Answers
Related Questions
Anthony was tracking the increasing number of animals in the zoo. at 9
a.m., there were 56 animals. at 11
a.m., there were 60 animals. if anthony made the function f(x) = 2x − 38, what would the 2 represent? the number of animals at midnight the rate at which the number of animals was increasing the length of time he recorded for the total change in the number of animals
Answers
It’s a little surprising that this question didn’t come up earlier. Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2). A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.
Answer:
2 would represent the rate at which the animals were increasing
Step-by-step explanation: This all comes back to the slope intercept form:
y = mx + b
2x is the slope, and the slope is the rate of which a point will increase or decrease.
How do you complete the square using fractions
Answers
we will complete the squaer for ax²+bx+c=0 regardless of the values of a,b, or c
we will factor it into a(x-h)²=r
so
first group x terms
(ax²+bx)+c=0
factor out a
[tex]a(x^2+\frac{b}{a}x)+c=0[/tex]
take 1/2 of the linear coefinet and squaer it
[tex]\frac{1}{2} \space\ of \space\ \frac{b}{a}=\frac{b}{2a}[/tex] square it to get [tex]\frac{b^2}{4a^2}[/tex]
add positive and negative of that inside parntheasees
[tex]a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2})+c=0[/tex]
factor perfect square
[tex]a((x+\frac{b}{2a})^2-\frac{b^2}{4a^2})+c=0[/tex]
expand
[tex]a(x+\frac{b}{2a})^2-\frac{b^2}{4a}+c=0[/tex]
and that's how you complete the square, just move the constants over to the left when you're done then divide both sides by a then square root both sides, remembering to take the positive and negative roots
Completing the square with fractions involves transforming the quadratic equation into a perfect square trinomial by adding the square of half the coefficient of x to both sides. This enables solving the equation more easily by then taking the square root of both sides and isolating x.
Completing the square using fractions involves a few steps tailored to work with fractional coefficients. To make it understandable, let's explain the process step by step:
Start with the quadratic equation and ensure it is in the form ax2 + bx + c = 0.Divide all terms by 'a' (the coefficient of x2) if 'a' is not equal to 1, to make the coefficient of x2 equal to 1.Rearrange the equation so that the constant 'c' is on the other side of the equation.Take half of the coefficient of x, which is now 'b/a', and square it. This value is added both sides of the equation to form a perfect square on one side.Rewrite the left side of the equation as a squared binomial.Finally, solve for x by taking the square root of both sides and then add or subtract the constant term.For example, let's complete the square for the equation x2 + (3/2)x = 4. We take half of the coefficient of x, (3/2)/2 or 3/4, and square it to get 9/16. Adding 9/16 to both sides gives us (x + 3/4)2 = 4 + 9/16. Simplify the right side to get a single fraction, and then proceed to solve for x. Additionally, in some scenarios, we might need to multiply both the numerator and denominator by a skillfully chosen factor, such as 1/2, to facilitate simplifying or cancelling out terms.
Find the 5th term in the expansion of (x – 3y)8
Answers
Then, you can use combination method:
C(8,3) * (-3)^5 = -13608
So, 5th term is -13608x^3y^5
[tex]\bf (x-3y)^8\implies \begin{array}{llll} term&coefficient&value\\ -----&-----&-----\\ 1&&(x)^8(-3y)^0\\ 2&+8&(x)^7(-3y)^1\\ 3&+28&(x)^6(-3y)^2\\ 4&+56&(x)^5(-3y)^3\\ 5&+70&(x)^4(-3y)^4 \end{array}[/tex]
now... hmmm notice... the first term in the binomial, starts off with a highest exponent of 8, in this case, and the exponent gradually goes down by 1 in each term
whilst for the second term in the binomial, is the opposite, starts off with an exponent of 0, and the exponent gradually goes up in each element
to get the coefficients for the expansion.... well, notice, the coefficient for the expanded 2nd element is always the exponent of the binomial, in this case 8
now, the next element's coefficient is, "the current coefficient, times the exponent of the first term, divided by the exponent of the second term in the next element"
to make it less muddy.... hmmm how did we get +28 for the 3rd element?
