Answer: (13, 47)
The expression t = 4 means that 4 units of time have come off the clock (possibly 4 seconds). Plug this value into each equation given for x and y
x = 2*t + 5 = 2*4 + 5 = 8 + 5 = 13
y = 3*t^2 - 1 = 3*4^2 - 1 = 3*16 - 1 = 48 - 1 = 47
In short, if t = 4 then it leads to x = 13 and y = 47 at the same time. These x and y values pair up to get the final answer (13,47)
--------------
Here's an update:
If t = 2, then,
x = 2t+5 = 2*2+5 = 4+5 = 9y = 3t^2-1 = 3*2^2-1 = 3*4-1 = 12-1 = 11In short, if t = 2, then x = 9 and y = 11
The point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].
To find the point on the graph at time [tex]\(t = 4\)[/tex] given the parametric equations [tex]\(x = 2t + 5\)[/tex] and [tex]\(y = 3t^2 - 1\)[/tex], substitute [tex]\(t = 4\)[/tex] into both equations.
1. For [tex]\(x\)[/tex]:
[tex]x = 2t + 5[/tex]
[tex]x = 2(4) + 5[/tex]
[tex]x = 8 + 5[/tex]
[tex]x = 13[/tex]
So, at [tex]\(t = 4\), \(x = 13\)[/tex].
2. For [tex]\(y\)[/tex]:
[tex]y = 3t^2 - 1[/tex]
[tex]y = 3(4)^2 - 1[/tex]
[tex]y = 3(16) - 1[/tex]
[tex]y = 48 - 1[/tex]
[tex]y = 47[/tex]
So, at [tex]\(t = 4\), \(y = 47\)[/tex].
Therefore, the point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].
Please help! Need answer ASAP!
Aliya lined up the interior angles of the triangle along line p below.
When the measure of angle A increases in the triangle, what happens to angle A on line p?
A) It also increases.
B) It decreases.
C) It stays the same.
D) It may increase, or it may stay the same.
The measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given that Aliya lined up the interior angles of the triangle along line p .
We have to find the what happens to angle When the measure of angle A increases in the triangle.
An angle is the figure formed by two rays, called the sides of the angle, sharing
When the measure of angle A increases in the triangles, the measure of angle A on line p also increases.
Hence, the measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.
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Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bikes and meet in between. One day they left their houses at 8 am and met at 11 am. Taylor rode at 12.5 miles per hour. How fast did Anya ride?
Answer:
Anya rode at 8.5 miles per hour.
Step-by-step explanation:
We have been given that Taylor and Anya live 63 miles apart. One day they left their houses at 8 am and met at 11 am riding toward each other. Taylor rode at 12.5 miles per hour.
We can see that Taylor and Anya met after 3 hours as 11-8=3. This means that both rode their cycles for 3 hours.
Let us find distance covered by Taylor.
[tex]\text{Distance}=\text{Speed*Time}[/tex]
[tex]\text{Distance covered by Taylor}=12.5\frac{\text{Miles}}{\text{hour}}*3\text{ hours}}[/tex]
[tex]\text{Distance covered by Taylor}=12.5*3\text{ Miles}[/tex]
[tex]\text{Distance covered by Taylor}=37.5\text{ Miles}[/tex]
Therefore, Taylor covered 37.5 miles in 3 hours.
Let us find distance covered by Anya in 3 hours by subtracting distance covered by Taylor from total distance of 63 miles.
[tex]\text{Distance covered by Anya in 3 hours}=(63-37.5)\text{ Miles}[/tex]
[tex]\text{Distance covered by Anya in 3 hours}=25.5\text{ Miles}[/tex]
Now let us find speed at which Anya rode bike.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Speed at which Anya rode the bike}=\frac{25.5\text{ Miles}}{3\text{ Hour}}[/tex]
[tex]\text{Speed at which Anya rode the bike}=8.5\frac{\text{ Miles}}{\text{ Hour}}[/tex]
Therefore, Anya rode the bike at the speed of 8.5 miles per hour.
Which of the following situations describes a helpful adaptation for a mole?
Question 2 options:
A mole is blind and cannot see underground.
