Mathematics High School

## Answers

**Answer 1**

The **triangles **Δ BCD and Δ BFD are **congruent **by SSS rule.

What are congruent triangles?

Two **triangles **are said to be **congruent **when their corresponding side and angles are **congruent**.

Since, the figure is not given we will consider the figure attached in the solution.

We have a quadrilateral BCDF, having a **diagonal **BD, we need to prove Δ BCD and Δ BFD are **congruent**,

We are given,

BC ≅ BF

CD ≅ FD

BD ≅ BD

Therefore,

Δ BCD ≅ Δ BFD by SSS rule

Hence, the **triangles **Δ BCD and Δ BFD are **congruent **by SSS rule.

Learn more about **congruent triangles**, click;

https://brainly.com/question/22062407

#SPJ1

## Related Questions

a survey of 130 college graduates was conducted. students were asked whether they were employed and if they were looking for a job. the following table shows the results. job searching no job searching total employed 28 61 89 not employed 18 23 41 total 46 84 130 according to the table, what is the probability that a randomly chosen student is not employed given that they are job searching? give your answer as a fraction in simplest form.

### Answers

The** probability** that a randomly chosen student is not employed given that they are job searching is 9/23.

What is the probability that a randomly chosen person is not employed despite job searching

The **probability **of a student not being employed given that they are job searching is given by the conditional probability:

P(not employed | job searching) = P(not employed and job searching) / P(job searching)

We can find the probabilities for the numerator and denominator from the table:

P(not employed and job searching) = 18

P(job searching) = 46

Therefore, the** conditional probability **is:

P(not employed | job searching) = 18 / 46

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

P(not employed | job searching) = 9 / 23

Learn more **probability **here;

https://brainly.com/question/23286309

#SPJ1

n a sample with a mean of 98, a raw score of 83 corresponds to a z score of -1.5. what is the sample standard deviation? you must show your work or explain your reasoning to get full credit for this question.

### Answers

The sample **standard deviation **is 10.

What is Statistics?

Statistics is the discipline that concerns the collection, **organization**, analysis, interpretation, and presentation of data.

We know that the **raw score** of 83 corresponds to a z-score of -1.5. We also know that the formula for calculating a **z-score** is:

z = (X - μ) / σ

where X is the raw score, μ is the **population** **mean**, and σ is the population standard deviation.

**Substituting** the given values into the formula, we get:

-1.5 = (83 - 98) / σ

Simplifying, we get:

-1.5σ = -15

**Dividing** both sides by -1.5, we get:

σ = 10

Therefore, the sample **standard deviation **is 10.

To learn more on **Statistics** click:

https://brainly.com/question/29093686

#SPJ1

multiply and simplify (7ab+3c)(7ab-3c)

### Answers

**Answer:**

49a²b² - 9c²

**Step-by-step explanation:**

(7ab+3c)(7ab-3c)

= 49a²b² - 21abc + 21abc - 9c²

= 49a²b² - 9c²

So, the answer is 49a²b² - 9c²

**Answer:** 49a²b² - 9c²

**Step-by-step explanation:**

We will apply the **difference of two squares formula**:

(7ab+3c)(7ab-3c)

(7ab)² - (3c)²

49a²b² - 9c²

A rocket blasts off at a 90° angle from Earth. A second rocket launches at a different angle as shown in the diagram. A diagram of two rocket launches is shown. The horizontal line is labeled Earth. Rocket one goes up at at a ninety degree angle from Earth. Rocket two goes up at an angle to the right of Rocket One's path. The angle between Earth and the path of Rocket two is labeled five x plus three degrees. The angle between the paths of Rocket one and Rocket two is labeled three x plus seven degrees. Question 1 Part A Write an equation that can be used to determine the value of x.Part B What is the value of x? Enter the correct answer in the box.Part C What is the measure of the angle of the second rocket launch in relation to Earth?

### Answers

Answer:

i don't

Step-by-step explanation:just needed more points lol

Part A: The **equation **that can be used to determine the value of x is

(3x +7°)+(5x +3°)= 90°

Part B: The value of x = 10°

Part C: The measure of the angle of the second rocket launch in relation to Earth is 53°

Define an Angle.

When two lines meet at a certain point, then they produce an angle. The "opening," also referred to as the distance between these two rays, is quantified as a "angle." It is represented by this ∠ character. For describing the circularity or rotation of an angle, **degrees **and **radians **are typically utilized. A right angle is one with a length of 90°. There is a right angle that is obvious because it looks like the letter L.

Let the first rocket be R1.

Let the second rocket be R2.

They blast from a point on Earth, let that point be E.

