The solution of the system of equations are x = 7 and y = 77
Given data
y = 9x + 14
y = 6x + 35
How to solve the system of equationssolving using substitution method to solve the simultaneous equation we have
y = 9x + 14 equation 1
y = 6x + 35 equation 2
equating the both equations will give
9x + 14 = 6x + 35
9x - 6x = 35 - 14
3x = 21
x = 7
plugging x = 7 into equation 1
y = 9x + 14
y = 9 * 7 + 14
y = 63 + 14
y = 77
The solution of the system of equations are x = 7 and y = 77
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Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the tickets.
The algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)
Algebraic expression to show how much Maria paid for the ticketsNumber of tickets Maria bought = 5Cost of each tickets = $20Additional fee per tickets = $2let
Total amount Maria paid for the tickets = yTotal amount Maria paid for the tickets = Cost of each tickets(Number of tickets Maria bought) + Additional fee per tickets(Number of tickets Maria bought)
y = 20(5) + 2(5)
y = 100 + 10
y = $110
Therefore, the algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)
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The balance sheet of Pacific Ocean Resort reports total assets of $720,000 and $870,000 at the beginning and end of the year,
respectively. The return on assets for the year is 21%.
Calculate Pacific Ocean's net income for the year.
Net income
Based on the return on assets of 21%, the net income of Pacific Ocean Resort for year is $166,950
What is return on assets?
The return on assets for the company is determined as the net income divided by the average total assets of Pacific Ocean Resort , bearing in mind that the average total assets is sum of the beginning and ending assets divided by 2
return on assets=net income/average total assets
return on assets=21%
net income=unknown
average total assets=($720,000+$870,000)/2
average total assets=$795,000
21%=net income/$795,000
net income=$795,000*21%
net income=$166,950
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Carla is riding her tricycle in a race. We only know that 20 seconds after the race began, she was 55 meters from the starting line, and 30 seconds after the race began, she was 85 meters from the starting line. Find the equation of the line describing Carla’s motion during the race, where y represents her distance from the starting line in meters, and x represents the time since the race began in seconds.
The equation of a line describing Carla's motion during the race is y = 3x - 5.
What is slope?The slope is defined as the rate of change of the y-axis with respect to the x-axis.
As we are representing y as distance in meters and x as time in seconds we can form two co-ordinates for the distance Carla covered, They are
(20,55) and (30,85).
Now to form an equation of a line we have to first determine the slope(m) and y-intercept (b).
We know slope(m) = (y₂-y₁)/(x₂-x₁).
∴ Slope(m) = (85 - 55)/(30 -20).
= 30/10.
= 3.
Now, The equation of this line can be written as slope intercept form as y = mx + b.
55 = 3(20) + b.
b = -5.
So, y = 3x - 5 is our required equation of this situation represented by a line.
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Can someone please help me? I’m confused. I’ll give brainliest :)
Rosa works 30 hours per week making $15.75 per hour. After her paycheck has 28% deducted for Taxes (federal, state, and social security), Rosa takes 10% of her take home pay and puts it into a savings account. How much money does she then have available from her paycheck to spend each week?
Please help me with this question.
Answer:14m
Step-by-step explanation:
3 1/2 x 4= 14
14.0.02943
Scientific notation?
The scientific notation of the number 140.02943 is 1.4002943 × 10⁻².
What is termed as the scientific notation?Scientific notation is a technique for expressing numbers that are too large or small to be written in basic decimal form. In some contexts, scientific notation is also recognised as standard form, scientific form, or standard index form.The primary reason for the importance of scientific notation is that it enables us to transform very large or extremely small numbers into much manageable sizes. It is much simpler to work with these numbers when they are written in scientific notation. Scientific notation is also crucial because it ensures that calculations involving large numbers remain accurate, as it is often easy to lose track of successfully counting extremely large numbers. For instance, someone will most likely be able to work with 10¹⁰ rather than 10,000,000,000.The given number is;
140.02943
Shift the 2 decimal to the left of the decimal; because of this, the resultant number will get multiplied by 10⁻².
