Mathematics High School

## Answers

**Answer 1**

Hence proved that **triangle **AB = 3(3) - 1 = 9 - 1 = 8.

**What is triangle?**

A **polygon **with three edges and three **vertices** is called a triangle. It is one of the fundamental geometric shapes. **Triangle** ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not **collinear **produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All **triangles** are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean **plane**.

Given that,

AB + AC = AC

3y - 1 + 7y = 29

10y = 29 + 1 = 30

y = 30/10 = 3

Therefore, AB = 3(3) - 1 = 9 - 1 = 8.

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## Related Questions

what is 1+1x3/2+10x3450/2+300-500 I don't know what is it

### Answers

**Answer:**

**17052 1/2**

**You're Welcome**

If you add Alex’s and bobs pie total together, they ate 22 pies, while bobs and chucks pies sum to 24. When you add Alex and chucks pie together, you find that they are 16 total. How many pies did each individual eat?

### Answers

The number of** pie** each got-

Alex -7**Bob **- 15Chuck - 9What is the method of elimination?To create an equation in one variable, use the elimination method and can either add or subtract this same equations. Whenever the** coefficients** with one variable are opposites, the equations are added to eliminate a variable; when the coefficients with one variable are equal, the equations are subtracted to eliminate a variable.

For the given question;

Let the number of **pie eaten** by Alex be 'a'.

Let the number of pie eaten by Bob be 'b'.

Let the number of pie eaten by Chuck be 'c'.

Then, for the given condition.

If you add **Alex’s** and bobs pie total together, they ate 22 pies,

a + b = 22 .....eq 1.

Bobs and chucks pies sum to 24.

b + c = 24 .......eq 2

Alex and **chucks **pie together be 16.

a + c = 16 .......eq 3

Solving equation 1 and 3 by **elimination**.

Subtract eq 3 from 1.

c = b - 6 .....eq 4

Solving equation 4 and 2.

b = 15

Put in eq 4

c = 9

Put the values of b and c in eq 1.

a = 7

Thus, the number of pie shared by Alex,** Bob** and Chuck are 7, 15 and 9 respectively.

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Write the equation of the line that passes through the given point and is perpendicular to the given line.

(Only need 20 and 22)

### Answers

**Answer:**

4x - 5y = 30

4x - 5(0) = 30

x1 = 7.5 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

4x - 5y = 30

4(0) - 5y = 30

y2 = -6 x2 = 0

(x1,y1) and (x2,y2)

(7.5,0) and (0,-6)

Solve for x

To solve for x, we solve the equation so the variable x is by itself on the left side:

4x - 5y = 30

x = 1.25y + 7.5

Solve for y

To solve for y, we solve the equation so the variable y is by itself on the left side:

4x - 5y = 30

y = 0.8x - 6

100 Points!!

Activity

A submarine is at a depth of 100 feet below sea level. Then it starts to dive at a rate of 50 feet per minute. Use this information to answer the following questions.

Question 1

Part A

For this situation, what is the independent variable (include units)?

Part B

What is the dependent variable (include units)?

Part C

What is the slope of the line that models this situation?

Part D

What is the y-intercept of the line that models this situation?

Question 2

Write the equation of the line that models the situation using the slope and y-intercept found in parts C and D of question 1.

### Answers

**Answer:**

See below.

**Step-by-step explanation:**

The initial depth is 100 feet below sea level or 100 ft.

Diving rate is 50 feet per minute or 50 ft/min.

Question 1

Part A

The **diving rate** is the independent variable, which is:

50 ft/min

Part B

**The depth at any point** is the dependent variable, which is different after number of minutes, in ft.

Part C

The **slope is the diving rate** in this situation.

Part D

The **initial depth is the y-intercept**, the starting point.

Question 2

The **equation **of the line is:

y = mx + b, substituting the values,y = 50x + 100

**Answer:**

Independent variable: Time in minutes

Dependent variable: The elevation in feet

Slope: -50

Y-Intercept: -100

**Step-by-step explanation:**

Just did the assignment

step by step 9 divided by 1557

### Answers

**Answer:**

0.00578034682

**Step-by-step explanation:**

9/1557

keep on adding .0 to the end of your number.

You will eventually get the answer.

**Answer:**

173.

