To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.
Now we can set up an equation:
7.5x + 0.3x + 6(0.3x) + 3 = x
Simplifying and solving for x, we get:
8.1x + 3 = x
7.1x = 3
x ≈ 0.42
However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.
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To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.
Now we can set up an equation:
7.5x + 0.3x + 6(0.3x) + 3 = x
Simplifying and solving for x, we get:
8.1x + 3 = x
7.1x = 3
x ≈ 0.42
However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.
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16 oranges and 13 lemons cost $9.29 while 19 oranges and 6 lemons cost $9.05. a pair of equations appropriate for determining the price of each is:
Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.
To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29
This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05
This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.
By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.
One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:
304x + 247y = 176.51
-304x - 96y = -144.8
Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41
So the cost of one orange is $0.41 and the cost of one lemon is $0.21.
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When we subtract a velocity vector from another velocity vector, the result is:
A. an acceleration.
B. another velocity.
C. a scalar.
D. a displacement.
When we subtract a velocity vector from another velocity vector, the result is B. another velocity.
When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.
It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.
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PLS!! HELP!! THIS IS ALSO DUE TOMORROW!!
Question 12 (1 point)
(15.03 LC)
Jimmy wants to draw a 50° angle. Fill in the missing step to make sure his drawing is completed in the correct order: (1 point)
Step 1: He draws a ray.
Step 2: He lines up his protractor with the baseline on the ray and the origin of the protractor on the vertex.
Step 3: He finds 50° on the protractor and draws a mark on the paper.
Step 4: ________
Step 5: He draws arrows on both ends to make them rays.
a
He uses the bottom of the protractor to draw a straight line connecting the arrow with the mark he made.
b
He uses the bottom of the protractor to draw a straight line connecting the mark he made with the arrow on the ray.
c
He uses the bottom of the protractor to draw a straight line connecting the vertex and the arrow on the ray.
d
He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
Option d) He uses the bottom of the Protractor to draw a Straight line connecting the mark he made with the vertex.
The correct step to complete the drawing of a 50° angle is:
Step 4: He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
In this step, Jimmy will connect the mark he made at 50° on the protractor with the vertex of the angle using a straight line. This line will complete the angle and ensure that it measures 50°. By connecting the mark with the vertex, Jimmy will have successfully drawn a 50° angle.
After completing Step 4, he can proceed to Step 5, which involves drawing arrows on both ends of the line to indicate that they are rays.
Therefore, the correct answer is option d) He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
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Lindiwe is a grade 10 leaner she walks for 3 kilometres from home to school during weekdays
3.1 convert Lindiwes walking distance to metres
(2)It takes Lindiwe’s teacher five minutes to walk to her classroom how long does it take her to walk in seconds
3.3 Lindiwe’s break starts at 10:30 and ends at 11:20 how long is the break ?
it takes Lindiwe's teacher 300 seconds to walk to her classroom and the break is 50 minutes long.
To convert 3 km to meters we multiply by 1000 (since there are 1000 meters in 1 km).
3 km = 3,000 meters
Therefore, Lindiwe walks 3,000 meters from home to school during weekdays.
3.2 To convert 5 minutes to seconds, we multiply by 60 (since there are 60 seconds in 1 minute).
5 minutes = 5 x 60 = 300 seconds
Therefore, it takes Lindiwe's teacher 300 seconds to walk to her classroom.
To find the length of Lindiwe's break, we subtract the start time from the end time:
11:20 - 10:30 = 0:50
The break is 50 minutes long.
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Two gears are connected and rotating at the same time. The smaller gear completes 1 3/4 rotations every time the larger gear completes 1/4 of a rotation. How many rotations does the smaller gear complete when the larger gear completes 1 rotation? Drag and drop the correct value into the box.
A. 1/7
B. 7/8
C.5 1/2
D.7
Answer: Which Option do You Drag and Drop into the Box?
