Mathematics High School

## Answers

**Answer 1**

The measure of all the **angles **of **triangle **are 27.5° , 110° and 42.5°.

The **angle sum property **states that the sum of angles in a triangle is 180°. That is if the **angles** of a **triangle **are A,B and C then

angle A + angle B + angle C = 180° (1)

According to the question,

Let the smallest angle be x°

Then the second angle will be 4 times the other on which is 4x°

And the third angle will be 15° greater than the smallest one which will be = 15° + x°

Now putting all the required values in equation (1) we get,

x° + (4x°) + (15° + x°) = 180°

6x° = 180° - 15°

x° = 165°/6

x° = 27.5°

Thus the **angles** will be,

Smaller angle = x° = 27.5°

Other angle = 4x° = 4*27.5° = 110°

Third angle = 15° + x° = 15° + 27.5° = 42.5°

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## Related Questions

write the number 0.9333 as a fraction

### Answers

**Answer:9333/10000**

**Step-by-step explanation:**

0.9333

=

0.9333 × 10000

___________

1 × 10000

=

9333

10000

the answer is 9333/10000

I need answers to this question

### Answers

**Answer:**

good luckkkkk...........

3x-2y=8

-2y=-3x+8

Y= (-3x+8)/2

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 56.

### Answers

Using the **hypergeometric distribution**, there is a **0.4894 = 48.94% probability** of selecting none of the correct six integers in a lottery.

What is the hypergeometric distribution formula?

The **formula **is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The **parameters **are:

**x **is the number of successes.**N **is the size of the population.**n **is the size of the sample.**k **is the total number of desired outcomes.

For this problem, we want to take 6 numbers from a set of 56, hence the **values of the parameters** are:

N = 56, k = 6, n = 6.

The **probability **of selecting none of the correct six integers in a lottery is of **P(X = 0)**, hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,56,6,6) = \frac{C_{6,0}C_{50,6}}{C_{56,6}} = 0.4894[/tex]

**0.4894 = 48.94% probability** of selecting none of the correct six integers in a lottery.

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what is the multiplicative inverse of x (if x equals 0)

### Answers

The **multiplicative** inverse of x is** 1/x**

Multiplicative inverse

A multiplicative inverse or reciprocal for a number x, denoted by 1/x. It is a number which when multiplied by x yields the multiplicative identity, 1.

According to the question we are to find the **multiplicative inverse of x**

Let the **multiplicative inverse** be b

b * x = 1

Divide both** sides by b**

bx/x = a/x

b = 1/x

Hence the **multiplicative** inverse of x is** 1/x**

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Irrational numbers, like 0.0123456...., can be written as a fraction.

True; all decimals can be written as a fraction

False; any decimal that does not terminate or repeat cannot be written as a fraction

### Answers

Fase; any decimal that does not terminate or repeat cannot be written as a fraction

False; any decimal that does not terminate or repeat cannot be written as a **fraction**.

**Irrational numbers** are a type of real number that cannot be expressed exactly as a fraction of two integers. Their decimal expansions neither terminate nor repeat in a predictable pattern. Classic examples of irrational numbers include the square root of 2 (√2) and the mathematical **constant** π (pi). While rational numbers can be represented as fractions, irrational numbers are fundamentally different, and their decimal representations go on forever without a repeating pattern.

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9 times1+9 times1\10+2 times 1\100+1 times1\1000

### Answers

Answer:9.921

Step-by-step explanation:

9x1=9+9/10+2x1/100+1/1000=9.921

Write the possible range of the measurement: 220 km ± 5%.

### Answers

5% of 25 km is:

0.05*25 = 1.25 km

25 - 1.25 = 23.75

25 + 1.25 = 26.25

The possible range is (23.75, 26.25). Hope it helps

Which property of equality matches the statement AB = BC and BC = CD, the AB = CD?

### Answers

**Answer:transversive property**

**Step-by-step explanation:**

My question wouldn't go through for some reason so I've put the question on the picture

### Answers

The **measures **of the **angles **are given as follows:

ABC = 46.2º.CBD = 35.8º.

What is the value of x?

Angle ABD is the sum of angles BCD and ABC, hence:

ABD = BCD + ABC.

We replace the measures to find the **value of x,** hence:

6x - 9 + 4x - 1 = 82.

10x - 10 = 82.

10x = 92.

x = 9.2.

What are the measures of the angles?

With x, we can find the **measures of the angles**, as follows:

ABC = 6(9.2) - 9 = 46.2º.CBD = 4(9.2) - 1 = 35.8º.

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what are solutions to the inequality -x-2y>3

### Answers

The coordinates (-1, -2), (-2, -1), and (2, -4) are solutions to the given **inequality.**

How to find the solutions to an Inequality?

