Mathematics High School

## Answers

**Answer 1**

By alternating internal angles, angles 1 and 2 are **equivalent**.

What does the triangle's angle sum property entail?

According to the triangle's "**angle sum property**," the inner angles of a triangle add up to 180 degrees.

1. Angles 1 and 2 complement one another. Angles 2 and 3 compliment one another.

These angles are **linear**, hence their sum is 180 degrees.

2.m angle

Angle 1 + m2 Equals 90° Angle m2 + m3 = 90°

Equals makes a straight angle

3. m angle1 plus m angle2 equals m angle2 plus m angle3

= 180 degrees when the total of the two sides

4. m angle2 equals m angle

= The **total **of the two sides is equal

5. m angle1 = m angle3

= The total of the two sides is equal

6.Angle1 and Angle3 are congruent.

**Alternate interior **angles are what they are.

Angle 1 and Angle 3 are therefore equivalent based on the triangle's **characteristics**.

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## Related Questions

Distribute 56 rupees among Jim and Tim in the ratio of 2:5 find how much each one get

### Answers

**Answer:**

Jim gets 16 Tim get 40

**Step-by-step explanation:**

Chris says that he can find the surface area faster by

thinking of the box as a triangular prism on top of a

rectangular prism. He finds the surface area of each one

and adds them together. Does his method make sense?

### Answers

**Chris's** **method** of finding the **surface** **area **of a box by thinking of it as a **combination** of a **triangular** **prism** and a **rectangular** prism is a **valid** and useful **approach**.

**What is Surface area?**

The **surface** **area** of a solid item is a **measurement** of the total **area** occupied by the object's **surface**.

**Yes**, Chris's method of finding the surface area of a box by thinking of it as a **combination** of a **triangular** prism and a **rectangular** **prism** makes **sense**.

A box can be thought of as a **combination** of a triangular prism and a rectangular prism because a box is made up of six faces, with three **rectangular** **faces** and three **triangular** faces. By finding the **surface** **area** of the triangular **prism** and the rectangular prism separately, and then adding them together, one can find the **total** **surface** **area** of the box.

This **method** can make finding the **surface area** of a box faster and easier because one can use **formulas** that are specifically designed for finding the **surface** **area** of triangular prisms and rectangular **prisms**. By breaking down the box into its constituent **parts**, one can simplify the calculation and avoid having to use a more **complex** **formula** for finding the **surface** **area** of a box.

In summary, Chris's method of finding the **surface** **area** of a box by thinking of it as a **combination** of a **triangular** prism and a **rectangular** **prism** is a **valid** and **useful approach**.

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Given two vertices and the centroid of a triangle , how many possible locations are there for the third vertex?

### Answers

**Answer:i don't realy now so 5 point 3**

How much of the circle is shaded write your answer as a fraction in simplest form one for 1/4 2/7

### Answers

Step-by-step explanation:

The circle as a whole is one.

So to find the shaded area find a common denominators for both first

1/4 = 7/28

2/7= 8/28

Add the two together

7/28 + 8/28 = 15/28

This is the area taken up the the white fractions areas

Now because the circle is one

28/28 - 15/28 = 13/28

So the area of the blue is

13/28

Hope this helped :)

A ladder leans against the wall of a building. The ladder measures

41 inches and forms an angle of 42° with the ground. How far from

the ground, in inches, is the top of the ladder? How far from the

wall, in inches, is the base of the ladder? Round to two decimal

places as needed.

### Answers

**We can use trigonometry to solve this problem. Let's call the height of the ladder "h" and the distance from the wall to the base of the ladder "d".**

**From the problem, we know that the ladder forms a 42° angle with the ground. This means that the sine of the angle is equal to the opposite side (h) over the hypotenuse (41 inches):**

**sin(42°) = h/41**

**We can solve for h by multiplying both sides by 41 and taking the sine of 42°:**

**h = 41 × sin(42°)**

**h ≈ 28.61 inches**

**So the top of the ladder is about 28.61 inches from the ground.**

**To find the distance from the wall to the base of the ladder, we can use the cosine of the angle:**

**cos(42°) = d/41**

**We can solve for d by multiplying both sides by 41 and taking the cosine of 42°:**

**d = 41 × cos(42°)**

**d ≈ 31.15 inches**

**So the base of the ladder is about 31.15 inches from the wall.**

Mark also has a 1:40 model Phantom II plane.The real Phantom II has a wingspan of 465”. What’s the wing span of the model in inches.

