If the given function is f '(t) = 20/1 + t², the value of the function f will be 20 tant+C.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that the function is,f '(t) = 20/1 + t² f(1) = 0
In order to find f integrate the function,
[tex]\rm f = \int \frac{20}{1+t^2}dt \\\\ f =20\cdot \int \frac{1}{1+t^2}dt \\\\ f =20\tan \left(t\right) \\\\ f =20\tan \left(t\right)+C[/tex]
f(1) = 0
0=20 tan(1)+C
0=20(1.55)+C
C= -31
Thus, if the given function is f '(t) = 20/1 + t², the value of the function f will be 20 tant+C.
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In the figure below, points D, B, E, F, and lie in plane X.
Points A and C do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
The blanks are filled as below
(b) G and E are distinct points that are collinear.(c) F, D, B, and G are distinct points that are coplanar.(d) Suppose line AD is drawn on the figure. Then AD and AC are distinct lines that intersect.What are collinear points?Collinear points are those that are situated along a single straight line.
Collinear points are those that are on a line either close to or far from another point, it can be more than two points.
While coplanar points imply lying on the same plane
In the diagram,
E, F, and G are collinear points
D, B, E, F, and G are coplanar points
A, B, and C are another collinear points
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A coffee shop sells various types of hot beverages. For one particular drink, the store owners are trying to determine the price that will result in the best sales. The revenue, cost, and profit functions for this drink, based on price, are represented on the graph. Using the graph, which price should result in the maximum profit for the sales of this drink?
A graph shows the Price per Drink in dollars on the x-axis and the Total in dollars on the y-axis. A parabola R of x vertex at (3.5, 2,800) intercepts the x-axis. Another parabola P of x vertex at (4, 1,600) and C of x intersect both parabolas
A.
$2.85
B.
$3.60
C.
$4.00
D.
$5.80
Answer:
C. $4.00
Step-by-step explanation:
Profit, which is given by [tex]P(x)[/tex], is maximized when the price per drink is $4.00, as shown on the graph.
what percent is 17 out of 40?
Answer:
below
Step-by-step explanation:
17/40 * 100 % = 42.5 %
Answer:
42.5%
Step-by-step explanation:
to get 40 (denominator) to 100, you need to multiply 40 by 2.5times.
so, multiply 17 (numerator) too: 17 times 2.5 = 42.5
42.5 percent is your answer
(pythagorean theorem mc) a tent pole that is 5 feet tall is secured to the ground with a piece of rope that is 13 feet long from the top of the tent pole to the ground. determine the number of feet from the tent pole to the rope along the ground. 12 feet 8 feet 25 feet 30 feet
Using the Pythagorean Theorem, the number of feet from the tent pole to the rope along the ground is 12 feet.
In the given question we have to determine the number of feet from the tent pole to the rope along the ground.
From the question;
A tent pole that is 5 feet tall is secured to the ground with a piece of rope that is 13 feet long from the top of the tent pole to the ground.
So the value of Hypotenuse(H) = 13 feet
Perpendicular(P) = 5 feet
Using the Pythagorean Theorem
H^2=P^2+B^2
Putting the value
(13)^2=(5)^2+(B)^2
169 = 25+B^2
Subtract 25 on both side, we get
B^2=169-25
B^2=144
Taking square root on both side, we get
B=12
Hence, the number of feet from the tent pole to the rope along the ground is 12 feet.
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23. Lisa has 240 stickers. She gave of it to Leela,to Pamela and kept the rest. How many stickers has Lisa now?
Answer: I think you forgot the number to subtract by.
Step-by-step explanation:
Estimate a 5 % tip on a bill of 83.46 by first rounding the bill amount to the nearest ten dollars.
The estimate of a 5 % tip on a bill of 83.46 by first rounding the bill amount to the nearest ten dollars is; 4 dollars.
What is the estimate of a 5% tip in a bill of 83.46 as required?It follows from the task content that the estimate of a 5 % tip on a bill of 83.46 by first rounding the bill amount to the nearest ten dollars is to be determined.
First, the bill amount; 83.46 must be rounded to the nearest ten dollars so that we have;
83.46 which is approximately; 80 dollars when rounded to the nearest ten.
