Answers
Answer:
g(x) = 4x² -x +64
Step-by-step explanation:
The integral of f(x) will be continuous. This means the value must be the same for x = 4- as for x = 4+.
For some constant c1, the integral in the region x ≤ 4 is ...
∫f(x)dx = (4x² -x +c1) +C = g(x) +C
The integral in the region x ≥ 4 is given as ...
∫f(x)dx = 31x +C
Evaluated at x=4, we must get the same value from either expression:
4(4²) -4 +c1 +C = 31(4) +C
60 +c1 = 124
c1 = 64
__
In order to make the integral continuous at x=4, we must have ...
g(x) = 4x² -x +64
Related Questions
x^2 + 7y + 12 = ?
x = -1 y = 4
Answers
(-1)^2 + 7(4) + 12 = 1 + 28 + 12 = 41
Therefore, x^2 + 7y + 12 is equal to 41 when x=-1 and y=4.
The value of the expression when x = -1 and y = 4 is 41.
Evaluating the expression \(x^2\)+7y+12 when x = -1 and y = 4, we get:
\(x^2\)+7y+12 = \((-1)^2\) + 7(4) + 12 = 1 + 28 + 12 = 41
Therefore, the value of the expression when x = -1 and y = 4 is 41.
Here is the step-by-step solution:
Substitute x = -1 and y = 4 into the expression.
Evaluate the exponent.
Multiply 7 by 4.
Add 1, 28, and 12.
The answer is 41.
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PLZ HELP
19 students were surveyed on the number of hours of Netflix they watched last week.
The data from the survey is below:
{0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 10, 11}
What is the mode for this data?
Answers
Answer:
Step-by-step explanation:
Answer:
i think the answer is 4
hope this help?
What is the slope of the line that passes through the point (7,-4) and (11,-4)? Write your answer in the simplest form.
Answers
The slope of the line that passes through the points (7,-4) and (11,-4) is 0.
The slope of a line is found by using the formula:
slope = (change in y)/(change in x)
To find the change in y, subtract the y-coordinate of one point from the y-coordinate of the other point:
-4 - (-4) = 0
To find the change in x, subtract the x-coordinate of one point from the x-coordinate of the other point:
11 - 7 = 4
Now we can use the formula to find the slope:
slope = 0/4 = 0
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You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answers
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
Need help with angles brainlest and points
Answers
Answer:
14
Step-by-step explanation:
Answer:
A, x=14
Step-by-step explanation:
We know that <HJL is a right triangle, therefore 90 degrees.
<HJK + < KJL = <HJL
<HJK + 50 = 90
<HJK = 40
We replace HJK with 3x-2
3x-2 =40
3x=42
x= 14, A
I hope this helped! :)
Question 4
1 pts
What is the midpoint of the segment containing the endpoints (-3.3) and
05.1:
Answers
Answer:
1, 2
Step-by-step explanation:
Given parameters;
Endpoints = (-3, 3) and (5, 1)
Unknown:
The midpoint of the segment = ?
Solution:
The midpoint between two endpoints is given as;
x\(_{m}\), y\(_{m}\) =( \(\frac{x_{1} + x_{2} }{2}\) , \(\frac{y_{1} + y_{2} }{2}\))
x and y are coordinates
x₁ = -3
x₂ = 5
y₁ = 3
y₂ = 1
x\(_{m}\), y\(_{m}\) = \(\frac{-3 + 5}{2}\), \(\frac{3+ 1}{2}\)
x\(_{m}\), y\(_{m}\) = 1, 2
Will records the wins and losses for his high school basketball team each year. He notices that the ratio of wins to losses has
been consistent each year,
VX
Wins
Losses
18
2
45
5
36
4
27
X
Using the information in the table, how many losses should he predict for next year if the number of games won is 272
1
ОО
3
6
9
Save and Exit
Next
Submit
Mark this and return
Answers
Answer:
3
Step-by-step explanation:
you have to multiply by 9.
2times9=18,5times 9=45,4times 9=36,
3times9=27.
Juanita has saved 10% of the money that she needs to buy a new bicycle.
If she has saved $22, how much money does the bicycle cost?
