Answer:
36
Step-by-step explanation:
5(4)+16=20+16=36
Find the vertex of the graph of the equation $y = -2x^2 + 8x - 15.$
Answer:
(2,-7)
Step-by-step explanation:
Find z.
What is the length of the missing leg?
b = _____ miles
Answer:
5√3
Step-by-step explanation:
tan30= 5/z
1/√3= 5/z
z= 5√3
4. Explain what an imaginary number is and its relationship to complex numbers. Then give
an example of where complex numbers occur naturally in mathematics.
Answer:
564643
Step-by-step explanation:
Answer:
In the real number system, there is no solution to the equation x^2=-1x
2
=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.
The backbone of this new number system is the number iii, also known as the imaginary unit.
i^2=-1i
2
=−1i, squared, equals, minus, 1
\sqrt{-1}=i
−1
=isquare root of, minus, 1, end square root, equals, i
By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i
5
i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.
However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−
2
i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.
Defining complex numbers
A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.
\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}
a
↑
Real
part
+
bi
↑i
Imaginary
part
\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.
The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.
Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts
7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.
4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd
9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd
-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd
Step-by-step explanation:
plz brian list and allways happy to help.
I NEED HELP PLEASE IT WOULD HELP ME ALOT
Answer:
Step-by-step explanation:
21 is the side opposite the angle you want.
67 is the hypotenuse. Those two sides define the Sin
Sin(theta) = opposite / hypotenuse
Sin(theta) = 21 / 67
Sin(theta) = .313432
theta or x = sin-1(0.313432)
x = 18.27
Sorry, I must have hit the wrong key the first time.
Answer:
18.27˚
Step-by-step explanation:
Pls do it for me thank you so much
Answer:
(a) Attached to this response.
(b)
(i) 0 cups = 0.275
(ii) 4 cups = 0.125
(iii) 8 cups = 0.025
Step-by-step explanation:
(a) The frequency and relative frequency table has been attached to this response.
i. The first column, labelled x, is the number of cups of coffee consumed per day.
ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.
For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.
iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).
For example, the relative frequency of 2 cups of coffee is given by:
r = 7 ÷ 40 = 0.175
Also, the relative frequency of 4 cups of coffee is given by;
r = 5 ÷ 40 = 0.125
(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;
Pₓ = frequency of x ÷ total frequency
This is also the relative frequency of x
Therefore,
(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;
the relative frequency of 0 = 0.275
(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;
the relative frequency of 4 = 0.125
(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;
the relative frequency of 8 = 0.025
Imani is a scientist working with a cylindrical beaker. The base of the right cylinder has a diameter of 19 cm. She fills the
beaker with 2256.254 Cms of an acid. Approximately how high did the acid fill up the beaker?
Answer:
7.96 cm
Step-by-step explanation:
radius of bottom: 19/2 = 9.5
area of bottom = pi * r^2 = 283.53
height * base area = volume
Find the volume of a pyramid with a square base, where the area of the base is 19 cm^2 and the height of the pyramid is 23.8 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
150.7
Step-by-step explanation:
Formula to the find volume of a pyramid:
V=1/3 (B)(h)
V=1/3 (19) (23.8)
What is the definition of mean?
Answer:
D. It is the sum of the data divided by the number of pieces of data
Step-by-step explanation:
It's also known as the average of the numbers in a data set.
What is the definition of mean?
[tex]{\boxed{\mathcal{\red{Answer.}}}}[/tex]
[tex]D.\:It \: is \: the \: sum \: of \: the \: data \: divided \: by \: the \: number \: of \: pieces \: of \: data.[/tex]
The mean is the average of the numbers.To find the mean, we add up all the numbers, then divide by how many numbers there are.[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Ryland rolls a numbered cube that has sides labeled 1 - 6 and then flips a coin. What is the probability that he rolls an odd number and lands on tails?
1/2
1/4
3/4
1/8
Answer:
1/4
Step-by-step explanation:
When solving a system of inequalities or just an inequality (like 2-4y > 14), in what condition the sign flip to the other way?
