Answer:
Step-by-step explanation:
To solve this problem, we need to use the concept of similar triangles.
Let's draw a diagram to visualize the situation:
* Statue top
|
|
| 9 m
|
|
|
/ \
/ \ 4 m
Kimberly
We can see that we have two right triangles, one formed by Kimberly, the ground, and the point where the statue touches the ground, and the other formed by the statue, the ground, and the point where Kimberly's head touches the ground.
These two triangles are similar because they have the same angles. In particular, the angle at Kimberly's eye is the same as the angle at the top of the statue. This means that the corresponding sides are proportional.
Let's call the height of the statue "h". Then, we have:
h/9 = (h+4)/4
We can solve for "h" by cross-multiplying:
4h = 9(h+4)
4h = 9h + 36
5h = 36
h = 7.2
Therefore, the height of the statue is 7.2 meters. To find out how much taller the statue is than Kimberly, we subtract their heights:
7.2 m - 1.5 m = 5.7 m
So the statue is 5.7 meters taller than Kimberly.
a tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12 meters. if water is being pumped into the pyramid at a rate of 23m3sec, at what rate is the height of the water increasing when the water is 2 meters deep? (the volume of a pyramid with height h and base area b is given by v
If a tank is shaped like an upside down square-pyramid, then the rate at which the height of water is increasing when the water is 2 m deep is 51.75 m/sec.
The tank is upside down square-pyramid, with sides as 4 meter,
Let the height of water at any time "t" be = "h",
The height of the tank is = 12 meter,
Let, the side of the base of pyramid shaped water at any time "t" be = "b",
So, b = (1/3)h ...because height of pyramid is 12 and each side is of 4, the ratio is 1/3,
The volume of water at nay time "t" is (V) = (1/3)b²h,
⇒ V = (1/3)(1/3h)²h,
⇒ V = h³/27,
Now, dv/dt = (d/dt)(h³/27),
On simplifying further,
we get,
⇒ dv/dt = (h²/9)(dh/dt),
⇒ dh/dt = (9/h²)(dv/dt),
We know that, when the water is 2 meter deep, and if water is pumped out at rate of 23 m³/sec, it means that h = 2, and dv/dt = 23,
So, dh/dt = (9/2²)(23) = 51.75 m/sec.
Therefore, the rate of change of height is 51.75 m/sec.
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gregs backyard is 42 feet wide how many yards and feet is that?
pls show your work. thx
Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.
So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.
To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.
Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
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sum1 help me please and asap put steps if possible
Answer:
8
Step-by-step explanation:
To find the length of the third side, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
So, in this case, we have:
x^2 + 6^2 = 10^2
Simplifying this equation, we get:
x^2 + 36 = 100
Subtracting 36 from both sides, we get:
x^2 = 64
Taking the square root of both sides, we get:
x = 8 or x = -8
Since the length of a side of a triangle can't be negative, the length of the third side is x = 8 cm.
this is a choose all that apply question
Answer: Option B
Step-by-step explanation:
A. The range of the ages are greater. This statement is false because in the box plot movies A, the range is 26 (subtract highest value from lowest value) which is not greater. Thus, this statement is false.
B. A smaller range normally means that there is a more consistent range. TRUE
C: The IQR, looking at the box plot, is much greater.
D: In Movie 2, the median ages of attendees are greater. False
the residual plots from two different sets of bivariate data are graphed below. explain, using evidence from graph a and graph b which graph indicates
According to the evidence from graph a and graph b, graph a indicates that the model for the data was a good fit because it is a random.
Hence, the correct option is B.
Based on graph a, the residual plot shows a random scattering of points around the horizontal line at y=0. This indicates that the residuals (the differences between the observed and predicted values) are distributed randomly and do not show any clear pattern. This suggests that the data points are evenly distributed around the regression line, indicating a good fit for a linear regression model.
On the other hand, graph b shows a residual plot with a clear pattern or trend. The residuals are not randomly scattered, but instead show a curved pattern or a fan-like shape. This indicates that the model used to fit the data may not be appropriate, as it is not capturing the underlying relationship between the variables accurately.
