4.
Find the perimeter of the triangle.

A. 294 m
B. 119 m
C. 84 m
D. 168 m

[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]

The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.

Given that,

The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.

Here, Lenght of an arc = 13 cm

The radius of an arc = 5 cm

Used the formula for the angles (θ);

Length of an arc = 2πrθ / 360°

Substitute all the values, we get;

13 = 2 × 3.14 × 5 × θ / 360°

Solve for θ;

13 × 360° = 31.4 × θ

4,680° = 31.4 × θ

θ = 4,680°/31.4

θ = 149.1°

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Answer:

[tex]p = x \\ r = 6\% \\ t = 2yrs[/tex]

[tex]p = 1600[/tex]

please see the attachment

Answer:

P = $1600

Step-by-step explanation:

We have to use the equation:

[tex]\boxed{I = Prt}[/tex] .

We know that:

• I = $192

• P = ?

• r = 6% = 0.06

• t = 2 years

Substituting these values into the equation:

[tex]192 = P \times 0.06 \times 2[/tex]

Solving for P:

[tex]P = \frac{192}{0.06 \times 2}[/tex]

[tex]P = \bf \$1600[/tex]

right angles. .... . . . . ......

The equations intersect at the point (3 ,3 ).

An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

4y –x = 9 (1)

y = 2x − 3 (2)

You should replace the variable y of equation 1 to equation 2. Then, you will have:

4*(2x-3)-x=9

8x-12-x=9

8x-x=9+12

7x=21

x=3

If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3

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Answer:

A.  y = 1/3x^2

Step-by-step explanation:

The red graph is stretched horizontally by a factor 1/3  to give the blue graph

Answer:

3 consecutive no.s are

5×6×7=210

sum of them is= 5+6+7

=18

So, I hope. it helps !!

Answer:

Step-by-step explanation:

190/x=100/63

(190/x)*x=(100/63)*x       - we multiply both sides of the equation by x

190=1.5873015873016*x       - we divide both sides of the equation by (1.5873015873016) to get x

190/1.5873015873016=x

119.7=x

x=119.7

now we have:

63% of 190=119.7

You are requesting a number, as the question clearly states. So, a number should be the response. However, because 63 and 190 are not stated and might indicate a variety of things, we must make an assumption in order to provide a response.

We will thus assume that 63 is a percentage and that 190 is a number in order to respond to the question, "What number is 63 of 190?"

We multiply 63 by 190 and then divide the result by 100 to obtain the solution. Here is the calculation and response to your query:

⇒ 63 x 190 = 11970

⇒ 11970 / 100 = 119.7

Assuming you meant 63 percent of 190, the answer to the question "What number is 63 of 190?" is 119.7, as shown and computed above.

Thank you,

Eddie

Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.

The total number of reds, yellows, and greens on a scale is 9.

The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44

pounds. There are 2 more greens than reds.

Therefore,

let

x = number of reds

number of greens = x + 2

y = number of yellow

Therefore,

x + x + 2 + y = 9

2x + y = 7

3x + 6y + 5(x + 2) = 44

3x + 6y + 5x + 10 = 44

8x + 6y = 34

Hence,

2x + y = 7

8x + 6y = 34

8x + 4y = 28

8x + 6y = 34

2y = 6

y = 6 / 2

y = 3

2x + 3 = 7

2x = 7 - 3

2x  = 4

x = 4 / 2

x = 2

Therefore,

the number red colour = 2

the number of green colour = 2 + 2 = 4

the number of yellow colour = 3

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The actual distance between the opposite corners of the school hall is; 10√34 m

The scale drawing showing the corners of the hall has been drawn and attached.

Now, from the attached scale drawing it was drawn with the scale;

1 cm to represent 5 m.

Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;

D² = 30² + 50²

D² = 900 + 3500

D² = 4400

D = √4400

D = 10√34 m

Thus, the actual distance between the opposite corners of the school hall is; 10√34 m

Complete question is;

Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.

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P/10 = 7.2/3

P = 7.2x10/3

P=72/3

P= 24

Step-by-step explanation:

cotθcosθ=1tanθ⋅1cosθ

Answer:

salary=120000

1/4×120000=30000= money spent

remainder=120000- 30000

= 90000

money spent on clothing =1/2×90000

=45000

Explanation: If his salary is $120,000 and 1/4 is used on food he has a remaining of $80,000. He uses 1/2 on clothing so he has a remainder of $40,000 so now we know that he used $40,000 on clothing

Answer: $40,000

Hope this helps you! :D

Answer:

  138.37 g

Step-by-step explanation:

Mass is the product of density and volume.

  M = ρV = (0.685 g/mL)(202 mL) = 138.37 g

The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7

The expression is given as:

(2a + 3b)^8

The power of the above expression is 8

When expanded, the sum of powers on each variable must be 8.

Using the above explanation, we have the following possible variable terms:

a^5b^3, b^8, a^4b^4, a^8, ab^7

This is because the sum of powers equals 8

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Answer:

Use the distance formula on both points AC and AB.

Distance formula is this:

\begin{gathered}d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\end{gathered}d=(x2−x1)2+(y2−y1)2d=(1−−5)2+(8−−7)2d=(6)2+(15)2d=36+225d=261

Distance for AC  is  16.16

Now do the same with the numbers for AB and get the distance of 5.39

2. To get the area, use the formula 1/2 x base x height

AB is the base and AC is the height.