Let O be a point of observation on the Earth.

Given, the first rocket blasts off at an angle of 90° from earth.

So, the angle created by R1 with the ground with respect to O,

∠R1EO = 90°

∠R1ER2 is given as 3x + 7°

∠R2EO is given as 5x + 3°

So, the equation that is derived here as per the right-angle rule is

(3x +7°)+(5x +3°)= 90°

Now solving the equation, we can get the value of x.

3x+7°+5x+3°=90°

⇒8x+ 10°= 90°

Subtracting both sides by 10°

⇒8x = 80°

Now dividing 8 from both sides, we get

⇒x = 10°

Now to find the angle of the second rocket launch in relation to Earth

i.e., ∠R2EO we can put the value of x.

∠R2EO=5x + 3°

=5×10° + 3°

=53°

Therefore, the value of the angle of the second rocket launch in relation to Earth is 53°.

To know more about **angles**, visit:

**https://brainly.com/question/29285631**

#SPJ1

can someone pls help me?? Im offering 50 points JUST PLS I NEED HELP!!!!!

If f(x) is an exponential function where (−2.5)=7 f(−2.5)=7 and f(3)=60, then find the value of f(5), to the nearest hundredth.

### Answers

If f(x) is an **exponential function** where (−2.5)=7 f(−2.5)=7 and f(3)=60, the value of f(5) = 135.13

What is an exponential function?

The mathematical expression f(x)=exp or eˣ is used to represent the exponential function. Unless otherwise stated, the word normally refers to the **positive-valued function** of a** real variable,** but it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

For instance, exponential functions can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, or the spread of disease.

Let, the exponential function is written as:

f(x) = abˣ

We are given the values of the function at x=-2.5 and x=3 as:

f(−2.5)=7

f(3)=60

therefore we can write:

ab^(-2.5) = 7 ................. (1)

ab³ = 60 ............ (2)

Now dividing equation (2) by (1) we get:

ab³ / ab^(-2.5) = 60 / 7

or, b^(3 + 2.5) = 60 / 7

or, b^(5.5) = 60/7

or, b = e^((1/5.5) ln(60/7))

or, b = 1.478

Now a is given as:

a (1.478)^(-2.5) = 7

a = 18.587

Now the function is written as:

f(x) = 18.587 (1.487)ˣ

Substituting x=5 to get f(5):

f(5) = 18.587 (1.487)⁵

or, f(5) = 135.13

Thus, the value of f(5) = 135.13

To know more about **exponential function **refer to:

**https://brainly.com/question/2456547**

#SPJ1

The difference between a number and three is multiplied by negative six. The result is eighteen. What is the number?

a. Write an equation that can be used to find the number, n.

b. Solve the equation you wrote in part A to find the value of the number. Include all of your work in your answer.

Need help ASAP!

### Answers

**Answer:**

n=0

**Step-by-step explanation:**

let the number be (n)

(a)

(n-3)×(-6)=18

(b)

to *solve **for **n **open **the **bracket**;**(**n-3)**×**-**6**=**1**8**-6n+**1**8**=**1**8**collect **like **terms**-6n=**1**8**-**1**8**-6n=**0**divide **both **sides **by **-**6**-6n/**-**6**=**0**/**-**6**n=**0*

find the number of terms and the expression for the nth term of the following Aps 1, 8, 15,....,78

### Answers

**Answer:**

see explanation

**Step-by-step explanation:**

the nth term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 , d = a₂ - a₁ = 8 - 1 = 7 and [tex]a_{n}[/tex] = 78 , then

1 + 7(n - 1) = 78 ( subtract 1 from both sides )

7(n - 1) = 77 ( divide both sides by 7 )

n - 1 = 11 ( add 1 to both sides )

n = 12

that is there are 12 terms in the progression.

from above

[tex]a_{n}[/tex] = 1 + 7(n - 1) = 1 + 7n - 7 = 7n - 6

then nth term is

[tex]a_{n}[/tex] = 7n - 6

Need help ASAP please

### Answers

Note that this prompt is designed to test ones knowledge on **cosigners **and **loans**. See the correct responses below.

What are the correct responses to the questions?

The correct definition of a **cosigner **for a loan is "Someone who will promise to pay a loan if the borrower doesn’t." (Option C)Sarah's late payments affect her character and make her unable to cosign for Chris. (Option D)The correct definition of capacity for **potential cosigners **is "The cosigner’s current financial situation." (Option D)Lenders evaluate if a borrower or cosigner will pay them back based on **capacity**, collateral, and character. (Option A)The correct definition of character for potential cosigners is "The cosigner’s past record of paying on time." (Option A)A borrower may get a cosigner for a loan if they can’t qualify for a loan by themselves. (Option A)The correct definition of **collateral **for potential cosigners is "The cosigner’s financial assets, such as a house or car." (Option A)A person with a steady job would be a good cosigner. A person with a good credit history and a car and house (option B).

