Answers
Related Questions
Pls help help Algebra1 due today
Answers
The quadratic function that models the number of mosquitoes is:
\(M(t) = -3/2t^2 + 21/2t\) and the quadratic function that models the number of mosquitoes in vertex form is: \(M(t) = -3/2(t - 7)^2 + 24.5\)
What is quadratic function?A quadratic function is a type of mathematical function that can be written in the form:
\(f(x) = ax^2 + bx + c\)
where a, b, and c are constants and x is the variable.
The number of mosquitoes, M, can be modeled as a quadratic function of the number of days, t. We can use the given information to set up a system of equations and solve for the coefficients of the quadratic function.
Let \(M(t) = at^2 + bt + c\) be the quadratic function that models the number of mosquitoes, where a, b, and c are constants to be determined.
From the given information, we have:
M(1) + M(2) + M(3) = 21
M(2) + M(3) + M(4) = 15
M(3) + M(4) + M(5) = 21
Substituting M(t) into these equations, we get:
a + b + c + 4a + 2b + c + 9a + 3b + c = 21
4a + 2b + c + 9a + 3b + c + 16a + 4b + c = 15
9a + 3b + c + 16a + 4b + c + 25a + 5b + c = 21
Simplifying these equations, we get:
14a + 4b + 3c = 21
29a + 5b + 2c = 15
50a + 9b + 3c = 21
We can solve this system of equations to get a = -3/2, b = 21/2, and c = 0. Therefore, the quadratic function that models the number of mosquitoes is:
\(M(t) = -3/2t^2 + 21/2t\)
To write the quadratic function in vertex form, we can complete the square. The vertex form of a quadratic function is:
\(M(t) = a(t - h)^2 + k\)
where (h, k) is the vertex of the parabola. We can find the vertex by using the formula h = -b/2a and k = M(h).
Plugging in the values of a and b, we get:
\(h = -b/2a = -21/(2*(-3/2)) = 7\)
\(k = M(h) = M(7) = -3/2(7)^2 + 21/2(7) = 24.5\)
Therefore, the quadratic function that models the number of mosquitoes is:
\(M(t) = -3/2t^2 + 21/2ft\)
and the quadratic function that models the number of mosquitoes in vertex form is:
\(M(t) = -3/2(t - 7)^2 + 24.5\)
To learn more about quadratic function visit:
https://brainly.com/question/1214333
#SPJ1
Complete question:
POints XD helpppppp
Simplify (x2 • x4)3. Explain your steps
Answers
(8x^2)3
8x^2•3
24x^2
the variables x and y are related proportionally.
When x = 8, y = 20. Find y when x = 42.
Answers
Answer:
y = 2.5(42)
Step-by-step explanation:
Find the solution for the system of linear equations by graphing: y=x
Y=2x -4
Answers
Answer:
x and y = 4
Step-by-step explanation:
Since y=x ---> x=2x-4
-x -x
0=x-4
+4 +4 ------------------> Therefore, x= 4 and y= y
If you could graph both lines you would find they intersect at (4,4)
Answer:
(4,4)
Step-by-step explanation:
A group of 23 friends are at the theater but can't agree on which movie to see. some of the group decides to see lightyear which is playing for $4 per ticket and the rest of the group decides to see jurassic park which is playing for $9 per ticket. altogether the group spends $172, how many of them saw lightyear?
Answers
The number of people who watched light year are 7.
Let x= number of friends that watches light year
and y= number of friends that watches jurassic park.
Let the equations be
All together total cost => 4x+9y=172 ------> 1
And total number of people=> x + y=23 ------> 2
By multiplying both equations by 1 and 4 respectively we can get,
By Solving above two equations we get, x=7 and y=16
As X represents number of friends that watches light year, the answer is 7
Therefore, number of people that watches light year will be 7.
To learn more about light year click here:
brainly.com/question/27046045
#SPJ4
M<1=3x+7, m<5=5x-3. Find the value of each variable.
Answers
Answer: x=5
Step-by-step explanation:
To find the value of x, we set the measures of 1 and 5 equal to each other.
3x+7=5x-3 [subtract both sides by 5x]
-2x+7=-3 [subtract both sides by 7]
-2x=-10 [divide both sides by -2]
x=5
Now, we know that x=5.
a $12$-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. only six slices have pepperoni, and exactly ten slices have mushrooms. how many slices have both pepperoni and mushrooms?
Answers
The terms with "x" cancel out, and we're left with:
0 = 12
6 + 10 + x + (12 - (6 + 10 + x)) = 12
Simplifying the equation, we have:
16 + x - (16 + x) = 12
The terms with "x" cancel out, and we're left with:
0 = 12
Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.
Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:
Slices with only pepperoni: 6 slices
Slices with only mushrooms: 10 slices
Slices with both pepperoni and mushrooms: $x$ slices
Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices
We know that the total number of slices is 12, so we can write an equation:
6 + 10 + x + (12 - (6 + 10 + x)) = 12
Simplifying the equation, we have:
16 + x - (16 + x) = 12
The terms with "x" cancel out, and we're left with:
0 = 12
This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.
learn more about equation here:
https://brainly.com/question/29538993
#SPJ11
Write x^2+5x-7 in the form (x+a)^2+b.
Answers
Answer: −x2+
5
x
=
7
Move
7
to the left side of the equation by subtracting it from both sides.
−
x
2
+
5
x
−
7
=
0
Once the quadratic is in standard form, the values of
a
,
b
, and
c
can be found.
a
x
2
+
b
x
+
c
Use the standard form of the equation to find
a
,
b
, and
c
for this quadratic.
a
=
−
1
,
b
=
5
,
c
=
−
7
Step-by-step explanation:
Need this answered.
Please Show work, Thanks! :)
Answers
Answer:
A
Step-by-step explanation:
i use the foil method
you can find more information on yt
Bequests to Charity : At the time our mother left this Earth, she gave Rs 90000 to her children of birth. This we kept and each year added Rs 30000 more, as a lasting memorial from the children she bore. When Rs 4,20,000 is thusly attained, all goes to charity that her memory be maintained. (i) What was the balance in the sixth year? (ii) In what year was the goal of Rs 420,000 met
Answers
The amount after 6 yesrs and number of years to meet the goal of Rs 420,000 will be 2,250,000 and 0.9167 yesrs, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of months and 'y' be the total amount. Then the equation is given as,
y = 90,000 + 30,000 x
The amount after 6 yesrs is given as,
y = 90,000 + 30,000 (6 × 12)
y = 90,000 + 2,160,000
y = 2,250,000
The number of years to meet the goal of Rs 420,000 is given as,
420,000 = 90,000 + 30,000 x
30,000x = 330,000
x = 11 months
x = 11 / 12
x = 0.9167 years
The amount after 6 yesrs and number of years to meet the goal of Rs 420,000 will be 2,250,000 and 0.9167 yesrs, respectively.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
What is the prime factorization of 50? (Please Explain)
Answers
Answer:
So, the prime factors of 50 are 2 × 5 × 5 or 2 × 52, where 2 and 5 are the prime numbers.
Answer:
The prime factorization of 50 is \(2 * 5^{2} \)
Step-by-step explanation:
The prime numbers of 50 are 2 and 5 So, 2 x 5 x 5 = 2 x 25 = 50\(2 * 5^{2}\) = 50the sum of the first three terms of a sequence Is 42 The fourth term is 24. find u1 and the common difference
Answers
\(10=2d\)
Given:
The sum of the first three terms of a sequence Is 42.
The fourth term is 24.
To find:
The u₁ and the common difference
Step-by-step explanation:
nth term of a sequence is
\(u_n=u_1+(n-1)d\)
where, u₁ is first term and d is common difference.
4th term is 24.
\(u_4=u_1+(4-1)d\)
\(24=u_1+3d\) ...(i)
Sum of nth term of an AP is
\(S_n=\dfrac{n}{2}[2u_1+(n-1)d]\)
Sum of first three terms is 42.
\(S_3=\dfrac{3}{2}[2u_1+(3-1)d]\)
\(42=\dfrac{3}{2}[2u_1+2d]\)
Divide both sides by 3.
\(14=u_1+d\) ...(ii)
On subtract (ii) from (i), we get
\(10=2d\)
\(5=d\)
Put d=5 in equation (ii).
\(14=u_1+5\)
\(14-5=u_1\)
\(9=u_1\)
Therefore, the first term is \(u_1=9\) and common difference is \(d=5\) .
Please help!! Very important
Answers
Answer:
A
Step-by-step explanation:
the decreasing part is where is line goes downward. So it's A
Sonya made a graph showing the first ten minutes of her drive to the movies.
A graph with time on the x-axis and speed on the y-axis. The graph increases, increases rapidly, and then remains constant.
Which description is the best interpretation of the graph?
Answers
Answer: answer will be A
Step-by-step explanation:
Answer:A
Step-by-step explanation: sub to my yt clizey
Joy's math certificate is 10 inches tall and 13 inches wide. Joy wants to put the certificate in a fancy frame that costs $3.00 per inch. How much will it cost to frame Joy's math certificate?
Answers
In perimeter, The cost to frame Joy's math certificate in a fancy frame is $138.00.
The dimensions of Joy's math certificate are 10 inches tall and 13 inches wide.
Joy wants to frame it in a fancy frame that costs $3.00 per inch.
To determine the total cost of framing the certificate, we need to find its perimeter and then multiply that by the cost per inch.