1/2 x 16.16 x 5.39 = 43.55

the answer is 43.5

Answer:

x=16

Step-by-step explanation:

6= x/4 + 2

Subtract 2 from both sides.

4= x/4

Multiply 4 to both sides.

x=16

Hope this helps!

Answer:

x + 4y = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 2 )

2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form

multiply through by 4 to clear the fractions

4y = - x + 7 ( add x to both sides )

x + 4y = 7 ← equation in standard form

equation of line in two point form is needed here.

Based on the given parameters, the length of the missing length in the triangle is 12 units

The given triangle is an scalene triangle

Scalene triangles are triangles that have unequal three sides

The missing side is x, and the value of x is calculated using the following equivalent ratios

We have

4 : 8 = 6 : x

Express the above equation as a fraction

4/8 = 6/x

Evaluate the quotient

0.5 = 6/x

Solve for x

x = 6/0.5

Evaluate the quotient

x = 12

Hence, the length of the missing length is 12 units

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The values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4

The figure that completes the question is added as an attachment

From the figure, we have the third side of the triangle to be

Third = √(7^2 - 4^2)

Evaluate

Third = √33

The sin(α) is calculated as:

sin(α) = Opposite/Hypotenuse

This gives

sin(α) = 4/7

The cos(β) is calculated as:

cos(β) = Adjacent/Hypotenuse

This gives

cos(β) = 4/7

The tan(α) is calculated as:

tan(α) = Opposite/Adjacent

This gives

tan(α) = 4/√33

The cot(β) is calculated as:

cot(β) = Adjacent/Opposite

This gives

cot(β) = 4/√33

The sec(α) is calculated as:

sec(α) =  Hypotenuse/Adjacent

This gives

sec(α) = 7/√33

The csc(β) is calculated as:

sec(β) = Hypotenuse/Opposite

This gives

sec(β) = 7/√4

Hence, the values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4

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The value of output, h, when the input, x, is -18 for the given equation is 14

From the given question, we are to determine the value of the output, h, when the input x is -18

The given equation written properly is

h = 17 + x/6

Now, to determine the value of output, h, we will put in the value of x into the equation

h= 17 + x/6

The given value of x is -18

Thus, putting the given value of x into the equation, we get

h= 17 + x/6

h= 17 + -18/6

h = 17 + -3

h = 17 - 3

NOTE: + × - = -

h = 14

∴ h is 14 when x is -18

Hence, the value of output, h, when the input, x, is -18 for the given equation is 14

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Answer:

14×7=98 so multiply the same into 14×8=112

Answer:

112 watermelons

Step-by-step explanation:

7/8 = 7÷7/8÷7 = 1/1.14285714286

1 x 98/ 1.14285714286 x 98

98/112

One fourth of m minus six is equal to two times the sum of m and 9:

This is self-explanatory, please comment if something is unclear.

Drew has 50 marbles; red, green and blue.

Equation for this:

He has six more red marbles than blue marbles:

Equation for this:

He has four fewer green marbles than blue marbles:

Equation for this:

Substitute r and g into first equation and solve for b:

Drew has 16 blue marbles.

Answer:

As the number of files increases, the storage space used increases.

Answer:

A

Step-by-step explanation:

the answer is A because it is absolute so it would actually be x + 3

The cost for 10 people equals to $ 140.

What is cost simple word?

Cost of renting bowling alley = $ 100

Additional cost of renting bowling alley per person = $ 4

⇒ Total Cost for n no. of people = 100 + 4 × n

So, Cost for 10 people = Fix $100 for bowling alley  + $4 for each 10

people

                                         = 100 + 4 × 10

                                          = 100 + 40

                                           = 140

Therefore, The cost for 10 people equals to $ 140.

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Answer:

A=36°

B=54°

C=90°

a=7

b=9.6

c=11.9

Step-by-step explanation:

Upper case A,B,C are angles. B and C are given. Calculate A because the three angles in a triangle add up to 180°. See image.

Lower case a,b, and c are side lengths.

a is given. You need to use trigonometry and a calculator to find b or c or both. Or you can find one and use the Pythagorean Theorem to find the other. See image.

The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.

It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.

On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.

Hence, we have; 7^x(7+1 ) / 2×7^x.

And upon simplification, we have; 8/2 = 4.

Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.

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The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

The function we have is: [tex]f(x) = -x^{2} +50x-264[/tex]

That models the profit in dollars, where [tex]x[/tex] is the number of memberships sold.

In order to get the zeros we'll use the quadratic formula:

[tex]x_{1,2} =\frac{-b+-(b^{2}-4ac) }{2a} \\[/tex]

For,

[tex]a=-1,b=50,c=-264: x^{1,2} =\frac{-50+-\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} \\x_{1} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\\x_{2} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\\[/tex]

So, the zeroes are [tex]x=6, x=44[/tex].

Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

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The complete question is given below:

A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.

Answer:

The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.

Answer:

D. 13

Step-by-step explanation:

54 ÷ 3 = 18 (your age in 5 years)

18 - 5 = 13 (your age now)

Answer: they can buy about 8 dvds

Step-by-step explanation:

this is because 30 + 66 = 96 and if you do 96 divided by 12 it gives you 8