Type the correct answer in each box. Use numerals instead of words. Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately

Type The Correct Answer In Each Box. Use Numerals Instead Of Words. Find The Missing Side And Angle Measures

Answers

Answer 1

The measures of the angles of the triangles are

The measure of ∠B = 80.3°

The measure of ∠C = 59.7°

The length of side AB = 20.2 units

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AC = 23

The measure of side BC = 15

The measure of ∠A = 40°

From the law of sines , we get

( sin A ) / a = ( sin B ) / b = ( sin C ) / c

Substitute the value of A and a in the equation , we get

sin ( 40 )° / 15 = sin B / 23

On simplifying the equation , we get

sin B = ( 23/15 ) x sin ( 40 )°

Now , m∠B = 80.27°

So , the measure of angle ∠B = 80.3°

And ,

The interior angles of a triangle is 180°

So , The measure of angle ∠C = 180° - ( 80.3° + 40° )

On simplifying the equation , we get

The measure of angle ∠C = 59.7°

Now ,

From the law of cosines , c² = a² + b² - 2ab ( cos C )

Substitute the value of a , b and cos C in the equation , we get

c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°

On simplifying the equation , we get

c² = 225 + 529 - 348.12363

c² = 405.87

Taking square roots on both sides of the equation , we get

c = 20.156

c = 20.2 units

Therefore, the measure of side AB = 20.2 units

Hence , the measures angles of triangle is solved

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Related Questions

Is polynomial Y⁴+ 4y²+ 5 have zeroes or not?

Answers

The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

What is polynomial?

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

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A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?

Answers

hey ,

here is your answer,

_______________

Let the number of boxes filled, by using 20 bottles in each box, be x.

The following table is obtained.

______________________

| Number of bottles. 12. 20 |

| |

| Number of boxes 25. x. |

---------------------------------------------

More the number of bottles, lesser will be the number of boxes.

Hence, the number of bottles and the number of boxes required to pack these are inversely proportional to each other.

Therefore,

12 × 25 = 20× x

Hence, the number of boxes required to pack these bottles is 15.

Answer:

The answer is 15 Box.

No of bottles = 25 boxes × 12 bottles

= 300 bottles

So there were total 300 bottles in a box.

Now If 20 bottles are filled ina box then

no. of box required = 300/20

And answer is 15 boxes

Solve the formula V = πr²h for r.

Answers

Answer:

v=πr²h

divide both sides by πh

v/πh=r²

r²=v/πh

square root both sides

r=√v/√πh

I hope this helps

PLSS helpppppppppppppp like plssss

Answers

Answer:

f=21-16, 5

Step-by-step explanation:

Just subtract 16 from both sides to get 5  as the solution

Answer:

ADDITION

16+f=x

Step 1: Add -16 to both sides.

f+16+−16=x+−16

f=x−16

Answer:

f=x−16

Step-by-step explanation:

SUBTRACTION

16−f=x

Step 1: Add -16 to both sides.

−f+16+−16=x+−16

−f=x−16

Step 2: Divide both sides by -1.

−f /−1 = x−16 /−1

f=−x+16

Answer:

f=−x+16

A jar of coins contains only quarters and dimes. The total amount of money in the jar is $4.40, and there are 23 coins.

A. Write a system of equations that can be used to find d, the number of dimes, and q, the number of quarters, in the jar.

B. How many quarters are in the jar?

Answers

Answer:

(1) d+q=23 (the total number of coins is 23)

(2) 10d+25q = 440 (the total value of the coins, at 10 cents for each dime and 25 cents for each quarter, is 440 cents)

there are 14 quarters and 9 dimes

Step-by-step explanation:

NO LINKS... I WILL REPORT YOU
Find the measure of the indicated angle. Need help please.
I need explanation,
thank you

Answers

Answer:

107

Step-by-step explanation:

Sum of all angles is 180

12+BC+61 = 180

73+ BC = 180

73 - 73 + BC = 180 - 73

BC = 107

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

Answer:

Step-by-step explanation:

4/56\8

What type of graph is an inverse relationship?

Answers

On a graph, an inverse relationship always has a negative slope.

What is an inverse relationship?

In statistics, if higher values of one variable tend to be related to lower values of the other, there is a negative association or inverse relationship between the two variables.

A negative link between two variables typically denotes a negative correlation, or what is similar in some cases, a negative slope on the associated graph.

Anticorrelation or inverse correlation are other terms for a negative correlation between two variables.

