Mathematics High School

Find the possible values of the included angle of a triangle with: A) sides of length 5 cm and 8 cm, and area of 15 cm^2
B) sides of length 45 km and 53 km, and area 800 km^2.

Answers

Answer 1
we know that

The area of ​​a triangle can be calculated by applying the law of sines

Area=(1/2)*a*b*sin C-----> sin C=2*A/[a*b]

Part a) sides of length 5 cm and 8 cm, and area of 15 cm^2
a=5 cm
b=8 cm
A=15  cm²
sin C=2*A/[a*b]------> sin C=2*15/[5*8]----> sin C=3/4
C=arc sin (3/4)-----> C=48.59 degrees
the possible values of the included angle are
C1=48.59°
C2=180°-48.59----> C2=131.41°

the answer Part a) is
48.59° and 131.41°

Part b) sides of length 45 km and 53 km, and area 800 km^2
a=45 km
b=53 km
A=800 km²
sin C=2*A/[a*b]-----> sin C=2*800/[45*53]----> sin C=0.6709
C=arc sin (0.6709)-----> C=42.13°
C1=42.13°
C2=180-42.13°----> C2=137.87°

the answer part b) is
42.13° and 137.87°

Related Questions

A spinner is divided into 5 equal sections numbered 1 to 5. The theoretical probability of the spinner stopping on 3 is 20%. Which of the following is most likely the number of 3's spun in 10,000 spins?


A. 3358
B. 1243
C. 2589
D. 2067

Answers

1243 i believe my dood

Have you found a positive o negative correlation between the independent and dependent variables

Answers

your answer will be positive o. now please give me 5 stars

The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?

Answers

1.08x = 7.02

x = 7.02 / 1.08

x = $6.50

6.50

Hope this helps.

5 out of 8 bags of m&ms had exactly 32 pieces in them. How many bags out of 40 should have exactly 32 pieces

Answers

Probabilities; so 5/8 =32
So 8*?= 40
8*5=40
Then 5*5=25 that means 25 bangs is the answer

Please help me with this

Answers

y=3(x²+10x)+71
Now we need to complete square for (x²+10)
It should look like this
a²+2ab+b²=(a+b)²

y=3(x²+2*5x+5²)-3*5²+71
y=3(x+5)²-75+71
y=3(x+5)²-4
Vertex has coordinates x=-5, y=-4.
Vertex in this case is the extreme value (-5,-4)


ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.

Out of 100 students, how many should weigh between 64 and 96 pounds?

Answers

We first determine the z-scores for the given x-values of 64 and 96.
For x = 64: z = (64 - 80) / 8 = -2
For x = 96: z = (96 - 80) / 8 = 2
Therefore we find the probability that -2 < z < 2, which is around 0.95. Therefore, out of 100 students, approximately 100(0.95) = 95 students will weigh between 64 and 96 pounds.

Simon invested $1,550 at 6.5% simple interest. He earned $302.25 in interest after t years. What is the value of t?

Answers

Here's the equation:
0.065t(1550) = 302.25
100.75t = 302.25
t = 3
3 years

Answer:

Marco deposited $500 in a savings account earning 4% simple interest over 5 years.  

What was the total amount of interest earned at the end of 5 years?

 

$40

 

$50

 

$100

 

$200




Step-by-step explanation:


The area of a piece of construction paper is 204 inches. The paper is 17 inches long. What is the width of the paper?

Answers

The width of the construction paper is 12 inches.

The formula for area is length(l)*width(w)=area in units squared(a^2).

To find the width, we divide both sides by length, this gives us the following:

17*w=204in^2     w=204in^2/17  

To find the answer, you just perform the operation.

204/17=12

The width is 12 inches.

Will give brainliest! How many distinct triangles can be made? I think I have to first find the measure of length b and then compare measure a with b and h to find the answer. Please help me out on how to find measure length b

Answers

check the picture below.

this is a case of the ambiguous case with an SSA, AC and CB are the sides and the angle is at A.

the ambiguous case has two triangles, the case when B is acute, CB sticks out, and the case when B is obtuse, CB sticks inside, it just so happen that those two angles for B are "supplementary" angles.

if you check the sin⁻¹ of that, we'll get the acute version of B, that's because of the constraints on the range of the inverse sine function, and we get ∡B ≈ 36.86989765°.

and of course, the other angle for B will be 180 - 36.86989765.

Is quadrilateral JKLM the result of a dilation of quadrilateral ABCD by a scale factor of 2? Why or why not? Yes, because sides JK and ML are twice as long as sides AB and DC. Yes, because both figures are parallelograms, so corresponding sides are parallel. No, because sides JK and ML are not twice as long as sides AB and DC. No, because sides JM and KL have different slopes from sides AD and BC.