A mole is bright and attracts the attention of predator birds.
A mole has a sensitive sense of smell to help it find food underground.
I believe the answer is C because it is the only answer that proves helpfulness to the survival of a mole
Answer:
Which of the following situations describes a helpful adaptation for a mole?
Question 2 options:
A mole is blind and cannot see underground.
A mole is bright and attracts the attention of predator birds.
A mole has a sensitive sense of smell to help it find food underground.
Step-by-step explanation:
Despite their very poor eyes, moles can hunt worms and insects thanks to their keen sense of smell and capturing vibrations of their prey with their whiskers.
The answer is: A mole has a sensitive sense of smell to help him find food underground.
A farm grew 19.8 tons of wheat in 2013. The frams's wheat output increased by 9.8% from 2013 to 2014 and by 5.1 from 2014 to 2015. Which expression represents a strategy for estimating the total output of wheat in tons, in 2015?
Answer:
Quantity of wheat in 2015 is 19.8(1.098)(1.051) tons
Step-by-step explanation:
We are given
A farm grew 19.8 tons of wheat in 2013
In 2013:
quantity of wheat =19.8 tons
In 2014:
The farms's wheat output increased by 9.8% from 2013 to 2014
So, quantity of wheat becomes
[tex]=19.8(1+0.098)[/tex]
[tex]=19.8(1.098)[/tex]
In 2015:
The farms's wheat output increased by 5.1 from 2014 to 2015
so, it is increased by 5.1 % of 2014 quantity
so, we get
quantity of wheat in 2015 is
[tex]=19.8(1.098)(1+0.051)[/tex]
[tex]=19.8(1.098)(1.051)[/tex]
You can calculate how much 9.8% of 19.8 ton is and then add that to 19.8 and add 5.1 more to know the weight of wheat in tons produced in 2015.
The total output of wheat in tons, in 2015 is 26.84 tons.
How to know the wheat amount produced in 2015?In 2014, there was increase of 9.8% wheat production than last year(2013).
Thus,
Production in 2014 = Production in 2013 + 9.8% of production in 2013
9.8% of production in 2013 = [tex]19.8 \times \dfrac{9.8}{100} = 1.9404[/tex]
Production in 2014 = 19.8 + 1.94 = 21.74
Production in 2015 = Production in 2014 + 5.1 tons= 21.74 + 5.1 = 26.84 tons
Thus, the total output of wheat in tons, in 2015 is 26.84 tons.
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The results of the survey are shown in the table. If a student registered early, find the probability that the student is a undergraduate Registered early Registered On time Undergraduate= 211 347 graduate= 329 581
a. 0.474
b. 0.608
c. 0.391
d. 0.144
Answer: C (0.391)
I'm pretty sure that's right.
Answer:
0.391
Step-by-step explanation:
Gradpoint
What is the domain and range of the function?
Answer:
The correct option is (d)
domain= real numbers and Range= positive real numbers
Step-by-step explanation:
The given function is an exponential function in which the condition on the parameters are as follows-
f(x) = a^x
(1) Base condition is , a>0 and a≠1
(2) Domain = The value of x = x can take any value that is x∈ R
(3) Range = f(x)>0 that is f(x) can take positive values only.
The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22°. If the vertical distance from the bottom to the top of the mountain is 689 feet and the gondola moves at a speed of 130 feet per minute, how long does the ride last?
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
Using SOH CAH TOA in right triangle,
[tex]sin 22=\frac{opposite}{hypotenuse}[/tex]
[tex]sin 22=\frac{689}{x}[/tex]
[tex]x=\frac{689}{sin 22}[/tex]
Plugging the value of sin 22
[tex]x=\frac{689}{0.3746}[/tex]
[tex]x=1839.29[/tex] feet
So the distance is 1839.29 feet.
[tex]time=\frac{distance}{speed}=\frac{1839.29}{130}[/tex]
time=14.15 minutes : Answer
Hope it will help :)
The circle with center O has a radius of 4 centimeters. If x = 30°, what is the length of arc AB?
Answer:
The length of arc AB is 120 centimeters.
