graph the function f( x ) = |x+2| - 3
Answers
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
The graph of the function is as shown in the attachment below.
Answer:
Find the attached
Step-by-step explanation:
To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;
-5, -4, -3, 3, 4, 5
we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;
when x = -5, f(-5) = |-5+2| - 3 = 0
when x = -4, f(-4) = |-4+2| - 3 = -1
when x = -3, f(-3) = |-3+2| - 3 = -2
when x = 3, f(3) = |3+2| - 3 = 2
when x = 4, f(4) = |4+2| - 3 = 3
when x = 5, f(5) = |5+2| - 3 = 4
Related Questions
Assume that the price of a combo meal is the same price as purchasing each item separately. Find the price of a pizza, a coke, and a bag of chips.
Answers
Answer:
pizza: $4, coke: $3, chips: $2
Step-by-step explanation:
Lets make the price of a pizza=p a coke= k and a bag of chips=c
then we have the following equations
p+k+c=9
p+2k=10
2p+2c=12
Because p is common in all the equations we shall make it the subject of each equation.
p=9-(k+c)...........i
p=10-2k..............ii
p=6-c...................iii
We then equate i and iii
9-(k+c)=6-c
9-k-c=6-c
putting like terms together we get:
9-6=-c+c+k
1 coke, k=$3
replacing this value in equation ii
we get p=10-2(3)
p=10-6= 4
1 pizza, p=$4
replacing this value in equation iii
4=6-c
c=6-4
=2
a bag of chips, c=$2
Thus, a pizza, a coke and a bag of chips= pizza: $4, coke: $3, chips: $2
Simplify by using factoring: (2a+6b)(6b−2a)−(2a+6b)^2
Answers
Answer:
-8a(a+3b)
Step-by-step explanation:
(2a+6b)(6b−2a)−(2a+6b)^2
(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}
2(a+3b) (6b-2a-2a-6b)
2(a+3b) (-4a)
-2(a+3b) x 4a
-2 x 4a (a+3b)
-8a(a+3b)
The simplified expression is -8a² - 24ab.
Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2
First, let's expand the squared term (2a + 6b)^2:
(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)
Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:
(2a + 6b)[(6b - 2a) - (2a + 6b)]
Now, simplify the expression inside the brackets:
(2a + 6b)[6b - 2a - 2a - 6b]
Combining like terms within the brackets:
(2a + 6b)[-4a]
Now, multiply the remaining terms:
-4a(2a + 6b)
-8a² - 24ab
Therefore, the simplified expression is -8a² - 24ab.
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The greater of two consecutive integers is 7 less than one-third the smaller integer. Find the integers and show your work.
Answers
Answer:
{-12, -11}
Step-by-step explanation:
Let x represent the smaller of the two integers. The problem statement tells us ...
x +1 = (1/3)x -7
(2/3)x = -8 . . . . . . subtract 1/3x +1
x = -12 . . . . . . . . . multiply by 3/2
The integers are -12 and -11.
Final answer:
To find two consecutive integers where the greater is 7 less than one-third the smaller, we defined the smaller integer as x and set up an equation: x + 1 = (x/3) - 7. Solving through algebraic operations, we found the integers to be -12 and -11.
Explanation:
To solve for two consecutive integers where the greater is 7 less than one-third the smaller integer, let us denote the smaller integer as x and the greater as x + 1. According to the problem, the greater integer (x + 1) is 7 less than one-third the smaller integer (x/3). Thus, we can set up the equation:
x + 1 = (x/3) - 7
To solve for x, we perform the following steps:
Multiply all terms by 3 to eliminate the fraction: 3(x + 1) = x - 21.
Distribute the 3: 3x + 3 = x - 21.
Combine like terms: 2x = -24.
Divide both sides by 2: x = -12.
Now that we have found the smaller integer to be -12, the greater integer is just one more, so it is -11.
Therefore, the two consecutive integers are -12 and -11.