Therefore, 5% of the required bill is; (5/100) × 80
= 4 dollars.
Therefore, the required estimate of the tip is; 4 dollars.
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Find the length of the segment connecting (-4, 3) and (-5,2). Provide
an answer accurate to the nearest tenth.
The length of the segment connecting (-4, 3) and (-5,2) is 1.4.
How to find length of segment?The length of a line segment can be measured by measuring the distance between its two endpoints.
Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:
length of the segment = √(2 - 3)² + (-5 + 4)²
length of the segment = √(-1)² + (-1)²
length of the segment = √1 + 1
length of the segment = √2
length of the segment = 1.41421356237
length of the segment = 1.4
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Four more than twice the sum of a number and three is negative 5
Answer: It is A
Step-by-step explanation:
The average August temperatures (y) and geographic latitudes (x) of 12 cities in the United States were studied. The regression equation for these data is Temperature 90.4 -1.23*(latitude) What is the slope of the line? Interpret the slope The latitude changes by 90.4 for every change of temperature The temperature changes by 1.23 for every change of one latitude A one degree increase of temperature is a 1.23 drop in latitude O To get 90.4 more degrees of temperature you must climb one degree of latitude If you climb 90.4 degrees of latitude you will get an increase of one degree in temperature O An increase of one latitude is a 1.23 drop in temperature Estimate the mean August temperature for a city with latitude of 22. Use 2 decimal places San Francisco has a latitude of 39. What would you predict for the mean August temperature of San Francisco? Use 2 decimal places Given that the mean August temperature in San Francisco is actually 69 calculate the residual (prediction error) for San Francisco It should be observed minus predicted. If you do it wrong your answer have the positive and negative switched Use 2 decimal places The latitude at the equator is 0. Estimate the average August temperature at the equator. Use 1 decimal place
In the given regression equation, the slope of the line is - 1.23.
Regression equation:
in statistics, regression equation means the mathematical expression of the relationship between a dependent variable and one or more independent variables that results from conducting a regression analysis.
Given,
The average August temperatures (y) and geographic latitudes (x) of 12 cities in the United States were studied. The regression equation for these data is Temperature 90.4 -1.23*(latitude)
Here we need to the slope of the line.
While we looking into the given regression equation,
Temperature = 90.4 - 1.23x(latitude)
While we compare this one with the general slope of the line equation,
y = mx + c
where m refers the slope of the line.
Then we get the value of slope as -1.23.
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Which of the following is the graph of the linear inequality, 5x - 2y < 16?
Is C or D my answer?
Answer: Answer C is correct. :)
Step-by-step explanation:
The pink figure is a dilation image of the black figure. The labeled point is the center of dilation. Tell whether the dilation is an enlargement or reduction. Then find the scale factor of the dilation.
Clearly, it is a reduction with scale factor 2
The rightmost line of the black figure has 8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.
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The pink figure is a dilation image of the black figure. The labeled point is the center of dilation. The dilation is a reduction with scale factor 2.
In mathematics, what is dilation?In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.
The rightmost line of the black figure has 8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.
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you are a sales prep and you make 5% commison on all sales. you typicllay have $ 100,000 in sales each month. you have a retirement plant that takes 8% of your pay and you recieve 0 paid vaction or sicl days.
The commission that the sales rep will get monthly is $5000.
How to calculate the commission?From the information, there is a 5% commison on all sales and the person typicllay have $ 100,000 in sales each month.
The commission that will be made each month will be:
= Percentage of commission × Sales
= 5% × $100,000
= 0.05 × $100,000
= $5000
The commission is $5000.
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Complete question
you are a sales prep and you make 5% commison on all sales. you typicllay have $ 100,000 in sales each month. you have a retirement plant that takes 8% of your pay and you recieve 0 paid vaction or sicl days. What is the. commission each month?
Which ordered pair makes the equation equal?
y = x - 2
Select one:
A.
(7, 9)
B.
(5, 3)
C.
(7, 14)
D.
