The simplified form of the expression ( -4 + 9i )² such that it takes the form a + bi is; -65 - 72i.
What is the simplified form of the expression?It follows from the task content that the simplified form of the expression is to be determined.
Hence, since the given expression is; ( -4 + 9i )², we have;
( -4 + 9i ) ( -4 + 9i )
= 16 -36i - 36i + 81i²
However, recall that the i² = -1 which follows from the fact that i = √-1.
On this note, the expression can be written as;
= 16 - 72i + 81 (-1)
= 16 - 72i - 81
= -65 - 72i.
Hence, the required simplified form of the expression is; -65 - 72i.
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AB has endpoints A (2, 3) and B(5,-2). Determine the endpoints of the image of AB after a reflection in the line y = z.
The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).
What is endpoints of the graph?
On a graph, an endpoint is the place where a figure comes to an end. A genuine line has no terminal because it goes on indefinitely in both directions. A ray is a figure that resembles a line and only extends in one direction infinitum. It is one type of line. The endpoint of a ray is on the side that is not extending.
(x, y) → (x, -y), x-coordinate stays as is and y-coordinate changes its sign to opposite.
We have given points:
A(2, 3) and B(5,-2).
The image of AB will have coordinates:
A'(2, -3) and B'(5, 2)
The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).
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A slice of pizza has 1,200 calories. If 520 calories are from fat, what percentage of calories are fat?
Answer:
43.33%
Step-by-step explanation:
x : 100 = 520 : 1200
x = (520 * 100)/1200
x = 520/12
x = 43.333333%
Find the surface area of the prism.
Answer:
312 m^2
Step-by-step explanation:
Start by separating the shapes.
you will get:
2 triangles with the dimensions 6m x 8m
1 rectangle with the dimensions: 9m x 8m
1 rectangle with the dimensions: 6m x 9m
1 rectangle with the dimensions: 10m x 9m
1) find the area of every shape
2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2
1 rectangle with the dimensions: 9m x 8m ----> 72m^2
1 rectangle with the dimensions: 6m x 9m ----> 54 m^2
1 rectangle with the dimensions: 10m x 9m ---> 90m^2
2) add everything up
48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =
312m^2
A piece of notebook paper measures 8 1/2 inches by 11 inches. Which of the following metric approximations is the same?
2 m x 2.8 m
3 cm x 4 cm
22 cm x 28 cm
30 m x 40 m
The volume V of a sphere varies in direct proportion to the cube of its radius .
What change in volume reduces the radius by 10% ?
There will be no change in volume reducing the radius by 10%.
What is Direct Proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.
For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant. In contrast, x and y are represented as x 1/y or xy = C in the case of inverse proportion.
Let the radius be r then
The volume of every sphere is,
[tex]\mathrm{V}=4 \pi \frac{\mathrm{r}^3}{3}[/tex]
In the given question, It is given:
The volume V of a sphere varies in direct proportion to the cube of its radius.
That means:[tex]\mathrm{V}[/tex] ∝ [tex]r^{3}[/tex]
That means:[tex]4 \pi \frac{\mathrm{r}^3}{3} = kr^{3}[/tex]⇒[tex]4 \pi \frac{\mathrm{1}}{3} = k[/tex]
So, The equation is independent of radius.
Hence, There will be no change in volume reducing the radius by 10%.
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1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
7²
The expression above can also be written in the form
Va
For this expression, a =
b=
and c =
Undo
Next
In the given expression 7^(9/4) the values are found to be
a = 7b = 9c = 4How to determine the values of a, b, and cInformation given in the problem
the expression 7^(9/4)
This equation represents exponents in fraction form and the basics for the calculation is from
a^(b/c) = [tex]\sqrt[c]{a^{b} }[/tex]
Rewriting the expression is done as below
7^(9/4)
= [tex]\sqrt[4]{7^{9} }[/tex]
[tex]\sqrt[4]{7^{9} }[/tex] comparing with [tex]\sqrt[c]{a^{b} }[/tex] gives the following values
a will be equal to 7
b will be equal to 9
c will be equal to 4
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If qr = 20 in., rs = 7 in., and sq = 24 in., what is pn? 3 in. 7 in. 20 in. 24 in.
The value of PN is 20 in.
What are congruent triangles?
Congruent triangles are triangles in which all the sides and all the angles are congruent.
These triangles can appear identical when moved, rotated, flipped, and turned. They coincide if moved in a different direction.
In the diagram, two congruent triangles are given ΔPMN ≅ ΔQSR.
So by CPCTC (corresponding parts of congruent triangles are congruent)
In ΔPMN and ΔQSR
PN=QR=20 in.