Suppose at one point along the Nile River a ferryboat must travel straight across a 1.40-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.35 m/s. The ferryboat has a motor that can move the boat forward at a constant speed of 21.8 mph in still water. In what direction should the ferry captain direct the boat so as to travel directly across the river?
Answers
Answer:
about 14° south of east
Step-by-step explanation:
The river speed is about ...
(2.35 m/s)×(1 mi/(1609.344 m))×(3600 s)/(1 h) ≈ 5.2568 mi/h
The angle of interest is such that its sine is the ratio of river speed to boat speed:
sin(α) = (5.2568 mi/h)/(21.8 mi/h) = 0.241138
α = arcsin(0.241138) = 13.9537°
Since the river is flowing north, the boat should be directed south of its intended course by this angle.
The boat should be directed 14° south of east.
To counteract the effect of the river current, the boat should be directed slightly upstream. The specific direction can be calculated using trigonometric relationships between the boat's velocity and the river's velocity.
Explanation:In order to answer this question, one must understand the basic concepts of vectors and relative velocity in physics. These concepts are essential in determining the correct direction for the ferry captain to steer the boat.
To make the journey directly across the river, the captain needs to counteract the effect of the south-to-north current. This essentially means that the boat should be directed slightly upstream. Applying basic physics concepts, the velocity of the boat relative to the ground (or the river bank) is the sum of the boat's velocity relative to the river (21.8 mph toward the east) and the river's velocity (2.35 m/s to the north).
The direction to aim can be obtained by using trigonometric relationships. The direction is tan^-1((2.35 m/s)/(21.8 mph in m/s)) to the north of east. Note that you need to convert 21.8 mph to m/s before solving.
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A company issues auto insurance policies. There are 900 insured individuals. Fifty-four percent of them are male. If a female is randomly selected from the 900, the probability she is over 25 years old is 0.43. There are 395 total insured individuals over 25 years old. A person under 25 years old is randomly selected. Calculate the probability that the person selected is male.
Answers
Answer:
about 0.53
Step-by-step explanation:
54% of the insured, or .54×900 = 486 individuals are males. That leaves 900-486 = 414 that are females. 43% of those, or .43×414 = 178 are over 25, so the remainder of the 395 who are over 25 are male.
Since 395 -178 = 217 of the males are over 25, there are 486 -217 = 269 who are under 25. Then the fraction of insureds who are under 25 that are male is ...
269/(900 -395) = 269/505 ≈ 0.53
_____
It can be useful to make a 2-way table from the given information.
Final answer:
Using the provided data, the probability that a person under 25 years old selected randomly is male is calculated by dividing the number of males under 25 (found by subtraction from total males and males over 25) by the total number of individuals under 25.
Explanation:
The question asks us to calculate the probability that a person under 25 years old, selected randomly from a group of insured individuals, is male. To find this, we need to use the given data:
Total insured individuals: 900
Percentage of males: 54%
Individuals over 25 years old: 395
Probability that a randomly selected female is over 25: 0.43
To calculate the number of males and females, we take 54% of 900 to get the total males, which is 486. Since there are 900 insured individuals in total, the number of females would be 900 - 486 = 414. The number of females over 25 years old is 414 * 0.43 = 178.02, which we can round to 178.
Since there are 395 individuals over 25 years old in total and 178 of them are female, 395 - 178 gives us 217 males over 25 years old. Now, we need to find the number of individuals under 25 years old. There are 900 - 395 = 505 individuals under 25.
The probability that a randomly selected person under 25 is male can be found by dividing the number of males under 25 by the total number of people under 25. The number of males under 25 is the total number of males minus males over 25, which is 486 - 217 = 269. Therefore, the probability is 269 / 505.
What is the value of x?
Answers
What are the choices
Answer: 8 I think!
Hope it helps
1. Solve. r -7> 10 (1 point)
Ox>3
Or>7
O.x>17
Or> 70
Answers
Answer:
r > 17
Step-by-step explanation:
r -7> 10
Add 7 to each side
r-7+7 > 10+7
r > 17
How do I solve this?