“=inches

### Answers

The **wing span** of the 1:40 model Phantom II is **18.31 inches.**

What is unit conversion?

A **unit conversion** is a conversion with different units of measurements of same quantity. It is a process with multiple steps that involves multiplication or division by particular factor.

Wingspan of real Phantom II =465''(in millimeter)

**1 inch = 2.54 cm⇒25.4 mm.**

465''=[tex]\frac{465}{25.4}[/tex]

= 18.31 inches.

Hence,** wingspan** of the model 1:40 model Phantom II in **inches is 18.31.**

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K

M 3 J

Mark this and return

What is the length of line segment KJ?

O 2√3 units

O 3√2 units

O 3√3 units

O 3√5 units

Save and Exit

Next

Submit

### Answers

The** length of line segment** KJ is D. **3√5 units**

What is a Line Segment?

A** line segment **in geometry is a** section of a straight lin**e that is enclosed by two clearly defined endpoints and contains all of the points on the line that lie inside those endpoints. The** Euclidean distance **between two ends of a line segment determines its length.

∠KMJ = 180° - 90° (**adjacent angles** on a straight line)

= 90°

Using **Pythagorean Theorem,**

KJ² = 6² + 3²

KJ² = 45

**KJ = √45**

= √9√5

=** 3√5**

The **answer is D. **The length of line segment KJ is **3√5 units.**

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if a bakery produces 1,215 cupcakes during a 9 hour shift, what is the production rate of cupcakes per hour?

can u explain it in ratio

### Answers

They make 135 cupcakes per hour.

solve the following systems of linear equations by graphing

y=2/3x+4 and y=/x-1

### Answers

**Answer:**

The solution to the system is (1.8, 7.6)

**Step-by-step explanation:**

To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.

Plot the lines:

y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.

y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.

Find the intersection point:

To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.

Substitute x from y = 2/3x + 4 into y = -x + 1:

-x + 1 = 2/3x + 4

Multiplying both sides by -3, we get:

3x - 3 = -2x - 12

Adding 2x to both sides, we get:

5x - 3 = -12

Adding 12 to both sides, we get:

5x = 9

Dividing both sides by 5, we get:

x = 1.8

Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:

y = 2/3x + 4

y = 2/3 * 1.8 + 4

y = 3.6 + 4

y = 7.6

So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.

A factory sends cases of cereal boxes to a grocery store. There are 144 cereal boxes in every 24 cases shipped. On the coordinate plane on your hard copy test, plot points on the graph to show how many cereal boxes there are for shipments of 4, 8, 10, 14 and 16 cases.

### Answers

The below **points **can be plotted on the **graph **to show the relationship between the number of cases of cereal boxes shipped and the number of **cereal boxes **in those cases.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents **data **or **values**.

A graph can be plotted with the number of cases of cereal boxes on the x-axis and the number of cereal boxes in those cases on the y-axis.

Here is an example of how the **points **for 4, 8, 10, 14 and 16 cases can be plotted:

For 4 cases: (4, 4 x 144 = 576)

For 8 cases: (8, 8 x 144 = 1152)

For 10 cases: (10, 10 x 144 = 1440)

For 14 cases: (14, 14 x 144 = 2016)

For 16 cases: (16, 16 x 144 = 2304)

These points can be plotted on the graph to show the relationship between the number of cases of **cereal boxes **shipped and the number of cereal boxes in those cases.

The graph will be a **straight line**, showing that the number of cereal boxes is directly **proportional **to the number of cases shipped.

