real number can be a complex number but a complex number can not be a real number, verified.

the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.

Not all** complex numbers **are real numbers, despite the fact that every **complex number** is a **real number**.

In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.

Mathematical proof:

Let z = a+bi, where a and b = real numbers.

Let z* =complex conjugate of z.

Then the magnitude (absolute value) of z is:

|z| = √(a²+b²).

And the value of z* is:

|z*| = √[a²+(-b)²] = √(a²+b²).

So |z| = |z*|.

This Completes the Proof.

what are **real numbers**?

its a quantity whose decimal expansion has an endless range. In contrast to the **natural numbers **1, 2, 3,... that result from counting,** real numbers** are utilised in measurements of continuously altering quantities such as size and time.

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∠1 and ∠2 are vetical angles. If m∠1 =(5x+12)° and m∠2 =(6x−11)°. m∠1=

**⇒Vertical angles are equal .**

**This means that ∠1=∠2**

**⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.**

[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]

x=23°

To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:

[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]

**∠1=127°**

Please answer all 3 questions in the photo for easy point! ( 30 points + Brainliest )

**Answer:**

6. **a** because a rectangle with sides 8 and 2 has a perimeter of 20** but **its area is 16.

7. **d** because 4 is an even number and it is a perfect square.

8. **b** because a pen can be used to write but is not a utensil.

**Step-by-step explanation:**

solve for v: -28 = v +-12

**Answer:**

**v = -16**

**Step-by-step explanation:**

Move the variable to the left-hand side and change its sign, so it would then be **-28 - v = -12**

Then move the constant to the right-hand side and change its sign, so it would become **- v = -12 + 28**

Then you would calculate the sum: **- v = 16**

After doing so, change the sides on both sides of the equation, **v = -16**

So, your answer should be **v = -16**

Ming had 59 birthday cupcakes. He gave 30 cupcakes to his classmates at school. Ming's family ate another 11 cupcakes at home.

How many cupcakes does Ming have left?

**Answer:18**

**Step-by-step explanation:**

59 - 30 - 11 = 18

59-30=29

29-11=18

18 cupcakes left

29-11=18

18 cupcakes left

What do the Zero Exporient and Negative Exponent Properties mean?

**Answer:**

**Step-by-step explanation:**

**Zero exponent numbers = 1**

When you try to multiply an exponent by zero, it equals one.

**Negative exponents is just a 1/x**

Negative just flips over the equation.

For example, 9^-1

1/9^1

1/9

**Answer:**

**Step-by-step explanation:**

Zero Exponent Property: **The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.**

**Example: x^0 = 1**

Negative Exponent Properties: **the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.**

** An example of negative exponents is **[tex]3^{-2}[/tex].

Kaylie is 6 years old. Her sister, Amanda is 2x younger. Kaylie is now 36. How old is Amanda?

In a case whereby Kaylie is 6 years old and Her sister, Amanda is 2x younger. Kaylie is now 36 the, Amanda age will now be **expressed **as **33 years.**

This implies that when Kaylie is 6 years old then her Her sister, Amanda will be 6/2 = 3 years old.

Then we were told again that ** Kaylie** is now 36, then the age of Amanda will now be (36-3)= 33 years

This is because when Kaylie was 6 years old , she was older by her sisiter by just just 3 years, which is still the same when she grown in age again, the 3 years interval is maintained.

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write and simplify a division expression to find the number of cups of flour max needs to use if he has just 1 egg

The **division** **expression** to find the number of **cups** of **flour** Max needs to use if he has only 1 **egg** is M ÷ N cups of flour.

1 egg = M/N cups of flour.

What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let M **cups** of **flour** be needed for N **eggs**.

This can be written as:

N **eggs** = M **cups** of **flour**

Divide both sides by N.

1 **egg** = M/N **cups** of **flour**

Thus,

The **division** **expression** to find the number of **cups** of **flour** Max needs to use if he has only 1 **egg** is M ÷ N cups of flour.

1 egg = M/N cups of flour.

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[Isosceles and Equilateral Triangles] Solve for x.