Answers
Answer:
b. (w -4)(w +1)
Step-by-step explanation:
The problem statement asks for an expression for the rug area "based on the width of the room." Looking at the answer choices, we see that the variable "w" is used to represent the width of the room.
The dimensions of the room are its width (w) and its length, which is 5 more than its width (w+5).
The dimensions of the rug are 4 ft smaller in each direction (2 ft on each side), so the width of the rug is w-4, and the length of the rug is w+5-4 = w+1.
The area of the rug is the product of its width and length, so is ...
(w-4)(w+1) . . . . . matches selection B
Look at the table of values below. x y 1 -1 2 -3 3 -5 4 -7 Which equation is represented by the table? A. y = 1 − 2x B. y = -x − 1 C. y = x − 2 D. y = 2x − 1
Answers
Answer:
A. y=1-2x
Step-by-step explanation:
if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.
Answer:
A. y=1-2x
Step-by-step explanation:
if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.
Step-by-step explanation:
What is the greatest common factor of 8x and 40?
Answers
For this case we have that by definition, the Greatest Common Factor or GFC, of two or more integers is the largest integer that divides them without leaving a residue.
So:
We look for the factors of both numbers:
8: 1, 2, 4, 8
40: 1, 2, 4, 5, 8, 10, 20
It is observed that 8 is common.
So, the GFC of 8x and 40 is 8
Answer:
8
Use the discriminant to describe the roots of each equation. Then select the best description.
2m^2 + 3 = m
Answers
[tex]\bf 2m^2+3=m\implies 2m^2-m+3=0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}m^2\stackrel{\stackrel{b}{\downarrow }}{-1}m\stackrel{\stackrel{c}{\downarrow }}{+3} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\qquad \checkmark\\ &\textit{two \underline{non-real roots}} \end{cases} \\\\\\ (-1)^2-4(2)(3)\implies 1-24\implies -23[/tex]
g = 15 - (m/32)If Vera stars with a full tank of gas, the number of gallons of gas g, left in the tank after driving m miles is given by the equation above. When full, how many gallons of gas does Vera's tank hold?15 gallons.17 gallons.32 gallons.480 gallons
Answers
ANSWER
15 gallons
EXPLANATION
The equation that models the situation is
[tex]g(m) = 15 - \frac{m}{32} [/tex]
When the tank was full the man did not cover any mile.
To find the the number of gallons of gases Vera's tank holds, we substitute m=0 into the equation to get,
[tex]g(0) = 15 - \frac{0}{32} = 15[/tex]
Therefore the correct answer is is option A 15 gallons
Final answer:
When Vera's tank is full, it holds 15 gallons of gas. This is found by setting the miles driven to zero in the equation g = 15 - (m/32).
Explanation:
To determine how many gallons of gas Vera's tank holds when full, we need to set m, the number of miles driven, to zero in the given equation g = 15 - (m/32). This is because we are interested in the initial amount of gas before any driving occurs.
Plugging m = 0 into the equation gives us:
g = 15 - (0/32)
g = 15
Therefore, when full, Vera's tank holds 15 gallons of gas. Among the provided options, the correct answer is 15 gallons.
Dan buys a car for £2700.
It depreciates at a rate of 1.4% per year.
How much will it be worth in 5 years?
Give your answer to the nearest penny where appropriate.
Answers
The car, which depreciates at an annual rate of 1.4%, will be worth approximately £2590.34 in 5 years.
Explanation:This is a problem related to depreciation, which is a concept in finance and economics. In this case, the car depreciates at a rate of 1.4% per year. This means that each year, the value of the car decreases by 1.4% of its value at the start of that year. This is an example of exponential decay.
To calculate the car's value after 5 years, we raise the depreciation rate (99.6%, or 0.996 in decimal form because the value decreases) to the power of 5, and then multiply it by the initial price of the car, £2700.
That is, Car Value = £2700 * (0.996)^5 = £2590.34
So, the car will be worth approximately £2590.34 in 5 years to the nearest penny.
