Help please! How do I write an equation in standard form using the information on the graph?
Answers
Answer:
3x -y = 2
Step-by-step explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
SlopeThe slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
InterceptThe point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equationWith this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard formThe standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.
Related Questions
A hospital near a ski resort records the type of injuries treated during ski season and other seasons and other seasons over a year. the results shown in the table will help determine the medical staff that is required at different times of the year. according to the data in the table, what is the probability that a patient will need to be treated with a broken bone during ski season.
Answers
Answer:
The answer is C
Step-by-step explanation:
You have to divide both numerators then the denominater.
So, it would look like: 160 over 90 x 100 over 290
160x100=16 90x290=25 16/25
WHAT IS A PRICE OF A 7 - MINUTE DIAL DIRECT CALL TO NEW YORK, NY, WHEN YOU
CALL IN THE EVENING?
Answers
The price of a seven minute call direct to New York, in the evening, is given as follows:
$5.82.
How to obtain the cost of the call?The cost of the call is obtained considering the information given in the table, for which the proportions are applied.
We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.
Then the minute proportions, considering that the call happens in the evening, are given as follows:
First minute: 0.38 of $3.Each additional minute: 0.26 of $3.A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:
0.38 x 3 + 6 x 0.26 x 3 = $5.82.
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7. A group of friends orders pizza at a restaurant. Each person gives some money to Chris before they order.
a. Chris has $63 to spend on the order, including tax. The tax at the restaurant is 5%. What is the maximum cost of food the group can order and not go over $63? Explain your reasoning.
b. Chris wants to leave a 15% tip on the price of the food, calculated before sales tax. What is the maximum cost of food the group can order and not go over $63? Explain.
Answers
The answer to B is: 53.55$ because 15% of 63$ is 9.45$ so once again do the same thing you did to A and take away 9.45$ from 63$ and you get 53.55
Work out 2/3 - 2/5 in its simplest form
Answers
Answer:
It is in its simplest form
Step-by-step explanation:
June is buying a sweater using a coupon offering a 30% discount on items over $99. If the discounted price is $91, how much was the original price of the sweater?
Answers
Answer: 130
Step-by-step explanation:
The original price of the sweater is $303.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.
The discounted price is $91
Let the original price of the sweater be x.
So, 30% of x=91
30/100 ×x=91
0.3x=91
x=91/0.3
x=$303
Therefore, the original price of the sweater is $303.
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Question 2(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length and g the line segment shown
!!!!please help me!!!!
Answers
The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
According to the graph -
The perpendicular measures 4 units.
The base measures 3 units.
To find the hypotenuse g apply the Pythagoras theorem -
(hypotenuse)^2=(base)^2+(perpendicular)^2
(g)^2=(3)^2+(4)^2
(g)^2=9+16
(g)^2=25
g=[tex]\sqrt{25}[/tex]
g=5
Therefore, line segment g measures 5 units.
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find the slope for 1-6
Answers
Answer:
1) 10/3
2) -1./3
3) -2/5
4) 1
5) undefined
6) 0
Step-by-step explanation:
Find two easy to read points. Go from one point to the other by going vertically first then horizontally. Moving up is positive and down is negative. Moving right is positive and left is negative.
slope = rise/run = (difference in y)/(difference in x)
1) slope = 10/3
2) slope = -1/3
3) slope = -2/5
4) slope = 1/1 = 1
5) slope = undefined (The slope of a vertical line is undefined.)
6) slope = 0 (The slope of a horizontal line is 0.)
the graph of a function f is the collection of ____________ or (x,f(x)) such that x is in the domain of f
Answers
A new car loan has a term of loan from 2 - 6 years and the interest rate is between 4% and 8%. what is the longest amount of time you could take to pay off the loan? what is the best interest rate you could get?
Answers
a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.
b) Based on the above, the best interest rate the borrower could get is 8%.
How is the interest rate determined?Many factors are considered in determining the interest rate for a loan.
Some of the factors include:
Loan TermLoan TypeCredit ScoreLoan AmountDown PaymentInterest rate type.We know that the longer the term of a loan, the higher the interest rate charged. This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.
Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.
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1. Explain how place-value blocks can
help you with division.
Answers
Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.
What is division?
With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".
The bigger amount that is divided into equal halves is called the dividend.
The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.
The value of a digit in a number is determined by its place in the number, or place value.
Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.
Example - 4 ÷ 2 = 2
In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).
Example - 40 ÷ 20 = 2
For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).
Example - 400 ÷ 200 = 2
Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).
Therefore, place value blocks help in division for making it simpler.
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Roller coaster A can reach a top speed of 110 ft./s roller coaster B can reach a top speed of 85 mph which roller coaster has a greater top speed?
Answers
Roller coaster B has greater top speed than roller coaster A.
