Answer:
√294 = A. 7√6
Explanation:
Factor 49 out of 294 . √
49 ( 6 ) Rewrite
49 as 7 ² . √ 7 ² ⋅ 6
Pull terms out from under the radical.
7 √ 6
a and b are positive integers and a+b=2009!
what is the amount of ordered pairs of (a, b)?
Answer:
[tex]2000 \: and \: 9.[/tex]
[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]
Let's consider a much smaller value and work our way up to the factorial 2009!
Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.
The only solution to a+b = 2 is a = b = 1 as mentioned.
----------
Now move onto a+b = 3. We have two solutions:
a = 1, b = 2
a = 2, b = 1
-----------
Now move onto a+b = 4. We have three solutions
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.
So 'a' counts up to 3, while b counts down from 3.
We cannot reach 4 since 0 is not allowed for a or b.
-------------
The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so
a = 1, b = k-1
a = 2, b = k-2
a = 3, b = k-3
....
a = k-3, b = 3
a = k-2, b = 2
a = k-1, b = 1
Where k > 2
Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.
This confirms there are k-1 solutions listed above.
The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions
Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!
8x-13+4+1=90 helppppppp
Answer:
x = 49/4
Step-by-step explanation:
A cubic function is stretched by a factor of 0.4, opening downward and
shifted 10 units down and 5 units left.
Answer:
the answer is in the link
Step-by-step explanation:
https
bxaha zshkkkvxxxkvvvvwuqgceuuuegieg DONT KNO
According to the diagram, which statement is NOT true?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Counting
Numbers
А
All counting numbers are also rational numbers.
All whole numbers are integers.
B
C All rational numbers are real numbers.
D
AB rational numbers are integers
Answer:
all rational numbers are intergers
Step-by-step explanation:
whats the product of (3-2i) and (7+6i)?
Answer: the product is = 33+4i
Step-by-step explanation:
21+4i-12i^2
21+4i-12(-1) i^2=-1
21+4i+12
your answer would be 33+4i .
Please helpppp pleaseee
Answer:
-5x⁹ y⁵
Step-by-step explanation:
x⁵y² ((-5x⁴)(y³)) = -5x⁹ y⁵
Answer: x5y2(5x4y3) =5x9y5
Step-by-step explanation:
Susan had $30 before she bought 7 mugs. Afterwards, she only had $5.50 left. The scenario can be expressed by: 30 - 7k = 5.50 where k represents the price for 1 mug. What is the value of k? a) k = 24.50 b) k = -3.50 c) k = 5 d) k= 3.50
Answer:
Answer choice D. k is equal to 3.5
Step-by-step explanation:
In this equation, we must get the k all by its self. To do that, let's eliminate the 30. To do this, we must subtract 30 from both sides.
30 - 7k = 5.5
-30 -30
Then we get...
-7k = -24.5
Now we must get rid of the -7 that is multiplied by k. to do this, let's divide both sides by -7.
-7k = -24.5
-7 -7
And we get...
k = 3.5
And therefore, k is equal to 3.5. I hope this helps, and I hope it's not wrong, but I do not think it is.
WILL MARK BRAINLIST!!!!
DBA Study Guide –
2.01 ESSENTIAL QUESTIONS
• What are the Transformations and how do they move?
• How can you tell the difference between the preimage and the transformed image by looking at the figures on a graph?
•
• 2.03 ESSENTIAL QUESTIONS
• What are the names of the Theorems that we use to prove triangles congruent?
• What does it mean for two shapes to be congruent?
2.04 ESSENTIAL QUESTIONS
How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof:
• Isosceles Triangle Theorem
2.06 ESSENTIAL QUESTIONS
• What are the characteristics of squares, rhombi, kites, and trapezoids?
Answer: These are some of the questions not all of them
There are four types of transformations: reflection, rotation, translation and enlargement. Translation (also known as Slide) moves a shape by sliding it up, down, sideways or diagonally, without turning it or making it bigger or smaller. Reflection (also known as Flip) in a line produces a mirror image in which corresponding points on the original shape and the mirror image are always the same distance from the mirror line. Rotation (also known as Turn) turns a shape through a clockwise or anti-clockwise angle about a fixed point known as the Centre of Rotation. All lines in the shape rotate through the same angle. Rotation, (just like reflection) changes the orientation and position of the shape, but everything else stays the same. Enlargement (also known as Dilation) is a transformation. However, it is different from reflection, rotation and translation because it changes the size of an object. Transformations which leave the dimensions of the object and its image unchanged are called isometric transformations. Examples of isometrics are reflection, rotation and translation. Transformations which do alter the dimension of the object when they act on them are called non-isometric transformation Examples are the enlargement. The image of a transformation is the shape after the transformation. The preimage of a transformation is the shape before the transformation. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent. n geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Find a equation of the line for which (5,10) is a point on the line
Answer:
you go to the right 5 and go up 10
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
neither
Step-by-step explanation:
Answer:
(c)
Step-by-step explanation:
If these are
Parallel, slope of both the lines is same.
Perpendicular, if they are -ve reciprocal of each other.
In y = mx + c, slope is m.
