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The dimensions of a triangle are shown below.




What is the area of the triangle in square meters?

The unknown measures in similar triangles in which x is 24 in.

What is a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

We have given,

ΔABC ≈ ΔXYZ

In ΔABC

AC = 36 in, BC = 18 in and AB = x in

In ΔXYZ

XY = 16in, ZY = 12in and  XZ = 24in

We know that,

the side and angles of a similar triangle are in proportion to each other.

AC / XZ = 36 / 24 = 3/2

BC / ZY = 18 / 12 = 3/2

AB / XY = x / 16

AC / XZ = BC / ZY = AB / XY   --------(similar triangle)

x / 16 = 3/2

x  = 3/2 * 16

x = 3 * 8

x = 24

hence, the unknown measures in similar triangles in which x is 24 in.

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Answer:

(a) sin() = 1/2

degrees: 30, 150

radians: π/6, 5π/6

(b) sin() = − 1/2

degrees: 210, 330

radians: 7π/6, 11π/6

Note that these solutions are in the interval of 0 to 360 degrees or 0 to 2 radians. Also note that these are the primary solutions, there are infinitely many solutions that can be obtained by adding multiples of 360 degrees or 2π radians to these values.

Answer:

The expression 10√3 can be written as a single surd as (10√3) = (10 √3/1) = (10 √3)¹/¹ = (10√3)^(1/1) = 10√3.

The average speed is 75.33 miles per hour.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Distance = 565 miles

Time.

= 5:00 pm t0 12:30 am

= 7.5 hours

Now,

Average speed.

= 565 / 7.5

= 75.33

Thus,

75.33 miles per hour is the average speed.

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Answer:

The x intercept is going to be (-43/4) and the y intercept is going to be (0,-43)

Step-by-step explanation:

hope this helped

The number of guitars sold each year in Montana is given as follows:

7075 guitars.

The number of guitars sold per year in Montana is obtained applying the proportions in the context of this problem.

Ohio's average is seven times Montana's average, hence Montana's amount is obtained dividing Ohio's amount by 7.

Ohio's amount is given as follows:

49525 guitars.

Hence Montana's amount is obtained as follows:

49525/7 = 7075 guitars.

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Answer: 214.008

Step-by-step explanation: hope this helped :)

Answer: $270

Step-by-step explanation: You multiply 3*750, then multiply the product by 0.12 because 0.12 = 12%.

The equation of the quadratic function that contains the point (1,1) is

y = 2x² - 1.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree. A quadratic function must contain at least one term of the second degree.

Given  the quadratic function that contains the point (1,1)

x = 1 and y = f(x) = 1

the shape of the equation is the same as f(x) = 2x²

a quadratic equation is given by

y = a(x - k)² + h

here (k, h) is the vertex of the function

given vertex is on the y-axis,

so k = 0

y = ax² + h

and a = 2 from f(x) = 2x²

y = 2x² + h

substitute x= 1 and y = 1

1 = 2 + h

h = 1 - 2 =  -1

equation of function is y = 2x² - 1

Hence equation of the function is y = 2x² - 1.

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Answer:

n = 30

Step-by-step explanation:

Since it is not a right-angle triangle, you will need to use sine or cosine rule;

We have two side lengths and the angle between, this means you need to use the cosine rule:

a² = b² + c² - 2bc.cosA

[tex]{a}^{2} = ({4 \sqrt{3} })^{2} + {( \sqrt{6} )}^{2} - 2( 4\sqrt{3})( \sqrt{6} ). \cos(45) \\ {a}^{2} = 48 + 6 - 8 \sqrt{18}(0.707...) \\ {a}^{2} = 54 - 24 \\ {a}^{2} = 30 \\ a = \sqrt{30}[/tex]

Answer:

n = 30

Step-by-step explanation:

For this question, use the cosine law formula:

[tex]a=\sqrt{c^2+b^2-2cb*cosA} \\a=\sqrt{(\sqrt{6})^2+(4\sqrt{3})^2-2(\sqrt{6})(4\sqrt{3})*cos45 }\\a =\sqrt{6+48-(8\sqrt{18})*\frac{\sqrt{2} }{2} }\\a=\sqrt{54-\frac{8\sqrt{36} }{2} }\\a=\sqrt{54-24}\\a=\sqrt{30}[/tex]

If a = [tex]\sqrt{n}[/tex], then n must be 30

Answer:

23

Step-by-step explanation:
If x-16=7

Then X= 23

Let me know I’d this answer is incorrect

Answer:

Step-by-step explanation:

Answer is A

Answer:

Step-by-step explanation:

You want the measures of 5 marked angles in the figure showing two transversals crossing parallel lines.

