Answers
Answer:
x = 8Step-by-step explanation:
10x - 20 = 7x + 4
3x = 24
x = 24/3
x = 8
---------------------
10 * 8 -20 = 7 * 8 + 4
60 = 60
the answer is good
Related Questions
Find the value of x so that L||M
Answers
9514 1404 393
Answer:
x = 19
Step-by-step explanation:
The marked (consecutive interior) angles will be supplementary when the lines are parallel.
(3x +10)° +(5x +18)° = 180°
8x = 152 . . . . . . . . . . . . . . . divide by °, subtract 28
x = 19 . . . . . . . . . . . divide by 8
y = (x) = (1/9)^x
Find f(x) when x = (1/2)
Round your answer to the nearest thousandth.
Answers
Answer:
0.333
Step-by-step explanation:
How do you solve for incenter?
Answers
The approach for solving for incenter.
Incenter:
The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.
It can also be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.
Formula for solving incenter:
Let (x1,y1) , (x2,y2) and (x3,y3) are three points of triangle.
and a,b,c are lengths of sides.
I = ((ax1+bx2+x3 / a+b+c , ay1+by2+cy3 / a+b+c))
Learn more about the triangle here:
https://brainly.com/question/25813512
#SPJ4
Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
HELP!!
Calculate the residuals for your scatterplot in step 2d.
Answers
In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:
Step 1: Plot the data on a scatterplot.
Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.
Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.
Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.
Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.
For such more question on equation
https://brainly.com/question/29174899
#SPJ8
Divide 100 by 16 and write the answer as a mixed number. Reduce the
fraction part of the mixed number.
Answers
It says my answer needs more characters, so I’m adding this
Answer:
Step-by-step explanation:
Divide 100 by 16 and you get 6.25 then turn it into a mixed number which would be 6 25/100 then reduce 25/100 by dividing 100 by 25 and 25 by 25 which will give you 1/4 so the answer is 6 1/4.Welcome!
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
Answers
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
Nonsense will be reported!!
Plss I need solution Ty!!.
Answers
\(\\ \rm\Rrightarrow \sqrt{36x^{21}y^{64}}=6y^8x^{10.5}\)
\(\\ \rm\Rrightarrow \sqrt[15]{7^{10}a^{25}b^{-35}}=7^{2/3}a^5b^{-7}{3}\)
\(\\ \rm\Rrightarrow \sqrt[3]{648(3m-2n)^{64}}=648^{1/3}(3m-2n)^4\)
\(\\ \rm\Rrightarrow \sqrt[4]{(a^2-2a+1)^{29}(a^2-1)^7}=(a^2-a+1)^{29/4}(a^2-1)^{7/4}\)
\(\\ \rm\Rrightarrow \dfrac{3a^2b}{\sqrt[3]{18a^{21}b^{17}}}=\dfrac{3a^2b}{18^{1/3}a^7b^{17/3}}=\dfrac{3a^{-5}b^{-14/3}}{18^{1/3}}=\dfrac{3}{18^{1/3}a^5b^{14/3}}\)
Find the LCM of A= 3^2 x 5^4 x 7 and B= 3^4 x 5^3 x 7 x11
Answers
The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.
Given are two numbers which are showed in the prime factorized form.
A = 3² × 5⁴ × 7
B = 3⁴ × 5³ × 7 × 11
Prime factorization is the factorization of a number in terms of prime numbers.
In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.
A = 3² × 5³ × 5 × 7
B = 3² × 3² × 5³ × 7 × 11
Bring down the primes in each column.
LCM = 3² × 3² × 5³ × 5 × 7 × 11
= 3898125
Hence the LCM is 3898125.
Learn more about LCM here :
https://brainly.com/question/6756370
#SPJ1
Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit A = 8 oz and upper limit B = 10 oz. Describe how you would carry out simulation experiments to compare the sampling distribution of the (sample) fourth spread for sample sizes n = 5, 10, 20, and 30.
Answers
To compare the sampling distribution, first I would simulate the machine by randomly generating n number of samples between 8 and 10 oz with a uniform distribution and calculate the 4th spread for each sample size. I would then repeat this experiment multiple times and take the average of the fourth spread values for each sample size to compare the sampling distributions.
To compare the sampling distributions of the fourth spread for sample sizes n = 5, 10, 20, and 30, I would simulate the machine by randomly generating samples between 8 and 10 oz with a uniform distribution. For each sample size, I would calculate the fourth spread for each sample and then repeat the experiment multiple times. Finally, I would take the average of the fourth spread values for each sample size to compare the sampling distributions. This way, I would be able to see how the fourth spread changes as the sample size changes. It would also allow me to see how the fourth spread is affected by the uniform distribution of the machine's output.
To know more about sampling distribution refer to the link brainly.com/question/13501743
#SPJ4
What are the domain and range of the function f(x) x^2 +8x+7 over x+1
Answers
Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).