Compare,
Slope of y=4x+1, is 4.
of 8y-16=2x is 2/8 = 1/4, which is reciprocal of 4,but not -ve.
So it is neither ll nor perpendicular.
a cookie recipe calls for 1 2/3 cups of sugar. If you plan on changing the recipe to make 2 1/2 times as much, how many cups of sugar will you need?
Answer:
4 1/6
Step-by-step explanation:
2 1/2 times 1 2/3 change those numbers into an improper fraction which are 5/2 for 2 1/2 and 5/3 for 1 2/3 multiply 5/2 and 5/3 you get 25/6 change the 25/6 into a mixed number and you get 4 1/6
how do i put 5x^2+6+3xy^5-2x in standard form
Answer:
it's 3xy^5 + 5x^2 -2x +6
i need help ASAPPPP A spinner has 3 equal sections, one that is red, one yellow, and one blue. The spinner is spun 20 times and the results are recorded in the table.
Color Frequency
Red 7
Yellow 9
Blue 4
Based on these results, what is the experimental probability that the next time the spinner is spun it lands on yellow?
a.0.35
b.0.45
c.0.920
d.0.2
Answer:
B
Step-by-step explanation:
Hope this helps :)
If so mark brainliest
Hank draws a line with a zero slope through the points
(–2, 4) and (3, b). Which value of b could represent Hank’s second point?
–3
–1
4
9
Answer:
It's 4
Step-by-step explanation:
Answer:
The answer is C which is 4
Step-by-step explanation:
I just took the test and got it right
Hopefully this helps you
pls mark brainlest
PLEASE HELP QUICK WILL THANK AND GIVE BRAINLY
A doctor has office hours 3 days each week. Each day she sees 24 patients.
How many patients does she see in one year? Remember, there are 52 weeks in a year.
Answer:
3774
Step-by-step explanation:
Eric walks 7 km East in 2 hours and then 2.5 km West in 1 hour.
___ km/hr is the average speed and ___ km/hr is the average velocity for the whole journey that Eric takes.
Answer:
Average speed = 3.17 km/h and Average velocity = 1.5 km/h
Step-by-step explanation:
It is given that,
Eric walks 7 km East in 2 hours and then 2.5 km West in 1 hour.
Average speed = distance/time
Distance = 7km + 2.5 km = 9.5 km
Time = 2 h + 1 h = 3 h
Average speed,
[tex]s=\dfrac{9.5\ km}{3\ h}\\\\s=3.17\ km/h[/tex]
Average velocity = displacement/time
Displacement = 7 km +(-2.5 km) = 4.5 km
Average velocity,
[tex]v=\dfrac{4.5\ km}{3\ h}\\\\v=1.5\ km/h[/tex]
So, 3.17 km/h is the average speed and 1.5 km/h is the average velocity for the whole journey that Eric takes.
Follow the steps and finish the solution.
7 (x minus 3) = 28
Distributive property: 7 x minus 21 = 28. Addition property of equality: 7 x = 49. Division property of equality: x = blank.
What is the value of x?
7
9
42
56
Answer:
X=7
Hope this helps, and have a Great Day. You got this!!!
Step-by-step explanation:
Sarah is planning to download music and has purchased a monthly package for $12.00 plus $0.60 for each song that she downloads. If Sarah’s bill this month totaled $39.00 how many songs did she download?
Answer:
Sarah downloaded 65 songs.
Given QRS =TUV,QS=3n+4,and TV=6n-8,find the length of QS and TV.
Answer: A. 16
Step-by-step explanation:
It would be C, but at the end you have to plug it in the 3n + 4. :)
x - 17 = 32 * linear equations
Answer: x=49
x-17=32
Subtract 17 from both sides.
x=32+17
x=49
I WILL GIVE 30 POINTS PLEASE Sinorice put $7.200 in a savings account that pays 3.295 interest compounded annually.
After 3 years, he deposited another $5.000 in the account. What is the value of the account
after 8 years?
A $14 98240
B $15.116.25
C $15.596.30
D $16.073.60
Help me on this please
Answer:
It would be y=-6.
Coach Right is looking at his students' running times in order to place students into running groups. He is working on forming a group that matches Jim's pace of 4 miles in 38 minutes. Which of these student times would fit into a group that runs at the exact same rate as Jim?
Complete question :
Coach Right is looking at his students' running times in order to place students into running groups. He is working on forming a group that matches Jim's pace of 4 miles in 38 minutes. Which of these student times would fit into a group that runs at the exact same rate as Jim? Prax ran 6 miles in 57 minutes. Jose ran 5 miles in 45.5 minutes. Sandy ran 7 miles in 66.5 minutes. Zynep ran 3 miles in 27 minutes
Answer:
Prax and sandy
Step-by-step explanation:
Given that:
Jim's pace = 4 miles in 38 minutes
Jim's rate = Distance covered / time.