The perimeter of the certificate is:
Perimeter = 2 × (height + width)
Substituting the given values, we get:
Perimeter = 2 × (10 + 13)Perimeter = 46 inches
Therefore, the total cost of framing Joy's math certificate is:
Total cost = Perimeter × Cost per inch
Total cost = 46 × 3.00Total cost = $138.00
Thus, the cost to frame Joy's math certificate in a fancy frame is $138.00.
Know more about perimeter:
https://brainly.com/question/30252651
#SPJ11
in how many ways can a committee of 20 members choose a president, a vice-president, and a secretary?
Answers
There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.
To choose a president, a vice-president, and a secretary from a committee of 20 members,
We will use the formula for combinations,
which is: C(n, k) = n! / (k! (n - k)!)
where n is the total number of members and k is the number of members being chosen.
So, for n = 20 and k = 1, we have:
C(20, 1) = 20! / (1! (20 - 1)!) = 20
This gives us 20 choices for the president.
For the vice president,
We need to choose 1 member from the remaining 19 members.
So, for n = 19 and k = 1,
we have:
C(19, 1) = 19! / (1! (19 - 1)!) = 19
This gives us 19 choices for the vice president.
Finally, for the secretary,
We need to choose 1 member from the remaining 18 members.
So, for n = 18 and k = 1,
we have:
C(18, 1) = 18! / (1! (18 - 1)!) = 18
This gives us 18 choices for the secretary.
Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:
So, the required number of ways will be 20 * 19 * 18 = 6840
For more questions on Permutation and Combination
https://brainly.com/question/30366889
#SPJ4
Find the area of the rectangle with a length of (5x + 4) and a width of (3x - 2).
Answers
Answer: the answer is 9x
Step-by-step explanation:
Would it be appropriate to display the data with a pie chart?
Yes, because the data are grouped into categories.
Yes, because the data can be represented by a relative frequency compared to the whole.
No, because the data add up to more than 100%.
No, because the data categories are too broad.
Answers
Answer: Yes, because the data are grouped into categories.
Step-by-step explanation:
What does it mean when they ask if the data distribution is good?
Answers
Answer:
data distribution: shows all possible values of data/probability of how often it occurs.
if it is good distribution, the data will be scattered equally in a way which allows you to easily come up with a conclusion upon analysis.
if distribution is poor, the data will not make sense basically.
sorry if this doesn't make sense, i tried to phrase it as best as i could, good luck x
Given circle P, which of the following options are major arcs? Select all that apply.
Answers
The major arc are arc (ABC), arc (DCB) and arc (DAB).
We know the length of arc as
= θ/260 x 2πr
and length of Arc α θ
So, θ made by arc (ABC) = 300
θ made by arc (DCB) = 300
θ made by arc (AC) = 60
θ made by arc (BAD) = 300
θ made by arc (BAC) = 180
Then, the major will whose angles is greater.
Here the angles with greater measurement is angle 300 degree.
θ made by arc (ABC) = 300
θ made by arc (DCB) = 300
θ made by arc (BAD) = 300
Thus, the major arc are arc (ABC), arc (DCB) and arc (DAB).
Learn more about Major Arc here:
https://brainly.com/question/29028287
#SPJ1
The question attached here seems to be inappropriate or incomplete, the complete question is
Given circle P, which of the following options are major arcs? Select all that apply.
ABCDCBACarc(BAD)BACWhich equation is shown in the graph?
02x-7y=29
© 2x+7y=9
02r+ 7y=-29
02r-7y=-29
Answers
The equation is shown in the graph is 2x - 7y = 29.
From the graph take two points as (3, 5) and (-4, 3).
Now, Slope of line
= (3-5) / (-4-3)
= (-2) / (-7)
= 2/7
Then, the equation of line is
(y - 5) = (3-5)/ (-4-3) (x - 3)
y -5 = 2/7 (x-3)
7y - 35 = 2x - 6
2x - 7y = 29
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ1
2♥ Next O Pretest: Trigonometric Functions
2
Select all the correct answers.
If the measure of angle is , which statements are true?
U
tan (0) = 1
cos (0) = √2
The measure of the reference angle is 45°.
sin (0) = √2
The measure of the reference angle is 30°.
The measure of the reference angle is 60°.
Reset
Next
Answers
Answer:
look at bullet points bottom left
Step-by-step explanation:
I did my best to show why these answers are correct for you.