Step-by-step explanation:
Let's call the number of rotations of the larger gear "L" and the number of rotations of the smaller gear "S". We know that when the larger gear completes 1 rotation, the smaller gear completes 1 3/4 rotations.
We can set up a proportion to solve for S:
S/1 3/4 = L/1/4
Simplifying the right side of the equation, we get:
S/1 3/4 = 4L
Multiplying both sides by 7/4 to get rid of the fraction on the left side, we get:
S = 28/4 L
Simplifying, we get:
S = 7L
This means that the smaller gear completes 7 rotations every time the larger gear completes 1 rotation.
Therefore, the correct value to drag and drop into the box is 7.
{Hope This Helps! :)}
Which expression is equal to x−7x2+8−x2−x+6x2+8 ?
Responses
x2+2x−132x2+16
−x2+2x−13x2+8
x2+2x−13x2+8
−x2+2x−132x2+16
Answer:
x2+2x−132x2+16
Step-by-step explanation:
First, let's simplify the expression by combining like terms:
x - 7x^2 + 8 - x^2 - x + 6x^2 + 8
= -7x^2 + 5x^2 - x^2 + x + 16
= -x^2 + 2x + 16
Now we need to factor the quadratic expression -x^2 + 2x + 16. We can use the quadratic formula or complete the square to find the roots, but it turns out that the expression doesn't factor nicely. However, we can rewrite it as -(x^2 - 2x - 16) and then use the quadratic formula to find the roots of the expression inside the parentheses:
x = (-(-2) ± sqrt((-2)^2 - 4(-16)))/(2(1))
x = (2 ± sqrt(68))/2
x = 1 ± 2sqrt(17)/2
x = 1 ± sqrt(17)
So we have:
-x^2 + 2x + 16 = -(x - (1 + sqrt(17)))(x - (1 - sqrt(17)))
Therefore, the expression is equal to -x^2 + 2x + 16, which corresponds to the option:
x^2 + 2x - 13 / 2x^2 + 16
consider a binomial experiment with 2 trials and p 0.4. a. compute the probability of 1 success, f(1). b. compute f(0). c. compute f(2). d. find the probability of at least one success. e. find the expected value, variance, and standard deviation
The expected value is 0.8, variance is 0.48, and standard deviation is 0.693 with the given probability.
a. The probability of getting one success in two trials with p=0.4 is given by the binomial probability formula:
f(1) = 2C1 * (0.4)^1 * (0.6)^1 = 0.48
b. The probability of getting zero successes is:
f(0) = 2C0 * (0.4)^0 * (0.6)^2 = 0.36
c. The probability of getting two successes is:
f(2) = 2C2 * (0.4)^2 * (0.6)^0 = 0.16
d. The probability of at least one success is:
P(at least one success) = 1 - P(no success)
= 1 - f(0)
= 1 - 0.36
= 0.64
e. The expected value of a binomial distribution with n trials and probability of success p is given by:
E(X) = np
In this case, n = 2 and p = 0.4, so:
E(X) = 2 * 0.4 = 0.8
The variance of a binomial distribution is given by:
Var(X) = np(1-p)
So:
Var(X) = 2 * 0.4 * 0.6 = 0.48
The standard deviation is the square root of the variance:
SD(X) = sqrt(Var(X)) = sqrt(0.48) = 0.693.
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helpp A car manufacturer claims that the average top speed of its newest cars is 145 mph. A sample of 87 cars showed that their average top speed was 150 mph, with a sample standard deviation of 19 mph. Test this hypothesis using a 1% significance level.
a.Reject the null hypothesis. There is not enough evidence to oppose the car manufacturer's claim.
b.Fail to reject the null hypothesis. There is not enough evidence to oppose the car manufacturer's claim.
c.Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
d.Fail to reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
How to find the null hypothesisThe null hypothesis (H0) is that the true average speed is 145 mph, and the alternative hypothesis (H1) is that the average speed is not 145 mph.
