Answer:
81
Step-by-step explanation:
Area is multiplying all side
9 x 9 = 81
Simplify the following complex number in a+bi form
(1-i)^3
The following complex number (1-i)³ in a+ bi form is -2+4i
What is meant by complex number?In mathematics, a complex number is a part of a number system that includes an element with the symbol I often known as the imaginary unit, and extends the real numbers. Complex numbers satisfy the equation that any complex number can be represented as a + bi, where a and b are real numbers. Rene Descartes referred to me as an imaginary number because no real number can satisfy the aforementioned equation. A and b are referred to as the real and imaginary parts, respectively, of the complex number a+bi. Complex numbers are accepted in the mathematical sciences as being just as "real" as real numbers despite the historical appellation "imaginary."
(1-i)³
=1³-i³-3(1)(i)(1-i)
=1+i-3(1-i)
=1+i-3+3i
=-2+4i
Therefore, the following complex number (1-i)³ in a+ bi form is -2+4i.
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What is the volume of a cube with a mass of 20 grams and a density of 6g/cm3?
The volume of the cube with a mass of 20 grams and a density of 6 g/cm³ is 3.33 cm³
Calculating the volume of a cubeFrom the question, we are to determine the volume of the given cube
From the given information,
The mass of the cube is 20 grams
and
The density of the cube is 6 g/cm³
From the formula,
Density = Mass / Volume
Then, we can write that
Volume = Mass / Density
Thus,
The volume of the cube is
Volume = 20/6
Volume = 3.33 cm³
Hence, the volume is 3.33 cm³
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A beaker contains 235.5 milliliters of water. If the water is equally distributed among 15 test tubes, how many milliliters will be in each tube?
Answer: 356 mil
Step-by-step explanation:
Answer:
Each tube will contain 15.7 millimeters
Step-by-step explanation:
Since 235.5 milliliters of water is to be shared among 15 test tubes then the amount of water in each test tube is:
[tex]\frac{235.5}{15} \\\\= 15.7[/tex]
Thus each tube will contain 15.7 millimeters
Give proper explanation
Answer:
a = 84°
b = 21°
c = 48°
Step-by-step explanation:
Step 1.)
The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°
180°-75° = 105 = a° + b°
Step 2.)
We also know that the line RS is 180°. Therefore, it must be true that
75° + 4b° + b° = 180°
or simply
5b + 75 = 180°
Now solve for b. Subtract both sides by 75 and divide the right side by 5
5b = 105°
b = 21°
4b° = 4 x b = 4 x 21° = 84° = 4b°
Step 3)
Since we know that a + b = 105°, we use substitution to get:
a + 21° = 105
Now subtract both sides by 21
a = 84°
Now let's double check if a + b + 75 = 180
84 + 21 + 75 = 180 [check]
Step 4.)
Since we know that PQ is a straight-line that is 180°, we can say:
180° = 4b° + 2c°
Now substitute 4b with 84°
180° = 84° + 2c
Now solve by subtracting 84 from 180 and divide by 2, if needed.
96° = 2c°
48° = c°
Now double check
96° + 84° = 180° [check]
Therefore:
a = 84°
b = 21°
c = 48°
Hope that helps.
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Please help! Geometry, Tangents to circles! Please answer all 3! 50 points!! Thank you so much!!!
1. Construct two tangents to circle 0 through P
2. Construct two tangents to circle 0 through point P and one tangent through point A. Extend the tangents until they intersect. What relationship exists between the triangle and the circle?
3. Construct a common internal tangent for circle A and for circle B.
The Tangents of the three circles passing though point P and A are attached below
2.
The circle is inscribed in the triangle and is the largest circle which will fit within the triangle. The line from each triangle vertex to the center of the circle bisects each angle of the triangle
What is a tangent ?
A tangent in geometry is a line that originates at an outside point and travels through a curve's Centre. When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent. Let's use an illustration to better grasp what a tangent is. The arc S and point P outside of S are depicted in the following figure. S has been reached via a tangent from P. This serves as an illustration of a tangent.
Two crucial characteristics of the tangent are:
A tangent only hits a curve once.
A line that never reaches the inside of the circle is known as a tangent.
At the point of tangency, the tangent makes a right angle contact with the circle's radius.