= 1.4002943 × 10⁻²
Thus, the number in the scientific notations will be written as; 1.4002943 × 10⁻².
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The correct question is-
Write scientific notation of -
140.02943
pleaseee helpppp meeeee this is due sooonnnn
A rectangle has a height of b^3+b^2b
3
+b
2
b, cubed, plus, b, squared and a width of b^2+7b+4b
2
+7b+4b, squared, plus, 7, b, plus, 4.
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
What is the area of the rectangle?
The area of the rectangle is equal to the product of the height and the width, each of them represented by polynomials. In this question we must apply algebraic handling to simplify the product of the two polynomials:
A = h · w (1)
Where:
h - Heightw - WidthIf we know that h = b³ + b² and w = b² + 7 · b + 4, then the area of the rectangle is:
A = (b³ + b²) · (b² + 7 · b + 4)
A = b² · (b + 1) · (b + 0.628) · (b + 6.372)
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
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HELP PLSS
The graph shows the corruption ratings for the world's least corrupt and most corrupt countries. The ratings are on a scale from 0 to 10, where higher scores represent less corruption.
a. Write a set of four ordered pairs in which each of the least corrupt countries corresponds to a corruption rating. Each ordered pair should be in the form (country, corruption rating).
The ordered pairs in which each of the least corrupt countries corresponds to a corruption rating will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.
What is an ordered pair?It should be noted that an ordered pair is the pair of two numbers or variables that are written inside brackets and are separated by a comma.
An example, (1, 2) is an ordered pair. It should be noted it can represent a point. In this case, the pair should be in the form of:
(Country, corruption rating)
(A, 9.7)
(B, 9.6)
(C, 9.6)
(D, 9.1)
Therefore, this will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.
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6u+18+9u=-12 simplify
Answer:
u = -2
Step-by-step explanation:
Group
[tex]6u+9u+18=-12[/tex]
Add similar elements in the equation
[tex]15u+18=-12[/tex]
Subtract 18 from all sides
[tex]15u+18-18=-12-18[/tex]
Simplify this
[tex]15u=-30[/tex]
Divide all sides by 15
[tex]\frac{15u}{15}=\frac{-30}{15}[/tex]
Divide 15 by 15, removing u
[tex]\frac{15}{15} = u[/tex]
Transform [tex]\frac{-30}{15}[/tex] by using the fraction rule.
[tex]-\frac{30}{15}[/tex]
Divide 30 by 15.
[tex]\frac{30}{15} = 2[/tex]
Thus,
u = -2
PERSEVERE The sum of 4 consecutive odd integers is equal to zero.
a. Write an equation to model the sentence. Let n = the first odd integer.
b. Solve the equation to find the numbers. Write the numbers from least to greatest. Check your solution.
n =
The numbers are _________ ,__________, and __________
1. The equation that models the sentence is 4n + 12 = 0.
2. The numbers from least to greatest are -3, -1, 1, 3.
What are integers?Integers are whole numbers. An integer a number without a fraction or decimal component. Integers can either be positive, negative or zero. An odd number is a number that cannot be divided perfectly into two halves. An example of odd numbers are -11, 21.
Consecutive odd numbers are whole numbers that follow each other on the number line. Consecutive odd numbers increase by 2. Examples of consecutive odd numbers are 7, 9, 11.
If 4 consecutive odd integers are: n, (n +2) (n + 4) , (n + 6)
n + n + 2 n + 4 + n + 6 = 0
4n + 12 = 0
4n = -12
n = -12 / 4
n = -3
The numbers are -3, -1, 1 , 3
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the 3rd term of a linear sequence is 17. the 45th term is 269. determine the formula for the nth term.
