Simplify and express your answer in both polar and standard form.
Question 1
(7 cis(45°))²
Q2 below
(-2+2i√3)^5
Simplifying and expressing each term in standard and polar form are respectively; 49/2 and -512 - 512i√3
How to express an equation in polar form?
1) We are given the expression;
[7 cos (45)]²
We know that cos (45) in standard form is 1/√2. Thus;
[7 cos (45)]² = (7 * 1/√2)² = 49/2
2) We are given the expression;
(-2 + 2i√3)⁵
Using binomial theorem, we have;
(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵
Simplifying each term gives;
−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3
⇒ -512 - 512i√3
Read more about Polar form at; https://brainly.com/question/27844433
#SPJ1
Find the value of each card and put them in order, from lowest to highest.
Answer:
The highest is 1 but i cannot work out the rest
Step-by-step explanation:
Bidmas
In general, when solving a radical equation with square roots, you should first
isolate the __and then square both sides.
A. variable
B. radical
C. operator
D. coefficient
The correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.
How to solve radical equations?To solve radical equations, one common technique is to isolate the radical term first, then take both sides of the equation to a power to remove the radical.
Therefore the correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.
To know more about radical equations follow
https://brainly.com/question/8606917
#SPJ1
solve pls brainliest
Answer:
4 pt = 8 cups
28 qt = 7 gallons
Step-by-step explanation:
We know, from your chart, that 1 p = 2 c
4 p is four times 1 p
so, to scale up 1 pint to 4 pints, we multiply by 4
to figure out what the corresponding number of cups would be, we also have to multiply that value by 4
if 1 p = 2 c
then 4 p = 8 c
(1 x 4) (2 x 4)
8 cups
--------
If we have 28 quarts, and we know that 4 quarts is 1 gallon, we can divide 28 / 4 to find how many gallons are in 28 quarts (or, how many gallons can be made of 28 quarts)
28 / 4 = 7
7 gallons
Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f (x) = 5 x squared minus 3. g (x) = 5 x squared + 3.
a.
both f and g open downward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
b.
both f and g open upward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
c.
both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
d.
both f and g open downward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
The similarities/differences observed in the graph is (c) both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
How to describe the similarities/differences?The equations are given as:
f(x) = 5x² - 3
g(x) = 5x² + 3
Next, we plot the above equations on the same plane (see attachment)
From the attached graph, we can see that:
Both functions open upwardThe lowest point of f(x) is at y = 3; i.e 3 units above the x-axisThe lowest point of g(x) is at y = -3; i.e 3 units below the x-axisHence, the similarities/differences observed in the graph is (c)
Read more about quadratic graphs at:
https://brainly.com/question/18797214
#SPJ1
Does anybody know this? I keep getting different answers that don t make sense. Find the surface area of the cone
The range of 3,7,2,4,7,5,7,1,8,8
Answer:
7
Step-by-step explanation:
First put all the numbers in order. Like this,
1,2,3,4,5,7,7,7,8,8
Then subtract (take away) the lowest number from the highest. Like this,
8-1=7
Which trigonometric function requires a domain restriction of [0, pi/2) ∪ (pi/2 , pi]
The ANSWER is f(x) = secx ----- PLEASE EXPLAIN THANK YOU!!!!!
The trigonometric function requires a domain restriction of [0, π/2) ∪ (π/2, pi] is tan x, sec x.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
tan x = (sin x)/(cos x)
sec x = 1/(cos x)
cos x becomes zero at {-π/2,π/2}
Therefore, the both of the function are undefined at {-π/2,π/2}
Learn more about trigonometric;
https://brainly.com/question/21286835
#SPJ1
1. Solve the equation 2x ^ 3 + 7x ^ 2 - 10x - 24 = 0 in the real number system
The solution to the given equation in the real number system is x = 2 or x = -4 or x = -3/2
What is a real number system?A real number system comprises rational numbers, irrational numbers, integers, and whole numbers. When solving a polynomial in a real number system, we need to first factor the polynomial by grouping;
i.e.
