5.8x - 1.4 = 16 What is the solution of the equation

Write z = -8 in polar form:

\(z = -8 = 8e^{i\pi}\)

Then the cube roots of z are

\(z^{1/3} = 8^{1/3} e^{i\left(\frac{\pi+2n\pi}3\right)\)

where n ∈ {0, 1, 2}, or

\(z^{1/3} \in \left\{8^{1/3} e^{i\pi/3}, 8^{1/3} e^{i\pi}, 8^{1/3} e^{i\,5\pi/3}\right\} \\\\ z^{1/3} \in \left\{2 \left(\dfrac12 + i\dfrac{\sqrt3}2\right), -2, 2 \left(\dfrac12-i\dfrac{\sqrt3}2\right)\right\} \\\\ \boxed{z^{1/3} \in \left\{1+i\sqrt3, -2, 1-i\sqrt3\right\}}\)

Based on the given data on the average fuel cost to travel in the city and on the highway, the individuals in this data set are vehicles.

The types of variables given when matched correctly are:

Individual variables:

Categorical variables:

Quantitative variables:

The individual variables will be the vehicle names and models because they represent the individual subjects of interest.

The categorical variables group the types of vehicles into vehicle class and transmission type.

Quantitative variables are those that can be measured in quantitative units and so include the number of cylinders and annual fuel cost.

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Answer:

REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEeeeeEEEEEEEEEEEEeeeeeee make sure you thank it.

Step-by-step explanation:

Answer:

with those u can't lol but it's 6 11 and 13

Answer:

Inverse property

Step-by-step explanation:

Answer:

any number

Step-by-step explanation:

Answer:

Step-by-step explanation:

-3(2x-7) + 2y + 2 (x+y)

-6x+42 + 2y + 2x + 2y

Take the same coefficents and subtract or add

-6x + 2x= -4x

2y + 2y= 4y

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

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The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

Answer:

x≥-6

Step-by-step explanation:

The rectangle has a length of 8 units along the top and bottom sides, and a height of 6 units along the vertical sides.

A rectangle is a four-sided flat shape with four right angles (90 degree angles) between the sides. It is a type of quadrilateral, which means a shape with four sides.

To find the length of the sides of the rectangle, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

Using the coordinates (-4,4) and (4,4) for the two endpoints of the top side of the rectangle, we get:

d = √((4 - (-4))² + (4 - 4)²) = 8

Since the top side has length 8 and there are two top and two bottom sides of equal length, the perimeter is:

20 = 28 + 2L

where L is the length of one of the vertical sides. Solving for L, we get:

L = (20 - 2*8)/2 = 2

Therefore, the length of the vertical sides of the rectangle is 2 units.

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The length of rectangle is 8 units on the x-axis, and the width of rectangle is 4 units along the y-axis.

The whole distance encircling a rectangle's edge is known as its perimeter. It is the total of the measurements of the rectangle's four sides.

The formula for calculating the perimeter P of a rectangle with length L and width W is as follows:

P = 2L + 2W

According to question:

To find the length of the sides of the rectangle, we can use the distance formula:

\(d = \sqrt{((x_{2} - x_{1} )^2+ (y_{2} - y_{1})^2)}\)

Using the coordinates (-4, 4) and (4, 4)

\(d = \sqrt{((4 - (-4) )^2+ (4 - 4)^2)}\) = 8 units

L (length) = 8 Units

So, the length of the horizontal sides (x-axis) of the rectangle is 8 units.

then, the top side has length 8 and there are top and bottom sides are equal length, the perimeter is: P = (8+8) + 2W

20 = 16 + 2W

where, L is the length of one of the vertical sides. Solving for L, we get:

W = (20 - 16)/2 = 2

So, the length of the vertical sides (y-axis) of the rectangle is 2 units.

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Answer:

b and d

Step-by-step explanation:

edge 2021

If the first term (a) is 4 and the common ratio (r) is 0.9, then the sequence diverges. Then the correct option is D.

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

a, ar, ar², ar³, ...

The sequence is given below.

\(\rm a_n = 4 (0.9)^n\)

Then the sum of the sequence will be given as

The first term (a) is 4. And the common ratio (r) is 0.9.

Then we get

\(\rm S_n = \dfrac{a (1 - r ^n)}{ (1 - r)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{ (1 - 0.9)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{0.1}\\\\\rm S_n = 40 (1 - 0.9^n)\)

For n = 1, we have

S₁ = 40 (1 - 0.9)

S₁ = 40 x 0.1

S₁ = 4

For n = 2, we have

S₂ = 40 (1 - 0.9²)

S₂ = 40 x 0.19

S₂ = 7.6

For n = 3, we have

S₃ = 40 (1 - 0.9³)

S₃ = 40 x 0.271

S₃ = 10.84

If the common ratio is less than one then the sequence will diverge.