Using a z-test, we can calculate the z-score as [tex](150-145)/(19 \sqrt(87)),[/tex]which is approximately 3.67.
For a two-tailed test at the 1% significance level, the critical z-scores are -2.576 and 2.576.
Since the calculated z-score is beyond this range, we can reject the null hypothesis.
Therefore, there is enough evidence to oppose the car manufacturer's claim.
The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
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the international nanny association reports that in a random sample of 528 in-home child care providers (nannies), 20 work for either a nationally known, a locally known, or an internationally known celebrity (2011 international nanny association salary and benefits survey). find a 95% confidence interval for the true proportion of all nannies who work for a celebrity.
The 95% confidence interval for the true proportion of all nannies who work for a celebrity is approximately 0.0145 to 0.0613.
The confidence interval:
In this case, we have a random sample of 528 in-home childcare providers (nannies) and we want to estimate the proportion of nannies who work for a celebrity.
To do this, we calculate the sample proportion (p-hat) by dividing the number of nannies working for a celebrity by the total sample size.
Here we have
Sample size (n) = 528
Number of nannies working for a celebrity (x) = 20
First, we calculate the sample proportion (p-hat), which is the proportion of nannies working for a celebrity in the sample:
=> p-hat = x / n = 20 / 528
Next, we calculate the standard error (SE) using the formula:
SE = √(p-hat × (1 - p-hat)) / n)
SE = √((20 / 528) × (1 - 20 / 528) / 528)
Now, we can calculate the margin of error (ME) using the critical value associated with a 95% confidence level.
Since we have a large sample size, we can use the z-value:
z-value for a 95% confidence level ≈ 1.96
ME = z-value × SE
Finally, we can calculate the confidence interval:
Confidence Interval = p-hat ± ME
Substituting the values:
Confidence Interval = [ 20 / 528) ± (1.96×√(20 / 528)×(1 - 20 / 528) / 528) ]
Simplifying:
Confidence Interval ≈ 0.0379 ± 0.0234
Therefore,
The 95% confidence interval for the true proportion of all nannies who work for a celebrity is approximately 0.0145 to 0.0613.
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Mr ken has saved $5000. He will withdraw and spend $250 per month. What function can be used to find y, the total amount in ken’s saving account after x number of months?
The required function be y = 5000 - 250x.
Given that,
Amount of saving = $5000
Amount of withdraw and spend = $250
Number of months = x
If the total money in Ken's savings account after x number of months is represented by y,
Then, to calculate the entire amount in his savings account after x number of months, the program deducts 250x from the beginning amount of $5000.
Therefore, The function be,
y = 5000 - 250x
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What is the equation of the line that passes through (0,2) and (-3,14) in slope intercept form?
Answer: y = -4x + 2
Step-by-step explanation:
Help PLSS! Find the volume of the space inside the right cylinder that is not filled by the right cone using the information given below
The volume of the space inside the cylinder that is not filled with the right cone is 640π m³
What is volume?Volume is the total space occupied by a solid shape.
To calculate the volume of the space inside the cylinder that is not filled with the right cone, we use the formula below.
Formula:
V = πr²h-(πr²h/3)...............................Equation 1Where:
V = Volume of the space not filledh = Height of the cone/Cylinderr = Radius of the base of the cone and the cylinderFrom the question,
Given:
r = /AC/÷2 = 16/2 = 8 m/BD/ = 17 mh = √(BD²-r²) = √(17²-8²) = √225 = 15 mSubstitute these values into equation 1
V = (π×8²×15)-(π×8²×15/3)V = 960π-320πV = 640π m³Hence the right option is A. 640π m².
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The distance from building 1 to building 2 is 2,000 feet. The distance between building 2 and building 3 is 5,000 feet. The distance between building 1 and 3 is 1,000 feet. Do the building form a right triangle? Why or why not
Answer:
The angle between building 1 and building 3 at building 2 is not a right angle, and hence, the buildings do not form a right triangle.