The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.
Step-by-step explanation:
A bag of snacks contains 3 flavors: cherry, lemon, and grape. Carol will take 1 snack from the bag without looking. The probability for each flavor is shown in the table.
Answers
Middle - cherry
Most likely - grape
f(x)=- square root x-2. +3
Answers
Answer:
Hi, The.
The domain of a function is the set of all possible values for x. The range is all possible values for y.
You should be able to see these pretty easily from the graph. If I understand your function correctly:
f(x) = square root(x+2) - 3
then x cannot be less than -2. Your domain is x > -2. In interval notation [-2,∞)
The lowest value for y is -3 so the range is y > -3. In interval notation [-3,∞)
Hope this helps!
True or False Directions: Determine whether each statement below is correct or incorrect. Justify your response with a calculation, a description using complete English sentences, or a combination of both. If a statement is incorrect, make sure to include what the error is and state what the student should have done to evaluate the integral correctly in your explanation. All calculations must be done by hand and proper notation must be used. Correct responses with insufficient justification or that rely on technology will earn no credit.
A. [8 pts) Morgan claims that the improper integral * 4.re -2- dr converges to 1. esca 8
B. (8 pts] Avery is asked to compute dr and provides the following argument. (3 - 4.) 8 (3 - 4.0) (3 - 4.r) (-1) (3) lo dr =
Answers
Answer:
(A) true.
(B). False.
Step-by-step explanation:
(A). F(x) = 4xe^-2x.
Let's make the assumption that 2x = b -----------------------(1).
Therefore, taking the differentiation with respect to x, we have;
2x dx = db.
The next thing thing to do is to integrate, taking the upper limit to be infinity and the lower limit to be zero:
∫( b e^-b db).
Changing the Lim. infinity = 2.
= ∫( b e^-b db). ----------------------------(2).
The step (2) above can be solve with Integrations by part;
Lim. 2 ---> infinity [ b e^-b + ∫( 1 e^-b db|
( | = Upper boundary = 2 and the lower boundary = 0).
Lim. 2 ----> infinity [ 2 e^-2 - 0] - lim. 2 --> infinity [ 0 - 1].
Lim 2 ---> infinity [ 2/e^2 + 1].
Let 2/e^2 = j.
The, lim 2 ---> infinity j + 1.
To solve this, there is need to make use of L'hospital rule,
j = Lim 2 ---> infinity [ 1 /e^2] = 0.
Thus, j = 0. And 0 + 1 = 1.
(PROVED TO BE TRUE).
(B). Taking limit from 1 (upper) to 0( lower). Assuming that b = 3 - 4x.
Therefore, -4dx = db.
∫( 8 /(3 - 4x)^3 dx.
Taking the upper boundary = -1 and the lower boundary = 3.
∫ ( - 2db/ b^3.
= 2 ∫ ( - db/ b^3.
= 2 [ b^-3 + 2) / -3 + 1.
= 2 | - 1/ 2 db
= 8/9.
Not true.
let p be a point chosen uniformly at random in the interior of the unit square with vertices at (0, 0),(1, 0),(1, 1), and (0, 1). the probability that the slope of the line determined by p and the point 5 8 , 3 8 is greater than or equal to 1 2 can be written as m n , where m and n are relatively prime positive integers. find m n
Answers
The probability that the slope of the line determined by p and the point (5/8, 3/8) is greater than or equal to 1/2 is 5/8.
Let the coordinates of point p be (x,y). Then, the slope of the line determined by p and the point (5/8, 3/8) is:
(slope) = (y - 3/8)/(x - 5/8)For the slope to be greater than or equal to 1/2, we must have:
(y - 3/8)/(x - 5/8) >= 1/2Solving for y, we get:
y >= (x/2) + 7/16Graphing this inequality on the unit square, we see that the region satisfying this inequality is a trapezoid with vertices (5/8,3/8), (1,1/2), (1,1), and (3/4,1).
The area of this trapezoid is (1/2)*((5/8 - 3/4) + (1 - 5/8) + (1 - 1/2) + (3/8 - 3/16)) = 5/16.
The area of the unit square is 1, so the probability we seek is 5/16.
Hence, the answer is 5/16 written as a fraction in its simplest form, which is 5/16.
Learn more about Probability:
https://brainly.com/question/24756209
#SPJ4
valuate −8 + 10 × 4 ÷ (−2). Question 25 options: −4 −28 −3 −20
Answers
Answer: its -28
Step-by-step explanation:
i dont know i used a app
line a y=1/2x+2
line b y= -1/2 x +7
line c y=2x +4
line d y= 1/2x +5/4
which lines are perpendicular
Answers
Answer:
Line b and line c are perpendicular.
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes, and -1/2 and 2 are opposite reciprocals.