Answers
For Field Day, the 72 students in fourth grade will be divided into tears with the same number of students on each team. The 60 students in third grade will be divided into teams that each have the same number of students as the fourth grade teams. What is the largest number of students that a team could have? Help meeee
Answers
We do this because the factors are the numbers determining the number of people and the number of teams, for example if they used the factors 6 and 10 for 60, they would make 6 teams of 10 people. And since factors are whole numbers, it makes sense for people and doesn’t cut ppl in half.
So the greatest factor that 72 and 60 gave have in common is 12, bc 5 x 12 is 60 and 6 x 12 is 72, and they don’t have other factors in common that are higher than 12.
This means that 12 is the answer, bc it’s the largest number of students that a team could have, in both the fourth and third grades.
21) Kinzang is 1.49 m tall. He was 0.53 m at birth. How much did he grow?
Answers
Kinzang grew 0.96 meters.
We have,
To find how much Kinzang grew, we need to subtract his height at birth from his current height:
Height Kinzang grew = Current height - Height at birth
Height Kinzang grew = 1.49 m - 0.53 m = 0.96 m
Therefore,
Kinzang grew 0.96 meters.
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What is the inverse function of (2)
2
?
Answers
a,b,c,and d
Step-by-step explanation:
there came a time, when a child cheated on their math work. getting the answers they needed wasnt all
they needed someone to make them feel terrible abuot it
and thats what im here to do
PICK ALL OF THEM
MASH YOUR COMPUTER
The length of the diagonal of the square is approximately hi many feet?
Answers
The diagonal of a square is given by:
\(d=a\sqrt{2}\)where a = 6 ft.
Hence:
\(d=6\sqrt{2}=8.48\)ANSWER
The diagonal is aproximately 8.48 ft
I WILL MARK YOU BRAINLIEST!!
Which table shows a proportional relationship between x and y?
x 1 2 5 7
y 5 10 25 35
Answers
Answer:
Yes
Step-by-step explanation:
There is a proportional relationship between x and y it's 5.
Think about it when x is 1 y is 5
When x is 2 y is 10
When x is 5 y is 25
When x is 7 y is 35
To get this for this question all you have to do is multiply x by 5 to get y.
That's how you know it's proportional.
Hope this helps!!!
Answer: it’s x5
If I have a table (model) I would spilt it in half and mark one half “y” and the other “x”. I would put 1, 2, 5, 7 for the x side and 5, 10, 25, 35 for the y side. U see if it makes it easier 1 x 5=5, 2 x 5=10, 5 x 5=25, 7 x 5=35. Do u get it?
Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter the scale factor as a fraction in simplest form.
The circles are similar because the transformation rule (_ , _) can be applied to Circle 1 and then dilate it using a scale factor of (_/_)
Answers
Answer
its scale factor is 4/3 and 0.75
Step-by-step explanation:
what is b+b+b+b-b simplified
Answers
Answer:
5b* because we have no idea what it could stand for
Answer:
5b
Step-by-step explanation:
However many b's there are that's your number so in this case its 5 and then you just add be to it so 5b
The side of a cube is measured as 11.4 centimeters with a possible error of + - (positive and negative) 0.04 centimeters. Give an estimate for the possible error in the value of the volume of the cube.
Answer: _________ cubic cm
Answers
Answer:
The volume of a cube is given by the formula V = s^3, where s is the length of a side of the cube. In this case, the length of a side is 11.4 centimeters with a possible error of + - 0.04 centimeters.
To find the possible error in the value of the volume of the cube, we can use the formula for the maximum error in a product:
max error in V = |V| * (max error in s / s)
where |V| is the absolute value of the volume, and max error in s is the maximum possible error in the measurement of the side.
Substituting the given values, we get:
max error in V = |11.4^3| * (0.04 / 11.4)
max error in V = 538.516 * 0.00351
max error in V = 1.89 cubic centimeters (rounded to two decimal places)
Therefore, the estimate for the possible error in the value of the volume of the cube is 1.89 cubic centimeters
A group of cyclists recorded the distance they have traveled.
Draw a line plot and answer the questions below.