well, 8*7/2, coefficient * (first term's exponent) / (second term's exponent on following element)
how did we get 70 for the 5th term?
well 56*5/4
[tex]\bf 70(x)^4(-3y)^4\implies 70x^4[(-3)^4y^4]\implies 70x^4[81y^4]\implies +5670x^4y^4[/tex]
Evaluate f(x)= -x^2+1 for x=-3
A.4
B.-4
C.-8
D.-9
Answers
then
f(-3) = -(-3)^2+1 = -9 + 1 = -8
answer
C.-8
-(-3)^2+1
First apply the exponent.
-3^2=9
-(9)+1
Then add.
-9+1=-8
Final answer:C
What do the parallel lines shown on segment BD and segment DC represent?
Answers
it means both sections are equal.
so BD = 18 and DC = 18
Step by step on how to solve that equation
Answers
Add 5 to both sides
(1/4)x=13
Multiply both sides by 4
x=52
Final answer: x=52
x/4 -5 = 8
Common denominator 4
[(x) - (5)(4)]/4 = (8).(4)/4 → (x-20)/4 = (8).(4)/4
multiply both sides by 4:
x -20= 32 →→ x = 52
Denise is a professional swimmer who trains, in part, by running. she would like to estimate the average number of miles she runs in each week. for a random sample of 20 weeks, the mean is = 17.5 miles with standard deviation s = 3.8 miles. find a 99% confidence interval for the population mean number of miles denise runs. use a graphing calculator for this one and not the t chart from the book.
Answers
n = 20, sample size
xbar = 17.5, sample mean
s = 3.8, sample standard deiation
99% confidence interval
The degrees of freedom is
df = n-1 = 19
We do not know the population standard deviation, so we should determine t* that corresponds to df = 19.
From a one-tailed distribution, 99% CI means using a p-value of 0.005.
Obtain
t* = 2.8609.
The 99% confidence interval is
xbar +/- t*(s/√n)
t*(s/√n) = 2.8609*(3.8/√20) = 2.4309
The 99% confidence interval is
(17.5 - 2.4309, 17.5 + 2.4309) = (15.069, 19.931)
Answer: The 99% confidence interval is (15.07, 19.93)
Using a 99% confidence level and the given data, the confidence interval for Denise's average weekly running mileage can be calculated using the sample mean, standard deviation, and z-score for the confidence level.
Explanation:Denise, a professional swimmer, uses her running mileage as part of her training analysis. To estimate the population mean for the number of miles she runs weekly, we will calculate the 99% confidence interval using the sample mean and standard deviation from her 20 weeks of data. The formula for a confidence interval is:
CI = mean ± (z* × (s/sqrt(n)))
Where mean is the sample mean, z* is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
The given data for Denise's running mileage is a mean (μ) of 17.5 miles and standard deviation (s) of 3.8 miles with a sample size (n) of 20 weeks. Since the sample size is greater than 30, we can use the z-distribution to approximate the t-distribution.
To find the appropriate z-score for a 99% confidence interval, we can use a graphing calculator or a z-table. The z-score for a 99% confidence level is approximately 2.576. Plugging the values into the confidence interval formula:
CI = 17.5 ± (2.576 × (3.8/sqrt(20)))
Calculating the margins of error and applying them to the sample mean, we will obtain the confidence interval for the average number of miles Denise runs in a week.
A data set has the following characteristics: Mean: 4.9 Median: 6 Mode: 6 Variance: 4 The z-score is the number of
Answers
Answer:
Standard deviations and mean
Step-by-step explanation:
Answer:
I.
standard deviations
mean
II.
-1.95
0.05
0.8
Step-by-step explanation:
I.
