The absolute value of the expression given as -2i is 2i
How to determine the absolute value?From the question, we have the following parameters that can be used in our computation:
Expression = -2i
The absolute value of an expression is represented as
Absolute value = |Expression|
Substitute the known values in the above equation, so, we have the following representation
Absolute value = |-2i|
Evaluate the expression
Absolute value = 2i
Hence, the result of the expression is 2i
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Use the Remainder Theorem to evaluate P(c).
P(x) = x4 + 7x³ – 6x – 11,
-
X
f(-1) =
[
C = -1
Answer:
[tex]-11[/tex]
Step-by-step explanation:
[tex]P(-1)[/tex] is the remainder when [tex]P(x)[/tex] is divided by [tex]x+1[/tex].
[tex]\frac{x^4 + 7x^3 - 6x-11}{x+1}=x^3 + 6x^2 - 6x-\frac{11}{x+1}[/tex].
The remainder is [tex]-11[/tex], so [tex]P(c)=-11[/tex].
What is the range of the given function?
{(-2, 0), (-4, -3), (2, −9), (0, 5), (−5, 7)}
O {x|x = -5, -4, -2, 0, 2)
Oyly = -9, -3, 0, 5, 7)
{x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Oyly = -9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the given function is:
Range: {-9,-3,0,5,7}
We are given ordered pair of set (x,y)
where, first value of ordered pair shows domain of function and second value of ordered pair shows range.
Range: It is output value of function.
Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}
We can write as:
f(-2)=0, f(-4)=-3, f(2)=-9, f(0)=5, f(-5)=7
The values of f(x) are the range of function.
We will make a set of second value of all ordered pair of given set.
Range: {-9,-3,0,5,7}
Hence we get the required range of the function.
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A rectangular ground is 121/4m long and 41/2 m broad. Find the perimeter and area of the ground.
Answer:
Thank you,Hope you like it and it will help you
Choose which property of equality is demonstrated.
a. AB = AB
Only 9 people can be in a roller coaster cart. How many people can fit in nine train carts
Answer:
81 people
MARK AS BRAINLIEST
what is the inequality of the length of a rectangle is 1 unit more than its width.the width of the rectangle is 2 units and the length of the wire that is used to make this rectangle is a maximum of 57 units. what represent this situation using an inequality
Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives
Perimeter = 2(L + W) ≤ 57 units How to determine the inequality that shows the length and width of a rectangleThe perimeter of a rectangle, P is given by the formula
P = 2(L + W) ≤ 57 units of wire
width, W = 2 units
length, L = 1 + W
= 1 + 2
= 3
The perimeter of the rectangle is given by
P = 2(L + W)
plugging the values of L and W
P = 2 (3 + 1)
P = 2 (4 )
P = 8 units
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If you draw two cards from a standard deck of 52 cards without replacement, find
P (Queen ⋂ Queen).
The probability of drawing two queens without replacement from ths standard deck is 1/221.
What is probability?Probability is the likelihood that an event will occur.
In a standard deck of cards, the total number of cards is 52.
There are 4 queens, the probability of drawing the first queen is 4/52.
After the first draw, there'll be 3 queens left and 52 cards. Therefore, the probability will be:
= 4/52 × 3/51
= 1/13 × 1/17
= 1/221
The probability is 1/221.
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(2/7 , −3) ; r = 6 standard form of circle
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of the variables x and y are 2 and -7.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is y = -2x + 5. We are given two sets of ordered pairs. The ordered pairs are (6, y) and (x, 1). These points satisfy the given equation. We need to find the values of the variables x and y. We will substitute the coordinates into the equation.
y = -2x + 5
First, we will put (6, y).
y = -2(6) + 5 = -12 + 5 = -7
Now, we will put (x, 1).
1 = -2x + 5
2x = 4
x = 2
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A single ticket to the magic show costs ttt dollars, but there is a discount of 5\%5%5, percent per ticket if a group buys 101010 tickets.
