M is the midpoint of AB. Q is the midpoint of AM. and T is the midpoint of QM. If the coordinates of A and B are a and b. find the coordinates of Q and T in terms of a and b.
Answers
The the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4].
What is Mid-point of a Line segment?
The mid-point of a line segment is a point on the line segment which divides it into two equal parts.
Given is a line segment AB whose mid-point is M with a and b being the coordinates of A and B respectively. Further, Q is the midpoint of AM and T is the midpoint of QM.
[Refer to the image attached for clear explanation]
Since M is the mid-point of AB, therefore the coordinates of point M will be = M [(a + b)/2]
Now, Q is the mid-point of AM. Therefore, the coordinates of Q will be =
[(a + b)/2 + a]/2 = Q [(3a + b)/4]
and
T is the mid-point of QM. Therefore, its coordinates will be =
(a + b)/2 + (3a + b)/4 = T [(5a + 3b)/4]
Hence, the the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4]
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Related Questions
You have 10 quarters that you can use for a parking meter.
a. Copy and complete: Each time you put 1 quarter in the meter, you have 1 less quarter, so ? is a function of ?
b. Write a rule for the number y of quarters that you have left as a function of the number x of quarters you have used so far. Identify the domain of the function.
c. Make a table and identify the range of the function.
Answers
a) "how many quarters you have is a function of how many times you paid for the parking meter."
b) y = 10 - x
domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c) table:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
How to complete the blanks?Here we know that you have a total of 10 quarters, and the parking meter costs 1 quarter.
Then, each time if we define two variables:
y = how many quarters you have.
x = how many times you paid for the parking meter.
We can write:
"y is a function of x"
Or:
"how many quarters you have is a function of how many times you paid for the parking meter."
b) The rule is really simple, it would be a linear relation:
y = 10 - x
The domain (the set of possible values of x) is:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
You can't use less than 0 quarters and you can't use more than 10.
c) The range is also:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Which represents the possible numbers of quarters that you can have.
And the table will be:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
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Which of the following statements represents a function?
A. Students of their current age?
B. Countries to its capital?
C. A store to its merchandise
D. Teacher and student’s relationship
Answers
Answer:
B
Step-by-step explanation:
Capitals represents countries as the function
Susie saved up her money and bought a model train. Rack of the 8 cars on the train were the same length. When Susie put all the trains together the train was 3 feet long. How long was each car?
Answers
In linear equation , length of each car =.375 feet.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Rack of the cars on the train were the same length = 8
train was 3 feet long.
length of each car = 3/8 = .375 feet
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How is subtracting integers related to adding integers
Answers
Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.
Are there any consistent rules for adding and subtracting integers?
Integer addition and subtraction formulas: 1) Subtract the two numbers and indicate the sign of the larger number if the two numbers have different signs, such as positive and negative. 2) Add the two numbers and give the common sign if the two numbers have the same sign, that is, either positive or negative signs.What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Learn more about integer
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Question 6 (10 points)
=) Listen
The ratio of outdoor outdoor swimmers to indoor swimmers at the recreation center
is 3:2. If the center has 55 swimmers altogether, how many of them are indoor
swimmers?
22
44
none
33
Answers
Answer:
22
Step-by-step explanation:
The ratio tells us 2/5 of the swimmers are indoor swimmers.
55(2/5)=22
Omar has 24 camival ride tickets and it takes 5 tickets to ride the roller coaster how many times can he ride the ride and how many tickets will have left over
Answers
Answer:
Omar can ride the roller coaster 4 times and will have 4 tickets leftover.
Step-by-step explanation:
For a more simple problem like this, long division is not necessary.
You may have learned the technique of finding how many times a divisor can "go in" to the dividend.
In this case, 5 (the cost of riding the coaster) can go into 24 (the amount Omar has) 4 times, because 5, 10, 15, 20. However, going in one more time puts us at 25, which Omar does not have, so 5 can only go into 24 5 times.
Since there is still 4 tickets leftover, Omar can ride the coaster 4 times, and will have 4 tickets left.
expressions that are equivalent to k/2
A: k-2
B: 2/k
C: 1/2 k
D: k/2
E: k+k
Answers
The correct option is D: k/2 is the expression that is equivalent to the expression, K/2.
What is defined as the equivalent expressions?Two equations are equivalent unless and until they produce the same result for all matching variable values. As a result, we can determine whether 2 expressions seem to be equivalent by putting in many distinct corresponding values of the variables to ensure that each expression returns the same value in every instance.If we enter matching variable values into two mathematical expressions and get a different result from each expression, the two expressions really not equivalent.In response to the question;
We must determine the expression that is equivalent to k/2.
Among the options, Option D: k/2 is same as expression K/2.
Choice C, when written as (1/2)k, is equivalent to k/2 since they both imply half of k.
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Please help, I don’t know how to solve this!
Answers
Fill in the blank set of stamps below with the value that would make the sets equal.