Name
Gina
Rey
Faye
Mark
John
James
Albert
William
Nathan
Kate
Mary
Risa
Paul
Abi
Joan
Distance in
miles
40 1/2
50
35 3/4
60
45
55 1/4
60
45
40 1/2
50
45
40 1/2
60
40 1/2
35 3/4
Title:
1. How many cyclists were there?
2. What was the longest distance traveled?
3. How many cyclists traveled less than 50 miles?
4. What was the most common distance traveled by
the cyclists?
5. How many more cyclists traveled 45 miles than
55 1/4 miles?
6. How many cyclists traveled more than 45 miles
Answers
A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.
The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.
Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.
Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.
A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
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A man deposited 350 in his account in the bank.a simple interest of 4 percent per annum was paid on his deposit.calculate the total amount at the end of 4 years?
Answers
The total amount payable at the end of 4 years is 406
In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.
here we have to apply the formulla of simmple interest :
(principal × rate of interest × no. of years )/ 100
In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4
Simple interest = pnr/100
= (350 × 4 × 4)/100 = 56
Matured Amount = Principal + Interest
= 350 + 56 = 406
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(12²-15+17)+16= what is the answer
Answers
162
Step-by-step explanation:
(12 square - 15 + 17) + 16
=(144 - 15 + 17) + 16
=146 + 16
=162
What is the image point of (3, 6) after the transformation T0,-3 o R90°
Answers
Answer:
The image point of (3,6) after the transformation T0,-3 o R90° can be found by first applying the transformation T0,-3, which shifts the point 3 units to the right and 3 units down. This results in the point (6,-3). Then, the transformation R90° rotates the point 90 degrees counterclockwise around the origin. This results in the point (-3,6). Therefore, the image point of (3,6) after the transformation T0,-3 o R90° is (-3,6).
What is 6099 divided by 7
Answers
Answer:
The answer is 871.285. your welcome.
What is an equation of the line that passes through the point (2,-5) and is parallel
to the line 6x + y = 6?
Answers
Step-by-step explanation:
Hey there!
Given equation is; 6x + y= 6.
6x + y -6=0........……(i)
Slope (m1) = (-coefficient of X)/(coefficient. of y)
Slope (m1) = (-6)/(1)
Therefore, slope of the equation is -6.
As per the condition of parallel lines, slope of 1st equation is equal to 2nd equation.
Therefore, m1=m2= -6
The another straight line passes through the point (2,-5). So to find the equation, use one-point formula.
(i.e (y-y1) = m2(x-x1)).
So, the equation is;
(y+5) = m2(x-2)
Now, we know that m1=m2= -6. Let's keep its value on it.
y+5 = -6(x-2)
Or, y+5 = -6x +12
Or, 6x+ y -7 = 0
Therefore, the equation which is parallel to 6x + y= 6 equation and passes through the point (2,-5) is 6x+y-7=0.
Hope it helps...
Sarah, Lacey, and Mark stuffed envelopes with invitations for parents to an open house.
• Sarah stuffed 10 more envelopes than Lacey.
• Mark stuffed 3 less than twice as many envelopes as Lacey.
• Altogether they stuffed 503 envelopes.
If x represents the number of envelopes that Lacey stuffed, which equation BEST represents this situation?
x+10+2x−3=503
x+10x+3−2x=503
x+x+10+2x−3=503
x+x+10+3−2x=503
Answers
Answer: x+x+10+2x−3=503
Step-by-step explanation:
Let's define 3 variables:
S = # of stuffed envelopes by Sarah.
X = # of stuffed envelopes by Lacey.
M = # of stuffed envelopes by Mark.
S = 10 + X.
M = 2*X - 3.
X + S + M = 503.
Now we can replace the first two equations into the third equation:
X + (10 + X) + (2*X - 3) = 503.
Then the correct option is: x+x+10+2x−3=503
Now we can also solve the equation, just because it is fun:
X + 10 + X + 2*X - 3 = 503
4*X + 7 = 503
4*X = 503 - 7 = 496
X = 496/4 = 124
Lacey stuffed 124 envelopes.
For the same set of observations on a specified dependent variable, two different independent variables were used to develop two separate simple linear regression models. A portion of the results is presented below.
Based on the results given above, we can conclude that:_______.