**Step-by-step explanation:**

there are 10 boys and 15 girls. The teacher chooses a student by random. Eric says that the probability for a boy to be chosen is 0.5. Jenny says he is wrong. Who is correct. Give reasons

### Answers

In a case whereby there are 10 boys and 15 girls and the teacher chooses a student by random, then the **probability** that a boy will be chosen is 2/5 which means **Jenny** is right.

How can the probability be calculated?

Since there are there are 10 boys and 15 girls, then the total number of the population will be (10+15)=25

Then the **probability** of that a boy will be chosen if one of them is been chosen at random will then be =10/25 = 2/5

Therefore, Jenny is very correct because the **probability** of that a boy will be chosen if one of them is been chosen at random will then be** 2/5.**

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2-b/3= -5/2 if you guys can help me thank you very much.

### Answers

**Answer:**

**b = 13.5**

**Step-by-step explanation:**

**2-b/3 = -5.2****Multiply both sides of the equation by 6, the least common multiple of 3,2****12 - 2b = -15****Subtract 12 from both sides****-2b = -15 - 12****Subtract 12 from -15 to get -27****-2b = -27****Divide both sides by -2****b = -27/-2****You can simplify -27/-2 by dropping off the negative sings making it ****b = 27/2****Divide 27/2 to get ****13.5 ****Or you can just simplify 27/2 to ****13 1/2**

**There are different ways you can solve this equation. Let me know if you'd like to know a different way. **

**Have a Good Rest of Your Day. **

Suppose sin a + cos b = -0.2 while sin b + cos a = 1.6. What is the value of sin(a+b)?

### Answers

The value of the **trignometric **expression sin(a+b) is 0.3.

Given the **trignometric **equations sin a + cos b = -0.2 and sin b + cos a = 1.6

So, squaring both equations and adding them

we have

[tex](sin a + cos b)^2 = -0.2^2\\(sin a + cos b)^2 = 0.04\\sin^2a+cos^2b + 2 sina cos b= 0.04\\(sin b + cos a)^2 = 1.6^2\\sin^2b+cos^2a + 2 sinb cos a= 2.56\\\\[/tex]

adding both equations

[tex]sin^2a+cos^2b + 2 sina cos b + sin^2b+cos^2a + 2 sinb cos a= 0.04+2.56\\[/tex]

1+1+2( sina cos b + cos a sin b)= 2.6

2( sina cos b + cos a sin b) = 0.6

( sina cos b + cos a sin b) = 0.3

We know that sin(a+b)= ( sina cos b + cos a sin b)

So,

sin(a+b)=0.3

Therefore, the **value** of sin(a+b) = 0.3

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Do the ratios 9 6 and 12 8 form a proportion?

### Answers

The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.

Given we have two** ratios**:

9:6 and 12:8

An equation in mathematics that shows that two ratios expressed in **fraction** form are equivalent is known as a proportion. The** rule** that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.

To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.

That is, 9/12 = 8/6

If only if 9×6=12×8

Therefore, 9×6=54

and 12×8=96

since these** two products **are not **equal, **we have that 9:12 and 8:6 do not form a proportion.

Hence the ratios 9:6 and 12:8 are not in proportion.

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TASK E5.1

1 The length, width and height of the cuboid are

measured to the nearest cm.

volume = length x width x height

What is the lowest possible value

of the volume of the cuboid?

Main Book Page 139

7 cm-

4cm

9cm

### Answers

The length, width and height of the cuboid are measured to the nearest cm, **volume **= length x width x height, the lowest possible value of the volume of the **cuboid **is [tex]cm^{3}[/tex].

What is volume?

**Volume **is measurement of three-dimensional space that is occupied. Numerous imperial units or the SI-derived units, such as the **cubic meter** and **liter**, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). **Volume **and length (cubed) have symbiotic relationship. The volume of a container is typically thought of as its capacity, not as amount of space it takes up. In other words, volume is the amount of fluid (liquid or gas) that the container may hold.

Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. **Arithmetic formulas** can be used to quickly calculate volume of several straightforward **three-dimensional shapes**. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine volumes of more complex shapes. No object in the dimensions of zero, one, or two has volume; in the dimensions of four and above, the **hypervolume **is a concept similar to the standard volume.

