Answer: Could be 7.
Step-by-step explanation:
What is the polar form of negative 9 minus 9 i startroot 3 endroot ?
Using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
So, we have -9 - 9√3i:
This quantity has a modulus.
|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18
And argument θ to the effect:
tan(θ) = (-9√3) / (-9) = √3
We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:
θ = arctan(√3) - π = π/3 - π = -2π/3
The polar form is then:
18 (cos(-2π/3) + i sin(-2π/3))
And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))
Therefore, using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?
a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Answer:
18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Step-by-step explanation:
D
Which should equal 92° to prove that r ∥ s? w x y z
w should be equal to 92° to prove that r || s.
To prove whether the two lines are parallel we should know whether
the pairs of corresponding angles are congruent if a transversal cuts two parallel lines (Corresponding Angles Theorem)the pairs of alternate interior angles are congruent if a transversal cuts two parallel lines (Alternate Interior Angles Theorem)the pairs of alternate exterior angles are congruent if a transversal cuts two parallel lines (Alternate Exterior Angles Theorem)the pairs of consecutive interior angles are supplementary if a transversal cuts two parallel lines (Consecutive Interior Angles Theorem)So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.
From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.
The answer is w. Therefore, option a is correct.
The complete question is -
Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?
a)w
b)x
c)y
d)z
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Help me please please please please System of equations and inequalities aglebera 1
a cell phone plan costs $200 to start. Then there is a $50 charge each mont. what is the total cost for x months
Answer$200+$50x
Step-by-step explanation:
Answer:
4 Months
Step-by-step explanation:
if X = total (not sure)
thats means you must do $200 / $50 = 4 Months
design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The box's dimensions that reduce the overall cost of the materials are as follows:
L = W = 16 cm
H = 32 cm
Given,
What is the dimensions of the rectangle?
A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.
Here,
We've got
Volume = 512 cm3 L* W * H
Sides of the box cost = 1 cent/cm²
Top and bottom cost 2 cent/cm²
Then,
Box dimensions that reduce the overall cost of materials used
We are aware of
L× W × H = 512 cm³
Where,
L stands for length, W for width, and H for height.
So, when we reduce the cost function
C(L, W, H) = (1) 1 H + (2) 1 (L + W)
Thus insert H.
Replacing H with 512/LW yields,
C(L, W) = 512(1/L, 1/W), plus 2LW
So
When both partial derivatives are 0, there will be a minimum cost.
512/L2 - 2W = dC/dL = 0
So
512/W2 - 2L = 0 for dC/dW.
L = 256/W²
Now
The answer to the aforementioned equation is
L = W = (256)⁻³ = 16cm
And
H = 512/16 = 32
H = 32 cm
Consequently, the box's measurements that reduce the overall cost of the materials utilized are:
L = W = 16 cm
H = 32 cm
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The sum of two numbers is 31. The second number is 4 more than the first number.
Answer:
13.5, 17.5
Step-by-step explanation:
You have two numbers whose sum is 31 and whose difference is 4. The second number is larger.
SetupLet x represent the larger number. Then the smaller is x-4, and their sum is ...
x +(x -4) = 31
SolutionSimplifying the expression gives ...
2x -4 = 31
2x = 35 . . . . . add 4
x = 17.5 . . . . . divide by 2
x -4 = 13.5
The two numbers are 13.5 and 17.5.
__
Additional comment
As we have seen here, the larger number is half the total of the 'sum' and 'difference'. (31+4)/2 = 17.5. This is the generic solution to any "sum and difference" problem.
the base of a right triangle is 6 and the perpendicular height is 8, what is the length of a hypotenuse
If the base of the right triangle is 6 and the perpendicular height is 8 , then the length of the hypotnuse is 10 .
In the question ,
it is given that ,
the base of the right triangle is 6 , and
the height of the perpendicular is 8 ,
let the length of the hypotnuse of the given triangle be = h
Since the triangle is a right triangle , So , it follows Pythagoras Theorem ,
that means ,
h² = 6² + 8²
h² = 36 + 64
h² = 100
Simplifying further ,
we get ,
h = 10
Therefore , the length of the hypotnuse is = 10 .
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A student believes she can prove the two triangles are congruent using SAS. Which pieces of
information does she need.
Chose ALL that apply. This question has multiple answers.
W
X
Y
Z
A.
B.
C. WZ-WZ by reflexive property
D. WY-WY by definition of rectangle
Answer:
<XWZ ≅ < XZW by alternate interior angles & WZ = WZ by reflexive property
Step-by-step explanation:
Because they're parallel lines cut by a transversal. So, <W is where one angle is, and <Z is where another angle is. They both share a side as well. Always look out for those types of triangles because those are types of hidden information
a box contains 3 donuts cake, 4 jelly cake and 5 chocolate cake. if a person selects one cake at random, find the probability that it is either a donut or a chocolate cake
Answer:
50%
Step-by-step explanation:
It is a half chance, you could be lucky
what is the rate of change in y = 2x + 4 and initial value?