When two variables change in an inverse relationship, they do so in opposite directions: one increases while the other drops, and vice versa.

Y declines as X rises in an inverse relationship.

An inverse relationship always has a negative slope on a graph.

Therefore, on a graph, an inverse relationship always has a negative slope.

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Mr. Thompson earns $ 11.52 per hour. Last week he worked 37 hours how much F.I.C.A tax did he have to pay at 7.65%?

Answers

Answer:

$32.61

Step-by-step explanation:

First, we multiply the amount he earns per hour by the amount of hours he worked. $11.52 * 37 = $426.24. Then, we figure out what 7.65% of $426.24 is, which we can do by multiplying 426.24 by 0.0765. This gives us $32.60736, but since there is no form of US money that is worth less than 1 cent, we round to the nearest cent and get $32.61.

Hope this helps!

Find the measure of the given angle. Round to the nearest degree.
(O
6
?
13

Answers

I think it’s 13 yup because why not yk hahahha

15 degrees by eye i think                                                        

 

                                                                                                                     

A basking shark measures 25 feet long. A giant squid measures
33 feet long. How many inches longer is the basking shark than
the giant squid?
ounds and

Answers

Answer: 8 feet

Step-by-step explanation:

you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.

find the indicated sum

Answers

Step-by-step explanation:

option no 2 is correct

36 I hope is helpful

Use logarithmic table to evaluate 40.79÷0.003949​

Answers

Answer:

  1.033×10⁴

Step-by-step explanation:

You want the quotient 40.79÷0.003949​ using log tables.

Log of quotient

The log of a quotient is the difference of logs:

  log(a/b) = log(a) -log(b)

Log values

It can work well to start by writing the numbers in scientific notation:

  log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106

  log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965

Log of quotient

Then the log of the quotient is ...

  log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141

Antilog

The antilog of this number will be ...

  antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴

With our 4-digit log tables, 4 significant figures is the best we can expect.

The quotient is about 1.033×10⁴.

__

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Question 3 A student solved a quadratic equation as shown here

Answers

Answer:

Didn't move the 12 on the other side of the equal sign to make

2x^2 + 5x - 12 = 0

the other steps error city.

Step-by-step explanation:

2x^2 + 5x - 12 = 0

(2x - 3)(x + 4)= 0

2x - 3 = 0

2x = 3

x = 3/2

x + 4 = 0

x = -4

A weight is suspended from a spring is set into oscillating
motion by compressing it into a point 3 cm above its resting
position and releasing it. It will displace 3 cm past its resting
point. From the time it is released it will bounce at a rate of 3
cycles per second.

a. Draw a graphical representation and give the equation
involving the situation.

b. What is the displacement of the spring after 2.5
seconds?

Answers

a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).

b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.

What is an oscillation period?

By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.

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What is the value of x?

Answers

Answer:

x=9

Step-by-step explanation:

2x=x+9

Subtract x from both sides;

2x-x=x+9-x

Simplify;

x=9

Which matrix represents the system of equations shown below?
2x - 9y = 12
-5x - 7y = 15

O A.
[2 -9 12
5 -7 15

O B.
1-2 -9 127
5 -7 15

O C.
2 -9 127
-5 -7 15

O D. 13:53
1-2 -9 -121
-5 -7 -15

Answers

Answer:

c because c is c kkjwjwjjjwjwjsjssjsjjssmsswnsnsnsnnsns

The matrix that is represented by the system of equations is:

[tex]\left[\begin{array}{ccc}2&-9&12\\-5&-7&15\end{array}\right][/tex]

Option C is the correct answer.

What is a matrix?

A matrix is a set of numbers arranged in rows and columns such that it forms a rectangular array.

We have,

Here, the coefficient matrix is the matrix on the left-hand side, the variable matrix is the column matrix containing the variables x and y, and the constant matrix is the column matrix on the right-hand side containing the constants 12 and 15.

To solve the system of equations, we can use matrix operations to transform the coefficient matrix into the identity matrix, while performing the same row operations on the variable matrix and the constant matrix.

Once we have transformed the coefficient matrix into the identity matrix, the variable matrix will be transformed into the solution vector containing the values of the variables x and y that satisfy the system of equations.

Thus,

The matrix that is represented by the system of equations is:

[tex]\left[\begin{array}{ccc}2&-9&12\\-5&-7&15\end{array}\right][/tex]

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Work out the lengths of sides a and b.
Give your answers to 1 decimal place.