Angle 1 forms a linear pair with the angle marked 88°, so is supplementary to it.

  Angle 1 = 180° -88°

  Angle 1 = 92°

Angle 3 is a corresponding angle to the one marked 64° where the horizontal transversal crosses the parallel lines. Corresponding angles are congruent.

  Angle 3 = 64°

Angles 2 and 3 are "remote interior angles" with respect to the exterior angle marked 88°. Hence their sum is 88°.

  Angle 2 = 88° -Angle 3 = 88° -64°

  Angle 2 = 24°

Angles 3, 4, and 81° combine to form a straight angle of 180°.

  Angle 4 = 180° -64° -81°

  Angle 4 = 35°

Angle 5 is an alternate interior angle with respect to the one marked 81° where the downward-sloping transversal crosses the parallel lines. Alternate interior angles are congruent.

  Angle 5 = 81°

The 95% confidence interval estimate of the change in occupancy for the one year period is given as follows:

(0.1441, 0.1815).

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The percent change is given by the change divided by the initial value, hence the parameters are given as follows:

[tex]n = 1505, \pi = \frac{1750 - 1505}{1505} = 0.1628[/tex]

Hence the lower bound of the interval is of:

[tex]0.1628 - 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1441[/tex]

The upper bound of the interval is of:

[tex]0.1628 + 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1815[/tex]

Only the confidence interval can be calculated as the remainder of the problem is incomplete

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Answer:

x = 13

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

sum the 6 exterior angles and equate to 360

3x + 6 + 41 + 6x - 5 + 4x + 7 + 62 + 7x - 11 = 360

20x + 100 = 360 ( subtract 100 from both sides )

20x = 260 ( divide both sides by 20 )

x = 13

The equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5) is;   (x – 8)² + (y – 1)² = 25

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

The midpoint of the diameter of a circle is it's center.

As such; the coordinates of its center are;

x = (5+11)/2

x = 8

y = (-3 + 5)/2

y = 1

The coordinates of the center are then; (8, 1)

The radius of a circle is half the length of the diameter;

Radius, r = d/2

where; d = √(11-5)² + (5-(-3))²

d = √36 + 64

d = √100

d = 10

Therefore, radius, r = 10/2 = 5.

Therefore, the equation of the circle usually takes the form;

(x -f)² + (x -g)² = r²

In this scenario; the equation is;

(x – 8)² + (y – 1)² = 25.

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If Steve just got a new job working at a bank.  Steve's gross monthly income is $5,000, Steve's monthly net income is  $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.

a. Steve's gross monthly income is

Gross income = $60,000 / 12

Gross income = $5,000

b.  Steve's monthly net income

His deductions are:

Medicare: $72.50

Social Security: $310

Federal Tax: $500

State Tax: $262.50

Health insurance: $553

Dental insurance: $127

Total deductions = $72.50 + $310 + $500 + $262.50 + $553 + $127 = $1723.00

Steve's monthly net income = $5,000 - $1,723 = $3,277

c. In order to  see if Steve can afford the suit using the 5% spending guideline for clothing, we need to find the 5% of his monthly net income:

5% of $3,277 = $163.85

Since  the amount of $150 is less than $163.85, Steve can afford the suit based on the 5% spending guideline for clothing.

Therefore  Steve's gross monthly income is $5,000, Steve's monthly net income is  $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.

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At the clothing store, the number of customers that one employee can help is 4 customers.

At the coffee shop, the number of customers that one employee can help is 6 customers.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the clothing shop with these points (2, 4) and (3, 6) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (6 - 4)/(3 - 2)(x - 2)

y - 4 = 2(x - 2)

y = 2x + 2

When x = 1, we have:

y = 2(1) + 2

y = 4 customers.

Furthermore, a linear equation which models the coffee shop is given by:

y = kx

Where:

k = y/x

k = 6/1

Therefore, the required linear equation which models the coffee shop is y = 6x.

