[tex]\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}[/tex]
Write all fractions in terms of a common denominator:
[tex]\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
[tex]\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]
Then move all fractions to one side and simplify the numerator:
[tex]\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0[/tex]
The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that y cannot take any of the values -2, -9, -3, nor -8.
So the equation reduces to
[tex](y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0[/tex]
Expand the left side; you would end up with
[tex]-6(2y+11)=0[/tex]
[tex]2y+11=0[/tex]
[tex]2y=-11[/tex]
[tex]\implies\boxed{y=-\dfrac{11}2}[/tex]
Themes in The Heart of a Samurai?
Answer:
Family. Family is what you make of it in Heart of a Samurai.
Language and Communication.
Principles.
Art and Culture.
Identity.
Change.
Society and Class.
Step-by-step explanation:
Hope this helps:)
92+ 56/14−x =100.
Plz answer fast
Step-by-step explanation:
don't forget about PEMDAS
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction
first you're going to want to do 56 / 14.
sec²θ=4+2tan²θ
Find θ
Recall the Pythagorean identity,
[tex]\sec^2\theta=1+\tan^2\theta[/tex]
So we have
[tex]\sec^2\theta=4+2\tan^2\theta[/tex]
[tex]1+\tan^2\theta=4+2\tan^2\theta[/tex]
[tex]-3=\tan^2\theta[/tex]
But squaring any real number always gives a non-negative number, so there are no real solutions to this equation.
leroy draws a rectangle that has a length of 11.9 centimiters and a width of 7.6 centimieters.how much longer is the length than the width of leroys rectangle
Answer:
4.3 cm
Step-by-step explanation:
length - width: 11.9 - 7.6 = 4.3
The required answer is 4.3 cm.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Here given that,
He draws a rectangle that has a length of 11.9 cm.
And, a width of 7.6 cm
The required answer is:
length - width: 11.9 - 7.6 = 4.3
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What is the perimeter of rectangle JKLM with vertices J(-1,3),K(2,3),L(2,-5), and M(-1,-5)
Answer:
And we can find the distance between JK like this:
[tex] d_{JK} =\sqrt{(3-3)^2 +(2+1)^2}= 3[/tex]
And we can do something similar for KL and we got:
[tex] d_{KL} =\sqrt{(-5-3)^2 +(2-2)^2}= 8[/tex]
And we can do something similar for LM and we got:
[tex] d_{LM} =\sqrt{(-5+5)^2 +(-1-2)^2}= 3[/tex]
And we can do something similar for MJ and we got:
[tex] d_{MJ} =\sqrt{(-5-3)^2 +(-1+1)^2}= 8[/tex]
And the perimeter would be:
[tex] P = d_{JK} + d_{KL} +d_{LM} +d_{MJ} = 3+8+3+8 =22[/tex]
Step-by-step explanation:
For this case we can use the formula for the euclidean distance given by:
[tex] d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2}[/tex]
And we can find the distance between JK like this:
[tex] d_{JK} =\sqrt{(3-3)^2 +(2+1)^2}= 3[/tex]
And we can do something similar for KL and we got:
[tex] d_{KL} =\sqrt{(-5-3)^2 +(2-2)^2}= 8[/tex]
And we can do something similar for LM and we got:
[tex] d_{LM} =\sqrt{(-5+5)^2 +(-1-2)^2}= 3[/tex]
And we can do something similar for MJ and we got:
[tex] d_{MJ} =\sqrt{(-5-3)^2 +(-1+1)^2}= 8[/tex]
And the perimeter would be:
[tex] P = d_{JK} + d_{KL} +d_{LM} +d_{MJ} = 3+8+3+8 =22[/tex]
The perimeter of the rectangle with the given vertices is: 22 units.
Recall:
Perimeter of a rectangle = 2(length x width)Distance between two vertices is calculated using: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]Thus, find the length (JK) and width (KL) of the rectangle.
Width of rectangle = distance between J(-1,3) and K(2,3):
Substitute[tex]JK = \sqrt{(3 - 3)^2 + (2 - (-1))^2} \\\\JK = \sqrt{(0)^2 + (3)^2} \\\\JK = \sqrt{9} \\\\JK = 3[/tex]
Length of rectangle = distance between K(2,3) and L(2,-5)
Substitute[tex]KL = \sqrt{(-5 - 3)^2 + (2 - 2)^2} \\\\KL = \sqrt{(-8)^2 + (0)^2} \\\\KL = \sqrt{64} \\\\KL = 8[/tex]
Perimeter of the rectangle = 2(length x width)
SubstitutePerimeter of the rectangle = 2(8 + 3)
Perimeter = 2(11)
Perimeter = 22 units
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A girl was 6 and sister was 2,the girl is now 24,how old is the sister
Answer:
20
Step-by-step explanation:
There is 6-2 =4 years between them
24-4 =20
The sister is 20
Answer: 20 years old
Step-by-step explanation: So, we know the girl is 4 years older than the sister...how do we know that? Because...
