Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
What is an integer ?All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.
A straight line of numbers is shown visually as a number line.
This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.
The collection of integers can be shown on a number line much like other sets of numbers..
Hence, Get each number's absolute value first. Next, multiply the absolute values or calculate their product. Lastly, ascertain the final response's sign. According to the rule, the outcome will be negative if the signs of the two integers are different.
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This Stem-and-Leaf Plot represents the heights of the students on Ralph’s basketball team. One student’s height is missing from the plot. If the mean height of all the students on the team is 61 inches, what is the missing height?
A. 55 in.
B. 59 in.
C. 61 in.
D. 65 in.
The missing height is 65.
What is the missing height?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Missing height = (mean x total number of students) - sum of existing heights
Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423
Missing height = (8 x 61) - 423 = 64
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Given y=-x^2 if the function is shifted 5 units up which equation describes the new function
The equation that describes the new function is y' = x^2 + 5
How to determine the new function?The function is given as:
y = x^2
Shifting the function up by 5 units, the rule is
(x, y) = (x, y + 5)
So, we have:
y' = x^2 + 5
Hence, the equation that describes the new function is y' = x^2 + 5
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Answer:27 < AB < 81
Step-by-step explanation:
Answer:
27 < AB < 81
Step-by-step explanation:
in a triangle the sum of any 2 sides must be larger than the third side.
that must be true for every pair of sides you pick.
simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.
so,
AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".
AC + AB = 27 + AB must be longer than CB = 54.
so, AB must be longer than 27.
CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.
so only the other 2 conditions need to be true.
hence the answer.
A student scores 74, 87, 68, 63, 76 on his last five
exams. His teacher will drop the lowest grade to
compute the student's average. What is the
students average in the class?
Answer:
76.25
Step-by-step explanation:
In a movie theater, the number of seats in a row is 8 greater than the total number of rows. How many rows are in the movie theater, if the total number of seats in the theater is 884?
Answer:
26 rows
Step-by-step explanation:
this is like a rectangle length×width situation.
seats per row = s
number of rows = r
s × r = 884
s = r + 8
so, we can use e.g. the second equation in the first :
(r + 8) × r = 884
r² + 8r = 884
r² + 8r - 884 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = r
a = 1
b = 8
c = -884
r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =
= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =
= (-8 ± 60)/2 = -4 ± 30
r1 = -4 + 30 = 26
r2 = -4 - 30 = -34
a negative number did not make any sense for the number of rows, so r = 26 is our answer.
A box of chocolates contains hard-centred and soft-centred chocolates in the ratio 5 : 2. If there are 49 chocolates in the box, how many are hard-centred and how many are soft- centred?
Hard-Centred___________ Soft-Centred__________
There will be total 14 hard centred and 14 soft centred choclates in the box.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2
Hard centred/ Soft centred = 5/2
And total
Hard centred + Soft centred = 49
Now let say hard centred is H and soft centred S
H/S = 5/2 and H + S = 49
Now H = (5/2)S put into second equation
(5/2)S + S = 49
S(7/2) = 49
S = 14 now put into second equation
H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.
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Total area=
Help me please! Thanks so much
The surface area of the oblique prism is equal to 485 square units.
How to find the surface area of an oblique prism
In this question we have an oblique prism with seven faces, consistiting in two regular hexagons and five parallelograms. The surface areas is the sum of these seven faces:
A = 2 · 50 + 5 · 11 · 7
A = 485
The surface area of the oblique prism is equal to 485 square units.
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Task 1—Non-Linear Systems of Equations Create a system of equations that includes: One linear equation And one quadratic equation
One linear equation y=x ......(i)
And quadratic equation y=x^2 .....(ii)
(1)Solving them
y=x=x^2
x-x^2=0
x(x-1)=0
If x=0 then y=0
if x=1 then y=1
(x,y)=(0,0),(1,1)
(2) graphically [refer in attachemet]
What is linear equation ?
A linear equation is one in which the variable's maximum power is always 1. It is also known as a one-degree equation. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.There are only one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, all of the points fall on the same line.To learn more about linear equation visit:
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18. In AABC, 44 is a right angle, and m4B 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The
diagram is not drawn to scale.
054 ft
17√3 ft
17√2 ft
017
Answer:
17√3
Step-by-step explanation:
In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.
17*√3 = 17√3
The members of a cooking club are making cakes, which they will sell at a street fair for $8 apiece. It cost $30 for a booth at the fair, and the ingredients for each cake cost $2. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How many cakes will they have sold?
