=====================================================
Explanation:
Page 1 is labeled with 1 and 2, which sum to 1+2 = 3
Page 2 is labeled with 3 and 4 which sum to 3+4 = 7
Page 3 is labeled with 5 and 6 which sum to 5+6 = 11
and so on until we reach
Page 96 is labeled with 191 and 192, which sum to 191+192 = 383
Note how each page has an odd page number label and an even number label (odd on the front side; even on the back side). Adding any odd number to an even number will result in an odd number. We can prove it as such
x = some odd number = 2m+1, m is any integer
y = some even number = 2n, n is an integer
x+y = 2m+1+2n = 2(m+n)+1 = some other odd integer because it is in the form 2p+1 with p = m+n as an integer
This explains why the results 3,7,11,..,383 are all odd.
------------------------
So we effectively have this set of values {3,7,11,...,383}. This is an arithmetic sequence with 3 as the first term and 4 as the common difference.
If we add two odd numbers together, we get an even number (proof is similar to one shown above)
odd + odd = even
But if we add in another odd number, then we'll go back to an odd result
odd + odd + odd = odd
If we have an odd number of odd numbers added up, then the result will be odd. In this case, we're adding 25 values from the set {3,7,11,...,383}. The value 25 is odd, so we have an odd number of values from {3,7,11,...,383} being added up. Therefore, the result Bob will get will always be odd. There is no way to get a sum of 2012 because this value is even.
in a group of people for every 20 people 7 of them have blue eyes a) write the ratio of the number of people with blue eyes to the total of people in fraction form b) if there are 100 total people how many how many of them have blue eye? explain how u found your answer
Answer:
a) 7 : 20
b)There will be 35 people with blue eye
Step-by-step explanation:
a)
This question is asking you the ratio of the number of people with blue eyes to the total number of people.
So seven people with blue eyes to the total number of 20 people.
7 : 20
b)
you got the ratio 7 : 20, this also means that there will be 7 people with blue eyes in every 20 people.
so you use 100 divides by 20, you will get the number five, this means there are 5 groups of 20 in 100 people.
so then you use 5 times 7, then you got the number 35.
That means, there are 35 people with blue eyes in 100 people.
Which expression is equivalent to *picture attached*
Answer:
The correct option is;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex]
Step-by-step explanation:
The given expression is presented as follows;
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )[/tex]
Which can be expanded into the following form;
[tex]\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n[/tex]
From which we have;
[tex]\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}[/tex]
Therefore, substituting the value of n = 50 we have;
[tex]\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}[/tex]
Which gives;
[tex]4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}[/tex]
[tex]3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}[/tex]
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}[/tex]
Therefore, we have;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex].
Find $y$ if the point $(-6,y)$ is on the line that passes through $(-1,7)$ and $(3,-2)$.
Answer:
y = 18.25
Step-by-step explanation:
The 2-point form of the equation of a line can be used to write the equation of the line through the given points.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (-2 -7)/(3 -(-1))(x -(-1)) +7
y = -9/4(x +1) +7
For x = -6 this evaluates to ...
y = -9/4(-6 +1) +7 = (9/4)(5) +7 = 45/4 +7
y = 18 1/4
Please help me with this question! I will give the brainliest to the one with the right answer!!!
Answer:
x =4
Step-by-step explanation:
hope this is the correct answer
Answer: B
Step-by-step explanation: B: 5^2-3^2 = 25-9 = 16. the square root of 16 is 4, so x=4
3. What is the degree of the polynomial 3x^4 + 2x^2 + 5x? *
Answer:
the degree of that polynomial is 4
Jeremy is taking a photography class, but he doesn't own a camera. The class organizers will rent him a camera for $6 per day. Jeremy can spend up to $50 for the class, but he has to pay $15 to register for the class as well as rent the camera. The number of days, d, that Jeremy can rent the camera is represented by the inequality 6d + 15 < 50. Select the number of days Jeremy can rent the camera with the money he has. A. 5 B. 6 C. 8 D. 9 E. 10
Answer:
A. 5
Step-by-step explanation:
6d+15<50
subtract 15 from both sides
6d<50-15
6d<35
divide both sides by 6
d<35/6
d<5 5/6
So he can only rent it for 5 days. If he rented for 6, it would be $51, which is too much.
