(a) We want to find a scalar function [tex]f(x,y,z)[/tex] such that [tex]\mathbf F = \nabla f[/tex]. This means
[tex]\dfrac{\partial f}{\partial x} = 2xy + 24[/tex]
[tex]\dfrac{\partial f}{\partial y} = x^2 + 16[/tex]
Looking at the first equation, integrating both sides with respect to [tex]x[/tex] gives
[tex]f(x,y) = x^2y + 24x + g(y)[/tex]
Differentiating both sides of this with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C[/tex]
Then the potential function is
[tex]f(x,y) = \boxed{x^2y + 24x + 16y + C}[/tex]
(b) By the FTCoLI, we have
[tex]\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}[/tex]
[tex]\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}[/tex]
[tex]\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}[/tex]
emily is standing 150 feet from a circular target with radius 3 inches. will she hit the target if her aim is off by 0.2 degrees?
Answer:
no
Step-by-step explanation:
The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.
Applicationtan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600
The angle is found using the inverse relation:
α = arctan(1/600) ≈ 0.095°
If Emily's aim is off by 0.2°, she will miss the target by several inches.
__
Additional comment
Emily's projectile will miss her aiming point by ...
(150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in
what is 7/8 - 1/2 as a fraction
Answer: 3/8
Step-by-step explanation:
1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8
One company estimates same-day delivery as more than three less than half the total number of miles. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? Note that the graphs have miles for the independent variable on the x-axis, and the y-axis is a unit of time dependent on the number of miles.
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its delivery and total number of miles to be covered, we would assign variables as follows:
Let y represent same-day delivery.Let x be the total number of miles.Next, we would translate the word problem into an algebraic equation by using an inequality:
y > x/2 - 3
Also, we would determine the intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
y-intercept = (0, -3).
For the x-intercept, we have:
When y = 0, we have;
0 = x/2 - 3
x/2 = 3
x = 6.
x-intercept = (6, 0).
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
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Answer:
c
Step-by-step explanation:
c is the answer
So,some please help me with this question !
=============================================================
Explanation:
Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.
Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.
So,
(angleEBA) + (angleEBD) + (angleDBC) = 180
( x ) + (4x+12) + (x) = 180
(x+4x+x) + 12 = 180
6x+12 = 180
6x = 180-12
6x = 168
x = 168/6
x = 28
Angles EBA and DBC are 28 degrees each.
This means angle D = 3x+5 = 3*28+5 = 89
-----------
Then we have one last set of steps to finish things off.
Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.
D+B+C = 180
89 + 28 + C = 180
117+C = 180
C = 180 - 117
C = 63 degrees
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
From the diagram below, if the tree is 34 ft. tall, and the angle of elevation from point B to the top of the tree is 26 °, find the distance that the tree is from point B. (Round to the nearest whole foot.)
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
What is the distance between the tree and point B?
Given the data in the question;
Height of tree opposite angle of elevation = 34ftAngle of elevation θ = 26°Distance between tree and point B| Adjacent = ?Since the scenario form a right angle triangle, we use trig ratio.
tanθ = Opposite / Adjacent
tan( 26° ) = 34ft / x
We solve for x
x = 34ft / tan( 26° )
x = 34ft / 0.4877
x = 70ft
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
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is there anybody to solve this need step by step solution details
The circumference of the circles from biggest to smallest are; 30π, 15π and 7.5π
How to find the area of a circle?The formula for area of a circle is;
A = πr²
In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
The area of a circle formula is useful for measuring the region occupied by a circular field or a plot. Suppose, if you have a circular table, then the area formula will help us to know how much cloth is needed to cover it completely.
The area formula will also help us to know the boundary length i.e., the circumference of the circle. Does a circle have volume? No, a circle doesn't have a volume
Area of entire circle is 706 cm².
Thus;
πr² = 706
r² = 706/π
r = √(706/π)
r ≈ 15
Circumference of biggest circle = 2πr
Circumference of biggest circle = 2π * 15
Circumference of biggest circle = 30π
Circumference of second biggest circle = 2π * (15/2)
Circumference of second biggest circle = 15π
Circumference of smallest circle = 2π * (15/4)
Circumference of smallest circle = 7.5π
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6. Find the values of x and y. 30° 17
Answer:
X = 17√3
Y = 34
Step-by-step explanation:
TO calculate the values of X and y we use SOHCAHTOA.