Volume = 7cm*4cm*9cm = 252[tex]cm^{3}[/tex]

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-2x + 3y = -6 and -3x - 2y = 11

### Answers

**Step-by-step explanation:**

-2x + 3y = -6

-3x - 2y = 11

-5x + y = 5

y = 5 + 5

y = 10

-2x + 3(10) = -6

-2x + 30 = -6

-2x = -6 - 30

-2x = -36

x = -18

i have no idea

Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He iS going to work 15 hours

this week. How many hours does Trevor need to tutor to make at least $180?

hours

### Answers

**Inequality - **Trevor needs to **tutor** more than 6 hours in order to make at least $180.

**What is inequality?**

**inequality**, A declaration of an order relationship between **two numbers **or** algebraic expressions**, such as greater than, greater than or equal to, less than, or** less than or equal to**. Either questions or **theorems** can be used to express **inequality problems**, and both can be solved using methods similar to those used to **solve equations**. The **triangle inequality,** for instance, states that the length of the remaining side of a triangle is greater than or** equal **to the sum of the** lengths **of any two of its sides. Many of these **inequalities**, including the **Cauchy-Schwarz inequality**, are used by **mathematical analysis** to prove some of its most **significant theorems.**

Total number of hours = 15

Let the hours spent **tutoring French** is x

Therefor, hours spent in scooping ice cream = (15-x)

**Tutoring French** is $15 an hour, total for x hours = 15x

Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x

To make more than $180,

= 15x+ (150-10x)> 180

= 15x+150-10x>180

=15x-10x>180-150

=5x>30

=x>6

So, Trevor needs to **tutor** more than** 6 hours.**

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-1 1/3 - 1/6 subtract using number line

### Answers

The **addition **of the **two negative numbers **has a result of -3/2, and is illustrated on the **number line** given at the end of the answer.

How to add two negative numbers?

To add two negative numbers, we keep the negative signal and then we add the quantities, that are represented by the numbers without the signal.

For this problem, the **numbers **are given as follows:

-4/3, which is the **mixed number** -1 and 1/3, given by -1 - 1/3 = -3/3 - 1/3 = -4/3.The fraction -1/6.

Hence the **addition **of the negative numbers is given as follows:

-4/3 - 1/6 = -8/6 - 1/6 = -9/6 = -3/2.

The **result **is of -3/2.

As for the **number line**, we have two negative numbers, hence each increment is to the left of the number line. The sum of the two increments, starting at zero, of 1/6 and of 4/3, combine to 3/2, as given by the **image **at the end of the answer.

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if c=4 work out the value of

c/2 + 6

### Answers

Using **arithmetic operations**, If the value of c = 4 then the value of (c/2) + 6 is 7

The given **expression** is (c/2) + 6

The value of c = 2

To find the value of (c/2) + 6 we have to do the suitable arithmetic operation after substituting the value c in the expression

Substitute the value of c in the given expression (c/2) + 6

(c/2) + 6 = (2/2) + 6

**Divide** 2 by 2 first

(2/2) + 6 = 1+6

**Add** one and six

1+6 = 7

Hence, by using the arithmetic operation, if the value of c = 4 then the value of (c/2) + 6 is 7

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Arrange the numbers 1 to 9 so that the sum of the three numbers in any straight line = 15

### Answers

**Answer:**

**1 8 6**

**9 4 2**

**5 3 7**

**Step-by-step explanation:**

**1) **When solving problems like this it is best to start with the smallest number. In this case the smallest number was 1, so that was placed in the top left corner.

**2) **The smallest number must be next to the two largest numbers so, 8 and 9 can be placed on its sides

**1 8**

**9**

3) solve for the final spots in the first row and the first column.

Row:

1 + 8 = 9

15 - 9 = 6

Column:

1 + 9 = 10

15 - 10 = 5

So,

**1 8 6**

**9**

**5**

**3)** Looking at the largest unused number, number 7, we can see that it is too large to go in the second row or the second column. This means it must be placed in the lower right corner

**1 8 6**

**9**

**5 7**

**4)** At this point you have enough information to solve for the rest of the numbers using simple addition and subtraction

The sum of twice a number and eight is 20. What is the number?