6 - 2 = 4
She's 4 years older...we know the girl is 24, then the sister must be 20.
24 - 4 - 20...
The sister is 20 years old, I hope this helps
QUICK QUESTION!!WILL GIVE BRAINLIEST
If you pay bus fair for the year ahead , what advantages can I get out of the bus fair, like can I use it to get to other places??
Answer:
it matters were you are going
Step-by-step explanation:
Write the equation of the circle graphed below
Answer:
O
Step-by-step explanation:
THIS IS ASSUMING THAT THE RADIUS OF THE CIRCLE IS 4 1/4 UNITS!
Answer:
Standard Equation: (x + 5)^2 + (y+5)^2 = 18.06
General Form: x^2 + 10x + y^2 + 10y + 31.94 = 0
Triangle ABC work out area of triangle
Answer:
Step-by-step explanation:I don't say you must have to mark my ans as brainliest but my friend if it has really helped you plz don't forget to thank me...
Answer:
2.5*4.6*0.5
= 2.5*2.3
= 5.75
Rounded to one decimal = 5.8
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C: 1-0.2p
Expression D: p-0.2p
Expression E: p-0.8p
Which two expression each represent the sale price of the item?
Expression A and E
Expression B and C
Expression B and D
Expression C and D
Answer:
B
Step-by-step explanation:
A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth?
Answer:
2/9 of a foot in one month / 8/3 inches in one month
Step-by-step explanation:
Answer:
2/9 of a foot
Step-by-step explanation:
It grows 2/3 ft in 3 months
Therefore it grows in one month
2/3. / 3 = 2/3 × 1/3= 2/9 of a foot
Rate is the amount taken for one of a unit of measure, in this case, it is month.
What is the value of h?
40°
h = 20
h = 35
n = 55
h = 70
Answer:
55
Step-by-step explanation:
All triangles have a sum of 180°
180 - 40 = 140
Since the triangle is an isosceles triangle, then you are going to divide 140 by 2 because the base angles of an isosceles triangle are congruent.
140 / 2 = 70
Now that we know that the measurement of the two base angles is 70, we can find h.
2h represents the exterior angles. Exterior angles are always supplementary to the interior angles. So, we can simply subtract 70 from 180.
180 - 70 = 110
Now, we can divide 110 by 2 to find h.
110 / 2 = 55
So, h equals 55. So, the answer is the third option.
Someone please help me with this :3
Answer:
2
Step-by-step explanation:
[tex]\dfrac{\frac{2}{3}}{\frac{1}{3}}=\frac{2}{3}\cdot \frac{3}{1}=\frac{6}{3}=2[/tex]. Hope this helps!
Answer:
2/3 divided by 1/3
Multiply the reciprical
2/3 x 3/1 = 6/3
6/3=2
2 is your answer
Step-by-step explanation:
What' the mean 3,2,2,12 6,5,14,4
Answer: 6
Explanation: The mean of a data set is the sum of the numbers in the data set divided by however many numbers are in the data set.
So, let's begin by adding the numbers.
So we have 3 + 2 + 2 + 12 + 6 + 5 + 14 + 4 which is 48.
Now we divide 48 by the number of numbers in the set which is 8.
48 ÷ 8 is 6.
So the mean of the given data set is 6.
whats the answer for G over 13 equals 52
Answer:
g = 676
Step-by-step explanation:
Multiply by 13:
g/13 = 52
13(g/13) = 13(52)
g = 676
The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.
6,6, 5, 8, 10
Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Answer:
2
Step-by-step explanation:
Given: 5 quiz scores of a student in a statistics course are 6,6, 5, 8, 10
To find: standard deviation of the population
Solution:
Mean (M) = [tex]\frac{\sum_{i=1}^{n}x_i}{n}[/tex]
here, [tex]x_i[/tex] denotes number of observations and n denotes number of observations.
Variance = [tex]\frac{\sum_{i=1}^{n}(x_i-M)^2}{n-1}[/tex]
Standard deviation = [tex]\sqrt{variance}[/tex]
[tex]M=\frac{6+6+5+8+10}{5}=\frac{35}{5}=7[/tex]
Variance = [tex]\frac{\sum_{i=1}^{n}(x_i-7)^2}{n-1}[/tex]
[tex]=\frac{\left [ (6-7)^2+(6-7)^2+(5-7)^2+(8-7)^2+(10-7)^2 \right ]}{5-1}\\=\frac{1+1+4+1+9}{4}\\=\frac{16}{4}\\=4[/tex]
Standard deviation = [tex]\sqrt{4}=2[/tex]
Please help me?? I am struggling and i need help :?/
I will mark you as the brainliest and i will give you points :)
Answer:
ZYX- CBA
Step-by-step explanation:
ZYX is backwards
so cba needs to be too
Answer:
ZYX-CBA
Step-by-step explanation:
welcome
A recipe calls for one-half of a tablespoon of baking powder for 3 cups of flour. How
many tablespoons of baking powder is needed if 1 cup of flour is used?