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In the diagram shown, BC, EF, DK, and AK intersect at point K. Determine the values

of x and y

### Answers

**Answer:**

x=65

y=25

**Step by step explanation:**

**90+90+25+x+x+y= 360**

**2x+y=155 (1)**

**90+25+x= 180**

**x= 65 (2)**

**sub (2) into (1):**

**2(65)+y=155**

**y= 25**

A group of researchers is studying the relationship between cortisol (stress hormone) levels and memory, and they want to see if a sample of 25 adults that has been recruited is a good representation of the population it came from, before they conduct additional research. The population has been found to have an average cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have an average cortisol level of 15 mcg/DL, with a standard deviation of 3 mcg/dL. For this assignment, construct a confidence interval to determine if this sample mean is significantly different from the population mean. Explain how you know, based on the confidence interval, and specific the confidence level you used. Be sure to show your work and calculations. This can be tricky with Word, so if necessary you may take a photo of your hand calculations and add it to the Word document

### Answers

The **sample mean** is significantly different from the population mean. The confidence level used was 95%.

To build a** confidence interval** to decide whether this example mean is fundamentally not the same as the populace mean, there are a few stages that should be taken.

To begin with, work out the standard error of the mean (SEM) for the example, which is the standard deviation separated by the square base of the example size (SEM = σ/√n). For this situation, the SEM is 3/5 = 0.6 mcg/dL.

Then, compute the** critical value** for the confidence interval picked by increasing the SEM by the t-esteem from the t-dissemination for the given confidence interval. For instance, in the event that a 95% confidence interval is picked, the t-esteem is 1.96. This provides us with a basic worth of 0.6 x 1.96 = 1.176 mcg/dL.

At last, build the certainty span utilizing the example mean and the basic worth. The certainty span is (15 - 1.176, 15 + 1.176), or (13.824, 16.176). This implies that we are 95% sure that the genuine populace **mean **exists in this reach.

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9/4-7/3 pls answer fast

### Answers

**Answer: -1/12**

**Step-by-step explanation:**

**Answer:**

-1/12

**Step-by-step explanation:**

9/4 - 7/3

To start, we need to make the denominators the same number. In order to do that, we need to identify the factor they have in common.

4, 8, 12

3, 6, 9, 12

Twelve is the common factor, so we will use this. Remember, whatever you do to the bottom, you must do to the top, and vice versa.

4 * **3** = 12

/12

3 * 9 (numerator) = 27

27/12

Now, we must figure out 7/3.

3 * **4** = 12

4 * -7 = -28

-28/12

Now, take the new fractions and subtract them.

27/12 - 28/12

-1/12

45 medals were given out at a band competition. There were 22 bronze medals and 14 silver medals. The rest were gold medals. What percentage of medals were gold medals?

### Answers

**Answer:**

20%

**Step-by-step explanation:**

45

22 bronze

14 silver

so 45- 22 -14 =9 gold

9/45 = 1/5 =20%

Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!

### Answers

**Answer:**

EG/HJ=GF/JI or EG/HJ=FE/IH

**Step-by-step explanation:**

Given

AngleF=AngleI

AngleE=AngleH

Therefore triangles EGF AND HJI are similar by Angle-Angle Similarity Theorem

So

EG/HJ=GF/JI=FE/IH as they are the corresponding sides of a similar triangle

A rocket is launched in the air. Its height in feet is given by h(t)= -16t^2+88t where t represents the time in seconds after launch. How long is the rocket in the air?

Answer: ___ seconds

### Answers

A rocket is launched with **height **function h(t)= -16t²+88t for** time **'t' in seconds the rocket** **is in the air for the time **t = 5.5 seconds.**

A** rocket **launched with** **height** **function** :**

h(t)= -16t²+88t

't' represents the time in seconds

'h' is the height of rocket.

**Time **for which rocket is in the air given by :

When h(t) = 0

Substitute the value we get,

⇒ -16t²+88t = 0

⇒ -16t ( t - 5.5 ) = 0

⇒ -16 ≠ 0 or t ≠ 0 or ( t - 5.5 ) = 0

Time can never be zero.

hence,

( t - 5.5 ) = 0

⇒ t = 5.5 seconds

Therefore, the **time** of the rocket when it is in the air is equal to 5.5 seconds.

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Right triangle TMR is a scalene triangle with the right triangle at M. Which equation is true? Please show work.

### Answers

For a **right triangle** TMR the** equation** that is true is -

Option 3:** **sin T = cos R

**What is a right-angled triangle?**

Any two sides of a **triangle's** three sides must always add up to more than the third side since a **triangle** is a regular **polygon** with three sides. This distinguishing characteristic of a triangle. A **right-angle** triangle is one that has **angles** between its two sides that equal 90 degrees.

