An inscribed triangle with the hypotenuse being the diameter of the circle has angle A be 42 degrees. Angle C is 90 degrees. The area of the triangle ACK is 50cm^2. Find the radius of the circle

1. Let us first find the missing interior angle.

m<C+53+61=180

m<C=66 degrees

law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]

a,b, and c represents the lengths of the triangles and A,B, and C represents the measures of the interior angles opposite to the sides.

For the purposes of this problem let us use a shorthand version for the law of sines.

[tex]\frac{sin(B)}{b} =\frac{sin(C)}{c}\\\frac{sin(61degrees)}{b} =\frac{sin(66degrees)}{142}\\b=142sin(61degrees)/sin(66degrees)\\[/tex]

b=134.95 meters approx.

AC is equal to length b in this case so AC=134.95 meters approx.

2. law of cosines: a²=b²+c²-2bccos(A)

Let us rearrange this formula so that we can solve for cos(C) in terms of a, b, and c (the sides lengths of the triangle).

a²=b²+c²-2bccos(A)

a²-b²-c²=-2bccos(A)

[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]=cos(A)

cos(A)=[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]

Now, because we want to find measure of angle A...

cos(A)=[tex]\frac{13.7^{2}-12.2^{2}-22.1^{2}}{-2(12.2)(22.1)}[/tex]

cos(A)=0.83 approx.

A=33.52 degrees approx.

3. Solving with law of cosines.

law of cosines: a²=b²+c²-2bccos(A)

a²=16²+18²-2(16)(18)cos(52 degrees)

a²=256+324-576cos(52 degrees)

a²=580-576cos(52 degrees)

a²=225.38 approx.

a=15.01 units approx.

Solving with law of sines.

law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]

For the purposes of this problem let us use a shorthand version for the law of sines.

[tex]\frac{sin(71 degrees)}{18} =\frac{sin(52 degrees)}{x}\\xsin(71 degrees)=18sin(52degrees)\\x=\frac{18sin(52degrees)}{sin(71 degrees)} \\[/tex]

x=15.00 un approx.

We have 1 square with side length 8 inches, and 4 triangles with a base length of 8 inches and a height of 15.

Surface area = (8 × 8) + 4(0.5 × 8 × 15)

The first part of this equation is the area of the square

The second part is the area of a triangle, multiplied by 4 (because there are 4 triangles)

= 64 + 4(60)

= 64 + 240

= 304 in²

The total surface area is 304 square inches.

Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

Is called a letter that stands for the number

Answer:

Step-by-step explanation:

√10x - 1 = 7

Square both sides,

10x - 1 = 7²

10x - 1 =  49

10x = 49 + 1

10x = 50

x = 50/10

x=5

Answer:

December 1st

Step-by-step explanation:

Apex

Answer: December 1st

Step-by-step explanation:

Mathematics of personal finance sem 1

Answer:

3

Step-by-step explanation:

For this question, you need to make change the denominators of the fractions to be equal, making them the same lowest common denominator.

8/9 -> 40/45

4/15 -> 12/45

Since 12 goes into 40 3 1/3 times, he can patrol that many neighborhoods in 8/9's of an hour, which is rounded to 3 because he doesn't have enough time for 4.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value. The answer is 10/3, which means the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value.

Given that it takes 4/15 of an hour to patrol a single neighborhood, we can divide 8/9 by 4/15.

To divide fractions, we multiply by the reciprocal, so 8/9 ÷ 4/15 becomes 8/9 × 15/4. Multiplying across, we get (8 × 15) / (9 × 4) = 120 / 36 = 10 / 3.

Answer:

[tex]0\leq 4x+8\leq 12[/tex]

Step-by-step explanation:

Compound inequality contain at least 2 or more inequality which is separated by "either" or "or". The end result has to satisfy both the inequality to be correct.

Now, creating compound inequality.

Lets assume a number "x" to create inequality.

As per given word problem: The sum of four times a number and eight.

∴[tex]4\times x + 8[/tex] = [tex]4x+8[/tex]

Next, as given the equation has to be between zero and twelve.

∴ [tex]0\leq 4x+8\leq 12[/tex]

∴ We have the inequality for word problem is [tex]0\leq 4x+8\leq 12[/tex].