A tangent to the circle also has mathematical theorems linked with it, which are needed when doing important computations in geometry in addition to the qualities mentioned above. Let's go into further depth on a couple tangents to circle theorems.
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The smaller of two numbers is one more than half the larger number. If their sum is 133, write an equation to solve for the two numbers.
Answer:
The two numbers are 44 as the smaller number and 89 as the larger number.
Step-by-step explanation:
Hope it helps!
Let's call the larger number x, and the smaller number y. We know that y is one more than half of x, so we can write y = x/2 + 1. We also know that the sum of the two numbers is 133, so we can write x + y = 133. We can use these two equations to solve for the values of x and y. Substituting the first equation into the second, we get:
x + (x/2 + 1) = 133
Combining like terms, we get:
1.5x + 1 = 133
Subtracting 1 from both sides, we get:
1.5x = 132
Dividing both sides by 1.5, we get:
x = 88
Substituting this value for x in the first equation, we get:
y = 88/2 + 1 = 44 + 1 = 45
Therefore, the two numbers are 88 and 45, and we can check our solution by verifying that the sum of these numbers is indeed 133.
x + y = 88 + 45 = 133
This confirms that our solution is correct.
c = t + s
ts = c + t - s
3c = t + 10s
p = (c + t)/s
solve for P
Answer:
p = 8
Step-by-step explanation:
Given 4 equations in 4 unknown values, you want to find the value of p.
c = t +sts = c +t -s3c = t +10sp = (c +t)/sSolutionSubstituting for c in the second equation, we have ...
ts = (t +s) +t -s
ts = 2t . . . . . . simplify
s = 2 . . . . . . . divide by 2
Substituting for c and s in the third equation, we have ...
3(t +2) = t +10·2
2t = 14 . . . . . . . . . subtract t+6
t = 7
Substituting for c, t, s in the equation for p gives ...
p = ((t +s) +t)/s = (2·7 +2)/2 = 8
The value of p is 8.
__
Additional comment
The variable values are (c, p, s, t) = (9, 8, 2, 7).
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. The law firm assigned a total of 16 lawyers to the case and was able to charge the client $11800 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system of equations.
The system of equations that could be used to solve the problem are;
400a + 1000p = 8800
a + p = 13
Where a is associate and p is partner
How to write a system of equations?Let the variables be defined as:
Associate is denoted by a
Partner is denoted by p
We are told that the daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. Thus, the equations are:
400a + 1000p = 8800 -----(1)
a + p = 13 ------(2)
Make a the subject in eq 2 to get;
a = 13 - p -----(3)
Put 13 - p for a in eq 1 to get;
400(13 - p) + 1000p = 8800
5200 - 400p + 1000p = 8800
5200 + 600p = 8800
5200 + 600p = 8800
600p = 3600
p = 6 partners
a = 13 - p
a = 13 - 6
a = 7 associates
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Peter enters a hot dog eating contest. Peter's friend calculates that on average, Peter eats 2 hot dogs per minute. They write the equation y = 2x in order to predict how many hot dogs Peter can eat in a 30-minute contest, where x stands for the amount of time in minutes and y stands for the total number of hot dogs.
A) Does the equation represent a proportional relationship? Explain your reasoning.
B) What is the unit rate of change for this situation?
Answer:
A) The equation y = 2x represents a proportional relationship. This is because the values of y are directly proportional to the values of x. In other words, as x increases, y also increases by the same factor. This is the definition of a proportional relationship.
B) The unit rate of change for this situation is 2 hot dogs per minute. This is because the equation y = 2x represents a linear relationship, where the rate of change (the slope) is constant. The unit rate of change is the slope of the line, which in this case is 2. This means that for every 1 minute that passes, Peter eats 2 hot dogs.
Find the quotient using multiplication.
3/4 ÷ 6/7
Fill in the blanks to show the steps.
Answer:
1) 3/4 x 7/6
2) 21/24
3) 7/8
Step-by-step explanation:
1) KCF, Keep change flip. 3/4 stays the same, division sign changes into multiplication, and 6/7 changes into its reciprocal.
2) Multiply numerator by numerator and denominator by denominator
3) Find their greatest common factor (GCF) and divide the numerator and denominator by it. There's your simplified answer.
