What is the equation of the line graphed below?

Answer:

[tex]z^{5}[/tex] =  - 12 + 316 i

Step-by-step explanation:

Given that -

z = 3 + i

[tex]z^{2}[/tex] = [tex]( 3 + i )^{2}[/tex]

[tex]z^{2}[/tex] = 9 + [tex]i^{2}[/tex] + 6 i

[tex]z^{2}[/tex] = 9 - 1 + 6 i

[tex]z^{2}[/tex] = 8 + 6 i

[tex]z^{3}[/tex] = [tex]z^{2}[/tex] × z

[tex]z^{3}[/tex] = ( 8 + 6 i ) × ( 3 + i )

[tex]z^{3}[/tex] = 24 + 8 i + 18 i + 6 i²

[tex]z^{3}[/tex] = 24 + 26 i - 6

[tex]z^{3}[/tex] = 18 + 26 i

[tex]z^{5}[/tex] = [tex]z^{2}[/tex] × [tex]z^{3}[/tex]

[tex]z^{5}[/tex] = ( 8 + 6 i ) × ( 18 + 26 i )

[tex]z^{5}[/tex] = 144 + 208 i + 108 i + 156 i²

[tex]z^{5}[/tex] = 144 + 316 i -156

[tex]z^{5}[/tex] =  - 12 + 316 i

Step-by-step explanation:

The answer will be 380 inches as of what I have done

Answer:

12

Step-by-step explanation:

B is equal to -2, and D is equal to -6. A negative times a negative is a positive, and 2 x 6 = 12 (aka 6+6)

Answer:

[tex]\text{Area of quadrilateral QRST}=216[/tex]

Step-by-step explanation:

Please find the attached image for the quadrilateral QRST.

We have been given that [tex]QS=18 \text{ and } RT=24[/tex]. We are asked to find the area of quadrilateral QRST.

Upon looking at the image of quadrilateral QRST, we can see that quadrilateral QRST is a kite as it has one pair of diagonally opposite equal angles (98 degrees).

We know that area of kite is equal to half the product of its diagonal.

We can see from our image that QS and RT are diagonal of kite, so the area of quadrilateral QRST would be:

[tex]\text{Area of quadrilateral QRST}=\frac{QS\cdot RT}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=\frac{18\cdot 24}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=\frac{432}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=216[/tex]

Therefore, the area of quadrilateral QRST is 216 square units.

The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Step-by-step explanation:

The function transformations are defined as:

Shifting function upwards b units

[tex]f(x) => g(x) = f(x)+b[/tex]

Shifting functions to the left b units

[tex]f(x) => g(x) = f(x+b)[/tex]

Given function is:

[tex]g(x) = \frac{1}{x}[/tex]

Shifting the function 4 units to the left will give us:

[tex]g(x) => g(x+b)\\= \frac{1}{x+4}[/tex]

Now shifting the function 4 units upwards

[tex]g(x) = \frac{1}{x+4} + 4[/tex]

Simplifying

[tex]g(x) = \frac{1+x+4}{x+4}\\= \frac{x+5}{x+4}[/tex]

The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Keywords: function, transformations

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Answer:

Step-by-step explanation:

buying the windows and having them installed costs $ 7699.25

installation alone costs 3325

therefore, the cost of the windows is : 7699.25 - 3325 = 4374.25

and if they are paying 230.25 per window, then there is

4374.25 / 230.25 = 18.997 windows

let me check something...

18 * 230.25 = 4144.50

19 * 230.25 = 4374.75

if ur numbers are written correctly, they can only buy 18 windows.....they would be short 50 cents from buying 19 windows

To determine the number of windows the Rayhills purchased, the total cost minus the installation cost was divided by the cost per window, leading to an estimate of approximately 19 windows.

To find out how many windows Rayhills bought, we need to subtract the installation cost from the total cost and then divide the result by the cost per window. The total cost of buying the windows and having them installed is $7,699.25, and the company charges $3,325 for the installation. If each window costs $230.25, we can calculate the number of windows as follows:

Now let's perform the division:

$4,374.25 / $230.25 ≈ 19 windows (rounded to the nearest whole number since you can't buy a fraction of a window).