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Given,
speed of roller coaster A = 110ft./s
speed of roller coaster B = 85mph
1 mile = 5280 feet
⇒ 85 mile = 5280 × 85 = 448800 feet
1 hour = 3600 seconds
speed of roller coaster B = 448800/3600 ft/s = 124.67 ft/s
comparing speed of both
Speed of roller coaster B > speed of roller coaster A
Hence roller coaster B has greater top speed.
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is 10/12 and 40/64 a proportion
Answers
Answer:
No, it is not a proportion
Step-by-step explanation:
10/12 and 40/64 is not a proportion since although the numerator is constant because when multiplied by 4, it gives us 40, however, when you multiply 4 by 12, you get 48, therefore, it is not a proportion since the changes in the value of a proportion must be constant in both the numerator and denominator.
Hope this helped! :D
Which graph represents the solution to the following inequality? 3x - 2y ≥ 6
Answers
Answer:
First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
For:
x
=
0
(
3
⋅
0
)
+
2
y
=
6
0
+
2
y
=
6
2
y
=
6
2
y
2
=
6
2
y
=
3
or
(
0
,
3
)
For:
y
=
0
3
x
+
(
2
⋅
0
)
=
6
3
x
+
0
=
6
3
x
=
6
3
x
3
=
6
e
d
)
(
3
)
x
=
2
or
(
2
,
0
)
We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}
Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.
graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}
Step-by-step explanation:
Need it ASAP, please!!!
Answers
Answer:
27y - 45 + 7z
There is a proportional relationship between the weight and total cost of a bag of lemons. One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94. Describe how you would graph the proportional relationship i need help asp
Answers
There is a directly proportional relationship between the weight and total cost of bag of of lemons.
What is constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.
Given data :
One bag weighs 2.4 pounds and cost $5.28.
Another bag weighs 2.7 pounds and cost $5.94
2.4k = 5.28
k= 2.2
2.7k = 5.94
k = 2.2
k > 1
The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.
Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answers
The equations that are true for x = –2 and x = 2 are:
x^2-4=0 and 4x^2 = 16
How can the equation be known?We can determine the equations that are true for x = –2 and x = 2 by testing the given options:
After testing the options option 1 ; x^2-4=0 putting x = 2 or -2 into the equation will give zero.
(2^)2-4=0
(-2)^2-4=0
Then option 4: 4x^2 = 16
4(2)^2 = 16
4(-2)^2 = 16
Therefore, option 1st and 4th are correct.
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coefficient: The number in BLANK of the variable within the BLANK BLANK
Answers
The blank spaces of the statement coefficient: The number in BLANK of the variable within the BLANK BLANK are, front, addition, subtraction.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
We know a coefficient is a constant value combined with a variable.
For example, In 7x the coefficient of x is 7.
Given, A fill-in-the-blank statement,
coefficient: The number in BLANK of the variable within the BLANK BLANK.
Therefore,
coefficient: The number in front of the variable within the addition subtraction.
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For polynomial function f, if f(3)=5 and f(5)=-2, what do we know about any roots of f(x)?
Answers
Answer:
There is a root between x=3 and x=5.
Step-by-step explanation:
Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.
The rate of change increased by about _____ bass per a year. Round to the nearest tenth
Answers
From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65
What is Exponential FunctionAn exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.
In this problem, we have to calculate the rate of increase per year.
Data;
rate = 2%
P = 3000
The exponential growth can be calculated by;
A = P(1 + r)ⁿ
In year 1
A = 3000(1 + 0.02)¹
A = 3060
In year 4
A = 3000(1 + 0.02)⁴
A = 3247.3
a)
The average rate of change from year 1 to year 4 will be
A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1
A = 62.43
The average rate of change from year 1 to year 4 is 62.43
b)
The average rate of change from year 5 to year 8 is calculated as
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5
A = 67.57
C)
The rate of change increase can be calculated as;
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1
A =65
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Hafiz has $25. His sister has 1/5 as much as Hafiz. His father has 40% as much as Hafiz. Calculate how much money Hafiz, his sister and his father have in total.
please answer it
Answers
Answer:
Step-by-step explanation:
According to question, we know that
His Sister has "1/5*$25 which is equal to $5, and his father has "40%*$25 which is equal to 0.4 * $25 = $10". So, the money Hafiz, his sister and his father have in total
= $25+$5+$10 = $40
Hafiz = $25
Sister = [tex]\frac{1}{5}[/tex]
Father = 40%
FindTotal money of Hafiz, Sister, and Father altogether.
SolutionSister[tex]\frac{1}{5} X[/tex] $25
= $5
Father40% (0.4) x $25
= $ 10
Add all$ 25 + $ 5 + $ 10
Answer$ 40An Item costs $450 Before tax. and the sales tax is $31.50
Find the sales tax rate. Write your answer as a percentage
Answers
The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%
What is tax rate?The tax rate is the percentage of an income or an amount of money that has to be paid as tax.