Answer:
7/8
Step-by-step explanation:
Divide 3/4 with 6/7
3
4
÷
6
7
is
7
8
.
Steps for dividing fractions
Find the reciprocal of the divisor
Reciprocal of
6
7
:
7
6
Now, multiply it with the dividend
So,
3
4
÷
6
7
=
3
4
×
7
6
=
3 × 7
4 × 6
=
21
24
After reducing the fraction, the answer is
7/8
Find the value of n.
(3×9) × 8 = (8×3) × n
Answer:
9
Step-by-step explanation:
Because it is multiplication, the parenthesis are not important. It is the equivalent of 3*9*8 = 8*3*n. From here, you can tell that the 9 is missing.
what are the variables in an experiment that tests the distance honey flows at different temperatures?
The variables in an experiment that tests the distance honey flows at different temperatures is the distance honey flows is the dependent variable and temperature is the independent variable .
Given :
In the experiment " Temperature" is dependent variable and the distance honey flows is independent variable.
What is independent variable ?
It is the factor that one can purposely control or change to observe its effect , is called independent variable.
What is dependent variable ?
It respond to the change in the independent variable , is called dependent variable.
Hence temperature is dependent and distance honey flow is independent variable.
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9. In a combined class of 60 Art and science
Students, the result of their mock examing-
tion showed that 39 of them passed physics
36 Passed Geography and 40 passed History,
of these, 22 passed both physics and History
21 passed both physics and Geography an
23 passed Geography and History. Given
that 10 of them passed all the three subjects
Find:
a. The number of Students who passed only
physics
b. The number of Students who passed
only Geography.
C. The number of student who passed
only History
The number of students who passed only physics is 6, the number of students who passed only geography is 2, and the number of students who passed only history is 5.
First, let's represent the number of students who passed each subject with the variables P, G, and H. Then, we can represent the number of students who passed multiple subjects with the variables PG, PH, and GH.
We are given the following information:
39 students passed physics (P)
36 students passed geography (G)
40 students passed history (H)
22 students passed both physics and history (PH)
21 students passed both physics and geography (PG)
23 students passed both geography and history (GH)
10 students passed all three subjects (PHG)
We can set up the following equations to represent these relationships:
P = 39
G = 36
H = 40
PH = 22
PG = 21
GH = 23
PHG = 10
We can use these equations to solve for the number of students who passed only physics (P - PH - PG + PHG), only geography (G - GH - PG + PHG), and only history (H - PH - GH + PHG).
So, the number of students who passed only physics is:
P - PH - PG + PHG = 39 - 22 - 21 + 10 = 6
The number of students who passed only geography is:
G - GH - PG + PHG = 36 - 23 - 21 + 10 = 2
The number of students who passed only history is:
H - PH - GH + PHG = 40 - 22 - 23 + 10 = 5
Thus, there are 6 students who passed only physics, 2 students who passed only geography, and 5 students who passed only history.
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~Describe each transformation in words.
10.) ___________________________.
Paige is filling her tub at a rate of 3/4 gallons every 2/3 minutes how many gallons
Devora tested two engines. As each engine's rotation got faster, its temperature increased at a constant rate.
The first engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is given by the following table of values:
\text{Rotation}Rotationstart text, R, o, t, a, t, i, o, n, end text (cycles per second) \text{Temperature}Temperaturestart text, T, e, m, p, e, r, a, t, u, r, e, end text (degrees Celsius)
888 26.426.426, point, 4
111111 28.828.828, point, 8
141414 31.231.231, point, 2
The graph of the second engine's temperature (in degrees Celsius) as a function of its rotation speed (in cycles per second) is shown below.
The temperature of which engine increased more for each increase of 111 cycle per second?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
The temperatures of both engines increased the same
Which engine was hotter when it rotated at 202020 cycles per second?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The first engine
(Choice B)
B
The second engine
(Choice C)
C
Both engines were equally hot
The correct option is B in the given Temperature problem by Calculation T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius,
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
According to the given information:
For the first question, we need to compare the rate of change of temperature with respect to rotation speed for both engines. We can do this by calculating the difference in temperature for a change in rotation speed of 111 cycles per second for both engines.