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Find the radius of a circle with circumference of 45.84 meters. Use 3.14
Answers
Answer:
3.8 meters
Step-by-step explanation:
In order to find the circumference for a circle, we use the formula π(radius)²
The circumference give is 45.84 and the π given is 3.14
All we have to do is to just substitute them.
45.84 = 3.14(radius)²
45.84 / 3.14 = radius²
14.6 = radius²
radius = √14.6
radius = 3.82 ≅ 3.8
Answer:
approx. 7.3 m
Step-by-step explanation:
The formula for the circumference of a circle is s = r·Ф, where r is the radius and Ф is the central angle in radians.
Here C = 45.84 m = 2π·r. Solving for the radius, r, we get:
45.84 m
r = --------------- = 7.299 m, or approx. 7.3 m.
2(3.14)
Part A
the beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20.
Part B Explain whether the inequality Jack writes is correct or incorrect. In your explanation, include a description of each value in the inequality in terms of what it represents. The beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20. The change in elevation is greatest between the beginning of the trail and which rest stop? Explain your reasoning.
please help ,need help now
Answers
Part A is incorrect because for negative numbers, the greater the magnitude the smaller the number. -2 is smaller than -1, for example, and -20 is smaller than -15.
An elevation of -15ft means 15 ft below sea level, an elevation of -20ft means 20 ft below sea level, and an elevation of (+) 7ft means 7 ft above sea level.
If John started the trail at sea level (0ft elevation), then the greatest change in elevation would be between that and the second rest stop. Take the absolute value of all the numbers and see which one is the largest.
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and across the x-axis to obtain point C. What are the coordinates of points B and C?
A) B(2, 3) and, C(−2, −3)
B) B(−2, −3) and C(2, 3)
C)B(2, −3) and C(−2, 3)
D) B(−2, 3) and C(2, −3)
Answers
Answer:
B) B(2,-3) and C(-2,3)
Step-by-step explanation:
The given point A, has coordinates (-2,-3).
When point A(-2,-3) is reflected over the y-axis to obtain point B, then the coordinates of B is obtained by negating the x-coordinate of A.
Therefore B will have coordinates (2,-3).
When point A(-2,-3) is reflected over the x-axis to obtain point C, then the coordinates of C is obtained by negating the y-coordinate of A.
Hence the coordinates of C are (-2,3)
help quickly please!!!
Answers
Answer:
Problem 12 is 112° and problem 13 is 68°
Step-by-step explanation:
Angles EPF and DPG are vertical angles; therefore, they are congruent. That means, algebraically, that
4x + 48 = 7x
Solving for x:
48 = 3x and x = 16
Now that we know the value of x we can sub it back into the expression for the angle:
4(16) + 48 = 112.
For problem 13, angles DPE and EPF are supplementary, so that means that they add up to equal 180 degrees. Therefore, 180 - 112 = 68 degrees.
a 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the third piece is two feet more than five times the length of the first piece. What is the length of the longest piece?
A. 5 feet
B. 15 feet
C. 27 feet
D. 32 feet
Answers
Answer:
27 ft
Step-by-step explanation:
I hope I helped
Answer:
C
Step-by-step explanation:
We need to write this in an algebraic form.
Let's name x the first piece of pipe. If the second piece is three times as long as the first piece, this would be represented as 3x.The third piece is two feet more than five times the first piece, this would be represented as 5x + 2Lastly, the three pieces sum up 47 foot.Therefore, the equation we would have is: [tex]x+3x+5x+2=47\\9x+2=47\\9x=45\\x=45/9\\x=5[/tex]
Therefore, the first piece is 5 feet long.The second piece is 5(3) = 15 feet long.The third piece is 5(5) + 2 = 27 feet long.Thus, the longest piece is 27 feet long.
The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is
g(x)?