To find the tax rate of $31.50 from $450
The formula is
Amount taxed/Principal amount x 100
= $31.50/$450 x100
=$3150/450
=7%
Hence, the tax rate is 7%
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Please i have a question you can help me for answer.
The question is
Follow the construction program to build below the figure
° Draw a segment {ST} of length 9 cm.
°Draw the circle with center T and radius 4 cm
.
° Draw the circle with diameter {ST}
° The two circles intersect at A and B. Without measuring, give the length of the segments {TA} and {TB}:
Answers
The length of segments TA and TB are both 4 cm.
How to determine the diagram and the lengthsTo solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.
Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.
Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.
Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.
Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.
Therefore, the length of segments TA and TB are both 4 cm.
The figure is attached
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Please help me I can’t figure it out
Answers
The number of times each number divides is 8 divides LCM into 11 times
11 divides into LCM 8 times and 22 divides into LCM 4 times .
What is LCM ?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
The LCM of 8 , 11 and 22 is 88
∴ 8 divides into LCM 11 times
11 divides into LCM 8 times
22 divides into LCM 4 times
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Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price. f
Answers
p = 0.82 * 55
In this equation, p represents the new price after the discount has been applied, and 0.82 represents the percentage of the original price that remains after the discount has been applied (100% - 18% = 82%).
Solving this equation, we find that the new price, p, is equal to $45.90.
Note: This equation represents a discount, which means that the final price, p, will be less than the original price. If you want to represent a markdown (i.e., a price increase), you would use a value greater than 1 for the percentage factor (e.g., 1.18 for a markdown of 18%).
One number is three more than twice another number. If the sum of the two numbers is 30 , find the numbers
Answers
Answer:
9 = 1st number
21 = 2nd number
Step-by-step explanation:
given that :
1st number = x __eq_i
2nd number (in terms of the first number) = 2x + 3 __eq_ii
1st number + 2nd number = 30 __eq_iii
input eq_i and eq_ii in eq_iii
x + 2x + 3 = 30
3x + 3 = 30
3x = 30 - 3
x = 27 ÷ 3
x = 9
9 = 1st number
input the value of x in eq_ii
2x + 3
2(9) + 3
18 + 3
21 = 2nd number
hope that helps.
In Circle O, mAB = 72. Find m
Answers
Check the picture below.
In triangle JKL, angles J and L each measure 51° and JK = 18. Triangle PQR is similar to triangle JKL, where J corresponds to P, K corresponds to Q, and QR = 36. Which expression represents the length of segment PR?
Answers
Answer:
Step-by-step explanation:
Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:
(PR)/(JK) = (PQ)/(JL) = (36)/(18)
Cross multiplying and solving for PR, we find:
PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36
Given A(0, a) and B(b, 0) , find coordinates of C so that the orthocenter of triangle ABC lies on the triangle.
Answers
The coordinate of the point C is (0, a)
How to determine the coordinates of point CFrom the question, we have the following parameters that can be used in our computation:
A = (0, a)
B = (b, 0)
As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.
This means that we start by calculating the equation of the altitude from B to line AC.
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the above as a guide, we have the following:
slope = (y₂ - y₁)/(x₂ - x₁)
This gives
m(BC) = (0 - 0)/(b - 0) = 0
y-intercept (c) = a
So the equation of the line BC is
y = 0 * x + a
y = a
For line AC, we have
m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.
This means that the equation of the line AC is
x = 0
The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)
At this stage, we have the coordinates of the points from lines AC and BC to be
(0, a) and (0, a)
Next, we calculate the C as follows
C = Midpoints of (0, a) and (0, a)
This gives
C = 1/2 * (0 + 0, a + a)
Evaluate
C = (0, a)
Hence, the coordinate of C is (0, a)
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Please help me solve
Answers
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]
[tex](-6x^3 y^5 + 11x^3 y^2) \div (-2x^2 y^3)\implies \cfrac{-6x^3 y^5 + 11x^3 y^2}{-2x^2 y^3} \\\\\\ \cfrac{-6x^3 y^5}{-2x^2 y^3}+\cfrac{11x^3 y^2}{-2x^2 y^3}\implies \cfrac{-6}{-2}\cdot \cfrac{x^3 y^5}{x^2 y^3}+\cfrac{11}{-2}\cdot \cfrac{x^3 y^2}{x^2 y^3} \\\\\\ 3\cdot x^3 x^{-2}y^5 y^{-3}+\cfrac{11}{-2}\cdot \cfrac{x^3 x^{-2}}{y^3 y^{-2}}\implies 3x^{3-2}y^{5-3}-\cfrac{11}{2}\cdot \cfrac{x^{3-2}}{y^{3-2}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x y^2 -\cfrac{11x}{2y} \end{array}}~\hfill[/tex]
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Answers
Answer:
both are right
Step-by-step explanation:
2/5x = 14
multiply both sides by 5/2:
(5/2)(2/5)x = 14(5/2)
x = 70/2 = 35
However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.