Step-by-step explanation:
Given information: O is the center of circle and radius of the circle is 4 centimeters. It is given that [tex]x=30^{\circ}[/tex].
Length of arc is
[tex]l=2\pi r(\frac{\theta}{360})=r\theta[/tex]
Since the radius of circle is 4 and [tex]x=30^{\circ}[/tex], therefore
[tex]AB=4\times 30=120[/tex]
Therefore the length of arc AB is 120 centimeters.
Answer:
2π/3 cm
Step-by-step explanation:
usatestprep
What is the interest earned on $20000 for 5 years, at an interest of 3 3/5% compound continuously
The compound interest for 5 year is $3868.7.
What is compound interest?Interest accrued on both the principal sum of money and the interest already earned.
The formula for compound interest is p(1+r/100)ⁿ - p
Where p is principal amount, r is rate and n is time.
Given that,
Principal = $20000,
Time = 5 years,
And rate of interest = 18/5 %
To find compound interest, use formula,
Compound interest = p(1+r/100)ⁿ - p
Compound interest = 20000(1+18/(5×100))⁵-20000
Compound interest = 23868.7 - 20000
= 3868.7
The compound interest for 5 years is $3868.7.
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Point a is the incenter of triangle def. which must be true? check all that apply. point a is the center of the circle that passes through points d, e, and f. point a is the center of the circle that passes through points x, y, and z. aex aez zea zfa
Answer:
B C E
Step-by-step explanation:
Just did it on edg
The incenter of a triangle is the center of the triangle
The true statements are:
Point A is the center of the circle that passes through points X, Y, and Z. ZA≅YA AX≅AYFrom the diagram (see attachment), we have the following observations.
The lines from points X, Y and Z to point A are perpendicular to lines DX, DY and EF.
This mean that, point A is the center of a circle that passes through points X, Y and Z.
Hence, (b) is true
Also it means that:
[tex]\mathbf{AX \cong AY \cong AZ}[/tex] --- the radius of the circle.
Hence, (c) and (e) are true.
So, the true statements are: (b), (c) and (e)
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Which set of measurements could be the side lengths of a triangle?
a- 2 cm, 8 cm, 12 cm
b- 13 cm, 7 cm, 4 cm
c- 9 cm, 4 cm, 4 cm
d- 7 cm, 10 cm, 8 cm
Answer:
c is the correct answer i believe
Step-by-step explanation:
Because a triangle must have two equal sides
Final answer:
The sets of measurements that could be the side lengths of a triangle are c (9 cm, 4 cm, 4 cm) and d (7 cm, 10 cm, 8 cm), as they both satisfy the Triangle Inequality Theorem.
Explanation:
The question asks which set of measurements could be the side lengths of a triangle. To determine if three lengths can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Let's analyze each option:
a- 2 cm, 8 cm, 12 cm: 2 + 8 is not greater than 12, so this set cannot form a triangle.b- 13 cm, 7 cm, 4 cm: 13 is not less than the sum of 7 + 4, so this set cannot form a triangle.c- 9 cm, 4 cm, 4 cm: 9 is less than the sum of 4 + 4, so this set can form a triangle.d- 7 cm, 10 cm, 8 cm: Each side is less than the sum of the other two, so this set can also form a triangle.Therefore, options c (9 cm, 4 cm, 4 cm) and d (7 cm, 10 cm, 8 cm) could be the side lengths of a triangle.
Patrik rotated the pentagon about its center. What degree measure could he have rotated the pentagon so that is mapped onto itself? A.108 B.180 C.288 D.540
Answer:
Option C is correct.
288 degree measure could he have rotated the pentagon so that is mapped onto itself
Step-by-step explanation:
Given: Patrik rotated the pentagon about its center.
A Rotational symmetry of a regular polygon is based on the number of vertices it has.
If the Pentagon figure is rotated [tex]360^{\circ}[/tex] about its center, each vertex lands exactly on the top of where it started.
Since you have 5 vertices, so your starting vertex can land in 5 different starting places and still come up with the same figure.
So if you take [tex]\frac{360}{5} = 72^{\circ}[/tex] rotations to each consecutive vertex.