Learn more about **Cosigners**:

https://brainly.com/question/30307922

#SPJ1

Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 3%. After 12 years, the interest earned on the account was $2,520. How much money did Mike's grandmother deposit in the account?

### Answers

Using** simple interest **formula, the grandmother deposited $7000 into the account.

What is the amount the grandmother deposit in the account

We can use the formula for **simple interest **to solve the problem:

I = P * r * t

where I is the interest earned, P is the **principal** (the amount deposited), r is the interest rate (as a decimal), and t is the time (in years).

In this case, we know that r = 0.03 (3% expressed as a decimal) and t = 12 years. We also know that I = $2,520. Therefore, we can solve for P:

P = I / (r * t) = $2,520 / (0.03 * 12) = $7,000

Therefore, Mike's grandmother deposited $7,000 in the account.

Learn more on** simple interest** here;

https://brainly.com/question/3575751

#SPJ1

3x-2=-12 is equivalent to

### Answers

**Answer:**

x = -10/3 is the solution.

What is the area of the parallelogram?

four hundred forty-four and three-eighths ft2

four hundred twenty-one and seven-eighths ft2

four hundred twelve and one-half ft2

four hundred five and one-half ft2

### Answers

The **area **of the **parallelogram **is given as follows:

421 and 7/8 ft².

How to obtain the area of a parallelogram?

The area of a parallelogram is given by the **multiplication **of the base of the parallelogram by the height of the parallelogram, that is:

A = bh.

The **parameters **for this problem are given as follows:

b = 22 and 1/2 ft = 45/2 ft.h = 18 and 3/4 ft = 75/4 ft.

Hence the **area **is given as follows:

A = 45/2 x 75/4

A = 3375/8 ft².

A = 421 and 7/8 ft².

(3375 divided by 8 has a quotient of 7 and a remainder of 8, which is the reason for the mixed number notation).

Hence the **second option** is the correct option.

Missing Information

The parallelogram is given by the image presented at the end of the answer.

More can be learned about the **area of a parallelogram** at https://brainly.com/question/10744696

#SPJ1

A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent.

Probability and Fuel Cost by Region

Region

Probability in Region

Fuel Cost per Gallon

Southeast

20%

$3.10

Southwest

30%

$3.50

California

50%

$4.05

$3.53

$3.55

$3.68

$3.70

### Answers

The amount that the company should put on average for a **gallon across **the **operations** is $ **3.70**. This** option D is correct**.

What does the trucking operations of the company?

The **company** of trucks runs** operations** in several countries as per the table each region has distinct scores of probability and as the company that is farthest from the market has more wages as compared to that is the nearest

The percentage is** 100** and probability counts as compared to **one**. Thus 50% is 0.50. If assuming X is the** cost of fuel** then using the formula we get.

[tex]Mean=E(X)=f(xi)xi[/tex]

E(X) = 3.10 x 0.2 +3.5 x 0.3 +4.05 x 0.5 = 3.69 that is** 3.70 dollars**.

Find out more information about the **company operates**.

https://brainly.com/question/26676604.

The company should budget on average $3.53 for a gallon of fuel across its operations.

To calculate this, we can use the **weighted **average formula:

(0.2 x $3.10) + (0.3 x $3.50) + (0.5 x $4.05) = $0.62 + $1.05 + $2.03 = $3.70

Therefore, the average fuel cost is $3.70 per gallon. Rounded to the nearest cent, this is $3.53.

**What is Gallon ? **

A **gallon** is a unit of size used to degree quantity, especially inside the context of fluids. It's miles normally used in the U.S.A. And a few other international locations, but isn't used within the metric system. One gallon is equal to 128 fluid oz. Or three.785 liters. It's far used to degree portions of liquids, including gasoline, milk, and water. In the context of fuel fees, the fee according to gallon is used to calculate the overall price of filling up a car's fuel tank. The gallon is an important unit of measurement in many industries, together with **transportation** and agriculture.

To know more about **Gallon** visit:

https://brainly.com/question/19638640

#SPJ1

a gym teacher defines an experiment to be running a mile race three times in gym class. sue runs the mile three times. sue's fastest time was 6:10. this time can best be described as .

### Answers

The time of 6:10 can best be described as Sue's **best **or **fastest **time in the mile race.