They need to sell 5 pieces to cover their expenditures (have a profit of zero).
How many cakes will they have sold?
We know that the costs are:
$30 for the booth at the fair.$2 for each piece of cake they sell.And the revenue is:
$8 for each piece of cake.So, the profit (the difference between the revenue and the cost) for selling x pieces is:
p(x) = $8*x - $2*x - $30
p(x) = $6*x - $30
We want to find the value of x such that p(x) = 0, then:
0 = $6*x - $30
x = $30/$6 = 5
They need to sell 5 pieces to cover their expenditures (have a profit of zero).
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find the slope of y=6x+2
Hello,
y = ax + b where a is the slope ! so here the slope is 6
Someone please help me
The top number is 18
Answer:
x = 24
Step-by-step explanation:
Since this is a right angle, we can use the Pythagorean Theorem to find x. In the formula, a^2 + b^2 = c^2, variables a and b represent the lengths of the legs, and variable c represents the length of the hypotenuse.
a^2 + b^2 = c^2
18^2 + x^2 = 30^2
324 + x^2 = 900
x^2 = 576
x = 24
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The predicted value of y when x =7 is -8.5
How to predict the y value?Start by drawing the line of best fit through the points
See attachment for the graph.
From the attached graph, we have the following value
y = -8.5 when x = 7
Hence, the predicted value of y when x =7 is -8.5
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A poll worker analyzing the ages of voters found that mu = 65 and sigma = 5. what is a possible voter age that would give her zx = 1.14? round your answer to the nearest whole number.
If the value of μ is 65, σ is 5 and z is 1.14 then the value of possible voter age would be 70.6 years.
Given that value of μ is 65, σ is 5 and z is 1.14.
We have to calculate the possible voter age that can satisfy the given values of σ,μ and z.
We know that in z test,
z=X-μ/σ
in which μ is population mean,σ is population standard deviation.
We have to just put the values in the above formula to get the value of X which is our possible voter age.
Putting the values we get,
1.14=x-65/5
5.7=X-65
X=65+5.7
X=67.7
Hence the possible voter age is 67.7 which would satisfy the value of μ=65,σ=5 and z=1.14.
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Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
The steps in evaluating each of the following expressions is shown below.
What is an expression?An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.
How to evaluate the given expressions?15 - 35/7 - 2 + 3 - 4
15 - (35/7) - 2 + 3 - 4 (bracket and division)
15 - 5 - 2 + 3 - 4 (regroup)
15 + 3 - 5 - 2 - 4 (subtract and add)
18 - 11 = 7.
Expression 2.10 + 2(9 - 5) - 16/18
10 + (2 × 4) - 8/9 (bracket and division)
10 + 8 - 8/9 (add)
18 - 8/9 (subtract)
162/9 - 8/9 = 17 1/9 or 154/9.
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Complete Question:
Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.
A. 15 - 35/7 - 2 + 3 - 4
B. 10 + 2(9 - 5) - 16/18
Calculate the future value in five years of $8,000 received today if your investments pay future value a. 5 percent compounded annually $ b. 7 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly.
The Future value is:
a) $10,210.25
b) $11,220.41
c) $12,308.99
d) $18,938.90
e) $44,835.28
What is future value?
The future value (FV) of any asset can be understood as an increase in its value at a fixed rate over a period of time. For a given principal sum P, rate of interest r, and time period t, the future value of an asset can be calculated as:
FV=P*(1+r) ^t
We can find future value as shown below:
P=$8,000
t=5 year
a) r=6%=0.06
FV=8000*(1+0.05) ^5
=8000*(1.0) ^5
=$10,210.25
b) r=7%=0.07
FV=8000*(1+0.07) ^5
=8000*(1.07) ^5
=$11,220.41
c) r=9%=0.09
FV=8000*(1+0.09) ^5
=$12,308.99
d) r=9% compounded semiannually
= 0.09
t=2*5=10
FV=8000*(1+0.09) ^10
=8000*(1.09) ^10
=$18,938.90
e) r=9 percent compounded quarterly
=0.09
t=5*4=20
FV=8000*(1+0.09) ^20
=8000*(1.09) ^20
=$44,835.28
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Identify the distance between points (- 3, 0, - 7) and (- 8, - 9, - 11) , and identify the midpoint of the segmen for which these are the endpoints . Round to the nearest tenth, if necessary
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
What is the distance between the two points and what is the midpoint of the line segment?
