An equation in slope-intercept form that represents the situation is y = 3x - 208.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided, we have the following points:
Points on x-axis = (103, 105).
Points on y-axis = (101, 107).
Substituting the given points into the formula, we have;
Slope, m = (107 - 101)/(105 - 103)
Slope, m = 6/2
Slope, m = 3
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (103, 101), an equation in slope-intercept form is given by:
y - y₁ = m(x - x₁)
y - 101 = 3(x - 103)
y - 101 = 3x - 309
y = 3x - 309 + 101
y = 3x - 208.
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Write the equation of the line in fully simplified slope-intercept form.
Answer:
Y = 1/4 -1
Step-by-step explanation:
To find slope, count how many units are between points on the line. How many times you count up or down will be found on top of the fraction symbol. How many times you count left or right will be found below the fraction symbol. This line goes to the right four times, and up once to reach its next point. That means our slope will appear as 1/4.
Next, go to the spot where the line hits the Y-axis. That is where the y-intercept is. -1 is where the line crosses the Y-axis, so that's our y-intercept.
Very simply, you find slope by counting, and y-intercept by looking. Up one time, to the right four times; 1/4 for slope. Line crosses at -1; y-intercept. Y = 1/4 -1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
3
6
5
The expression above can also be written in the form
a
b
c
.
For this expression, a = , b = , and c = .
From knowledge of numerals the answer to the given Question is: a = 3 b = 6 c = 5
What are Numerals?
Numerals are symbols or numerals used to represent numbers. They are used in math and other fields to represent quantities and measurements. Numerals can be written in different forms, such as Arabic numerals (1, 2, 3, etc.) or Roman numerals (I, II, III, etc.). Numerals are also used to label items, such as dates (e.g. May 4th, 2020), addresses (e.g. 1234 Main Street), and telephone numbers (e.g. 555-123-4567). Numerals are an important part of our everyday lives, used to count, measure, and express amounts.
Numerals are just a combination of digits that we know
for example if 0,1,2,3,4,5,6.....9
are the fundamental digits then numbers from these like
12,34,668,389,23,39 etc are called numerals
We can also conclude that all numbers have originated from numerals itself and numerals are basic unit of formation of numbers
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A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity. (The Effective Date is the date the note was written.) Assume the year is not a leap year.Principal Rate Effective Date Partial Payment Maturity Date Amount Date $2000 4% April 1 $1000 May 1 June 1 The balance due on the note at the date of maturity is $nothing.(Round to the nearest cent as needed.)
The balance due on the note at the date of maturity is $1010.13.
What is meant by partial payment?The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.
Given permission to apply the US rule
In the United States, a year is deemed to have 360 days for the purposes of calculating interest.
Given that the principal is $ 2000,
Interest rate = 4% = 0.04
The effective date is April 1.
The whole amount is $1,000.
May 1 = partial payment
Duration = 30 days (May 1 - April 1)
Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67
So value = $ 2000 + $6.67 = $6.67
Partial payment received = $1,000
As a result, value = $ 1006.67 = $2006.67 - $ 1000
Time T= 31
Interest = PTR * 31/360 * 0.04 = 3.46
So the total value is $1006.67 + $3.47 = $1010.13.
The note's outstanding balance at maturity is $1010.13.
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In a school there are 1,970 pupils. If there are 799 boys, how many more girls are there than boys?.
If in the school of 1970 pupils, there are 799 boys, there are 372 girls more than the boys.
What do you understand by linear equation?A linear equation is an equation with the maximum degree of one. No variable in a linear equation, thus, has an exponent greater than 1. The graph of a linear equation is always a straight line.
Both linear equations with one variable and those with two variables exist. This is already taught in schools. Let's use the examples below to understand how to distinguish between linear and non-linear equations.
y = 8x - 9 Linear
y = x2 - 7 Non-Linear, the power of the variable x is 2
√y + x = 6 Non-Linear, the power of the variable y is 1/2
y + 3x - 1 = 0 Linear
How to solve?
total number of pupils = 1970
number of boys = 799
number of girls = 1970 - 799 = 1171
number of girls more than the boys = 1171 - 799 = 372
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Calculate how far each of the following travels. A helicopter flies at a speed of 72miles per hour for 10 minutes
Answer:
12 miles
Step-by-step explanation:
72 x [tex]\frac{10}{60}[/tex] = 12
which equation has roots of 3+i and 3-i
is x^2-6x+10=0
but can you show me the work
The quadratic equation with the roots 3+i and 3-i is:
x^2 - 6x + 10 = 0
How to find the equation with the given roots?We know that a quadratic equation with the roots a and b is written as:
(x - a)*(x - b) = 0
Here the roots are 3 + i, and 3 - i.
Replacing that we get:
(x - 3 - i)*(x - 3 + i) = 0
Expanding the product on the left we get:
x^2 + x*(-3) + x*i + (-3)*x + (-3)*(-3) + (-3)*i + (-i)*x + (-i)*(-3) - i^2 = 0
Remember that i^2 = -1, then:
x^2 -3x + x*i - 3x + 9 - 3i - x*i + 3i + 1 =0
x^2 - 6x + 10 = 0
That is the equation for the given roots.
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carla's cell phone company charges $35 a month for phone service plus $0.50 for each text message. carla's bill was $52 this month.
The number of text messages sent by carla in a month is 34.
What is an algebric equation ?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
For given question,
Phone service = $35
For each text message = $0.50
Total bill = $52
Let x be the no. of total text messages.
Equation: 52 = 35 + 0.50x
Solving for x,
52 - 35 = 0.50x
17 / 0.50 = x
34 = x
The number of text messages sent by carla in a month is 34.
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In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means thatthe estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constantthe estimated mean of Y is 2 when X1 equals zero.the relationship between X1 and Y is significant.
The solution is y will increase by 2 units with every unit increase in x1
What do you mean by multiple regression?A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
What is the difference between multiple and single regression?X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.
In the above question:-
Interpretation of b1=2
it means that y will increase every 2 units for every unit increase in x1
holding x2 constant.
Hence option B is the correct answer.
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Calculate the average rate of change from x = −2 to x = 1 of the function below. f(x) = x2 + 5x − 12 First, find the change in y by evaluating the function at −2 and 1:
The average rate of change over the interval x = -2 and x = 1 is 4
How to determine the average rate of changeThe equation is given as
f(x) = x² + 5x - 12
The interval is given as:
x = -2 to x = 1
Start by calculating the functions f(-2) and f(1)
So, we have
f(-2) = (-2)² + 5(-2) - 12 = -18
f(1) = (1)² + 5(1) - 12 = -6
So, the average rate over these intervals is calculated as:
Average rate = [f(1) - f(-2)]/[1 - -2]
This gives
Average rate = [-6 - -18]/[1 - -2]
Evaluate
Average rate = 4
Hence, the average rate of change is 4
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how many baskets did Elijad make during his seoncd game
Answer:
[tex]\huge\boxed{\sf 3 \ baskets}[/tex]
Step-by-step explanation:
Let the baskets missed in game 2 be x.
Says that, the shooting of both the games were accurate.
So,
Using proportionality:[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]
!!50 Points!! Pls help ASAP!!!
Simplify
[tex](3\sqrt{-5} + 2)(4\sqrt{-12} - 1)[/tex]
The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62
How to simplify numbers and expressions?Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.
Given: the expression (3√-5 + 2)(4√-5 -1)
(3√-5 + 2)(4√-5 -1)
Clear the parenthesis:
(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)
= -60 - 3√-5 + 8√-5 -2
= 5√-5 - 62
Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62
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please help!!!!!!!!!!!!!!
Answer:
109 degrees
Step-by-step explanation:
all three of those angles will equal 180
42+29+x=180
71+x=180
-71. -71
x=109
Hopes this helps please mark brainliest
Can someone please help me with this? I’ll be really thankful if you do! :D
H represents integer -2 on the number line
Opposite value of -2 is 2
Absolute value of -2 is 2
What is opposite and absolute value of an integer?
Opposite integers: Two numbers that are the same distance from zero but on opposite sides.
Absolute value of integer: The integer’s distance from zero on the number line.
Every integer has an opposite.
The sum of two opposites is always zero.
For example 5 is opposite of -5
According to the given question:
The integer represented by the H lies on the left hand side of zero that is negative side of number line.
H represents -2 on the number line
Opposite value of -2 is 2
Absolute value of -2 is 2
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a riverboat travels at an average of 14km per hour in still water. the riverboat travels 110km east up the Ohio river and 110km west down the same river in a total of 17.5 hours. To the nearest tenth of a kilometer per hour, what was the speed of the current of the river?
The speed of the current of the river will be 4.47 km per hour.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.
Let 'y' be the speed of the current of the river. Then the equation is given as,
T = T₁ + T₂
17.5 = [110 / (14 + y)] + [110 / (14 - y)]
17.5 / 110 = (14 - y + 14 + y) / (196 - y²)
196 - y² = 176
y² = 20
y = 4.47 km per hour
Then the speed of the current of the river will be 4.47 km per hour.
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A) Patricia runs a small events-organizing company based in Nairobi. She has just received an order to organize an SME development seminar at the Sarova Stanley Hotel hosted by the World Bank. She has concluded that there is a linear relationship between her costs and the number of participants attending the event. She is billing World Bank Ksh 10,000 per participant while the hotel charges her Ksh 2,500 per participant for meals in addition to Ksh 225,000 fixed charge for the hall. Required:
i)Find the number of participants who would need to attend the forum for Patricia to break even (2 Marks)
ii. How many would need to attend for her to make a profit of Ksh 337,500? (5 Marks)
i) The number of participants that would need to attend the forum for Patricia to break even is of: 30.
ii) The number of participants that would need to attend the forum for Patricia to obtain a profit of Ksh 337,500 is of: 75.
What is the linear function that defines the situation?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing the rate of change.b is the y-intercept, representing the value of y when x = 0.Hence in the context of this problem, the meaning of each coefficient is given as follows:
Slope: profit per participant.Intercept: fixed costs.Hence the values of each coefficient are given as follows:
m = 7500, as she is billing 10000 per participant while the hotel charges 2500 per participant.b = -225000, which is the fixed charge.Hence the profit function is given as follows:
P(x) = 7500x - 225000.
She breaks even when P(x) = 0, hence:
7500x - 225000 = 0
7500x = 225000
x = 225000/7500
x = 30 participants.
She makes a profit of 337500 when:
7500x - 225000 = 337500
x = (337500 + 225000)/7500
x = 75 participants.
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HELP ANSWERpleaseeee im timed
The percentage of the campers that are participating in a nature hike that are females is 57.1% (first option)
What is the percentage?
Percentage is the fraction out of an amount expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.
Percentage of the campers that are participating in a nature hike that are females = (number of females in the nature hike / total number of campers in the nature hike) x 100
Total number of campers in the nature hike = 20 + 15 = 35
Percentage of the campers that are participating in a nature hike that are females = (20 / 35) X 100 = 57.1%
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How much interest will I earn the first year? (3.2% of $500)
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (500)(0.032)(1) \implies I = 16[/tex]
2 and 2/3 simplified
[tex]\stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}}[/tex]
how does weather existe? I need help
Answer: How Weather Exists
Step-by-step explanation:
~I think you mean, how weather exists.
You see, "Weather" exists because of the atmosphere. Evidently, weather is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.
~Hope this helped :)
solve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7
DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.
Whais the explanation?1.) 2+3 = y + 12
Make y the formula's subject after adding the LHS.
5 = y + 12
Y = 5 - 12
Y = - 7
The answer to the equation is -7
2.) 2 + 13 = 1 +8
The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).
3.) y - 7 = 2 - 11
RHS is added, and y is become the formula's subject.
Y - 7 = -9
Y = -9 + 7
Y = -2
The equation's answer is -2.
The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12
2 + 13 = 1 +8
y - 7 = 2 - 11
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graph a line for function d = 0.25t
The graph line for function d = 0.25t is added as an attachment
How to graph the line of the function?The equation of the function is given as
d = 0.25t
The above function is a linear function
One way to create the graph is to make a list of ordered pairs
So, we have
When t = 0, d = 0.25 * 0 = 0
When t = 1, d = 0.25 * 1 = 0.25
When t = 2, d = 0.25 * 2 = 0.5
So, the ordered pairs are (0, 0), (1, 0.25) and (2, 0.5)
We plot these points on a graph and connect them through a line
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Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula. The value of f(-1) is. The value of f(-4) is. The average rate of change of f(x) over the interval [-4, -1] is.
The average rate of change of f(x) over the interval [-4,-1] is 2 , the value of f(-1) is 3 and value of f(-4) is -3 .
In the question ,
a linear graph of the function f(x) is given ,
we have to find the rate of change of the function f(x) ,
We know that the Rate Of Change of the function f(x) over interval [a,b] is calculated using the formula ;
Rate Of Change [tex]=[/tex] (f(b) - f(a))/(b - a)
the interval is [-4,-1] ,
So , a = -4 and b = -1 .
From the graph , the value of f(-1) is = 3 ,
and the value of f(-4) is = -3 ,
So , By the Rate Of Change formula ,
we get ,
Rate Of Change = (f(-1) - f(-4))/(-1 -(-4))
= (3 -(-3))/(-1 + 4)
= (3 + 3)/3
= 6/3
= 2
Therefore , the rate of change over the interval [-4,-1] is 2 .
The given question is incomplete , the complete question is
Calculate the average rate of change of f(x) (shown in the graph) over the interval [-4, -1] using the formula. The value of f(-1) is. The value of f(-4) is. The average rate of change of f(x) over the interval [-4, -1] is .
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5. If g = -2 and h = -3 find the value of
a) 7g - 2h
b) 3gh - 4h
c) 2g²-4h²
Answer: a
Step-by-step explanation:
simetrico de [tex]\frac{8}{4}[/tex]
The symmetric fraction to 8/4 is given as follows:
1/2.
How to obtain the symmetric fraction?A fraction is a numerical representation of the division of the two terms, symbolized x and y, as follows:
Fraction = x/y.
The technical terms of x and y are given as follows:
The top term x of the fraction is the numerator of the fraction.The bottom term x of the fraction is the denominator of the fraction.The symmetric fraction is obtained exchanging the numerator and the denominator, hence it is of:
Symmetric fraction = y/x.
The fraction in this problem is given by:
8/4.
Hence the symmetric fraction is of:
4/8 = 1/2.
(as both 4 and 8 are divisible by 4).
TranslationThe problem asks for the symmetric fraction to 8/4.
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A study conducted by Norman Hollenberg, professor of medicine at Brigham and Women’s Hospital and Harvard Medical School, involved 27 healthy people aged 18 to 72. Each subject consumed a cocoa beverage containing 900 milligrams of flavonols (a class of flavonoids) daily for five days. Using a finger cuff, blood flow was measured on the first and fifth days of the study. After five days, researchers measured what they called "significant improvement" in blood flow and the function of the cells that line the blood vessels.³³ What flaw in the design of this experiment makes it impossible to say whether the cocoa really caused the improved blood flow? Explain.
There was no control group for comparison answers.
There was no control group to compare the results to change in blood flow could have been caused by something else .
What is meant by blood flow ?The movement of blood through the vessels from arteries to capillaries and then into veins is referred to as blood flow.
There are two blood circulatory systems in the human body, which are linked: The systemic circulation transports blood to organs, tissues, and cells, supplying them with oxygen and other vital substances. The pulmonary circulation is where fresh oxygen enters the bloodstream.
As the heart beats, blood is pumped through a network of blood vessels known as the circulatory system. The vessels are flexible tubes that transport blood to all parts of the body.
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I NEED HELP ASAP PLS HURRY
Answer: C
Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.
The sum of three numbers is 23.
Three times the smallest is 4 less than the largest, while the sum of the largest
and smallest is 16. Use a linear system in three variables to find the three numbers.
The three numbers are __ , __
and __
Answer:
The three numbers are 3, 7 and 13
Step-by-step explanation:
Considering the 3 numbers: x, y and z
x + z = 16
z=16-x
3x=z-4
3x=16-x-4
4x=12
x=3
3+z=16
z=16-3
z=13
3+13+y=23
y=23-13-3
y=7
Hope this helps :)
What i the value of x in the equation 0. 2(x 1) 0. 5x = –0. 3(x – 4)?
Negative even-halve
–1
1
Seven-halve
The value of x for the given equation is 1.
What is solving an equation?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Consider the given expression
0.2(x + 1) + 0.5x = -0.3(x - 4)
Simplifying,
0.2x + 0.2 + 0.5x = -0.3x + 1.2
0.7x + 0.2 = -0.3x + 1.2
Add 0.3x on both sides,
0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x
x + 0.2 = 1.2
Subtract 0.2 from both sides,
x + 0.2 - 0.2 = 1.2 - 0.2
x = 1
Hence, the value of x for the given expression is, 1.
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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
[tex]S=\{-2,-3\}[/tex]
Step-by-step explanation:
Required integers are: -2 and -3
Where is the gap in the data?
Number of Patients Per Hour Who Waited Longer than 15 Minutes
A dot plot going from 0 to 5. 0 has 8 dots, 1 has 6 dots, 2 has 1 dot, 3 has 5 dots, 4 has 0 dots, and 5 has 3 dots.
0
2
4
8
Answer:
4 hours
Step-by-step explanation:
I don’t work with data points too much but I believe the gap is at 4 because it is where no one waited that long and where the date kind of stops and then start back up at 5 hours
Hopes this helps