Calculating for Xtan 30 = opposite/adjacent
tan30 = 17/X
Cross multiply
tan30 ×X = 17
Divide bothsides by tan30
Note: tan30= 1/√3X = 17/1/√3
X=17√3
X= 29.4X = 29 ( approximately)
Calculating for y[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]
Cross multiply[tex]sin30 \times y = 17[/tex]
Divide bothsides by sin30[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation
Assuming you mean
[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]
where
[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]
we have by the binomial theorem
[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]
so that the given sum has a value of [tex]\boxed{2^n}[/tex].
A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate but on a loan for 15 years.
(a)
Calculate the monthly payment for each loan. (Round your answers to the nearest cent.)
30-year $
15-year $
(b)
Calculate the savings in interest by using the 15-year loan. (Round your answer to the nearest cent.)
$
(c)
The term of the 15-year loan is one-half the term of the 30-year loan. Is the monthly payment for the 15-year loan twice that of the 30-year loan?
Yes
No
(d)
Is the interest savings for the 15-year loan more or less than one-half of the interest paid on the 30-year loan?
more
less
a) The monthly payment for each loan is as follows:
30-year $1,954.93
15-year $3,053.25
b) The savings in interest by using the 15-year loan is $154,189,20 ($286,774.20 - $132,585).
c) No. the monthly payment for the 15-year loan is not twice that of the 30-year loan as the loan term.
d) The interest savings for the 15-year loan are more than one-half of the interest paid on the 30-year loan.
How are the calculations for periodic payments done?The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:
30-year Loan:N (# of periods) = 360 months (12 x 30 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $1,954.93
Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)
Total Interest = $286,774.20 ($703,774.80 - $417,000)
15-year Loan:N (# of periods) = 180 months (12 x 15 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $3,053.25
Sum of all periodic payments = $549,585 ($3,053.25 x 180)
Total Interest = $132,585 ($549,585 - $417,000)
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a box with a square base has length plus girth of 108 in. What is the length of the box if its volume is 2200 in^3?
The missing length of the box with square base is 20.370 inches.
What is the missing length of the box?
This box can be represented by a right prism, whose volume (V), in cubic inches, is the product of the area of the base (A), in square inches, and the height of the box (h), in inches. The area of the base is equal to the square of the side length (l):
V = l² · h (1)
If we know that V = 2 200 in³ and l = 108 in, then the height of the box is:
h = V / l²
h = (2 200 in³) / (108 in)
h = 20.370 in
The missing length of the box with square base is 20.370 inches.
Remark
The statement presents typing mistakes, correct form is shown below:
A box with a square base has a side length of 108 in. What is the length of the box if its volume is 2 200 in³?
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As part of a summer internship, five people -- Cindy, Damaris, Eugenio, Fareed, and Guzal -- are to be assigned to floors 1-5 in a dormitory. Each person will occupy his or her own entire floor and no other people will be in the dormitory. The assignment of people to floors must follow the following rules: Eugenio lives immediately above Damaris. Cindy is not on the first floor. Fareed does not live immediately below Damaris. Guzal lives either on the first floor or the fifth floor. Which one of the five people could be assigned to live on any of the five floors in the dormitory?
Based on the information, it is expected Fareed can be assigned to live on any of the floors.
What condition limits Fareed's assignment?The only condition that limits the floor Fareed can be assigned to is that he cannot be immediately below Damaris. This means that as long as Damaris is not immediately above him, he can be assigned to all floors. Here are two possible arrangements:
Eugenio (5th floor)DamarisCindyFareedGuzal (1st floor)Guzal (5th floor)EugenioDamarisCindyFareed (1st floor)Learn more about arragements in: https://brainly.com/question/27909921
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A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
please help :,)
(geometry involving arc lengths)
Answer:
bx/a (3rd choice)
Step-by-step explanation:
The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is
s = rΘ
Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.
x = aΘ
Solve for Θ:
Θ = x/a Eq. 1
Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.
s = bΘ
Solve for Θ:
Θ = s/b Eq. 2
Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.
x/a = s/b
Multiply both sides by ab.
abx/a = abs/b
bx = as
as = bx
s = bx/a
Answer: bx/a
\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}
Answer:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
=
[tex]\frac{ \sqrt{2} }{a + b} [/tex]
Step-by-step explanation:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
[tex](a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )[/tex]
[tex] \frac{(a - b)( {2}^{ \frac{1}{2} }) }{(a - b)(a + b)} = \frac{ \sqrt{2} }{a + b} [/tex]
Choose the equation that
matches the graph.
a. (1/2)x-4
b. y = 4x-1
C.
y = (1/1)
(¹²) ² − 4
-
d.
e.
x-4
y = (1/1)
y = 4x + 1
y = 4x+1
Answer: d
Step-by-step explanation:
The graph is increasing, so the base must be more than 1.