First, we find the vector between the two points by vector sum:
[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]
[tex]\vec r = (- 5, - 9, - 4)[/tex]
The distance between the two points is found by the following Pythagorean expression:
[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]
d ≈ 11.1
And the midpoint is found by linear algebra:
[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]
[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]
[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
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find the values of A and B
please help giving brainliest
Answer:
A=3Bz/2
B=2A/3z
Step-by-step explanation:
if you need more explanation you can ask me :)
An expression is shown below:
f(x) = 5x^2+ 2x - 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
(2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or
minimum? What are the coordinates of the vertex? Justify your
answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that
you can use the answers obtained in Part A and Part B to draw the
graph. (5 points)
(10 points)
Answer:
a: (-1,0) , (3/5,0)
b:(-0.2,-3.2). It will be a minimum
c: To graph, you would first find the vertex using (-b/2a) and then plug that back into the equation to find the y coordinate of the vertex. Once you have the vertex plotted, you can then find the x-intercepts. This can be found by factoring the equation and finding the zeros. These 3 points you plot are enough to graph the line.
Step-by-step explanation:
For showing work on part a:
Turn 5x^2+2x-3 into
(5x^2+5x) (-3x-3)
5x(x+1) -3(x+1)
Finally:
(5x-3)(x+1)
The zeros from that are -1 and 3/5
40 points and I will choose brainlyist
below is the question.
Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:
p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.
Hence, out of 44,000 adults, the expected number is found as follows:
0.4412 x 44000 = 19,413.
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party planners recommend that, for every eight quests, two orders of appetizers be provided. which function reflects this ratio
The ratio guest to appetizers at the party was 4 guest per appetizer.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.
The ratio guest to appetizers at the party was 4 guest per appetizer.
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Help me out on this, ASAP!!! (Geometry)
Write formal proofs using the HL Theorm.
Answer:
Given PR is perpendicular to QS, and PQ and PS are congruent. Angle PRQ and angle PRS are right angles by the definition of perpendicular segments. Therefore triangle PRQ and triangle PRS are right triangles. Segment PR is congruent to segment PR by the reflexive property of congruence. By the HL Theorem, triangles PRQ and PRS are congruent.
The box-and-whisker plots show the points scored in each Super Bowl by the AFC and NFC. About how many points higher is the upper quartile for the NFC than the AFC?
The upper quartile for NFC is 3 points higher than that of AFC.
What is the difference in the upper quartiles?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.
Upper quartile for AFC : 26
Upper quartile for NFC : 23
Difference = 26 - 23 = 3
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In general, the arithmetic average return is probably too _____ (low/high) for longer periods and the geometric average is probably too _____ (low/high) for shorter periods.
The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.
What is Arithmetic Average Return?
When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.
To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.
Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.
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In a bag are three red marbles and three white marbles. If
two marbles are taken from the bag at the same time,
what is the probability that both marbles will be red?
The probability is 1/5.
How to find the probability?
There are 3 red marbles and 3 white marbles, for a total of 6.
The probability that the first marble is red is:
P(red) = 3/6
The probability that the second marble is also red is:
P(red') = 2/5 (because now there are 2 red marbles and a total of 5).
The joint probability is:
P = (3/6)*(2/5) = 1/5
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PLEASE HELP OUT ASAP!!!!!!
WILL GIVE 15 POINTS!!!!
a) The approximate area below the curve using five rectangles is 1280 square units.
b) The approximate area below the curve using ten rectangles is 1320 square units.
c) The approximate area below the curve using infinite number of rectangles is 1333.333 square units.