⇒a rotation of 72 degree, 144 degree, 216 degree, 288 degree and 360 degree will result in the same figure.
Therefore, 288 degree measure could he have rotated the pentagon so that is mapped onto itself.
Answer: Yes option C
Step-by-step explanation:
according to what shortcut are two triangles congruent if all three of their corresponding sides are congruent
Answer:
SSS congruency
Step-by-step explanation:
Here’s an easy way to remember it. S stands for side so it is side side side congruency.
Please help me!!!!!!!!:(
Answer:
24% chance
Step-by-step explanation:
First, find the total number of graduates in the table, that number is 2610, that will be your numerator.
You will look at the table for the total number of students, that is 10730, that will be the denominator.
Now divide the smaller number/numerator (2610) by the larger number/denominator (10730)
[tex]\frac{2610}{10730}[/tex] = 0.2432432...
Then, multiply by 100 to get the percentage: 24.32432...%
Now, round to the nearest percentage: 24%
Lilly has read seven-eighths of her book and is on page 147. How many pages does lilly have left to read?
Answer:
21
Step-by-step explanation:
Since Lilly has read 7/8 of her book (aka 147 pages), divide 147 by 7 and you get 21.
This means 1/8=21
Since she has read 7/8 of the book, and the full book is 8/8, 8/8-7/8= 1/8
Meaning she has 1/8 of the book left to read.
As said before, 1/8 =21
Thus, she has 21 pages left to read.
which is an equation in Point-Slope form for the given point and slope
Point: ( -3,7); Slope: 4
A. y - 7 = 4 ( x - 3 )
B. y - 7 = 4 ( x + 3 )
C. y + 7 = 4 ( x + 3)
D. y + 7 = 4x - 12
Answer:
The equation of this line is y - 7 = 4(x + 3)
Step-by-step explanation:
To find this, start with the base form of point-slope form.
y - y1 = m(x - x1)
Now put the slope in for m and the two coordinates in for (x1, y1).
y - 7 = 4(x + 3)
Final answer:
The equation in Point-Slope form for the given point ( -3,7) and slope 4 is B. y - 7 = 4 ( x + 3 ). (Option B)
Explanation:
The correct equation in Point-Slope form for the given point and slope, where the point is ( -3,7) and the slope is 4, can be written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Substituting the given values, we obtain y - 7 = 4(x + 3).
Therefore, the correct equation in Point-Slope form is:
B. y - 7 = 4 ( x + 3 )
Please help me out :)
Answer:
[tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Each term in the sequence is half of the previous term, thus multiply the previous term by 1/2 to obtain the next term in the sequence
1 × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]
When making a snack bowl, Drew mixes 76 cereal pieces with 19 marshmallows. How many cereal pieces are in Drew's snack mix for every one marshmallow?
Answer:4
Step-by-step explanation:
76/19=4
State the point of concurrency (Centroid, Incenter, Circumcenter or Orthocenter) that you would use for the given scenario. (4 points)
ABC Widget Company wants to build a central location for it’s new distribution center. They need the center to be equally located between their 3 stores. Which point of concurrency is needed to determine the best location?
______________________________________________
Build it Furniture Company is designing a triangular pedestal table and need to determine the exact center of the table top. Which point of concurrency is needed to determine the exact location of the table top?
______________________________________________
We could come up with a unique scenario for this point of concurrency but unfortunately this point is good for absolutely nothing.
______________________________________________
Charleston is building a statue of Euclid to celebrate his influence in mathematics. The center of the park that they would like to build the statue of Euclid has a triangular walkway that borders the location for the statue. They want the statue to be the same distance from each side of the walkway. Which point of concurrency is needed to determine the best location within the triangular region?
Solution:
Centroid: Point of intersection of Medians of Triangle which is drawn from opposite vertex.
Incenter : Point of intersection of Angle Bisectors drawn from opposite vertex of triangle.
Circumcenter : Point of intersection of Perpendicular bisectors of sides of triangle.
Orthocenter: Point of intersection of perpendiculars drawn from opposite vertex of triangle.
1.ABC Widget Company wants to build a central location for it’s new distribution center. They need the center to be equally located between their 3 stores. Which point of concurrency is needed to determine the best location?