For the first engine, the temperature increased by:
31.2 - 28.8 = 2.4 degrees Celsius
For the second engine, the temperature increased by:
60 - 50 = 10 degrees Celsius
Since the temperature increase for the second engine is greater, we can conclude that the second engine's temperature increased more for each increase of 111 cycles per second. Therefore, the answer is (B) The second engine.
For the second question, we can use linear interpolation to estimate the temperature of each engine at 20 cycles per second.
For the first engine, we can use the two closest data points (8.8 and 11.1 cycles per second) to estimate the temperature at 20 cycles per second:
T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius
For the second engine, we can use the same method with the two closest data points (10 and 20 cycles per second):
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
Therefore, we can conclude that the second engine was hotter when it rotated at 20 cycles per second. The answer is (B) The second engine.
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What value for a in the system of equations below would yield no solutions for the system? Explain how you obtained your answer.
ax+12y=−6
2x−6y=4
a=
The value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.
What is the equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given:
ax + 12y = −6
2x − 6y = 4
Calculate the value of a by using the condition of no solution of the system given below,
[tex]a_1 / a_2 = b_1 / b_2 \neq c_1/c_2[/tex]
So, a₁ / a₂ = b₁ / b₂
a / 2 = 12 / (-6)
a / 2 = - 2
a = -4
And -4 / 2 ≠ -6 / 4
Therefore, the value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.
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Helppppp. I can’t figure this out
Answer: B
Step-by-step explanation:
Multiply matrices
AB = [ 4 5 ] x [ 3 ]
[ 8 7 ] [ 9 ]
4 x 3 + 5 x 9 = 12 + 45 = 57
8 x 3 + 7 x 9 = 24 + 63 = 87
[ 57 ]
[ 87 ]
-x +5y = 28
x+3y=20
Show your work please
The solution to the given system of linear equations is x = 2, y = 6.
Solving system of linear equationsFrom the question, we are to solve the given system of linear equations
The given system of linear equations is
-x +5y = 28
x+3y=20
To solve the equation, add the equations
-x +5y = 28
+ x + 3y=20
------------------
8y = 48
Divide both sides by 8
8y/8 =48/8
y = 6
Substitute the value of y into the second equation
x+3y=20
x + 3(6) = 20
x + 18 = 20
x = 20 - 18
x = 2
Hence, the solution is x = 2, y = 6
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[tex]\frac{hx^{-5} }{hx^{-9} }[/tex]
The solution is h⁴ for the equation h⁻⁵ / h⁻⁹.
What is simplification?The process of making something less complicated and thus easier to do or understand, or the product of such a process:Begin by solving all of the terms in parentheses to simplify math expressions using the order of operations. After that, solve the exponents and do any necessary multiplication. Next, solve division problems, followed by adding and finally subtracting. This leads to another exponent rule: the Power Rule for Exponents. To simplify a power of a power, multiply the exponents while maintaining the same base.Given equation,
h⁻⁵ / h⁻⁹
We know that ,
According to law of exponents ,
xᵃ / xᵇ = xᵃ⁻ᵇ
So here
h⁻⁵ / h⁻⁹ = h⁻⁵ ⁺⁹
= h⁴
Therefore the solution of the equation h⁻⁵ / h⁻⁹ is h⁴.
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Expand the expression 1.5(4p+2q)
Answer:
6p+3q
Step-by-step explanation:
1.5(4p+2q)
Distribute property
1.5(4p)+1.5(2q)
6p+1.5(2q)
6p+3q
pleasee need brainliest
Answer:
3 x (2p+q)
Step-by-step explanation:
STEP 1:
3
Simplify —
2
The equation at the end of step 1:
3
— • (4p + 2q)
2
STEP 2:
Pulling out like terms
3.1 Pull out like factors :
4p + 2q = 2 • (2p + q)
Final result :
3 • (2p + q)
Here is some data showing the age and value of 12 cars.
Draw a scatter diagram in your book and state the coordinates of the point that is most likely an outlier.
Age (years) 4 6 5 4 2 8 3 3 5 7 1 5
Value (£ 000's) 46 37 52 60 74 21 65 11 67 27 86 40
(3, 11) is the coordinate of the point that is most likely an outlier
How to draw a scatter diagram?