PM=SQ=24 in.
MN=RS= 7 in.
If two triangles are said to be congruent then all corresponding parts must be equal.
So, the value of PN is 20 in.
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Answer:
C. 20 in
Step-by-step explanation:
the mean monthly electric bill for 43 residents of the local apartment complex is $69. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
The best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.
It is given that the mean monthly electric bill for 43 residents of the local apartment complex is $69.
That means the sample mean X for 43 residents is $69.
And we know that the sample mean, X is the best point estimate of the population mean, μ.
Therefore the best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.
The point estimate for the population mean is the sample mean. Point estimate is the one value that is used to estimate the population parameter. It is also known as the unbiased estimate of the population mean is the sample mean.
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The points given in the table lie on a line. Find the slope of the line.
x –1 2 5 8
y 3 –1 –5 –9
Answer:
Slope = -4/3 or -1.33 in decimal form
Step-by-step explanation:
To find the slope divide the rise by the run. The rise would be the difference between the 2 y points (y2-y1) divided by the run (x2-1x)
Here the rise is (-9-3 = -12) and the run is (8-(-1) = 9) So -12/9 is -4/3 in fraction form and -1.33 in decimal form.
What is the probability that a standard normal random variable will be between. 3 and 3. 2?.
The probability that a standard normal random variable will be between. 3 and 3. 2 is 0.99932.
What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.
Z∼N(0,1)
P(Z<3)=.99865
P(Z>3.2)=.99931
P(3<Z<3.2)=2(0.99931-0.99865)−1=0.99932
Hence the standard normal random variable will be 0.99932.
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what is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?
If a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units
If a, b and c are the sides of the triangle
Then it will be
a + b > c
b + c > a
c + a > b
Given that the side length of the measures are consecutive integer
Smallest consecutive integer is 1, 2 and 3
But
1 +2 > 3
3 = 3
Therefore it will not be the sides of the triangle
Next smallest consecutive integers are 2, 3 and 4
Then,
2+3 > 4
5 > 4
3+4 > 2
7 > 2
2+4 > 3
6 > 3
This will be the sides of the triangle
The perimeter of the triangle is the sum of sides of the triangle
The perimeter = 2 + 3 + 4
= 9 units
Hence, if a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units
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Write an equation of a line
that passes through the
point (-5, 1) and is
perpendicular to y = -x - 3
A) y = x + 6
B) y = -x - 5
C) y = -x-4
D) y = x + 4
E) y = x - 6
From perpendicular line, we have m1
Knowing m1 * m2 = -1 for perpendicular lines gives us
-1 *m2 = -1
m2 = 1
Using y-b = m(x-a) with the point provided gives
y-1 = 1(x--5)
y = x+6
Therefore (A) is the correct answer
calculate the amount of goodwill that would be recorded by brave for this acquisition. (be careful to count your zeros in your answer since this is a big number!)
Purchase consideration less fair value of net assets is goodwill (Purchase Consideration-Fair Value of Net Assets) $690,000,000
What does "goodwill" mean?
Goodwill cannot be purchased or sold on its own; rather, it is a premium over fair value that is paid during a transaction. Other intangible assets include things like licenses or patents that are independent purchases or sales. While most intangibles have a set useful life, goodwill has an unlimited lifespan.
Estimating goodwill
The extra payment made as purchase consideration over the acquiree's net assets' fair market value is referred to as goodwill.
The calculation looks like this:
(Millions of Dollars)
Cost of the purchase: $ 900,000,000
Fair value of net assets is less.
True Cost of the Assets
$15,000,000 in supplies
$200,000,000 in intangible assets
$20,000,000 for property, plant, and equipment
Total $235,000,000
True Cost of Liabilities
$5,000,000 in current liabilities
$20,000,000 in Notes Payable
Total $25,000,000
Goodwill (Purchase Consideration-Fair Value of Net Assets) (Purchase Consideration-Fair Value of Net Assets) $690,000,000
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Which shows the following expression after the negative exponents have been eliminated? startfraction a cubed b superscript negative 2 baseline over a b superscript negative 4 baseline endfraction, a not-equals 0, b not-equals 0 startfraction a cubed b superscript negative 4 baseline over a b superscript negative 2 baseline endfraction startfraction a b superscript 4 baseline over a cubed b squared endfraction negative startfraction a cubed b superscript 4 baseline over a b squared endfraction startfraction a cubed b superscript 4 baseline a b squared endfraction.
Which shows the following expression after the negative exponents have been eliminated
[tex]a^{2} b^{2}[/tex]
Given the algebraic expression:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0[/tex]
We are required to eliminate the negative exponents and find the resulting expression.