The compound inequality that represents the given word problem is [tex]\( 0 < 4x + 8 < 12 \).[/tex]

To create a compound inequality for the given word problem, we need to translate the words into a mathematical expression. The problem states that "the sum of four times a number and eight is between zero and twelve." Let's break this down:

1. Identify the variable: The problem is asking about "a number," which we will represent with the variable [tex]\( x \).[/tex]

2. Translate "four times a number" into a mathematical expression: This phrase becomes  [tex]\( 4x \).[/tex]

3. Translate "the sum of four times a number and eight" into a mathematical expression: This phrase adds 8 to the previous expression, resulting in[tex]\( 4x + 8 \).[/tex]

4. Translate "is between zero and twelve" into a mathematical inequality: This phrase indicates that the expression [tex]\( 4x + 8 \)[/tex]  should be greater than zero and less than twelve. In mathematical terms, this is written as two separate inequalities:[tex]- \( 4x + 8 > 0 \)- \( 4x + 8 < 12 \)5.[/tex]  Combine the two inequalities into a compound inequality: Since we want both conditions to be true at the same time, we use the logical "and" to combine them. The compound inequality is then:[tex]\( 0 < 4x + 8 < 12 \[/tex] )This compound inequality states that the expression [tex]\( 4x + 8 \)[/tex]  should yield a value that is greater than 0 and less than 12, which accurately represents the conditions given in the word problem.

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

Let "p" be the cost of one peppermint cookies

Let "c" be the cost of one cinnamon sugar cookies

To find: cost of each cookie

We can frame a equation as:

120  peppermint cookies x cost of one peppermint cookies + 30  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81

[tex]120 \times p + 30 \times c = 81[/tex]

120p + 30c = 81  --------- eqn 1

70  peppermint cookies x cost of one peppermint cookies + 60  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60

[tex]70 \times p + 60 \times c = 60[/tex]

70p + 60c = 60 --------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "c"

Multiply eqn 1 by 2

240p + 60c = 162  --- eqn 3

Subtract eqn 2 from eqn 3

240p + 60c = 162

70p + 60c = 60

(-) -------------------------

170p = 102

Substitute p = 0.6 in eqn 1

120p + 30c = 81

120(0.6) + 30c = 81

72 + 30c = 81

30c = 9

Summarizing the results:

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

Answer:

Anna is incorrect.

Step-by-step explanation:

Find lengths of diagonals SQ and OM.

1. Consider right triangle SQR. By the Pythagorean theorem,[tex]SQ^2=SR^2+RQ^2\\ \\SQ^2=14^2+7^2\\ \\SQ^2=196+49\\ \\SQ^2=245\\ \\SQ=\sqrt{245}=7\sqrt{5}\ units[/tex]

2. Consider right triangle OML. By the Pythagorean theorem,

[tex]OM^2=OL^2+LM^2\\ \\OM^2=7^2+7^2\ [\text{In square LMNO, side } OL \text{has the same length as side }LM]\\ \\OM^2=49+49\\ \\OM^2=98\\ \\OM=\sqrt{98}=7\sqrt{2}\ units[/tex]

Since [tex]7\sqrt{5}\neq 2\cdot 7\sqrt{2}=7\sqrt{8},[/tex] diagonal SQ is not two times diagonal OM. Thus, Anna is incorect.

Answer:

Anna is not correct

Step-by-step explanation:

 Part A: No, anna is not correct because first the rectangle (PQRS) its says that the length of (SR) is 14 inches and if cut in half at the diagonal a rectangle or a square would have 2 triangles so if A2 + B2 = C2 then if C = the length of the diagonal and A would = 14 in ( the length of the rectangle) and then B would = 7 inches which is the width of the rectangle. It concludes that 14 to the power of 2 + 7 to the power of 2 = 245 which its square root is 15.65 ( if rounded to the hundredth place) 

Part B: Next, is the square (LMNO) if its length and width are both 7 inches then A2 = 7 to the power of 2 and also B2 will also = 7to the power of 2 and C2 will = will be the length of the diagonal.So, all of that 7 to the power of 2 + 7 to the power of 2 = 98 and its square root is 9.89 ( if rounded to the hundredth place) so lets just say 9.9.

Then you can see that 9.9 times 2 does not equal 15.65 so Anna was wrong.  

Answer:

2.133333

Step-by-step explanation:

He didn't simplify it

Answer:

Step-by-step explanation:

She might have not moved the decimal point in the right direction/right spaces

Answer:

weight * (4 / 5) = 30

weight * .8 = 30

weight = 30 / .8

weight = 37.5 pounds

Step-by-step explanation:

Good evening ,

Answer:

Look at the photo below for the Answer.

:)

Answer:

431547619  / 12500000000

0.03452380 …

Step-by-step explanation:

Both are the simplified versions of 3452380952/100000000000.