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Answer: \(0\leq x\leq 2\)

Step-by-step explanation:

\(460-270.71-3.09*4-33.71=143.22\)

After all his purchases, he has $143.22 left. Outfits cost $68.20 each.

\(143.22/68.20=2.1\)

He has enough to buy at most, 2 outfits.

So, your inequality would be

\(0\leq x\leq 2\)

Answer:

v

Step-by-step explanation:

v

on solving the provided question, we can say that by equation we Consequently, he will sell 16 automobiles at this price.

A number, a variable, or a mix of both, combined with certain operation symbols, make up an expression. An equal sign is used to denote the separation of two expressions in an equation.

Here,

Given: Number of cars sell in a day = 12

Price of a car =\($23,000\)

For each $300 price reduction dealer can sell two more cars per day.

Solution: Let there be x unit 300 price reduction

2x unit increase in sale of car

\(|R(x)=(15000-300x)(12+2x)\)

Cost

\(|C(x)=1000+12000 (12+2x)\)

Profit

\(|P(x)=(15000-300x)(12+2x)-1000+12000 (12+2x)\\15000(12+2x)–12000 (12+2x)-300x(12+2x)-1000\\=180000-144000+30000x-24000x -3600x -600-1000\\=36000+2400x-600 = P'(x)=-1200x +2400 = P"(x)=-1200\)

For critical points

\(P'(x)=0= -1200x + 2400=0= x=2\)

Since P"(x) <0at x = 2it is max profit 12+2x=12+2(2)=16

16cars per day he will sell

\(Price = 15000-300*16 = $10200\)

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An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.

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Answer:

Yes, these triangles are congruent

∠E≅∠M

Step-by-step explanation:

Yes, these triangles are similar.

Proof:

Each side in LNM is \(1\frac{2}{3}\) times longer than the sides in GFE

\(30/18 = 1\frac{2}{3}\)

\(25/15=1\frac{2}{3}\)

\(20/12 = 1\frac{2}{3}\)

According CPCTC (corresponding parts of congruent triangles are congruent), angle E is similar to angle M.

Hope this helps :)

Have a good day!

Answer:

415people

Step-by-step explanation:

20%of250=100people

15%of the 100people=15people

So 100 went out remaining(500-100)400

Then 15 returned=400+15

415

Answer:

458 people in the building now.

Step-by-step explanation:

20%x500/2 = 20% x 250=50

15% x 50 = 7.5

7.5 + (500 - 50) =457.5 =458people.

Tell me if it's correct plz.

Hope this helps..

Answ32fn333w3243333

Step-by-step explanation:

euefuehgegwhed

The reflection of points P(-4, 1), Q(-2,-8), and R(8, -1) across y-axis is P'(4, 1), Q'(2, -8) and R'(-8, -1).

Option (C) is correct.

Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.

The given points are,

P(-4, 1), Q(-2,-8), and R(8, -1).

The reflection of point A(x, y) is (-x, y).

Implies that, coordinate of x axis changes and coordinate of y axis remains same.

Reflection of P(-4 , 1) = P'(4, 1)

Reflection of Q(-2, -8) = Q'(2, -8)

And reflection of R(8, -1) = R'(-8, -1)

So the required points are P'(4, 1), Q'(2, -8) and R'(-8, -1).

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Answer:

24

Step-by-step explanation:

Area of the 1st upright rectangle: 3x4=12

Area of 2nd rectangle: rectangle: 6x1=6

area of triangle: ((1st leg)x(2nd leg))/2=(4x3)/2=6

1st leg=4

2nd leg=6-3=3

12+6+6

24=area

Hope this helps :)

\(\huge\boxed{Hi\;there!}\)

Thirty-four thousand ninety-seven and six thousandths looks like so: (If we write it numerically)

34,097.006

That's the way to write this number numerically.

\(\huge\bold{Hope\;it\;helps!\;Good\;luck!}\)

\(\rm{-StillEnjoyingLife-\)

Answer:

Answer: She can make 9 steps from the rope.

Step-by-step explanation:

Given : The width of each step of the ladder = 2\dfrac{1}{3}\text{ feet}2

3

1

feet = \dfrac{2(3)+1}{3}=\dfrac{7}{3}\text{ feet}

3

2(3)+1

=

3

7

feet

The length of the rope = 21 feet

Then , the number of required steps = ( length of the rope ) ÷ (width of each step of the ladder)

=21\div\dfrac{7}{3}=21÷

3

7

=21\times\dfrac{3}{7}=3\times3=9=21×

7

3

=3×3=9

Hence, the number of steps can she make from the rope = 9.

Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

Solving steps:

\(\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}\)

\(\sf P(HH|C) = \dfrac{4 }{10}\)

\(\sf P(HH|C) = \dfrac{2 }{5}\)

Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.

It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.

It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.

Hence, an example of a number that is ten times greater is; 10 × 80,000.

Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

5y + 8

and

8y +5 are the same solutions.