= 2x³ + 7x ² - 10x - 24
= 2x³ + 11x² + 12x - 4x² - 22x - 24
= x(2x² + 11x + 12) - 2(2x² + 11x + 12)
= (x - 2) (2x² + 11x + 12)
= (x - 2) (2x² + 8x + 3x + 12)
= (x - 2) (2 (x² + 4x) + 3(x + 4))
= (x - 2) (2x (x + 4) + 3(x + 4) )
= (x - 2) (x + 4) (2x + 3)
In a real number system;
x = 2 or x = -4 or x = -3/2
Learn more about the real number system here:
https://brainly.com/question/540415
#SPJ1
Which represents a perfect cube? 8 times 8 times 8 8 8 8 9 times 9 times 9 times 9 9 9 9 9 9
Answer:
by o of u 999987ui87 u ko9h u kgnnh b mjuokkwuij
What percent of 3 is 1.8
Answer:
60%
Step-by-step explanation:
Step-by-step explanation:
100% = 3
1% = 100%/100 = 3/100 = 0.03
how many % are 1.8 ? well, as many % as 1% fits into 1.8 :
1.8 / 0.03 = 60%
A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings. A 6-column table has 5 rows. The first column has entries walks to school, bikes to school, rides bus to school, driven to school, total. The second column is labeled 0 siblings with entries 24, 8, 18, 32, 82. The third column is labeled 1 sibling with entries 37, 9, 36, 58, 140. The fourth column is labeled 2 siblings with entries 12, 8, 12, 22, 54. The fifth column is labeled 3 or more siblings with entries 3, 2, 9, 10, 24. The sixth column is labeled Total with entries 76, 27, 75, 122, 300. Which statement is true about whether A and B are independent events
The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.
How to depict the events?Let A be the event that the person rides the bus to school, then:
P(A) = 75/300
P(A) = 0.25
Let B be the event that the person has 3 or more siblings, then:
P(B) = 24/300 = 0.25
P(A/B)=9/24
P(A/B)=0.375
Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.
Learn more about events on:
https://brainly.com/question/14279727
#SPJ1
What is the absolute deviation of 4 in this data set?
{6, 22, 14, 9, 11, 4}
02
O 3
07
11
Answer:
n
6
Mean
11
Average Absolute Deviation (MAD)
4.6667
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
The zeros of the function f(x) = -(x+1)(x-3) ( x+ 2) are -1,3, and blank the y-intercept of the function is located at (0, blank)
Answer:
see explanation
Step-by-step explanation:
f(x) = - (x + 1)(x - 3)(x + 2)
to find the zeros let f(x) = 0 , that is
- (x + 1)(x - 3)(x + 2) = 0
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 3 = 0 ⇒ x = 3
x + 2 = 0 ⇒ x = - 2
the zeros are x = -1, 3 and x = - 2
to find the y- intercept let x = 0
f(0) = - (0 + 1)(0 - 3)(0 + 2) = - (1)(- 3)(2) = - (- 6) = 6
y- intercept is located at (0, 6 )
If you exchange 120 dimes
for dollars, then how many
dollars would you get?
Answer:
12
Step-by-step explanation:
you divide 120 by 10 since dimes are equal to ten cents
To determine how many dimes are in dollars:
⇒ must know the rate of conversion
⇒ for every dollar, there are 10 dimes
⇒ [tex]\frac{1_. dollar}{10_. dimes}[/tex]
Let's solve:
[tex]120_. dimes * \frac{1_.dollar}{10_.dimes} = \frac{120}{10} *\frac{dimes}{dimes} *dollar=12_.dollars[/tex]
Thus you would get 12 dollars
Answer: 12 dollars
Hope that helps!
Takeout orders on a typical saturday
hours since noon
(x)
number of
takeout orders
(v)
0
0
12
9
10
11
8
6
7
2
3
4
1
6
14
24
28
30
16
5
6
12
10
3
0
If triangle abc and triangle def are similar, then their corresponding sides are proportional. if , then . answer the following questions what is the hypothesis? what is the conclusion? what is the converse? is it true? if the converse is not true, give a counter-example. what is the inverse? is it true? what is the contrapositive? is it true?
The answer to the questions are given below.
What are Similar Triangles ?The triangles which do not have same side length or angles but are similar in appearance are called similar Triangles .
It is given in the question that
If triangle abc and triangle def are similar, then their corresponding sides are proportional.