In the experiment defined by the gym teacher, Sue was required to run the mile race three times. This implies that she ran the same **distance **under the same conditions (in the gym class) three times. By doing so, Sue was able to record her times for each of the three runs.

Of the three times, Sue's fastest time was 6:10. This means that out of all the times she recorded, 6:10 was the shortest and thus the best time that she achieved in the **mile race**.

It is important to note that the context of the experiment defined by the gym teacher is limited to the gym class and the three **runs **that Sue made during that class.

It is possible that Sue may have run **faster **times outside of the gym class, or in a different running context. However, within the context of the gym class experiment, 6:10 represents her best or fastest time in the mile race.

To learn more about **time **click on,

https://brainly.com/question/13458499

#SPJ4

Alexa's family is driving to Los Angeles. They drove 1/6 on the first day, the second day they drove 1/5. how much of the trip have they done

### Answers

**Answer: ***11/30 *

**Step-by-step explanation:**

*If Alexa's family drove 1/6 of the trip on the first day, and 1/5 of the trip on the second day, the total distance they have driven can be found by adding these fractions:*

*1/6 + 1/5*

*To add these fractions, we need to find a common denominator:*

*1/6 + 1/5 = 5/30 + 6/30 = 11/30*

*So the family has completed 11/30 of the trip.*

Mon

Lesson Word Problems with me and Manay (6)

word Problems with me and Money

Carlotte shorts cleaning her ream at 10:49 am the finishes cleaning at 11:28 a.m.

How much time did Carletto spend eleaning her room?

### Answers

**Answer: 1 hour and thirty-nine minutes**

**Step-by-step explanation: 10:49 + 1 hour and thirty-nine minutes = 11:28**

Sam wants to make 2 muffins. His mum says this would be difficult. Explain why.

### Answers

**Answer:**

1. Overmixing the batter.

2. Not lining or greasing the pan.

3. Overfilling the muffin cups.

4. Overbaking or underbaking the muffins.

there are many ways to mess up making muffins,

Hope this helps!

If not tell me and I'll fix it!

Thank you!

**Answer:**

overmixing the batter.

2. Not lining or greasing the pan.

3. Overfilling the muffin cups.

4. Overbaking or underbaking the muffins.

5. don't drown it when it comes to put any liquid

question in picture!!

Please help!!

### Answers

**Answer: 1.5; 2/3**

**Step-by-step explanation: Find the ratios to answer both questions. For the first one it is the ratio between soy sauce and vinegar so you would find the ratio of when there is one unit of soy. When you divide both sides to even out, you will get 1.5 milliliters for the answer. Do the same thing for the next one and you get 2/3 or 0.66666.....**

A Ferris wheel has a radius of 48 feet. What is the distance a passenger will travel one time around the Ferris wheel?

### Answers

[tex]\stackrel{ ~\hfill Ferris~Wheel }{\textit{circumference of a circle}}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=48 \end{cases}\implies C=2\pi (48)\implies C=96\pi \implies C\approx 301.59[/tex]

Which relationship represents a function with a lesser rate of change than the function graphed?

### Answers

The which relationship represents a **function** with a lesser rate of change than the function graphed is y=3x+2, the correct option is D.

How to find the function which is used to make graph?

There are many tools we can use to find the information of the relation which was used to form the **graph**.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the **function** must be having increasingly output for inputs greater than that value of x.

If we know that the **function** crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that;

The graph of straight line

Now,

The slope-intercept form of a linear function is y = mx + b, where m is the slope and b is the y-intercept. We can rearrange the equation 4x+y=5 into slope-intercept form by solving for y:

y = -4x + 5

So, the slope of this function is -4.

In general, any **linear** function of the form y = mx + b, where m is a number between -4 and 0, will have a smaller rate of change than 4x+y=5.

y=3x+2

Therefore, by the graphed **function** the answer will be y=3x+2.

Learn more about finding the graphed **function** here:

https://brainly.com/question/27330212

#SPJ1

Determine the general solution of cos²x - Sin²x =√3/5

### Answers

The **general solution** to the equation cos²x - Sin²x = √3/5 is x = 2nπ ± arcsin(√3/5) where n is any **integer**.

To solve the equation, first use the **double-angle formula** for **cosine**, cos²x = 1 - sin²x, to rewrite it as 1 - sin²x - sin²x = √3/5. Then subtract 1 from both sides and isolate the sine term to get -2sin²x = -1 + √3/5.

Next, take the square root of both sides, giving -2sinx = ±√(1 - √3/5). Then divide both sides by -2, resulting in sinx = ±√3/5.