We are given the **Inequality** as;

-x - 2y > 3

Now, for us to find the points that are the solutions to the given inequality, substitute the given points into -x - 2y, and anyone that gives a result greater than 3 is a **solution** to the **inequality**

For the **coordinate** (-1, -2), substitute x = -1, and y = -2 into -x - 2y

-(-1) - 2(-2)

= 1 + 4

= 5

Since 5 > 3, then (-1, -2) is a solution to the inequality

For the **coordinate** (1, -2)

Substitute x = 1, and y = -2 into -x - 2y

-(1) - 2(-2)

= -1 + 4

= 3

Since the result is not greater than 3, then (1, -2) is **not a solution** to the inequality.

For the **coordinate** (-2, -1);

Substitute x = -2, and y = -1 into -x - 2y

-(-2) - 2(-1)

= 2 + 2

= 4

Since 4 > 3, then we say that (-2, -1) is a **solution** to the inequality

For the **coordinate** (2, -4);

Substitute x = 2, and y = -4 into -x - 2y

-(2) - 2(-4)

= -2 + 8

= 6

Since 6 > 3, then we say that (2, -4) is a solution to the** inequality**

Therefore, (-1, -2), (-2, -1), and (2, -4) are solutions to the inequality

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When an integer is subtracted from 8 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.

### Answers

The **value** of the **lesser integer** is **7**

What are algebraic expressions

**Algebraic expressions** are expressions consisting of both variables and constants and are also made up of mathematical operations such as addition, subtraction, division, multiplication, etc.

From the information given, we have;

Let the integers be (x) and ( x + 2)

8(x + 2) - (x)= 23

Expand the bracket

8x + 16 - x = 23

collect like terms

8x - x = 23 - 16

Add/subtract like terms

7x = 7

Make 'x' the subject

x = 7/7

The value for the lease integer = x

Substitute the value of x

7

Thus, the **value**** **of the **lesser**** ****integer**** **is **7**

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The graph shows the height of a

roller coaster in terms of its distance away from the

starting point. Describe and interpret the end behavior

in the context of the situation.

### Answers

The **end behavior **of the function means that when the **roller coaster gets farther** from it's starting point, it's **height approaches 0**.

What is the end behavior of a function?

The end behavior of a function is the **output of the function **when it **moves to infinity,** either to the left and to the right.

For this problem, the function is defined only towards negative infinity, when it moves toward zero with waves of decaying amplitude, but we can **state **that:

[tex]\lim_{x \rightarrow \infty} h(x) = 0[/tex]

Distances toward infinity means that the **roller coaster gets farther** from it's starting point, and the **result **of the limit means that it's **height approaches 0**.

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It cost Blake $8.00 to send 80 text messages. How much would it cost to send

130 text messages?

### Answers

**Answer:**

13

**Step-by-step explanation:**

$. : text message

8. : 80

= ? : 130

? = ( 8 * 130) / 80

? = 13

**Answer:**

**13**

**Step-by-step explanation:**

** $. : text message**

** 8. : 80**

**= ? : 130**

**? = ( 8 * 130) / 80**

**? = 13**

Estimate the solution to the system of equations. You can use the interactive graph below to find the solution. { y = − 2 x − 5 y = 2 x − 2 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−2x−5 y=2x−2 Choose 1 answer: Choose 1 answer: (Choice A) A x = − 3 4 , y = − 2 1 2 x=− 4 3 ,y=−2 2 1 x, equals, minus, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 2, start fraction, 1, divided by, 2, end fraction (Choice B) B x = − 1 3 4 , y = − 3 1 2 x=−1 4 3 ,y=−3 2 1 x, equals, minus, 1, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 3, start fraction, 1, divided by, 2, end fraction (Choice C) C x = − 3 4 , y = − 3 1 2 x=− 4 3 ,y=−3 2 1 x, equals, minus, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 3, start fraction, 1, divided by, 2, end fraction (Choice D) D x = − 1 3 4 , y = − 2 1 2 x=−1 4 3 ,y=−2 2 1 x, equals, minus, 1, start fraction, 3, divided by, 4, end fraction, comma, y, equals, minus, 2, start fraction, 1, divided by, 2, end fraction 1 1 2 2 3 3 4 4 5 5 6 6 - 2 - 2 - 3 - 3 - 4 - 4 - 5 - 5 - 6 - 6 1 1 2 2 3 3 4 4 5 5 6 6 - 2 - 2 - 3 - 3 - 4 - 4 - 5 - 5 - 6 - 6 y y x x Stuck

### Answers

The **solution** to the **system **is (-3/4, -9/2)

What are linear equations?

**Linear equations **are equations that have constant average rates of change. Note that the **constant average rates of change **can also be regarded as the slope or the gradient

How to determine the solution to the system?

A **system of linear equations **is a collection of at least two linear equations.