Answer: rate of change is 2
Step-by-step explanation:
nine people sit down for dinner where there are three choices of meals. three people order the beef meal, three order the chicken meal, and three order the fish meal. the waiter serves the nine meals in random order. find the number of ways in which the waiter could serve the meal types to the n
There are a total of 216 ways in which the waiter could serve the meal types.
Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.
Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.
If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.
If the two B people both get F's, the situation is identical to the above and three possibilities arise.
If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.
In total, we see there are 24 possibilities, so the answer is 9*24 = 216
Thus, there are a total of 216 ways in which the waiter could serve the meal types.
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Your question was incomplete. Check for missing part below-
Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.
Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1 A 125-page document is being printed by five printers. Each page will be printed exactly once. (a) Suppose that there are no restrictions on how many pages a printer can print. How many ways are there for the 125 pages to be assigned to the five printers? One possible combination: printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer
The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.
As per the question,
A 125-page document is being printed by four printers.
Each page will be printed exactly once.
There are no restrictions on how many pages a printer can print.
One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.
Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.
⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways
⇒ Number of possible ways 125 pages can be assigned to the four printers
= 5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )
= ways.
Therefore, In ways we can assign 125 pages to four printers with no restrictions.
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Given the image below, complete find the missing parts of the proof to find the value of x.
(2x +43)°
(2x – 3) °
.
°
Statements
1. Line 1 is parallel to line mi
and
2. (2x +43) + (2x - 3) = 180
3. 4x + 40 = 180
4. 4x = 140
| 5. x = 35
Reasons
1. Given
2. ?
3. Simplifing Equation
4. Subtraction POE
5. ?
Answer:
just telling you but we need to see the image which we cannot but I'm not entirely sure but I think it's 2 although I cannot see the image and the other one is 4 I thinke
please help me solve this problem I will give 20 points
Answer:
94
Step-by-step explanation:
if 3 pairs of mittens equal 30 then 1 pair of mitten is 10
And 1 mitten is 5
2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11
X+11+10=24
x+21=24
x=3
One hat is 3
We can write the last problem like this
2(3)+11x(11-3)
6+11x8
6+88
94
Hopes this helps and I hope this is right with these riddles I’m sure I missed something
Answer:
Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10
And 1 mitten is 5
2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11
X+11+10=24
x+21=24
x=3
One hat is 3
We can write the last problem like this
2(3)+11x(11-3)
6+11x8
6+88
94
Hopes this helps and I hope this is right with these riddles I’m sure I missed something
how many students say yes to liking pizza
Find the angel between the two vectors (4,1) and (-8,3)
The angle between the two vectors (4,1) and (-8,3) will be 145.4°.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is possible to calculate the angle () between two vectors using the formula
[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
Calculate dot product:
=a · b
= ax · bx + ay · by
= 4 · (-8) + 1 · 3
= - 32 + 3
= -29
=|a|
= √ax² + ay²
= √4² + 1²
= √16 + 1
= √17
=|b|
=√ bx² + by²
= √(-8)² + 3²
= √64 + 9
= √73
[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
α = 145.40771131249005°
Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.
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Adam has 5 blue pencils. How many red pencils would he need to have so that the ratio of blue pencils to red pencils is 1:2?.
The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
Explain the term ratio of the number?A ratio in mathematics demonstrates how several times one number is present in another. An set of points of numbers an as well as b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Let the number of number of red pencils be 'x'.
Total blue pencils = 5.
Ratio = blue pencils/red pencils
5/x = 1/2
x = 5 x 2
x = 10
Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
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if 11600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
The compound interest after 5 years is $7,081.916.
Compound interest:
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Here we have to find the interest earned after 5 years.
Data given:
Principle (P) = $11600
rate(r) = 10%
time(t) = 5 years.
Formula to find compound interest:
CI = P( 1 + r/100[tex])^{t}[/tex] - P
Now put the values in the formula.
CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600
= 18681.916 - 11600
= 7081.916
Therefore the compound interest is $7081.916.
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Please help!
Matrix Pre-calc
Answer:
M+N is defined
All others not defined
Step-by-step explanation:
Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns
Only M and N with dimensions (4 x 2) each can be added or subtracted.
(4 x 2 ) means 4 rows and 2 columns
So the only defined operation is
M + N
All the others are not defined
Answer:
[tex]\textsf{De\:\!fined}: \quad \boxed{M + N}[/tex]
[tex]\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}[/tex]
Step-by-step explanation:
Generally, a matrix is referred to as [tex]n\times m[/tex] where n is the number of rows and m is the number of columns.
