4√7 - 9i
Write the trigonometric form of the complex number. (around your angle to two decimal places. Let 0< theta < 2pi
Answers
[tex]\stackrel{a}{4\sqrt{7}}~~ - ~~\stackrel{b}{9}i ~~ \begin{cases} r=\sqrt{a^2 + b^2}\\\\ \theta =\tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{(4\sqrt{7})^2 + 9^2}\implies r=\sqrt{16(7)+81}\implies r=\sqrt{193} \\\\\\ \theta =\tan^{-1}\left( \cfrac{9}{4\sqrt{7}} \right)\implies \theta \approx 40.38^o \\\\[-0.35em] ~\dotfill\\\\ z~~ = ~~\sqrt{193}( ~~ \cos(319.62^o)~~ + ~~i\sin(319.62^o) ~~ )\qquad \textit{\LARGE IV Quadrant}[/tex]
let's take a quick look at the (a , bi) pair, "a" is positive whilst "b" is negative, that means the IV Quadrant, now let's keep in mind that tan⁻¹(x) has a range that lies on the I and IV Quadrants, so, if you check in your calculator for tan⁻¹(x) for those values, you'll notice it gives the one in the I Quadrant, namely 40.38°, however our coordinate pair is on the IV Quadrant, so we need its twin.
Make sure your calculator is in Degree mode.
Related Questions
Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=1/2⋅P(x)?
Answers
Given,
The expression for function P(x) is | x |.
The expression for function I(x) is | x |/2.
Required:
The graph of the function.
The graph of the function is,
The function P(x) is represented by black line.
The function I(x) is represented by Red line.
Hence, option A is correct.
Cal made the graph at right. Use the graph to write a problem involving fractions.
Answers
We need to come up with a question involving the graph.
Very simple!
We can ask how much time in a day Cal spends for different activities.
We can say:
According to the graph, how much time of the day does Cal spend studying and sleeping?
answering this question:
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{3} \\ =\frac{3(1)+8(1)}{3\times8} \\ =\frac{3+8}{24} \\ =\frac{11}{24} \end{gathered}[/tex]If M is a centroid of triangle WOR and YR =16, what is the length of WR
Answers
If M is a centroid of triangle WOR and YR =16, the length of WR
side will be WR = 48.
What is the triangle's centroid?The centroid of the thing represents its center. A triangle's centroid is the point at which its three medians intersect. It can also be described as the point at which the three medians intersect.The median is a line that connects the midpoints of two sides and the opposite vertex of a triangle. A triangle is a two-dimensional shape with three sides. The three angles add up to 180 degrees.The centroid of a triangle divides the triangle's medians in a 2: 1 ratio.The ratio of the two sides will be given here as:
WY/ YR = 2/1
Determine the value of YR to determine the value of WR.
WY/16 = 2/1
WY = 32
WR will have the following value:
WR = WY+ YR
WR = 32+ 16
WR = 48
As a result, the value of the side WR is 48.
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If 7 ballpoint pens cost $9.66, how much will 12 pens cost? (100 points)
Answers
Answer:
16.56
Step-by-step explanation:
9.66/7
=1.38 each
1.38x12=16.56
Answer:
16.56
Step-by-step explanation:
the ladder to the slide is 21 feet high. how long is the slide
Answers
To find the slide we can us the pythagorical theorem that say:
[tex]h=\sqrt[]{l^2_1+l^2_2}[/tex]Where l1 and l2 iare the leg of the triangle so in our problem will be:
[tex]\begin{gathered} h=\sqrt[]{28^2+21^2} \\ h=\sqrt[]{784+441} \\ h=\sqrt[]{1225} \\ h=35 \end{gathered}[/tex]So the slide is 35 ft
Can u help me answer question 24 BTW this is lesson 6 the distributive property 24. 5(2x+7) = __________
Answers
We have the following:
[tex]5\mleft(2x+7\mright)=_{}[/tex]We apply the distributive property that tells us that the multiplication of a number by a sum is equal to the sum of the multiplications of said number by each of the addends.