Using the Negative Exponent Law of Indices: [tex]x^{-y} = \frac{1}{x^{y} }[/tex]
Using the Division Law of Indices: [tex]\frac{t^{x} }{t^{y} } = t^{x-y}[/tex]
Therefore:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\[/tex]
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What is the slope-intercept form of the line represented in the table of values?
Answer:
y = -7x + 10
Step-by-step explanation:
As the y's are decreasing by 7, the x are increasing by 1. This gives us a slope of -7. When x is 0, y is 10 that is our y intercept.
Alizay sold 15 shirts priced equally for Rs.2800. She spent Rs. 14,000 of her earned amount on shopping and Rs. 7500 on buying grocery. How much is she left with?
The amount of money left with Alizay after shopping is Rs 17700 .
Alizay sold shirts for Rs. 2800.
She sold 14 shirts.
Cost earned from selling 14 shirts = 14 × 2800 = Rs. 39200
Spent on shopping =Rs. 14000
Spent on Grocery = Rs. 7500
Total amount spent = Rs.(14000+7500) = Rs. 21500
Amount of money left = Rs 39200 - Rs 21500 = Rs 17700
Therefore she is left with Rs 17700 .
In the case of a single variable, there is only one viable response. This particular case, in which the variable is accurately referred to as the "unknown," is one to which the term linear equation sometimes relates implicitly.
The Cartesian coordinates of a point on the Euclidean plane can be used to understand each solution in the scenario with two variables. A linear equation's solutions define a line in the Euclidean plane, and each line is the collection of all solutions to a linear equation with two variables.
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Please help. 10 points.
The new circle be made with double radius of the given circle.
Also, the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.
Given, a circle
If the radius of the given circle is 'r'
then, the radius of the new circle '2r'
Now, the Circumference of the new circle be,
C' = 2π(2r)
As, the Circumference of the given circle be,
C = 2πr
On dividing, we get
C'/C = 2
C' = 2C
So, the circumference of the new circle is double of the given circle.
Now, the Area of the new circle be,
A' = π(2r)²
As, the Area of the given circle be,
A = πr²
On dividing, we get
A'/A = 4
A' = 4A
So, the Area of the new circle is Four times of the given circle.
Hence, the new circle be made with double radius of the given circle.
Also, the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.
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Which system of linear equations has no solution?
Which system of linear equations has no solution?
A. 2x+3y=6
−2x−3y=−6
B. 2x+3y=6
4x+6= 8
C. 2x+3y=6
3x−2y=−6
Which system of linear equations has no solution?
D. 2x+3y=6
10x+15y=30
Answer:
Below
Step-by-step explanation:
A Both are the same line
**** B If that is 4x + 6 y = 8 the lines are parallel ===> no solution***
C Intersecting lines
D same line
Simplify the complex expression to the standard form (a+bi). 2(8-8i)-9(8+4i)
The simplified expression for the complex expression is -56-52i
What is a complex expression?
A complex expression is an expression of the form a+ ib where a , b are constant and i is the imaginary number known as iota. In a + ib a is the real part and b is the imaginary part.
We are given two complex number as (8-8i) and (8+4i)
We have to simplify the given expression
As Complex number are added multiplied subtracted same as real number we can simplify the expression easily
2(8-8i)-9(8+4i)
We multiply the constants inside the bracket
16-16i-72-36i
Separating the terms and simplifying them we get
-56-52i
Hence the simplified expression is -56-52i
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In a farm composed of cows and chickens, there are total of 13 heads and 42 feet. How many cows are there?.
In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.
Let 'h’ represent the number of hens the farmer has.
Let 'c’ represent the number of cows the farmer has.
Assume that all hens have two legs and all cows have four.
There are a total of 42 legs. So
2h + 4c = 42 (1)
There are 13 animals in total.
h + c = 13 (2)
Now that we have our system of equations, we can solve by either substitution or elimination.
Elimination
(2) x 2
2h + 2c = 26 (3)
(2)—(3)
2c = 6
c=3
From (2):
c + h = 13
3+h = 13
h= 10
Therefore, the farmer has 3 cows and 10 hens.
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Carrie works as a library assistant in Orpington Library. She earns $9. 75 per hour. How much will
she get paid, if she puts in 40 hours of work in a week?(Tutors please explain how You do your division,multiplication,etc)
Carrie will be paid $390 if she puts in 40 hours of work in a week.
The total amount of time of work = 40 hours.
As we are stated that the earnings for 1 hour is $9.75, so, we will perform multiplication to find the earnings for the time she worked. We are performing multiplication because the amount will increase as the number of hours increases.