Therefore, the Rayhills bought approximately 19 windows.

Answer:

y-4=-2(x+4)

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

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

y-4=-2(x+4)

The equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]y = -2x - 4[/tex].

To find the equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex], we need to do the following steps:

Determine the slope of the given line:
The slope of the given line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]\frac{1}{2}[/tex].

Find the slope of the perpendicular line:
The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the given line is [tex]\frac{1}{2}[/tex], the slope of the perpendicular line will be [tex]-2[/tex] (since [tex]-1 \div \frac{1}{2} = -2[/tex]).

Use the point-slope form to find the equation:
The point-slope form of a line is [tex]y - y_1 = m(x - x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point on the line, and [tex]m[/tex] is the slope.
Here, the point is [tex](-4, 4)[/tex] and the slope [tex]m = -2[/tex].

Substituting these values into the point-slope form, we get:
[tex]y - 4 = -2(x + 4)[/tex]

Simplify the equation:
Distribute the slope on the right side:
[tex]y - 4 = -2x - 8[/tex]

Add 4 to both sides to solve for [tex]y[/tex]:
[tex]y = -2x - 4[/tex]

Answer:

-85

Step-by-step explanation:

Answer:

-85

Step-by-step explanation:

Answer:

1][tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]

2][tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]

3][tex]18\ degree+3x+3x=180\ degree[/tex]

4][tex]x=27[/tex]

Step-by-step explanation:

Given:-measure angle DCA = 18 degree

line AB II line DC

Solution:-

1] measure angle DCA and measure angle CAB are interior  alternate angles and interior alternate angles are equal.

[tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]------------------ (Equation 1)

Therefore the equation for statement number 1 is [tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]

2]Sum of interior angles of triangle is equal to 180 degree.

In Triangle ABC,

measure angle A+measure angle B+measure angle C=180 degree

Therefore the equation for statement number 2 is measure angle A+measure angle B+measure angle C=180 degree

3] In Triangle ABC,

[tex]measure\ angle\ B=3x---------------(Given)[/tex]

[tex]measure\ angle\ C=3x---------------(Given)[/tex]

[tex]measure\ angle\ A=18\ degree---------------(from\ equation\ [tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]

Now substituting the value of angles we get,

[tex]18\ degree+3x+3x=180\ degree-------------(Equation\ 2)[/tex]

Therefore the equation for statement number [tex]3\ is\ 18\ degree+3x+3x=180\ degree[/tex]

4] After solving the equation 2 we get,

[tex]18+3x+3x=180[/tex]

[tex]6x=180-18[/tex]

[tex]6x=162[/tex]

[tex]x=27\ degree[/tex]

Therefore value of [tex]x=27\ degree[/tex]

To calculate the probability of a student scoring 75% or above, count how many scores are 75 or higher, and then divide by the total number of scores. In this case, the probability is 6 out of 15, or 0.4.

The question asks about the probability that a student picked at random scored 75% or above based on a list of exam scores.

To find this probability, one must count the number of scores that are 75% or higher and divide by the total number of scores.

Out of the provided scores (61, 74, 60, 70, 83, 90, 90, 80, 100, 102, 28, 75, 98, 21, 49), we see that there are 6 scores that are 75 or above (83, 90, 90, 80, 100, 102, 98, 75).

Since there are 15 scores in total, the probability is calculated as -

= 6/15

= 0.4.

Answer:

The slope of f(x) is 1.5

Step-by-step explanation:

step 1

Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1

so

we have the points

(2/3,0) and (0,-1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-1-0}{0-2/3}[/tex]

[tex]m=\frac{-1}{-2/3}[/tex]

[tex]m=\frac{3}{2}=1.5[/tex]

step 2

Find the slope of the function graphed

take the points

(0,-1) and (3,6)  approximately

substitute in the formula

[tex]m=\frac{6+1}{3-0}[/tex]

[tex]m=\frac{7}{3}=2.33[/tex]

step 3

we know that

f(x) represents the function with the smaller slope

The smaller slope is 1.5

therefore

The slope of f(x) is 1.5

Answer:

5.4

Step-by-step explanation:

1350/250=5.4

Final answer:

A truck with a maximum capacity of 1350 pounds can carry 5 full 250-pound loads of dirt, as partial loads cannot be accommodated.

