The sum of the complex number in standard form is 8 + 3i
Complex numbersComplex numbers are square roots of negative numbers. The square root of -1 for example is equal to "i" as shown;
√-1 = i
The complex number is written as x + iy. Given the expression
(9 + 6i) − (1 + 3i)
Expand to have:
9 + 6i − 1 - 3i
Collect the like terms
9-1 + 6i - 3i
Group into real and imaginary parts
(9-1) + (6i-3i)
8 + 3i
Hence the sum of the complex number in standard form is 8 + 3i
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It cost Taub $5.00 to send 100 text messages. How many text messages did she send if she spent $9.55
[tex]\begin{array}{ccll} \$&messages\\ \cline{1-2} 5 & 100\\ 9.55& x \end{array} \implies \cfrac{5}{9.55}~~=~~\cfrac{100}{x} \\\\\\ 5x=955\implies x=\cfrac{955}{5}\implies x = 191[/tex]
The number of text messages that can be sent with $9.55 is 191.
Given that, it cost Taub $5.00 to send 100 text messages.
We need to find how many text messages did she send if she spent $9.55.
What is the proportion?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of text messages she sent with $9.55.
Now, 5:100::9.55:x
⇒5x=955
⇒x=955/5
⇒x=191
Therefore, the number of text messages that can be sent with $9.55 is 191.
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The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $8.50, and bags of cookies cost $4.50, and sales equaled $79.00 in total. There were 6 more bags of cookies than candy sold.
Find the number of bags of candy and cookies sold by the drama club. Show your work.
The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively
Simultaneous equationlet
number of bags of candy = xnumber of bags of cookies = yThe equation:
8.50x + 4.50y = 79
y = x + 6
Substitute x = y + x into
8.50x + 4.50y = 79
8.50x + 4.50(x + 6) = 79
8.50x + 4.50x + 27 = 79
8.50x + 4.50x = 79 - 27
13x = 52
x = 52/13
x = 4
Recall,
y = x + 6
y = 4 + 6
y = 10
Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.
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How long can it take for the body to process the alcohol in one standard drink (0. 6 ounces)? 2 hours 1. 5 hours 1 hour 30 minutes
Answer:
1 hour
Step-by-step explanation:
6. In a standard deck of cards:
Event A: Card is red
Event B: Card is a heart
Events A and B are ____
A)None of these
B)Dependent
C)Independet
D)Both
Events A and B are dependent (option B).
What are dependent events?Dependent events are events that can occur together. If event A occurs then event B would occur. In a standard deck of cards, cards that are hearts are red in colour. If a heart card is picked, then it would be red in colour.
Independents events are events whose occurrence do not depend on each other. They are random events.
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Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?
177.8 centimeters.
What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.The shortest distance between the tip of the cone and its rim:
cos θ= base/Hypotenuse
cos 77°=[tex]\frac{40}{H}[/tex]
[tex]0.22495=\frac{40}{H}[/tex]
[tex]H=177.8[/tex]
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The shortest distance between the tip of the cone and its rim exits 51.11cm.
What is the shortest distance between the tip of the cone and its rim?If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.
Cos 38.5 = 40 / x
Solving the value of x, we get
Multiply both sides by x
[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]
[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]
Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]
[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
simplifying the above equation, we get
[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
x = 51.11cm
The shortest distance between the tip of the cone and its rim exits 51.11cm.
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Put in decimal form, out to the nearest hundredth and explain how you got your answer.
This problem is meant to be done in order of operations.
Answer: [tex]\Large\boxed{2}[/tex]
Concept:
Here, we need to know the idea of the PEMDAS method.
PEMDAS is an acronym for the order of operations.
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionSolve:
Given expression
[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]
Simplify the exponents
[tex]=\dfrac{27~-~13}{11~-~4}[/tex]
Simplify by subtraction
[tex]=\dfrac{14}{7}[/tex]
Simplify the fraction
[tex]\Large\boxed{=2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 14t + 85, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The constant in the expression represents that the company earned 85 billion dollars in 2008.
What does the constant represent?The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward
An example of a quadratic function is ax² + bx + c
Where: a,b, c are real numbers not equal to zero
c = constant.
The constant in this question is 85. It is the amount earned in 2008
Here are the options:
The company earned 85 billion dollars from 2008 to 2018
The company earned 85 billion dollars in 2008
The company earned 14 billion dollars from 2008 to 2018.