Eliminate a and c.Also, the y-intercept is 2.
Eliminate b and e.This leaves d.
please help with the first one
Answer:
y = x +5
Step-by-step explanation:
The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.
ApplicationThe given line is y = x +1. The equation you're looking for is
y = x +c . . . . . . for some new constant c
We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.
3 = -2 +c
5 = c . . . . . . add 2
The desired equation is y = x +5.
A worker uses a small table in a notebook to track the cost of materials. On the current job he has used seven sheets of plywood at $43.75 each, two boxes of screws at $4.69 each and a tube of adhesive which cost $9.89, as shown below.
The total cost of the materials calculated by the worker on the notebook is $325.52
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The total cost of materials = 7(43.75) + 2(4.69) + 9.89 = $325.52
The total cost of the materials calculated by the worker on the notebook is $325.52
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Can I just get the answer for this I feel like it’s wrong.
The initial membership fee for Club A is; $2.5.
The initial membership fee for Club B is; $3.
Hence, Club A has a lower initial membership fee.
What is the initial membership fee for each Club?It follows from the concepts of linear graphs that the interpretation of the initial membership fee is the y-intercept of the graphs given.
This is so because, it corresponds to the total cost at a point when the number of movies watched is; 0. That is, before any movie is watched.
Consequently, the graph calibrations (including the missing Club A graph) allow the determination of the initial membership fee (y-intercept) as declared above.
Ultimately, Club A has a lower initial membership fee.
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Pls answer these questions ASAP
From the given descriptions and dimensions, we have;
6. 2000 cm²
7. 81 m²
8. a. 138 m²
b. 538 m²
c. 62 cm²
9. $107.25
Which method can be used to calculate the surface areas and cost?6. Type of box = Open box with no lid
Side length of the box = 20 cm
Therefore;
Number of faces of the box, painted = 5
Area of a face of the box = 20² = 400
Area of the surface painted, A = 5 × 400 cm² = 2000 cm²7. Area of the plastic to cover one book, A, is found as follows;
A = 2 × 20 × 15 + 2 × 3 × 15 + 2 × 20 × 3
Which gives;
A = 600 + 90 + 120 = 810The area of plastic needed to cover 1000 books is therefore;
Total area = 1,000 × 810 cm² = 810,000 cm²
Conversion of cm² to m² gives;
1 m² = 10,000 cm²Therefore;
A = 810,000 cm² = 810,000 cm² × 1/10,000 m²/cm² = 81 m²
The area of plastic needed to cover 1000 books is A = 81 m²8. The surface areas are;
a. A = 2 × 3 × 6 + 5 × 6 + 7 × 6 + 2×3×(3+7)/2 = 138
The surface area is 138 m²b. A = 2 × 15 × 5 + 2×(10×5 + (6×8)/2) + 2×8×15 = 538
A = 150 + 148 + 240 = 538
The surface area is 538 m²c. From the congruent marks, we have;
A = 5 × 3 × 3 + 5×1×3 + 2×1×1 = 62
The surface area is 62 cm²9. From the congruent markings, we have;
A = 2 × (1.5 × 1.5 + (1.5 × 1.3)/2) + 5×2×1.5
A = 6.45 + 15 = 21.45
Surface area of a the canvas, A = 21.45 m²
Cost per unit area of the canvas, c = $5
Cost of the canvas for the tent, C, is therefore;
C = $5/m² × 21.45 m² = $107.25Learn more about the finding the surface area of solids here:
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PLEASE HELP ALOT OF POINTS
Answer: B
Step-by-step explanation:
7x+28=7(x+4) how many solutions
The equation 7x + 28 = 7(x + 4) has infinite many solutions
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the number of solutions?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
7x + 28 = 7(x + 4)
Open the bracket
7x + 28 = 7x + 28
Subtract 7x from both sides of the equation
28 = 28
Subtract 28 from both sides of the equation
0 = 0
The above equation is true, because both sides of the equation are the same
This means that the equation has infinite many solutions
Hence, the equation 7x + 28 = 7(x + 4) has infinite many solutions
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In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2
What was the population density of Rio de Janeiro in people per square meter
2/120=X/80=Y/300
x=? & y=?