### Answers

**Answer:**

6

**Step-by-step explanation:**

let the number be equal to x

The sum of twice a number= 2x

2x+8=202x=20-82x=122x/2=12/2x=6

find the compound interest on $1500 for 2years at 2%per annum compounded anually

### Answers

**Answer:**

$1560.60

**Step-by-step explanation:**

PV (1+V)^n

= 1500 (1+2%)² = 1560.6

Write an equation for the line through the points (6, 10) and (3, 5) in point-slope form.

y =

+

### Answers

**Point slope form **of the equation through the points (6, 10) and (3, 5) is** y - 5 = 5/3 (x - 3)**

**Point slope form:**

The point slope form of equation is used to find the equation of the **straight line** which is inclined at a given angle to the** x-axis **and passes through a given point.

The general form of the equation is

(y - y1) = m (x - x1)

y=y coordinate of second point

y1=y coordinate of point one

m=**slope**

x=x **coordinate **of second point

x1=x coordinate of point one

Given,

Here we have the points (6, 10) and (3, 5).

Through the given points we have to find the point slope form of the equation.

To find the point slope of the equation, first step is to find the slope of those points,

It can be calculated using the formula,

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

Where the values of (x1,y1) is (6,10) and the values of (x2,y2) is (3,5).

Then the value of slope after applying the values,

m = (5 - 10)/(3-6)

m = -5/-3

m = 5/3

Use the slope and a given point (3,5) to substitute for x1 and y1 in the point-slope form

y−y1=m(x−x1),

which is derived from the slope equation.

Then we get the equation as,

y - 5 = 5/3 (x - 3)

Therefore, the point slope form equation is y - 5 = 5/3 (x - 3).

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PLEASE HELP THIS IS DUE❗️❗️❗️❗️❗️

### Answers

**Answer:**

**Step-by-step explanation:x=-2x**

Question

What numbers are a distance of 23 unit from 12 on a number line

### Answers

**Answer:**

distance: 11

there are 11 points between 12 and 23, they are:

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.

**Step-by-step explanation:**

Identify which graph can be used to solve each equation. Enter the letter of the correct graph next to the

equation.

Pleaseee help me

### Answers

The first ones C

Second is A

Last is B

is Figure C a scaled copy of Figure D (Thank you!)

### Answers

yes it is because it’s a transformation

**Answer:**

**Step-by-step explanation:**

Figure D is a dialation of Figure C.

Each of the sides of Figure D is proportionate to Figure C

The scale factor is 1.5

3:2 = 4.5:3 = 3:2=3:2

G(x)=-x^2/4+7

Over which interval does have a negative average rate of change?

### Answers

**Answer: **[tex](-\infty, 0][/tex]

**Step-by-step explanation:**

This is a parabola that opens down (because of the negative leading coefficient).

So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.

The function is decreasing to the left of the vertex, which is at (0, 7).

So, the function has a negative average rate of change for [tex](-\infty, 0][/tex].

Note that although there is a stationary point at x = 0, and that the graph isn't decreasing at this point, the average rate of change is still negative when considering a point to the left.

A cylindrical container is to be constructed so that the sum of its height and its diameter is 15 feet.

a) Write an equation relating the height of the cylinder, h, to its radius, r. Solve the equation for h in terms of r.

b) The volume of a cylinder is given V=πr^2h. Use your answer in part A to express the volume of the cylindrical container in terms of r alone. Leave your expression in factored form so that it will be easier to analyze.

c) What are the values of r for which this problem makes sense? Explain.

### Answers

From the characteristics of the given **cylinder**, we have that:

**a) **The **equation **is h = 15 - 2r.

**b) **The **volume **of the cylinder is of V = πr²(15 - 2r).

**c) **The **values of r** should be in the range of 0 < r < 7.5.

What is the volume of a cylinder?

The volume of a cylinder of** radius r and height h **is given according to the following equation:

V = πr²h.

The **sum **of the **height **and the **diameter **is of 15 feet, hence:

h + d = 15.

The diameter is **twice the radius**, hence:

h + 2r = 15.

For **item a,** the **solution **of h in terms of r is:

h = 15 - 2r.

Hence, in** item b**, the **equation **is:

V = πr²h.

V = πr²(15 - 2r).

For** item c, **there are two **constraints**, as follows:

**r > 0**, as the radius of a cylinder cannot be negative nor zero.**r < 7.5,** as the height must be positive.

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what is the answer to (b+3f)a=g

### Answers

**Answer:**

**f= -g/3**

**Step-by-step explanation:**

a researcher is interested in the travel time of utrecht university students to college. a group of 50 students is interviewed. their mean travel time in 16.7 minutes. for this study the mean of 16.7 minutes is an example of a:

### Answers

For this study, the mean of 16.7 minutes is an example of a (B) **Statistic**.