The hypothesis is
if the triangle abc and def are similar
The conclusion is
that the triangle abc and def are similar and the sides corresponding are proportional.
The converse is
If the sides of two triangles are proportional then two triangles are similar
Yes it is true
Inverse is if the two triangles are not similar then the sides corresponding are not proportional.
Contrapositive statement is if the sides are not proportional then the two triangles are not similar.
Yes , it is true.
To know more about Similar Triangles
https://brainly.com/question/25882965
#SPJ1
What two congruent triangles share the side AC?
△AEB and △CEB
△GFA and △GDC
△ADC and △CFA
The two congruent triangles that share the side AC are (c) △ADC and △CFA
How to determine the congruent triangles?For two triangles to share the sides AC, then the points A and C must appear on the names of the triangles
In option (c), we have A and C in the names of the triangles ADC and CFA
Hence, the two congruent triangles that share the side AC are (c) △ADC and △CFA
Read more about congruent triangles at:
https://brainly.com/question/1675117
#SPJ1
Help pleaseeeee. ill give 10 points
a sample of the students at a middle school is selected by writing the name of every student in the school on a slip of paper and putting all the names into a bin. the bin is then rotated to mix the slips of paper and 25 names are drawn without looking. if the bin is rotated after every draw, which kind of sampling method is this?
a. non-random sampling
b. simple random sampling
c. stratified random sampling
d. systematic random sampling
Answer:B
Step-by-step explanation: it's because you're choosing random peoplepeoplepeople
PLEASE HELP ME. NO PHONY ANSWERS TY, ANSWER IF YOUR 100% RIGHT!
A sample of 317 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified
according to major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table bel
Biology Business Engineering Mathematics
Computer science
Female 17
22
27
36
41
Male
19
45
29
34
47
Among all the students in the sample, what is the relative frequency of female mathematics majors?
Round your answer to two decimal places.
0
X
?
The relative frequency of female mathematics majors will be 0.5142.
How to find the relative frequency?The proportion of the examined subgroup's value to the overall account is known as relative frequency.
A sample of 317 students at a university is surveyed.
The students are classified according to gender (“female” or “male”).
The table is given below.
Then the relative frequency of female mathematics majors will be
⇒ 36 / (36 + 34)
⇒ 36 / 70
⇒ 0.5142
Learn more about conditional relative frequency here:
https://brainly.com/question/8358304
#SPJ1
Find the product using Distributive property. 625 x 129 – 625 x 90
Answer:
63,750
Step-by-step explanation:
1. Simplify the expression
625*192-625*90
120000-625*90
120000-56250
63750
What is distributive propertyAn algebra property which is used to multiply one integer by one or more other integers inside a set of parentheses.What are order of operations The order in which operations in an expression to be evaluated are carried out.Why learn this:
Order of operations is a basic rule of algebra. It tells us what to solve first when we have an equation with multiple functions, which is something that you will likely encounter throughout your maths studies. The order is: Parentheses, Exponents, Multiplication and Division, then finally Addition and Subtraction. Remember that when you're solving within the parentheses, the Order of Operations applies!Terms and topics
Order of operations[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\textbf{Assuming that you meant}\bf\downarrow[/tex]
[tex]\mathbf{625\times129 - 625\times90}[/tex]
[tex]\large\textbf{If so, let's solve for the answer, shall we?}[/tex]
[tex]\mathbf{= \boxed{\bf 80,625} - 625\times90}[/tex]
[tex]\mathsf{= \bf 80,625 - \boxed{\bf 56,250}}[/tex]
[tex]\mathbf{= 80,625 - 56,250}[/tex]
[tex]\large\textbf{We have met your answer to this question.}[/tex]
[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{24,375}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Pleazzzz helpppp meee!!!
The graph below represents the result of a survey in which a number of students
reported how many letters were in their last names.
What was the range of name lengths?
The range of name lengths is equal to 8.
What is a range?In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;
Range = Highest number - Lowest number
From the given data set, we have:
Highest number = 10.
Lowest number = 2.
By substituting, we have:
Range = 10 - 2
Range = 8.
Read more on range here: brainly.com/question/32352196
#SPJ1
Which combination represents the empty set? motor ⋃ manual motor ⋃ bicycle motor ∩ manual motor ∩ bicycle
The combination that denotes the empty set{∅} is motor ∩ bicycle.
