Simplify the following using trigonometric identities:
( 1 + sin (x) ) ( sec (x) - tan (x) )

Opposite angles of a parallelogram are congruent.

[tex]9x-13=14+6x \\ \\ 3x-13=14 \\ \\ 3x=27 \\ \\ x=9[/tex]

This means [tex]m\angle ADC=68^{\circ}[/tex].

The average value of the function f(x)=cos(x) on the interval [0,π]=0 and c=pi/2.

The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function. If you look at the picture below, you know already that the integral of the function is all of the areas between the function and the x-axis

The average value of the function f(x)=cos(x) on the interval [0,π] and determine a number c in this interval for which f(x) is equal to the average value.

The average value of the function f(x) on interval [0,pi]

can be evaluated through the following expression:

[tex]A.V=\frac{1}{(b-a)}{\int_a^b f(x) dx[/tex]

Here we have f(x)= cosx  and interval [0,pi]

[tex]A.V = \frac{2}{\pi}{\int_0^{\pi} cosx dx\\\\=2/\pi[sin\pi-sin0]\\=0.[/tex]

Avarege value 0 and c=pi/2.

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Answer:

your answer should be 8 according to the bearing given

-59/80 is the value of the expression -3/16 + (-11/20).

A fraction represents a part of a whole.

The given expression is -3/16 + (-11/20)

-3/16-11/20

LCM of 16 and 20 is 80

-3(5)-11(4)/80

(-15-44)/80

-59/80

Hence, -59/80 is the value of the expression -3/16 + (-11/20).

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Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.

Given that Jon's jump was 1 inch short of the required height, yet Anthony was his friend

reached the necessary height by 2 inches.

In this instance, subtracting the values will yield the difference in the jump. It will be demonstrated by:

= Anthony's jump - Jon's jump

= 2 - (-1)

= 2 + 1

= 3

Therefore, Jon was 3 inches lower.

Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

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Answer:

Becca's birthday is June 10th, which is a Wednesday this year. November 10th is exactly 6 months after June 10th, so the friend's birthday is also a Wednesday this year.

The increase in the area of the circle is 64π, not 39π. If the original circle had an area of 25m, then the original radius was 5. The new radius would be 5 + 3 = 8. The new area would be 8^2 * pi = 64 * pi = 64π.

Let X be the number of 4 point scores that Hunter made and Y be the number of 9 point scores. X + Y = total number of scores and 4X + 9Y = 755. Substituting Y = 100 + X, we get 4X + 900 = 755. Solving for X, we get X = 41. Therefore, Hunter made 41 4 point scores.

Answer:

√61

Step-by-step explanation:

Pythagoras Theorem states that :

a²+b²=c²

Where c is the hypotenuse and a and b are the lengths of the legs

So this formula needs no adjustments and only substituting values:

5²+6² = c²

25+36= c²

61 = c²

Square root both sides

c = √61

Hope this helped and have a good day

The equation she could use is 8 tan(56) =x. the value of x is 4.89

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that Tyler and Jada wish to find the value of x, B the length of side BC in this triangle.

Tyler decides to set up the equation 8 tan(56) =x

So, 8 tan(56) =x

x = 8 (0.611)

x = 4.89

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Answer:

No

Step-by-step explanation:

I think

x times y = xy

Not x + y = xy

Answer:

the answer is 1 and 3 true and other false

27 is the equivalent expression of (-81) and the evaluation of the expression's value is solved by dividing it by three-fourths.

You can multiply, reduce, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and expressions is possible. An algebraic expression is any mathematical statement that has parameters, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, all of which are isolated by that of the algebraic sign +.

given

Condense the phrase.

= (-81)^ 3/4 = (-81)^ 3/4 

the common factor of 4 = 3^3 is canceled.

Raise 3 to the power of 3

= 27

27 is the equivalent expression of (-81) and the evaluation of the expression's value is solved by dividing it by three-fourths.

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The required probability for the number of phone calls more than two in next 30 minutes is equal to ( 18 / 5)e⁻⁶.

Number of phone calls between 6pm and 8.00 pm 'n' = About 6 calls

Using Poisson's distribution we have,

P ( X = x ) = ( e⁻ⁿ nˣ ) / x!

Probability of receiving more than 2 phone calls in next 30 minutes

= P( X > 2 )

= P ( X = 3 ) + P ( X = 4 ) + P ( X = 5) + P( X = 6)

= ( e⁻⁶ 6³ ) / 3! +  ( e⁻⁶ 6⁴ ) / 4! +  ( e⁻⁶ 6⁵) / 5! +  ( e⁻⁶ 6⁶ ) / 6!

=  ( e⁻⁶ 6³ ) / 3! [ 1 +  (6 / 4) + (6² / 5× 4 ) + ( 6³ / 6 ×5× 4) ]

= ( e⁻⁶ 6³ ) / 3! [ ( 20 + 30 + 72 ) / 20 ]

= ( 18 / 5)e⁻⁶.

Therefore, the probability of more than two phone calls is  ( 18 / 5)e⁻⁶.