Answers

Answer:

  (d)  No, because sides JM and KL have different slopes from sides AD and BC

Step-by-step explanation:

You want to know if quadrilateral JKLM is a dilation of ABCD by a factor of 2, and why or why not.

Dilation

Dilation multiplies the distance of each point on the figure from the center of dilation by the scale factor. Dilation by a scale factor of 2 will move JKLM twice as far from the origin as ABCD. This preserves slopes and angles, but changes lengths by the scale factor.

In the given figure, ABCD is 2 units wide and 2 units high. If JKLM is a dilation by a factor of 2, it will be 4 units wide and 4 units high.

JKLM is 5 units high, so is not a dilation. JK and ML are twice as long as AB and DC, so choice C is not an appropriate explanation.

Sides JM and KL have different slopes from sides AD and BC, choice D.

__

Additional comment

The slopes of JM and KL are 5/2. The slopes of AD and BC are 2/1, a different value.

Answer: D

Step-by-step explanation:

the amount that results when $4000 is compounded at 6% annually over seven years

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &7 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 7}\implies A=4000(1.06)^7[/tex]

What happened to the cat who swallowed a ball of yarn?

Answers

the cat who swallowd the yarn died
Depending on the size of the ball of yarn. I the ball of yarn was small he'll live but if it was bigger than he would have died from it being stuck in it's throat or possibly could have lived if rushed to the hospital immediately. But in this case she had Mittens.

jack paid $2.60 sales tax on a $52 pair of shoes that he purchased. how much sales tax will his friend pay if his friend purhases a $28 shirt?

Answers

$2.60 is 5% of $52 because: 2.6 ÷ 52 = 0.05(5 %)

5% = 0.05

Find 5% of $28:

0.05 × 28 = 1.4

Answer = His friend will pay $1.40 for sales tax

Hope this helped☺☺

At the local grocer, the prices for apples are the following: 9 ounces for $1.89 or 1 pound for $2.49. How much will you save per pound, by buying the least expensive? Round to the nearest cent.

A.) $0.87
B.) $0.10
C.) $0.60
D.) $0.21

Answers

Answer: Option 'A' is correct.

Explanation:

Cost of  9 ounces of apples = $1.89

Cost of 1 ounce of apple is given by

[tex]\frac{1.89}{9}=\$0.21[/tex]

Now, if he bought 1 pound of apple,

Cost of 1 pound of apple = $2.49

Cost of 16 ounces = $2.49

(∵ 1 pound = 16 ounces)

Cost of 1 ounce of apple is given by

[tex]\frac{2.49}{16}=\$0.156[/tex]

So, Second option is the least expensive if he bought 1 pound of apple for $2.49

Then, he will save which is given by

[tex]0.21-0.156=0.054\times 16=$0.87\ per pound[/tex]

Hence, option 'A' is correct.

Final answer:

You will save $0.87 per pound by purchasing apples at the price per pound rate ($2.49) compared to the 9-ounce rate ($1.89 for 9 ounces), with the savings calculated by converting the 9-ounce price to a per pound rate and comparing it to the given per pound price.

Explanation:

To determine how much you will save per pound by buying the least expensive option for apples, first convert the price for 9 ounces into the equivalent price per pound. Since there are 16 ounces in a pound, you need to calculate the price per ounce and then multiply by 16 for the pound equivalence. The price per ounce for the first option is $1.89/9 ounces = $0.21 per ounce. Hence, the price per pound would be $0.21 per ounce × 16 ounces/pound = $3.36 per pound.

Now compare the price per pound of both options. The specified price per pound is $2.49, and the calculated price per pound for the 9-ounce option is $3.36. The savings per pound when buying the least expensive option ($2.49 per pound) would be $3.36 - $2.49 = $0.87 per pound, rounded to the nearest cent.

Therefore, the correct answer is (A) $0.87.

If the area is 72 and the perimeter is 34, what are it's dimensions

Answers

xy = 72
2x + 2y = 34                 (Im assuming uts a rectangle or square)

2 (72/y) + 2y = 34
144 + 2y^2 = 34y
2y^2 - 34y + 144 = 0
 y = 9 or 8

So the length is 9 and width = 8

List the following stocks and bonds in order from lowest default risk to highest default risk.

A. foreign government bond, common stock, preferred stock

B. foreign government bond, preferred stock, common stock

C. common stock, preferred stock, foreign government bond

D. preferred stock, common stock, foreign government bond

Answers

The list of the stocks and bond in order from the lowest default risk to the highest default risk is as follows:

Foreign government bond, preferred stock, common stock.

