Mathematics College

## Answers

**Answer 1**

**Answer:**

Angle C is 68° (or 50°)

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

According to angle sum property the **sum of** three interior **angles is 180°**.

Set **equation **and solve for x:

x² + x + 40 + x + 60 = 180x² + 2x + 100 = 180x² + 2x = 80x² + 2x + 1 = 81(x + 1)² = 81x + 1 = ± 9**x = 8 **or **x = - 10**

**Angle C is**:

8 + 60 = 68° or-10 + 60 = 50°

**Answer 2**

**Step-by-step explanation:**

x²+X+60+X+40=180 [sum of angles of ∆]

or,x²+2x+100-180

or,x²+2x-80=0

or,x²+10x-8x-80=0

or,x(x+10)-8(x+10)=0

or,(x-8)(x+10)=0

Either,. OR,

X=8. x=-10

when,x=8 then <A=(8)²=64°,<B=8+40=48°,<C=8+60=68°

When,x=-10 then

<A=(-10)²=100°,<B=-10+40=30°,<C=-10+60=50°

## Related Questions

6. if a is a square matrix that is row equivalent to the identity matrix then a is diago- nalizable.

### Answers

False, If A is **row equivalent** to the** identity matrix**, then A is invertible.

Given :

if a is a** square** matrix that is row equivalent to the identity matrix then a is diago - nalizable.

Identity matrix :

An identity matrix is a square matrix having 1s on the main **diagonal**, and 0s everywhere else .

Invertible matrix :

An invertible matrix is a matrix for which matrix **inversion** operation exists, given that it satisfies the requisite **conditions**.

so given **statement** is false if A is row equivalent to the identity matrix, then A is invertible.

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Grace read a total of 170 pages over the last 3 days. On the second day, the number of pages she read was 5 more than 2 times the number of pages she read on the first day. On the third day, she read 15 pages less than the number of pages she read on the second day.

### Answers

170= x + (x *2+5) + (x *2+5-15).

x = 35

Day 1 = 35

Day 2 = 75

Day 3 = 60

Write a doubles fact you can use to find the sum. Write the sum.

1 + 2 =

### Answers

The **doubles** to find the **sum** is 1+1+1

How to find doubles?

We should know that the **double** is the figures when added to the original figure, will give us exact value

So by definition, a double is any **amount **of number which is **twice **as large as the given amount of a number.

The give parameter is 1+2

We can write 2 as 1+1

So this means that 1+2 can be written as

1+2=1+1+1=3

Since 1+2=3

Therefore 1+1+1=3

Hence a double is any **amount **of number which is **twice **as large as the given amount of a number,

In conclusion the **doubles** to find the **sum** of 1+2 is 1+1+1

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suppose you roll one fair six-sided die and then flip as many coins as the number showing on the die. (for example, if the die shows 4, then you flip four coins.) let y be the number of heads obtained. compute e(y)

### Answers

When y be the number of **heads** obtained then the **value** of [tex]$E(Y)=\frac{1}{8}[/tex].

As per question **roll** one **fair six-sided die** and then **flip** as many **coins** as the number showing on the die.

Let [tex]$Y$[/tex] be the number of **heads obtained**.

[tex]$E(Y)=\Sigma_{y=1}^{y=6} y P_y(y)$[/tex]

We will define X as the number on the **die**.

Therefore

[tex]$$E(Y)=\sum_{y=1}^{y=6} y P_y(y)\\\\=\sum_{y=0}^{y=6} \sum_{x=1}^{x=6}(y) P(X=x, Y=y)\\\\=\sum_{y=0}^{y=6} y \sum_{x=1}^{x=6}(1 / 6)\left(\begin{array}{l}x \\y\end{array}\right)(1 / 2)^x$$[/tex]

This inner equation is valid:

[tex]$(1 / 6)\left(\begin{array}{l}x \\ y\end{array}\right)(1 / 2)^x$[/tex]

Basically, it says that if I roll a 3 , and I get 1 head only, what is the **probability** of that occurring [tex]=\frac{1}{6}[/tex]

From 3 rolls, we choose one head [tex]=\frac{1}{8}[/tex]

Therefore

[tex]$E(Y)=\frac{1}{8}[/tex]

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What is the remainder when the sum of 1^99+2^99+3^99+....+2022^99 is divided by 2023? PLS ANSWER FAST

### Answers

The **remainder **when the** sum** of 1⁹⁹ + 2⁹⁹ + 3⁹⁹ +.... + 2022⁹⁹ is divided by 2023 is 0.