Answers
The number in each of the set of blank boxes is 10
How to find the number set equivalent?
From the first number set of stamps, we see that the sum of each row is;
5 + 5 + 5 + 5 = 20
There are four rows. Thus;
Total sum of set of stamps = 20 + 20 + 20 + 20
Total sum of set of stamps = 80
Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.
If the number in each box is x, then;
8x = 80
x = 80/8
x = 10
Thus, the number in each of the set of blank boxes is 10
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Can someone please help me with This question? I don’t understand it. Please and thank you I would really appreciate it!! :)
Answers
(A∩B)∪(A∩C) using roster method is as follows:
(A∩B)∪(A∩C) = {a, e, f}
What are sets?Sets are an organized collection of objects that can be represented in set-builder form or roster form.
Therefore,
The universal sets is as follows:
U = {a, b, c, d, e, f, g, h}
The subsets are as follows:
A = {c, e, f}
B = {a, e, f}
C = {a, b, d, g, h}
Therefore, let's find (A∩B)∪(A∩C) using roster method.
The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
Hence,
(A∩B) = {e, f}
(A∩C) = {a}
Finally,
(A∩B)∪(A∩C) = {a, e, f}
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mathematics [tex]what is the product of 17 and 41?[/tex]
Answers
Answer: 697
Step-by-step explanation:
17 * 41=
17 * (40+1)=
17 * 40 + 17 * 1=
17 * 10 * 4 + 17=
170 * 4 + 17=
680+17=697
What is the value of this expression if h 8, j = -1, and k = -12?
Answers
Value of the given expression j³k/h0 is 12
h = 8
j=-1
h = 8
In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0 ....(1)
Find the denominator by using (1)
(-1)³ (-12) / 1
Analyze each exponent.
= 12/1
Hence, j³k/h0 = 12
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Complete Question -
What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0
NO LINKS!! Please help me with these problems. Part 11a1
y = 3x^2
Answers
Domain: (−∞,∞) , {x|x ∈ R}
Range: [0,∞) , {y|y ≥ 0}
Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)
Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.
Intervals: both x and y start to increase from the origin
Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical
Answer:
Domain: (-∞, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain (-∞, ∞). Minimum stationary point (turning point) at (0, 0).Increasing function: (0, ∞)Decreasing function: (-∞, 0)Symmetry: Even (symmetry about the y-axis).Step-by-step explanation:
Given function:
[tex]y=3x^2[/tex]
DomainThe domain is the set of all possible input values (x-values).
The domain of the given function is unrestricted.
Therefore, the domain is (-∞, ∞).
RangeThe range is the set of all possible output values (y-values).
As x² ≥ 0, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain (-∞, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]
[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]
Therefore, the stationary point of the given function is (0, 0).
To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]
As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (0, ∞).The function is decreasing in the interval (-∞, 0).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As x² ≥ 0 and there is symmetry about the y-axis,
[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.
The formula for the nth number is Sn=n^2. Use the formula to find the 17th number.
The 17th number is
enter your response here. (Simplify your answer.)
Answers
The 17th term of the sequence is 289
How to determine the 17th term of the sequence?The nth term is given as
Sn = n^2
The 17th term of the sequence implies that
n = 17
So, we have
S17 = 17^2
Evaluate
S17 = 289
Hence, the 17th term of the sequence is 289
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Find the equation of a line whose graph passes through the points (8,1) and (0,1)
Answers
Answer: y=1
Step-by-step explanation:
Slope formula: m=(y2-y1)/(x2-x1)
m=(1-1)/(0-8)
m=0/(-8)
m=0
y=mx+b
1=0(0)+b
b=1
y=0x+1
y=1
Help plss
If m/ABF = 8w - 6 and m/ABE = 2(w + 11), find m/EBF.
B
ㅏ
Answers
Answer:
∠ EBF = 47°
Step-by-step explanation:
since BE bisects ∠ ABF , then
∠ ABE = ∠ EBF = 2(w + 11) = 2w + 22
∠ ABF = ∠ ABE + ∠ EBF ( substitute values )
8w - 6 = 2w + 22 + 2w + 22
8w - 6 = 4w + 44 ( subtract 4w from both sides )
4w - 6 = 44 ( add 6 to both sides )
4w = 50 ( divide both sides by 4 )
w = 12.5
Then
∠ EBF = 2w + 22 = 2(12.5) + 22 = 25 + 22 = 47°
Use braces to write the members of the set, or state that the set has no members.
The integers between 2 and 6 (not inclusive)
A.
{3, 4, 5}
{3, 4, 5}
B.
{3, 4, 5, 6}
C.
{2, 3, 4, 5}
D.
{2, 3, 4, 5, 6}
Answers
Answer: A. {3, 4, 5}
Explanation:
Write out the whole numbers from 2 to 6 to get 2,3,4,5,6
But we erase the first and last values since we aren't including those endpoints. So we end up with 3,4,5
A company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. What is the implied valuation of the business?