(5, 7)
Answer:
B: (5,3)
Step-by-step explanation:
We just fill in the coordinates
A: (7,9)
9=7-2
9=5
not true
B: (5,3)
3=5-2
3=3
true
C: (7,14)
14=7-2
14=5
not true
D: (5,7)
7=5-2
7=3
not true
so b is the only correct answer
hopes this helps please mark brainliest
The tree in your friend's yard casts a shadow that is 27 feet long. Your friend is 5 feet tall and casts a shadow that is 4. 5 feet long. What is the height of the tree?
By using unitary method, it can be calculated that Height of the tree is 30 feet
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
This is a problem on unitary method
A shadow of 4.5 feet long is casted by my friend 5 feet tall
A shadow of 1 feet is casted by an object of height [tex]\frac{5}{4.5} \ feet[/tex]
A shadow of 27 feet is casted by a tree of height [tex]\frac{5}{4.5}\times 27 \ feet[/tex]
A shadow of 27 feet is casted by a tree of height 30 feet
Height of the tree is 30 feet
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WILL MARK AS BRAINLIEST
Match each solid cone to its surface area. Answers are rounded to the nearest square unit.
options are:
996 square units
829 square units
628 square units
525 square units
444 square units
758 square units
Answer:
1. 628 square units
2. 758 square units
3. 996 square units
4. 525 square units
Step-by-step explanation:
A set of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviation of 101010 centimeters. Ikue is an elementary school student with a height of 90. 490. 490, point, 4 centimeters. What proportion of student heights are lower than ikue's height?.
The 0.0721 proportion of students have less height than Ikue's height. It can be obtained by Z score table and Z score formula.
What is the formula of Z score?
The Z score is given by the following expression:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Here, Z is the Z score, x is the observed value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standered deviation.
We need to watch the negative Z score if we want the proportion of students less than the observed value and we need to watch the positive Z score if we want the proportion of students more than the observed value.
Substitute 90.4 for x, 105 for [tex]\mu[/tex], and 10 for [tex]\sigma[/tex] in the above equation.
[tex]Z=\frac{90.4-105}{10}\\=-1.46[/tex]
Since we need to find the proportion of student heights lower than ikue's height hence, watch the value of negative z score in the z table. Watch the value in frunt of - 1.4 and below 0.06. It is 0.0721.
Hence, 0.0721 proportion of students have less height than Ikue's height.
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Write an inequality that could be used to represent all solutions for x: the quotient of a number and three minus twelve is less than 12
We can write the given statement as inequality as -
-(x/9) < 12
What is linear inequality? What is the law of Reversal and law of Trichotomy? What is the general equation of a Straight line?Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.
y > mx + cy < mx + cy ≥ mx + cy ≤ mx + cReversal property : If (a > b) then (b < a) and if (a < b) then (b > a).
Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).
The general equation of a straight line is y = mx + c
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the following statement -
"the quotient of a number and three minus twelve is less than 12".
We can write the inequality as -
-(x/9) < 12
Therefore, we can write the given statement as inequality as -
-(x/9) < 12
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-5x - Зу = 9
4x 18y = 54
can someone help out by using the substitution method?
By using substitution method, x = 0, and y = -3 are the solutions of the given system of equations.
What is substitution method?
In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this method before the variable's value is substituted in the second equation.
Consider the given system of equations
-5x - 3y = 9 ..(1)
4x - 18y = 54 ..(2)
From equation (1),
-5x = 9 + 3y
[tex]x =- \frac{9+3y}{5}[/tex] ..(3)
Plug the value of x in equation (2),
[tex]4(-\frac{9+3y}{5})- 18y = 54\\-36-12y-90y = 270\\ -36 - 102y=270\\102y = -36-270\\102y=-306\\y = -3[/tex]
Plug y = -3 in equation (3)
[tex]x = -\frac{9+3(-3)}{5} =-\frac{9-9}{5} =0[/tex]
x = 0
Hence, by substitution method x = 0 and y = -3.
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Segment BD bisects angle ABC measure angle ABC equals 7x. The measure angle ABD equals 3x+25. Find the measurement of angle DBC
The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.
What is angle bisector?
An angle bisector is the ray or line segment that divides the angle into two equal parts.