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Answer:

D

Leah spent y

15 times ryan's

ryan spent x

y = 15x

Step-by-step explanation:

A -  Leah spent x

      15 times more than

      Ryan spent y

x = 15 * y

B - Leah spent y

     15 more

     Ryan spent x

y = x + 15

C- Leah spent x

    15 less

    Ryan spent y

x = y-15

The result of the normal probability distribution being bell-shaped is that the mean, median, and mode are at the center.

This means that the center of the bell-shaped curve represents the most likely occurrence of the data and that the values are symmetrically distributed around the mean.

The mean, median, and mode of a normal distribution are equal, which means that they are all located at the center of the bell-shaped curve. This is an important characteristic of the normal distribution and sets it apart from other distributions where the mean, median, and mode may not be equal.

In a normal distribution, the area on each side of the mean does not equal 1.00, but rather approaches 1.00 as the curve becomes more symmetrical. The height of the curve at the mean represents the highest probability of occurrence, and the probabilities decrease as the values deviate from the mean.

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According to the problem,The area of the figure is approximately 34 square units.

A square is a four-sided plane figure where all sides are equal length and all angles are right angles. It is a two-dimensional shape with four equal-length sides and four equal angles of 90°. Squares are often used in designs and architecture, and are an important part of Euclidean geometry. They are also found in nature, such as in a honeycomb, in a checkerboard pattern, and in tessellations.

To calculate this, we need to calculate the area of the square and the area of the circle's segment. The side of the square is 4 units, so the area of the square is 4 x 4 = 16 square units. The radius of the circle is also 4 units, so the area of the circle's segment is (1/2)πr^2, which is (1/2)π(4^2) = 16π/2 = 16 x 3.14/2 = 24.96 square units.

Therefore, the area of the figure is 16 + 24.96 = 40.96 square units, which is approximately 34 square units to the nearest whole number.

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Answer: B- 7, 24, 25

Hope this helps :)

Step-by-step explanation:

Use the Pythagorean Theorem

a^2 + b^2 = c^2

49 + 576 = 625

625 = 625

Answer:

$27

Cost = 20 + 1x = 20 + x

Step-by-step explanation:

Membership fee is $20 per month. This amount has to be paid whether he buys pizzas or not that month

If x is the number of pizzas, the total cost for 7 pizzas at discounted price of $1 is  20 + 7 x 1 = $27

For  x pizzas, the equation is

Cost = 20 + x

Kyle spending on this shirt at end up is, $63.07.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Kyle is looking to buy a shirt that normally costs $85.

Here, Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items.

Hence, The discount price is,

⇒ 30% of 85

⇒ 30/100 × 85

⇒ $25.5

So, The price of shirt after discount = $85 - %25.5

                                                       = $59.5

Since, After the discount, Kyle must pay 6% sales tax on the shirt.

Hence, The sales tax is,

⇒ 6% of 59.5

⇒ 6/100 × 59.5

⇒ $3.57

Thus, The amount to pay at endup by Kyle = $59.5 + $3.57

                                                                  = $63.07

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Using the properties of triangle, the value of x = 10.5 and y = 8.75.

A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.

The sum of the angles of the triangle is 180 degrees.

A triangle's exterior angles add up to 360 degrees.

The shortest side of a triangle is always on the opposite side of its smallest angle.

From the given figure,

If we consider the line measuring 4, divides the triangle into 2 equal halves,

The sides of triangle will be in equal ratio,

⇒ [tex]\frac{5}{y} = \frac{6}{x} = \frac{4}{7}[/tex]

⇒ x = 10.5

⇒ y = 8.75

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Answer:

PR = 3.6

Step-by-step explanation:

Triangles PQR and STR are similar figures. PQ is the base of triangle PQR just like ST is of triangle STR. PR is parallel to SR and RQ is parallel to RT.

[tex]\frac{Side PQ}{Side ST} =\frac{Side PR}{Side SR}[/tex]

=[tex]\frac{1.8}{1.2} = \frac{PR}{2.4}[/tex]

Cross-multiplying:

=(1.8)(2.4) = (1.2)(PR)

= PR = [tex]\frac{(1.8)(2.4)}{(1.2)}[/tex]

= PR = 3.6

Answer: 36.87 degrees.

Step-by-step explanation:

In a right-angle triangle, the length of the opposite side of an angle and the length of the hypotenuse can be used to find the value of the angle using the trigonometric ratios.

If we let the angle in question be denoted as "theta" and the length of the opposite side be "opp" and the length of the hypotenuse be "hyp", we can use the trigonometric ratio "sine" to find the value of the angle.

sin(theta) = opp/hyp

We are given that opp = 3 cm and hyp = 5 cm, so we can substitute these values into the equation:

sin(theta) = 3/5

We can now use an inverse trigonometric function, such as arcsin, to find the value of theta:

theta = arcsin(3/5)

The result of this calculation is theta = approximately 36.87 degrees. Therefore, the value of the angle is 36.87 degrees.