Solving the given inequality for d, we get...
6d + 15 < 50
6d + 15-15 < 50-15 <<-- subtract 15 from both sides
6d < 35
6d/6 < 35/6 <<--- divide both sides by 6
d < 5.83
Which means that d can be any of the values in this set: {0, 1, 2, 3, 4, 5}
The smallest d can be is 0. In this scenario, Jeremy pays the $15 registration but doesn't rent the camera at all
The largest d can be is 5. In this scenario, Jeremy rents the camera for 5 days
Any larger value of d is not allowed as it would make the total cost go over $50
Notice how I'm rounding down regardless how close 5.83 is to 6
why is the site not working i am clicking see answers and nothing pops up is this only happening to me?
Answer:same here
Step-by-step explanation:
The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = length. It is surrounded by a brick walkway 4ft wide. Suppose the total area of the walkway is 400ft^2.
a. Write a polynomial to represent the length of PQ
b. What are the dimensions of the garden?
Answer:
[tex]PQ = x + 13[/tex]
The dimension of the garden is 52.5ft by 43.5ft
Step-by-step explanation:
Given
The shape above
Required
Determine PQ
Determine dimension of the garden
Calculating Length PQ
Represent the length of the inner rectangle as L
Represent the width of the inner rectangle as W
[tex]W = x[/tex]
[tex]L = x + 9[/tex]
The distance between the inner rectangle and the outer triangle is 4ft
This implies that;
[tex]PQ = L + 4[/tex]
Substitute [tex]x + 9[/tex] for [tex]L[/tex]
[tex]PQ = x + 9 + 4[/tex]
[tex]PQ = x + 13[/tex]
Also;
[tex]QR = W + 4[/tex]
Substitute [tex]x[/tex] for [tex]W[/tex]
[tex]QR = x + 4[/tex]
Calculating The Dimension of The Garden
First, we need to determine the Area of the inner rectangle
[tex]Area_1 = L * W[/tex]
Recall that [tex]W = x[/tex] and [tex]L = x + 9[/tex]
So;
[tex]Area_1 = x * (x + 9)[/tex]
For the bigger rectangle
[tex]Area_2 = PQ * QR[/tex]
Recall that [tex]PQ = x + 13[/tex] and [tex]QR = x + 4[/tex]
So;
[tex]Area_2 = (x + 13)(x + 4)[/tex]
Given that the Area of the walkway is [tex]400ft^2[/tex]
This implies that
[tex]Area_2 = Area_1 + 400[/tex]
Substitute [tex]Area_1 = x * (x + 9)[/tex] and [tex]Area_2 = (x + 13)(x + 4)[/tex]
[tex](x + 13)(x + 4) = x * (x + 9) + 400[/tex]
Open All Brackets
[tex]x^2 + 13x + 4x + 52 = x^2 + 9x + 400[/tex]
[tex]x^2 + 17x + 52 = x^2 + 9x + 400[/tex]
Collect Like Terms
[tex]x^2 - x^2 + 17x - 9x = 400- 52[/tex]
[tex]8x = 348[/tex]
Divide both sides by 8
[tex]\frac{8x}{8} = \frac{348}{8}[/tex]
[tex]x = \frac{348}{8}[/tex]
[tex]x =43.5[/tex]
Since the dimensions of the garden is [tex]W = x[/tex] and [tex]L = x + 9[/tex]
Substitute 43.5 for x in both cases
[tex]L = 43.5 + 9 = 52.5[/tex]
[tex]W = 43.5[/tex]
Hence, the dimension of the garden is 52.5ft by 43.5ft
FIRST RIGHT ANSWER GETS BRAINLLEST If you spin the spinner below 20 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 18 times B) Lands on red 6 times C) Lands on yellow 4 times D) Lands on blue 4 times
Answer:
B) Lands on red 6 times
C) Lands on yellow 4 times
Step-by-step explanation:
The rest are way too much/too little for their predicted probability.