The company earned 14 billion dollars in 2008.
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Elena reflects the word 'MOM' over the x-axis and finds that it makes a new word. What is the new word?
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.
Hope this helps!
What is the solution to this inequality?
7x+18>−3
x>−3
, , x greater than negative 3, ,
x<−3
, , , , x less than negative 3, , , ,
x>3
, , x greater than 3, ,
x<3
Answer:
x>-3
Step-by-step explanation:
7x+18>-3
transpose 18 to the other side to group the like terms
7x>-3-18
7x>-21
You divide bother sides by a 7 to get the value of x
7x/7>-21/7
therefore x>-3
A company estimates that its cost and revenue can be modeled by the functions C)-0.75x+20,000
and R(x)-1.50x where x is the number of units produced. The company's profit, P, is modeled by
P(z) R(x)-C(z). Find the profit function P(x).
Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)
P(x) = -1.50x - (-0.75)x + 20,000
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
How to find profit function?
The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).
Given:
C(x) = -0.75x+20,000 and R(x)= -1.50x
P(x) = R(x) - C(x)
= -1.50x - (-0.75)x + 20,000
= -1.50x + 0.75x + 20,000
Apply rule -(-a) = a
= -1.5x + 0.75x + 20000
Add similar elements:
-1.5 x + 0.75x = -0.75x
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
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if 7 cosec^2 theta-9 cot^2theta=7 then what is the value of tantheta
The value of tanθ = ±∞ or tanθ = ±√(7/5)
The question is a trigonometric equation
What is a trigonometric equation?A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.
How to find the value of tanθ?Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.
So, 7cosec²θ - 9cot²θ = 7
using the trigonometric identity 1 + cot²θ = cosec²θ.
Substituting this into the equation, we have
7cosec²θ - 9cot²θ = 7
7(1 + cot²θ)² - 9cot²θ = 7
7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7
7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7
14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7
14cot²θ + 7cot⁴θ - 9cot²θ = 0
7cot⁴θ + 14cot²θ - 9cot²θ = 0
7cot⁴θ + 5cot²θ = 0
Factorizing out cot²θ, we have
cot²θ(7cot²θ - 5) = 0
⇒ cot²θ = 0 or 7cot²θ - 5 = 0
⇒ cotθ = ±√0 or 7cot²θ = 5
⇒ cotθ = ±0 or cot²θ = 5/7
⇒ cotθ = ±0 or cotθ = ±√(5/7)
⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)
⇒ tanθ = ±1/0 or tanθ = ±√(7/5)
⇒ tanθ = ±∞ or tanθ = ±√(7/5)
So, the value of tanθ = ±∞ or tanθ = ±√(7/5)
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What is the constant of variation for the following table? If your answer is in the form of a fraction, write your answer in as a/b.
(where a is the numerator and b is the denominator)
Answer:
1/4
Step-by-step explanation:
Change is y (f9x) over the change in x.
Look at the f(x) column.
What is the change from -2 to -1? 1
What is the change from -1 to 0? 1
What is the change from 0 to 1? 1
What is the change from 1 to 2? 1
We see that this change is constant. It is always 1.
Look at the x column.
What is the change from -8 to -4? 4
What is the change from -4 to 0? 4
What is the change from 0 to 4? 4
What is the change from 4 to 8? 4
We see that the change is constant. It is always 1.
When we put this change the form a/b we get 1/4
Which function displays this end behavior
- As x approaches negative infinity, y approaches positive infinity.
- As x approaches positive infinity, y approaches negative infinity.
Step-by-step explanation:
Since you haven't provided any functions, I can answer this question generally as to what the function would look like.
So when a polynomial has an even degree, then the two end behaviors will go in the same direction, and when it has an odd degree, then the two end behaviors will be in opposite directions. When a polynomial has a positive leading coefficient the right side will go towards infinity, and if a polynomial has a negative leading coefficient the right side will go towards negative infinity.
So let's look at the information:
As x approaches negative infinity, y approaches positive infinity.
Just given this we can't really say anything about the polynomial since we have to relate this to the right end behavior, or as x approaches infinity, so let's look at that.
As x approaches positive infinity, y approaches negative infinity.
This means that as x increases, y decreases, so that means the leading coefficient is negative. Since we know both end behaviors, and they're opposite (one y-value goes to negative infinity, and the other positive infinity), that means the polynomial is an odd degree.