How to determine the reminder?

We can use the formula for the **sum** of an arithmetic series to find the sum of the series 1⁹⁹ + 2⁹⁹ + 3⁹⁹ +.... + 2022⁹⁹. The formula is:

Sum = (n/2) (2a + (n - 1)d)

Where n is the number of terms in the series, a is the first term, and d is the common difference.

In this case, the first term is 1, the common difference is 1, and the number of terms is 2022.

Plugging these values into the formula, we have:

Sum = (2022/2)(2×1 + (2022 - 1) × 1) = (2022/2)(2 + 2021)

We can simplify this to:

Sum = (2022/2)(2023) = (2022/2)(2023) = (2022 × 2023)/2

To find the **remainder** when this sum is divided by 2023, we can use the property of **modular arithmetic**:

(a + b) mod n = ((a mod n) + (b mod n)) mod n

Applying this property to the sum we have:

(Sum mod 2023) = (((2022 × 2023)/2 mod 2023) + (0 mod 2023)) mod 2023

The remainder when 2022 × 2023 is divided by 2023 is 0, so the expression simplifies to:

(Sum mod 2023) = (0 + 0) mod 2023 = 0

Thus, the remainder is 0

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Twice the difference of a number and 9 is equal to three times the sum of the number and 8.

### Answers

The number= -25

**Step-by-step explanation:**

To solve this equation, you can start by expressing the difference between the number and 9 as 2 times the sum of the number and 8 divided by 3. This gives you the equation:

2 * (x + 8) / 3 = x - 9

You can then multiply both sides of the equation by 3 to get rid of the fraction:

6 * (x + 8) = 3 * (x - 9)

This simplifies to:

6x + 48 = 3x - 27

You can then combine like terms on both sides of the equation to get:

3x + 48 = -27

You can then add 27 to both sides of the equation to get:

3x + 75 = 0

You can then subtract 75 from both sides of the equation to get:

3x = -75

You can then divide both sides of the equation by 3 to get the solution:

x = -25

Therefore, the number x is equal to -25.

Hope this helps you??

Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true? a) A = BUC b) B is a singleton set. c) A = CU{2} d) All of the mentioned

### Answers

Let A be the set of all **prime **numbers, B be the set of all **even **prime numbers, and C is the set of all **odd **prime numbers, then A = BUC, B is a singleton set and A = CU{2}. Hence, the **correct **option for this question is **option D - All of the mentioned**.

We have,

A = set of all **prime **numbers

A = {2, 3, 5, 7, 11, 13, ...}

B = the set of all **even prime **numbers

B = {2}

C = the set of all **odd prime **numbers

C = {3, 5, 7, 11, 13, ...}

We know that 2 is the **only **even prime number. hence, Set B is a **singleton **set, containing only **one **element.

Also, if we take the **union **of set B and set C, we will get the set of all the **prime **numbers, which is set A. Hence, we get, A = B U C.

If we have A = B U C, we can also say A = C U {2}, since B = {2} is a **singleton **set.

Hence, **all **the options mentioned above are **correct**.

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The equation 6x+3y=15 represents the total cost, in dollars, of a customer’s order at a bakery, where x is the price of a doughnut, and y is the price of a muffin. Which represents the equation when solved for the price of a muffin y?

### Answers

**Answer:**

I hope this helps

**Step-by-step explanation:**

solving for the price of **y**

6x + 3y = 15

3y = 15 – 6x

=

[tex]y = \frac{15 - 6x}{3} [/tex]

Let B be the set of all infinite sequences over {0, 1}. Show that B is uncountable,

using a proof by diagonalization.

### Answers

Each **element** in B is an **infinite sequence** (b1, b2, b3, ...), where each

** bi ∈ {0, 1}.**

**Infinite Sequence:**

An **infinite sequence** (sometimes simply called a sequence) is a function with a **domain **of all **positive integers**. At the beginning of calculus, the domain of infinite sequences is usually the set of** real numbers**, but the domain can also include **complex numbers.**

The **general form** of the **infinite sequence** is

** f(1), f(2), f(3),…f(n),…**

where:

… = continues indefinitely,

n = **Positive intege**r (input),

f(n) = **real number **(output).

**Diagonalization:**

Converting a matrix to **diagonal** form is called **diagonalization.** The **eigenvalues **of a **matrix **are clearly represented by a diagonal matrix. A **diagonal matrix** is a **square matrix **in which all **elements** except the main **diagonal **are zero. In this article, let's take a look at the definition, **process**, and example solution of diagonalization.

