Answer:
See explanation
Step-by-step explanation:
The given complex number are:
[tex]z_1=-3\sqrt{3}+3i[/tex]
and
[tex]z_2=6\cos 150\degree+6i\sin 150\degree[/tex]
When we rewrite [tex]z_1=-3\sqrt{3}+3i[/tex] in complex form, we obtain;
[tex]z_1=r(\cos \theta+i\sin \theta)[/tex]
where
[tex]r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6[/tex]
and
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]
[tex]\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree[/tex]
Hence,
[tex]z_1=6(\cos 150\degree+i\sin 150\degree)[/tex]
[tex]z_1=6\cos 150\degree+6i\sin 150\degree[/tex]
Hence
[tex]z_1=z_2[/tex]
What is the value of x?
Answer:
X= O.8 or 10 over 12.5
Step-by-step explanation: Hope this helps darling
In triangle XYZ, angle Z is a right angle. If sinX=3/4, find tanY.
ANSWER
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
EXPLANATION
[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]
[tex]\sin(x) = \frac{3}{4} [/tex]
This means the opposite side is 3 units and the hypotenuse is 4 units.
We use Pythagoras Theorem to find
[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{ |ZX| }^{2} +9=16[/tex]
[tex]{ |ZX| }^{2} =16 - 9[/tex]
[tex]{ |ZX| }^{2} = 7[/tex]
[tex]{ |ZX| } = \sqrt{7} [/tex]
[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
Final answer:
Given sin(X) = 3/4 in a right-angled triangle XYZ, by using trigonometric identities and the Pythagorean theorem, we find that tan(Y) is 1/3.
Explanation:
In triangle XYZ with angle Z being a right angle (90 degrees or π/2 radians), if we are given that sin(X) = 3/4, we can use trigonometric identities to find tan(Y). Since sin(X) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, we have a side opposite angle X which is 3 units long and a hypotenuse that is 4 units long. From this, we can deduce that the side adjacent to angle X, which is also the side opposite to angle Y, is 1 unit long (using the Pythagorean theorem, as the square of the hypotenuse is equal to the sum of the squares of the other two sides: 3² + 1² = 4²).
Now, to find tan(Y), which is the ratio of the side opposite to Y to the side adjacent to Y, we just take the length of the side opposite to X (which is the same as the side adjacent to Y) and the length of the hypotenuse. Therefore, tan(Y) = opposite side / adjacent side, which in this case is 1/3.
What is the selling price of a dining room set at Macy’s? Assume actual cost is $870 and 51% markup on selling price.
$1313.70 is the answer after a 51% markup
Final answer:
The selling price of a dining room set with a 51% markup on the selling price, and an actual cost of $870, is calculated to be $1775.51.
Explanation:
To determine the selling price of a dining room set with a 51% markup on the selling price based on the actual cost of $870, we first need to recognize the markup is on the selling price and not on the cost. Let the selling price be represented by the variable S. The markup can be represented by S multiplied by 51% (or 0.51), so we have:
Actual Cost + Markup = Selling Price
$870 + (0.51 × S) = S
To solve for S, we need to isolate it on one side of the equation:
$870 = S - (0.51 × S)
$870 = S(1 - 0.51)
$870 = S(0.49)
Now we divide both sides by 0.49 to solve for S:
S = $870 / 0.49
S = $1775.51
Therefore, the selling price of the dining room set at Macy's is $1775.51.
What is the r value of the following data to three decimal places x y 4 2 5 9 8 10 9 12 13 23
Answer:
0.953081279
Step-by-step explanation:
we have been given the following data set;
x; 4, 5, 8, 9, 13
y; 2, 9, 10, 12, 23
We are required to determine the r value of the data set.The r-value is the correlation coefficient that is used to measure the degree of association between two variables. It gives us information on the strength and direction of the association.
We can easily compute r in Ms. Excel;
We first enter the data into any two adjacent columns of an excel workbook.
Then we proceed to type;
=CORREL
into any blank cell. This is an in-built function that computes the correlation coefficient. Ms. Excel returns a value of 0.953081279
as the r value
Answer:
The value of r is 0.953.
Step-by-step explanation:
The correlation coefficient i.e. r is calculated by the formula,
[tex]r=\dfrac{n\sum{xy}-(\sum x)(\sum y)}{\sqrt{(n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2)}}[/tex]
where n=5 is the sample size.