Answer: Circumcenter , as it is equidistant from three vertices A, B and C.
2. Build it Furniture Company is designing a triangular pedestal table and need to determine the exact center of the table top. Which point of concurrency is needed to determine the exact location of the table top?
Answer: Centroid , it is located exactly inside the center of Triangle.
3. We could come up with a unique scenario for this point of concurrency but unfortunately this point is good for absolutely nothing.
Answer : Orthocenter,
4. Charleston is building a statue of Euclid to celebrate his influence in mathematics. The center of the park that they would like to build the statue of Euclid has a triangular walkway that borders the location for the statue. They want the statue to be the same distance from each side of the walkway. Which point of concurrency is needed to determine the best location within the triangular region?
Answer: Incenter, as it is a point which is equidistant from three sides of triangle.
Matt is climbing a mountain. When his elevation is higher than 16001600 meters, breathing is difficult for Matt. Write an inequality that describes hh, the elevation at which breathing is difficult for Matt.
Answer:
[tex]h>1600[/tex]
Step-by-step explanation:
We have been given that Matt is climbing a mountain. When his elevation is higher than 1600 meters, breathing is difficult for Matt.
We are asked to write an inequality that describes h, the elevation at which breathing is difficult for Matt.
We know when elevation (h) will be higher than 1600 meters Matt will face difficulty in breathing. We can represent this situation as:
[tex]h>1600[/tex]
Therefore, inequality representing the elevation at which breathing is difficult for Matt will be [tex]h>1600[/tex].
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Write 4^x = 1024 in logarithmic form.
Answer: B
Step-by-step explanation:
4ˣ = 1024
1024 = 4ˣ
log⁴1024 = x
please help me with this question
Bruce evaluates the expression on a math quiz, 8.8 ÷ 2.7 and gets an answer of 4.14.
Is this a reasonable answer?
A.
Since 8.8 rounds to 8 and 2.7 rounds to 3, so division rounds to 3. His answer of 4.14 rounds to 4. So, it is reasonable.
B.
Since 8.8 rounds to 9 and 2.7 rounds to 3, so division rounds to 3. His answer of 4.14 rounds to 5. So, it is reasonable.
C.
Since 8.8 rounds to 9 and 2.7 rounds to 2, so division rounds to 5. His answer of 4.14 rounds to 4. So, it is not reasonable.
D.
Since 8.8 rounds to 9 and 2.7 rounds to 3, so division rounds to 3. His answer of 4.14 rounds to 4. So, it is not reasonable.
Answer:
the answer is D
Step-by-step explanation:
As per linear equation, since 8.8 rounds to 9 and 2.7 rounds to 3, so division rounds to 3. His answer of 4.14 rounds to 4. So, it is not reasonable.
What is a linear equation?
A linear equation is an equation that contains one or multiple variable with the highest power of the variable is one.
Given expression is:
8.8 ÷ 2.7
≈ 9 ÷ 3
= 3
His answer is 4.14 ≈ 4.
Therefore, this is not a reasonable answer.
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Which ordered pair is a solution to the inequality?
Help please!!
Choice A is the answer which is the point (1,-1)
=========================================
How I got this answer:
Plug each point into the inequality. If you get a true statement after simplifying, then that point is in the solution set and therefore a solution. Otherwise, it's not a solution.
-------------
checking choice A
plug in (x,y) = (1,-1)
[tex]y - 2x \le -3[/tex]
[tex]-1 - 2(1) \le -3[/tex]
[tex]-3 \le -3[/tex]
This is true because -3 is equal to itself. So this is the answer.
-------------
checking choice B
plug in (x,y) = (2,4)
[tex]y - 2x \le -3[/tex]
[tex]4 - 2(2) \le -3[/tex]
[tex]0 \le -3[/tex]
This is false because 0 is not to the left of -3, nor is 0 equal to -3. We can cross this off the list.
-------------
checking choice C
plug in (x,y) = (-2,3)
[tex]y - 2x \le -3[/tex]
[tex]3 - 2(-2) \le -3[/tex]
[tex]7 \le -3[/tex]
This is false because 7 is not to the left of -3, nor is 7 equal to -3. We can cross this off the list.