Answers
If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
Implied valuationFirst step is to calculate the equity valuation
Using this formula
Equity valuation=Amount invested/Equity rate
Let plug in the formula
Equity valuation=$800,000/.15
Equity valuation=$5,333,333
Second step is to calculate the implied valuation
Implied valuation=Equity valuation-Amount invested
Let plug in the formula
Implied valuation=$5,333,333-$800,000
Implied valuation=$4,533,333
Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
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Please help solve…………………
Answers
Answer:
22.5
Step-by-step explanation:
∠EAB=2x (alternate interior angles)
∠AEB=180°-4x (linear pair)
2x+180-4x=6x (exterior angle theorem)180-2x=6x180=8xx=22.5If f(x) = -2x² + 4 and g(x) = 3x - 3, find f (4) + g(-6).
Answers
Answer:
(-2[tex]x^{2}[/tex]+3x+1)
Step-by-step explanation:
f(x) = -2x² + 4 g(x) = 3x - 3 find f (4) + g(-6).
f(x)+g(x)
(-2[tex]x^{2}[/tex]+4) +(3x-3)
(-2[tex]x^{2}[/tex]+3x+4-3)
(-2[tex]x^{2}[/tex]+3x+1)
Which expressions are equivalent to the one below? Check all that apply.
25X
A. (5.5)*
B. 52x
C. 5.5x
D. 52.5x
E. 5.52x
F. 5.5X
Answers
Answer:
bca
Step-by-step explanation:
5x5=25 5 to the power of 2 is 25 plus the power of x on all of them
In 2016, 6.76% (1,026) of Cincinnati college and university graduates majored in Registered Nursing. That combined statement provides both the percentage (6.76%) and the number (1,026) of Cincinnati college and university students who majored in Registered Nursing in 2016. Based on that statement, how many students graduated from Cincinnati universities and colleges altogether in 2016? Round to the nearest whole number.
Answers
The total number of students who graduated from the Cincinnati universities and colleges are 15382.
We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.
The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.
We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.
Let the total number of students be x.
ATQ:
6.67 % x = 1026
6.67 x = 102600
667 x = 10260000
x = 10260000 / 667
x = 15382.309
Rounding off to the nearest whole number is:
x = 15382.
Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.
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Use the above table to determine how much is paid toward mortgage loan every month?
Group of answer choices
$675.00
$591.67
$121.74
$365.22
Answers
Answer:
$675.00
Step-by-step explanation: The chart says it all
A 20-year U.S. Treasury bond has a 3.50 percent interest rate, while a same maturity corporate bond has a 5.25 percent interest rate. Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.
Answers
The liquidity premium for the corporate bond is 0.25%.
What is liquidity?Any additional compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. For instance, due to its relative illiquidity, a long-term bond will have a higher interest rate than a short-term bond.
Liquidity premium for corporate bond will be:
= 5.25 - 3.5 - 1.5
= Interest - Treasury - Default risk
= 0.25%.
Therefore, the liquidity is 1.25%.
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The product of 0.61 and 4 please
Answers
Answer:
4.61
Step-by-step explanation:
4.00 is the same as 4
4.00
0.61
--------+
4.61
X 4
4 times 1 is 4
4 times 6 is 24
Move the two from 24 to the ones place
You should have 244 then add the decimal
The answer is 2.44
Question Write an equation of the line that passes through point (−3, 8) and has the slope m=−2.
Answers
Answer:
y = - 2x + 2
Step-by-step explanation:
[tex]y-8=-2(x-(-3))\\y-8=-2(x+3)[/tex]
[tex]y-8=-2x-6[/tex]
[tex]y=-2x-6+8[/tex]
[tex]y=-2x+2[/tex]
Hope this helps
Convert the angle to Degrees, Minutes, and Seconds. 56.38°
Answers
Answer:
56 degrees
22 minutes
48 seconds
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 15 steps forward, and Shaunte walked 6 steps backwards. Which expression correctly represents the distance between the friends?
Answer choices
|−15| + 6 = 21 steps
|−15| + |−6| = 21 steps
15 + 6 = 21 steps
15 + |−6| = 21 steps
Answers
Answer: 15 + |−6| = 21 steps
Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.
Which classifications within the real number system decribe all numbers in the set -1, 1, 0, 14/2, square root 25
Answers
The classification within the real number system that describes all numbers in the set -1, 1, 0, 14/2, square root 25 is; Rational Numbers
How to classify real numbers?
Real numbers can be defined as the union of both rational and irrational numbers.
Rational numbers are numbers that can be represented by fractions, such as exact roots and repeating decimals.
Irrational numbers cannot be represented by fractions, such as non-repeating decimals and non-exact roots.
Now;
-1 is a rational number
1 is a rational number
14/2 is a rational number
The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is an integer and can be expressed in the form of p/q root, then we say that 25 is rational number
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49.95 pair of shoes;5% tax