So this means the polynomial will look something like this:
[tex]ax^n+bx^{n-1}+cx^{n-2}...[/tex]
where the leading coefficient "a" is negative and the degree of the polynomial (degree of leading coefficient) will be odd.
Answer:A
Step-by-step explanation:
edge 2023
Ethan's school has a sports field with an area of 6,450.35 square yards. if the length of the field is 90.85 yards, what is the width of the field? a. 81 yards b. 77 yards c. 75 yards d. 71 yards e. 65 yards
Answer:
6450.35/90.85 = 71 yards.
Step-by-step explanation:
The slope of the line below is -3 which of the following point-slope form of the line?
Answer:
The "point-slope" form of the equation of a straight line is:
\begin{gathered}y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line\end{gathered}y−y1=m(x−x1)(x1; y1) is a known pointm is the slope of the line
We have:
m=-3;\ (x_1;\ y_1)=(2;-2)m=−3; (x1; y1)=(2;−2)
Substitute
\begin{gathered}y-(-2)=-3(x-2)\\\\y+2=-3(x-2)\end{gathered}y−(−2)=−3(x−2)y+2=−3(x−2)
Answer: B. y + 2 = -3(x - 2
The price of a television was reduced from 250 to 200. by what percentage was the price of the television reduced
Answer:
20%
Step-by-step explanation:
We can start by finding out how much the price of the television was reduced by.
250 - 200 = 50
Now, we need to know what percent of 250 is 50? Let x represent the percent of 250 that is 50. Using this, we can set up an equation:
[tex]x\%\times 250=50[/tex]
Notice that a percentage can also be written as that number over 100.
[tex]\frac{x}{100}\times250=50[/tex]
[tex]\frac{250x}{100}=50[/tex]
Reduce the fraction (250 and 100 have a common factor of 10)
[tex]\frac{25x}{10}=50[/tex]
Reduce the fraction again (25 and 10 have a common factor of 5)
[tex]\frac{5x}{2}=50[/tex]
Multiply both sides by two
[tex]5x=100[/tex]
Divide both sides by 5
[tex]x=20[/tex]
Therefore the price of the television was reduced by 20%.
Which elementary row operation will reduce the x–element in row 2 to 0 in this matrix?
The elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2
How to determine the elementary row operation?The complete question is added as an attachment
The matrix is given as:
1 1 1 12
2 1 0 14
2 0 3 19
Rewrite as:
x y z
1 1 1 12
2 1 0 14
2 0 3 19
So, the x-element of the second row is
x = 2
When the first row is multiplied by negative 2 and added to the second row, the x-element of the second row is reduced to 0
This is represented as;
-2R1 + R2
i.e.
-2(1 1 1 12)
+ 2 1 0 14
---------------------------
0 -1 -2 -10
Hence, the elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2
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The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma is [tex]a=\frac{F}{m}[/tex]
Why is the formula F=ma?The equation for Newton's Second Law of Motion is F = ma. Force is equal to the rate of change of momentum, according to the definition of Newton's Second Law of Motion. Force is defined as mass times acceleration for a constant mass.The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma
F= force
m= mass
a= acceleration
[tex]F = ma[/tex]
Divide both sides by the mass
[tex]a=\frac{F}{m}[/tex]
F = ma is [tex]a=\frac{F}{m}[/tex]
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Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts.
Answer:
dave needs 3/5
Step-by-step explanation:
Step-by-step explanation:
what is the question ?
what problem needs to be solved ?
is it to find the ratio between fruit and nuts ?
then remember, a ratio is a fraction.
so, the ratio fruit : nuts is
1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5
or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?
to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.
how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.
1/5 = 1/5 × 3/3 = 3/15.
and with the same line of thinking :
1/3 = 1/3 × 5/5 = 5/15.
so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.
here you can clearly see the ratio again : 3/15 : 5/15 = 3:5
the first solution to get only full cups of trail mix is
3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.
anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).
What is the domain of the following points? Group of answer choices {-4, 1, 4} {-4, -1, 1, 4} {-1, 4, 1} {1, 4}
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The complete question is added as an attachment
The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
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Kim purchased a dress that was originally $35. It was on sale for 30% off. She also bought a pair of shoes for 1/2 off the original price of $17. If the store added a 4% sales tax, how much would she pay for both items?
Answer: $34.32
Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.
Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range
Answer:
58, 66, 79, 84, 87 (see explanation for the exact answer)
Step-by-step explanation:
{58, 66, 79, 84, 87}
minimum = 58
lower quartile = 66
median = 79
upper quartile = 84
maximum = 87
Answer + Step-by-step explanation:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
The data set is in order then :
the minimum = 58
The maximum = 87
Determining the median :
first ,we notice that the data set has an even number (14) of numbers
Then
The median is the average of the two central values of the data set :
the two central values are the 7th and 8th numbers:
[tex]\text{median} =\frac{79+79}{2} =79[/tex]
Determining the lower quartile :
The lower quartile is the median of the set :
58, 60, 65, 67 , 68, 72, 79
this set has an odd number (7) of values
Then
The central value is 67
Therefore
The lower quartile is 67
Determining the upper quartile :
The upper quartile is the median of the set :
79, 80, 81, 82 , 86, 86, 87
this set has an odd number (7) of values
Then
The central value is the 4th number which is 82
Therefore
The upper quartile is 82
Interquartile range :
82 - 67 = 15
Find the length of CB.
5x – 3
3x + 1
Assumed that sides are equal
5x-3=3x+15x-3x=1+32x=4x=2CB
5(2)-37Three fair, standard six-faced dice of different colors are rolled. In how many ways can
the dice be rolled such that the sum of the numbers rolled is 15?
These are some of the ways you can make 15 by adding three numbers together.
The first way is doing 6+6+3.There are some more ways to do it too.
2nd way is 6+4+5.
3. 1+6+6
4. 5+5+5
Which values below belong in this table? Select all that apply.
The possible value of y are 16, 32 and 64
How to find the values of an exponential table?The table above is an exponential table.
Therefore, let's confirm the ratio of the y axis.
8 / 4 = 2
4 / 2 = 2
Therefore, the other y axis can be gotten as follows:
y = 8 × 2 = 16
y = 16 × 2 = 32
y = 32 × 2 = 64
y = 64 × 2 = 128
Therefore, the possible value of y are 16, 32 and 64
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The likelihood of the frequency of an event in repeated trials under similar conditions is?
The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.
What is Statistical analysis?The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
What accomplishes statistical analysis?Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.
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i want to solve this problem i forgot maths lol 4/5 + 8/5
Answer:
The correct answer is 2 [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
To get this answer, we first have to add the numerators.
We can easily say that 4 + 8 = 12
That leaves us with the improper fraction, [tex]\frac{12}{5}[/tex].
To make this fraction proper, we must first find out how many times 5 can go into 12.
5 can go into 12 two times which leaves us with 2 left over from the numerator.
Now all that's left to do is add 2 (the amount of times 5 can go into 12) and [tex]\frac{2}{5}[/tex] (the left over fraction) to get the answer 2[tex]\frac{2}{5}[/tex].
Hope this helps:) Goodluck!
(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has
three vertices with integer coordinates. Show your work by providing an example and
including a graph. Consider an equilateral triangle whose base lies along the x-axis.
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
Location of point CWith reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC never passes through a point with integer coordinates. (Any point with integer coordinates would be on a line with rational slope.)
Equilateral triangleThe line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
[tex]\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right][/tex]
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
HELP, i really need help with these for questions, I’ll give Brainliest to whoever answers first, random answers will be reports.
The angles and lengths of each of the given triangles are;
5) m∠B = 57.52°
6) B = 70.81°
7) AB = 55.43 Km
8) AC = 39.06 ft
How to use cosine rule?
The cosine rule is expressed as;
c = √[a² + b² - 2ab(cos C)]
5) Using cosine rule;
BC = √[21² + 13² - 2(21*13)(cos 91)]
BC = 24.89
Using sine rule, we can find angle B as;
21/sin m∠B = 24.89/sin 91
sin m∠B = (21 * sin 91)/24.89
sin m∠B = 0.8436
m∠B = sin⁻¹0.8436
m∠B = 57.52°
6) Using cosine rule;
14² = 11² + 13² - 2(11*13)(cos B)]
196 = 121 + 169 - 286(cos B)
cos B = (121 + 169 - 196)/286
cos B = 0.3287
B = cos⁻¹0.3287
B = 70.81°
7) Using cosine rule;
AB = √[24² + 36² - 2(24*36)(cos 134)]
AB = 55.43 Km
8) Using cosine rule;
AC = √[21² + 26² - 2(21*26)(cos 112)]
AC = 39.06 ft
Read more about cosine rule at; https://brainly.com/question/4372174
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