Answer:
When the coefficient of the variable is negative, as shown below,
Step-by-step explanation:
2-4y>14
-4y>14-2
-4y>12, divde through by - 4
y>-3
A stack of 500 pieces of paper is 1.875 inches tall. Compute the thickness of each piece of paper. Show your reasoning.
Answer:
0.003750 inches
If the thickness of 500 pieces is given as 1.875. the thickness of one sheet of paper can be determined by dividing the total inches by 500
Thickness of each paper = thickness of total paper / 500
1.875 / 500 = 0.003750 inches
Step-by-step explanation:
Answer:
If the thickness of 500 pieces is given as 1.875. the thickness of one sheet of paper can be determined by dividing the total inches by 500
Thickness of each paper = thickness of total paper / 500
1.875 / 500 = 0.003750 inches
Step-by-step explanation:
PLS HELP 6TH GRADE PLEASE
Answer:
6 x 5 x 1/2(divide by 2) = 15, 15 x 2(two triangles) = 30
27 x 6 = 162 (area of base)
27(width) x 6(height) x 2(two rectangles on both slanted sides) = 324
Add given areas:
30 + 162 + 324 = 516 ft2 is your answer.
A Dilation has a center (0,0). Find the image of this point for the given scale factor: P (2-4); D 0.5 (P)
Answer:
(1, -2)
Step-by-step explanation:
The dilation that has a center of (0, 0) means that you would multiply each number in your coordinate point by your given scale factor.
For your given point (2, -4) with a scale factor of 0.5:
2 times 0.5 = 1
-4 times 0.5 = -2
Therefore your new point will be (1, -2).
On a map, 1 inch equals miles. Two houses are inches apart on the map. What is the actual distance between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios.
Answer:
The actual distance between the houses is 18.9 miles.
Step-by-step explanation:
The exact question is as follows :
Given - On a map, 1 inch equals 5.4 miles. Two houses are 3.5 inches apart on the map.
To find - What is the actual distance between the houses?
Solution -
Given that,
1 inch = 5.4 miles
⇒3.5 inches = 3.5 × 5.4 miles
= 18.9 miles
∴ we get
The actual distance between the houses is 18.9 miles.
The number of patients treated at Dr. Frank's dentist office each day was recorded for nine days: 18,
19, 19, 4, 14, 8, 22, 3, 1. Using the given data, find the mean for this sample.
A. 12
B.19
C. 29
D. 14
Answer: 12
Step-by-step explanation: The mean is basically the average. So, start by lining up the numbers from smallest to largest. 1, 3, 4, 8, 14, 18, 19, 19, 22. Then, add them all together. You get 108. Then, divide 108 by the number or numbers in the data set, which in this case is 9. So 108 divided by 9 = 12. Your answer is A. --> 12
Hope that helped!!
The amount of rona cases in Gotham city is 540 people for the first ½ of 2020. In July, a rona spike at the rate of 5.2 people for each day in the month hits. Additionally, the joker has infected all of Arkham Asylum’s 225 patients with the virus. What month will you hit 1,000 cases of rona in Gotham?
Answer:
Imma but it in the comments because i can't put it on here plus i can't put the thing on here either that's why i didn't do it yesterday
Step-by-step explanation:
What is the measure of the reference angle for a 112 degrees angle?
Answer:
68
Step-by-step explanation:
A P E X
Witch product is less then 5/8
7/10x5/8
4/3x5/8
9/7x5/8
3/2x5/8
Thank you
Answer:
Answer is 7/10 × 5/8
Step-by-step explanation:
only answer which is under 5/8ths being 7/16 :)
Answer:
7/10x5/8
Step-by-step explanation:
7/10x5/2=7/16
4/3x5/8=5/6
9/7x5/8=45/56
3/2x5/8=15/16
PLS HELP ILL GIVE BRAINLIEST
Answer:
answer is 8
Step-by-step explanation:
take Lcm of 8 and 32
Answer:
8
Step-by-step explanation:
the radius of a circle is 14.2 m. Find the circumference to the nearest tenth.