Step-by-step explanation:
Perform the following area application
If 600 bricks measuring 12" by 18" are required to build a wall 10 ft. high (one brick thick), how long is the wall?
_________ft.
The first step is to calculate the total area of 600 bricks.
Area of one brick = 12 inches x 18 inches = 216 square inches
Area of 600 bricks = 600 x 216 = 129,600 square inches
Next, we need to convert the height of the wall from feet to inches since the area of the bricks is in square inches.
10 feet = 120 inches
Now, we can divide the total area of the bricks by the height of the wall to find the length of the wall.
Length of the wall = Area of 600 bricks / Height of the wall
Length of the wall = 129,600 square inches / 120 inches
Length of the wall = 1080 inches
Finally, we can convert the length of the wall back to feet by dividing by 12 since there are 12 inches in a foot.
Length of the wall = 1080 inches / 12 inches/foot
Length of the wall = 90 feet
Therefore, the length of the wall is 90 feet.
To solve this problem, we need to use the formula for calculating area which is length x width. We also need to convert units from feet to inches and vice versa as necessary to ensure we are working with the same units throughout the problem.
The length of the wall is 90 feet.
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If QT is the perpendicular bisector of PR, find each measure.
Please help!!
Given that QT is the perpendicular bisector of PR.The bisector of any line segment divides it into two equal parts, each of which has the same measure.To begin, let's define a few terms.
Angle bisector - An angle bisector is a line or segment that divides an angle into two equal parts.The given figure is shown below: We are given QT is the perpendicular bisector of PR. That means QT is perpendicular to PR and it bisects it. That is, it divides it into two equal halves.Suppose, PR = 2xFrom the given information, we know that the perpendicular bisector QT divides PR into two equal halves.
So,PQ = QR
Now, In right triangle
TPQ,QT² = TP² + PQ²QT² = TP² + QR² (since PQ = QR)QT² = TP² + (2x)² (since PQ = QR = 2x)QT² = TP² + 4x²
Also, In right triangle
TRQ,QT² = TR² + QR²QT² = TR² + (2x)²QT² = TR² + 4x²
We now have two equations:
QT² = TP² + 4x² QT² = TR² + 4x²
The above two equations can be equated:
TP² + 4x² = TR² + 4x²TP² = TR²
Thus, we can say that
TP = TRLet TP = TR = a
By Pythagoras theorem in right angled triangle
TPQ,TP² + PQ² = TQ²a² + (2x)² = QT²a² + 4x² = QT²
The answer is 4x² + a² = QT².
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¿Cuál es la masa que tienen 700 ml de un líquido que posee una densidad de 855 kg/m°?
Solve for x.
3-8x = 95-3x
Answer:
x = -18.4
Step-by-step explanation:
3-8x=95-3x
add 3x to both sides
3-5x=95
subtract 3 from both sides
-5x=95-3
-5x=92
divide both sides by -5
x=-18.4
A sphere has a diameter of 10.5 cm. What is the approximate volume
of the sphere? SHOW WORK
A. 115 cm3
B. 455 cm3
C. 463 cm3
D. 606 cm
The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.
To find the approximate volume of a sphere, we'll use the formula:
Volume = (4/3) × π × r³
Given that the sphere has a diameter of 10.5 cm, we can find its radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 10.5 cm / 2 = 5.25 cm
Now, we can plug the radius into the volume formula:
Volume = (4/3) × π × (5.25 cm)³
Volume ≈ (4/3) × 3.14 × (144.703125 cm³)
Volume ≈ 4.1867 × 144.703125 cm³
Volume ≈ 606.25 cm³
The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.
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Find the volume of a hemisphere with a diameter of 18
Answer:
972
Step-by-step explanation:
The data set shows the admission prices at several glass-blowing workshops.
$20, $20, $16, $12, $15, $25, $11
Find and interpret the range, interquartile range, and mean absolute deviation of the data.