The z-score is the number of standard deviations a data value is away from the mean.
II.
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
Solve this equation using an algebraic method: (x + 4)( x - 4) = 9
Help me out please
Answers
[tex](x+4)(x-4)= x^{2} -4x+4x-16= x^{2} -16[/tex]
Now if you move the 9 over with it, you get this:
[tex] x^{2} -16-9=0[/tex]
which simplifies to
[tex] x^{2} -25=0[/tex]
Now you can either solve this by recognizing that is the difference of perfect squares, or you can move the 25 over to the other side and take the square root of both sides, like this:
[tex] x^{2} =25[/tex]
[tex] \sqrt{ x^{2} } = \sqrt{25} [/tex]
[tex]x=+/-5[/tex]
How to determine if a series has a sum?
Answers
It can be written mathematically, such that there exists a term k for which the sum from k to infinity is bounded, but you may not need all the jargon.
Again, make sure there was not an assumption about a specific type of series, like geometric, which is the one considered in the other answer
A certain bag of potting soil is 1/4 peat moss,and the rest is dirt. What part is dirt?
Answers
4/4-1/4
3/4
So 3/4 bag is dirt.
The part of the bag that consist of dirt is:
3/4
Step-by-step explanation:It is given that the amount of peat moss that is present in a bag of potting soil is:
1/4
Hence, the remaining space that is left in the bag consist of dirt.
Remaining space is calculated as :
[tex]1-\dfrac{1}{4}\\\\\\=\dfrac{3}{4}[/tex]
( Since we subtract 1/4 from a whole of a bag)
Hence, the part that is dirt in the bag of potting soil is:
3/4
Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, vertex B' has coordinates (5, ?).
Answers
Let OB be the radius of circle with center O.
Let B' be the image of B after the described rotation
OB and OB' are sides of the equilateral triangle OBB'.
The x coordinate of B' is the midpoint of OB, that is 5.
In the right triangle B', point (5, 0) and B:
Distance point (5, 0) to B is 5
|B'B|=|OB|=10
so by the pythagorean theorem:
[tex]a= \sqrt{ 10^{2} - 5^{2} } = \sqrt{ 2^{2} *5^{2} - 5^{2} }= \sqrt{5^{2}(4-1)}=5 \sqrt{3} [/tex] units
Answer: [tex]5 \sqrt{3}[/tex]
A line with a slope of 4 passes through (6, 11). Which choice is an equation of this line?
Answers
Use the equation y = mx + c
11 = 4(6) + c
11 = 24 + c
c = (11 - 24) = -13
Therefore the equation is y = 4x - 13
Hope it helped!
Answer:PLEASE MARK AS BRAINIEST
y – 11 = 4(x – 6)
Kris wanted to understand whether studentstudents at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
In favor
Opposed
Undecided
Grade 9
6
4
8
Grade 10
10
11
9
Grade 11
12
15
11
Grade 12
15
6
14
If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?
Answers
Answer:
The probability that the student is opposed to extending the school day is 0.3666 or 36.67% approx.
Step-by-step explanation:
Arranging the table properly and adding a column of total students.
In favor Opposed Undecided Total students
Grade 9 6 4 8 18
Grade 10 10 11 9 30
Grade 11 12 15 11 38
Grade 12 15 6 14 35
If the principal randomly selects a student in grade 10 from this survey, this means we will only consider grade 10 students.
The probability that the student is opposed to extending the school day is = [tex]\frac{number of opposed students}{total number of students}[/tex]
There are 11 students who are opposed and total students in grade 10 are 30.
So, probability is : [tex]\frac{11}{30}= 0.3666[/tex] or 36.67% approx.