Answer:
B C
Step-by-step explanation:
If u spin the spinner below 20 times it will land on red around 4 times.
6 is only 2 greater than 4 so it works.
Same thing with yellow.
Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values. 3x^2 + kx - 8 Thanks anyone for help :)))
Answer: The answer is (-1/6, -k/6- 95/12)
Step-by-step explanation:
I copy and and pasted the question on to an online calculator because mathmatics is not my strongsuit.
The values of k for the quadratic equation 3x² + kx -8 are (-∞, ∞).
Given Quadratic equation: 3x² + kx -8.
The quadratic expression can be factored into two binomials if it has two real roots.
Discriminant
When b² - 4ac > 0, two real roots.
When b² - 4ac = 0, one real roots.
When b² - 4ac < 0, no real roots.
So, k² - 4(3)(-8) ≥ 0
k² + 96 ≥ 0
k² ≥ - 96
This is true for any value of k and k ∈ (- ∞, + ∞).
Therefore, the values of k are (-∞, ∞).
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Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the
solution set on a number line.
4m + 24.25 < 34.25
Answer:
126
4m + 24.25 < 34.25
Answer:
Idek I just need points
Step-by-step explanation:
Umm
Which of the following is a valid reason why the quadrilateral shown below is
a parallelogram?
A. Both pairs of opposite sides are parallel.
B. The diagonals bisect each other.
C. The diagonals are congruent.
D. Both pairs of opposite sides are congruent.
A parallelogram is a quadrilateral with two pairs of parallel sides.
Option A is the correct answer.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
A parallelogram is a quadrilateral with two pairs of parallel sides.
So, option A is a valid reason for the given quadrilateral to be a parallelogram.
The other options do not necessarily hold true for all parallelograms. For example, the diagonals of a parallelogram bisect each other and are congruent, but not all quadrilaterals with bisecting diagonals are parallelograms.
Similarly, not all parallelograms have congruent diagonals or congruent opposite sides.
Thus,
A parallelogram is a quadrilateral with two pairs of parallel sides.
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Please help me on this answer, I am very confused and don't know the correct steps to take. Solve
Answer:
102
Step-by-step explanation:
Since 2 + 8 = 10, then the cube root of 5x+2 = 8
Since 8×8×8=512, then 5x+2=512
5x=510, so x=102
Answer:
C) 102
Step-by-step explanation:
Hello !
2 + ∛(5x + 2) = 10
∛(5x + 2) = 10 - 2
∛(5x + 2) = 8
(∛(5x + 2))³ = 8³
5x + 2 = 512
5x = 512 - 2
5x = 510
x = 510 : 5
x = 102
Good luck !
Which is a factor of x2 + 5x − 24?
Answer:
(x−3)(x+8)
Step-by-step explanation:
The middle number is 5 and the last number is -24.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 5
Multiply together to get -24
Can you think of the two numbers?
Try -3 and 8:
-3+8 = 5
-3*8 = -24
Fill in the blanks in
(x+_)(x+_)
with -3 and 8 to get...
(x-3)(x+8)
Find the odds in favor of rolling two different numbers when rolling a pair of dice.
Answer:
5/6Step-by-step explanation:
The total number of outcomes is 6 x 6 (because a dice has 6 sides) or 36. On the dice, there are 6 sets of matching numbers:
1,1
2,2
3,3
4,4
5,5
6,6
The probability of this is 6/36 or 1/6. The probability of not matching is 30/36 or 5/6.
I'm always happy to help :)The probability of rolling a pair of different numbers when two dices are rolled is 5/6.
What is probability?The probability is the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
How to calculate probability?Total number of combinations when two dices are rolled=[tex]6^{2}[/tex]=36.
Combinations having same pair of numbers=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6).
Number of combinations having same pair of numbers=6.
Number of combinations having different pairs of numbers=36-6=30.
Probability of having different pair of numbers=Number of combinations having different pair of numbers/Total combinations
Probability=30/36
=5/6
Hence the probability of rolling a pair of different numbers when two dices are rolled is 5/6.