Explanation:

How many 250-pound loads of dirt can a truck carry?

To determine how many 250-pound loads of dirt a truck can carry if its maximum capacity is 1350 pounds, you need to divide the truck's maximum capacity by the weight of one load of dirt:

1350 pounds ÷ 250 pounds per load = 5.4 loads

Since the truck cannot carry a fraction of a load, it can carry a maximum of 5 full 250-pound loads of dirt before it reaches its weight limit.

Let X = the number of hours the server works.

The equation for the amount Nick spends is 15x + 47

The next job pays 14x + 54

Set the equations to equal and solve for x:

15x + 47 = 14x +54

Subtract 14x from both sides:

X + 47 = 54

Subtract 47 from both sides:

X = 7

Now replace x with 7 in the second equation:

14x + 54 = 14(7) + 54 = 98 +54 = 152

The job would pay $152 and be 7 hours long.

Answer:

Step-by-step explanation:

[tex]1+3+9+27+81\\\\a_1=1,\ a_2=3,\ a_3=9,\ a_4=27,\ a_5=81\\\\r=\dfrac{a_{n+1}}{a_n}\Rightarrow r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}\\\\r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=\dfrac{81}{27}=3[/tex]

Good evening ,

Answer:

Step-by-step explanation:

Since it’s a geometric series then

a₁ = 1 ( because 1 is the first term of the series)

3/1 = 9/3 = 27/9 = 81/27 = 3 then r=3.

:)

Answer:

No, it's not a counterexample, because 48 is a multiple of 8

Step-by-step explanation:

I think like 4 x 3 + 8 x 2 = 28 is a counterexample, because 28 is not a multiple of 8.

Perl's conjecture that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8 is incorrect. In fact, the sum would definitely be a multiple of 4 but not necessarily a multiple of 8, since the sum of integers multiplied by 4 does not guarantee that it's a multiple of 8.

The subject of this question is Mathematics, specifically dealing with number theory and the properties of multiples and factorization. Perl's conjecture is that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8. We can examine this by understanding how multiples work.

A multiple of 4 can also be considered as 4n, where n is an integer. Similarly, a multiple of 8 is 8m, where m is integer. If we add both, we get 4n+8m. Now, as per distributive property of multiplication over addition, the expression becomes 4n+4(2m), which can be further simplified as 4(n+2m).

We can now see that the sum is actually 4 times the sum of some integer, so it must indeed be a multiple of 4. However, since it's not necessarily the case that 'n+2m' itself is a multiple of 2, we cannot say that the overall sum is guaranteed to be multiple of 8.

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Answer:

Account C will give George at least a 4% annual yield.

Step-by-step explanation:

This problem can be solved by using simple maths formula given below

Year rate = (1+i)^n-1

where i = compounding rate and n = interval period

Now checking annual rate for each option using above formula

Account A)

Yr = 3.8% ( n= 12 and i= 3.75/12)

Account B)

Yr = 3.9 % ( n= 4 and i= 3.85/4)

Account C)

Yr = 4 % ( n= 365 and i= 3.95/365)

Answer:

4/3

Step-by-step explanation:

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

m=(-20-(-8))/(-12-(-3))

m=(-20+8)/(-12+3)

m=-12/-9

m=12/9

simplify

m=4/3

Answer:

Percent change is −31.19%.

Step-by-step explanation:

It is given that "a price of a dirt bike dropped from $872 to $600".

Initial price = $872

New price = $600

We need to find the Percent change.