The range is . The interquartile range is . The mean absolute deviation is .
Question 2
The prices vary by no more than $. The middle half of the prices vary by no more than $. The admission prices differ from the mean price by an average of $
The range is $14.
The interquartile range is $8.5.
The mean absolute deviation is $4.
What are measures of spread and central tendency in the prices?The Data set of the admission prices are: [tex]20, 20, 16, 12, 15, 25, 11[/tex]
The range = Maximum value - Minimum value
The range = $25 - $11
The range = $14
To get interquartile range, we will calculate first and third quartiles.
Arranging data in order, we get: [tex]11, 12, 15, 16, 20, 20, 25[/tex]
The first quartile is the median of the lower half of the data which is:
= (11+12)/2
= $11.5
The third quartile (Q3) is the median of the upper half of the data which is:
(20+20)/2
= $20
IQR = Q3 - Q1
IQR = $20 - $11.5
IQR = $8.5
To find the mean absolute deviation, we will calculate the mean.
Mean = sum of values / number of values
Mean = ($11 + $12 + $15 + $16 + $20 + $20 + $25) / 7
Mean = $17
|$11 - $17| = $6
|$12 - $17| = $5
|$15 - $17| = $2
|$16 - $17| = $1
|$20 - $17| = $3
|$20 - $17| = $3
|$25 - $17| = $8
MAD = Sum of absolute deviations / Number of values
MAD = (6 + 5 + 2 + 1 + 3 + 3 + 8) / 7
MAD = 4
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What multiplies to 71 and adds to 72
If 8sintheta = 4+costheta then find the value of tantheta
The value of Tan θ is -5/12
Given that 8 Sin θ = 4 + Cos θ, we need to find Tan θ,
So,
8 Sin θ = 4 + Cos θ
Dividing by Cos θ,
8 Sin θ / Cos θ = (4 + Cos θ) / Cos θ
8 Tan θ = 4 Sec θ + 1
Squaring both sides,
64 Tan² θ = 16 Sec² θ + 1 + 8 Sec θ
64 Tan² θ - 16 Tan θ + 1 = 16 (1 + Sec² θ)
48 Tan² θ - 16 Tan θ - 15 = 0
4 Tan θ(12 Tan θ + 5) -3(Tan θ + 5) = 0
(12 Tan θ + 5) (4 Tan θ - 3) = 0
Tan θ = 3/4 or Tan θ = -5/12
Since Tan θ = 3/4 does not satisfy the equation so Tan θ = -5/12
Hence the value of Tan θ is -5/12
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Im actually dying please explain this ASAP (its a buttload of questions)
The value of x is equal to 0.8603 units.
How to calculate the value of x?In order to determine the adjacent side (value of x), we would apply the law of tangent because the given side lengths represent the opposite side and angles of a right-angled triangle.
tan(θ) = Opp/Adj
Where:
Adj represent the adjacent side of a right-angled triangle.Hyp represent the opposite side of a right-angled triangle.θ represent the angle.Based on the information provided in the image, we can logically deduce the following parameters:
Adj = x units.
Opp = 8.3 units.
By substituting the parameters into the tangent ratio formula, we have the following;
Tan16 = 8.3/x
x = 3tan16
x = 0.8603 units.
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A bus is traveling from Miami, Florida to Charlotte, North Carolina. The distance it travels in miles, d, is
related to the rate in miles per hour, r, by the equation d 60t.
What is the average rate of speed for the bus?
1
How far will it travel in 2.5 hours?
T
miles How long will it take to go 330 miles? Round to the nearest tenth.
Answer:
the other day I dey bro you doing today I hope
Which angle is an obtuse angle? (1 point)
Figure A is an angle measuring ninety degrees, Figure B is an angle measuring between zero and eighty nine degrees, Figure C is an angle measuring between ninety one and one hundred seventy nine degrees, Figure D is an angle measuring one hundred eighty degrees.
a
Figure A
b
Figure B
c
Figure C
d
Figure D
who ever answer this first again, will get a brainlist :)
please help i dont understand this question
According to the information, the cuboid in the image is missing 3 faces of the following dimensions 1 face of 1 * 4, 1 face of 1 * 3 and 1 face of 3 * 3.