Hence, the correct option is B.
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-- The given question is incomplete, the complete question is
"The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph a and graph b which graph indicates that the model for the data was a good fit and what is the reason?
A. Graph A because it is symmetrical
B. Graph A because it is random
C. Graph B because there is a pattern
D. Graph B because it is symmetrical" --
solve the system of equations
Answer:
(2, 3)
Step-by-step explanation:
9x - 7y = -3
+ -9x + 15y = 27
8y = 24 (Divide by 8 on both sides)
8 = 8
y = 3
Substitute y = 3 in any of the two equations.
9x - 7(3) = -3
9x - 21 = -3
+21 = +21 (Add 21 on both sides)
9x = 18 (Divide by 9 on both sides)
9 = 9
x = 2
there are 25 people competing in a rubber duck regatta. each person is allowed only one entry. if there are no ties, how many ways are there to have the first, second, and third place winners?
There are 13,800 different ways to have the first, second, and third place winners without any ties.
In a rubber duck regatta with 25 people competing and each person having only one entry, we can determine the number of ways to have the first, second, and third place winners by using permutations.
Step 1: Calculate the number of options for the first place winner.
There are 25 contestants, so there are 25 options for the first place.
Step 2: Calculate the number of options for the second place winner.
Since the first place winner has been determined, there are 24 remaining contestants to choose from for the second place.
Step 3: Calculate the number of options for the third place winner.
After determining the first and second place winners, there are 23 remaining contestants to choose from for the third place.
Step 4: Multiply the number of options for each place to get the total number of possible outcomes.
25 options (first place) × 24 options (second place) × 23 options (third place) = 13,800 possible outcomes.
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Empirical Rule Khan Academy; all, if not most, of the answers.
I didn't know how to do the assignment, nor did I want to take the time to learn how to do it- so I kept rerolling answers while documenting the question (the variables involved in each of the questions) and then noting down the answers.
Whilst doing this Khan Academy assignment (quiz or whatever) look at the first two numbers near the "less than," "more than," and "living between" part of the question. Proceed to align the next numbers to whichever ones I have on the pdf.
- The answers will be under the numbers that have "and" or "&." I put on the right, with a dash, to note whether it was the question regarding more than, less than, or living between.
This took me a while to do (I was going for 4 stars on Khan). I thought it was worth sharing. Goodluck, folks.
Answer:
dont no ok i dont konow ask an easy one
#
PLEASE HELP!!!!!!!!!!!!!
What is the value of the expression 5x - 3y ?
3x - 4y= -24
3x +2y= -6
The value of the expression 5x - 3y, is -29 obtained by elimination method by eliminating the two equations.
The equations are :
3x - 4y= -24 ----------- A
3x +2y= -6 ----------- B
On multiplying minus sign in B equation, to eliminate the x- component in the equation.
3x +2y= -6 becomes (-3x - 2y = 6)
Then, the equation becomes,
3x - 4y= -24
-3x - 2y = 6 (+ 3x - 3x are equal and opposite becomes zero.)
------------------
-6y = -18
------------------
6y = 18 (both minus sign gets cancelled)
y = 18/6
= 3
The value of y=3.
Substitute the value of y=3 in A equation.
Equation A is, 3x - 4y= -24
3x - 4(3) = -24
3x = -24 + 12
3x = -12
x = -12 / 3
= -4
The value of x= -4.
Thus, the value of x= -4 and y = 3. By using this x and y values, the equation 5x - 3y, can be solved as,
= 5x - 3y
= 5(-4) - 3 (3)
= -20 -9
= -29
The value of the expressions 5x - 3y = -29.
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PLEASE HELPP
Sara is paid semi-monthly. Her annual salary is $37,560. What is her semi-monthly to the nearest cent?
A)$1,444.62
B)$1,502.40
C)$1.565,00
D)$727.31
Step-by-step explanation:
To find Sara's semi-monthly salary, we need to divide her annual salary by the number of semi-monthly periods in a year.