Answers
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Suppose ABCD is a rhombus and that the bisector of ∠ABD meets
AD
at point K. Prove that m∠AKB = 3m∠ABK.
m∠AKB = m∠KBD + m∠
by reason
Find the angle that missing angle so that angle kbd and that angle will equal angle akb.
explain
Answers
Answer:
missing angle: ∠DBCStep-by-step explanation:
Proof:
m∠ABK ≅ m∠KBD — given that BK bisects ∠ABDm∠ABD = m∠ABK + m∠KBD = 2·m∠ABKm∠ABD ≅ m∠DBC — properties of a rhombus: a diagonal bisects the anglesm∠DBC = 2·m∠ABK — transitive property (both equal to m∠ABD)m∠KBC = m∠KBD + m∠DBC — adjacent anglesm∠KBC = m∠ABK + 2·m∠ABK = 3·m∠ABK — substitute for m∠KBD and m∠DBCm∠AKB = m∠KBC — alternate interior angles of parallel lines AD, BCm∠AKB = 3·m∠ABK — substitute for m∠KBC_____
Proof is always in the eye of the beholder, and the details depend on the supporting theorems and postulates you're allowed to invoke. The basic idea is that you have cut a vertex angle in half twice, and you're trying to show that the smallest part to the rest of it has the ratio 1 : 3.
Leif took out a payday loan with an effective interest rate of 26,600%. If he has $180 to invest for a year at this interest rate, how much would he make in interest?
Answers
Answer: $47,880
Step-by-step explanation:
APEX
Answer:
Leif makes $47880 in interest.
Step-by-step explanation:
Given: Interest rate (r) = 26,100%
r = [tex]\frac{26600}{100} = 266[/tex]
Principle (p) = $180
time (t) = 1
Now we have to find the simple interest. The simple interest formula is I=prt
Plugging in the given values, we get
I = 180×266×1
I = $47880
So Leif makes $47880 in interest.
Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a. r= 4 + cose
b. r= 2 + 3 cose
c. r= 3 + 2 cose
d. r= 2 + 2 cose
Answers
Answer:
c. 3 + 2 cosθ
Step-by-step explanation:
a = 3, b = 2
Since a > b, 1 < [tex]\frac{3}{2}[/tex] <2
we get a dimpled limacon.
Answer:
Correct option is C ) [tex]r=3+2\,cos\theta[/tex]
Step-by-step explanation:
Limacons are polar functions of the type:
[tex]r=a\pm\,b\,cos\theta[/tex]
[tex]r=a\pm\,b\,sin\theta[/tex]
Where [tex]|\frac{a}{b}|<1\,or\,1<|\frac{a}{b}|<2\,or\,|\frac{a}{b}|$\geq$2[/tex]
In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,
in part (b) and (c) both satisfies the condition but in part (b) we get loop inside the sketch.
so, [tex]r=3+2\,cos\theta[/tex] satisfies the condition of graph.
hence correct option is c ) [tex]r=3+2\,cos\theta[/tex] .
The math problem is 3x - 7 > 5 = 4 so is x greater than 4?
Answers
Answer:
yes, x > 4
Step-by-step explanation:
Add 7 to your inequality to get ...
3x > 12
Then divide by 3, and you have ...
x > 4
_____
We're not understanding the meaning of your " = 4" in the problem statement. It appears to have no place, either in the problem or in the solution.
A magazine has a total readership of 750,000; 65 percent of readers report seeing a company's advertisement in one issue. The cost of the ad was $97,500. Calculate the cost per customer.
Answers
Answer:
$0.20
Step-by-step explanation:
Cost per customer is cost divided by the number of customers:
cost/customer = $97,500/(0.65·750000) = $0.20
The cost per customer is 20¢.
A regular octagon can be concave.
True or False? Please explain.
Thanks!
Answers
a regular polygon has all equal angles, interior and exterior, as well as all equal sides.
Check the picture below.
the one on the left is a regular octagon, as well as a convex one.
the one on the right is also an octagon, but is concave, the issue is that, though all sides remain equal, the angles do not, and so is not a regular octagon.
Which inequality best represents that ice cream at −5°C is cooler than ice cream at 4°C?
Answers
-5°C < 4°C
An object that is cooler, or colder, than a second object means that the first object has a lower, or lesser, temperature than the second object. So, we write the inequality that states that -5°C is less than 4°C.
