A alvin makes 3,200 and spends 701 each month leaving 2,499.
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
It is Given that alvin has done research and found that he spends an average of $123 on his phone/internet/cable service, $213 on his electric bill, and $270 on his health insurance premium.
Subtract expenditures from earnings;
= 3200 - (178 + 203 + 320)
= 3200 - 701
= 2499
Thus, Grant will have $2,499 after paying these bills each month
Therefore, alvin makes 3,200 and spends 701 each month leaving 2,499.
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Perform the indicated operation and express the result as a simplified complex number.
6 + 7i
6-7i
The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85
What are complex numbers?Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).
Given the complex number is -
6 + 7i / 6-7i
⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i
⇒ (6+7i)² / 6² - 7²(i²)
Using (a+b)² = a² + b² + 2ab
⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)
⇒ 36 - 49 + 84i / 36 + 49
⇒ -13 + 84i / 85
⇒ -13 / 85 + 84i/85
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Given T(1,5), U(-2,-8), V(7,-9), and W(-6, y). Find y such that
TU VW
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of TU
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}} \implies \cfrac{-13}{-3}\implies \cfrac{13}{3}[/tex]
hmmmm, well, if that's so, then the slope of VW will be the negative reciprocal of that only if both are really perpendicular, so
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{13}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{13}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{13}}}[/tex]
since now we know the slope if VW, let's use it
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{7}}} \implies \cfrac{y +9}{-13}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{13}}\implies y+9=\cfrac{3(-13)}{-13} \\\\\\ y+9=3\implies {\LARGE \begin{array}{llll} y = -6 \end{array}}[/tex]
A line has no thickness, but it does have direction and ___ length.
(Fill in the blank)
A line has no thickness, but it does have direction and infinite length.
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the geometry is described. For instance, a line in the plane is frequently defined in analytic geometry as the collection of points whose coordinates satisfy a given linear equation, but in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.
In cartesian plane the general equation of a line is given by :
y=mx+c where the slope is denoted by m and the y-intercept by c.
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What’s the GCF of 42, 70, 84
Answer: 14
Step-by-step explanation:
First. take the prime factorization of all three numbers:
42: 21*2 ==> 3*7*2
70: 35*2 ==> 5*7*2
84: 42*2 ==> 21*2*2 ==> 3*7*2*2
Notice any common factors? That's the GCF.
GCF: 7*2=14
GCF: 14
Answer:
14
Step-by-step explanation:
The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The GCF of 42, 70, and 84 is 14.
The greatest number that divides 42, 70, and 84 is 14.
What is GCF?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.
How do I get the GCF of something?
The greatest common factor among numbers can be discovered in a number of ways.
Factoring:
List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.
Example: Find the GCF of 18 and 27
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 27 are 1, 3, 9, 27.
The common factors of 18 and 27 are 1, 3 and 9.
The greatest common factor of 18 and 27 is 9.
Prime Factorization:
List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.
You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.
Example: Find the GCF (18, 27)
The prime factorization of 18 is 2 x 3 x 3 = 18.
The prime factorization of 27 is 3 x 3 x 3 = 27.
The occurrences of common prime factors of 18 and 27 are 3 and 3.
So the greatest common factor of 18 and 27 is 3 x 3 = 9.
There is another method but it focuses on more complex numbers.
Hope this helps!
Why it is very important to follow the steps in solving an equation with 2 or more operations involve?
The area of a certain desert (Desert 1) is four times the area of another desert (Desert 2). If the sum of their areas is 15,000,000 square miles,
find the area of each desert.
Question content area bottom
Part 1
What is the area of Desert 1?
What is the area of Desert 2?
Answer:
Area of Desert 1 = 12,000,000 Area of Desert 2 = 3,000,000
Step-by-step explanation:
x+y=15,000,000
x=4y
4y+y=15,000,000
5y=15,000,000
y=3,000,000
In exercises 19 and 20, find the indicated angle measure. (See photo)
Answer:
See below to complete
Step-by-step explanation:
ABC = 37 +21 °
LMN = 85 +23 °
The base of a triangle is 3 inches more than 2 times the height. If the area of the triangle is 76 square inches, find
the base and height.
Height is h = 8 and base = 19 inch in triangle .
What Does a Triangle's Area Mean?
The space bounded by a triangle's three sides is known as the area of a triangle. Depending on the type of triangle, it is computed using a variety of methods and expressed in square units like cm2, inches2, and so forth.Area of a triangle whose base is b and height is h is =1/2 * b * h
Let the height of given triangle be h inch and as base of a triangle is 3 inch greater than the height, base is ( 2h + 3)
b = 2h + 3
Hence, its area is 1/2 × h × (2h + 3 ) = 76 inch²
So, 1/2 × h × (2h + 3) = 76
2h² + 3h = 76 × 2
2h² + 3h - 152 = 0
2h² + 19h - 16h - 152 = 0
h( 2h + 19 ) -8 (2h + 19) = 0
(h-8) ( 2h - 19)
now h = 8 and h = -19/2 but height of triangle cannot be negative.