[tex]\text{Percent change}=\dfrac{\text{New price - Initial price}}{\text{Initial price}}\times 100[/tex]

[tex]\text{Percent change}=\dfrac{600-872}{872}\times 100[/tex]

[tex]\text{Percent change}=\dfrac{-272}{872}\times 100[/tex]

[tex]\text{Percent change}=-31.19266[/tex]

[tex]\text{Percent change}\approx -31.19[/tex]

Therefore, the percent change is −31.19%.

Final answer:

The chance change in the price of the dirt bike is-31.2, indicating a  drop in price from$ 872 to$ 600.

Explanation:

To calculate the chance change in the price of a dirt bike that dropped from$ 872 to$ 600, we follow this formula given in the reference  Chance change = (( change in value)/( original value)) × 100  

First, we find the change in value, which is the new price abated from the original price $ 600-$ 872 = -$ 272  also, we divide this change by the original price  -$ 272/$ 872 ≈-0.312  

Eventually, to find the chance change, we multiply this bit by 100  -0.312 × 100 = -31.2  This means the price of the dirt bike  dropped by31.2.

The question is missing the table. So, it is attached below.

Answer:

The function is not linear. The student didn't evaluate the rate of change for the given points on the function.

Step-by-step explanation:

Given:

From the table, the set of points of the function are:

(-1, -5), (0, 0), (2,5), (3, 10), and (4, 15)

A function is said to be linear if the rate of change of the function is always a constant.

Rate of change for any two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, the rate of change for the points (-1, -5) and (0, 0) is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-(-5)}{0-(-1)}\\\\m=\frac{5}{1}=5[/tex]

Now, the rate of change for the points (0, 0) and (2, 5) is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-0}{2-0}\\\\m=\frac{5}{2}=2.5[/tex]

Hence, we can observe that, the rate of change is different for the given points. Hence, it is not a linear function.

Therefore, the student didn't evaluate the rate of change for the given points on the function.

A function is linear if the difference between y-values is constant when the difference between the corresponding x-values is constant. This is known as a constant rate of change and can be identified in a table of values for an x-y relationship. However, without the actual table's values, it's impossible to confirm its linearity.

In mathematics, a function is said to be linear if its graph forms a straight line. When analyzing a table of values, a function is linear if the difference between y-values is constant when the difference between the corresponding x-values is also constant. This is often called a constant rate of change.

For example, let's say we have an x-y table: for every 1 unit increase in x, if y increases by 2 units consistently, then the function represented by that table is linear. It directly satisfies the general definition of a linear function, y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.

However, without the actual values from the student's table, it's impossible to confirm whether the function is indeed linear. Always remember to check for a constant rate of change when reasoning about linearity.

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Answer:

y=-2/3x+20/3

Step-by-step explanation:

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

m=(4-6)/(4-1)

m=-2/3

y-y1=m(x-x1)

y-6=-2/3(x-1)

y=-2/3x+2/3+6

y=-2/3x+2/3+18/3

y=-2/3x+20/3

well 4 is basically 1/5 of 20, so that would be about 20%

and since 4 x 4 is 16, my guess is that 16 is 80% of 20

Answer: 80%

Step-by-step explanation: To answer the question what percent of 20 is 16, we translate the question into an equation.

So we have "what percent" that's x, "of 20" means times 20, "is 16" = 16. So now we have the equation (x)(20) = 16.

Now to solve for x, since x is being multiplied by 20, we need to divide by 20 on both sides of the equation. On the left side of the equation the 20's cancel and we have x and on the right side of the equation we have 16 divided by 20 which is 0.8.

Now, remember that we want to write our answer as a percent so we need to convert 0.8 into a percent.

We can convert a decimal into a percent by moving the decimal point two places to the right so we can change 0.8 to a percent by simply moving the decimal point two places to the right and we have 80%.

This means that 80% of 20 is 16.

To find the total number of people surveyed, you divide the number of people who chose chocolate (51) by the percentage that represents (0.68), resulting in 75 people surveyed.