A. A prediction based on Model 1 is better than a prediction based on Model 2.
B. A prediction based on Model 2 is better than a prediction based on Model 1.
C. There is no difference in the predictive ability between Model 1 and Model 2.
D. There is not sufficient information to determine which of two models is superior for prediction purposes.
Answers
Answer:
A. A prediction based on Model 1 is better than a prediction based on Model 2.
Step-by-step explanation:
Given :
Model 1 :
R² = 0.92
s = 1.65
Model 2 :
R² = 0.85
s = 1.91
The Coefficient of determination of the first model is 0.92 which is greater than the coefficient of determination of the Second model, the coefficient of determination gives the proportion of variation in the dependent variable which is caused by the regression line. Hence, we can say a prediction based on Model 1 is better than a prediction based on Model 2 because a larger proportion of the variation in the dependent variable is predictable from the independent variable.
calculate the following 2+2
Answers
Answer:4
Step-by-step explanation:
2+2 is 4
Pedro can drive 3 times as fast as Rico can ride his bicycleIf it takes Rico 2 hours longer than Pedro to travel 45 miles, how fast can Rico ride his bicycle ?
Answers
Given that Pedro can drive 3 times as fast as Rico can ride his bicycle and it takes Rico 2 hours longer than Pedro to travel 45 miles. We can find how fast Rico ride his bicycle below.
Explanation
\(\begin{gathered} rico\text{ speed =x} \\ Rico^{\prime}s\text{ }time=\frac{45}{x} \\ Since,\text{ }Pedro\text{ }can\text{ }drive\text{ }4times\text{ }as\text{ }fast\text{ }as\text{ }Rico\text{ }can\text{ }ride \\ Pedro^{\prime}s\text{ }speed=3x \\ Pedro^{\prime}s\text{ time =}\frac{45}{3x} \end{gathered}\)If it takes Rico 2 hours longer than Pedro to travel 45 miles,
\(\begin{gathered} Rico^{\prime}stime-Pedro^{\prime}stime=2hours \\ \frac{45}{x}-\frac{45}{3x}=2 \\ \mathrm{Multiply\:both\:sides\:by\:}x \\ \frac{45}{x}x-\frac{15}{x}x=2x \\ 45-15=2x| \\ 30=2x \\ x=\frac{30}{2} \\ x=15mph \end{gathered}\)Answer: 15mph
marking as brainlist pls help
Answers
Explanation:
For this problem, we can use the law of cosines to find the length C. We rearrange the formula for C and solve:
c^2 = a^2 + b^2 - 2ab cos(C)
c = sqrt(a^2 + b^2 - 2ab cos(C))
So for the values, use the following from our image:
a = 61
b = 63
C = 142 degrees
c = sqrt( 61^2 + 63^2 - 2(61)(63)cos(142))
c = sqrt( 3721 + 3969 - (-6056.65))
c = sqrt( 13746.65 )
c = 117.246
So, we have found the value of c to be 117.246.
To round to the nearest tenth, we will have 117.2
Cheers.
95% of what number is 114?
Answers
114 is 95% of 120
100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.
114 is 95 Percent of What Number?
Formula = Number x 100
Percent = 114 x 100
95 = 120
The following shows the steps to derive this formula and find out 95% of the number is 114.
Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.
114
95% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
95Y = 114 x 100
95Y = 11400
Y = 11400
100 = 120
Express each relation is a table, a graph, and mapping. Then determine the domain and range. 2. {(0,4), (-4,-4), (-2,3), (4,0)}
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the relation
{(0,4), (-4,-4), (-2,3), (4,0)}
Determining the table:
x y
0 4
-4 -4
-2 3
4 0
Mapping
X Y
0 → 4
-4 → -4
-2 → 3
4 → 0
It is clear from the table and mapping that the given relation is a function because each input has exactly one output.
In other words, the given relation is a function because there is no duplicated or repeated x-value.
The graph is also attached below.
Determining the domain
We also know that the domain is the set of all the first elements or members of ordered-pairs.
First elements are also termed as x-coordinates.Thus, the domain of the function in ascending order.
Domain: {-4, -4, 0, 4}
Determining the range
We also know that the domain is the set of all the second-elements or members of ordered-pairs.
The second-elements are also termed as y-coordinates.Thus, the range of the function in ascending order.
Domain: {-4, 0, 3, 4}
Write an equation to find p, the number of pounds of food that an adult manatee can eat in d days?
Answers
Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.
Here,
Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d
Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.
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