When x = 1, we have:

y = 6(1)

y = 6 customers.

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Answer:

(f - g)(x) = f(x) - g(x) = (x² - 8x + 12) - (x - 2) = x² - 8x + 12 - x + 2 = x² - 9x + 14. So, (f - g)(x) = x² - 9x + 14.

According to the question, the solution to the equation is x = -7.

The equation is a representation of a mathematical relation between two or more variables. It is usually expressed as an equation, where one side of the equation is equal to the other. For example, the equation y=mx+b is a linear equation with two variables, m and b, which are known as the slope and the y-intercept, respectively.

To solve this equation, we must first combine like terms on both sides of the equals sign.

-3x + 3 - x + 10 = -3x + 6

Next, we can subtract 3 from both sides of the equation to isolate the x-term.

-4x + 13 = -3x + 6

Finally, we can subtract -3x from both sides of the equation to isolate the constant term.

-7x = 7

We can then divide both sides of the equation by -7 to solve for x.

x = -7

Therefore, the solution to the equation is x = -7.

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Answer:

If Joe invested x dollars in company A, he invested x + 40 dollars in company B.

According to the problem the domain of this function is all real numbers x greater than or equal to 0.

Real numbers are any number that can be used to represent a quantity on the number line. They include both rational numbers (integers, fractions, and decimals) and irrational numbers (numbers that cannot be expressed as a fraction). Real numbers can be positive, negative, or zero and include the number line's endpoint values of positive and negative infinity. Real numbers are used in many areas of mathematics, including algebra and calculus. They are also found in everyday life, in the measurements of length, temperature, and in currency values.

The domain of this function is all real numbers x greater than or equal to 0. The range of this function is all real numbers y greater than or equal to 3. This is because all values of x are mapped to values of y that are greater than or equal to 3.

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Answer:

answer is D

Step-by-step explanation:

A={h,I,j,k l} and B={h,j,l m,n}

n(A U B)={h,I,j,k,l,m,n }

number is 7

The values that, the function intersect the x axis at 2 different points is -4 < b < 4. So correct option is D.

A function in mathematics is a relationship between a set of inputs (also known as independent variables or arguments) and a set of outputs (also known as dependent variables or values). The output of a function is determined by the inputs, and the function assigns exactly one output value to each input value.

A function can be represented in many ways, including a formula, a table, or a graph. The formula of a function defines the relationship between the inputs and outputs, and can be used to calculate the output for a given input. A table lists input and output values, and a graph represents the function by plotting the input and output values.

Functions are a fundamental concept in mathematics and are used in many areas, including algebra, calculus, and other branches of mathematics, as well as in science, engineering, and other fields. Functions can be simple, such as linear functions, or complex, such as exponential functions or trigonometric functions.

For the function f(x) = x^2 + bx + 4 to intersect the z-axis at two different points, it must have two real roots. This means that the discriminant of the quadratic equation must be greater than 0. The discriminant of the quadratic equation is given by b^2 - 4(1)(4). Hence, b^2 - 16 > 0, or b^2 > 16, which simplifies to -4 < b < 4.

Therefore, the answer is D: -4 < b < 4.

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The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

h(x) = √(x - 7) + 5

The value inside the square root should be greater than or equal to zero. Then we have

x - 7 ≥ 0

x ≥ 7

The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

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Answer:

Step-by-step explanation:

check the image

Answer:

y = 5

Step-by-step explanation:

The angle formed is a right angle which has a measure of 90 degrees. This means that the sum of the two angles is 90 degrees. Using this information we can set up an equation and solve for y

Set up equation

7y + 8 + 8y + 7 = 90

==> combine like terms

15y + 15 = 90

==> subtract 15 from both sides

15y = 75

==> divide both sides by 15

y = 5

Answer:

Yolanda served 13 times , Kareem served 38 times and Jose served 19 times.

Step-by-step explanation:

No of orders served by Yolanda = x

No of orders served by Kareem = y

No of orders served by Jose = z

x + y + z = 82  ------------- (1)

y = 2z  ------------ (2)

x = z - 6  ---------(3)

substituting (2) and (3) in (1) :-

z - 6 + 2z + z = 82

4z - 6 = 82

4z = 76

z = 19

y = 2(19)

y = 38

x = 19 - 6

x = 13