Answer:

30 mm

Step-by-step explanation:

3 x 10 mm ? hopefully its the right answer for you

The Polynomials which is of the highest degree using the whole numbers 1 through 9 as required is; x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + x.

As required in the task content, it is required that the polynomial of the highest degree by using the whole numbers 1 through 9 at most one

time each is to be determined.

Hence, an example of such polynomial as required is; x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + x.

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Answer:

B

Step-by-step explanation:

So they want to get r alone. In order to do that, we would have to do the opposite of what's shown, and we would do it to both sides of the equal sign. As follows...

A = (pi)(r)^2

I would first divide by pi, since it's multiplying pi originally. And we'll do it on both sides

A/Pi = r^2

Now the opposite of squared is square root, so we'll square root both sides

✓A/Pi = r

Giving us B

Answer:

B is the right answer....

B

[tex].a = \sqrt{ \frac{a}{\pi} } \: \: is \: the \: right \: answer..[/tex]

The inequality that describes a pizza with an area larger than a mall pizza (with an area of 730730730 square centimeters) can be written as:

p > 730730730

The inequality "p > 730730730" is a mathematical expression that compares the area of a pizza (represented by the variable "p") to the area of a mall pizza (730730730 square centimeters).

The inequality uses the greater than symbol ">" to indicate that the area of the pizza represented by "p" must be greater than the area of the mall pizza.

"p" represents the area of the larger pizza in square centimeters. The inequality states that the area of the larger pizza (p) must be greater than the area of the mall pizza (730730730 square centimeters).

This inequality can be useful in situations where we want to compare the size of two pizzas and determine which is larger. By evaluating whether the area of a pizza (represented by "p") satisfies the inequality, we can determine whether it is larger or smaller than the mall pizza (with an area of (730730730 square centimeters).

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The equation be |2x-3| = 7 then the set of values is the solution set be (2, -5).

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. When two expressions are joined by an equal sign, a mathematical statement is called an equation.

In mathematics, to solve an equation is to identify its solutions, which are the values (numbers, functions, sets, etc.) that satisfy the requirement expressed by the equation. An equation typically consists of two expressions connected by an equals sign. A variable or variables are labeled as unknowns when looking for a solution.

Any combination of a number, a variable, and operation symbols is considered an expression. Two expressions are combined to form an equation, which is joined by the equal sign.

Let the equation be |2x-3| = 7

We know that if [tex]$|a|=b, a=\pm b$[/tex].

Since we do not know if 2x - 3 exists positive or negative, we will need a [tex]$\pm$[/tex] on the 7 :

[tex]$|2 x-3|=7 \Rightarrow 2 x-3=\pm 7$$[/tex]

Add 3 to both sides, and finally divide by 2, we get

[tex]$$\begin{aligned}& 2 x=3 \pm 7 \\& x=\frac{3}{2} \pm \frac{7}{2}\end{aligned}$$[/tex]

So x exists equal to either 10/2 = 5 or -4/2 = -2.

Therefore, the correct answer is option b) (2, -5).

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(a)Tax Schedule Notation:

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.

What is the inequality notation?

An inequality is a mathematical statement that represents the relationship between two quantities but states that they are not exactly equal. The four symbols of inequality notation are. ≥,>,<,and≤

(a) Tax Schedule Notation:

Income Tax = Tax bracket rate * (Income - Bracket Lower Bound) + Fixed Amount

Example:

Income = $172,876.99

Tax bracket rate = 37% (for 2022 taxes, 37% applies to taxable income over $518,400 for singles)

Bracket Lower Bound = $518,400

Fixed Amount = $208,725 + 37% * ($172,876.99 - $518,400)

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation:

The interval notation for the income $172,876.99 would be $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation:

The compound inequality notation for the income $172,876.99 would be $518,400 < $172,876.99 < ∞.

Hence,  (a)Tax Schedule Notation:

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.

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Answer:

$174,850.10

Step-by-step explanation:

the future value of $7000 at the end of 5 periods at 8% compounded interest is

$10,285.30

so you multiply $10,285.30 x 17 = 174,850.10 that's the amount you have to invest. After thirty years you will have $1,049,100.60

The value of x the will make 20+2x to be zero is

-10 ( option C)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The expression 20+x is a linear expressions when it is equated to zero it is a linear equation.

20+2x = 0

collect like terms

x = 0-20

2x= -20

x = -20/2

x = -10

Therefore the value of x that make 20+2x to be zero is -10

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The equivalent of log (6) = 0.778 indicates the logarithmic base 10 of 6 is approximately 0.778.

Logarithms are a mathematical concept that are used to simplify exponential calculations. They are the inverse of exponents and are denoted as log base b (x), where b is the base of the logarithm and x is the number you want to find the logarithm of.

In this case, when your calculator computes log (6) as 0.778, it means that the logarithm base 10 of 6 is approximately 0.778.

=> log₁₀ 10 = 1 (10¹ = 10).

=> log₁₀ 6 = 0.778, because [tex]10^{0.778}[/tex] is approximately 6.

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