The required **value** of x is 34° in **figure** 4, x is 57° in figure 5, x is 81° in figure 6, x is 122° in figure 7, x is 65° in figure 8, x is 54° in figure 9, x is 90° in figure 10, x is 60° in figure 11, and x is 62° in figure 12.

What are the Equilateral Triangles?

In any **equilateral** **triangle**, the three **angles** are of equal measure and they equal 60 degrees.

As per **figure** 4,

x° + 56° + 90° = 180

x = 180 - 146

x = 34°

As per figure 5,

x = 57°

As per figure 6,

36 + 90/2 + 180-x = 180

36 + 45 - x = 180 - 180

x = 36 + 45

x = 81°

As per figure 7,

By the property of **Equilateral** Triangles

⇒ x = 180 - 58

⇒ x = 122°

As per figure 8,

By the property of **Isosceles** Triangles

x + 115 = 180

x = 180 - 115

x = 65°

As per figure 9,

6 + x + 60 + 60 = 180

x = 180 - 60 - 60 - 6

x = 54°

As per figure 10,

By the property of Equilateral Triangles

60/2 + 60 + x = 180

x = 180 - 60 - 30

x = 90°

As per figure 11,

By the property of **Equilateral** Triangles

2(30) + 60 + x = 180

x = 180 - 60 - 60

x = 60°

As per figure 12,

28 + 90 + x = 180

x = 180 - 118

x = 62°

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a design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. he knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. on three recent production batches, he tested service life on random samples of four headlamps, with these results: sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 what is the mean of the sampling distribution of sample means when the service life is in control? multiple choice 500 hours 515 hours 495 hours 250 hours 470 hours

The **mean** of the sampling distribution of sample means is 495 hours.

**What is the mean of the samples?**

The **mean** of samples is the average of a set of samples or data.

This can be calculated using the formula:

**Mean**= (Sum of terms)/(Number of terms)

Find the **mean** of each sample as shown below:

**Mean** service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]

= 500 hours

**Mean** service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]

= 515 hours

**Mean** service life of sample 3 = [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]

= 470 hours

Find the **mean** of the sampling distribution of sample means using the formula:

**Mean** of the sampling distribution (M)

=(Sum of **mean** of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the **mean** of the sampling distribution of sample means is 495 hours.

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The **mean** of the sampling distribution of sample means is 495 hours.

**What is the mean of the samples?**

The **mean** of samples is the average of a set of samples or data.

This can be calculated using the formula:

**Mean**= (Sum of terms)/(Number of terms)

Find the **mean** of each sample as shown below:

**Mean** service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]

= 500 hours

**Mean** service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]

= 515 hours

**Mean** service life of sample 3 = [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]

= 470 hours

Find the **mean** of the sampling distribution of sample means using the formula:

**Mean** of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the **mean** of the sampling distribution of sample means is 495 hours.

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The total surface area of this cuboid is 112 cm². Find the value of x. 10 cm length 2 cm width x height

**Answer:**

3 cm

**Step-by-step explanation:**

Given **dimensions **of the **cuboid**:

If the **total surface area **of the cuboid is 112 cm²:

[tex]\begin{aligned}\textsf{Total SA of cuboid}&= 2 (\sf lh +wh + lw)\\\implies 112&=2(10x+2x+10 \cdot 2)\\112&=2(12x+20)\\112&=24x+40\\24x&=72\\x&=3\end{aligned}[/tex]

Therefore, the **height **of the **cuboid **is **3 cm**.

Circle O has a circumference of 88π cm.

Circle O has a radius length of r.

What is the length of the radius of the circle?

The **length **of the **radius **of the circle is **44cm.**

This problem bothers on the mensuration of flat shapes, a circular shape.

Given data

**Circumference** of circle C= 88πcm

Radius of circle r=?

To find the length of the **radius** of the **circle**.