The expression 10t-10\cdot 0.05t10t−10⋅0.05t10, t, minus, 10, dot, 0, point, 05, t describes the total cost of buying 101010 tickets for a group.
Match each amount in the situation with the expression that represents it.
Situation
Expression
(Kahn academy)
The total cost for the group of ten people after discount is 10 t - 0.5 t.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Discount = 5%
Total tickets= 10
We have t represents the cost of one ticket.
So, For 10 person the cost of the ticket = 10t
Now, after discount the price of tickets
= 5% of 10t
= 0.5 t
Hence, the total cost for the group of ten people after discount is 10 t - 0.5 t.
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Find the coordinate of the midpoint of the segment with the given endpoints.
- 5 and 4
The midpoint of the segment with the given endpoints.-5 and 4 is -0.5.
What are coordinates?
A pair of numbers is used to express a point's position on a coordinate plane using the horizontal and vertical distinctions from the two reference axes.
What is a midpoint?
A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line.
Here,
A midpoint can also be written as an average or mean of two points.
Mean of -5 and 4 = (- 5 + 4)/2 = -0.5
Hence "The midpoint of the segment with the given endpoints.-5 and 4 is -0.5".
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Please help 18points
A company gives yearly raises to their employees. The salaries at the company are based on the equation below, where S is the salary before taxes and t is the time since the date of hire in years.
S = $33,113 + $600t
What is the minimum number of years an employee would have to stay to make a salary of over $40,000 per year?
A. 13 years
B. 12 years
C. 11 years
D. 1 year
Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.
What is an equation?An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.
Equations show equality using the equation symbol (=).
When one expression is more or less than, or not equal to another expression, it is an inequality.
If S = $33,113 + $600t
Where S = the salary before taxes
t = the time since the date of hire in years.
For S ≥ $40,000:
$33,113 + $600t ≥ $40,000
$600t ≥ $40,000 - $33,113
$600t ≥ $6,887
t ≥ 11.48
t = 12 years
Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.
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Eva says you can use the conversion for 60 km into
miles to convert 600 km into miles. Use Eva's
method to convert 600 km into miles.
300
miles
After using conversion of measurements , the answer is
60 km = 37.28 miles and 600km = 372.83 miles.
What is conversion of measurements?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet. We must convert between different units in order to have accuracy and prevent measurement confusion.
Here the given we need to convert them km into miles.
To convert km to miles we need to divide the value by 1.609 .
=> 60 km
=> 60/1.609
=> 37.28 miles.
Now ,
=> 600 km
=> 600/1.609
=> 372.83 miles.
Therefore after conversion of measurement answer is
60 km = 37.28 miles and 600km = 372.83 miles.
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If A and B are independent events, P(A)=0.15, and P(B)=0.77, what is P(B|A)?
The Probability of P(B│A) is 0.77
What are independent events?Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.
If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears
P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3
Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that
P(A ∩ B) = 1/6
P(B│A) = P(A ∩ B)/ P(A)
= 1/6 /1/2= 1/3 = P(B)
Therefore P(B│A) = P(B)
if A= 0.15 and P(B)= 0.77
P(B│A) = 0.77
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What is the geometric mean of 5 and 11? *
Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.
WILL GIVE BRAINLYIST
The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.
Function
The function is referred as a mathematical expression that defines a relationship between one variable and another variable.
Given,
Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.
Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.
Here the x = 3 is a vertical asymptote.
So the one factor in the denominator is (x - 3),
And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.
Therefore, the rational function would be :
f(x) = (x + 2)/(x - 3)(x + 2)
So, the rational function would be (x + 2)/(x - 3)(x + 2).
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Solve the following system of equations.
Provide your answer below:
-3x+4y= 7
7x- 12y = -11
Answer:
x = -5
y = -2
Step-by-step explanation:
-3x + 4y = 7 ⇒ ( 1 )
7x - 12y = -11 ⇒ ( 2 )
Multiply the equation ( 1 ) by 3.