[tex]\left[\begin{array}{ccc}4&0&0\\0&5&0\\0&0&6\end{array}\right] = I_3 \left[\begin{array}{ccc}4&0&0\\0&5&0\\0&0&6\end{array}\right] I_{3} ^-1[/tex]

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Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. 85% of the possible Z values are smaller than . Use your z-table and give your answer to 2 decimal places. Find the area under the standard normal curve that lies to the right of -0.91. Calculate answers to four decimal places. The variable X is normally distributed with μ = 61.00 and σ = 13.00. Determine the z-score for the randomly chosen value 76.00. Round your z-score to 2 decimal places. Find the area under the standard normal curve that lies in between -5.10 and 1.0. Calculate answers to four decimal places. Determine the z-value that has area 0.9922 to the left. (Report the z-value to 2 decimal places.)

### Answers

To find the **area **under the standard normal curve that lies to the right of -0.91, we can use a z-table to look up the corresponding probability. We find that the area to the right of -0.91 is approximately 0.1587.

To find the **z-score** for the value 76.00, we can use the formula for a z-score: (x - μ) / σ. Plugging in the values given, we get: (76.00 - 61.00) / 13.00 = 2.77. So the z-score for the value 76.00 is approximately 2.77.

To find the **area **under the standard normal curve that lies between -5.10 and 1.0, we can use a z-table to find the corresponding probabilities for each of these values and then subtract the probability for -5.10 from the probability for 1.0. We find that the probability of -5.10 is approximately 0.0000, and the probability of 1.0 is approximately 0.8413. Subtracting these values gives us an area of approximately **0.8413**.

To find the z-value that has an area of **0.9922 **to the left, we can use a z-table to look up the corresponding z-value. We find that the z-value that corresponds to an area of 0.9922 to the left is approximately 2.33.

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A segment has a midpoint at (2,-7) and an endpoint at (8,-5). What what are coordinates of the other midpoint

### Answers

The **coordinates** of the other endpoints is (-4, -9).

What is midpoint of a line segment?

The **midpoint** of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the **midpoint** and (a, b) and (c, d) are the two **endpoints**.

We have,

**Midpoint**: (2, -7) = (x, y)

**Endpoints**: (a, b) and (8, -5) = (c, d)

Now,

x = (a + c)/2

2 = (a + 8)/2

4 = a + 8

a = 4 - 8

a = -4

y = (b + d)/2

-7 = (b - 5)/2

-14 = b - 5

b = -14 + 5

b = -9

Thus,

The other **endpoint** is (-4, -9).

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Compare using <, > or =

|-5| |-7|

### Answers

|-5| < |-7|, this is because the absolute of -5 is 5, and the absolute of -7 is 7, and 7 is greater than 5

Suppose a 95% confidence interval for the proportion of Canadians who exercise regularly is [0.30;0.42]. Which one of the following statements is FALSE? (a) We are at least 95% confident that more than 25% of Canadians exercise regularly. (b) We are at least 95% confident that more than 45% of Canadians exercise regularly. (c) The hypothesis that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05 . (d) We are at least 95% confident that fewer than half of Canadians exercise regularly. (e) Several statements are false.

### Answers

The correct answer is **(c)**: "The **hypothesis **that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05".

The confidence interval **[0.30;0.42] represents** our estimate of the true proportion of Canadians who exercise regularly, with a confidence level of 95%. This means that if we were to repeat the survey multiple times, using the same sampling method and sample size, we would expect the confidence interval to contain the true proportion of Canadians who exercise regularly 95% of the time.

Based on the confidence interval provided, we can say that we are at least 95% confident that more than 30% and fewer than 42% of Canadians exercise regularly. This means that statements (a) and (d) are both true. However, statement (c) is false because the hypothesis that 33% of Canadians exercise regularly is not contained within the confidence interval, and therefore cannot be rejected at significance level α = 0.05.

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I need some help please

### Answers

**Answer:**

The answer is B

**Step-by-step explanation: A trick I use for these type of problems is pick a point from the highest part of the graph, then make a right triangle. A right triangle with this graph will make the answer -2/3 since it goes down 2 right 3**

Suppose the given confidence level is 85%, what is the corresponding z critical value?

### Answers

Since the given confidence level is 85%, the value of a is 1- 0.85. Compute a. 1-0.85 = 0.15 (Type an integer or a decimal.) The critical value z/2 is the positive z value that is at the boundary separating an area of a /2 in the right tail of the standard normal distribution.