To solve for the radius let us apply the formula for the circumference of a circle

C=2πr

Substituting our given data

88π=2πr

Making r subject of formula we have

r= 88π/2π

r= 44cm

Hence, The **length **of the **radius **of the circle is **44cm.**

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Solve for x. Leave your answer in simplest radical form

**Answer:**

x = √213

**I would appreciate this being marked as brainliest... **

**Step-by-step explanation:**

This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.

That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.

We can use radicals to represent the common side.

Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.

a² + b² = c²;

Substitute the first triangle.

10² + 7² = c²;

100 + 49 = c²;

149 = c²;

c = √149;

Substitute the second triangle.

(√149)² + 8² = x²;

149 + 64 = x²;

213 = x²;

x = √213;

ANSWER QUICK FOR BRAINLIEST!!! THREE MATH QUESTIONS!!!

Question 10 (Multiple Choice Worth 2 points)

(One-Step Inequalities MC)

Write the inequality for the statement:

the difference between a number and seven eighths exceeds negative two thirds

f plus 7 over 8 is greater than 2 over 3

f minus 7 over 8 is less than or equal to negative 2 over 3

f minus 7 over 8 is greater than negative 2 over 3

f minus 7 over 8 is less than negative 2 over 3

Question 11 (Multiple Choice Worth 2 points)

(Adding and Subtracting Linear Expressions MC)

Simplify the expression.

the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths

negative 37 over 24 times j minus 17 over 12

negative 37 over 24 times j plus 17 over 12

43 over 24 times j plus 1 over 12

negative 43 over 24 times j plus negative 1 over 12

Question 13 (Multiple Choice Worth 2 points)

(Solving Two-Step Equations MC)

Solve the equation for x.

−0.28x − 15.3 = 1.92

x = 61.5

x = −61.5

x = 47.8

x = −47.8

1. The **inequality** for the statement is C. f minus 7 over 8 is greater than **negative** 2 over 3

2. The value of the **expression** is C. 43 over 24 times j plus 1 over 12.

3. −0.28x − 15.3 = 1.92 will be B. -61.5.

What is the inequality?1. The **difference** between a number and seven eighths exceeds **negative** two thirds is:

Let the number be f.

This will be:

f - 7/8 > -2/3

2. The **expression** negative one eighth j plus two thirds **minus** the expression five thirds j plus nine twelfths will be:

= -1/8j + 2/3 - 5/3j + 9/12

= -1/8j - 5/3j + 9/12 - 8/12

= -3/24j - 40/24j + 1/12

= -43/24j + 1/12

3. −0.28x − 15.3 = 1.92

Collect like **term**

−0.28x = 1.92 + 15.3

-0.28x = 17.22

x = 17.22 /- 0.28

x = -61.5

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Please help the Asap the question is in the picture

The** length **is **16.6ft** and the **width **is **8.9ft**

Area of the rectangular** area** = **Length × width**

A = LW … 1

If he wants to have a **rectangular **area of turf with length one foot less than 3 times the width, then

L = 3W - 1 … 2

Substitute 2 into 1

A = (2W-1)W

A = 2W^2 - W

Since area = 150sq.ft

150 = 2W^2 - W

2W^2 - W - 150 = 0

Factorize

2W^2 - W - 150 = 0

W = 1±√1+4(300)/2(2)

W = 1±√1201/2(2)

W = 1±34.655/4

W = 35.655/4

W = 8.91375

W = 8.9 (to nearest tenth)

Get the length

L = A/W

L = 150/8.9

L = 16.85

L = 16.6ft

Hence the** length is 16.6ft** and **the width is 8.9ft**

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Write an equation of the parabola in vertex form.

(-2, 6)

(-1,3)

The **equation of parabola** in vertex form is y=-3(x+2)^2+6

**What is parabola and equation of parabola in vertex form?**

**Parabola** is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the **parabola**, and the fixed line is called the **directrix** of the **parabola**.

