Find the area of the triangle, given that sin(C) = 1/2. Round the answer to the nearest whole number.
A. 26 square units
B. 75 square units
C. 150 square units
D. 299 square units

Step-by-step explanation:

Did you mean.

[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]

[tex] \: [/tex]

[tex] = \sin( - \frac{4\pi}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]

[tex] = \sin( - 4 \times 60 \degree) [/tex]

[tex] = \sin( - 240 \degree) [/tex]

[tex] = \sin(0 - 240 \degree) [/tex]

[tex] = \sin(360 \degree - 240 \degree) [/tex]

[tex] = \sin(120 \degree) [/tex]

[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]

Answer:

Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.

Step-by-step explanation:

Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.

Perimeter of polygon C = 60in

Perimeter of polygon D = 12in

Length of side of polygon C = 4in

Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.

First equation, 4n = 60

Second equation, xn = 12

Dividing second by first

(xn) / (4n) = 12 / 60

x / 4 = 1 / 5

x = 4 / 5 = 0.8in

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The range:
[tex]{x|70\leq x\leq 82[/tex]

Answer:

it should be 319

Step-by-step explanation:

Answer:

639 is the answers for the question

Step-by-step explanation:

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Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x    where r is the growth rate (interest rate)

So the equation can be written as

[tex]m= P(1.04)^t[/tex]    where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

[tex]I = P(1.04)^t-P[/tex]  where I represents the interest paid.

plug the values into the equation

[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]

Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

The system of equation has an infinitely many solutions

The equations are given as:

2x + y = -3

-2y = 6 + 4x

Express 2x + y = -3 in slope-intercept form

y = - 3 -2x

Divide through by -2 in -2y = 6 + 4x

y = -3 - 2x

So, we have:

y = - 3 -2x  and y = -3 - 2x

Both equations are the same.

This means that the system of equation has an infinitely many solutions

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An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.

[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]

Hence, The simplified version of the given expression is (3√2-2)√x³.

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Answer:

Step-by-step explanation:

The value of angle x is 67 degree.

A right angled Triangle is a triangle with one angle as 90 degree.

It is given that the for the angle x , the base of the triangle is 28 ft.

The hypotenuse = 72ft.

The trigonometric ratios can be used to find the value of x

cos x = 28 /72

x = cos⁻¹ (28/72)

x = 67 degree (Rounded off to nearest tenth)

Therefore the value of angle x is 67 degree.

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The weight of the smallest rectangular block is 1400 pounds.

The density refers to the heaviness of an object. It is the ratio of mass to volume.

Then we have

Density = Mass / Volume

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.

The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.

The composite stone weighs 40 pounds per cubic foot.

To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

Then the weight of the smallest rectangular block will be

Mass = density x volume

The volume will be

V = 5 x 2 x 3.5

V = 35 cubic feet

Then the weight will be

Mass = 40 x 35

Mass = 1400 pounds

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Answer:

15

Step-by-step explanation:

divide the perimeter by two and minus 1

Answer: 15ft

Step-by-step explanation:

Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!

Answer:

15°

Step-by-step explanation:

angle FGH = angle HGI ( since GH bisects angle FGI)

that means

(2x + 1) = (3x - 9)

= -x = -8

x = 8

angle HGI = (3x - 9)

= 3(8) - 9

24 - 9

= 15°

Answer:

21

Step-by-step explanation:

To find the measure of <HGI we first need to find the value of x

GH bisects angle <FI which means it divided the angle into two equal parts:

<FGH = <HGI

2x + 1 = 3x - 9 transfer like terms to the same side of the equation

1 + 9 = 3x - 2x

10 = x now replace x with 10

3*10 - 9 = 21

Answer:

Is the second expression written correctly?  It reduces to y>-2, since no x is in the equation.

Step-by-step explanation:

We can graph the two equations.  See attached image.  If y>2 is the correct expression, all points to the right.