In this case, the **system of equations **is given as

y = -2x - 5

y = 2x - 2

Substitute y = 2x - 2 in y = -2x - 5

2x - 2= -2x - 5

Evaluate the like terms

4x = -3

Divide by 4

x = -3/4

Substitute x = -3/4 in y = 2x - 2

y = 2 * -3/4 - 2

This gives

y = -3/2 - 2

Evaluate

y = -9/2

Hence, the **solution** to the **system **is (-3/4, -9/2)

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Jenny has 1.5 times more tennis balls than Janis. Together they have 50 tennis balls. Jenny wrote this equation to model the number of tennis balls they have, where x represents the number of tennis balls that Janis has. How many tennis balls does each girl have?

x + 1.5x = 50

### Answers

The **number **of **tennis balls **that **Jenny **and **Janis **have are **30 **and **20 **respectively.

How many tennis balls does Jenny and Janis have?

Given the equation that models the number of tennis balls Jenny and Janis have.

x + 1.5x = 50

We **solve **for the **value **of **x**

x + 1.5x = 50

2.5x = 50

x = 50/2.5

**x = 20**

Hence,

Janis's tennis balls = x = **20 **

Jenny's tennis balls = 1.5x = 1.5(20) = **30**

Therefore, the **number **of **tennis balls **that **Jenny **and **Janis **have are **30 **and **20 **respectively.

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Which ordered pairs make the open sentence true?

3x+y<14

Select all the correct answers.

(3, 6)

left parenthesis 3 comma 6 right parenthesis

(7, −7)

left parenthesis 7 comma negative 7 right parenthesis

(6, 0)

left parenthesis 6 comma 0 right parenthesis

(−1, 6)

left parenthesis negative 1 comma 6 right parenthesis

(4, −1)

### Answers

The **ordered pairs** which make the open sentence **true **are:

(-1, 6).(4, -1).

What is an inequality?

An **inequality** can be defined as a mathematical relation that compares two (2) or more integers and **variables** in an algebraic **expression** based on any of the following arguments:

Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).

For this exercise, you should evaluate each of the given **expressions** to determine which **inequalities** is true when the **ordered pairs** are substituted. This ultimately implies that, you would have to substitute the **ordered pairs** into each of the given algebraic **expressions** and then evaluate.

When **ordered pairs **= (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When **ordered pairs **= (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When **ordered pairs **= (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When **ordered pairs **= (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (**True**).

When **ordered pairs **= (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (**True**).

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Simplify.

3 – (−2) + |−7|

I am dum dum

### Answers

The **simplified** form of the expression as given in the task content is; **1****2****.**

What is the simplified form of the expression given in the task content?

The expression given in the task content can be simplified by means of **PEMDAS** guidelines as follows;

3 – (−2) + |−7|

= 3 +2 +7

= 12.

Hence the **simplified** form of the expression is **12**.

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The box plot represents the distribution of the number of points scored by a cross country team at 12 meets. If possible, find the median. If not possible, explain why not.

### Answers

The median is the **value equivalent** to the vertical line as shown. Hence the** median poin**t is** 34**

What is a median?

The median is defined as the value at the middle after rearrangement.

From the g**iven boxplot, **we have the following

The minimum value is equivalent to the lower position of the whisker = 22

The maximum value is equivalent to the upper position of the whisker = 42

The **median **is the value vertical line in **between the box = 34**

The lower quartile (Q1) = starting point of the box = 33

Upper quartile (Q3) = end point of the box = 38

For the **boxplot**, the median is the **value equivalent** to the vertical line as shown. Hence the** median poin**t is** 34**

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Organizing Information and Activating Prior Knowledge Fill in the blanks to complete the chart

### Answers

1) The equation of a line in **slope intercept form** is used when we know the **slope** and **y-intercept.**

2) The linear equation is in **Point Slope form**

**What is the interpretation of equation of a line?**

1) The equation of a line in **slope intercept form** is;

y = mx + b

where;

m is **slope**

b is **y-intercept**

We use this equation form when we know the **slope** and **y-intercept.**

2) The equation of a line in **Point Slope form** is;

y - y1 = m(x - x1)

This is used when we know the slope and a point on the line.

Thus, we conclude that;

1) The equation of a line in **slope intercept form** is used when we know the **slope** and **y-intercept.**

2) The linear equation is in **Point Slope form**

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when x=-5 what does y= ?

when x=-1 y=?

when x= 3 y= ?

### Answers

The value of y is ** x are -5, 1 and 3 **are **3, -3 and -4** respectively.

What are piecewise functions?

A piecewise-defined **function is a function** defined by multiple sub-functions, where each** sub-function** applies to a different interval in the domain.