Pls no gobolegook no noncenes plsss answer it right:-(
Answers
Answer:
1) Place value is hundreds; The value is 600
2) Place value is thousands; The value is 6 000
3) Place value is tens; The value is 60
4) Place value is millions; The value is 6 000 000
5) Place value is hundreds; The value is 600
Step-by-step explanation:
In the number 1 234 567,
7 is in the units place, then its place value is units and its value is 76 is in the tens place, then its place value is tens and its value is 605 is in the hundreds place, then its place value is hundreds and its value is 5004 is in the thousands place, then its place value is thousands and its value is 4 0003 is in the ten-thousands place, then its place value is ten-thousands and its value is 30 0002 is in the hundred-thousands place, then its place value is hundred-thousands and its value is 200 0001 is in the millions place, then its place value is millions and its value is 1 000 000Let us solve the question
1)
∵ The number is 545 674
∵ The digit 6 is in the hundreds place
∴ Place value is hundreds
∴ The value is 600
2)
∵ The number is 4 306 789
∵ The digit 6 is in the thousands place
∴ Place value is thousands
∴ The value is 6 000
3)
∵ The number is 457 567
∵ The digit 6 is in the tens place
∴ Place value is tens
∴ The value is 60
4)
∵ The number is 6 154 298
∵ The digit 6 is in the millions place
∴ Place value is millions
∴ The value is 6 000 000
5)
∵ The number 625
∵ The digit 6 is in the hundreds place
∴ Place value is hundreds
∴ The value is 600
charlie and zach are each making a scale drawing of the school garden. the garden measures 30ft by 12ft. charllie plans to use a scale of 1in:2ft. zach plans to use a scale of 2in:1ft.
Answers
Answer:
Charlie's diagram: 15 inches by 6 inches
Zach's diagram: 60 inches by 24 inches
Can you guys help me on the number 2 I’m really stuck
Answers
Answer:
we have to see question 1 to help with number two
Simplify the following expression using Boolean algebra and its identities. List the identity used at each step. x(yz
′
+x)(y
′
+z)
Answers
The expansion of Boolean algebra is x^2y + xzy' + xz^2
To simplify the expression using Boolean algebra and its identities, let's break it down step by step:
1. Distributive Property (x(yz' + x)(y' + z)): Distribute the x to both terms inside the first parentheses. xy' + x^2yz' + xy'z + xz
2. Distributive Property (xy' + x^2yz' + xy'z + xz)(y' + z): Distribute the second parentheses to all the terms inside. xy'y + x^2yz'y + xy'zy' + xzy' + xy'z + xz^2
3. Complement Law (xy'y = 0): Since y and y' are complements, their product is always 0. 0 + x^2yz'y + xy'zy' + xzy' + xy'z + xz^2
4. Simplification (x^2yz'y = x^2y): Combine like terms, as z'y + zy' = 1 (by the Complement Law). x^2y + xy'zy' + xzy' + xy'z + xz^2
5. Simplification (xy'zy' = 0): Since y and y' are complements, their product is always 0. x^2y + xzy' + xy'z + xz^2
6. Simplification (xy'z = 0): Since z and z' are complements, their product is always 0. x^2y + xzy' + xz^2
Learn more about Boolean algebra
https://brainly.com/question/2467366
#SPJ11
How can we find that when a system of two equations, two unknowns has Infinite Solutions. I want a solution with matrix. I know this method (which is not with matrix):
Answers
Step-by-step explanation:
To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.
In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.
he gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7. (a) What are the mean and standard deviation of the average number of moths ž in 60 traps? (b) Use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4.
Answers
The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.
(a) To find the mean and standard deviation of the average number of moths in 60 traps, we can use the properties of the normal distribution and the central limit theorem.
The mean of the average number of moths in 60 traps is equal to the mean of the individual moth counts, which is 0.5.
The standard deviation of the average number of moths in 60 traps is equal to the standard deviation of the individual moth counts, divided by the square root of the sample size.
standard deviation = 0.7 / sqrt(60) = 0.0905
the mean and standard deviation of the average number of moths in 60 traps are 0.5 and 0.0905, respectively.
(b) To use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4, we need to standardize the distribution of sample means using the Z-score formula:
Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the given values, we have:
Z = (0.4 - 0.5) / (0.7 / sqrt(60)) = -1.94
Using a standard normal table or a calculator with a normal distribution function, we can find that the probability of getting a Z-score greater than -1.94 is approximately 0.9738.
The probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738 or 97.38%.
To learn more about probability :
https://brainly.com/question/30034780
#SPJ4
Question attached through files! Can anyone help?? Thank you!
Answers
Answer:
(-1.732,0) and (1.732,0)
Step-by-step explanation:
Ignore f(x). The solutions are also called x-intercepts and zeros. So the solutions would be where the parabola crosses the x axis. In my answer ignore the 0 in the coordinates. Just put in the -1.732 and 1.732.
The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x. On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 2) and (0, 0). Everything to the right of the line is shaded. The second line has a negative slope and goes through (negative 2, 2) and (0, 0). Everything to the left of the line is shaded. Which symbol could be written in both circles in order to represent this system algebraically? y Circle x y Circle –x ≤ ≥
Answers
Answer:
C.<
Step-by-step explanation:
got it wrong on the exam review and it told me the right answer after.
Answer:
It is C. <
Step-by-step explanation:
edge 2021