Hence height is h = 8 and base = 2 * 8 + 3 = 19 inch
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A county has 225 acres of vacant land.
Residents voted to turn some of the vacant land.
into parks. Now, there are 36% less acres of
vacant land. How many acres of vacant land
does the county have now?
The acres of vacant land that the county have now will be 144 acres.
How to calculate the value?Since 36% has been used, the remaining percentage will be:
= 1 - 36%
= 64%
Therefore, the acres of vacant land that the county have now will be:
= 64% × 225
= 64/100 × 225
= 0.64 × 225
= 144
Therefore, the acres of vacant land that the county have now will be 144 acres.
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You sold your car for $1,000 which had cost $1,450. How much did you lose expressed as a %?.
Answer:
45%
Step-by-step explanation:
1,450 - 1,000 = 450
the 450 becomes 0.45
to make 0.45 a percent, we multiply it by 100
0.45 x 100 = 45
45%
Suppose that you are playing blackjack against a dealer. in a freshly shuffled deck, what is the probability that neither you nor the dealer is dealt a blackjack?
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck.
Then the total number of the event will be
Total events = 52
Then the probability that neither you nor the dealer is dealt a blackjack will be
Favorable event = 2 {Spade of Jack and Club of Jack}
Then the probability of that events will be
P = 2 / 52
P = 1 / 26
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
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if f(x) = mx +c, f(4) = 11 and f(5) = 13, find the value of f(2).
Answer:
7
Step-by-step explanation:
[tex]f(4)=4m+c=11 \\ \\ f(5)=5m+c=13[/tex]
Subtracting the equations yields that m=2, and thus c=3.
[tex]\implies f(2)=2(2)+3=7[/tex]
Math's Question. Please answer
Answer:
i think 15.84 is right
Step-by-step explanation:
bcz Ian all there is 99 4/5 paper towels and tere were 5 rolls. so, to calculate meters of each roll of paper towels we should divide the given value by 5
99 4/5 /5
Taynia makes a quilt using fabric squares.
The side length of each fabric square is
the square root of the area. The area of
each fabric square is 40 square inches.
Which could be the approximate side
length of a square on the quilt?
The approximate side length of a square on the quilt = 6.32 inch
In this question,
Taynia makes a quilt using fabric squares.
We have been given the side length of each fabric square is the square root of the area.
Here, the area of each fabric square is 40 square inches.
We need to find the approximate side length of a square on the quilt.
Let A be the area.
A = 40 square inches
To find the side length, we need to take the square root of 40.
Let s be the side length.
⇒ s = √A
⇒ s = √40
⇒ s = 6.32 inch
Therefore, the approximate side length of a square on the quilt = 6.32 inch
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Can ya'll help me? This problem has stumped me for a few days.
Melissa buys 2 1/2 pounds of salmon an 1 1/4 pounds of swordfish. She pays a total of $31.25, and the swordfish costs $0.20 per pound less than the salmon. What would be the combined cost of 1 pound of salmon and 1 pound of swordfish
Answer:
$16.60
Step-by-step explanation:
Setup the formula to calculate the cost of each pound of salmon and swordfish for the 2.5 pounds of salmon (x) and 1.25 pounds of swordfish (y) which is equal to $31.25
2.5x + 1.25y = 31.25
Setup a formula to figure out how much a single pound of swordfish (y) is. The problem states it cost $0.20 less than a pound of salmon (x).
y = x - .20
Plug the y = x - .20 into the first equation.
2.5x + 1.25(x - .20) = 31.25
Distribute the 1.25 by multiplying it with x and -.20
2.5x + 1.25x - .25 = 31.25
Combine like terms, x on the left side
3.75x - .25 = 31.25
Add .25 to both sides to get x on one side
3.75x = 31.50
Divide both sides by 3.75 to get x by itself
x = 8.4
So, each pound of salmon, x, cost $8.40 per pound
Use y = x - .20 and plug in x = 8.4 to figure out how much a pound of swordfish cost.
y = 8.4 - .20
So, a pound of swordfish cost $8.20 per pound
The question wants to know the combined cost, z, of 1 pound of salmon, x, and 1 pound of swordfish, y.
x + y = z
8.4 + 8.2 = 16.6
The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.60
find the value of sqrt 361
40 35 37 40 39 41 39 39 36 38 36 39 36 39 35 39 36 37 41 37 38 36 35 40 40 41 39 38 39 35 35 40 39 39 37 38 38 39 35 35 41 37 40 39 38 37 37. Calculate the mode
The mode of the data is 39 as it's frequency is highest .