Answer:
The answer for this question would be 4°C > −5°C
ruben is making a display that includes dinosaurs in their habitat. the dinosaurs will need to be decreased in size to fit the display.
Answers
What's the question?
Answer:
80%
Step-by-step explanation:
"He will start with the Brachiosaurus which has an estimated height of 15 meters and make the model 3 meters on height. by what percent will Ruben decrease the size of the Brachiosaurus in order to fit it into the display"
The percent decrease is the difference in heights divided by the original height.
(15 - 3) / 15
12/15
0.8
So Ruben will decrease the size by 80%.
Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C.
left parenthesis 4 comma 7 right parenthesis and left parenthesis 3 comma 4 right parenthesis(4,7) and (3,4)
The equation of the line in the form Ax+By=C is
Answers
Answer:
[tex]\boxed{3x - y = 5}}[/tex]
Step-by-step explanation:
The coordinates of the two points are (4, 7) and (3, 4).
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\&= & \dfrac{7 - 4}{4 - 3}\\\\& = & \dfrac{3}{1}\\\\ & = &3\\\end{array}[/tex]
(b) Calculate the y-intercept
[tex]\begin{array}{rcl}y & = & mx + b\\7 & = & 3 \times 4 + b\\7 & = & 12 + b\\b & = & -5\\\end{array}[/tex]
(c) Write the equation for the line
y = 3x - 5
This is the point-slope form of the equation.
(d) Convert to standard form
[tex]\begin{array}{rcl}y & = & 3x - 5\\-3x + y & = & -5\\3x - y & = & -5\\\end{array}\\\text{The standard form of the equation is }\boxed{\mathbf{3x- y = -5}}[/tex]
The equation of the line in the form of Ax + By = C is 3x - y = 7.
Given that,
The equation of the line in the form Ax +By = C,
Which passes through the points (4, 3) and (3,4).
We have to determine,
The equation of the line.
According to the question,
The equation of the line in the form Ax +By = C,
The co-ordinate passes through the points (4, 3) and (3,4).
To determine the equation of the line following all the steps given below.
Step1; The slope of the two points can be written as,[tex]m = \dfrac{y_2-y_1}{x_2-x_2}\\\\m = \dfrac{4-7}{3-4}\\\\m = \dfrac{-3}{-1}\\\\m = 3[/tex]
The slope of the line is 3.
Step2; The y-intercept of the line,[tex]y = mx + c\\\\7= 3 \times 4 + c\\\\7 = 12+ c\\\\c = 7-12\\\\c = -5[/tex]
The y-intercept of the line is -7.
Step3; The equation for the line is,
[tex]y = mx + c \\\\y = 3x-7[/tex]
Step4; The equation can be written as standard form,[tex]y = 3x - 7\\\\3x -y = 7[/tex]
Hence, The equation of the line in the form of Ax + By = C is 3x - y = 7.
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Select the correct answer from each drop-down menu. y = x2 + 2x − 1 y − 3x = 5 The pair of points representing the solution set of this system of equations
Answers
ANSWER
(-2,-1)
(3,14)
EXPLANATION
The given system is
[tex]y = {x}^{2} + 2x - 1[/tex]
[tex] y - 3x = 5[/tex]
or
[tex]y = 3x + 5[/tex]
Equate both of them:
[tex]{x}^{2} + 2x - 1 = 3x + 5[/tex]
This implies that,
[tex]{x}^{2} - x - 6 = 0[/tex]
[tex](x - 3)(x + 2) = 0[/tex]
x=-2 or x=3
When x=-2, y=y=3(-2)+5=-1
(-2,-1) is a solution.
When x=3 , y=3(3)+5=14
(3,14) is also a solution.
what is an equation of the line containing the points (-1,5) and (3,9)
Answers
Answer:
y = x+6
Step-by-step explanation:
You can find an equation by using the 2-point form of the equation for a line:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
Filling in the given values, we have ...
y = (9 -5)/(3 -(-1))·(x -(-1)) +5
y = (4/4)(x +1) +5 . . . . simplifying a bit
y = x +6