Since the segment BD bisects angle ABC hence,
∠ABC = ∠ABD+∠DBC ..... (1)
Also, since segment BD bisects angle ABC hence,
∠ABD = ∠DBC
Use this fact in equation (1)
∠ABC = ∠ABD+∠ABD
∠ABC =2 ∠ABD
Now, substitute values and use algebriac multiplication.
7x = 2(3x+25)
7x = 6x+50
7x - 6x= 50
x=50
Now, substitute the value of x in the expression of ∠ABD.
∠ABD = 3x+25
∠ABD = 3(50)+25
∠ABD = 100
Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.
Hence, the measurement of angle DBC is 100°.
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when comparing the means of two populations, it is often preferable to use a two-sample t test, rather than a one-way anova f test because the non-pooled t statistic does not require the assumption that the populations have equal .
When comparing the means of two populations, it is often preferable to use a two-sample t test, rather than a one-way ANOVA f test because the non-pooled t statistic does not require the assumption that the populations have equal Variances.
What are the assumption of non-pooled t statistics are following:The observations should be independent and randomly selected.The parent population from which observations are taken is normally distributed.The observations should be continuous.In non-pooled t statistic, the population variances need not to be equal.The assumptions of one-way ANOVA F test are following:The observations should be independent and randomly selected.The population from which observations are taken is normally distributed.The observations are continuous in nature.The variances of population are equal.To know more about Statistics here: https://brainly.com/question/218301
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An artit make a cale drawing of a parallelogram-haped culpture. The cale i 10cm on the drawing for every 8 m on the culpture. If the actual culpture ha a bae of 6 m and height of 4. 2 m, what i the area of the cale drawing? Show your work. Area = bae x height
The area of scale drawing, based on the scale of drawing and specifications of sculpture is 0.315 m².
The scale drawing is -
10 cm for 8 m
As 100 cm = 1 m
So, the ratio for scale is 0.1 m for 8 m
Calculating the area -
Area = 6 × 4.2
Performing multiplication on Right Hand Side
Area = 25.2 m²
As 8 m sculpture is 0.1 m on drawing
So, 25.2 m² sculpture will be (25.2 × 0.1)/8
Performing multiplication and division on Right Hand Side
Area of scale drawing = 0.315 m²
Hence, the area of scale drawing is 0.315 m².
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Gianna can wash 6 cars in 2 hours. At this rate, how many cars can Gianna wash in 5 hours?
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
What is unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
According to the given question:
Gianna can wash 6 cars in 2 hours
Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.
Gianna's rate of washing cars is 3 cars per hour
Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
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solve the inequality $\frac{29}{289z<\frac{16}{161}z$. try to solve the problem without doing a lot of messy computations!
The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.
What is the solution to the given inequality?It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.
Since the given inequality is;
( 29 / 289z ) < ( 16 / 161 ) z
By cross multiplication; we have;
161 × 29 < ( 16z × 289z )
( 161 × 29 ) / ( 16 × 289 ) < z²
1.00973183 < z²
Therefore;
1.00485413 < z. OR. -1.00485413 > z.
Ultimately, z < - 1.00485413 OR z > 1.00485413.
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Melissa is planning to rent out a limo for her friends and herself for prom. Limousine rates charge a 450 flat rate plus an additional 30 cents for every mile traveled. If Melissa aid the limousine driver $200 for prom, how many miles did she travel that night?
The number of miles Melissa travelled that night is approximately 667 miles.
How to find the distance travelled by Melissa?Melissa is planning to rent out a limo for her friends and herself for prom.
Limousine rates charge a 450 flat rate plus an additional 30 cents for every mile travelled.