Answers

Step-by-step explanation:

[tex] {a}^{2} = {8}^{2} + {5}^{2} \\ {a }^{2} = 64 + 25 \\ {a}^{2} = 89 \\ a = \sqrt{89} = 9.4 \: cm[/tex]

[tex] {17}^{2} = {12}^{2} + {b}^{2} \\ {b}^{2} = {17}^{2} - {12}^{2} \\ {b}^{2} = 289 - 144 \\ {b}^{2} = 145 \\ b = 12 \: cm[/tex]

Which set of ordered pairs represents a function?

1-{(−5,−4),(3,4),(7,−6),(7,1)}

2-{(8,−2),(6,8),(6,3),(−4,−2)}

3-{(7,5),(7,−9),(−2,−3),(4,−1)}

4-{(−8,−7),(0,−7),(−4,0),(4,−5)}

Answers

Answer:

The 4th set only has unique x values as it is not repeated making it a function frm the others

Anybody got an answer for this

Answers

Answer:

11

Step-by-step explanation:

brainliest me pls

The diagram below represents a street intersection. The dashed lines are new streets that are being proposed. If the turn represented by

Answers

Answer:

Step-by-step explanation:

Solve using system of elimination. -x-10y=5 -x-10y=9​

Answers

Answer:

No Solution.

Step-by-step explanation:

-x-10y=5

-x-10y=9

--------------

-x-10y=5

-(-x-10y)=-9

------------------

-x-10y=5

x+10y=-9

----------------

0=-4

no solution

r a t e me 1 0 and thank u

Answers

Answer:

10

Step-by-step explanation:

10/10 For sure. I see that musical ly logo. Good times

10-9=1
using your fingers, you can take all your fingers away. you have 10 fingers and take all of them away but leave one. thats equivalent to 10-9.

y = 3x + 13
y = -2x - 22

substitution method show work

pls someone help quick

Answers

Answer:

x = -7

Step-by-step explanation:

3x + 13 = -2x - 22

subtract 13 from both sides

3x = -2x - 35

Add 2x to both sides

5x = -35

Divide each side by 5

x = -7

Math Subject: Symmetry.

Question is attached below.

Answers

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.

What is Symmetry?

A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.

Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.

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Answer:

1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.

2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.

3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.

4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.

5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.

6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.

7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.

8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.

Please provide step by step and answer what x and y is.

Answers

Answer:

Step-by-step explanation:

x=11

y=14

Pls answer! this problem

Answers

Answer:

9k + 36 represent the perimeter of the triangle. (I think)

Step-by-step explanation:

3k + 5 + 15 + 4k + 2k + 16 = the perimeter of the triangle

reorganize:

(3k + 4k + 2k) + (5 + 15 + 16)

9k + 36

Have a nice day!

WASTE Suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y=1000(2)0.3x.


a. Identify key features.

y-intercept: , 1 of 8.
domain: , 2 of 8.
range: , 3 of 8.

b. Identify the relevant domain and range.

Because time , 4 of 8. , the relevant domain is , 5 of 8. .

Because the amount of recycled paper and cardboard , 6 of 8. , and the amount when x=0
is , 7 of 8.tons, the relevant range is , 8 of 8. .

Answers

a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:

y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.

b. The relevant domain and range are given as follows:

Domain: x ≥ 0.Range: y ≥ 1000.

What are the features of the exponential function?

The exponential function for this problem is modeled as follows:

y = 1000(2)^(0.3x).

The features are given as follows:

Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.

The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.

However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.

The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.

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what is the difference of 1 and a number?

Answers

the number i hope this helps you out some it helps me out because i need more points

You buy a gallon of milk that costs $3. 50. The milk is discounted for 10% off. You also have to pay tax of 6. 25% on the discounted price. What is the final cost?

Answers

As per the given percentage of tax and discount, the final cost of the milk is $3.8186

The term percentage in math is known as a relative value indicating hundredth parts of any quantity.

Here we have given that You buy a gallon of milk that costs $3. 50.

And here we also know that the milk is discounted for 10% off.

Here we have also have to pay tax of 6. 25% on the discounted price.

First we have to calculate the discounted prices, that can be obtained by the following calculation,

=> 3.50 - [3.50 x 10/100]

=> 3.50 - [3.50 x 0.1]

=> 3.50 - 0.35

=> 3.15.

Now, we have to calculated the tax for the price of the milk,

=> 3.50 + [3.50 x 6.25/100]

=> 3.50 + [3.50 x 0.0625]

=> 3.50 + 0.2186

=> 3.8186.

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