( 1 ) × 3
3( -3x + 4y = 7 )
-9x + 12y = 21 ⇒ ( 3 )
Let us find the value of x.
Add equations ( 2 ) & ( 3 ).
( 2 ) + ( 3 )
7x - 12y - 9x + 12y = - 11 + 21
Combine like terms.
-2x = 10
Divide both sides by -2.
x = -5
Let us find the value of y.
For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.
- 3x + 4y = 7
-3 × -5 + 4y = 7
15 + 4y = 7
Subtract 15 from both sides.
4y = 7 - 15
4y = -8
Divide both sides by 4.
y = -2
what is the distance between 2 + x and 2?
Answer:
The difference is the what the sum of 2+x is
Step-by-step explanation:
suppose x=3 2+3 = 5
the difference between 5 and 2 is 3
A manufacturer of fax machines find that the cost (in dollars) generated by manufacturing x
units per week is given by the function C(x) = 0.15x²-39x+4500. How many units should
be manufactured to minimize the cost?
130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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130 units should be manufactured to minimize the cost.
How to solve a quadratic equation using quadratic formula?Only a factorable quadratic expression can be solved using the factoring approach, and a quadratic equation with real roots can be solved using the graphing method, etc. However, the quadratic formula can be used to solve any kind of quadratic problem and gets over all these restrictions. step 1: Get into the standard form as the first step.step 2: Determine the values of a, b, and c by comparing the equation to [tex]ax^{2} +bx+c=0[/tex]Step 3: Replace the numbers in the quadratic equation, which is written as[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex] step 4: simplifyCalculation
by using the quadratic formula
[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]
where, a = 0.15, b = -39 and c = 4500
x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]
Hence, 130 units should be manufactured to minimize the cost of fax machines
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Which expression uses the commutative property of addition and the associative property of
multiplication to rewrite the expression 3 (28) +7?
O 7+(3-2).8
O 3 (8-2)+7
O 7+3 (16)
O (3-2) 8+7
The expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer.
a + b = b + a
3(2x8) + 7 = 7 + 3(2x8)
The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.
a(b x c) = (a x b) c
7 + 3(2x8) = 7 + (3.2)8
Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
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Quinn is baking sweet potato pies. The table shows the ratio of cups of sugar to number of pies.
Number of Pies 3 5 9
Cups of Sugar 1 and one half 2 and one half 4 and one half
How many cups of sugar will Quinn need to make 12 pies?
5 and one half cups
6 cups
6 and one half cups
8 cups
The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.
What is ratio?Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.
If a and b are two values, there ratio will be a:b.
Given that,
For 3 potato pies required sugar is 3/2,
For 5 potato pies required sugar is 5/2,
for 9 potato pies required sugar is 9/2,
From the given information,
For 1 potato pies required sugar is 1/2
⇒For 12 potato pies required sugar=12×1/2=6
To make 12 potato pies, required sugar will be 6.
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Five thousand dollars is deposited into an ordinary annuity after each quarter for 3 years. The account pays 6
percent interest compounded quarterly. What is the future value of the account in 3 years?
The future value of the account in 3 years is $15,918.
What is a future value?
The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.
Here, we have
FV =C×[ ((1+i)ⁿ −1)/i]
where:
C = cash flow per period
i = interest rate
n = number of payments
By applying the future value formula, we get
= $5,000×[ ((1+0.06)³ −1)/0.06 ]
= $5,000×3.1836
= $15,918
Hence, the future value of the account in 3 years is $15,918.
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2. Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It
turns out Clare's work has three mistakes!
8(2 + 7x)
10+56x
10+56x
10
12
3
16
3x - (2+5x)
3x - 2 + 5х
8r-2
642-2
64x
The mistakes that Claire made in solving the equation are;
1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.
2) - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x
3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x
How to solve Linear Equations?