A scatter diagram is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data
Given: The Age and Value as shown in the question
Age (years) 4 6 5 4 2 8 3 3 5 7 1 5
Value (£ 000's) 46 37 52 60 74 21 65 11 67 27 86 40
The values of Age against Value will then be plotted on a scatter plot as shown in the image attached. Note that Age will be on the horizontal while Value will be on the vertical.
Therefore, the coordinate of the point that is most likely an outlier is (3, 11). This is because it is too far from the line
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Consider the line y = 5x-7.
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 6).
Find the equation of the line that is parallel to this line and passes through the point (-3, 6).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
Recheck
Try again
0
X
□=□
S
Answer:
Step-by-step explanation:
perp. -1/5
y - 6 = -1/5(x + 3)
y - 6 = -1/5x - 3/5
y - 30/5 = -1/5x - 3/5
y = -1/5x + 27/5
parallel: 5
y - 6 = 5(x + 3)
y - 6 = 5x + 15
y = 5x + 21
Which of the following is not an identity?
The answer to this question would be (B)
Answer: csc^2x+sec^2x=1
Step-by-step explanation:
A system of linear equations is graphed below.
Which of the following appears to be true?
A. The system has exactly one solution, at (-1,0)
B.the system has no solution
C. The system has more then one solution.
D. The system has exactly one solution, at (3,0)
The system has no solution.
The solution to the system would be the intersection point of the two lines. Since these lines don't appear to intersect, there's no solution.
Determine whether test point (-8,9) is a solution to the linear inequality x + y ≤ 4.
Answer:
This is a solution to the linear inequality.
Step-by-step explanation:
(-8, 9)
x + y ≤ 4
-8 + 9 ≤ 4
1 ≤ 4
This is a solution to the linear inequality.
Answer:
Step-by-step explanation:
According to the graph that I graphed online, the point (-8,9) is a solution to the linear inequality. To find out that, (-8,9) is a solution you have to look if that point is shaded if it is shaded then it is a solution to the inequality.
(-8 is the x variable and 9 is the y variable, to find out if that is a point you look for the -8 in the graph but you would look down on the the x side and then you go up looking for a 9.)
what would be a reason you might want to increase the confidence level, even though it means that precision is lost and the interval widens?
The confidence interval gets broader as the confidence level rises because the error bound rises as well. The confidence interval gets narrower as the confidence level is reduced since the error bound is also reduced.
This can be the reason why you might want to increase the confidence level, even though it means that precision is lost and the interval widens.
We must widen the distance in order to obtain greater trust. The multiplier, which rises with confidence level, shows this clearly. The width of confidence intervals will rise when sample size is increased.
An unknown population parameter's likely range of values is known as a confidence interval. A certain proportion of the confidence intervals will include the population mean if you repeatedly take random samples. The confidence level is expressed as this percentage.
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24 ft, 52 ft find the range for the third side of the triangle
The range of possible lengths for the third side is [46.13,57.27] .
What is pythagoras theorem?
The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.
Main Body:
To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²
given = 24 ft , 52 ft
24² =576
52² =2704
2704+576=3280
√3280 =57.27
AND
52² = 24²+b²
b²= 2704-576
b=√2128
b = 46.13
range of possible lengths for the third side is [46.13,57.27]
Hence the range of third side is found out.
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For each equation, determine whether it is linear.
Equation
(a) y=x-6
(b) y=2x²-1
(c) y=6x
(d) y=-x³
Is the equation linear?
Yes
No
Answer:
Step-by-step explanation:
For an equation or function be linear, it should be in the form:
Y= mX +b
then
a) YES Linear
b) NO linear
c) YES Linear
d) NO linear
Find the inverse of the given relation {(5,1), (4,-3), (3, -1)}
The inverse of the given relation {(5, 1), (4, -3), (3, -1)} is {(1, 5), (-3, 4), (-1, 3).
What is the inverse of a relation?The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.
The ordered pair (x, y) of f(x) becomes (y, x) of f⁻¹(x).
Given, A relation in form of a set of ordered pairs {(5, 1), (4, -3), (3, -1)} let this be f(x).
∴ The ordered pair of f⁻¹(x) will be {(1, 5), (-3, 4), (-1, 3).
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