Government bonds are generally referred to as a low risk investment as they have a very low chance of default.

Preferred shared holders are considered first in the disbursement of dividend before common stockholder are considered. Thus, preferred stock is of less risk than common stock.

Which transformation of Figure A results in Figure A'?




a reflection across the y-axis

a reflection across the x-axis

a clockwise rotation of 90° about the origin

a translation 12 units right and 2 units down.

Answers

the answer is D a translation 12 units right and 2 units down.

Answer:

A translation 12 units right and 2 units down.

Step-by-step explanation:

Given : Figure A and figure A'.

To find : Which transformation of Figure A results in Figure A'.

Solution : We have given that

Parent Triangle A with coordinates ( -6 ,-3) ; ( -4 ,-5) ; ( -8 , - 4)

Transformed triangle with  coordinates ( 6 ,-5) ; ( 8 ,-7) ; ( 4 , - 6)

We can see from the coordinates

( -6 +12 ,-3-2) = ( 6 ,-5)

( -4+ 12 ,-5 -2) = ( 8 ,-7)

( -8 + 12 , - 4 -2) =  ( 4 , - 6).

Therefore, A translation 12 units right and 2 units down.

Write the equation of the perpendicular bisector of RS. Point R is located at (–1, 3), and point S is located at (3, 1).

Answers

we have that
Point R is located at (–1, 3), and point S is located at (3, 1)

we know that
the perpendicular bisector of RS go through the midpoint of RS

step 1

find the midpoint RS

midpoint M (Mx,My)
Mx=(x1+x2)/2
My=(y1+y2)/2

Mx=(-1+3)/2------> Mx=1
My=(3+1)/2-------> My=2

the midpoint M is (1,2)

step 2
find the slope RS
m=(y2-y1)/(x2-x1)-------> m=(1-3)/(3+1)-----> m=-2/4-----> m=-1/2

we know that two lines are perpendicular if the slopes
m1*m2=-1

step 3
find the slope of the perpendicular bisector of RS
m2=-1/m1------> m2=2

step 4
 with m=2 and the midpoint M (1,2) find the equation of a line

y-y1=m*(x-x1)------> y-2=2*(x-1)----> y=2x-2+2-----> y=2x

the answer is
y=2x

see the attached figure

What is the value of x?

Answers

the outside angles of a polygon equal 360 degrees

total of the 3 known angles: 140 + 34 + 56 = 230
 so x = 360 - 230
x = 130 degrees

Find d: ??? Ft. Plz help idk this question

Answers

check the picture below.

Consider a single spin on the spinner shown below. Which events are mutually exclusive? Check all that apply.

landing on an unshaded portion and landing on 2
landing on a shaded portion and landing on 3
landing on a shaded portion and landing on an even number
landing on an unshaded portion and landing on a number greater than 3
landing on a shaded portion and landing on an unshaded portion

Answers

Answer:

Options A, B and E represent mutually exclusive events.

Step-by-step explanation:

Two events are mutually exclusive that can not happen at a same time.

Now let us look at our options and find which statements represent mutually exclusive events.

A. We can see that landing on an unshaded portion and landing on 2 are mutually exclusive events as unshaded portion contains 3 and 4 and 2 lies on shaded portion.

B. Landing on a shaded portion and landing on 3 is also mutually exclusive as 3 lies on unshaded portion.

C. Landing on a shaded portion and landing on an even number can happen at the same time as 2 is an even number and it lies on shaded portion.

D. Landing on an unshaded portion and landing on a number greater than 3 can happen at the same time as 4 in greater than 3 and it lies on unshaded portion.

E. Landing on a shaded portion and landing on an unshaded portion  are mutually exclusive events as spinner can be either in shaded portion or in unshaded portion.

Therefore, Options A, B and E are our correct choices.

Answer:

A, B, E

Step-by-step explanation:

I just did it on edge and got it right

At a local baseball game there are 3 hot dog vendors. collectively the vendors sold 1,700 hot dogs. if vendor a sold 456, vendor b sold 607, and vendor c sold 637, what percentage of the total did each vendor sell? (round to the nearest percent.) a) 26 percent, 40 percent, 44 percent b) 45 percent, 37 percent, 18 percent c) 27 percent, 36 percent, 37 percent d) 30 percent, 35 percent, 35 percent

Answers

The answer is C.