Therefore:
L is a 2 x 2 matrixM is a 4 x 2 matrixN is a 4 x 2 matrixP is a 2 x 2 matrixQ is a 2 x 1 matrixMatrices can be added or subtracted only when they are the same size.
[tex]\boxed{N - Q}[/tex]
Matrices N and Q are different sizes. Therefore, the operation is not defined.
[tex]\boxed{M + N}[/tex]
Matrices M and N are the same size. Therefore, the operation is defined.
[tex]\boxed{Q + L}[/tex]
Matrices Q and L are different sizes. Therefore, the operation is not defined.
[tex]\boxed{M - P}[/tex]
Matrices M and P are different sizes. Therefore, the operation is not defined.
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 170 engines and the mean pressure was 6.7 lbs/square inch. assume the standard deviation is known to be 1. if the valve was designed to produce a mean pressure of 6.6 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
What is the Null hypothesis?In inferential statistics, the null hypothesis states that two possibilities are equal.
The observed difference is thought to be the sole product of chance, which is the underlying premise.
Statistical tests can be used to calculate the likelihood that the null hypothesis is true.
So,
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
As the population standard deviation is given when n > 30
So, we'll run the Z test.
Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]
Replace the values:
[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]
For the p-value, see the z table.
Consequently, p = 0.9927.
The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146
α = 0.1
p value< α
Thus, we disregard the null hypothesis.
Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.
Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
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Charolette earns 3,595 per month at her job. She will receive a 7% raise. How much more money will Charolette earn each year after her raise?
The increase in the salary for Charolette will be $251.65.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.
This will be illustrated thus:
= Percentage × Salary
= 7% × $3595
= $251.65
The value of $251.65 will the increase in the salary.
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It costs a craftsperson 110 to bring 150 picture frames to market and the picture frames sell for 2. The difference between the cost and the income from sales is the craftsperson’s profit?
HELP
For the diagram below, calculate the value of x. Show your work
Answer: x = 6
Step-by-step explanation:
2x + 7 = 9x - 35
-7x + 7 = -35
-7x = -42
x=6
Two interior angles of a triangle are 54 and 112. What is the measure of the third angle?
Answer: 14 degrees.
Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.
In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:
180 degrees = 54 degrees + 112 degrees + x
180 degrees = 166 degrees + x
x = 180 degrees - 166 degrees
x = 14 degrees
Therefore, the measure of the third angle of the triangle is 14 degrees.
1.15 x240 not the answer the work I want.
Answer:
Step-by-step explanation:
The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 8000.(a) Find a function n(t) = n0ert that models the population after t hours.(b) Find the population after 1.5 hours.(c) After how many hours will the number of bacteria reach 15,000?(d) Sketch the graph of the population function.
(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, the population is 22646.
(c) t=1.7 will it take for there to be 15,000 bacteria
(d) The population function's graph is in the picture.
Given that,
One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.
We have to find
(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, locate the population.
(c) How long will it take for there to be 15,000 bacteria?
(d) Draw the population function's graph.
We know that,
(a) The initial size of the culture is 1000 bacteria.
So,
n₀=500
The size of the culture after one hour (for t =1) is 4000 so we extract the equation:
n(1) = 8000
1000er¹=8000
e to the power of r =8
[taking logarithms both side]
r ln e = ln 8
r=2.080
[ln e = 1]
So, we got
n₀=1000 and r=2.08
The function will be,
n(t)=1000[tex]e^{2.08t}[/tex]
(b) for t = 1.5
n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]
22646
(c) 15000=1000[tex]e^{2.08t}[/tex]
15=[tex]e^{2.08t}[/tex]
Taking log on both sides
ln15= 2.08(t)lne
t=3.68/2.08
t=1.7
(d) Since we have have the exponential equation therefore our graph should be curve not straight line.
Also at t=1, population of bacteria is 4000
Hence the correct graph will be in picture.
Therefore,
(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, the population is 22646.
(c) t=1.7 will it take for there to be 15,000 bacteria
(d) The population function's graph is in the picture.
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PLEASE HELP WILL GIVE BRAINLIST ! , PLEASE MAKE IT FAST
Answer:
t >28= the temp is warmer than 28
t >29= the table is heavier than 29 kilos
t <29= tony is you get than 29 yrs old
t <28= tia ran the race in under 28 secs
Step-by-step explanation:
hope this helps
write in slop form of the equation and each line given the slope and y intercept. slope = 1/2. y intercept = 2
Answer:Y=1/2x+2
Step-by-step explanation:
Slope intercept form is y=mx+b
m=slope
b= y intercept
y=1/2x+2
Sara has 7,241 beads. She wants to make them into necklaces to sell at a charity fundraiser. She wants to use 13 beads on each necklace. How many necklaces is she able to make?
Answer:
557
Step-by-step explanation:
7,241 divided by 13 = 557