We create a table of required values,
x y x² y² xy
4 2 16 4 8
5 9 25 81 45
8 10 64 100 80
9 12 81 144 108
13 23 169 529 299
∑ 39 56 355 858 540
Substitute the values in the formula,
[tex]r=\dfrac{5\times 540-(39)\cdot (56)}{\sqrt{(5\times 355-(39)^2)(5\times 858-(56)^2)}}[/tex]
[tex]r=\dfrac{2700-2184}{\sqrt{(254)(1154)}}[/tex]
[tex]r=\dfrac{516}{\sqrt{293116}}[/tex]
[tex]r=\dfrac{516}{541.4018}[/tex]
[tex]r=0.9530[/tex]
Therefore, the value of r is 0.953.
it takes 23 minutes for 6 people to paint 6 walls
To find out how many minutes it takes for 1 person to paint 1 wall, we can set up a proportion using the rate of 6 people painting 6 walls in 23 minutes. Cross-multiplying and solving for the unknown, we find that it would take approximately 3.83 minutes for 1 person to paint 1 wall.
Explanation:This question falls under the subject of Mathematics and is suitable for students in Middle School. To solve this problem, we can use the concept of rate. We know that 6 people can paint 6 walls in 23 minutes.
We can set up a proportion to find out how many minutes it would take for 1 person to paint 1 wall. Let x represent the unknown time:
6 people / 23 minutes = 1 person / x minutes
Cross-multiplying, we get 6x = 23. Dividing both sides by 6, we find that x = 23/6. Therefore, it would take approximately 3.83 minutes for 1 person to paint 1 wall.
Remember to always read the question carefully and identify the given information and the unknown variable in order to solve the problem accurately.
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The time that it would take for 8 people to paint the walls would be 18 minutes.
How to find the time taken ?The number of walls painted is proportional to the number of people painting, and the time it takes to paint the walls is inversely proportional to the number of people painting.
Using the following formula, we can calculate the amount of time it will take 8 people to paint the 6 walls:
Time = (Number of walls) / (Number of people) * Time per wall
Time = (6 walls) / (8 people) * 23 minutes/wall
Time = 18 minutes
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The full question is:
It takes 23 minutes for 6 people to paint 6 walls. How long would it take 8 people to paint those same 6 walls
What whole number comes right before 105?
Answer:
104
Step-by-step explanation:
Answer:
104
Step-by-step explanatio
What is The 12th term in the sequence ?
Answer:
-26
Step-by-step explanation:
Plug in 12 for n.
-4-2(12-1)
-4-2(11)
-4-22
-26
-26 !!!!!!!!!!!!!!!!!!!!!
Suppose the sides of a traingle have the given measures. Classify the triangle by its sides. 3a, 3a, 5a
Answer:
Obtuse isosceles
Step-by-step explanation:
Two sides are the same length, so we know this is an isosceles triangle.
To determine if it's acute, right, or obtuse, we can compare it to a right triangle using Pythagorean Theorem:
c² = a² + b²
c² = 3² + 3²
c² = 18
c = √18
So if this were a right triangle, c would be √18, which is somewhere between 4 and 5.
Since the long side is greater than √18, we know this must be an obtuse triangle.
So this is an obtuse isosceles.
Write an equation in standard form of an ellipse that is 50 units high and 40 units wide. The center of the ellipse is (0,0).
Answer:
[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]
Step-by-step explanation:
The equation of an ellipse that has its center at the origin is given by the formula:
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
The given ellipse is 50 units high.
This means that length of the major axis is 50.
[tex]2a=50[/tex]
[tex]2\implies a=25[/tex]
The ellipse is 40 units wide.
[tex]2b=40[/tex]
[tex]\implies b=20[/tex]
We substitute these values into the formula to get:
[tex]\frac{x^2}{20^2}+\frac{y^2}{25^2}=1[/tex]
[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]
Can someone give me a decent explanation on how you came up with your answer. Thanks!
Answer:
the correct option is C.
Step-by-step explanation:
The x-intercept of both functions g(x) and f(x) occur at point (1, 0).
Now, we need to find where g(x) > f(x) and f(x) > g(x)
We know that the greater the base of a logaritmic function is, the faster it will grow/decay.
For that reason, we can say that g(x) > f(x) on (1, +inf).
Now, when x<1 then y<0. So on the interval (0, 1) the function g(x) will decay much faster than the function f(x), so we can say that f(x) > g(x) on (0, 1). So the correct option is C.
Check the graph, to verify all this.
Which statements can be used to describe the original functions f(x) and g(x)? Select three options. (See picture attached) PLEASE ANSWER QUICKLY I AM TIMED!!!!