What is it help me was the answer correct

### Answers

The correct option is 3

**Step-by-step explanation:**

Multiple inputs can give the same output, but not vice versa.

Naomi's dining room is 7 yards wide and 7 yards long. Naomi wants to install wooden trim around the top of the room. The trim costs $9.00 per yard. How much will it cost Naomi to buy enough trim?

### Answers

7*7=49. Each yard is 9 dollars. So 49*9=441$

7x7 which is 49. multiplying 7 by 7 gives you your answer

DeShawn earned $66,000 last year. If the first $30,000 is taxed at 9% and income above that is taxed at 15%, how much does DeShawn owe in tax?

### Answers

Hello,

I hope you and your family are doing well!

DeShawn will owe 9% tax on the first $30,000, which is $30,000 * 9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be taxed at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in tax.

**In total, DeShawn will owe $2,700 + $5,400 = 8,100 in tax.**

Please consider giving this 5 stars and brainliest if you find this answer helpful.

Happy Holidays!

The **tax **DeShawn has to pay is $8100

What is Tax?

**Taxes **are mandatory contributions levied on individuals or corporations by a government entity.

Given that, DeShawn earned $66,000 last year and the first $30,000 is **taxed **at 9% and income above that is **taxed **at 15%,

DeShawn will owe 9% **tax **on the first $30,000, which is $30,000×9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be **taxed **at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in **tax**.

In total, DeShawn will owe $2,700 + $5,400 = $8,100 in **tax**.

Hence, The **tax **DeShawn has to pay is $8100

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a) given any set of seven integers, must there be at least two that have the same remainder when divided by 6? to answer this question, let a be the set of 7 distinct integers and let b be the set of all possible remainders that can be obtained when an integer is divided by 6, which means that b has elements. hence, if a function is constructed from a to b that relates each of the integers in a to its remainder, then by the ---select--- principle, the function is ---select--- . therefore, for the set of integers in a, it is ---select--- for all the integers to have different remainders when divided by 6. so, the answer to the question is ---select--- . (b) given any set of seven integers, must there be at least two that have the same remainder when divided by 8? if the answer is yes, enter yes. if the answer is no, enter a set of seven integers, no two of which have the same remainder when divided by 8.

### Answers

Given any set of seven **integers**, there are no two numbers that have the same remainder when **divided **by 6.

The **remainder **is the value left after the division. If a number is not completely divisible by another number then we are left with a value once the **division **is done. This value is called the Remainder.

Given any set of seven integers, there must be at least two numbers that have the same remainder when divided by 6.

So there can be six remainders when divided by 6 i.e. 0,1,2,3,4 and 5.

According to the **Pigeonhole **principle,

in any set of seven integers, two must have the same remainder when divided by seven.

Consider the set of integers 0,1,2,3,4,5 and 66. All of these have different remainders upon division by 8.

Hence there need not be **two **numbers such that they have the same remainders when divided by 6.

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Find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive 1s. Be sure to include the initial conditions Solution an an-1+ an-2 Initial condition: a 2, a2 = 3

### Answers

The two case given below are disjoint and cover all the cases for n **length strings**, hence the numbers add up to give [tex]a_{n} =a_{n-1}+a_{n-2}[/tex].

In the given question we have to find a** recurrence relation **for the number of n-digit binary sequences with no pair of consecutive.

Be sure to include the initial conditions Solution an [tex]a_{n-1}+ a_{n-2}[/tex]** Initial condition**: [tex]a_{1}=2,a_{2}=3[/tex]

Clearly [tex]a_{1}[/tex] = 2 (0,1) and [tex]a_{2}[/tex] = 3 (00,10,01). Now for the case of n. Suppose we are given a string with no consecutive 1's. There are two cases:

**Case 1: **the given string starts with a 0. In this case the n-1 length string after the first bit can be any string without consecutive 1's of length n-1. Hence there are n-1 of those.

**Case 2:** the given string starts with a 1. In this case the second bit has to be a 0 since we don't want consecutive 1's. Not the last n-2 length string can be any string without consecutive 1's of length n-2. Hence there are [tex]a_{n-2}[/tex] of those.

These two case are disjoint and cover all the cases for n length strings, hence the numbers add up to give [tex]a_{n} =a_{n-1}+a_{n-2}[/tex].