X=1.33
Y=4.9875;approx. 5.0
Answer:
(2/120=X/80)=Y/300
2×80=120×X
X=160/120
X=1.33
X/80=Y/300
But X=1.33
By substituting
X=1.33, We have that
1.33/80=Y/300
80×Y=1.33×300
80Y=399
Y=399/80
Y=399/80
Y=5.0 approx.
The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that will model the population of the colony after, t, days have passed.
Answer:
DO not working in you
Step-by-step explanation:
PLEASE help me in answering
Answer:
Step-by-step explanation:
The population at various days is as follows since population triples every 3 days
Day Population
0 10
3 30
6 90
9 270
.... ......
This can be modeled by the general equation
[tex]n_{t} = n_{0}(r)^{t/k}[/tex]
where
[tex]n_{t}[/tex] is the population after t days
[tex]n_{0}[/tex] is the population at start (10)
[tex]r[/tex] is the rate at which population changes ie 3
[tex]t[/tex] is the number days from start
[tex]k[/tex] is the number of days at which the population triples(here k =3 days)
We can check this by plugging in values for each of the variables
At day 0, population = 10(3)⁰ = 10. 1 = 10
Similarly populations for days 3, 6, 9 are:
[tex]\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270[/tex]
if x varies directly as y, and
X = 24 when y= 21, Find x when
Y=6
Answer:
x = 48/7
Step-by-step explanation:
There's two good ways to do this problem.
Option 1:
Translate "x varies directly as y" into the equation y=kx
Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.
Option 2:
Translate "varies directly" into a proportion, which is two fractions equal to each other:
x/y = x/y
Fill in the three numbers given and cross multiply and solve to find the fourth number. See image.
will give brainliest
Find X:
J:58
K:70
L:111
M:121
Answer:
L
Step-by-step explanation:
interior angle formula so
(number of sides - 2)*180
2*180 = 360
you can also just take an example from a square 4*90 = 360
360-121-58-70 = 111
PLEASE HELP ME OUT WITH THIS QUESTION!
Answer: Choice 3
Step-by-step explanation:
Oof, this is a tough one. But anyways
Angle 19 + Angle 20 = 180
So Angle 20 = 180 - Angle 19
As l and m are parallel, Angle 20 = Angle 6 from the z rule
So Angle 6 = 180 - Angle 19
Substitute the information given at the start into the equation
2x - 4 = 180 - (5x - 8)
180 - 5x + 8 = 2x - 4
7x = 192
x = 27.42
From what we have found earlier, Angle 20 = Angle 6 so
Angle 20 = 2x - 4 = 2 * 27.42 - 4 = 50.85 rounding it to 50.9
So the answer is 50.9 or Choice 3
Melissa is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Melissa has been adding money. Suppose that x and y are related by the equation y = 550+20x.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
Check the picture below.
The graph shows a system of inequalities.
Graph of two inequalities. One is a dashed line increasing from left to right passing through negative 5 comma 0 and 0 comma 5, and it has shading above the line. The second is a dashed upward opening parabola with a vertex at negative 2 comma negative 9 and x-intercepts at negative 5 comma 0 and 1 comma 0. This parabola is shaded on the inside.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities having the given feasible regions and points at (-5, 0), and (0, 5), and (-2, -9), (-5, 0), and (1, 0) is the option;
y > x² + 4•x - 5
y > x + 5
How can the required system of inequalities be found?The coordinates of the given points on the linear inequality are;
(-5, 0), and (0, 5)
Slope, m, of the linear inequality is therefore;
m = (5 - 0)/(0 - (-5)) = 1
The equation of the inequality is therefore;
y - 0 > 1•(x - (-5)) = x + 5
Which gives;
y > x + 5Quadratic Inequality;
The coordinates of the points on the quadratic inequality are;
Vertex point = (-2, -9)
x-intercept = (-5, 0), and (1, 0)
Therefore, we have;
y > (x + 5)•(x - 1) = x² + 4•x - 5
y > x² + 4•x - 5The correct option is therefore;
y > x² + 4•x - 5
y > x + 5
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Answer:
y > x2 + 4x – 5
y > x + 5
Step-by-step explanation:
If you put this system into desmos you will see that it matches the photo shown in the question, and it would need to be both greater than symbols because the dotted lines indicate that it is not included in the solution.