Melissa aid the limousines driver $200 for prom. The number of miles she travel can be calculated as follows;
using equation,
y = 450 + 0.3x
where
x = number of miles travelledy = total costTherefore,
200 + 450 = 450 + 0.3x
650 = 450 + 0.3x
650 - 450 = 0.3x
200 = 0.3x
x = 200 / 0.3
x = 666.666666667
x = 667 miles
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(3×2)×8 = k×(8×3) what dose the k stand for
Answer:
k=2
Step-by-step explanation:
if you look at the first equation the things being multiplied are 3, 2 and 8 and in the other side it’s 8 and 3 and since only 1 is missing on the other side k is 2 or you can do it like this below
(3x2)x8=k x(8 x3)
6 x 8= k x 24
48= k x 24
/24. /24
2=k
Hopes this helps please mark brainliest
Answer:
[tex]\sf k=2[/tex]Step-by-step explanation:
[tex]\sf \left(3\times \:2\right)\times \:8=k\left(8\times \:3\right)[/tex]
[tex]\sf k\left(8\times \:3\right)=\left(3\times \:2\right)\times \:8[/tex]
Remove parentheses:-
[tex]\sf k\left(8\times \:3\right)=3\times \:2\times \:8[/tex]
Multiply numbers:-
[tex]\sf \:3\times \:2\times \:8=\bf 48[/tex]
[tex]\sf k\left(8\times \:3\right)=48[/tex]
Multiply numbers:-
[tex]\sf 8\times \:3=\bf 24[/tex]
[tex]\sf k\times \:24=\bf 24k[/tex]
[tex]\sf 24k=48[/tex]
Divide both by 24:-
[tex]\sf k=2[/tex]
_____________________
Hope this helps!
Have a great day!
2 websites sell the same type of headphone cost of headphone in website A is 49.95 and the postage is 4.39. The headphones in website B is 47.68 and the postage is 6.95. Including the postage which website is cheaper and by how much
Answer:
Website A is cheaper by 29 cents
Step-by-step explanation:
A
49.95 + 4.39 = 54.34
B
47.68 + 6.95 = 54.63
54.63 - 54.34 = 0.29
Answer:
the difference is 0.29 cents
website A is cheaper
Step-by-step explanation:
(47.68 + 6.95) - (49.95 + 4.39)
54.63 - 54.34 = 0.29
The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
---------------------------------------------
Ingredients Amount
Brown Sugar 1/4 c
Cider Vinegar 1/2 c
Ground Cumin 1 tsp
Ketchup 2/3 c
Pepper 1 tsp
Answer:
1/2
Step-by-step explanation:
9 x 3 x 1/2 = 27 x 1/2 = 27/2 = 13 1/2
13 1/2 - 13 = 1/2
1/2 cups of ketchup are remaining.
Which set of ordered pairs represents a function?
The set of ordered pairs which represents a function as required in the task content is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.
Which set of ordered pairs represents a function?It follows from the task content that the set of ordered pairs which represents a function is to be identified among the answer choices.
It is noteworthy to know that a function is a special kind of relation in which case each input value is assigned only one output value.
Put simply, no one input value has more than one output value assigned to it.
On this note, the answer choice which correctly represents a function among the answer choices is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.
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Janell bought 2 __ 3 4 pounds of peaches and 3 __ 5 8 pounds of oranges. How many pounds of fruit did Janell buy?
Answer: 6 and 3/8
Step-by-step explanation:
2 3/4 + 3 5/8=?
Find LCM of the 2 numbers
LCM is 8
Multiply 2 to 3/4 in 2 3/4
2 6/8 + 3 5/8
Add whole numbers
2 + 3 = 5
Add the fractions itself
6/8 + 5/8 = 11/8
11/8 = 1 3/8
Combine whole numbers and fractions
5 + 1 + 3/8
6 3/8
Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0), and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = x2 − 3 ? A parabola declines through (negative 5, 4), (negative 4 point 5, 2), (negative 4, 1), (negative 3, 0), (negative 2, 1), (negative 1 point 5, 2) and (negative 1, 4) on the x y coordinate plane. W. A parabola declines through (negative 1, 4) and (0, 3) and rises through (1, 4) on the x y coordinate plane. X. A parabola declines through (negative 2 point 5, 4), (negative 2, 1), (negative 1, negative 2), (0, negative 3) and rises through (1, negative 2), (2, 1) and (2 point 5, 3) on the x y coordinate plane. Y. A parabola declines through (1, 4), (1 point 5, 2), (2, 1) and (3, 0) and rises through (4, 1), (4 point 5, 2) and (5, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Reset Next
Answer:
the answer is y
Step-by-step explanation:
got it right on edmentum :)