The question posed involves determining the total number of people surveyed based on the percentage who favored chocolate ice cream. Since 68% of the people surveyed stated that chocolate was their favorite flavor, and it is known that 51 people chose chocolate, we can set up a proportion to find the total number of people surveyed. The proportion to find the total number of respondents (let's call it x) is as follows:

0.68 x = 51

To solve for x, you would divide both sides of the equation by 0.68, which gives you:

x = 51 / 0.68

x = 75 people

Therefore, the total number of people surveyed was 75.

Answer:

(x - 5)² + (y - 7)² = 169

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (5, 7), thus

(x - 5)² + (y - 7)² = r²

The distance from the centre to a point on the circle is the radius

Calculate the radius using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (5, 7) and (x₂, y₂ ) = (10, 19)

r = [tex]\sqrt{(10-5)^2+(19-7)^2}[/tex]

  = [tex]\sqrt{5^2+12^2}[/tex]

  = [tex]\sqrt{25+144}[/tex] = [tex]\sqrt{169}[/tex] = 13, hence

(x - 5)² + (y - 7)² = 169 ← equation of circle

You know that m<TSU=m<PSR because they make a vertical angle pair.

So...m<PSR=4x.

If, m<QSR=3x then m<PSQ=4x-3x=x because they are adjacent.

And, m<PQS=180-68=112 degrees (linear pair).

Now we know all the interior angles in triangle PQS so we can say that...

x+x+112=180 (sum of interior angles in triangle)

2x=68

x=34 degrees

The requried value of x is 34 in each case, as of the given conditions

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
As given in the question,

PU ∩ RT = S, Q ∈ PR

Since the sum of the remote interior angles is equal to the sum of the remote exterior angles.
∠SPQ + ∠PSQ = ∠SQR
∠PSQ = 68 - x

Now, When two lines intersect each other, their alternate angles are equal,
∠TSU = ∠PSR
4x = ∠PSQ + ∠QSR
4x = 68 - x + 3x
2x = 68
x = 34

Thus, the requried value of x is 34.

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The equivalent expressions to [tex]5^2/5^8[/tex] are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]

The expression[tex]5^2/5^8[/tex]can be simplified using the properties of exponents. When you have the same base raised to different exponents and they are being divided, you can subtract the exponents.

So, [tex]5^2/5^8 = 5^(^2^-^8^)[/tex] = 5^(-6).

Therefore, the equivalent expressions are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]

In mathematics, equivalent expressions are algebraic expressions that have the same value for all possible values of the variables involved

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The expression 5^2/5^8 simplifies to 5^-6 due to the laws of exponents that allow subtracting of exponents when dividing like bases.

The expression 5^2/5^8 can be simplified by understanding the laws of exponents. When dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator. By applying this law, the expression 5^2/5^8 simplifies to 5^(2-8) which equals 5^-6.

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Answer:

It's your friend at school. 8360 is your answer.

Step-by-step explanation:

88 + 88

= 176 + 88

= 264 + 88

= 352 + 88

= 440 + 88

= 528 + 88

= 616 + 88 =

704 x 88

= 8360

Answer:

8,360

Step-by-step explanation:

88 + 88 + 88 + 88 + 88 + 88 + 88 + 88 × 88 is our problem.

Instead of adding all of these 88's together, we will just multiply 88 by 8 because there are 8 of these 88's.

That will leave us with: 704

But that is not our answer.

We still have one more step, and it is to multiply 704 by 8.

After we do that we will have: 8,360 as our answer.

I hope this helps! :>

Answer:

15i+15

Step-by-step explanation:

(6+3i)(3+i)

18+9i+6i+3i^2

18+15i+3(-1)

18+15i-3

15i+15

After multiplyinh complex numbers (6+3i)(3+i), the final answer will be 15+15i.

To multiply complex numbers, we can use the distributive property.

First, distribute 6 to both terms of (3+i), giving us 18+6i.

Then, distribute 3i to both terms of (3+i), resulting in 9i+3i².

We can simplify 3i² by using the fact that i²=-1, so 3i²=-3.

Putting it all together, we have (6+3i)(3+i)

= 18+6i+9i-3

= 15+15i.

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Answer:

BC=16.992

Step-by-step explanation:

Answer:

16.992

Step-by-step explanation: