Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Opposite side = 14 in.
Adjacent side = 22 in.
cos θ = ?

Answer:

  Line D

Step-by-step explanation:

You want to know which line is not parallel or perpendicular to the other given lines:

 A: 2y -x = 2

  B: 4y = -8x -4

  C: y = -2x +4

  D: 5y = 10x +15

We can write each of these equations in standard form to make it easier to compare them. That form is ...

  ax +by = c

where a > 0 and a, b, c are mutually prime.

The equations are ...

  A: x -2y = -2

  B: 2x +y = -1

  C: 2x +y = 4

  D: 2x -y = -3

Equations with the same coefficients of x and y will be parallel:

  2x +y = -1  and  2x +y = 4 . . . . lines B and C

Equations with coefficients that have been swapped, with one negated, will be perpendicular:

  x -2y = -2  and  2x +y = -1 . . . . lines A and B

Line A is perpendicular to parallel lines B and C, so line D is the odd one out.

  Line D doesn't fit.

Answer:

2 2/4 or 2 1/2

Step-by-step explanation:

3-1=2

3/4-1/4=2/4

2/4=1/2

Answer: 9x - 2 >= 19.

Step-by-step explanation:

The sentence can be translated into the inequality 9x - 2 >= 19.

Here is a step-by-step breakdown:

"Two subtracted from the product of 9 and a number" can be written as 9x - 2.

"Is greater than or equal to 19" can be written as >= 19.

Putting these two pieces together, we get the inequality: 9x - 2 >= 19.

Answer:

Let the total number of people in the group=x

So total number of men =3x/8

Hence total number of women=5x/8

No. of men having brown eyes=2/3*3x/8=x/4

Total no. of people having brown eyes=3x/4

No.of women having brown eyes

=3x/4 -x/4=2x/4=x/2

No. of women who don't have brown eyes= 5x/8-x/2 = x/8

So the fraction is x/8x= 1/8

Step-by-step explanation:

Answer: 28 children

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

First, we would need to figure out the total number of students. To do this, we can divide 84 by 3, then add that to the total.

84 ÷ 3 = 28

28 + 84 = 112

This means that there are 112 students in the classroom.

If 3/4 of the children in the school have blue eyes, we know that 1/4 of the children will have brown eyes. We can convert 1/4 into a decimal, or into a percentage, to get the number of children with brown eyes.

1/4 = 0.25 = 25%

To figure out how much 25% of 112 is, we can simply multiply 112 by 0.25.

112 × 0.25 = 28

So, this means that there are 28 children with blue eyes in the school.

Answer:

D

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex]  Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]

7[tex]\frac{9}{8}[/tex]

7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex]  Another name for [tex]\frac{8}{8}[/tex] is 1

7 + 1 + [tex]\frac{1}{8}[/tex]

8[tex]\frac{1}{8}[/tex]

Answer: 12

Step-by-step explanation: Because of the ratio we know that half of the screens will be showing action films. Half of 24 is 12, so 12 screens will be playing action.

The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.

Given the equation of the parabola;

-x² - 2x + 10 = 0

First, the maximum of a quadratic function occurs at;

x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)

f_max(x) = ax² + bx + c occurs at;

x = -b/2a

Now, find the value of x = -b/2a

Plug in a = -1 and b = -2

x = -( -2/2(-1) )

x = -( -2/-2) )

x = -( 1 )

x = -1

Hence;

f(x) = -x² - 2x + 10

f( -1 ) = -( -1 )² - 2( -1 ) + 10

f( -1 ) = -1 + 2 + 10

f( -1 ) = -1 + 12

f( -1 ) = 11

Therefore, maximum occurs at (-1,11).

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Answer:

That's easy! four thousand two hundred and seven or 4,000+200+7

Step-by-step explanation:

Answer: 0.155

Step-by-step explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.

Answer:

a = -20/13

Step-by-step explanation:

7 - 13a = 27

-13a = 20

a = -20/13

Let's check

7 - 13(-20/13) = 27

7 + 260/13 = 27

7 + 20 = 27

27 = 27

So, a = -20/13 is the correct answer!

The rate of the plane in still air is 800 km/h while the rate of the wind is 210 km/h

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the speed of the airplane in still air and y represent the speed of the wind.

Flying against the wind, an airplane travels 4720 kilometers in 8 hours. Hence:

x - y = 4720 km / 8 hr

x - y = 590    (1)

Flying with the wind, the same plane travels 4040 kilometers in 4 hours. Hence:

x + y = 4040 km / 4 hr

x + y = 1010    (2)

From both equations:

x = 800, y = 210

The speed of the airplane is 800 km/h

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On solving the provided question, we cans ay that the value of x from the polynomial [tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]  is = 16 and 1

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

here,

[tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]  

as x = 0 and y = 1

answer   is = 16 and 1

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Answer:

Option E) 1400

Step-by-step explanation:

Based on the given conditions, formulate: 70‰ x 2000

Convert the percentage to decimals: 0.7 x 2000

Calculate the product or quotient: 1400

Hence , the answer is 1400

The accumulated amount in the savings account on 21 November 2020 will be $426.63.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

On 4 January 2020, Thabo deposited $7,800 into a savings account. The simple interest rate agreed upon was 6.2% per annum.