The answer above is also correct! I hope this helps you!

- sincerelynini

Answer:

B. 3x² – 10x + 13

Step-by-step explanation:

given:

f(x) = 3x² – 8x + 5

g(x) = 2x – 8

f(x) - g(x)

= (3x² – 8x + 5) - (2x – 8)

= 3x² – 8x + 5 - 2x + 8

= 3x² – 10x + 13

The gardeners should buy 48 white and 116 pink hydrangeas altogether

Step-by-step explanation:

The given is:

We need to find how many white and how many pink hydrangeas the gardeners should buy altogether

Assume that the number of white hydrangeas is x and the number of pink hydrangeas in the first bed

∵ The first bed has x white hydrangeas

∵ The first bed has y pink hydrangeas

∵ The total of white and pink hydrangeas in 1st bed is 45

- Equate the sum of x and y by 45

∴ x + y = 45 ⇒ (1)

∵ In the 2nd bed the number of the white hydrangeas is 2 times

   as in the 1st bed

∵ The number of the pink hydrangeas is 3 times as in the 1st bed

∵ The number of the hydrangeas in the 2nd bed is 119

- Multiply x by 2 and y by 3, then add the products and equate

  the sum by 119

∴ 2x + 3y = 119 ⇒ (2)

Now let us solve the system of equations

Multiply equation (1) by -3 to eliminate y

∵ -3x - 3y = -135 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -16

- Divide both sides by -1

∴ x = 16

- Substitute the value of x in equation (1) to find y

∵ 16 + y = 45

- Subtract 16 from both sides

∴ y = 29

∵ The number of the white hydrangeas in the 1st bed is x

∵ The number of the white hydrangeas in the 2nd bed is 2x

∴ The total number of the white hydrangeas = x + 2x = 3x

∵ x = 16

∴ The total number of the white hydrangeas = 3(16) = 48

∵ The number of the pink hydrangeas in the 1st bed is y

∵ The number of the pink hydrangeas in the 2nd bed is 3y

∴ The total number of the pink hydrangeas = y + 3y = 4y

∵ y = 29

∴ The total number of the pink hydrangeas = 4(29) = 116

The gardeners should buy 48 white and 116 pink hydrangeas altogether

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

Answer:

a) Given in attachment.

b) Quadrilateral formed is a rhombus. Because length of all the sides are equal and angle between adjacent sides is not 90°.

c) 24 unit².

Step-by-step explanation:

Let rectangle be ABCD with length 8 and width 6

And mid-points be E,F,G,H

Now, join the mid-points .

we know that angle between adjacent sides in a rectangle is 90°.

⇒ ΔFAE forms a right angle triangle with 90° at A.

By, pythagoras theorem , EF² = AF² + AE²

⇒ EF² = 3² + 4² = 25

⇒ EF = 5;

In the same way, FG = GH = HE = 5

⇒ the quadrilateral is either square or rhombus.

Now, from ΔFAE,   sin(∠AEF) = [tex]\frac{4}{5}[/tex]

(sinФ = opposite side / hypotenuse)

⇒ ∠AEF = 53°;

In similar manner;

∠DEH = 53° . Now ∠FEH = 180 - 53 - 53 = 74° (sum of angles on a straight line is 180°)

⇒ the quadrilateral is rhombus has angle between adjacent sides is 53° and not 90°.

Now, to find the area of rhombus, join EG and FH. And name the intersection point as J.

consider ΔEJF,

it is a right angled triangle at J, and also quadrilateral AFJE forms rectangle, as diagonals intersect perpendicular in a rhombus.

⇒ FJ = 3 and EJ = 4.

⇒ area of this triangle = 1/2 × base × height

                                     = 1/2 × EJ × JF = 1/2 × 3 ×4 = 6

similarly triangles FJG, GJH, HJE.

⇒ area of rhombus = 6+6+6+6 = 24.

Answer:

3 pounds and 3/4th of a pound

Step-by-step explanation:

2000 x 3 is 6000 and you have 1500 left

you can divide 2000 equally by 4 and get 500.

Multiply 500x3 and get 1500

(the 3 and the 4 is how i got the fraction)

6000+1500 = 7500

boom big brain answer good luck

In this question, we know that 1 ton = 2000

We're trying to find how many tons is 7500 tons.

In order to find your answer, you would divide 7500 by 2000 in order to know how many tons there are.