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Solve the triangle PLEASEEEEEE

### Answers

Part 1

[tex]a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}[/tex]

Part 2

[tex]\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}[/tex]

Part 3

[tex]\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}[/tex]

how do i do this

the possible answers are

30, 40, 50, 60

### Answers

The figure in the question is a **kite** and the value of the **angle** 4 is equal to 40°

Interior angles of a kite

A **kite** has4 interior **angles**and the sum of these interior angles is 360°. In these angles, it has one **pair** of opposite angles that are obtuse angles and are equa

Let us represent the angle 3 with x, so that;

angle 1 = 2x,

angle 2 = x + 20

angle 1 + **angle** 4 = one of the pair of opposite angles

angle 1 + angle 3 + 90° = 180° {sum of interior angles of a triangle}

2x + x + 90°= 180°

3x = 180° - 90° {subtract 90° from both sides}

x = 90°/3 {divide through by 3}

x = 30°

so;

angle 1= 60°

angle 2 = 50°

sum of interior angles of **kite** (quadrilateral) = 360°

2(angle 3) + 2(angle 2) + 2(angle 1 + **angle** 4) = 360°

60° + 100° + 2(60° + **angle** 4) = 360°

60° + 100° + 120° + 2(**angle** 4) = 360° {open bracket}

280° + 2(**angle** 4) = 360°

2(**angle** 4) = 360° - 280° {subtract 280° from both sides}

2(**angle** 4) = 80°

**angle** 4 = 80°/2 {divide through by 2}

**angle** 4 = 40°

Therefore, the **angle** 4 of the **kite** is equal to the value of 40°.

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angle of is a right angle. the sides of are the diameters of semicircles as shown. the area of the semicircle on equals , and the arc of the semicircle on has length . what is the radius of the semicircle on ?

### Answers

The **radius **of the semicircle having an arc of length equal to 8.5 [tex]\pi[/tex] in a right-angle triangle ABC is equal to 7.5 cm.

Given:

Angle ABC of triangle ABC is a right angle. The sides of ABC are the diameters of semicircles.

The area of the semicircle on AB equals 8[tex]\pi[/tex].

**Area **of a **semicircle **=** **[tex]\pi r^2/2[/tex]

Therefore:

[tex]\pi r^2/2[/tex] = 8[tex]\pi[/tex]

[tex]r^2 = 16[/tex]

[tex]r = 4[/tex]

Next, the arc of the semicircle on AC has a length of 8.5[tex]\pi[/tex].

Length of the arc of a semicircle = [tex]\pi r[/tex]

[tex]\pi r[/tex] = 8.5[tex]\pi[/tex]

[tex]r = 8.5[/tex]

Using **Pythagoras theorem**

[tex]8.5^{2} = 4^{2} + x^{2}[/tex]

[tex]x^{2} = 8.5^2 - 4^2\\[/tex]

[tex]x^{2} = 56.25[/tex]

[tex]x = \sqrt{56.25}[/tex]

[tex]x = 7.5[/tex]

The radius of the semicircle of BC = 7.5 Units.

Refer to this complete question for this:

Angle ABC of triangle ABC is a Right angle. The sides of ABC are the diameters of semicircles as shown. The area of the semicircle on AB equals 8pi and the arc of the semicircle on AC has a length of 8.5pi. What is the radius of the semicircle of BC?

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Graph x-3y=9

Helppppppoopppp

### Answers

**Answer:**

Slope: 1/3 ---- y-intercept: (0,-3)

**Step-by-step explanation:**

The coordinates of the vertices of trapezoid EFGH are E (-8, 8), F (-4, 12), G (-4, 0), and H(-8, 4). The coordinates of

the vertices of trapezoid E'F'GH' are E' (-8, 6), F' (-5, 9), G′ (-5, 0), and H' (-8, 3).

Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E'F'GH'?

### Answers

**Trapezoid **EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’. Option D is correct .

**What is a trapezoid simple definition?**

A **trapezoid**, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides.

A trapezium's parallel bases and **non-parallel legs** are referred to as its bases and legs, respectively.

1) We have and isosceles trapezoid DEFG and and another trapezoid D'E'F'G' dilated.

2) E'F'G'H' is not congruent to EFGH (due to its legs) Besides that, E'F'G'H has undergone not to rigid motions. Rigid motions are better known as translations and rotations and they preserve length and angles. That was not the case.

3) So it's d, the only correct choice:

d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

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The complete question is -

The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4). The coordinates of the vertices of trapezoid E’F’G’H’ are E’(-8, 6), F’(-5, 9), G’(5, 0), and H’(-8, 3). Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E’F’G’H’? a) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions. b) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions c) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

suppose you start with one penny and repeatedly flip a fair coin. each time you get heads, before the first time you get tails, your number of pennies is doubled. let x be the total number of pennies you have at the end. compute e(x).