Performing calculation now.
Amount earned in a week = 9.75 × 40
Performing multiplication on Right Hand Side of the equation to find the amount earned in a week
Amount earned in a week = $390
Thus, the amount paid to Carrie in a week is $390.
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-2( y-4 ) + 8y + 2 < 16
Answer: y<1
Step-by-step explanation:
The median house price in Dallas, Texas is $405,000. Property tax is 3%. How much does a homeowner pay in property tax?
Answer:
Step-by-step explanation:
I believe the tax would be $ 12,150
What is the domain of the function y = startroot x endroot 4?
The values of the domain is the which satisfies the function is x > - 4.
According to the statement
We have to find the domain of the given function
For this purpose, we know that the
In Mathematics,The domain of a function is the set of values that we are plug into our function.
The given function is a
[tex]y = \sqrt{x+4}[/tex]
And in this function
The domain is the values of the x which we able to put in the function according to the definition.
x+4=0
x=-4.
It means the value of the domain is the [tex]x > - 4[/tex].
The values according to the upper expression satisfies the domain of the function.
So, The values of the domain is the which satisfies the function is x > - 4.
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Substitution
3x + 5y = 5
Y = -x -2
Find ( x , y )
As per the substitution method, the value of (x , y) is (-15/2, 11/2)
Substitution method:
Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.
Given,
Here we have the following expression.
3x + 5y = 5
Y = -x -2
Now, we need to find the value of x and y.
According to the substitution method, let us consider
3x + 5y = 5 -------------------(1)
Y = -x -2 ---------------------(2)
Now, we have to apply the value of y as -x - 2 in equation (1), then we get,
=> 3x + 5(-x - 2) = 5
When we expand it then we get,
=> 3x - 5x - 10 = 5
Simplify the expression,
=> -2x - 10 = 5
=> -2x = 5 + 10
=> -2x = 15
Then the value of x is,
=> x = -15/2
If the value of x is -15/2. then the value of y is calculated by using the equation (2),
=> y = -(-15/2) - 2
=> y = 15/2 - 2
=> y = (15 - 4)/2
=> y = 11/2
Therefore, the value of (x, y) is (-15/2, 11/2).
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What is the image of (-1,-1) after a dilation by a scale factor of 5 centered at the origin
Answer:
If the plot point was dilated by a scale factor, it would be multiplying the scale factor with each X and Y. Therefore it would be (-5,-5)
The image of (-1, -1) after the dilation by a scale factor of 5 centered at the origin is (-5, -5).
To find the image of (-1, -1) after a dilation by a scale factor of 5 centered at the origin, we can apply the formula for dilation in the coordinate plane.
The formula for dilation with a scale factor of k centered at the origin is (k * x, k * y), where (x, y) is the original point.
In this case, the original point is (-1, -1), and the scale factor is 5. Applying the dilation formula, we have:
Image = (5 * (-1), 5 * (-1))
= (-5, -5)
This means that the point (-1, -1) is dilated by a factor of 5, and its position is shifted five times farther from the origin in both the x and y directions.
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You are holding a balloon and have let out 24 feet of string. If the angle of elevation to the balloon is 32 degrees and you are 5 feet tall. How high is the balloon above the ground
The balloon is above 17.7180 the ground
What is the trigonometry ?
A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.
Given
The angle Ф is 32°
The hypotenuse becomes 24 feet
Let AB be the opposite side
Using trigonometric function of sinФ
ie sinФ = Opposite / hypotenuse
sin Ф = AB / 24
AB = sin Ф * 24
AB = sin 32° * 24
AB = 12.7180
As that person is 5 feet tall we have to add 5 to the value
ie
12.7180 + 5
= 17.7180
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#Sam want to enlarge a triangle with side lengths 3, 6, and 9 inches. If the shortest side of the new triangle is 12 inches, what is the perimeter of the new triangle?
Answer: 72 in
Step-by-step explanation:
The shortest side length of the original triangle was 3in, and the newer one is now 12in. From 3in to 12in, you use a scale factor of 4. Hence, we multiply each side length of the original triangle by 4. And to find the perimeter of the new triangle, you add all the sides up.
3(4) + 6(4) + 9(4) = 72 in
Enter the ratio of students who chose
alternative to the total number of students.
Answer:
1 : 4
Step-by-step explanation:
the ratio of
alternative : total
= 15 : 60 ( divide each part by 15 )
= 1 : 4
austin prepared 20 kilograms of dough after working 4 hours. how much dough did austin prepare if he worked for 5 hours? solve using unit rates.
Answer:
Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.