Finally, use the inverse sine function to find x = 2nπ ± arcsin(√3/5). Here, n is any **integer**.

Learn more about **Cosine**:

https://brainly.com/question/26993851

#SPJ11

Unit 8: Right Triangles & Trigonometry Homework 3: Similar Right Triangles and Geometric Mean

### Answers

The jpg shows the formulas I used to solve the problems. I hope this helps!

3. Draw a line with the given slope through the given point. What other point lies on that line?

### Answers

**Answer:**

**Step-by-step explanation:**

a

What is the inverse of the function h(x)=3/4x+12?

h^-1(x)=

### Answers

The inverse of the **function** h(x)=3/4x+12 is h^-1(x)=(4x-48)/3.

The **inverse** of a **function** is found by switching the x and y variables and solving for y. In this case, the inverse of the function h(x)=3/4x+12 can be found by following these steps:

1. Switch the x and y variables:

x = 3/4y + 12

2. Isolate the y variable on one side of the **equation**:

x - 12 = 3/4y

3. Multiply both sides of the equation by 4/3 to get y alone:

(4/3)(x - 12) = y

4. Simplify the equation:

(4x - 48)/3 = y

5. Rewrite the equation with y on the left side:

y = (4x - 48)/3

Therefore, the inverse of the function h(x)=3/4x+12 is h^-1(x)=(4x-48)/3.

Learn more about **Function**:

https://brainly.com/question/3831584

#SPJ11

What is the coordinates of the third vertex to the nearest tenth.

### Answers

**Answer:**

(9,88)

**Step-by-step explanation:**

h(x) = -2x + 3 find h(0)

### Answers

**Answer:3**

**Step-by-step explanation:**

-2*0+3=3

Write as a fraction 72/90 in its simplest form

### Answers

**Answer:**

4/5

**Step-by-step explanation:**

72/90

Simplify by 9, and we get

8/10

Continue simplify by 2, we get

4/5

So, the answer is 4/5

If five people work with me for 12 hours from mon to thurs how many hours did we work for

### Answers

**Answer: 240 hours**

**Step-by-step explanation: Monday through Thursday is 4 days, 5 people work 12 hours per day = 60 hours a day, 4 days x 60 hours = 240 hours worked in total.**

The line from “The Shell” that has the "ta da ta ta da" rhythm pattern is line (blank)

options: 1 2 3

The Shell

A secret whorl

of pink and cream.

The sound of the sea--

a child's dream.

(There's the poem) Help immediately make the answers quick hurry

### Answers

**Answer:**

**Step-by-step explanation:**

3

sam is able to choose from two job positions at one company. he has the option to choose the day shift or the night shift, so it is impossible for sam to work the day and night shift. if the probability that sam chooses the day shift is 0.9, and the probability that sam chooses the night shift is 0.03, what is the probability that sam chooses the day or night shift?

### Answers

The **probability** that Sam chooses either the day or the nightshiftis0.93.

What's probability?

Probability is a fine conception that **measures** the liability or chance of an event being. It's expressed as a number between 0 and 1, with 0 indicating that an event is insolvable, and 1 indicating that an event is certain.

Given to the question.

Since Sam can only choose moreover the day shift or the night shift, and the events" choosing the day shift" and" choosing the night shift" are mutually exclusive (i.e., they cannot do at the same time), we can use the addition rule of **probability** to find the probability that Sam chooses either the day or the night shift.

The addition rule states that the probability of the union of two events A and B, denoted as P (A or B), is given by.

P (A or B) = P(A) P(B)- P (A and B)

where P (A and B) is the probability of the crossroad of events A and B.

Since Sam cannot choose both the day and night shift, P (A and B) = 0. thus, the probability that Sam chooses either the day or the night shift.

The **addition** rule states that the probability of the union of two events A and B, denoted as P (A or B), is given by:

P (A or B) = P(A) + P(B) - P (A and B)

where P (A and B) is the probability of the** intersection** of events A and B.

Since Sam cannot choose both the day and night shift, P (A and B) = 0. Therefore, the probability that Sam chooses either the day or the night shift is:

P (day or night) = P(day) + P(night) - P (day and night)

P (day or night) = 0.9 + 0.03 - 0

P (day or night) = 0.93

To learn more about** addition**:

https://brainly.com/question/29560851

#SPJ1

Write an expression to describe the sequence below. Use n to represent the position of a term

in the sequence, where n = 1 for the first term.

-16, -15, -14, -13,

### Answers

**Answer:**

n - 1

**Step-by-step explanation:**

If we start by 1, we are then going 0, -1, -2, -3, etc. judging by the pattern of the sequence of numbers