How to find the area below the curve by Riemann's sum
In this problem we must estimate the value of the area below the curve by finite number of rectangles using Riemann sums, whose expression is:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n], for i = {0, 1, 2, 3, ..., n - 1} (1)
Where:
n - Number of rectanglesa - Lower limit of the interval.b - Upper limit of the interval.i - Index of the rectangle.The approximate area below the curve using five rectangles is: f(x) = 20 · x - x², a = 0, b = 20, n = 5
A ≈ [(20 - 0) / 5] · ∑ f[0 + i · (20 - 0) / 5]
A ≈ 4 · ∑ f(4 · i)
A ≈ 4 · [f(0) + f(4) + f(8) + f(12) + f(16)]
f(0) = 20 · 0 - 0² = 0
f(4) = 20 · 4 - 4² = 64
f(8) = 20 · 8 - 8² = 96
f(12) = 20 · 12 - 12² = 96
f(16) = 20 · 16 - 16² = 64
A ≈ 4 · (0 + 64 + 96 + 96 + 64)
A ≈ 1280
And using ten rectangles:
A ≈ [(20 - 0) / 10] · ∑ f[0 + i · (20 - 0) / 10]
A ≈ 2 · ∑ f(2 · i)
A ≈ 2 · [f(0) + f(2) + f(4) + f(6) + f(8) + f(10) + f(12) + f(14) + f(16) + f(18)]
f(0) = 20 · 0 - 0² = 0
f(2) = 20 · 2 - 2² = 36
f(4) = 20 · 4 - 4² = 64
f(6) = 20 · 6 - 6² = 84
f(8) = 20 · 8 - 8² = 96
f(10) = 20 · 10 - 10² = 100
f(12) = 20 · 12 - 12² = 96
f(14) = 20 · 14 - 14² = 84
f(16) = 20 · 16 - 16² = 64
f(18) = 20 · 18 - 18² = 36
A ≈ 2 · (0 + 36 + 64 + 84 + 96 + 100 + 96 + 84 + 64 + 36)
A ≈ 1320
And using infinite rectangles:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n]
A ≈ (20 / n) · ∑ [20 · (20 / n) · i - (20 / n)² · i²]
A ≈ (20 / n) · ∑ [400 · i / n - 400 · i² / n²]
A ≈ ∑ (8000 · i / n² - 8000 · i² / n³)
A ≈ (8000 / n²) · ∑ i - (8000 / n³) · ∑ i²
A ≈ (8000 / n²) · [n · (n + 1) / 2] - (8000 / n³) · [n · (n + 1) · (2 · n + 1) / 6]
A ≈ (8000 / n²) · [(n² + n) / 2] - (8000 / n³) · [(n² + n) · (2 · n + 1) / 6]
A ≈ 4000 · (n² + 2) / n² - (8000 / n³) · [(2 · n³ + 3 · n² + n) / 6]
A ≈ 4000 · (1 + 2 / n²) - (4000 / 3) · [2 + 3 · (1 / n) + (1 / n²)]
As n → + ∞, then:
A ≈ 4000 - 8000 / 3
A ≈ 1333.333
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I needed help solving this
Answer:
Answer C: m = 26, f = 22
there is a typo in answer D.
Step-by-step explanation:
There are 48 vehicles, so m + f = 48.
They have 140 wheels, so 2m+4f = 140.
You can rewrite the first as m = 48-f and then plug it into the second:
2(48-f) + 4f = 140 =>
96 - 2f + 4f = 140 =>
2f = 140 - 96 =>
2f = 44
f = 22
m = 48 - 22 = 26
Answer:
D
Step-by-step explanation:
Let m = motorcycles and c = cars
m + c = 48 2m + 4c = 140
m + c = 48 Multiple this equation through by -2
-2m -2c = -96 Add this to the second equation above
2m +4c = 140
2c = 44 Divide both sides by 2
c = 22. There are 22 cars. Plug this back into the top equation to find the number of motorcycles.
m + c = 48
m + 22 = 48 Subtract 22 from both sides
m = 26
If the length of one leg in this triangle is .find the length of the hypotenuse.
By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].
How to find the length of the hypotenuse
In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:
[tex]r = \sqrt{l^{2}+l^{2}}[/tex]
[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.
By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].
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Find the length of side a.
sorry for the bad quality, camera is broken. the one on top is 13 and the one below is 12.
SOLUTION :
a² = hypo² - base²
a² = 13² - 12²
a² = 169 - 144 = 25
a = √25
a = 5 units.
________________________________
HOPE IT HELPS
Solve the following system of equations and show all work.
y = -x² + 4
y = 2x + 1
Answer:
Step-by-step explanation:
The ys have to have the same value. That allows you to equate the right side of each y to each other.
-x^2 + 4 = 2x + 1 Subtract the right side from the left side.
-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1 Combine
-x^2 - 2x + 3 = 0 Multiply both sides by - 1
-1(-x^2 - 2x + 3) = 0*-1 Remove the brackets
x^2 + 2x - 3 Factor
(x - 1)(x + 3 )
x - 1 = 0
x = 1
x + 3 = 0
x = - 3
So the line goes through x = 1 or x = - 3
x = 1
y = 2x + 1
y = 2(1) + 1
y = 3
x = - 3
y = 2(-3) + 1
y = - 6 + 1
y = - 5
Does the graph confirm this? See below.
red: y = -x^2 + 4
green: y = 2x + 1
Yes the graph is in agreement.