Step-by-step explanation:
a linear or arithmetic sequence has a start value as first term, and then every following term is created by adding the same constant to the previous term.
a1 = a
a2 = a1 + c = a + c
a3 = a2 + c = a + c + c = a + 2c
a4 = a3 + c = a + c + c + c = a + 3c
...
as we can easily see
an = an-1 + c = a + (n-1)c
in our case
a3 = 17 = a + 2c
a = 17 - 2c
a45 = 269 = a + 44c = 17 - 2c + 44c = 17 + 42c
252 = 42c
c = 6
a = 17 - 2c = 17 - 2×6 = 17 - 12 = 5
so,
an = 5 + (n-1)×6
At a dogs shelter a 24 pound bag of dog food will feed 36 dogs a day how many dogs would you expect to feed with a 16 pound bag of dog food
Answer:
24 dogs
Step-by-step explanation:
36 divided by 24= 1.5
1.5 times 16=24
so 24 dogs :)
Pls help only one question :( im stuck!
Answer:
-√26, 5.15, 5.2, 16/3
Step-by-step explanation:
-√26 = -5.09
16/3 = 5.33
Which expressions are equivalent to -9? Select all that are correct
The expressions that are equivalent to -9 are -(9) and -|9|
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals. This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the expression?The expression is given as
-9
According to the identity law of algebra, we have the following equation
-x = -(x)
This means that
-9 = -(9)
Also, we have
-9 = -|9|
Hence, the expressions that are equivalent to -9 are -(9) and -|9|
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need help with question 2 pleasee
Answer:
A: 24
B: 3
C: -1
D: 12
Step-by-step explanation:
(-2 3/5)(3)(-0.5) what does this equal?
Answer:
3.9
Step-by-step explanation:
im not sure :<
Answer:
9/25 = 0.36 = nine twenty-fiths
Step-by-step explanation:
7. Using the test of divisibility rule, determine which of the following numbers are divisible by 11.
(a) 1001935
(b) 154451
(c) 4313101
(d) 213596
Please Explain in paper
The number that is divisible by 11 is 154451
Which of the numbers are divisible by 11?The divisor is given as
Divisor = 11
Using the test of divisibility rule, numbers are divisible by 11 are palindrome numbers
This means that the numbers remain the same when reversed
From the list of options, 154451 is a palindrome
Hence, the number that is divisible by 11 is 154451
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Austin has two magnets. The shaded parts of the magnets represent the poles.
What will happen if she brings the dark side of magnet P closer to the dark side of magnet Q?
A They will repel each other.They will repel each other.
B Poles of the magnets will change.Poles of the magnets will change.
C Both the magnets will break.Both the magnets will break.
D They will attract each other.
Answer:
D They will attract each other
Determine which equation is false based on the solution set.
S:{5}
A: 6 = 2y − 4
B: 4(b + 5) = 40
C: one fifth times x plus 16 equals 17
D: −32 = 2(3p − 6)
Answer:
d) -32 = 2(3p - 6) is false.
Step-by-step explanation:
A) 6 = 2y - 4
→ 6 = 2(5) - 4
→ 6 = 10 - 4
→ [ 6 = 6 ]
So, the equation is true.
B) 4(b + 5) = 40
→ 4(5 + 5) = 40
→ 4(10) = 40
→ [ 40 = 40 ]
So, the equation is true.
C) (1/5)x + 16 = 17
→ (5/5) + 16 = 17
→ 1 + 16 = 17
→ [ 17 = 17 ]
So, the equation is true.
D) -32 = 2(3p - 6)
→ -32 = 2(15 - 6)
→ -32 = 2 × 9
→ [ -32 ≠ 18 ]
So, the equation is false.
how much is this quarter
Jane is a cleaner the table shows information about the time it will take to clean each four rooms in the house. Jane wants to clean all four rooms in one day she will have breaks for a total time of 45 minutes. Jane is going to start at 7am what time will she finish?
Answer:
Dat is
45/7
6.43
6.43+4+4
14.43
Answer:
b c
Step-by-step explanation:
have a great day
The perimeter of an equilateral triangle is 15 inches more than the perimeter of a square, and the side of the triangle is 7 inches longer than the side of the square.
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the side of the equilateral triangle and y represent the side of the square. Hence:
For the perimeter:
3x = 4y + 15
3x - 4y = 15 (1)
Also:
x = y + 7
x - y = 7 (2)
From the equations:
y = 6, x = 13
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
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On a sunny day, you and your friend were taking a long walk. You got tired and stopped near a telephone pole for a little rest, but your nervous
friend couldn't stand still. He paced out your shadow and discovered it was 5 meters long even though you are really only 1.5 meters tall. He
paced the long shadow of the telephone pole and found that it was 35 meters long. How high is the telephone pole in meters? Enter your answer
with one digit to the right of the decimal point.
The telephone pole will stands 10.5 meters tall.
Given shadow of you = 5 meters
The true height is 1.5 meters.
We must determine the telephone pole's height because its lengthy shadow is 35 meters long.
Assume that x is the height of the telephone pole..
Now we can write this as
height of shadow/ actual height
5 / 1.5 = 35 / x
By cross multiplication we get
5 * x = 35 * 1.5
We get it by dividing '5' by both sides
x = 35 * 1.5 / 5
x = 10.5 meters
Therefore ,The telephone pole is 10.5 meters tall.
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Estimate approximately how many people were born on a Sunday. Give a step-by-step process for your estimate and show all calculations. State any assumptions clearly.
Answer:
Step-by-step explanation:
World Population = 7,750,000,000
7,750,000,000 / 7 (for amount of days in a week) = 1,100,00,000 people born on Sunday (roughly)
what is the least whole number that rounds to 230000 when rounded to the nearest ten thousand?
The least whole number that can be rounded to 230,000 is 225,000.
What is the least whole number?The ten thousand number (10,000) is usually the fifth digit in a number when counting from the right to the left. For example, in 132,456, 3 is the ten thousand number.
To round off to the nearest ten thousand, if the thousand digit is equal to or greater than 5 (i.e. 5,6, 7, 8, 9), 1 is added to the ten thousand digit and other numbers less than the ten thousand digit becomes 0. For example, when 234,612 is rounded to the nearest ten thousand, the number becomes 235,000.
If the thousand digit is less than 5 (i.e. 0, 1, 2, 3, 4), there is no change in the ten thousand digit other numbers less than the ten thousand digit becomes 0. For example, when 234,412 is rounded to the nearest ten thousand, the number becomes 234,000.
The numbers that can be rounded off to 230,000 are: 225,000, 226,000, 227,000, 228,000, 229,000, 230,000, 231,000, 232,000, 233,000, 234,000
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HELP PLEASE!! (9,-4);slope=-2/3 write the equation of the line
Given the point and slope, the equation of the line is in slope-intercept form is y = (-2/3)x + 2
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point ( 9, -4 )
x = 9y = -4Slope m = -2/3Since already have the slope, we determine the y-intercept b by substituting the given values into the equation of line formula.
y = mx + b
-4 = (-2/3)9 + b
Solve for b
-4 = -18/3 + b
-4 = -6 + b
b = -4 + 6
b = 2
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-2/3)x + 2
Given the point and slope, the equation of the line is in slope-intercept form is y = (-2/3)x + 2
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Help pls this is kinda urgent thank you
The coordinates of the midpoints of the segment with the endpoints are (-1, 0.5)
How to determine the coordinates of the midpoints of the segment with the endpoints?The endpoints of the segment are given as
J = (-6, 3)
K = (4, -2)
The coordinates of the midpoints of the segment with the endpoints are calculated as
Midpoint = 1/2 * (J + K)
So, we have
Midpoint = 1/2 * (-6 + 4, 3 - 2)
Evaluate the sum and the difference
So, we have
Midpoint = 1/2 * (-2, 1)
Evaluate the product
So, we have
Midpoint = (-1, 0.5)
Hence, the coordinates of the midpoints of the segment with the endpoints are (-1, 0.5)
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Tina feeds her dog pound of dog food per day. If she
buys a bag containing 9 pounds of dog food, how many
days will it last?
Answer:
If Tina buys a bag containing 9 pounds of dog food, it will last for 9 days.
Step-by-step explanation:
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