Since there are 24 semi-monthly periods in a year (twice a month), we can divide her annual salary by 24 to get her semi-monthly salary:
$37,560 ÷ 24 = $1,565.00
Therefore, Sara's semi-monthly salary to the nearest cent is option C) $1,565.00.
Michael solved this inequality as shown:
Step 1: -6(x + 3) + 10 < -2
Step 2: -6x − 18 + 10 < -2
Step 3: -6x − 8 < -2
Step 4: -6x < 6
Step 5: x > -1
What property justifies the work shown between step 3 and step 4?
A.
transitive property
B.
division property of inequality
C.
distribution property
D.
addition property of inequality
The property used between step 3 is the D)addition property of inequality and step 4 is the B) division property of inequality.
What is inequalities?In mathematics, an inequality is a mathematical statement that indicates that twο expressiοns are nοt equal. It is a statement that cοmpares twο values, usually using οne οf the fοllοwing symbοls: "<" (less than), ">" (greater than), "≤" (less than οr equal tο), οr "≥" (greater than οr equal tο).
The property used between step 3 is the addition property of inequality and step 4 is the division property of inequality. answer is D addition property of inequality.
In step 3, -6x - 8 < -2 is οbtained by adding 8 tο bοth sides οf the inequality -6x - 8 + 8 < -2 + 8.
Then, in step 4, -6x < 6 is οbtained by dividing bοth sides οf the inequality -6x - 8 < -2 by -6, which requires the use οf the division property of inequality.
Therefore, the property used between step 3 and step 4 is the addition property of inequality.
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Find ratio in which line joining of points A(–7, –1) and B(8, 2) is divided by x + y = 2 ?
After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
[tex]m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\[/tex]
[tex]y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\[/tex]
The ratio in which AB is divided by x + y = 2 is:
[tex]AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\[/tex]
As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
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Jose worked for 12 hours each day for 7 days. Then the next day he worked 8 hours. How many hours did Jose work in all?
Answer:
92 hours
Step-by-step explanation:
7 * 12 + 8 = 92
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed
Answer: C. The median of 20 is the most accurate to use, since the data is skewed.
The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.
In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.
Step-by-step explanation:
Find the answer and explain
Answer:
660cm^2
Step-by-step explanation:
area of 2 triangle= 10×12
= 120cm^2
area of 3 rectangles= (13×15×2)+(10×15)
= 390+150
= 540cm^2
surface area of triangular prism
= 540+120
= 660cm^2
what is the length of AC in the graph below
The length AC of the triangle is 4.47 units.
How to find the length on a graph?The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.
To find the length AC in the triangle, we have to use distance formula as follows:
Therefore,
A = (1, 1)
C = (3, 5)
AC = √(y₂ - y₁)² + (x₂ - x₁)²
AC = √(5 - 1)² + (3 - 1)²
AC = √4² + 2²
AC = √16 + 4
AC = √20
Hence,
AC = 4.472135955
AC = 4.47 units
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the weather reporter stated that the probability of rain last week was 3 out of 7 days. It rained on Mont\day, Tuesday, Thursday, and Friday last week.How did the reporter's stated probabilty for rain last week compare to the actual results
If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.
Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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as shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. what is the distance, in feet, between the centers of the two wheels?
The distance between the centers of the two wheels is approximately 11.86 feet.
The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.
Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula
C = πd
Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:
C = πd = π(0.5) = 1.57 feet (approx.)
The length of the conveyor belt is given as 15 feet. So we can write
2C + d = 15
Substituting the value of C, we get
2(1.57) + d = 15
3.14 + d = 15
d = 11.86 feet
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Help meeeee pleaseee!
Using the given clues, we can fill out the table as follows:
Section Number Color
A 3 Green
B 5 Purple
C 9 Brown
D 8 Orange
E 1 Yellow
F 6 Blue
G 4 Pink
Completing the table of valuesUsing this information, we can deduce the values of each section:
The number 8 is in all shapes
So, D = 8
Number C is the largest
So, C = 9 because the numbers used are BETWEEN 0 and 10 i.e. 1 to 9Also, C = BrownFor the blue section, we have
F = Blue
For the triangle, we have
DEF = 48
D + E + F = 15
So, we have
EF = 6
E + F = 7
This means that
(E, F) = (1, 6) or (6, 1)
Number 1 is yellow
So, we have
E = 1 = YellowF = 6 = BlueSince F is not yellow, then
A = Green
A and G add up to 7, and A's number is smaller than G's.