In a **right triangle**, the sine of an **acute angle** is defined as the length of the** opposite side** divided by the length of the **hypotenuse**, and the cosine of an acute angle is defined as the length of the **adjacent side **divided by the length of the** hypotenuse**.

In triangle TMR, the right angle is at M, which means that T and R are acute angles.

Using the definitions of **sine **and cosine, determine which **equation** is true -

1. sin M = cos T

The angle M is the right angle, which means that its sine is 1 and its cosine is 0.

Therefore, this **equation** is false.

sin R = cos R

2. The sine and cosine of the same angle cannot be equal, except in the case of a 45° angle where both **sine** and **cosine** are equal to 1/√2.

Therefore, this **equation** is false.

3. sin T = cos R

The angle T is the acute angle **opposite** the side TR, and the angle R is the **acute angle** adjacent to the side TR.

Therefore, this **equation** is true.

4. sin T = cos M

The angle M is the right angle, which means that its cosine is 0.

Therefore, this **equation** is false.

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Work out the volume of the cuboid below.

Remember to give the correct units.

13 m

5m

13 m

3 m

### Answers

**Answer:**

195m^3

**Step-by-step explanation:**

Volume of a rectangle = Length x Width x Height

L = 5m

W = 3m

H = 13m

V = 5m x 3m x 13m

V = 195m^3

At a small high school, 5 students took Mrs. Jones's AP Statistics class last year. The student's names are Ashley, Brayden, Carmen, Dale, and Eve. Ashley, Brayden, and Carmen each got a 5 on the AP Statistics exam. Mrs. Jones would like to use the results of these 5 students to demonstrate how to create a sampling distribution of the sample proportion for simple random samples of size n = 2 for her current students. a) What is the value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam? Explain. b) Using the table provided, list all 10 possible simple random samples of size n = 2, and for each sample calculate the sample proportion of students who got a 5 on the AP Statistics exam. The first one is completed for you. SRS n = 2 А, В P 1 c) Using the number line provided, create a dotplot to display the sampling distribution of p. d) is the sample proportion an unbiased estimator of the population proportion? Explain.

### Answers

**Answer:**

**Step-by-step explanation:**

a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.

b) The 10 possible simple random samples of size n = 2 are:

Ashley, Brayden; P = 2/2 = 1

Ashley, Carmen; P = 2/2 = 1

Ashley, Dale; P = 1/2 = 0.5

Ashley, Eve; P = 1/2 = 0.5

Brayden, Carmen; P = 2/2 = 1

Brayden, Dale; P = 1/2 = 0.5

Brayden, Eve; P = 1/2 = 0.5

Carmen, Dale; P = 1/2 = 0.5

Carmen, Eve; P = 1/2 = 0.5

Dale, Eve; P = 0/2 = 0

c) To create the dotplot for the sampling distribution of p:

Label the number line with 0, 0.5, 1

For each sample proportion calculated, place a dot above the corresponding value on the number line

Repeat this process for all sample proportions

d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.

Write an expression for the sequence of operations described below.

raise 4 to the 2nd power, then find the quotient of the result and q

Do not simplify any part of the expression.

### Answers

Both **BODMAS **and PEMDAS are valid and in use in various parts of the globe. In the UK, BODMAS is frequently utilized, whereas in the US, PEMDAS is. Brackets, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS.

Which mathematical procedure comes first?

The acronym **PEMDAS**, which stands for parenthesis, **exponents**, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations. Start by using parenthesis first.

For the list of operations, we wish to create an expression.

9 to the second power raised then, determine the ratio between the outcome and z

First, raise 9 to the second power.

9 divided by two equals

Find the product of the result and z in step two.

Today, quotient refers to "division."

The outcome of step 1 is =[tex]9^2[/tex]

Therefore:

Indicator of and z

As a result, the statement that describes the specified order of operations is [tex]\frac{9^2}{z}[/tex]

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find the slope of line represented by the data below

### Answers

**Answer:**

-4

**Why? **I subtract the numbers. How to do that is by looking at the table. You always use two ordered pairs. Let's choose (-3,12) and (-2,8).