A: 1/6
B: 1/4
C: 1/2
D: 1 1/2
Answer:1/4
Step-by-step explanation:
A circle has an area of 49 cm^2. how do I find the circumference?
Answer:
28.81cm
Step-by-step explanation:
c=2TTy
4. A circle has a circumference of 100 cm. What is the radius of the circle?
A 10
B. 15
C. 100
D200
Answer:
[tex]15.90cm[/tex]
hope this helps
brainliest appreciated!
good luck! have a nice day!
4(5x + 3y) equal expressions
Answer:
20x + 12y
Step-by-step explanation:
Apply distributive property.
(4 * 5x) + (4 * 3y)
=> (20x) + (12y)
Answer:
=(4)(5x+3y)
=(4)(5x)+(4)(3y)
=20x+12y
Step-by-step explanation:
=(4)(5x+3y)
=(4)(5x)+(4)(3y)
=20x+12y
Answers above.
Hope this helps.
Estimate the difference. 9 1/2- 1 6/7
Answer:
[tex] = 7 \frac{9}{14} \\ [/tex]
Step-by-step explanation:
[tex]9 \frac{1}{2} - 1 \frac{6}{7} \\ \frac{19}{2} - \frac{13}{7} \\ \frac{133 - 26}{14} \\ = \frac{107}{14} \\ = 7 \frac{9}{14} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters?
a
12.25 meters
b
52.5 meters
c
8.75 meters
d
26.25 meters
Answer:
The answer is c because I just took the quiz.
Step-by-step explanation:
Your welcome!
how many numbers do y’all see? add them all together- once u have found them all.
Answer:
24
Step-by-step explanation:
6+2+0+4+1+3+8=24
All the numbers to see are, 6, 8, 0, 2, 4, 1.
And, The sum of all the numbers are 21.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Here,
In the figure,
All the numbers which can be seen are,
⇒ 6, 8, 0, 2, 4, 1
Now, Add all the numbers, we get;
⇒ 6 + 8 + 0 + 2 + 4 + 1
⇒ 21
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PLEASEEE HELPP MEE WITH QUESTION 4 AND 5
Answer:
4) c = 38
5) x = 50
Step-by-step explanation:
4) The marked angles are a "linear pair", meaning their total is 180°:
3c° +(2c -10)° = 180°
5c = 190 . . . . . . . divide by °, add 10, collect terms
c = 38 . . . . . . . . . divide by 5
__
5) The interior angle at C brings the total of the marked angle and the interior angle to 360°
330° + (interior angle) = 360°
(interior angle) = 30° . . . . . . . . . subtract 330°
The interior angles of the triangle total 180°, so we have ...
x° +2x° +30° = 180°
3x = 150 . . . . . . . . . . . . . divide by °, subtract 30
x = 50 . . . . . . . . . divide by 3
Suppose A is an m × n matrix in which m> n. Suppose also that the rank of A equals n Show that A is one to one. Hint: If not, there exists a vector x such that Ax = 0, and this implies at least one column of A is a linear combination of the others. Show this would require the rank to be less than n.
Step-by-step explanation:
If T:Rn→Rm is a linear transformation and if A is the standard matrix of T, then the following are equivalent:
1. T is one-to-one.
2. T(x) = 0 has only the trivial solution x=0.
3. If A is the standard matrix of T, then the columns of A are linearly independent.
Here, A is a mxn matrix where m ≥ n and the rank of A equals n. It implies that the columns of A are linearly independent, for, otherwise, the rank of A would be less than n. Hence the linear transformation represented by A is one-to-one.
Calculate the missing amounts for companies a to e
Answer:
where is the question?
Step-by-step explanation:
What is the length of line segment AB, rounded to the
nearest tenth?
3.4 cm
O 4.8 cm
24 cm
0 27 cm
Answer:
A on e2020
Step-by-step explanation:
The solution is, The length of line segment AB is 3.4cm.
What is Line segment?Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.
here, we have,
The area of octagon is given as 2a^2(1+sqrt{2})
Where a is the side of octagaon.
All sides of octagon are same.
now, we get,
As, 2a^2(1+sqrt{2}) = 54cm
so, we have,
Then, a^2 = 54/2(1+sqrt{2})
a^2 = 54/4.828
a^2 = 11.19
a = 3.4 cm
Hence, The solution is, The length of line segment AB is 3.4cm.
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6x - y = 5
3x + y = 4
Answer:
1.6x-y=5--->equ.(i)
3x+4=y--->equ.(ii)
substitution method
6x-y=5
y=5+6x--->equ (iii)
Replace y=5+6x into equ--->(ii)
3x-5+6x=4
3x+6x=4+5
9x=9
divide both side by 9
9x/9=9/9
x=1
Replace x=1 into equ (iii)
6(1)-y=5
6-y=5
y=5+6
y=11
then your x and y is
x=1,y=11
Radha is trying to choose between two bike rental companies, Comapny A and Company B. Company A charges a $25 initial fee and additional $5 for each hour rented . Company B charges an initial $18 fee and an additional $6