If the equation was meant to read y=-3x+1, then graph the revised expression.

Answer:

the distance between DE is 2

The distance of EF is 5

The distance of FD is [tex]\sqrt{29}[/tex]

Perimeter is 7+[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Distance of DE

[tex]\sqrt{(-3-(-3))^2+(3-1)^2}[/tex]

sqrt([tex](-3+3)^2+(2)^2[/tex])

sqrt([tex](0)^2+4[/tex])

[tex]\sqrt{4}[/tex]

=2

Distance of EF

[tex]\sqrt{(2-(-3))^2+(3-3)^2}[/tex]

Solve that like DE and it equals 5

Distance of FD

[tex]\sqrt{(2-(-3))^2+(3-1)^2}[/tex]

equals to [tex]\sqrt{29}[/tex]

P=DE+EF+FD

P=2+5+[tex]\sqrt{29}[/tex] = 7+[tex]\sqrt{29}[/tex]

Answer:

infinity 2 is the slope for these point .

Step-by-step explanation:

given points are

(-2,-5) and (3,5)

comparison to

(x1,y1) and (x2,y2)

here ,

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

slope= 5-(-5)/3-(-2)

slope =10/5

slope=2

glad to help you this may help you :)

The value of a₃₂ is 7 , Option A is the correct answer.

Matrix is an array or an arrangement of numbers or expression in rows and column format.

The matrix is given

For a matrix of size mxn , m is the row and n is the column of the matrix.

a₃₂ = This term means 3rd row and 2nd column of the matrix

which is 7

Therefore the value of a₃₂ is 7 , Option A is the correct answer.

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1) Given

2) Segment addition postulate

3) Substitution property

4) Segment addition postulate

5) Transitive property of equality

Answer:

The answer is 105.

Step-by-step explanation:

Answer:

The horizontal asymptote is y=1 and

The vertical asymptote is x=5

Answer:

Step-by-step explanation:

Calculate 50% of 684 m.

Give your answer in metres (m).

50% = 1/2

so

684 : 2 = 342 m

Step-by-step explanation:

50% of 684

50/100 × 684

342m ans

The expected length of the arc containing the point (1,0) is; π

First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.

The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.

Thus, we have;

L₁ + L₂ + L₃ + L₄ = 2π

Whereas, the expected value of several random variables is additive as;

E[ L₁ + L₂ + L₃ + L₄] =  [EL₁] + [EL₂] + [EL₃] + [EL₄]

By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.

Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,

π/2 + π/2 = π

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Gene earns 2% interest after depositing $150 into his account , Option D.

A function is a law that relates an independent variable and a dependent variable with each other.

The function given is

f(x) = 0.02 x +150

Option D , Gene earns 2% interest after depositing $150 into his account

So this verbal description matches the function given as it represents , the total account balance of Gene .

Therefore Option D is the correct answer.

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Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

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Even numbers = 2x +2

Consecutive even numbers = 2x+4

then

(2x+2) + (2x+4)= 38

2x + 2 + 2x + 4 = 38

2x + 2x + 2 + 4 = 38

    4x + 6 = 38

                   4x = 38 - 6

                     x = 32 :4

                    x = 8

2x+ 2 = 2(8)+2 = 16 + 2 = 18

2x+4 = 2(8) +4 = 16 + 4 = 20

The smallest number is 18

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Answer:

18 is the smaller number

Step-by-step explanation:

Let us take X for the first even number (it will also be the smallest)

x, x+1, x+2, so on..

the consecutive even number of x+2 is the next even number after x.

so you now get this equation...

x+(x+2) = 38

2x + 2 = 38

2x = 36

x=18

Hey there ! please refer to the attachment .

I hope its help you !

Answer:

128, -256, -1024

Step-by-step explanation:

multiply 32 by 4, multiply 128 by -2, multiply -256 by 4

Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

[tex]y = \frac{1}{2} x[/tex]