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thanks for helping me out y’all if anyone of y’all play roblox mine is ( colIapsinq ) the second L is a capital ( i )
Answer:
1. 5
2. 6
3. 8
4. 200
Step-by-step explanation:
I said the answer already
first 5
next 6
then 8
lastly 200 my accounts (try both of them) king1ev15 and/or king1ev151
Given: Circumscribed △XYZ XY=7, YZ=8. ZX=5 Find: AX, BY, CZ
Answer:
AX=2 BY=5 CZ=3
Step-by-step explanation:
Lets call AX (x). Once you do so, one can tell that AZ=5-x. CZ is also 5-x. BX is also x. Therefore you can say that BY=7-x which makes CY 7-x. Now for side YZ, CZ is 5-x and CY is 7-x.
5-x+7-x=8
solving that you get x=2
AX=2
BY=7-x=5
CZ=5-x=3
Hope this explains some more than the other answer. Please ask any questions.
Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.
==================================================
Explanation:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2
A = (0,0) becomes A' = (0,0). No change happens. This point is fixed
B = (2,-4) becomes B' = (4,-8). This point does move
C = (-4,-4) becomes C' = (-8,-8). This moves as well
So all you need to do from here is draw triangle A'B'C'.
-----------------
Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.
Triangle with the three corner points at
A' = (0,0). B' = (4,-8). C' = (-8,-8). what is Dilation?Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.
Given:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2
A = (0,0) --> A' = (0,0).
B = (2,-4) --> B' = (4,-8).
C = (-4,-4) --> C' = (-8,-8).
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15 POINTS!!!!! How is a linear function affected when a constant is multiplied by y?
Answer:
a constant multiplied by y can affect the linear, because it determines a dependent variables.
Step-by-step explanation:
a linear relationship is a statistical term used to described a straight line relationship between two variables.
what is 3^3/2 equal to?
Answer:
D. 2^3/2
Explanation:
3 3/2
= ²√3³
= ²√27
Hope this helped! :D
Answer:
The answer is D
Step-by-step explanation:
hope this helps ^_^
Graph a line with this information: a slope of -5 and y intercept of 4.
Answer:
See below.
Step-by-step explanation:
The y intercept is 4 so you can mark a point on the line at (0, 4).This is a point on the y-axis 4 units up from the origin (origin is where the axis cross).
The slope is negative so the line will rise to the left.
Mark a point which is 1 unit horizontally to the left of point (0, 4) and 5 units vertically upwards.
Then draw the line to pass through this point and the point (0, 4)
The equation of the line is y = -5x + 4.
WILL GIVE BRAINLIEST George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan. Recall the formulas for area and perimeter: A = lw and P = 2l + 2w. A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet. How many feet of fencing will George need for the dog run? 22 feet 68 feet 76 feet 82 feet
Answer:
b68
Step-by-step explanation:
Answer:
68 FEET
Step-by-step explanation:
B pls give me brainliest
HELP PLZ I AM BEING TIMED!!!
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS IN 2 MINUTES!!
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
Option A.
Step-by-step explanation:
The vertices of square S are (0,0), (5,0), (5,-5) and (0,-5).
The vertices of square S' are (0,1), (0,3), (2,3) and (2,1).
It is given that center of dilation is (0,0). From the point it is clear that the distance between point of S and origin is greater that S'. It means the scale factor is less than 1.
If scale factor is 2/5, then
[tex](x,y)\to (\dfrac{2}{5}x,\dfrac{2}{5}y)[/tex]
[tex](0,0)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(0))=(0,0)[/tex]
[tex](5,0)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(0))=(2,0)[/tex]
[tex](5,-5)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(-5))=(2,-2)[/tex]
[tex](0,-5)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(-5))=(0,-2)[/tex]
If the figure translated 3 units up, then
[tex](x,y)\to (x,y+3)[/tex]
[tex](0,0)\to (0,0+3)=(0,3)[/tex]
[tex](2,0)\to (2,0+3)=(2,3)[/tex]
[tex](2,-2)\to (2,-2+3)=(2,1)[/tex]
[tex](0,-2)\to (0,-2+3)=(0,1)[/tex]
These are the vertices of square S'.