Options 1, 2, and 3 are valid based on the given information and calculations.
1. When added, the sum of the y-intercepts must be 8:
- If the y-intercepts are denoted as b₁ and b₂ for f(x) and g(x) respectively, then . [tex]b_1 \times b_2 = 8[/tex].
2. When multiplied, the product of the y-intercepts must be 8:
- This translates to [tex]b_1 \times b_2 = 8[/tex].
3. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change:
- This implies that the slopes of the lines have opposite signs.
Checking the given U-turn points (-2, 8) and (8, 2). The slope (rate of change) between these points can be calculated as:
[tex]\[ m = \frac{change\:in\:y}{change\:in\:x} \][/tex]
[tex]\[ m = \frac{2 - 8}{8 - (-2)} = \frac{-6}{10} = -\frac{3}{5} \][/tex]
4. f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3:
- This statement is inconsistent with the calculated slope.
5. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1:
- This statement is also inconsistent with the calculated slope.
Therefore, options 1, 2, and 3 are valid based on the given information and calculations.
Answer:
1 When multiplied the product of the y intercepts must be 8
2 Either f(x) or g (x) has a positive rate of change and the other has a negative rate of change
3 f (x) could have a rate of change equal to 2 and g (x) could have a rate change of -1
What is a1 for the geometric sequence for which a8= -3584 and a3 = 112 ?
Answer:
The first term is 28.
Step-by-step explanation:
Given: 8th term of Geometric sequence , [tex]a_8=-3584[/tex]
and 3rd term of Geometric Sequence, [tex]a_3=112[/tex]
We have to find First term of given geometric Sequence.
Let a be the first term of geometric sequence.
We know that,
[tex]a_n=ar^{n-1}[/tex]
So,
[tex]\frac{a_8}{a_3}=\frac{ar^{8-1}}{ar^{3-1}}=\frac{-3584}{112}[/tex]
[tex]\frac{r^{7}}{r^{2}}=-32[/tex]
[tex]r^5=-32[/tex]
[tex]r=-2[/tex]
So, 3rd term = 112
a × (-2)² = 112
a = 112 / 4
a = 28
Therefore, The first term is 28.
Answer:
1 and a8 =16,384
Step-by-step explanation:
Three cars are driving on a racetrack. The mean speed of the three cars is 100 miles per hour. Car X drives 109 miles per hour and Car Y drives 111 miles per hour. Use the mean to estimate the speed of Car Z. Then find the actual speed of Car Z.
Estimate the speed of Car Z. Choose the correct answer below.
A.
The speed of Car Z is about 100 miles per hour.
B.
The speed of Car Z is less than 100 miles per hour.
C.
The speed of Car Z is greater than 100 miles per hour.
D.
It is impossible to estimate the speed of Car Z.
Answer:
B
Step-by-step explanation:
The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 109, 111, and Z or unknown. The mean of them is 100. Solve for Z.
100 =(109+111+Z)/3
300=220+Z
80=Z
The speed of Car Z is less than 100.
The correct answer is B. The speed of Car Z is less than 100 miles per hour.
To estimate the speed of Car Z, we can use the given mean speed of the three cars. The mean speed is given as 100 miles per hour. Since Car X is driving at 109 miles per hour and Car Y is driving at 111 miles per hour, both of these speeds are above the mean. To maintain an average of 100 miles per hour, Car Z must be driving at a speed less than 100 miles per hour to balance the speeds of Car X and Car Y, which are pulling the average up.
To find the actual speed of Car Z, we can use the formula for the mean speed of the three cars:
[tex]\[ \text{Mean speed} = \frac{\text{Speed of Car X} + \text{Speed of Car Y} + \text{Speed of Car Z}}{3} \][/tex]
Given that the mean speed is 100 miles per hour, we can plug in the known values and solve for the speed of Car Z:
[tex]\[ 100 = \frac{109 + 111 + \text{Speed of Car Z}}{3} \][/tex]
Multiplying both sides by 3 to clear the denominator:
[tex]\[ 300 = 109 + 111 + \text{Speed of Car Z} \][/tex]
Adding the speeds of Car X and Car Y:
[tex]\[ 300 = 220 + \text{Speed of Car Z} \][/tex]
Subtracting 220 from both sides to isolate the speed of Car Z:
[tex]\[ \text{Speed of Car Z} = 300 - 220 \] \[ \text{Speed of Car Z} = 80 \text{ miles per hour} \][/tex]
Thus, the actual speed of Car Z is 80 miles per hour, which confirms our initial estimation that it is less than 100 miles per hour.
please help i’m so confused asap!!!!!