So A and G must be (1, 6), (3, 4) because 2 and 7 are not used
Because of the values of E and F, we have
A = 3 and G = 4
Green and pink are in the rectangle only
So:
G = Pink
Purple and Orange are in the circle
So:
(B, D) = (Orange, Purple), (Purple, Orange)
The purple section is 5 and D = 8
So:
(B, D) = (Purple, Orange) = (5, 8)
The table has been completely filled
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The formula for the general term of 14,11,8,5,2
The formula for the general term of an arithmetic sequence is:
an = 14 - 3(n-1)
What do you mean by Arithmetic progression ?Arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant value, called the common difference, to the preceding term. For example, 2, 4, 6, 8, 10, 12, 14... is an arithmetic progression with a common difference of 2. The formula for the nth term of an arithmetic progression is given by:
an = a1 + (n-1)d
The given sequence 14, 11, 8, 5, 2 is an arithmetic sequence with a common difference of -3.
The formula for the general term of an arithmetic sequence is:
an = a1 + (n-1)d
where:
an = the nth term of the sequence
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the position of the term we want to find
Using the values given in the sequence, we have:
a1 = 14
d = -3
To find the general term, we need to determine the value of n. Let's assume that the first term of the sequence corresponds to n = 1.
For the first term (n = 1):
a1 = 14
For the second term (n = 2):
a2 = a1 + d = 14 - 3 = 11
For the third term (n = 3):
a3 = a1 + 2d = 14 - 6 = 8
For the fourth term (n = 4):
a4 = a1 + 3d = 14 - 9 = 5
For the fifth term (n = 5):
a5 = a1 + 4d = 14 - 12 = 2
Therefore, the general term for the given sequence is:
an = 14 - 3(n-1)
or
an = 17 - 3n (Alternative form)
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write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0
-4x1 – 4x2 – 8x3 = 0
-3x2 – 9x3 = 0
[ x1 ]
Where the solution set is x = [ x2 ]
[ x3 ]
X = x3 _____
The solution set can be written in parametric vector form as: [tex]X = x3 [-1 0 1]^T + x2 [-2 1 0]^T[/tex]
How we get the solution of homogeneous system?We can rewrite the system of equations in matrix form as AX = 0, where [tex]A =[2 2 4]\\[-4 -4 -8]\\[0 -3 -9][/tex]
[tex]X = [x1 x2 x3]^T[/tex]
To solve for the solution set, we can row reduce the augmented matrix [tex][A|0].\\[2 2 4|0]\\[-4 -4 -8|0]\\[0 -3 -9|0][/tex]
[tex]R2 < - R2 + 2R1 and R3 < - R3 - 3R1[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 -3 -9|0][/tex]
[tex]R3 < - -1/3 R3[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - R1 - R2[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - 1/2 R1 and R2 < - 1/2 R2[/tex] to obtain:[tex][1 1 2|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
Therefore, the system has two free variables, x2 and x3, while x1 is a pivot variable. where x2 and x3 are arbitrary constants.
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can you help me solve this e - 3.4 = 18.7
Answer:
evaluate: −0.68171817=18.7
Step-by-step explanation:
How do -4.1 and -3 1/2 compare?
Step-by-step explanation:
you have to subtract them which would be -1.05
Lily makes $8.25 an hour at her job. She has been offered a different job that pays $10.40 hour. What is the percent increase in her pay?
The percent increase in her pay is by 26.06% if she takes the new job.
What is percentage increase?A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.
Given that, the pat increases from $8.25 an hour to $8.25 an hour.
percent increase = [(new value - old value) / old value] x 100%
Substituting the values we have:
percent increase = [(10.40 - 8.25) / 8.25] x 100%
percent increase = 26.06%
Therefore, Lily's pay would increase by 26.06% if she takes the new job.