A dilation by a scale factor of two-fifths and then a translation of 3 units up are used to get square S' from S.
Therefore, the correct option is A.
A train traveling at 100 km an hour takes 3 seconds to enter a tunnel and an additional thirty seconds to pass completely through it. Find the length, in kilometers, of the train. Express your answer as a common fraction
If your good in math pls help me I’m not that great and I’m ineed of help !
Answer:
The base is 2
Step-by-step explanation:
Exponents or powers are on top of the base.
[tex]2^x[/tex]
x is the exponent and the base is 2.
What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x? Discriminant = b2 – 4ac
Answer:
The answer is 16.
Step-by-step explanation:
First, you have to make the equation into 0 by moving all the terms to one side :
[tex] - 3 = - {x}^{2} + 2x[/tex]
[tex] {x}^{2} - 2x - 3 = 0[/tex]
Next, you have to apply Discriminant Law, D = b² - 4ac :
[tex]D = {b}^{2} - 4ac[/tex]
[tex]let \: a = 1 \: , \: b = - 2 \: , \: c = - 3[/tex]
[tex]D = {( - 2)}^{2} - 4(1)( - 3)[/tex]
[tex]D = 4 + 12[/tex]
[tex]D = 16[/tex]
Which of the following equations demonstrate that the set of polynomials is
not closed under the certain operations?
IN
O A. Division: (x2-5x+3) =(x- 2) = x- 3+
X-2
B. Subtraction: 8x* + x*)-(-2x + x) = 5x
O C. Addition: (x2 + x) + (x + 1) = x2 + 2x+1
D. Multiplication: (x2 - 5x+3)(x-5)= x - 10x2 +28x - 15
Answer:
A. Division: (x2-5x+3) =(x- 2) = x- 3+
X-2
Step-by-step explanation:
A. Division: (x2-5x+3) =(x- 2) = x- 3+ -3/X-2
This is not a polynomial since we have an x in the denominator
What are the remaining angle measures if the figure is
to be a parallelogram?
mZB=
mZC=
m2D =
Answer:
The answer is given below
Step-by-step explanation:
Given that the parallelogram ABCD has m∠A = 79°
A parallelogram is a quadrilateral with two pairs of parallel lines. For a parallelogram, opposite sides of a parallelogram is equal and opposite angles are also equal. Also the diagonal of a quadrilateral bisect each other.
m∠C = m∠A = 79° (opposite angles of a parallelogram are congruent)
m∠C = 79°
m∠B + m∠A = 180° (consecutive angles of a parallelogram are supplementary)
m∠B + 79 = 180
m∠B = 180 - 79
m∠B = 101°
m∠B = m∠D = 101° (opposite angles of a parallelogram are congruent)
m∠D = 101°
The stem-and-leaf plot shows the number of points scored by the Bears in each of their basketball games this season. Identify the mean and median, as
well as how many games they scored at least 30 points. Round to nearest tenth for any calculations.
STEM
LEAF
1
89
2
02336889
3
01 4 4 5 6 8 9
4
012
113
8 = 18 points
Answer:
Mean = 30.3
Median = 30
They scored 30 or more points on 11 games.
Step-by-step explanation:
Mean = all the numbers added together divided by 21
636/21 = 30.3
Median is the middle number (the 11th) = 30
Solve the system using elimination 7x+2y=10 -7x+y=-16
Answer:
x=2, y=-2
Step-by-step explanation:
7x+2y=10
-7x+y=-16
-------------------
0x + 3y = -6
Divide each side
3y/3 = -6/3
y = -2
Now find x
7x +2y = 10
7x + 2( -2) = 10
7x -4 = 10
Add 4 to each side
7x -4+4 = 10+4
7x= 14
Divide by 7
7x/7 = 14/7
x = 2
Since one equation has a 7x and and the other equation has a -7x,
when we add the equations together, the x's will cancel out.
So we have 3y = -6 and y = -2.
To find x, plug -2 back in for y in either of the two original equations.
I've chosen to plug -2 into the first equation to get 7x + 2(-2) = 10.
Solving from here, x = 2.
So our final answer is the ordered pair (2, -2).
Now, check your answer.