Answer:
I would say the second car.
Step-by-step explanation:
372/15.2 = 24 miles per gallon
198/7.2 = 27.5 miles per gallon
So the answer is the second car is better on gas mileage!
70 -7.7 show your work
The simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
The number expression is:
= 70 -7.7
The expression can be defined as the combination of constants and variables with mathematical operators.
Using the rule of BODMAS
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.
On simplification
= 62.3 [after subtracting 7.7 from 70]
Thus, the simplification form of the number expression 70 -7.7 is 62.3 after using the concept of the BODMAS the answer is 62.3.
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Final answer:
To subtract 7.7 from 70, align the decimal points and subtract to find the result is 62.3.
Explanation:
The problem at hand requires us to subtract a decimal number from a whole number. Here's the step-by-step calculation for 70 - 7.7:
Write the numbers one under the other, aligning the decimal points: 70.0Therefore, the subtraction of 7.7 from 70 gives us 62.3.
what is the area of a cirlce with the diameter of 42ft
____________________________________________________
Answer:
Your answer would be 1,385.44 ft²
____________________________________________________
Step-by-step explanation:
To find the area of a circle, we would use the equation [tex]\pi r^2[/tex]
In this case we have the diameter, and that's 42.
The radius of a circle is half of the diameter, therefore the radius would be 21.
Now we know the radius,we can plug that in to our equation.
Your equation should look like this:
[tex]\pi (21)^2[/tex]
Pi would be 3.14159
Now, you can solve.
[tex]3.14159(21)^2\\\\3.14159*441\\\\=1,385.44[/tex]
When you'r edone solving, you should get 1,385.44
1,385.44 ft² would be your FINAL answer.
____________________________________________________
Answer:
1384.74
Step-by-step explanation:
diameter = 42
radius = 42/2 = 21
area of a circle = πr2 (pie r square)
= 3.14 X 21 X 21
=1384.74 sq.ft
PLEASE HELP RIGHT AWAY!!1
Answer:
3,172
Step-by-step explanation:
The "Money saved that week" is an arithmetic progression, where the next term is found by adding a constant value to the previous term. In this case, the variation is 2.
So that could be modeled with this equation: [tex]a_{n} = a_{1} + (n-1)V[/tex]
Where a1 is the first term of the series, in our case: 10, and the V is the variation each week, in our case: 2.
To be able to calculate the overall sum and answer the question, we first need to calculate the amount she will save on the last week (n=52).
[tex]a_{52} = 10 + (52-1) * 2 = 10 + 102 = 112[/tex]
Now that we know she'll save $112 on the 52nd week, let's calculate the total, using this formula:
[tex]S_{n} = \frac{(a_{1} + a_{n}) * n}{2}[/tex]
We know n (52), a1 (10) and an (112), so...
[tex]S_{52} = \frac{(10 + 112) * 52}{2} = \frac{122 * 52}{2} = 3,172[/tex]
At the end of the year, she will have saved $3,172
clay learned that solids have a definite shape. now he measured the mass of a bead. the bead has a mass of 10 grams. he estimates that 10 beads will have a mass of 1 kilogram. is he correct. explain
Incorrect
1000g=1kg
Therefore we would need 100 beads with a mass of 10g to estimate a total mass of 1kg or 1000g
So the estimate of 10beads at 10g each is only about 100g or 0.1kg or 1/10kg
jane's age is 5 years less than 3 times her brothers age. jane is 11 minus her brothers age. how old is jane?
Answer:
Step-by-step explanation:
Let x represent Jane's age
Let y reprsent her brother's age
x=3y-5
x=11-y
subtract
0=4y-16
-4y=-16
y=4
plug back into equation
x=3y-5
x=3(4)-5
x=7
Given y inversely proportional to x and x = 3 for y = 4, what is x if y = 12?
A.) 1
B.) 9
C.) 16
B
12 is equal to 4y, or 4(3)
you can multiply 4 by x to get 9 since they’re inversely proportionate.
Answer:
A) 1.
Step-by-step explanation:
y is inversely proporcional to x so the equation has the form:
y = c/x
With c been any constant, to find the value of c we use y=4 and x=3:
4 = c/3
c=4*3
c=12
So the equation is
y=12/x
Using y=12 to find x:
12=12/x
(12/12)=x
x=1
HELP 10 POINTS! Larry was able to walk 4 more than twice as many dogs as his friend Kyle. Write an algebraic expression to represent the number of dogs Larry walked compared with Kyle.