The **equation of parabola** in vertex form is

y=a(x-h)^2+k

Given the vertex (-2,6) and (-1,3)

h=-2 and k=6

y=a〖(x+2)〗^2+6

To find the value of a at vertex (-1,3)

Put y = 3 and x = -1

3=a(-1+2)^2+6

3=a+6

a=-3

The **equation of parabola** is given by y=-3(x+2)^2+6

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ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D

Answer is 86.3 m from A to C

This is using 3.14 for pi and rounded to tenths

Step by step

First we will find the diagonal by using Pythagorean theorem a^2 + b^2 = c^2

We know the a & b sides, looking for c the hypotenuse or diagonal

40^2 + 70^2 = c^2

1600 + 4900 = c^2

6500 = c^2

80.6 = c = the full diagonal length.

Now we know the circle has a diameter of 10, so we subtract that from the diagonal length.

80.6 - 10 = 70.6m

Now we need to find the circumference of the circle using C = 2 TT r

We know the diameter is 10, so radius is half of that, so r=5

C = (2) (3.14) (5)

C = 31.4

Since we walk only half of the circle to get from A to C, we divide our circumference by 2.

31.4 / 2 = 15.7

So we have diagonal length of 70.6 + half the circle 15.7 for a total of 86.3m for the path as highlighted on the attachment

This is using 3.14 for pi and rounded to tenths

Step by step

First we will find the diagonal by using Pythagorean theorem a^2 + b^2 = c^2

We know the a & b sides, looking for c the hypotenuse or diagonal

40^2 + 70^2 = c^2

1600 + 4900 = c^2

6500 = c^2

80.6 = c = the full diagonal length.

Now we know the circle has a diameter of 10, so we subtract that from the diagonal length.

80.6 - 10 = 70.6m

Now we need to find the circumference of the circle using C = 2 TT r

We know the diameter is 10, so radius is half of that, so r=5

C = (2) (3.14) (5)

C = 31.4

Since we walk only half of the circle to get from A to C, we divide our circumference by 2.

31.4 / 2 = 15.7

So we have diagonal length of 70.6 + half the circle 15.7 for a total of 86.3m for the path as highlighted on the attachment

Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.

The **equation **y = 2/3x + 1 has a solution of (6, 5) and not (9, 8)

From the question, the equation is given as

y = 2/3x + 1

Also, we have the **ordered pairs **to be

(6, 5) and (9, 8)

For (6, 5), we have

x = 6 and y = 5

So, the **equation **becomes

5 = 2/3 x 6 + 1

Evaluate

5 = 5 --- true

For (9, 8), we have

x = 9 and y = 8

So, the **equation **becomes

8 = 2/3 x 9 + 1

Evaluate

8 = 7 --- false

Hence, (6, 5) is part of the **solution **and (9, 8) is not

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Samir and Elizabeth deposit $600.00 into a savings account which earns 1% interestcompounded quarterly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?nt)"Use the formula A = P 1 + , where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.$

To determine a compound Interest

The above formular is for solving compound interest

[tex]\begin{gathered} P\text{ = Principal = \$600, A = Amount , r = rate = 1 \% = 0.01 } \\ n\text{ = number of times quartely = }\frac{12}{4}=3\text{ , t = time in years = 2} \end{gathered}[/tex][tex]\begin{gathered} A\text{ = P ( 1 + }\frac{r}{n})^{nt} \\ A\text{ = \$ 600 ( 1 + }\frac{0.01}{3})^{3x2} \\ A=600(1+0.003)^6 \end{gathered}[/tex][tex]\begin{gathered} A=600(1.003)^6 \\ A\text{ = 600(1.020167)} \\ A\text{ = 612.1}002 \\ A\text{ = 612.10 (nearest cent)} \end{gathered}[/tex]**Hence the compound interest = ****612.10 ****(nearest cent)**

Find (a) f(-8) and (b) f(3).

(a) f(-8)=

(b) f(3) =

**Answer:**

[a] 15

[b] 13

**Step-by-step explanation:**

We can use the **visual diagram **given to **solve**. We can see that when you **input **-8 (on the left side) the arrow leads to the **output **15, our answer.

We use the same **method **for part b. When you **input **3 (on the left side) the **arrow **points to 13 (on the right side) giving us an answer of 13.

What is the equation of the line below?