Therefore:
[tex]5(2x+7)=_{}10x+35[/tex]Write the number in standard notation.5.8 × 10−3
Answers
0.0058
Explanation:The given scientific notation is:
[tex]5.8\times10^{-3}[/tex]This can also be written as:
[tex]\begin{gathered} 5.8\times\frac{1}{1000} \\ \\ =\frac{5.8}{1000} \\ \\ =0.0058 \end{gathered}[/tex]Therefore 5.8 x 10^-3 in standard form is 0.0058
This graph shows how fast the international space station travels in orbit around Earth What is the meaning of the point with an x-coordinate of 3?A. In 1 second, the space station travels 3 miles B. In 3 seconds, the space station travels 3 miles in 15 miles.C. The space station travels 3 miles in 15 seconds D. It takes the space st 3 seconds to go 5 miles.
Answers
From the graph, x coordinate 3 mean it takes 3 seconds to travels 15 miles.
Option B is the correct answer.
Which expression is equivalent to 10x – 6?
Answers
Answer:
1. -6 + 10x
Step-by-step explanation:
The expression 10x – 6 is the same as adding -6 to 10x, or 10x + -6. Since addition equations can be rearranged, 10x + -6 can also be written as -6 + 10x.
Answer:
[tex] \sf{ \large{ - 6 + 10x}}[/tex]
Step-by-step explanation:
10x - 6
note: there is a plus sign at 10x
+10x - 6
so when you switch it will be like this
-6 + 10x
123456Previous Activity78910Juanita wants to perform row operations on the augmented matrix for the system below.x+ 2y = 3-x+y+z=2y-2z=-3Which matrix should Juanita use to perform the operations?1 2 3 0-⠀⠀⠀⠀-1 1 1 21 -2 -3 0Next A
Answers
The given system of equation is
x + 2y + 0z = 3
- x + y + z = 2
0x + y - 2z = - 3
The augumented matrix is formed by using the coefficient of the variables. The required matrix is shown below
[tex]\begin{bmatrix}{1} & {2} & {0} & {3} \\ {-1} & {1} & {1} & {2} \\ {0} & {1} & {-2} & {-3} \\ {} & {} & {} & {}\end{bmatrix}[/tex]The correct option is the second one
The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice. Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice.6 weeks | kilograms of rice left12 weeks | kilograms of rice leftw weeks | kilograms of rice
Answers
The total kg of rice bought is 75kg
Each week, 4.5kg is used,
Let the number of weeks be represented by n
The remaining amount of rice is represented by r
The relationship between the values above can be given as,
[tex]r=75-4.5n[/tex]For 6 weeks, the kilogram of rice left where n = 6 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(6)=75-27=48\operatorname{kg} \end{gathered}[/tex]For 12 weeks, the kilogram of rice left where n = 12 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(12)=75-54=21\operatorname{kg} \end{gathered}[/tex]For w weeks, the kilogram of rice left where n = w is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(w)=75-4.5w \end{gathered}[/tex]Hence, after 6 weeks, the remaining rice left is 48kg
Hence, after 12 weeks, the remaining rice left is 21kg
Hence, after w weeks, the remaining rice left is (75-4.5w)kg
Can someone explain to me how to find the answers
Answers
Part a: The missing length = 28 units.
Part b: The missing length = 25 units, for the given similar triangle.
What is termed as the similarity of the triangle?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size. The triangles have been congruent if their side lengths are also of equal length.Part a: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
63/x = 27/12
x = (63×12)/27
x = 28 units.
The missing length is 28 units.
Part b: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
21/15 = (10 + x)/x
21x = 150 - 15x
6x = 150
x = 25
The missing length is 25 units.
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In the diagram of LPN below, QM ||PN, QP=32, LM=10, and MN=40. What is the length of LP? L 10 M M 32 40 P N Answet Submit Answer
Answers
2
(b) The area of a rectangular painting is 8134 cm².
If the length of the painting is 98 cm, what is its width?
Width of the painting: cm
Answers
Answer:
Step-by-step explanation:
To answer this question do 8134 cm²÷98 cm
8,134÷98=83cm
use nPr formula 11P0=
Answers
we know that
the formula is equal to
P(n,r) = n! / (n-r)!
we have that
nPr = n!/(n-r)!
we have
11P0
so
n=11
r=0
= 11!/(11-0)!
