ST = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

S(-1, 2) => (x1, y1)

T(2, 3) => (x2, y2)

\( ST = \sqrt{(2 -(-1))^2 + (3 - 2)^2} \)

\( ST = \sqrt{(3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10} \)

\( TA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

T(2, 3) => (x1, y1)

A(3, 0) => (x2, y2)

\( TA = \sqrt{(3 - 2)^2 + (0 - 3)^2} \)

\( TA = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \)

\( AR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

A(3, 0) => (x1, y1)

R(0, -1) => (x2, y2)

\( AR = \sqrt{(0 - 3)^2 + (-1 - 0)^2} \)

\( AR = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10} \)

\( RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

R(0, -1) => (x1, y1)

S(-1, 2) => (x2, y2)

\( RS = \sqrt{(-1 - 0)^2 + (2 -(-1))^2} \)

\( RS = \sqrt{(-1)^2 + (3)^2} = \sqrt{1 + 9} = \sqrt{10} \)

\( Perimeter = ST + TA + AR + RS \)

\( Perimeter = \sqrt{10} + \sqrt{10} + \sqrt{10} + \sqrt{10} = 4\sqrt{10} \)

Answer:

420 dollars.

Step-by-step explanation:

a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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The expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4

The expression is given as:

(-2)^4/(-2)^2

Apply the law of indices

(-2)^4/(-2)^2 = (-2)^(4 -2)

4 - 2 has the same value as 6 - 4

So, we have:

(-2)^4/(-2)^2 = (-2)^(6-4)

Apply the law of indices

(-2)^4/(-2)^2 = (-2)^6/(-2)^4

Hence, the expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4

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Answer:

7 and 9

Step-by-step explanation:

a. The linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

b. If the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

a. Let's first find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

where (x1, y1) = (117, 73) and (x2, y2) = (180, 80).

slope = (80 - 73) / (180 - 117)

= 7 / 63

= 1/9

Now, let's use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (117, 73):

T - 73 = (1/9)(N - 117)

Simplifying the equation:

T - 73 = (1/9)N - (1/9)117

T - 73 = (1/9)N - 13

Now, let's rearrange the equation to solve for T:

T = (1/9)N - 13 + 73

T = (1/9)N + 60

Therefore, the linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

(b) If the crickets are chirping at 155 chirps per minute, we can estimate the temperature T using the linear equation we derived.

T(N) = (1/9)N + 60

Substituting N = 155:

T(155) = (1/9)(155) + 60

T(155) = 17.22 + 60

T(155) ≈ 77.22

Therefore, if the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

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Answer:

∴ x = 10

Step-by-step explanation:

Since (x, 3) is the solution to the provided equation, then x = x and y = 3.

Substitute y = 3 into equation 5x - 2y = 44:

5x - 2(3) = 44

        5x = 50

       ∴ x = 10

Answer:

1.25

Step-by-step explanation:

Give the data:

X : 1 1/2 ___ 0 _____ 4 ______ 2 1/2

Mean absolute deviation (MAD) :

Σ|x - xbar| ÷ n

xbar = Σx/ n

Σx = (1 1/2 + 0 + 4 + 2 1/2) = 8

xbar = 8/4 = 2

|x - xbar| :

|1 1/2 - 2|= 1/2

|0 - 2| = 2

|4 - 2| = 2

|2 1/2 - 2| = 1/2

Therefore,

MAD = (1/2 + 2 + 2 + 1/2) / n

MAD = 5/4

MAD = 1.25

Answer:

This phrase translates to the mathematical expression:

9 + (N x 3) = 7

If you want to solve for the missing number,

N x 3 = -2

N = -2/3

Answer:

Step-by-step explanation:

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

6x² + 41x + 48

Step-by-step explanation:

Area (A) = l × w

Therefore,

A = (3x + 16)(2x + 3) (distribute)

A = 6x² + 9x + 32x + 48 (combine like terms)

A = 6x² + 41x + 48

Therefore, the area of the playground is 6x² + 41x + 48.

Answer:

1.25 lawns/per hour

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Hope this helped! :)