**Answer: Y = -2x + 1**

**Step-by-step explanation:**

The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.

in the united states, the mean birth weight for boys is kg, with a standard deviation of kg. assuming that the distribution of birth weight is approximately normal, complete parts a through e.

The **proportion **of baby boys in the United States that are born with low birth weight is 0.0495

In a set with **mean **u and standard deviation σ , the z score of a measure X is given by:

Z= X - u / σ

Z = 2.5- 3.41/ 0.55

Z= -1.6545

Z= -1.65 has a p value of 0.0495

The **proportion **of baby boys in the United States that are born with low birth weight is 0.0495.

**the complete question is**

In the United States, the **mean **birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What **proportion **of baby boys in the United States are born with low birth weight

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Please help super confused ASAP.

Find f(-9) if f(x) = -2x + 5.

Enter DNE if the value does not exist.

f(-9)=

Work Shown:

f(x) = -2x+5

f(-9) = -2(-9)+5

f(-9) = 18+5

f(-9) = **23**

donuts are sold in bags and cartons. a bag holds four donuts and a carton holds 10 donuts. tom buys b bags of donuts and c cartons of donuts. he buys a total of t donuts. write down a formula for t in terms of b and c

**Answer:**

t = b+ c

total = bags + cartons

2b+3=7

2z+2=8

6b+2=14

7d−3=18

**Answer:**

b=2

z=3

again b=2

d=3

**Step-by-step explanation:**

don't know what to explain

What real-world knowledge did you use to understand the STEM Task?

The **real world knowledge **we use to understand the **STEM task** are :

A) STEM integrates it's **concepts and applications** to real life.

B) STEM helps in** finding solution** to the practical issues.

C) **Focuses on** building models and replicating scenarios.

**What is STEM ?**

**STEM education **refers to the **integrated teaching and learning **of the subjects such as science, technology, engineering, and mathematics.

We know that **STEM** teaches **critical thinking skills **and instills a passion for innovation. Beyond the **advantages** of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.

The real world knowledge we use to understand the STEM task is as follows :

STEM education stresses the application of knowledge to real-life situations whileTherefore , the **real world knowledge **we use to understand the **STEM task** are :

A) STEM integrates it's **concepts and applications** to real life.

B) STEM helps in** finding solution** to the practical issues.

C) **Focuses on** building models and replicating scenarios.

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Help I don’t understand what’s happening

Solution of **Square root**, x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30

Solution of **Cube root**, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30

Given,

Square root x² = 30

Then, the** value** of:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

x = ∛30 = ∛30² = 3.107

x = -∛30 = -∛30² = -3.107

Now,

Cube root, x³ = 30

x = √30 = √30³ = 164.317

x = -√30 = -√30³ = -164.317

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

Therefore,

Solution of** Square root**, x² = 30:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

Solution of **Cube root**, x³ = 30:

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

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HELPP Determine which integer will make the inequality 5x + 12 > 2x + 6 false.

S:{−3}

S:{3}

S:{−1}

S:{1}

The response of Africans to the challenges of modernity as revealed is as follows: Alteration of self-image: It is a stereotype that the people of Africa are still living in the past. We'll, not only Africa but also Asia has always taken a hold of their tradition

A $1,000 deposit is made at a bank that pays 12% compounded

How much will you have in your account at the end of 10

monthly.

years?

**Answer- 3,315.53007332**

**Step-by-step explanation:**

In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .

At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have

displaymath228

9. Find the area of the shaded region.

22 cm

10 cm

7 cm

Answer: 255cm2

Explanation: see photo

Explanation: see photo

What is the value of x in the equation −x = 6 − 3x + 8?−14−7147

**S={7}**

1) Let's solve for x, for the given equation :

-x = 6 -3x +8 *Add 3x to both sides*

**3x**-x=-3x**+3x **+6 +8

2x =14 *Divide both sides by 2*

x= 7

**S={7}**

**And that is the answer**

make a list of narrators and subject of mini sagas
Please help me its due today!!!!
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help me i need a good grade on this
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