=11!/11!
=1
answer is 1What is the variable being tested in an experiment?0 A.response variableO B. placeboO C.control variableOD.explanatory variable
Answers
Given
Variables
Find
Which variable being tested in an experiment
Explanation
The dependent variable is the variable that is being measured or tested in an experiment
response variable is often referred as dependent variable.
Final Answer
hence , the correct option is A.
The greatest common factor of 36 and 60 is 12. Explain what this means.
Answers
For 12 to be the GCF (Greatest common factor) between 36 and 60, means that the greatest number that can divide both 36 and 60 at the same time is 12.
I need to find the inequality 5-12x<29
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > −2
Interval Notation:
(−2, ∞)
X is greater than -2
Pythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.18Х11
Answers
Solution
For this case we can use the Pythagoras theorem and we have:
[tex]18^2=11^2+x^2[/tex]And solving for x we got:
[tex]x=\sqrt[]{18^2-11^2}=\sqrt[]{324-121}=\sqrt[]{203}=14.25[/tex]Then the answer is:
14.25
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).5,4, 16/5... Find the 7th term.
Answers
In order to find the 7th of the sequence, first let's find the common ratio of the sequence.
To do so, let's divide one term by the term before:
[tex]q=\frac{4}{5}[/tex]Now, we can use the following formula to find the 7th term:
[tex]a_n=a_1\cdot q^{n-1}[/tex]For n = 7, we have:
[tex]\begin{gathered} a_7=5\cdot(\frac{4}{5})^6 \\ a_7=1.311 \end{gathered}[/tex]A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each. There are 135 boxes in all. If the truck is carrying a total of 4350 pounds in boxes, how many of each type of box is it carrying?
Number of large boxes:
Number of small boxes:
Answers
Number of large boxes will be 65.
Number of small boxes will be 70.
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each.
There are 135 boxes in all.
If the truck is carrying a total of 4350 pounds in boxes.
Let number of large boxes = x
Number of small boxes = y
Since, There are 135 boxes in all.
So, We get;
x + y = 135 ... (i)
And, The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each and the truck is carrying a total of 4350 pounds in boxes.
So, we can formulate;
40x + 25y = 4350 ... (ii)
Solve equation (i) and (ii) as;
Multiply 40 by (i) and subtract by (ii) we get;
40x + 40y - 40x - 25y = 5,400 - 4,350
15y = 1,050
y = 70
And, x + y = 135
x + 70 = 135
x = 135 - 70
x = 65
Thus, Number of large boxes will be 65.
Number of small boxes will be 70.
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[tex](9x^{2} - 2x) - (5x^{2} -8x-3)[/tex]
Answers
Answer:
[tex]4x^{2} +6x+3[/tex]
Step-by-step explanation:
Distribute and multiply the 1.
[tex]1(9x^{2} -2x) - 1(5x^{2} -8x-3)[/tex]
Collect like terms and sort them in descending order.
[tex]9x^{2} -2x -5x^{2} +8x +3[/tex]
[tex]4x^{2} +6x+3[/tex]
Can someone help me with this geometry question? My instructor said I was wrong?
Answers
Solve Each system of equations.
-r + t = 5
-2r+t=4
Answers
Solve equations
-(1) + 6 = 5
5= 5
-2(1) + 6 = 4
4=4
_________
Step by step
We have two equations
-r + t = 5 to t = r + 5 when put in y intercept form for easy math
t = r + 5
-2r + t = 4
To solve, substitute the t value from the first equation for t in the second
-2r + (r + 5) = 4
Combine like terms
-1r + 5 = 4
Subtract 5 from both sides to solve for r
-1r + 5 - 5 = 4 - 5
Combine
-1r = -1
Divide both sides by -1 to solve for r
-1/-1 r = -1/-1
r = 1
Now substitute the r value into one of the equations to solve for t
(-1)(1) + t = 5
-1 + t = 5
Subtract (-1) from both sides to solve for
t = 6
Graph in the attachment
4. A fruit stand sells boxes of apples. Each box weighs the same amount. The table shows the number of boxes and the total number of pounds. AppIGN Number of Boxes Tocal Number of Pounds И. 7 8 72 10 Which of the following correctly describes the relationship in the table? A. Number of boxes + 4 = total number of pounds B. Number of boxes x 9 + total number of pounds C. Number of boxes - 9 total number of pounds D. Number of boxes x 6 = total number of pounds
Answers
From the table it can be observed if we multiply the number of boxes by 9, then it gives total number of pounds for the corresponding number of boxes.