Line k is the perpendicular bisector of (line)PQ. If line k intersects (line)PQ at point R, which of the following statements must be true?
check all that apply
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
D. Point R is the midpoint of line k
E. Line k is parallel to PQ
Answers
A B C are correct
|
|
_____|_____
|
Answer:
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
Step-by-step explanation:
A perpendicular bisector of a line is a segment that cuts right in the middle a line, and that segment forms a 90º degree angle with the line. This means that the point where the segment cuts the line would be exactly the half, making both resultant segments on the line congruent. So the options that are correct are ABC.
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
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The formula v = (radical)64h can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
A ) 184 feet per second
B ) 306.93 feet per second
C ) 38.37 feet per second
D ) 736 feet per second
Answers
V = sqrt (64 * 23)
V = sqrt 1472
V = 38.366 rounds to 38.37 ft <==
Answer:
The answer is the option C
[tex]V=38.37\ ft/sec[/tex]
Step-by-step explanation:
we have that
[tex]V=\sqrt{64h}[/tex]
In this problem we have
[tex]h=23\ ft[/tex]
Substitute in the formula and solve for V
[tex]V=\sqrt{64(23)}[/tex]
[tex]V=\sqrt{1,472}\ ft/sec[/tex]
[tex]V=38.37\ ft/sec[/tex]
4x-5=4x+10 solve for x
Answers
The equation 4x - 5 = 4x + 10 has no solution because subtracting 4x from both sides yields -5 = 10, which is a contradiction.
Explanation:The equation 4x - 5 = 4x + 10 cannot be solved for x in the usual way because attempting to isolate x on one side will result in a contradiction. If we subtract 4x from both sides of the equation, we get -5 = 10, which is not true for any value of x. Therefore, this equation has no solution.
HELP ROUND 604703.472883 TO THE NEAREST HUNDRED
Answers
Answer:
The required number is 604703
Step-by-step explanation:
Consider the provided number 604703.472883
The rule for rounding a number is:
If the number on the right side of rounding digit is 0, 1, 2, 3, 4 then no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
If the number on the right side of rounding digit is 5, 6, 7, 8, 9 then rounding digit rounds up by one number and change the rest of the digit right to rounding digit with 0.
The number on the hundred place is 7 and the number on right side is 0.
Thus, no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
Hence, the required number is 604703
How many ways can we put 7 adults and 3 kids in line (where order matters) so that no two kids are next to each other?
Answers
7P3
=210
There are more than 210 ways we can do this.
Could someone show me the work for 1/2 divided by 2/3 x 3/4
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If 5+3+2=151012, 9+2+4=183662, 8+6+3=482466, 5+4+5= 202504 , then 7+2+5= ?
a.141035
b.143510
c.143542
d.143524
Answers
Alyosha and Ivan are standing between two buildings they know to be equal height. The buildings are 500 feet apart. Looking up at the westernmost building, they form a 30 degree angle. Looking to the northeastern building, they form a 45 degree angle.
A) Ivan guesses they are halfway between the buildings. Why is this a bad guess?
B) How far away from each building are they?
Answers
h = height of each building
x = distance from the left building
y = distance from the right building
Because the distance between the buildings is 500 feet, therefore
x + y = 500 (1)
By definition,
tan 45° = h/y = 1
y = h (2)
Also,
tan 30° = h/x = 1/√3
x = h√3 (3)
Part (a)
If Alyosha and Ivan were halfway between the building, then x = y.
Because x ≠ y, they are not halfway between the buildings.
Part (b)
From (1), (2) and (3), obtain
h + h√3 = 500
h(1+√3) = 500
2.732h = 500
h = 183.0 ft
Therefore
x = 183.0 ft
y = 500 - x = 317.0 ft
Answer:
Alyosha and Ivan are 183 feet from the left building, and 317 feet from the right building.
A science experiment begins with a metal at −100° Celsius. The following function describes the temperature change per minute: f(x) = 89x − 100°. How will the graph of this function change if the metal is at 25° at the start of the experiment?
Answers
f ( x ) = 89 x - 100°.