**Step 1:** Choose two ordered pairs (you can choose any two, it doesn't matter).

Now, subtract the y's together and subtract that x's together. So, what is 12-8? That's obvious, it's 4. Alright, how about -3-(-2)? Well, two negatives make a positive, so the problem is actually -3+2. So, what's that? Correct, -1. And, since slope is y/x, the answer would be -4/1, or -4.

If one bestfriend went to the store with $5 and the other bestfriend went with $20 how many they had in total?

### Answers

The amount of** money** they had in total is $25

How to calculate the amount of money that the best friends had in total?

One bestfriend went to the store with $5

The other best friend went to the store with $20

The amount of** money** they had in total can be calculated as follows

= 20 + 5

= 25

Hence the amount of **money** the best friends had in total is $25

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Answer: 25$

Step-by-step explanation: 20 plus 5 equals 25.

Divide a restaurant bill of $204 evenly among six people

### Answers

You can solve this by diving the total by 6

$204 / 6 = $34

Therefore each person should pay $34

**Answer: $34**

**Step-by-step explanation:**

204 divided by 6 = 34

A local bike race is broken into 12 parts. Each stage is 14 1/2 miles. What is the total distance of the bike race?

### Answers

**Answer: 174 miles**

**Step-by-step explanation: 14.5 (14 1/2) times 12 is 174**

Solve the equation and check your solution: x + 4 = -2 +

### Answers

**Answer:**

x = -6

**Step-by-step explanation:**

Solving an equation:

x + 4 = -2

**Subtract** 4 from both sides,

x + 4 - 4 = -2 - 4

x = -6

[tex]\boxed{\bf x = -6}[/tex]

Check: Substitute x = -6 in the LHS of the equation,

LHS = x +4

= -6 + 4

= -2 = RHS

a room has a floor dimension of 6 meters by 8 meters the height of the basem*nt is 8 meters what is the total area of all four walls

### Answers

**Answer:**

**224 m^2**

**Step-by-step explanation:**

The dimensions of the four walls are:

6x8, 8x8, 6x8, 8x8

The area of all of these walls is 2(6x8 + 8x8) = 224 m^2

The lengths of the sides of a triangle are in the extended ratio 7 : 9 : 10. The perimeter of the triangle is 104cm. What is the length of the sides ?

### Answers

**Answer:**

28, 36, 40

**Step-by-step explanation:**

Add up the numbers in the ratio, giving us 26. Perimeter divided by 26 equals 4. Then, four times each of the numbers in the ratio gives you the lengths

**I WILL GIVE 50 POINTS AND BRAINLIEST**

A cone has a volume of 192π cubic inches. Its height is 9 inches, what it's radius? Show all your work.

### Answers

**Answer:**

4.5 inches

**Step-by-step explanation:**

Si la hipotenusa de un triángulo rectángulo mide 2 cm y uno de sus lados mide 1 cm ¿ cuánto mide el otro lado ?

### Answers

**Answer:**

**Step-by-step explanation:**

**a^2+b^2=c^2**

**c^2-b^2=a^2**

**2^2-1^2=c^2**

**c^2=3**

**c=**[tex]\sqrt{3}[/tex]

espero que esto te ayude, pero no se si esta correcto lo siento

Kim used sticks to make a pattern of squares. Number of squares: 1, 3, 6, 10, 15. Number of sticks: 4, 10, 18, 28, 40. When a shape consists of 28 squares, how many sticks will the shape have?

### Answers

**Answer:**

70

**Step-by-step explanation:**

Find the number pattern (check image)

The shape consisting of 28 **squares **will have 812 sticks.

Determining the number of sticks the shape will have

From the given data, we can see that the number of squares is increasing by **consecutive** odd numbers, starting from 1:

1, 3, 6, 10, 15, ...

Also, the number of **sticks** is increasing by consecutive even numbers, starting from 4:

4, 10, 18, 28, 40, ...

This suggests that the number of sticks required to make a **pattern **of n squares can be found using the formula:

sticks = 2n + (n-2) + (n-4) + ... + 4

This formula represents the sum of the first n even numbers, which can be simplified to:

sticks = n(n+1)

Using this formula, find the number of sticks required to make a pattern of 28 squares:

sticks = 28(28+1) = 28(29) = 812

Therefore, a **shape **consisting of 28 squares will have 812 sticks.

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