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 1 unit wide.
There are [tex]18[/tex] square units in the area of the shaded rectangle.
What makes it a rectangle?The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.
What other name does rectangle go by?In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.
width [tex]= 7[/tex] units
length [tex]= 10[/tex] units
We remove the frame, each measure will lose[tex]2*2[/tex] units, or [tex]4[/tex] units
[tex]width = 7 units - 4 units = 3 units[/tex]
[tex]length = 10 units - 4 units = 6 units.[/tex]
[tex]A = (3 units)*(6 units) = 18[/tex] square units.
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The completed question is:
One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 1 unit wide.
10
5
NEED HELP DUE TODAY WELL WRITTEN ANSWERS ONLY!!!!
Here is a graph of f given by f(Θ) = tan(Θ). What are the Θ-intercepts of the graph of f? Explain how you know.
The straight lines that pass through the points Θ = π, Θ = 2π, Θ = 3π, and so on are known as the f-intercepts. At the multiples of, these lines cross the x-axis (or -axis).
What do you mean by x and y intercepts?The points where a line intersects an axis are known as the x-intercept and the y-intercept, respectively.
A periodic function, f(Θ) = tan(Θ), oscillates between positive and negative infinity at certain points that correlate to the function's zeros. These zeros are referred to as the function's x-intercepts or roots.
The x-intercepts are not clearly specified, though, because the function has a periodic nature with a period of. Or, to put it another way, the function has an unlimited number of x-intercepts at each integer multiple of π (i.e., π, 2π, 3π, -π, -2π, -3π, and so on).
The values are represented by the x-axis in the setting of the function's graph. As a result, the values of for which the function equals zero correlate to the x-intercepts or roots of the function.
We can see that the function equals zero when sin() = 0, which happens when is an integer multiple of, by using the equation tan() = sin() / cos().
As a result, the vertical lines going through Θ = π, Θ = 2π, Θ = 3π, and so on are the -intercepts of the graph of f. These lines cross the x-axis (also known as the -axis) at multiples of.
In conclusion, the straight lines at = n, where n is an integer, are the -intercepts of the graph of f(Θ) = tan(Θ).
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What is the increasing and decreasing?!?!?!?!?!?!?!??!?!?!?!?!?!
Answer:
Function decreasing: where x is (-4; 0) and (2; 4)
Function increasing: where x is (0; 2)
Step-by-step explanation:
Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.
The vertex of f(x)=-4.9x^(2)+26.1+65
Is the vertex a maximum/minimum?
The y-intercept and x-intercept of f(x)=-4.9x^(2)+26.1+65
(703. When asked to find the equation of the parabola pictured
at right, Ryan looked at the z-intercepts and knew that the
answer had to look like y a(x+ 1)(x-4), for some coefficient
a. Justify Ryan's reasoning, then finish the solution by finding
the correct value of a.
AND
704 (Continuation) Find an equation for the parabola, in fac-
tored form, y a(z-p)(z-g), whose symmetry axis is parallel
to the y-axis, whose a-intercepts are -2 and 3, and whose y
intercept is 4. Why is factored form sometimes referred to as
intercept form?
The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)
What is parabola?
A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.
Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.
To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:
2 = a(0 + 1)(0 - 4)
2 = -4a
Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.
To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:
0 = a(-2 - h)² + k
0 = a(3 - h)² + k
Solving for h and k, we get:
h = 1/2
k = 4
Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:
y = a(z - 1/2)² + 4
We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:
4 = a(0 - 1/2)² + 4
4 = a(1/4)
a = 16
Therefore, the equation of the parabola in factored form is:
y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.
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The perimeter of a rectangle is 50 inches. Its width measures 11 inches. What is its length? Let x= length of the rectangle. A.) 2x - 11 = 50
B.) 2x + 11 = 50
C.) x + 11 = 50
D.) 2x + 22 = 50
Answer: D.) 2x + 22 = 50
Step-by-step explanation:
P=2(l+w)
2x+22=50 is correct because
2 times x is 2 times the unknown length
11 times 2 is 22 so, you add that to the 2x
50 is the perimeter