A population of values has a normal distribution with �=189.7 and �=96.7. You intend to draw a random sample of size �=62.
Find the probability that a single randomly selected value is between 189.7 and 213.
P(189.7 < X < 213) =
Find the probability that a sample of size �=62 is randomly selected with a mean between 189.7 and 213.
P(189.7 < M < 213) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answers
The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.
Step 1: Calculate the z-scores for the given values using the formula:
z = (x - μ) / σ
For 189.7:
z1 = (189.7 - 189.7) / 96.7 = 0
For 213:
z2 = (213 - 189.7) / 96.7 ≈ 0.2417
Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.
P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939
Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.
To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance
Step 1: Calculate the standard error of the mean (σ_m) using the formula:
σ_m = σ / sqrt(n)
σ_m = 96.7 / sqrt(62) ≈ 12.2878
Step 2: Convert the given qualities to z-scores utilizing the equation:
z = (x - μ) / σ_m
For 189.7:
z1 = (189.7 - 189.7) / 12.2878 = 0
For 213:
z2 = (213 - 189.7) / 12.2878 ≈ 1.8967
Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.
P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702
Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
For more such questions on probability, click on:
https://brainly.com/question/7965468
#SPJ8
elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is
Answers
the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m
We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.
Learn more about elevation difference here
https://brainly.com/question/6689872
#SPJ4
multiple inveres of -34/56
Answers
Answer:
-56/34 is the answer
Step-by-step explanation:
Mark as brainlist if it's helpfull
Two pounds of grapes costs $6 as shown in the table. At this rate, how much does 1 pound of grapes cost?
Answers
Answer:
1 pound of grapes cost 3$
Step-by-step explanation:
If 2 pounds of grape cost 6$ then 1 pound of grape cost 3$ Since 1 is half of 2 and 3 is half of 6
Henry has a bag of potting soil that is 3/4
full. He uses 1/16 of a bag to fill small
flower pots. How many small flower pots
can he fill?
A. 48
B.12
C.11/16
D.3/64
Answers
Answer:
B
Step-by-step explanation:
3/4 of 16 (which is 1 whole) is 12
At a swimming pool the ratio of children to adults was 3 : 2
Out of 930 people, how many were adults?
Answers
Answer:
372
Step-by-step explanation:
We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.
930 / 5 = 186
This means that there are 186 groups of 3 children to 2 adults
So, in each of the 186 groups, there are 2 adults.
Therefore, we can multiply (186)(2)
to find the total number of adults: 372
The number of the children and adult will be 558 and 372.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
At a swimming pool, the ratio of children to adults was 3 : 2.
C / A = 3 / 2
Then solve the equation for C, then the equation will be
C = (3/2)A
The total number of the people is 930. Then the equation will be
C + A = 930
Substitute the value of C in the above equation. Then the equation will be
(3/2)A + A = 930
(5/2)A = 930
A = 930 x (2/5)
A = 372
The number of the adult will be 372.
Then the number of the children will be
C + 372 = 930
C = 930 – 372
C = 558
The number of the children will be 558.
Thus, the number of the children and adult will be 558 and 372.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v= \(\sqrt{x} 19.6h\). If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?
Answers
If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .
In the question ,
it is given that
the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula
v = √(19.6×h)
to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,
we substitute v = 25.7 in the equation v = √(19.6×h) ,
we get ,
25.7 = √(19.6×h)
squaring both the sides , we get
19.6 × h = 25.7²
19.6 × h = 660.49
h = 660.49/19.6
h = 33.698
h ≈ 33.7
Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .
The given question is incomplete , the complete question is
Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?
Learn more about Equation here
https://brainly.com/question/20359474
#SPJ1
Here are the cost of tickets at a cinema venue
Answers
Answer:
A=40.8 B=8
Step-by-step explanation:
A Explanation
£7.20*3=£21.6
£9.60*2=£19.2
19.2+21.6=40.8
B Explanation
£9.60*3=£28.8
86.40-28.8=57.6
57.6/7.20=8
This grid shows where a squirrel hid different nuts which ordered pair shows wheee the squirrel hid the acorns
2,8
2,10
8,2
8,8
Answers
How many 20kobo make up #20
Answers
Answer:
100
Step-by-step explanation:
#20 naira - 20 * 100
= 2000kobo
2000/20
100
QED✅✅
you can support by rating brainly it's very much appreciated ✅ ✅
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answers
Answer:
D
Step-by-step explanation:
We have the quadratic function:
\(f(x)=-x^2-4x+5\)
First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.
So, we can eliminate choices A and B.
Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).
Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.
So, the range of the function is all real numbers less than or equal to 9.
Our answer is D.
It is not C because the maximum value is dependent on y and not x.
Meghan swam 84 kilometers in 3 days.
How many kilometers did Meghan swin per day?
Answers
84:3=28 (km)
............