The number of days from 4 Jan 2020 to 21 Nov 2020 will be given as,

Total days = 28 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 21

Total days = 322

The accumulated amount in the savings account on 21 November 2020 will be given as,

I = [$7,800 x 6.2 x (322 / 365)] / 100

I = $426.63

The accumulated amount in the savings account on 21 November 2020 will be $426.63.

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it is false but 4 is not y-4x=0

Answer: $272

Step-by-step explanation: you would multiply 250 * 0.022 = 5.5

then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272

The insurance company will pay $192, which is the asset's present value.

The sum of money required to fix your house at the cost of construction materials today, or to replace your possessions at the cost of an equivalent or comparable item today the cost of purchasing a comparable asset to replace an existing one at the going rate on the market.

To be fully insured, your dwelling limit must equal at least 80% of the rebuild value of your house. The average cost of reconstructing a home per square foot in your area can be multiplied by the square footage of your home to determine the replacement cost. Market value and replacement cost are not the same thing.

Therefore,

The distribution of cost over the course of an asset's useful life is known as depreciation. It speaks of the rate at which the value of an asset depreciates over time.

When figuring out depreciation, the original value is utilized. It does not use current market value.

Over the course of the asset's useful life, the value is distributed equally.

In this instance

Depreciation per year = Asset value ÷ Years of useful life

Depreciation per year = 288 ÷ 6 = $48

The asset has been used for 2 years

Amount depreciated = 48 × 2 = $96

Present value = Original value - Depreciation

Present value = 288 - 96 = $192

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Answer:

61.1

Step-by-step explanation:

Here, we simply add the two numbers together.

25+36=61

0.5+0.5=1

so, the answer is 61.1

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x  3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x  3/2 and it's output that is y exists between  (-∞ , 2).

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The complete table of values of the function is

x    0    1    2    3

y     0   2   5   10

From the question, we have the following parameters that can be used in our computation:

The equation of the function is given as

y = x² + 1

The above function is a quadratic function

This is so because it has the following representation

y = ax² + bx + c

When this function is compared to the equation y = x² + 1, we have the following notations

a = 1

b = 0

c = 1

From the incomplete table of values, we have the x values to be

x = 1, 2, 3

Substitute x = 1, 2, 3 in the equation y = x² + 1

So, we have

When x = 1, y = (1)² + 1 = 2

When x = 2, y = (2)² + 1 = 5

When x = 3, y = (3)² + 1 = 10

When these values are represented on a table, we have

x    0    1    2    3

y     0   2   5   10

The above represents the complete table

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Complete question

Complete table with the Y-values for the equation y=ײ+1

x    0    1    2    3

y     0

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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Answer:

6√2

Step-by-step explanation:

-√2×2×2 -√2×3×3×3 + 2√3×3

-2√2 - 3✓6 + 2×3

-2√2 - 3√2×2 +2 + 6

6√2

Answer:

10

Step-by-step explanation:

[tex] \sqrt{26 {}^{2} - 24 {}^{2} }[/tex]

[tex] = \sqrt{676 - 576} [/tex]

[tex] = \sqrt{100} [/tex]

[tex] = 10[/tex]

Answer: 10

Step-by-step explanation: You can use the Pythagorean theorem which is a^2+b^2=c^2. Plug in the numbers that you already have and square them to find the answer, which is 10. Hope this helps! If you need more of an explanation pls let me know ;)

Answer: y=20-2x

Step-by-step explanation:

The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.

The equation is given as,

aₙ = 8.4 · (1/2)ⁿ⁻¹

The distance that he jumped in the sixth jump will be given as,

a₆ = 8.4 · (1/2)⁶⁻¹

a₆ = 8.4 / 64

a₆ = 0.13125

a₆ ≈ 0.13

The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.

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On solving the provided question, we can say that - the area of the following rectangle is 200 cm sq.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

we have

L = 20 cm

and B = 10 cm

Area of rectangle, A =L X B = 20 X 10 = 200 cm sq.

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The maximum number of zeros is 2, and the x-intercepts are -9, 9.

The x-intercept is where the graph crosses the x-axis.

Here, we have,

The function is given as:

y=(x+9)(x-9)^2

The above function can be rewritten as:

y=(x+9)(x-9)(x-9)

The x-intercept is the point where the graph crosses the x-axis

To determine the x-intercepts, we remove the common factors

So, we have:

y=(x+9)(x-9)

Equate to 0

(x+9)(x-9)=0

Split

(x+9)=0 and, (x-9)=0

Solve for x

x=9 & x=-9

So, the maximum number of zeros is 2, and the x-intercepts are -9, 9.

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Answer:

3/20

Step-by-step explanation:

[tex]\frac{0.3}{2}=\frac{0.3*10}{2*10}=\frac{3}{20}[/tex]