Answer:
x = 16
Step-by-step explanation:
Angles in a triangle add up to equal 180
Hence, 9x - 8 + x + 10 + x + 2 = 180
^ ( note that we just created an equation that we can use
to solve for x )
We now solve for x using the equation created.
9x - 8 + x + 10 + x + 2 = 180
step 1 combine like terms
9x + x + x = 11x
-8 + 10 + 2 = 4
we now have 11x + 4 = 180
step 2 subtract 4 from each side
180 - 4 = 176
4 - 4 cancels out
we now have 11x = 176
step 3 divide each side by 11
176 / 11= 16
11x / 11 = x
we're left with x = 16
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!!
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.
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).
What is the measure of the reference angle for a 112 degrees angle?
Answer:
68
Step-by-step explanation:
A P E X
Find the vertex of the graph of the equation $y = -2x^2 + 8x - 15.$
Answer:
(2,-7)
Step-by-step explanation:
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.
please simplify
4(57ab)⁰
no links, answer quickly,please
Answer:
4
Step-by-step explanation:
Using the rule of exponents
[tex]a^{0}[/tex] = 1
Then
4[tex](57ab)^{0}[/tex] = 1 and
4[tex](57ab)^{0}[/tex] = 4 × 1 = 4
Answer:
4
Step-by-step explanation:
since 57ab has power 0 it is equal to 1
1×4 is 4
What is the length of the hypotenuse?
Answer:
h=15feet.
Step-by-step explanation:
using Pythagoras theorem
h²=p²+b²
h²=12²+9²h²=144+81h=√225h=15feet.hope it helps.
stay safe healthy and happy.[tex]\huge\bold{To\:find:}[/tex]
✎ The length of the hypotenuse.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{The\:length\:of\:the\:hypotenuse \:"c"\:is\:15\:feet.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]( {perpendicular})^{2} + ( {base})^{2} = ( {hypotenuse})^{2} \\⇢ ({12 \: ft})^{2} + ( {9 \: ft})^{2} = {c}^{2} \\ ⇢ 144 \: {ft}^{2} + 81 \: {ft}^{2} = {c}^{2} \\ ⇢ 225 \: {ft}^{2} = {c}^{2} \\ ⇢ \sqrt{225 \: {ft}^{2} } = c \\ ⇢ \sqrt{15 \times 15 \: {ft}^{2} } = c \\ ⇢ 15 \: ft = c[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:15\:feet.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {12 \: ft})^{2} + ( {9 \: ft})^{2} = ( {15 \: ft})^{2} \\⇝144 \: {ft}^{2} + 81 \: {ft}^{2} = 225 \: {ft}^{2} \\ ⇝225 \: {ft}^{2} = 225 \: {ft}^{2} \\ ⇝L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
PLEASE ANSWER URGENT
Answer:
D
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.
Nicole received a $15.00 gift card for a photo center. She used it to buy prints that cost 7 cents each. The remaining balance, B (in dollars), on the card after buying x prints is given by the following.
What is the remaining balance on the card if Nicole bought 50 prints?
Answer:
$11.50
Step-by-step explanation:
Since it's 7 cents to buy 1 print, you do 7 times 50 = 350 cents for 50 prints which is $3.50 so then we do $15.00 - $3.50 = $11.50
Therefore, the remaining balance on the card is $11.50
Please mark my answer as brainliest, it will help a lot.
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
HELLLLPPPPPPP PLEASEEEEEE BEGGGGI G SOMEONE PLEASEEEEEEEEE
Answer:113
Step-by-step explanation:
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.
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]
pls answer thank you
435.6
mark me brainliestt pls :)))
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)
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
I NEED THIS QUICK no links !!!!! (math)
answer: the answer is c
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:
complete:
a 20% x ____ = $30
Answer:
20/100*x=$30
20x/100=$30
x/5=$30
x=$30*5
x=$150
Step-by-step explanation:
20 percent of 150 equals 30 so 150 times 20 percent would give you 30
Select the values that make the inequality n > -8 true.
(Numbers written in order from least to greatest going across.)
Answer:
9
Step-by-step explanation:
I'm somewhat confused I think you're forgot to put so more information
The value that makes the inequality n > -8 true will be -2. Thus, the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below:
n > -8
The value of n is greater than -9. Then the value that makes the inequality n > -8 true will be -2.
Thus, the correct option is A.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
The missing options are given below.
a) - 2
b) - 9
c) - 10
d) - 20
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
Santiago buys a new television for $989.76. If
the sales tax rate is 8.75%, what is the total cost
of the television?
Answer:
$1076.36
Step-by-step explanation:
The full price before tax can be represented by 1.00($989.76), and the 8.75% tax by 0.0875($989.76)
which can be combined to obtain the total cost: (1.0875)($989.76) = $1076.36
3x −3 y −4 ⋅ 3x 3 y 3
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
Which is a true statement based on the dot plots below?
10 20 30 40 50 60
10 20 30 40 50 60
Set A
PLZZZZZZZZZZZZZ HELPPPPPPPPP
Answer:
Given, Distributive property, Subtraction Property, Division Property, Prove
Step-by-step explanation:
This is what I think the answer is. So if the answer is wrong than I don't know
what is the answer? please helppp
Answer:
1/4
Step-by-step explanation:
Probability is: (ways to get a desired result) / (total possible outcomes)
Choosing a yellow ball would be a desired result.
So, using the numbers that the question gives us,
(3 ways to get a yellow ball) / (12 golf balls total) =
3 / 12 =
1 /4
The answer is 1/4 chance.
Answer:
3/12 0r 1/4 <--- Simplified
Step-by-step explanation:
so there are 3 yellow which are in 12 gold balls so
it would be 3/12 or simplified 1/4
The area of a rectangular piece of plastic is 10 square millimeters. The perimeter is 22 millimeters. What are the dimensions of the piece of plastic?