Mode is a measure of central tendency . It is the no . which has highest frequency in data .
Data - Frequency
40 - 6
35 - 7
37 - 7
39 - 12 ( max . )
36 - 5
38 - 6
41 - 4
The value of frequency corresponding to 39 is maximum .
Therefore , as 39 occurs most of the time in the data , hence it is the mode of this data .
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Jose earned 45 points in a video game. He lost 40 points, earned 81 points, then lost 35 more points. Enter and evaluate an expression to find his final score in the video game.
In a physical bus topology, both ends of the medium must be terminated in order to prevent what?
In a physical bus topology, both ends of the medium must be terminated in order to prevent "single bounce."
What is bus topology?Bus topology, also recognized as line topology, is a network topology in which all network devices are connected by a single RJ-45 network cable and coaxial cable.
The bus, backbone, or trunk is the single cable through which all data is transmitted among devices.
Some pros of bus topology are-
Installing and adding or removing devices is simple and inexpensive.It does not necessitate that much cabling as other topologies.If a device fails, the other devices are unaffected.Works well for small networks.Some cons of bus topology are-
If the connection fails, the network as a whole will fail or split.Problems are difficult to troubleshoot.Slow and unsuitable for larger networksTerminators are required at both ends of the line to avoid bouncing signals from causing interference.Increasing the number of devices and network traffic reduces the overall network performance.To know more about bus topology, here
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Greg burned 200 calories exercising, and then he drank a 200-calorie protein shake. which expression uses an additive inverse and represents his net calorie intake?
The expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.
What is additive inverse?In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation.
Now it is given that,
Calories burned by Greg = -200
Calorie taken from protien shake = + 200
Thus, Net calorie intake = Calorie taken + Calories burned
⇒ Net calorie intake = 200 + (-200) = 0
Thus, the expression that uses an additive inverse and represents his net calorie intake 200 + (- 200) = 0.
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Complete the table (again)
I would like the answers to one and two bit the bottom ones
The numeric values for the functions are given as follows:
6 - a) f(-2) = -13.
6 - b) g(4) = 11.
How to find the numeric value of a function?To find the numeric value of a function, we replace each instance of the variable by the desired value.
At item 6a, the function is given by:
f(x) = 5x - 3.
The numeric value at x = -2 is:
f(-2) = 5(-2) - 3 = -10 -3 = -13.
Hence f(-2) = -13.
At item 6b, the function is given by:
g(x) = 0.5x² + 3.
The numeric value at x = 4 is:
g(4) = 0.5(4)² + 3 = 8 + 3 = 11.
Hence g(4) = 11.
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Jackie makes $11.75 an hour and worked for 14 hours this week.
How much more money did she make?
Answer: $164.5
Step-by-step explanation:
11.75*14=$164.5
-4x-3=-2x-2 solving for x
Answer:
x = 1/2
Step-by-step explanation:
4x -3 = 2x - 2 There are many ways to approach this problem. I am going to start by subtracting 2x from both sides of the equation.
2x -3 = -2 I am going to add 3 to both sides of the equation
2x = 1 Divide both sides of the equation by 2
x = 1/2
Solve each question for the variable.
7. p+12,982= 25,000 (1 point)
Op = 12,010
Op=12,018
Op = 12,028
Solve each question for the variable.
8. 912+e=1,201 (1 point)
Oe=389
Oe=299
Oe=289
Solve each question for the variable.
3. 918.2 + v= 1,920.8 (1 point)
Ov=1,000.6
Ov=1,002.6
Ov= 1,001.6
Adam is re tilling his rectangular bathroom floor with one-square foot tiles.the bathroom floor is 1,770 square feet and the width is.he wants to know the approximate length of the bathroom show two methods
Answer:
length = area/width
Step-by-step explanation:
The width is missing.
area = length × width
length = area/width
Divide the area by the width to find the length.
Two points on the y axis that are 25 units from (-24,3)
The two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).
We are given a point:
( - 24 , 3 )
We need to find a point on the y - axis, that is 25 units away from the axis.
The coordinate of the point will be:
(0, y)
So, by using the distance formula, we get that:
D = √ ( y₂ - y₁)² + ( x₂ - x₁)²
25 = √ ( y + 3)² + (0 + 24)²
625 = y² + 9 - 6 y + 576
625 = y² - 6 y + 585
y² - 6 y - 40 = 0
y² - 10 y + 4 y - 40 = 0
y ( y - 10 ) + 4 ( y - 10 ) = 0
(y - 10)(y + 4) = 0
y = - 4 or y = 10.
So, the two points will be:
(0, 10) and (0, - 4)
Therefore, we get that, the two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).
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n+2.1 - 12
what is it
is the point with coordintaes (-2,-9) on the line whose equation is y=4x - 1?
Answer:
Yes
Step-by-step explanation:
If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.