This is the graph of a linear function in the slope-intercept form:
y = m x + b
Starting point is - 100°, so b = - 100°
If the metal is at the temperature of 25° at the start of experiment, then it would be: b = 35°
The new equation: g ( x ) = 89 x + 25°
g ( x ) || f ( x ) ( parallel functions ), 25° - ( -100° ) = 125°
Answer: The graph of the function will translate vertically 125° up.
Answer:
A
Step-by-step explanation:
Jacobysontop!
Use Gauss-Jordan elimination to solve the following linear system.
x – 2z = 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
A. (–5,–3,0)
B. (3,2,–3)
C. (5,3,–5)
D. (3,6,–4)
Answers
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
multiply (1st) equation by 5 and (2nd) equation by 2
-10y + 35z = - 125
10y - 14z = 62
-----------------------add
21z = - 63
z = -3
substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
answer
B. (3, 2, –3)
By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.
What is Gauss-Jordan's elimination method?
In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.
x – 2z = 9 so x = 2z + 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
Multiply (1st) equation by 5 and (2nd) equation by 2.
-10y + 35z = - 125
10y - 14z = 62
21z = - 63
z = -3
Substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
Substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.
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I I'm not good with math
Answers
a) total cost = 499 + 49.99x
b) x = 5 games
total cost = 499 + 49.99(5) = 499 + 249.95 = 748.95
8/3 , 2.28, 10/12 , 0.199 what number in the list above has the greatest value?
Answers
2.28
10/12 = 0.833
0.199
greatest value is : 8/3
Answer:
[tex]\frac{8}{3}[/tex] is the greatest value.
Step-by-step explanation:
The given numbers are [tex]\frac{8}{3}[/tex], 2.28, [tex]\frac{10}{12}[/tex], 0.199
In this question we have to find out greatest value.
So, first we convert all the values in decimals.
To convert [tex]\frac{8}{3}[/tex] in decimal form, we divide 8 by 3. The answer would be 2.67
2.28
[tex]\frac{10}{12}[/tex] = 0.83
0.199
Now we arrange these numbers in the increasing order.
0.199 < 0.83 < 2.28 < 2.67
So the greatest number is 2.67 that is [tex]\frac{8}{3}[/tex].
A quadratic equation is shown below:
9x2 − 16x + 60 = 0
Describe the solution(s) to the equation by just determining the radicand. Show your work.
: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
Answers
hello :
help :
the discriminat of each quadratic equation :
ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x =
(-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
We generally report a measurement by recording all of the certain digits plus ______ uncertain digit(s).
Answers
We generally report a measurement by recording all of the certain digits plus one uncertain digit.
What are significant figures?In positional nomenclature, a number's real numbers are its dependable and essential digits for indicating how much of something there is.
If a measurement's result is expressed by a number with more digits than the measurement resolution permits, only those digits up to the measuring resolution's maximum are trustworthy, and only those digits could be significant figures.
Typically, we record all the confirmed digits of measurement together with one questionable digit.
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For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range. The vertex is (3, –1), the domain is all real numbers, and the range is y ≥ –1. The vertex is (3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≥ –1.
Answers
we have
[tex]f(x)=-2(x+3)^{2}-1[/tex]
we know that
the equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
[tex](h,k)[/tex] is the vertex
If [tex]a > 0[/tex] ------> then the parabola open upward (vertex is a minimum)
If [tex]a < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
In this problem
the vertex is the point [tex](-3,-1)[/tex]
[tex]a=-2[/tex]
so
[tex]-2 < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
The domain is the interval-------> (-∞,∞)
that means------> all real numbers
The range is the interval--------> (-∞, -1]
[tex]y\leq-1[/tex]
that means
all real numbers less than or equal to [tex]-1[/tex]
therefore
the answer is
a) the vertex is the point [tex](-3,-1)[/tex]
b) the domain is all real numbers
c) the range is [tex]y\leq-1[/tex]
see the attached figure to better understand the problem