Kyle) y= x Larry) 4y= x^2
The algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .
What is an Algebraic Expression ?An algebraic expression can be defined as a mathematical statement which includes , variables , constant and mathematical operators.
It is given in the question that
Larry was able to walk 4 more than twice as many dogs as his friend Kyle have.
Let number of dogs Kyle has = x
and Let Larry walks y miles.
According to the given data
y = 2x + 4
Therefore , the algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .
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I need to find the domain for this
Answer:
[tex]\large\boxed{Domain:\ x\in\mathbb{R}\to\text{the set of all real numbers}}[/tex]
Step-by-step explanation:
The domain of roots:
[tex]\sqrt[n]{p(x)}[/tex]
If n is an odd number, then p(x) can be any real number.
If n is an even number, then p(x) must be a non-negative number.
We have
[tex]f(x)=\sqrt[3]{2x^2-3x-9}[/tex]
n = 3 → odd number.
Therefore the domain is the set of all real numbers.
Write an equation to represent the following statement.
28 is 12 less than K
Solve for k
What does K= ?
Step-by-step explanation:
"Is" means equals. "Less than" means subtracted from.
28 = k - 12
Add 12 to both sides to solve for k:
k = 40
The equation representing the statement '28 is 12 less than K' is 28 = K - 12. By adding 12 to both sides of the equation and simplifying, we find that K = 40.
Explanation:To represent the statement '28 is 12 less than K' with an equation, you write: 28 = K - 12. To solve for K, you would add 12 to both sides of the equation.
Step 1: Add 12 to each side of the equation to isolate K.
28 + 12 = K - 12 + 12
Step 2: Simplify each side.
40 = K
Therefore, the value of K is 40.
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factor the expression completely -15t-6
Answer: -3(5t+2
Step-by-step explanation:
Answer:
−3(5t+2)
Step-by-step explanation:
lets factor out "3" from -15t-6
so factoring out "3" would give you -3(5t+2)
you can check ur work by distributing "3" hope this helps!
4. What is the answer to this problem
Ueuhshsjaksjdsnygwhwhwhwhwg bdbehd jeuwjsnz ,judj
Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)
Answer:
Step-by-step explanation:
y=mx+b
8=-7m+b
2=0m+b
subtract
6=-7m
-6/7=m
2=0m+b
2=b
y=-6/7x+2
change to standard from
y+6/7x=2
HELPPPPP TIMEDDDDDDDDDDD
Answer:
The correct answer is option B.
x = 10 and y = 46
Step-by-step explanation:
From the figure we can see a trapezium.
To find the value of x
We can write,
2x - 13 = x - 3
2x - x = 13 - 3
x = 10
To find the value of y
from the figure we can write,
3y - 4 + y = 180
4y = 180 + 4
4y = 184
y = 184/4 = 46
Therefore the correct answer is option B
x = 10 and y = 46
there are 6 red, 4 freen, 5 blue, and 5 yellow marbles in a jar. What is the probabilty of picking a green marble, than a blue marble if you do not put bacj the first marble. A.) 1/20 B ) 9/20 C.) 9/40 B.) 1/19
Answer:
The first part is A then the second part is B 1/19
Step-by-step explanation:
If you add all together you get 20 then you get a green marble since you removed one that would make the odds into 1 out of 19 that's how you get the next answer. Hope this Helped! ʢ◉ᴥ◉ʡ
Agnes spent $10 for 5 feet of wood molding to frame a picture. Greg bought one yard of the same molding. How much did Greg spent?
Answer:
Greg spent $6.00
Step-by-step explanation:
Agnes spent $10 for 5 feet of wood molding to frame a picture.
Greg bought one yard of the same molding.
1 yard = 3 feet
We will calculate the answer with unitary method.
∵ 5 feet of wood molding costs = $10.00
∴ 1 feet of wood molding costs = [tex]\frac{10}{5}[/tex]
∴ 3 feet of wood molding costs = [tex]\frac{10}{5}[/tex] × 3 = $6.00
Greg spent $6.00 in the molding of 1 yard wood.
Answer:
$6
Step-by-step explanation:
I took the test .
which of the following best describes a bisector of an angle
Answer:
An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles.
Step-by-step explanation:
Answer:
The set of all points in a plane that are equidistant from the two sides of a given angle.
Step-by-step explanation: