Four ways to find the slope and y–intercept of straight line equation are;
Making use of the graph to find the slopeObtaining the coordinates of the x–intercept, Looking for the y–intercept when the slope and a point is knownSolving for the slope when two points are givenWhat is a straight line equation?A straight line equation is of the form, y = m•x + c
Where;
m = The slope of the graph of the equation
c = The point the graph intersects the x–axis.
The process by which the slope–intercept form of a straight line equation can be found from the above ways are as follows;
1. Making use of the graph of the equation
When the graph is given, the y–intercept is found from the point the graph crosses the y–axis
Note the y–intercept
Find two points on the graph where coordinates can be obtained
Find the ratio of the rise to the run to get the slope of the graph
[tex] \displaystyle{ Slope, \: m = \frac{ rise}{run} } = \frac{ \triangle y }{\triangle x} [/tex]
With the slope and y–intercept, the equation of the line can be written as; y = m•x + c
2. Obtaining the coordinates of the x–intercept
Given the slope and the y–intercept, the x–intercept can be found by plugging in the values of the slope, m, and the y–intercept, c, in the equation, y = m•x + c, to get the equation of the line
From the equation, the x–intercept can be found by plugging y = 0, to get;
0 = m•x + c
The x–intercept becomes, [tex] \displaystyle \frac{-c}{m} [/tex]
The graph can then be plotted by drawing a line through the x and y–intercept
3. Finding the y–intercept given the slope and the x–intercept
When the slope and the x–intercept and the slope is known, whole number part of the numerator can be added to the x–value of the x–intercept to obtain the x–coordinates of a second point on the graph
The process is repeated to find the y–coordinate of the second point
The slope is calculated using the two points and the equation for the slope given in the first method
4. When two points are known, the slope is calculated using the equation in method 1
The two are joined with a straight line and the y–intercept is obtained from the point the graph intersects the y–axis
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Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
[re post]
Answer:
there must be 14 students and each one can get 4 pencils and 3 erasers
Step-by-step explanation:
56 goes into 14 4 times. 42 goes into 14 3 times none left over
There are 14 red marbles and 20 blue marbles in a bag of marbles.
A. What is the ratio of red to blue marbles in simplest form?
B. What is the ratio of blue marbles to total marbles in simplest form?
Answer:
A. 7:10
B. 10:17
Explanation: The ratio of A. would be 14:20, simplified would be 7:10. The ratio of B. would be 20:34, simplified being half of both numbers. Giving you 10:17.
A silo containing 800 gallons of grain is emptied at a constant rate of 400 gallons every 1
hour.
Enter an equation in the form y = mx + b that represents the amount of grain y, in gallons,
remaining in the silo after x hours.
The equation of the line is y = -400x + 800
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation that represents the amount of grain?The given parameters are
Initial number of gallon, c = 800
Constant rate, m = -400 gallons per hour
This means that
Slope = -400
y-intercept = 800
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
So, we have
y = -400x + 800
Hence. the equation of the amount of grain is y = -400x + 800
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A reservoir has an area of about 1.8 × 104 square miles. Its volume is about 28,000 cubic miles. Find the area of the reservoir in standard form and its volume in scientific notation.
The area of the reservoir in standard form is 1.8 × 10⁴ square miles
The volume of the reservoir in scientific notation is 2.8 × 10⁴ cubic miles
Writing an expression in standard formFrom the question, we are to determine the area of the reservoir in standard form and the volume of the reservoir in scientific notation
Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form
Thus,
To write a number in standard form, we will write the number as a product of a number between 1.0 and 10.0 and a power of 10
From the given information,
The area of the reservoir is 1.8 × 10⁴ square miles.
The area of the reservoir is already written in standard form
Now,
To write the volume of the reservoir in scientific notation
NOTE: Standard form is the same as scientific notation
From the given information,
The volume of the reservoir is 28000 cubic miles
28000 = 2.8 × 10⁴
Hence, the volume in scientific notation is 2.8 × 10⁴ cubic miles
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At the sewing store, Brooke bought a bag of mixed buttons. The bag included 76 buttons, of which 75% were large. How many large buttons did Brooke get?
Answer:
57
Step-by-step explanation:
75/100 *76
5700/100 =57
Factorise completely.
Pq - 2rq + pr-2r²
i need help on this, thanks
Answer:
M∠2 = 37°
M∠3 = 143°
M∠4 = 37°
Step-by-step explanation:
∠3 is the complete opposite of ∠1
143° + 143° = 286°
there is 360° in a full circle or a repeating angle (aka the scissors)
360°-286°=74°
since ∠2 and ∠4 is opposite of each other
74°÷2=37°
Answer:
[tex]m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ 143° + m∠2 = 180°
⇒ m∠2 = 37°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠3 = m∠1 = 143°m∠4 = m∠2 = 37°If Andy continues descending at this rate, where will he be in relation to sea level after 6 minutes write your answer as a integer
1. The rate of the descent of Andy as a unit rate will be -4 feet per minute.
2. If Andy continues descending at this rate, the relation to sea level after 6 minutes is -24 feet.
How to illustrate the information?From the information, the following can be deduced'
1. Distance = -10 feet
Time = 2 1/2 minutes = 2.5 minutes
Speed = Distance / Time
Speed = -10 / 2.5
Speed = -4 feet per minutes
2. When Andy continues descending at this rate, the relation to sea level after 6 minutes will be:
= -4 × 6
= -24
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Andy is scuba diving. He starts at sea level and then descends 10 feet in 212 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet
What is the domain of this relation?
Answer:
(-5, -3, 1, 2, 3) .... the fourth one
Step-by-step explanation:
the domain is all the x values.
so look at your points and look at the x values ( the number on the X-axis) for those points!
on a drive, a football team gained 3 yards, lost 11 yards, and gained 15 yards. What was their total yardage for that drive?
Help me :(
By using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.
We are given that:
On a drive,
A football team first gains = 3 yards.
Then it lost = 11 yards.
Then it again gained = 15 yards.
We need to find its total yardage.
For this, we will subtract the yards lost from the yards gained by the team.
So, we get that:
total yardage = 3 + 15 - 11
total yardage = 18 - 11
total yardage = 7 yards.
Therefore, by using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.
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Work out √45 - √5
Give your answer as an integer or as a
surd in its simplest form.
Graph the line -3 with slope (-4,-2) passing through the point
The linear equation of the line that passes through point (-4,-2) and has a slope of -3 is y = -3x - 14.
What is the graph of the line with the given slope and point?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 ( -4, -2 )
x = -4y = -2Slope m = -3First we calculate the y-intercept 'b' using the equation of line formula.
y = mx + b
Plug in point ( -4, -2 ) and slope -3.
-2 = -3(-4) + b
-2 = 12 + b
b = -2 - 12
b = -14
Now that we have the values of slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = -3(x) + ( -14 )
y = -3x - 14
Therefore, the equation of the line is y = -3x - 14.
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what is the simplest form of the square root of 75
mother ate pies in the morning, she ate one pie, while she gave half of all those left to Little Red Riding Hood who gave it to her grandmother. On the way, Little Red Riding Hood ate 2 pies and gave a third of the rest to the wolf. Little Red Riding Hood brought 8 pies to her grandmother. How many pies did mother bake?
The number of pies that Red Riding Hood's mother made is 25.
How many pies did the mother bake?Let x represent the number of pies mother baked in the morning.
Pies left after mother ate 1 = x - 1
The number of pies that Red Riding Hood takes to her grandmother: 1/2(x - 1)
0.5(x - 1)
0.5x - 0.5
Pies left after Red Riding Hood ate 2: [(0.5x - 0.5) - 2]
Pie after she gave the wolf 1/3 ; (1 - 1/3) × [(0.5x - 0.5) - 2]
2/3 × [(0.5x - 0.5) - 2] = 8
In order to determine the value of x, take the following steps:
Multiply both sides of the equation by 3/2.
[(0.5x - 0.5) - 2] = 12
Add 2 to both sides of the equation: 0.5x - 0.5 = 12 + 2
0.5x - 0.5 = 12
Add 0.5 to both sides of the equation
0.5x = 12 + 0.5
0.5x = 12.5
Divide both sides by 0.5
x = 25
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I need helppppppppp I d don't know what to do
EXPLANATION
The perimeter Perimeter is given by the sum of the sides as follows:
P = z + 5 + z + 5 + z + z
Substituting P=26 and adding like terms,
26 = 10 + 4z
Subtracting -10 to both sides:
26 - 10 = 10 - 10 + 4z
Simplifying:
16 = 4z
Dividing both sides by 4:
16/4 = z
Switching and simplifying:
z = 4
So,
Equation: 26 = 10 + 4z
z = 4
Write 9.75 as a mixed number.
Answer:
9 57/ 100
Step-by-step explanation:o convert the decimal 9.57 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
9.57 = 9.57/ 1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,
9.57 / 1
= (9.57 × 100)
(1 × 100)
= 9 57/ 100
.
(This fraction is alread reduced, We can't reduce it any further).
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 9 57/ 100
is also equal to 9 57/ 100
when expressed as a mixed numbeR
Answer:
9 3/4
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.
Eli loads identical crates onto a truck with a load limit of 2000 pounds. Each crate weighs 125 pounds.
A function modeling this situation, where y represents the total weight of the crates in pounds, has a range described by which inequality?
0 < y < 16
0 ≤ y ≤ 125
0 ≤ y ≤ 2,000
0 < y < 2,000
The function modeling given situation, where y represents the total weight of the crates in pounds, has a range described by the inequality 0 ≤ y ≤ 2000. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The set that includes all the output values that the function expects is the range of a function.
The following information is provided regarding the input and output for this problem
The number of containers placed inside the vehicle as input.
Total weight of the crates loaded into the truck or output.
The range of this problem is represented by the following inequality:
0 ≤ y ≤ 2000.
The weight of an amount will never assume a negative value, and the maximum weight is 2,000 pounds, as stated in the problem.
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Please answer this question to 1 decimal place
Answer:
To one decimal place, x = 7.7 cm
Step-by-step explanation:
Let y equal BD.
Since AD is a bisector of angle BAC, angle DAB is 17°.
tan(17°) = y/21, so y = 21 tan(17°)
tan(34°) = (x + 21 tan(17°))/21
21 tan(34°) = x + 21 tan(17°)
x = 21(tan(34°) - tan(17°)) = 7.7 cm
Mayerlin is deciding between two different movie streaming sites to subscribe to. Plan A costs $34 per month plus $2 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Mayerlin watches xx per month, and let BB represent the monthly cost of Plan B if Mayerlin watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine the number of monthly movies watched, x,x, that would make the two plans have an equal monthly cost.
Considering the definition of an equation and the way to solve it, the number of monthly movies watched that would make the two plans have an equal monthly cost is 26.
Definition of equationAn equation is an algebraic equality in which there are unknowns with unknown value. The unknown represents the number, if any, that makes the equality true. This unknown number is the solution of the equation.
This is, the solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Number of monthly movies watchedBeing "x" the number of monthly movies watched, you know that:
Plan A costs $34 per month plus $2 per movie watched. → A= 34 + 2xPlan B costs $8 per month plus $3 per movie watched. → B= 8 + 3xIf the two plans have an equal monthly cost, the equation in this case is:
A= B
34 + 2x= 8 + 3x
Solving:
34 - 8= 3x - 2x
26= x
Finally, 26 monthly movies watched would make the two plans have an equal monthly cost.
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A binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment?.
The features of a binomial experiment are
Identical number of trialsEqual probability of successHow to determine the features of a binomial experiment?From the question, we understand that the experiment is a binomial experiment
As a general rule, a binomial experiment is any experiment that has only two possible outcomes
These outcomes are represented as
True FalseThese outcomes can also be represented as
SuccessFailureThe representation of the outcomes are:
Success = pFailure = qThere are other features of a binomial experiment.
One of these features is:
The binomial experiment has a number of n identical or unique trials
Another features of a binomial experiment is
The probability of success on one trial is the same for all other trials
Hence, the two other features of a binomial experiment are
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1/3(2x-3/7)+1/6x=4/7 find x
If the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7.
The given equation is
1/3(2x - 3/7)+(1/6)x = 4/7
First we have to apply the distributive property of subtraction in the equation
1/3(2x - 3/7)+(1/6)x = 4/7
(3/2)x - 1/7 + (1/6)x = 4/7
Here we have to rearrange the terms and group the like terms
Move the 1/7 to right hand side of the equation
(3/2)x + (1/6)x = (4/7)+(1/7)
Addition of like terms
(5/3)x = 5/7
Move the 5/3 to the right hand side of the equation
x = 5/7 ÷ 5/3
x = 5/7 × 3/5
x = 3/7
Hence, if the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7
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a study of how noise impacts student performance on exams is being proposed. eighty student volunteers will be randomly assigned to two groups of forty and each student will take a test on how much trivia they know. one group will take the test while construction sounds are being played and the other group will take the test without any background sounds. what will be the biggest problem with the results of this study?
The biggest problem with the results of this research study is B. Lack of realism.
What is realism about?It should be noted that when an experiment's procedures, participants, or setting are unrealistic. The ability of researchers to apply the findings of an experiment to the situations that hold the most interest may be constrained by a lack of realism.
The study is how how noise impacts student performance on exams is being proposed.
An experiment's subjects, medications, or environment might not accurately replicate the circumstances we truly wish to explore. In that circumstance, we are unable to extrapolate the experiment's findings broadly.
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The options are:
a. Lack of attention to experimental detail
b. Lack of realism
c. Placebo effect
Write the equation in slope-intercept form:
6x−3y=−18
The equation in slope-intercept form is y = 2x + 6
How to determine the slope-intercept form of the equation?The equation is given as
6x - 3y = -18
The above equation is a linear function, and it is in its general form
To determine the slope-intercept form of the equation, we simply make y the subject of the formula in the equation
So, we have
6x - 3y = -18
Divide through the equation by -3
So, we have
-2x + y = 6
Add 2x to both sides
y = 2x + 6
Hence, the slope-intercept form of the equation is y = 2x + 6
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i earn an annual salary of $30,572 and my commission is 5% on all sales. How much must my sales be if i want my annual salary to be $31,836?
If you want to make an annual salary of $31,836, then your sales must be $25,280
How much must my sales be to get the desired salary?
Ok, so you want to earn a total of $31,836, and he has a fixed salary of $30,572, so the missing amount is:
$31,836 - $30,572 = $1,264
Now, we know that you make a commission of the 5% of what you sell, so if X is what you sell, then to make the desired salary X must be:
X*0.05 = $1,264
Solving that linear equation for X we get:
X = $1,264/0.05 = $25,280
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Victoria's car used of a gallon to travel 21 miles. At what rate doesthe car use gas, in miles per gallon?
Answer:
26 1/4 miles per gallon
Explanation:
We are told that the car travels 21 miles per 4/5 gallons. Therefore, the rate at which the car uses the gas is
[tex]\frac{21\text{ miles}}{4/5\text{ miles}}[/tex]which can also be written as (by taking the reciprocal of the denominator)
[tex][/tex]Find the L.C.M of: 3x² + 7x + 2 and 2x² + 3x-2
Best of luck
Least Common Multiple of 3x² + 7x + 2 and 2x² + 3x-2 is (2x-1)(x+2)(3x+1)
What is lcm ?Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers. Finding the LCM of a given collection of numbers can be done in a variety of ways. Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
Given that : 3x² + 7x + 2 and 2x² + 3x-2
3x² + 7x + 2
3x² +6x +x + 2
3x(x +2)+1(x+2)
(3x+1)(x+2)
2x² + 3x-2
2x² + 4x-x -2
2x(x+2)-(x+2)
(2x-1)(x+2)
L.C.M of 3x² + 7x + 2 and 2x² + 3x-2 is
(2x-1)(x+2)(3x+1)
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On january 1, 2021, frontier world issues $39.3 million of 7% bonds, due in 10 years, with interest payable semiannually on june 30 and december 31 each year. the proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride.
The issue price (present value) of the bonds issued by Frontier World is $42,223,423.81.
What is the present value?The present value refers to the discounted future cash flows of the bonds (including interests and the repayment of the bonds).
The present value represents the current price of the bonds, at which they are issued.
The present value can be computed using the online finance calculator.
N (# of periods) = 20 (10 x 2)
I/Y (Interest per year) = 6% (Market Rate)
PMT (Periodic Payment) = $1,375,500
FV (Future Value) = $39,300,000
Bond Interest Rate = 7%
Semi-Annual Interest Payments:June 30 = $1,375,500 ($39,300,000 x 3.5%)
Dec. 31 = $1,375,500 ($39,300,000 x 3.5%)
Results:
Present Value (PV) = $42,223,423.81
Sum of all periodic payments = $27,510,000 ($1,375,500 x 20)
Total Interest = $24,586,576.19
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Question Completion:Required: 1-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)
An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 18 miles per hour faster than the westbound train. After 2.5 hours, they are 280 miles apart. At what speeds are the two trains traveling?
Answer: The eastbound train is traveling at 65mph while the westbound train travels at 47mph.
Step-by-step explanation:
You would use x as the variable for the speed of the westbound train. The eastbound train would be 18+x. your equation would be 2.5(18+x+x)=280
You would find that x=47 for the westbound train. You would then add 18 to get the speed of the eastbound train which would be 65.
The questions are at the bottom of the page. This is easy im just bad pls help
We have a translation of 3 units to the left and 4 units upwards.
How to identify the translation applied?
To find the translation, we only need to look at one of the vertices of the triangle.
We can see that the coordinates of B are (4, 1), while the coordinates of the translated point B' are (1, 5)
The translation is given by the difference:
(1, 5) - (4, 1) = (1 - 4, 5 - 1) = (-3, 4)
So the translation is defined by (-3, 4)
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Anyone know how to prove these are equal to one another? I also need all the steps.
Answer:
Step-by-step explanation:
it can be simplified to [tex]\frac{sec \theta}{cot\theta+tan\theta} =sin\theta[/tex] . if you multiply each side by the denominator, it becomes [tex]sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta[/tex] since [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex] and cotan is the reciprocal of that. Because [tex]sec\theta=\frac{1}{cos\theta}[/tex] so multiplying each side gives [tex]1=sin^2\theta+cos^2\theta[/tex], and [tex]sin^2\theta+cos^2\theta[/tex] is equal to 1.