Vendor A= 456/1700, which is .268 or 27%
Vendor B= 607/1700, which is .357 or 36%
Vendor C= 637/1700, which is .374 or 37%

For a total of 100%
the correct answer is c) 27%, 36%, AND 37% divide how many hot dogs the vendor sold by 1700 and then round to find the percentage

Lynh manages a small company with 12 employees. He offers profit sharing where 5% of profits at end of year is distributed evenly to the employees. Each employee earned $2,300 in profit sharing in 2013. What was the total profit?

Answers

We need to find the total profit of Lynh Mangoes. It is given that the 5 % of profit to be distributed equally between 12 employees.

Profit received by each employee = $ 2,300

Total profit received by 12 employees = $ 2,300 × Profit received by each employee

Total profit received by 12 employees = $ 27,600

It is given that 5 % to be distributed.

Thus, 5 % of total profit = $ 27,600

Total profit = $ 27,600 ÷ 5 %

Total profit = $ 552,000

Share out £80 between Tom and jerry in the ratio 3:2

Answers

So let's add variables according to the ratio:
3n + 2n = £80
5n = £80
n = 16
3(16):2(16)
48:32
Tom gets £48, and Jerry gets £32
Tom gets- 48
Jerry gets- 32
Hope I helped! tell if I missed something! :)

A child is standing at point c and flying a kite located at point a, 25 ft above the ground. as the child lets out more string, the kite rises to a point b, directly above point
a. if the angle of elevation changes from 50º to 65º, how much higher to the nearest foot, is the kite than it was initially?

Answers

Final answer:

To calculate the height increase of the kite, we can use trigonometry and the formula tan(angle) = h / distance. By plugging in the values, we find that the kite is approximately 25 * tan(65º) ft higher than it was initially.

Explanation:

To find how much higher the kite is than it was initially, we need to determine the difference in height between points a and b. Since point b is directly above point a, the difference in height can be calculated using trigonometry.

We can use the tangent of the angle of elevation to find the height increase. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is the height increase (h) and the adjacent side is the distance between points a and c. We can use the formula tan(angle) = h / distance to solve for h.

Given that the angle changes from 50º to 65º, we can calculate the height increase as follows:

tan(65º) = h / distance

Solving for h:

h = tan(65º) * distance

Plugging in the values:

h = tan(65º) * distance

h ≈ tan(65º) * 25 ft

Rounding to the nearest foot, the kite is approximately 25 * tan(65º) ft higher than it was initially.

Trains on the line reached an average speed of 125 miles per hour. Approximately, what is this speed in kilometers per hour?

Answers

125 miles per hour is equal to 201.168 kilometers per hour.

Does anyone know anything about The Distributive property? Please help!

Answers

when you distribute by multipling

What is the exact value of cos 30° ?

Answers

Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.

Side AB will be the hypotenuse.

cos 60° = AC / AB                 -------[ cos 60° = 1/2]

So, AB = 2 AC   -------------------------------(1)

Apply Pythagorean Theorem to find BC

AB² = BC² + AC²

4 AC² = BC² + AC²

So,  BC = √3 AC  ------------------------(2)

Now, we shall find the value of cos 30°

cos 30° = CB / AB

or,        =  √3 AC / 2 AC     -------using equations (1) and (2)

So,   cos 30° = √3 / 2

Hence, the exact value of

Since ∠A = 2∠B. So,  cos 30° will be √3 / 2

The answer is √3 / 2

The line graphed below passes through the points (-2, 0) and (0, -3). Use the slope formula to calculate the slope between the given points. Verify the slope by counting the rise over the run on the graph.

Answers

The slope = (-3 - 0) /  (0- -2)  = -3 / 2 

Answer:

The answer is -4/5

Step-by-step explanation:

It just is. The test said so.

Add. Express your answer in lowest terms. 8 3/10 + 7 2/15

Answers

[tex]8 \dfrac{3}{10} + 7 \dfrac{2}{15} [/tex]

[tex]= 8 \dfrac{9}{30} + 7 \dfrac{4}{30} [/tex]

[tex]=15 \dfrac{13}{30} [/tex]
Final answer:

To add 8 3/10 and 7 2/15, we need to find a common denominator. The sum is 15 1/15.

Explanation:

To add 8 3/10 and 7 2/15, we need to find a common denominator. The least common multiple of 10 and 15 is 30. So we convert both fractions to have a denominator of 30: 8 3/10 = 8 9/30 and 7 2/15 = 7 4/30. Now we can add the whole numbers and the fractions separately:

8 + 7 = 159/30 + 4/30 = 13/30

Combining the results, the sum is 15 13/30. To express the answer in lowest terms, we can simplify the fraction: 13 and 30 are both divisible by 13, so dividing both by 13 gives us 1 and 2/30. Therefore, the final answer is 15 2/30, which can be further simplified to 15 1/15.

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