**What do we mean by Statistic**?As opposed to methods for gathering statistical data, mathematical statistics is the application of **probability theory**, a subfield of mathematics, to **statistics**. Mathematical analysis, **linear algebra,** stochastic analysis, **differential equations,** and measure theory are some of the specific mathematical methods used in this. Due to the abstract concepts and ideas that you will encounter later in your study, statistics stands out as the more challenging area of math. When you actually try to understand what's happening in a statistics equation or problem, you'll discover that the concepts are very challenging.

So, the appropriate choice is an option (B).

In this case, a researcher is interested in how long it takes Utrecht University students to get to class. For this study, a sample of 50 students was gathered, and the sample mean for travel time was found to be 16.7 minutes.Since the** sample means** is a sample **statistic**, option (B) is the right choice.

Therefore, for this study, the mean of 16.7 minutes is an example of a (B) **Statistic**.

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**The correct question is given below:**A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study, the mean of 16.7 minutes is an example of a(n)

A. Parameter

B. Statistic

C. Population

D. Sample.

34= -w/7 solve for w

### Answers

Hey! Your question was incomplete because I have double-checked my work, and even checked reliable sources to see if I missed something in my work, but I keep getting –238. I did play around with the question by switching the negative symbol around in the equation to see if I would get a balanced answer. I say this because when you solve the question you posted, the answer I got was w = –238, but when I went back to check my work by plugging that number in as the value of w, I got –238 ≠ 238 (or something like that. The number is the same, but the signs are not). If the signs and numbers don't both equal each other something is wrong with the problem. I believe I figured out where your question went wrong. Instead of the question being 34 = –w/7, I believe that the correct question should have been –34 = w/7. What I think happened was that when you typed your question, you swapped the negative on the 34 with the variable of w. If I am incorrect, and you typed your question correctly, I am sorry in advance because my work wasn’t matching what I got for w. But for now, I will solve what I think the question should have said. Again, sorry in advance. Solve for w in the following equation: –34 = w/7.

Write the equation:

–34 = w/7

Multiply both sides by 7:

7 × –34 = w/7 × 7

Multiply:

–238 = 1w

Divide:

–238/1 = 1w/1

–238 = w or w = –238

Check your work by plugging –238 back into the equation as w:

–34 = w/7

–34 = –238/7

Multiply both sides by 7:

–34 × 7 = –238/7 × 7

–238 = –238 ✔

Thus, w = –238

Hope that helps! Have an amazing rest of your day!! :)

multiply 2^3x^3.6^3x^3

### Answers

The **expression **is **multiplied **to give 1728x^6

What are index forms?

**Index forms** are simply defined as the power or exponent of a variable, number or element.

It is also seen as an **arithmetic **method of writing numbers that are too large or too small into simpler forms.

The rules of exponents are;

Add the powers if they are being multiplied the bases are the sameSubtract the exponents if they are divided and have the same base.Multiply the exponents when the bases of the forms are the same

Given the expression;

2^3x^3.6^3x^3

We have to determine the product of the index forms

First, we have to multiply the numbers, we have;

2^3 = 2 × 2 × 2 = 8

6^3 = 6 × 6 × 6 = 216

Now, substitute the values

8x³ × 216x³

Multiply through

1728x^3 + 3

1728x^6

Thus, the **value **is 1728x^6

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-3x= 2x^2 -4 solve using quadratic formula

### Answers

Solution of the given **equation** -3x =2x² -4,using **quadratic formula** is **(-3 ±√41) /4.**

As given in the question,

Given **equation** is:

-3x =2x² -4

Rearrange the terms in proper order:

2x² + 3x -4 =0

Solve it using **quadratic formula**

x = (-b ±√b²-4ac)/ 2a

Here compare the given equation with general quadratic equation:

a =2 , b=3 , c=-4

Substitute the values in the quadratic formula we get,

x = [ -3± √(3)² -4(2)(-4)]/2(2)

= (-3 ± √9+32)/4

= (-3 ±√41) /4

Therefore, Solution of the given equation -3x =2x² -4, using **quadratic formula** is (-3 ±√41) /4**.**

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0.0158 rounded to the nearest tenth

### Answers

**Answer:**

**Step-by-step explanation:**