How to complete the cuboid?To complete the cuboid we must take into account that there are already three of its faces. Therefore, we must identify which faces are missing. As we know, cuboids are three-dimensional figures that have 6 faces. Another characteristic of non-regular cuboids is that they have pairs of equal faces.
Based on the information above, we can infer that the missing sides of this cuboid have the same dimensions as the existing sides on the graph. Therefore, the following sides would be missing:
1 face of 1 * 41 face of 1 * 31 face of 3 * 3Additionally, to know the surface of the area we must count the number of squares that the figure has in total, in this case it would be 38 squares, so the area is 38 units²
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four hundred draws will be made at random with replacement from the box (a) estimate the chance that the sum of the draws will be more than 1,500. (b) estimate the chance that the ticket [3] will be drawn fewer than 90 times.
In both cases, the estimates depend on the specific characteristics of the box and the probabilities associated with each draw.
To estimate the chance that the sum of the draws will be more than 1,500, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.
(b) Similarly, to estimate the chance that the ticket [3] will be drawn fewer than 90 times, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.
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Round the number represented on the number line to the nearest tenth 12.6---|---.---|---12.7
Answer:
Maybe add a picture
Step-by-step explanation:
i can solve it with a picture
the marketing club at school is opening a student store. they randomly survey 50 students about how much money they spend on lunch each day. what is the expected value for a student to spend on lunch each day? student lunch surveynumber of studentsdollars spent onlunch each day2$101$812$623$58$44$3$2.59$5.11$5.18$9.07
The expected value for a student to spend on lunch each day is $7.09.
To calculate the expected value for a student to spend on lunch each day based on the survey data,
we need to find the average amount spent by each student.
We can calculate the expected value by summing up the products of the number of students and the amount spent on lunch for each category, and then dividing by the total number of students:
Expected value = [tex](2 * 10 + 1 * 8 + 2 * 6 + 3 * 5 + 8 * 4 + 11 * 3 + 10 * 2.59 + 13 * 5.11 + 10 * 5.18 + 10 * 9.07) / 50[/tex]
Expected value = [tex](20 + 8 + 12 + 15 + 32 + 33 + 25.9 + 55.21 + 51.8 + 90.7) / 50[/tex]
Expected value = $354.71 / 50
Expected value ≈ $7.09
Therefore, based on the survey data, the expected value for a student to spend on lunch each day is approximately $7.09.
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What is the equation, in standard form, of a parabola that contains the following points (-2, 18), (0, 2), (4, 42)?
So the equation of the parabola in standard form is y = (5/4)x^2 - (7/4)x + 2.
One way to approach this problem is to use the standard form of the equation for a parabola, which is y = ax^2 + bx + c. We can set up a system of three equations using the three points given and solve for the coefficients a, b, and c.
Starting with the point (-2, 18):
18 = a(-2)^2 + b(-2) + c
18 = 4a - 2b + c
Using the point (0, 2):
2 = a(0)^2 + b(0) + c
2 = c
Using the point (4, 42):
42 = a(4)^2 + b(4) + c
42 = 16a + 4b + c
Substituting c = 2 into the second equation, we get:
2 = 2
This is always true, so it doesn't provide any additional information.
Substituting c = 2 into the first and third equations, we get:
18 = 4a - 2b + 2
42 = 16a + 4b + 2
Simplifying each equation:
9 = 2a - b
20 = 4a + b
Solving this system of equations, we get:
a = 5/4
b = -7/4
Substituting these values for a and b, and c = 2, into the standard form equation for a parabola, we get:
y = (5/4)x^2 - (7/4)x + 2
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