What is a set theory?Set theory is the mathematical study of well-defined groups of things called elements of the set.
In the given Venn diagram, the elements in the set of Motor, Manual, and Bicycle are as follows:
Motor = {8, 24}Manual = {24, 32}Bicycle = {44}The union of motor and manual i.e. Motor ⋃ Manual = {24}The combination that represents an empty set {∅} is the intersection that occurred between motor and bicycle and can be expressed as:
= motor ∩ bicycle
This is because there are no set elements overlapping between motor and bicycle, this makes it an empty set{∅}.
Learn more about set theory here:
https://brainly.com/question/13458417
#SPJ1
Answer: motor U bicycle
Step-by-step explanation:
The focus of a parabola is (2, 5) and the directrix is y = 3. Find the equation of the parabola in standard form.
The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)
How to derive the equation of a parabola
Since the directrix is a horizontal line, then we have a parabola with a vertical axis of symmetry. The standard equation of the parabola is described below:
y - k = [1/(4 · p)] · (x - h)² (1)
Where:
(h, k) - Location of the vertex.p - Distance between vertex and focus.By analytical geometry we understand that the least distance between the focus and the directrix is twice as the distance between the vertex and the focus. First, we find the coordinates of the vertex:
V(x, y) = 0.5 · F(x, y) + 0.5 · D(x, y)
V(x, y) = 0.5 · (2, 5) + 0.5 · (2, 3)
V(x, y) = (1, 2.5) + (1, 1.5)
V(x, y) = (2, 4)
By Pythagorean theorem we find that the distance between vertex and focus is 1. Then, the equation of the parabola in standard form is:
y - 4 = 0.25 · (x - 2)²
y - 4 = 0.25 · (x² - 4 · x + 4)
y - 4 = 0.25 · x² - x + 1
y = 0.25 · x² - x + 5
The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)
To learn more on parabolae: https://brainly.com/question/4074088
#SPJ1
From your observation : x⁰=
Answer:
=1
Step-by-step explanation:
does someone mind helping me with this question? Thank you!
Answer: 81
Step-by-step explanation:
Since x is given, just substitute the value.
5(10) + 31
50 + 31 = 81
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
The given expression is :
[tex]\qquad \sf \dashrightarrow \:5x + 1[/tex]
now, plug in the values of x as 10
[tex]\qquad \sf \dashrightarrow \:5(10) + 31[/tex]
[tex]\qquad \sf \dashrightarrow \:50 + 31[/tex]
[tex]\qquad \sf \dashrightarrow \:81[/tex]
So, required value is 81
I kinda need an explanation on how to solve this.
Answer:
36.
Step-by-step explanation:
There were 10 elephants that were marked. Only 4 of those were counted. The other 26 were new elephants. Because of this, we know that there were 6 other elephants that were not counted. There were the 30 counted, and the other 6. Add those and you get 36.
Answer:
75 elephants
Step-by-step explanation:
This sort of population study assumes that the probability of catching any particular elephant is the same as for any other.
__
We are given that there is a population of 10 painted elephants, of which 4 of them are caught in a sample of 30 elephants. We know the total population of painted elephants is 10/4 = 2.5 times the number caught in the sample. This suggests the total population of elephants is 2.5 times the sample size.
estimated population = 2.5 × 30 = 75 . . . elephants
Which is a true statement about the dot plot?
The team never scored exactly 2 goals in a single game.
The team scored exactly 1 goal in 3 games this season.
The most goals the team scored in a single game were 8.
The team scored exactly 3 goals in 4 games this season.
The statement that is true about the given dot plot is: A. Exactly 2 goals was never scored by the team in a single game.
What is a Dot Plot?A dot plot is a graphical representation of data using dots to denote the frequency of one data point in a distribution.
In the dot plot given, for number of goals scored per game, the data point 2 has no dot. Therefore, the statement that is true about the dot plot is: A. Exactly 2 goals was never scored by the team in a single game.
Learn more about dot plot on:
https://brainly.com/question/25957672
#SPJ1
Solve the following absolute value equation. |2+1 = 3 3 2 = -[ ]
Answer:
Sorry
Step-by-step explanation:
I not know this one