-------------
checking choice D
plug in (x,y) = (3,4)
[tex]y - 2x \le -3[/tex]
[tex]4 - 2(3) \le -3[/tex]
[tex]-2 \le -3[/tex]
This is false because -2 is not to the left of -3, nor is -2 equal to -3. We can cross this off the list.
What is thr value of f(-1) ?
Answer:
7
Step-by-step explanation:
The remainder from division by (x+1) is the value of f(-1). That remainder is the number at the lower right of the synthetic division tableau, 7.
Answer:
f(-1) is 7
Step-by-step explanation:
When using synthetic division, the value of the function is the final value of the division.
f(-1) is 7
Math help please im so confused
Answer:
Angle 3 is 49 degrees
=============================
Explanation:
Angle 1 is 50 degrees and angle 2 is 48 degrees. Added up, they total to 98 degrees. This is angle DEF.
Angle DEF is congruent to angle ABC because they are alternate exterior angles and because lines m and n are parallel
We are told that angle ABC is bisected (aka cut in half) because of line s; which means that the angles labeled "4" and "5" are exactly half that of angle ABC = 98 degrees
Therefore, angle 4 is 98/2 = 49 degrees and so is angle 3 (due to angles 3 and 4 being vertical angles; angle 3 = angle 4)
Find the two whole numbers that it falls between square root of 5
Answer:
Whole numbers are 1 and 2
Step-by-step explanation:
Given that a number 5 and we use the square root of 5.
We are to find two whole numbers that falls between square root of 5.
We know that whole numbers are 0,1,2.....
We know that square root of 5 is irrational approximately equal to 2.236.
Consider square root of 5.
Since square root of any number always has two solutions the solutions are
-[tex]\sqrt{5}[/tex] and [tex]\sqrt{5}[/tex]
We have to find two whole numbers lying between these values.
We see that 0, 1,2 are the whole numbers lying between these two values.
Let us select any two of them from these two.
Say 1,2
Then answer is 1,2.
How many pounds are there in 3 and 1 over 4 tons? (1 ton = 2000 pounds)
Answer: 3 1/4 tons = 6500 tons
Step-by-step explanation:
3 tons is 6000 since 3 * 2000 = 6000
1/4 would be 25% of 2000 which would be 500
because if you take 500 four times it will be 2000
So here you go bud.
3 1/4 tons in pounds.
if 2000 pounds are 1 ton multiply 2000 to 3 tons.
You get 6000.
Then you move on to 1/4.
2000 divided by 4 is 500.
500 is your 1/4.
So 6500 is your answer.
Hope this helped!
Using the conversions given, convert 2 pounds to grams (round to the nearest whole gram).
2 pounds is equal to 908 grams (rounded to the nearest whole gram).
Started by converting 2 pounds to kilograms using the conversion factor 1 pound = 0.454 kilograms.
So, 2 pounds * 0.454 kilograms/pound = 0.908 kilograms.
Then, I converted 0.908 kilograms to grams using the conversion factor 1 kilogram = 1000 grams.
So, 0.908 kilograms * 1000 grams/kilogram = 908 grams.
Finally, I rounded 908 grams to the nearest whole gram, which is 908 grams.
Therefore, 2 pounds is equal to 908 grams (rounded to the nearest whole gram).
Question
1 pound = 0.454 kg 1 kg = 1000 g Using the conversions given, convert 2 pounds to grams (round to the nearest whole gram).
pleaseeeeeee someone help me
Answer: D
Step-by-step explanation:
The orange color is represented by the bottom line, which is y > x - 2
The purple color is represented by the top line, which is y < x + 1
How do we know the equations of those lines?
The equations can be written in the form y = mx + b where;m = slopeb = y-interceptThe orange line:
crosses the y-axis at -2 --> b = -2 has a rise over run of 1 -> m = 1 --> y = x - 2the line is dashed and is shaded above so y > x - 2The purple line:
crosses the y-axis at +1 --> b = 1 has a rise over run of 1 -> m = 1 --> y = x + 1the line is dashed and is shaded below so y < x + 1