Answer:
C=89.2
Step-by-step explanation:
The formula of the circumference of a circle is C=2piR (or C=piD). Now, when calculating, plug in the numbers, giving you C=2pi14.2. Multiply everything, you get a super long irrational number; just round. You will get 89.2.
A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes.
Given :
A motorboat travels 9 miles downstream (with the current) in 30 minutes.
The return trip upstream (against the current) takes 90 minutes.
To Find :
The speed of stream and motorboat.
Solution :
Let, speed of stream is u and speed of motorboat is v.
Now, we know distance is same in both case.
Distance( downstream ) = speed × time
[tex]9 = ( v +u ) \times 0.5\\\\v + u = 18[/tex]....1)
Distance( upstream ) = speed × time
[tex]9 = ( v- u ) \times 1.5\\\\v-u = 6[/tex]....2)
Solving equation 1 and 2 , we get :
v = 12 miles/hour and u = 6 miles/hour
Hence, this is the required solution.
Answer:
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
Step-by-step explanation:
Downstream:
9 miles in 30 minutes (0.5 hour).
9 mi / 0.5 h = 18 mph
Upstream:
9 miles in 90 minutes (1.5 h).
9 mi / 1.5 h = 6 mph
Let s = speed of stream.
The speed of the stream adds to the speed of the boat downstream and is subtracted fromt he speed of the boat upstream.
Let speed of boat be b.
b + s = 18
b - s = 6
Add the equations.
2b = 24
b = 12
b + s = 18
12 + s = 18
s = 6
The speed of the stream is 6 mph, and the speed of the boat is 12 mph.
The number of hours that each of 6 students spent reading last week is shown in the bar graph below. For the data in the bar graph, which measure is the LEAST? *
1 point
Captionless Image
pls answer thank you
435.6
mark me brainliestt pls :)))
Kelly is making a rectangular garden that has a width of (2x + 3) and length of (2x - 4)
How much fertilizer would she need to lay down before she starts to
plant her flowers (area)?
the number of digits in the square root of 36000000 is
The ANSWER is Four Digits
When you'll square root - 36000000 you'll get 6000 there are four digits in 6000
NEED HELP HERE PLEASE!! π∆π
Give the value of the six trigonometric ratios in the figure.
Answer:
Step-by-step explanation:
take theta as reference angle
using sin rule
sin theta=opposite/hypotenuse
sin theta=3/5
sin theta=0.60
theta=sin 37 degree
therefore the value of theta is 37 degree.
There are 29 students in Mrs. Dixon's science class. On the last test, only 1 student earned the median score of 84.
How many students scored an 84 or lower?
A - 15
b - 14
C - 13
D - 12
Answer:
A
Step-by-step explanation:
Median can be described as the number that occurs at the middle of a set of observations.
for example, in the set of numbers, 1 2 3 4 5, the median is 3
median = (first number + last number) / 2
If there are 29 students,
median = (1 + 29) / 2 = 30/2 = 15
the 15th students scored 84
and students between 1 - 14 scored lower than 84
so, 15 students scored an 84 or lower
Ken recorded the weights (in pounds) of 78 boxes. He created a box plot of his data. What is the interquartile range of Ken’s data?
A) 8
B) 10
C) 17
D) 48
The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.
What is the interquartile range of a data?The interquartile range(IQR) = third quartile(Q3) - first quartile(Q1)
The third quartile of in the box plot given is : 56 pounds
The third quartile of the data as represented in the box plot given :
39 pounds
The interquartile range(IQR) of ken's data = 56 - 39
= 17 pounds
Hence, The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.
Find more information about the interquartile range here
https://brainly.com/question/4102829
#SPJ2
y=7(3)^-4 please helpppp
Answer:
Step-by-step explanation:
y=7(3)^-4
y=7*1/3^4
y=7/81
#1: Find the area of the triangle shown below.*
6 ft
14 ft
Answer:
42 Square feet
Step-by-step explanation:
A=(1/2)bh
A=(1/2)(14)(6)
A=42