From the given graph, we need to find the cooresponding y-values if the value of** x are -5, 1 and 3**

From the given graph, the value of y is ** x are -5, 1 and 3 **are 3, -3 and -4 respectively.

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Equations & Inequalities Task Card # 9

The number of seventh graders in

choir is three times the number of

sixth graders. There are 72

seventh graders in the choir. Write

and solve an equation to find s, the

number of sixth graders that are in

the choir?

..

### Answers

**Answer:**

72/3=S=24

**Step-by-step explanation:**

The question states that there are 3 time as many 7th graders as their are 6th graders in choir so to find S we would have to do the opposite equation which is division so we divide 72 by 3

Find (cd)(x).

c(x) = 5x + 6

d(x) = 3x

Write your answer as a polynomial in simplest form.

(cod)(x)

### Answers

**Answer: **15x+6

**Step-by-step explanation:**

c(x) = 5x + 6

d(x) = 3x

(cod)(x)=

c(d(x))=

5(3x)+6=**15x+6**

When testing the differences between means, the null hypothesis suggests that any observed difference is due to?

### Answers

The **null hypothesis **suggests that any **observed difference **is due to random error.

What is a null hypothesis?

This refers to the type of **conjecture **in statistics that proposes that there is no **difference **between certain characteristics of a population or data-generating process.

While the **alternative hypothesis** does proposes that there is a difference, the **null hypothesis** does proposes that there is no difference between the characteristics.

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Ralph Chase plans to sell a piece of property for $155000. He

wants the money to be paid off in two ways - a short-term note at 10% interest and a long-term note at 8% interest. Find the amountof each note if the total annual interest paid is $14100.

### Answers

Ralph chase invested **$85000 a**t an interest o**f 10%** and** $70000** at an interest of** 8%**

What is an **equation**?

An equation is an **expression** that shows the **relationship **between two or more numbers and variables.

An independent variable is a **variable** that does** not depends** on other variable while a** dependent variable **is a variable that **depends **on other variable.

Let** a** represent the amount invested at** interest of 10% **and** b** represent the amount** invested at 8%,** hence:

**a + b = 155000** (1)

Also:

**0.1a + 0.08b = 14100** (2)

From both equations:

**a = 85000, b = 70000**

Ralph chase invested **$85000 a**t an interest o**f 10%** and** $70000** at an interest of** 8%**

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Graph this line:

y - 3 = -(x + 9)

Click to select points on the graph.

### Answers

**Answer:**

See picture below

**Step-by-step explanation:**

Pls help again for this as well algebraic proofs

### Answers

**Answer:**

answer =0

**Step-by-step explanation:**

2(x+2) = -4(x-1)

2x+4 = -4x+4

4x+2x = 4-4

6x = 0

x = 0

Please help me. Will give brainliest.

### Answers

Based on the given formula of **compounding interest**, and the amount that **Javier **invested, the **value of n** in this situation is** 2. **

What is the value of n?

In the **compound interest **formula given, the parts of the formula are shown to be:

n = number of times the interest compounds per year

p = principal amount

r = interest rate

t = number of years

We are told that the **investment compounds **every **six months **which means in a year, the **number of times** compounded is:

= 12 months in year / 6 months

= 2 times

In conclusion**, n is 2.**

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Find the equation of a line passing through the given point and parallel to the given equation. Write you answer in slope-intercept form.

(-2,4) and y= -x + 3

### Answers

The **equation of a line** passing through the given point and parallel to the given equation is** y = -x + 2**

Equation of a line

The equation of a line in **slope-intercept form** is expressed as y = mx + b

where

m is the slope

b is the intercept

The equation in point-slope form is expressed as y - y1 =m(x - x1)

Given

Slope = -1

Point = (-2, 4)

**Substitute**

y - 4 =-1(x - (-2))

y - 4 = -(x+2)

y - 4 = -x - 2

y = -x - 2+ 4

y = -x + 2

Hence the **equation of a line** passing through the given point and parallel to the given equation is** y = -x + 2**

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When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates that?

### Answers

When we describe relationships between variables, a **correlation** nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of **correlation**, which is given as a number. However, a **correlation **between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When **correlation** is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the **correlation** between/among the variables.

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In your own words, why will rigid transformations always produce congruent figures? Could non-rigid transformations also produce congruent figures?

### Answers

Rigid transformation are** transformation **that **preserve t**he shape and size hence producing **congruent figure**s such as t*ranslation, reflection and rotation.*

Dilation is a** non rigid transformation** and does** not **produce** congruent figures.**

What is a **transformation**?

Transformation is the **movement **of a point from its** initial location** to a **new l**ocation. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation are** transformation **that **preserve t**he shape and size hence producing **congruent figure**s such as t*ranslation, reflection and rotation.*

Dilation is a** non rigid transformation** and does** not **produce** congruent figures.**

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