We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)
Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x
Step 2; Simplify the right hand side to get;
16 + 56x = -2x - 2
Step 3; Rearrange to get;
16 + 2 = -58x
Step 4; Add up the left hand side to get;
18 = -58x
Step 5; Divide both sides by -58 to get;
x = -9/29
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Complete question is;
Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It
turns out Clare's work has three mistakes!
find all three mistakes explain the below
8(2 + 7x) = 3x - (2+5x)
10 + 56x = 3x - 2 + 5х
10 + 56x = 8x - 2
10 = 64x - 2
12 = 64x
x = 3/16
41 is 10 1/4% of what number
By the concept of percentage, 41 is [tex]10\frac{1}{4}[/tex] % of the number 400.
What is meant by percentage?The percentage is a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. Percent is derived from the Latin word per centum, which means "by the hundred." In the 16th century, the Latin expression was adopted by English. Later, it was shortened to % with a period in the end. The present one-word form % was created after the period was eliminated and the two elements were combined. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage.
Let the number be x.
Then, according to the question
[tex]10\frac{1}{4}[/tex] can be written as 41/4
So,
41/400 × x = 41
41 x = 41 ×100
x =400
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ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST
The value of constant C is 50.
Explain linear equation.Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.
A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.
Given, the linear equation is 12.5x+5y = C
Here, constant C.
Consider one points from given table x = -2 and y = 15,
Putting the value of x and y,
C = 12.5×(-2) + 5×15
= -25 + 75
= 50
For point, x = 0 and y = 10,
Putting the value of x and y,
C = 12.5×0 + 5×10
= 50
For point, x = 2 and y = 5,
Putting the value of x and y,
C = 12.5×2 + 5×5
= 25 + 25
= 50
Given, x = 4 and y = 0,
Putting the value of x and y,
C = 12.5×4 + 5×0
= 50
Therefore, the value of constant C was found to be 50.
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Judy mom prepared 30 sandwiches for her friends. Her mom added chicken breast to 2/5 of the buns. How many chicken sandwiches did her mom make.
if after 40 month amount of 2375 is received by 15/2% interest rate, how much is principal ?
The principal is 1900
From the question, we have
after 40 month amount of 2375 is received by 15/2% interest rate
T = 40/12 = 10/3
amount = 2375 = P+I
R = 15/2%
amount = P+I
2375 = P+(PRT)/100
2375 = P(1+(RT)/100)
substituting the value we get
2375 = P(1+(25)/100)
2375 = P*125/100
P = 2375*100/125
P = 1900
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells. What is the value of Q(3), and what is its interpretation?
Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
Q(3) = 0; If Quincy sells 0 bracelets, he will earn $3.
Q(3) = 3.36; If Quincy sells 3 bracelets, he will earn $3.36.
Q(3) = 3.36; If Quincy sells 3.36 bracelets, he will earn $3.
The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.
So, for x= 3 them Q(3)
Q(3)= 8.25 (3) - 24.75
Q(3) = 24.75 - 24.75
Q(3) = 0
Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
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Abigail Henderson has $1360 budgeted for spending money on an upcoming trip to country and country be countries currency is trading $1.30 per Curren$y a and country bees currencies trading at $1.60 per currency be she plans to spend more time In country a so she wants to four times as much of currency a as currency be
Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;
The equation that represents the total cost is; 1.3·x + 1.4·y = 1,360The number of each currency Abigail plans to buy are;
The number of units of currency of country A, x = 800The number of units of the currency of country B, y = 200What is a budget?A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.
The amount Abigail Henderson budgeted = $1,360
The per currency exchange rate for country A = $1.30
The per currency exchange rate for country B = $1.60
The number of currency A Abigail wants = 4 × The number of currency B
Which gives; x = 4·y
The equation that represents Abigail's total cost of buying currencies is presented as follows;
1.3·x + 1.6·y = 1,360
Plugging in the value of x gives;
1.3 × (4·y) + 1.6·y = 1,360
6.8·y = 1,360
y = 1,360 ÷ 6.8 = 200
The number of currency of country B, Abigail purchases, y = 200
The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800
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