Rate = 4 / 38 = 0.1052631 miles /min
Prax ran 6 miles in 57 minutes:
Prax rate : 6miles / 57 mins = 0.1052631
Jose ran 5 miles in 45.5 minutes:
Jose's rate = 5 miles / 45.5 = 0.1098901 miles /
minute
Sandy ran 7 miles in 66.5 minutes:
Sandy's rate = 7 / 66.5 = 0.1052631 miles / minutes
Zynep ran 3 miles in 27 minutes:
Zynep's rate : 3 / 27 = 0.1111111 miles / minutes
A realtor makes a 3% commission on every house they sell. If they just sold a house for $314 000, how much did the realtor make?
Answer: $9420
Step-by-step explanation: 314000x0.03 is 9420
Answer: 314,000 x 0.03 = $9,420
just had a brain spat. help?
Answer:
6
Step-by-step explanation:
First you multiply both sides by 3. Than you simplfiy. Next you add 24 to both sides. Simplify. Finally you divide both sides by 12 & simplify. Which should give you 6.
(Answer = 6)
Answer:6
Step-by-step explanation:
Four different towns in the same state grew in size due to a revitalization effort. The population of town A grew from 22,000 to 24,500 in 4 years. The population of town B grew from 31,200 to 34,770 in 6 years. The population of town C grew from 18,000 to 22,000 in 5 years. The population of town D grew from 32,000 to 34,100 in 3 years. Which town had the greatest average change in population over the corresponding time period?(1 point)
Answer:
Town C.
Step-by-step explanation:
Average change of population with time for town A = [tex] \frac{24,500 - 22,000}{4} = \frac{2,500}{4} = 625 [/tex]
Average change of population with time for town B = [tex] \frac{34,770 - 31,200}{6} = \frac{3,570}{6} = 595 [/tex]
Average change of population with time for town C = [tex] \frac{22,000 - 18,000}{5} = \frac{4,000}{5} = 800 [/tex]
Average change of population with time for town D = [tex] \frac{34,100 - 32,000}{3} = \frac{2,100}{3} = 700 [/tex]
Town C had the greatest average change in population over time (800/yr).
Answer:
its c
Step-by-step explanation:
Write an equation for the line with slope that contains the point (-4, 8)
Answer:
y= 2(-4) + 8
hope it helps
50 POINTS!!!
Write two linear functions, f(x) and g(x). For example, f(x) = 3x – 7 and g(x) = –2x + 5. Then see whether f(x) – (–g(x)) is equivalent to f(x)+ g(x). Hint: To find –g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function.
This can be any equation that would work for this, there is no specific answer.
9514 1404 393
Answer:
f(x) = xg(x) = -2x+1f(x) -(-g(x)) = -x+1f(x) +g(x) = -x+1f(x)-(-g(x)) = (f+g)(x) is true for all functions f and g, linear or notStep-by-step explanation:
We can define a couple of linear functions as ...
f(x) = x
g(x) = -2x+1
Then the reflected function -g(x) is ...
-g(x) = -(-2x +1) = 2x -1
And the difference from f(x) is ...
f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))
We want to compare that to the sum of the functions:
f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)
The two versions of the function expression have the same value.
These results are a property of addition, so do not depend on the nature of f(x) or g(x). They will hold for every function.
Answer:
f(x) = x
g(x) = -2x+1
f(x) -(-g(x)) = -x+1
f(x) +g(x) = -x+1
f(x)-(-g(x)) = (f+g)(x) is true for all functions f and g, linear or not
Step-by-step explanation:
We can define a couple of linear functions as ...
f(x) = x
g(x) = -2x+1
Then the reflected function -g(x) is ...
-g(x) = -(-2x +1) = 2x -1
And the difference from f(x) is ...
f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))
We want to compare that to the sum of the functions:
f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)
The two versions of the function expression have the same value.
These results are a property of addition, so do not depend on the nature of f(x) or g(x). They will hold for every function.
A fruit basket has 6 apples.
It has twice as many oranges as apples and twice as many
apples as bananas. How many more oranges than bananas
are there? Write the equation & answer
Answer: There are 9 more oranges than bananas because there are 6 apples, 12 oranges, and 3 bananas. (12-3=9)
12. If a family is chosen at random from the set of all families with exactly three children, find the probability
that: (2Marks)
a) the family has three boys if it is known that one child is a boy.
b) the family has three boys if it is known that the first child is a boy.
Answer:
(a) 0.25
(b) 0.125
Step-by-step explanation:
The probability of the child being a boy or a girl is 50%.
That is, P (B) = 0.50 = P (G).
It is provided that the family selected has three children.
(a)
Compute the probability that the family has three boys if it is known that one child is a boy as follows:
[tex]P(3B|1B)=\frac{P(3B\cap 1B)}{P(1B)}[/tex]
[tex]=\frac{P(3B)}{P(1B)}\\\\=\frac{(0.50)^{3}}{0.50}\\\\=0.25[/tex]
Thus, the probability that the family has three boys if it is known that one child is a boy is 0.25.
(b)
Compute the probability that the family has three boys if it is known that the first child is a boy as follows:
The gender of the children are independent of each other.
So, if the first child is a boy then the probability of having three boys is:
P (3 boys | 1st boy) = P (1st boy) × P (2nd boy) × P (3rd boy)
= (0.50)³
= 0.125
Thus, the probability that the family has three boys if it is known that the first child is a boy is 0.125.