### Answers

The total **number** of pennies you have at the end are 2^26 pennies

Imagine, at the first day have only one penny. Then tomorrow have 2 pennies, next day have 4 (2x2), next day have 8 (4x2), next day have 16 (8x2) and so forth.

**Geometric Sequence**

A geometric sequence is a** sequence** of numbers that follows a pattern were the next term is found by **multiplying** by a constant called the common ratio

It looks like geometric sequence (the ratio between the number of pennies that from the 2nd day and the 1st day is 2)

So, by using geometric sequence theorem can total those **pennies** until day 27

S (total pennies at day-27) = (1)(2^27-1) / 2-1 = 2^26 pennies

So, have 2^26 pennies.. a big number of pennies=))

The formula is: S = a( r^n-1) / r-1

a= the number of pennies that have got at the 1st day

n= number of days spent to collect those pennies)

r= the **ratio **of the number of pennies

2^26 pennies

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A graphs

relationship y = x on a coordinate plane.

She says the slope is 0 because there is no

coefficient. Find her mistake and correct it.

### Answers

**Answer:**

the slope is 1, the coefficient of x.

**Step-by-step explanation:**

You want to know the **mistake** in declaring the **slope of y=x is 0**, because there is **no coefficient**.

Coefficient

In algebra, **a coefficient of 1 is usually not written**. We let 1 times something be represented by the something itself. Its existence is indication there is one of it. No multiplier is needed.

y = x ⇔ y = 1·x

Whether the 1 is there or not, there is still exactly one 'x'.

So, the coefficient of x is 1 in y=x, meaning **the slope is 1, not zero**.

Find a power series representation centered at x=0x=0 for f(x)=x15x2+1f(x)=x15x2+1.Answer: f(x)=∑n=0[infinity](−1)n(15x2)n+1f(x)=∑n=0[infinity](−1)n(15x2)n+1.

### Answers

The power **series **representation for f(x)=x15x2+1f(x)=x15x2+1 is a series of terms of the form (−1)n(15x2)n+1, starting with x and going up to the nth power of x. The **coefficients **of each term are determined by alternating signs and multiplying the previous term by 15x2.

The power **series **representation for f(x)=x15x2+1f(x)=x15x2+1 can be calculated as follows: The first term is x, as this is the first power of x. The second **term **is -15x3, which is obtained by multiplying the first term by -15x2. The third term is 45x5, which is obtained by **multiplying **the second term by -15x2. The fourth term is -135x7, which is obtained by multiplying the third term by -15x2, and so on. This process is repeated for each successive term, **alternating **between multiplying the previous term by -15x2 and changing the sign.

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√ 7 x ( √ x − 7 √ 7 )

### Answers

The **expression **√(7x) × (√x − 7√7) in the **simplified form **will be x√7 − 49√x.

What is simplification?

Algebra is the **study **of abstract symbols, while **logic **is the manipulation of all those **ideas**.

The definition of **simplicity **is making something **simpler **to achieve or grasp while also making it a little **less difficult**.

The **expression **is given below.

⇒ √(7x) × (√x − 7√7)

**Simplify **the expression, then the **expression **is written as,

⇒ √(7x) × (√x − 7√7)

⇒ x√7 − 7 × 7√x

⇒ x√7 − 49√x

The **expression **√(7x) × (√x − 7√7) in the **simplified form **will be x√7 − 49√x.

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the length of the median trapezoid efgh is 17 centimeters. if the bases have lengths of 2x 4 and 8x-50 find the value of x

### Answers

The value of **X=8 **when the bases have lengths of 2x+4 and 8x-50

A **trapezoid **is a quadrilateral with exactly one pair of **parallel** sides. The parallel sides are called the **bases **of the trapezoid. The nonparallel sides are referred to as the legs of the trapezoid.

A **median** of a trapezoid is the segment that joins the **midpoints **of the nonparallel sides (legs). The median is also **parallel** to the two bases, and it is the average length of the two bases.

The **formula **to find the median is

**median=a+b/2**

where a and b are the lengths of the bases or **parallel **sides.

we have the values of a=2x+5 b=8x-50 m=17 now substitute the values in the above formula and we get x value:

(17)=2x+4+8x-50/2

17=10x-46/2

2(17)=10x-46

10x=80

**x=8**

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