As 4 multiply by 9 is 36, which is total number of pounds for 4 boxes. In similar manner total number of pounds can be obtained for different number of boxes.
So answer is,
[tex]\text{ Number of boxes}\times9=\text{ total number of pounds}[/tex]Option B is correct.
Which of the following are true?
A.-2.7<- 4.6
B.-7.3 1.2
C.-5.2 - 2.9
D. 4.7 3.4
O A and D
O B and C
OC and D
O A and B
Answers
Answer:
B and C are correct
Step-by-step explanation:
What is the missing numerator in 1 1/8=?/16
Answers
Answer:
12
Step-by-step explanation:
12/18 is just. 11/6*2
Bismuth-210 has a half-life of about 6 days. After 21 days, how many milligrams of a1,220 mg sample will remain? Round answer to the nearest tenth place. If answerdoes not have tenths place use a zero so that it does.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Bismuth-210 has a half-life of about 6 days.
After 21 days, how many milligrams of a 1,220 mg sample will remain?
Round answer to the nearest tenth place.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} We\text{ have that:} \\ 0.5\text{ = e}^{-6k} \\ Taking\text{ In of both sides, we have that:} \\ ln\text{ 0.5 = -6k} \\ That\text{ means that:} \\ k\text{ =}\frac{-ln\text{ 0. 5}}{6} \end{gathered}[/tex][tex]Let\text{ the number to remain, A=1220e}^{-(-\frac{ln0.5}{6})(21)}[/tex][tex]\begin{gathered} 107.83378\text{ mg} \\ \approx\text{ 107. 8 mg \lparen to the nearest tenth\rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]107.\text{ 8 mg \lparen to the nearest tenth\rparen}[/tex]Let f(t) = 3 + 2, g(x) = -x^2?, and
he) = x - 2/5. Find the indicated value.
Question 22
Answers
To find h(f(-9)), first, we need to find f(-9) substituting x = -9 into f(x), as follows:
[tex]\begin{gathered} f(x)=3x+2 \\ \text{ Substituting x = -9,} \\ f\mleft(-9\mright)=3(-9)+2 \\ f(-9)=-27+2 \\ f(-9)=-25 \end{gathered}[/tex]Substituting f(-9) = -25 into h(f(-9)), we get h(-25).
To evaluate h(-25) we have to substitute x = -25 into h(x), as follows:
[tex]\begin{gathered} h(x)=\frac{x-2}{5} \\ \text{ Substituting with x = -25,} \\ h(x)=\frac{-25-2}{5} \\ h(x)=-\frac{27}{5} \end{gathered}[/tex]Higher Order Thinking Veronica needs to buy 13 pounds of cheese. When the clerk places some cheese in a container and weighs it, the scale shows 1 pounds. The container weighs pound. How many more pounds of cheese should be added to the scale to get the amount that Veronica needs? Explain how you solved the problem.
Answers
After calculating some basic arithmetic we have come to find that, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
What is arithmetic?Using the four operations, arithmetic is a branch of mathematics that deals with the characteristics of numbers.
Division, multiplication, and subtraction are the four operations. The rules for each operation are very detailed.
As an illustration of arithmetic, one of the rules of addition and subtraction is that addition increases the overall value of a number while subtraction decreases the overall value of a number.
Veronica needs to buy 13 pounds of cheese
Cheese in a container weighs = 1 pounds
Mass of cheese clerk needs to add = 13 - 1
= 12 pounds
(as 1 pound is already there)
Thus, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
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