Divide:

7500 ÷ 2000 = 3.75

This means that there are 3.75 tons in 7500 pounds

Answer:

3.75 tons

The equation for the height, h, in terms of the base, b, and area, A is [tex]h = \frac{2A}{b}[/tex]

Solution:

Given that area of a triangle is given by the formula:

[tex]A = \frac{1}{2}bh[/tex]

Where,

A is the area of triangle

b is the base of triangle

h is the height of triangle

We have to find the equation for height in terms of base and area

So we have to arrange the equation in such a way that height can be found by using area and base

Given formula is:

[tex]A = \frac{1}{2}bh[/tex]

Keep "h" alone in L.H.S and move the other terms to other side of formula

[tex]A = \frac{bh}{2}\\\\2A = bh\\\\h = \frac{2A}{b}[/tex]

Thus height is expressed in terms of base and area

Step-by-step explanation:

Picture############

Answer:3/8 as a fraction and 3/8%

Step-by-step explanation:

Answer:

All the points on (x - 2)² + (y - 5)² = 100

Step-by-step explanation:

It should be the circle with its center on point (2,5) and radius is 10.

(h , k) : center of circle (2,5)    h = 2     k = 5

r: radius     r = 10

Circle: (x - h)² + (y - k)² = r²

(x - 2)² + (y - 5)² = 100

Answer:

Below.

Step-by-step explanation:

There are many .

Two are  (2+10, 5) =  (12,5) and (2,5+10) = (2, 15).

To find the solution to the system of equations 5x - 8y = -45 and 9x - 8y = 49, you can solve by elimination. The solution is x = 23.5 and y = 20.3125.

To find the solution to the system of equations:

5x - 8y = -45

9x - 8y = 49

Answer:

9 pizzas

Step-by-step explanation:

Maria is planning a party. She should order 3 pizzas for every 7 people. Let x be the number of pizzas Maria will order for 21 people, then

3 pizzas - 7 people

x pizzas - 21 people

Write a proportion:

[tex]\dfrac{3}{x}=\dfrac{7}{21}[/tex]

Cross multiply:

[tex]7\cdot x=21\cdot 3\\ \\7x=63\\ \\x=\dfrac{63}{7}=9\ pizzas[/tex]

Answer:

y = - 3x + 5

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 4) and (x₂, y₂ ) = (1, 2)

m = [tex]\frac{2+4}{1-3}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3, thus

y = - 3x + c ← is the partial equation

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

Using (1, 2), then

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - 3x + 5 ← equation of line

Answer:

y=-3x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-(-4))/(1-3)

m=(2+4)/-2

m=6/-2

m=-3

y-y1=m(x-x1)

y-(-4)=-3(x-3)

y+4=-3(x-3)

y=-3x+9-4

y=-3x+5

Answer:

18 feet

Step-by-step explanation:

1 inch = 6 feet

3 * 6 = 18

Answer:

C

Step-by-step explanation:

Answer:

[insert name here] drove his scooter around. When he started, his speed increased constantly to 10 mph (O-A). He cruised at 10mph for a few seconds. (A-B) Then he slowed down (B-C) and stopped for a few seconds (C-D). He then started speeding up (D-E) and cruised for a few more seconds. (E-F)

Answer:

please include more info

Step-by-step explanation:

Answer: Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.

Step-by-step explanation:

The complete question is:

"Lucy is a dress maker. She sew [tex]\frac{4}{7}[/tex] of a dress in [tex]\frac{3}{4}[/tex] hour. At this rate, how many dresses does Lucy sew in one hour?"

Let "x" represents the number of dresses that Lucy sews in one hour.

You need to analize the information given in the exercise.

According to the exercise, you know that, in [tex]\frac{3}{4}[/tex] hour, Lucy sews [tex]\frac{4}{7}[/tex] of a dress.

Then, knowing this data, you can set up the following proportion:

[tex]\frac{\frac{4}{7}}{\frac{3}{4}}=\frac{x}{1}[/tex]

Therefore, you must solve for "x" in order to find the he number of dresses that Lucy sew in one hour.

You get this result:

[tex](1)(\frac{4*4}{7*4})=x\\\\x=(1)(\frac{16}{21})\\\\x=\frac{16}{21}[/tex]

Then, Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.

The first link is for the first question, and the second one is to the second question I hope this helps!

Answer:

Amy spent $11 for lunch.

Step-by-step explanation:

x+y=25

x+(x+3)=25

2x+3=25

2x=25-3

2x=22

x=22/2

x=11

Answer:amy spent 11 dollars.

Step-by-step explanation:I did math