Consider, we need to find the expanded form of the given expression.
Given:
The expression is:
[tex]\left(a+b\right)^2[/tex]
To find:
The expanded form of the given expression.
Solution:
We have,
[tex]\left(a+b\right)^2[/tex]
It can be written as:
[tex]\left(a+b\right)^2=(a+b)(a+b)[/tex]
Using distributive property of multiplication over addition, we get
[tex]\left(a+b\right)^2=a(a+b)+b(a+b)[/tex]
[tex]\left(a+b\right)^2=a(a)+a(b)+b(a)+b(b)[/tex]
[tex]\left(a+b\right)^2=a^2+ab+ab+b^2[/tex]
[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]
Therefore, the expanded form of the given expression is [tex]a^2+2ab+b^2[/tex].
Miranda's financial aid stipulates that her tuition not exceed $1500. If her college charges a $55 registration fee for the term plus $275 per course, what is the greatest number of courses for which Miranda can register? Miranda can register for at most how many courses?
Answer:
5
Step-by-step explanation:
275x5= 1375
1375+55=1430
How many ways can a person toss a coin 16 times so that the number of heads is between 7 and 14 inclusive
50626 ways with a probability of 0.77
Step-by-step explanation:If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2
If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4
If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.
Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.
From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;
Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]
Where;
n = number of tosses
x = number of selection
number of ways of getting 7 heads;
n = 16
x = 7
=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]
=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]
=> C₁₆, ₇ = 11440
number of ways of getting 8 heads;
n = 16
x = 8
=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]
=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]
=> C₁₆, ₈ = 12870
number of ways of getting 9 heads;
n = 16
x = 9
=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]
=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]
=> C₁₆, ₉ = 11440
number of ways of getting 10 heads;
n = 16
x = 10
=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]
=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]
=> C₁₆, ₁₀ = 8008
number of ways of getting 11 heads;
n = 16
x = 11
=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]
=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]
=> C₁₆, ₁₁ = 4368
number of ways of getting 12 heads;
n = 16
x = 12
=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]
=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]
=> C₁₆, ₁₂ = 1820
number of ways of getting 13 heads;
n = 16
x = 13
=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]
=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]
=> C₁₆, ₁₃ = 560
number of ways of getting 14 heads;
n = 16
x = 14
=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]
=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]
=> C₁₆, ₁₄ = 120
Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e
11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways
P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]
= [tex]\frac{50626}{65536}[/tex]
= 0.77
HELP THIS IS DUE SOON MATH
Answer: the answer is x= -11.
What is the equation of the line that passes through the point (-7, -4) and has a
slope of 1?
Answer:
Y=x+3
Step-by-step explanation:
we have :
x1= -7
y1= -4
m=1
as we know Y-y1=m(X-x1)
Y+4=(X+7)
Y+4=X+7
Y=X+7-4
Y=X+3
Tập nghiệm của phương trình 2^x=-1 là
Step-by-step explanation:
Tập nghiệm của [tex]2^x=-1[/tex] là tập rỗng nha bạn. Vì 2 là số dương nên mũ mấy cũng dương hết.
Making of a muffin requires 32 ounces of sugar. Convert ounces to pounds?
Answer:
2 pounds
Step-by-step explanation:
1 pound = 16 ounces
x pound = 32 ounces
[tex]x = \frac{32}{16} = 2 \ pounds[/tex]
Answer:
the answer to 32ounces is 2 pounds
- 10 + x < - 2 what is the solution of the inequality shown below
Answer:
x<8
Step-by-step explanation:
GIVING OUT BRAINLIEST HELP PLEASE ❤️
Answer:
C
Step-by-step explanation:
Dùng kiến thức về suy luận
3.1. Phát biểu các quy tắc suy diễn modus ponens, lựa chọn và bắc cầu.
3.2. Em hãy viết một đoạn văn ngắn (không quá 30 từ, không giống giáo trình) thỏa:
1) Quy tắc modus tollens.
2) Quy tắc
, ( )
( )
x p x
p a
∀
.
3.3. Em hãy xem đoạn suy luận sau đây theo quy tắc logic nào, có hợp logic hay không?
1) Một đất nước muốn phát triển về nhiều mặt thì cần phải hội nhập quốc tế. Việt Nam muốn
phát triển về nhiều mặt. Vậy Việt Nam cần phải hội nhập quốc tế.
2) Nếu trường học không có thầy giáo tốt và không có cơ sở vật chất tốt thì không có chất
lượng giáo dục tốt. Trường X không có cơ sở vật chất tốt mà có chất lượng giáo dục tốt.
Vậy trường X có thầy giáo tốt.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hagg
What is the measure of angle O in parallelogram LMNO?
Answer:
O=74
Step-by-step explanation:
L=N
180-106=74
M=O
Find the value of x and the value of y.
Please help :(
Answer:
Step-by-step explanation:
chia hình tứ giác thành 1 hình chữ nhật và một tam giác vuông từ đó y=4/sin(45)= 4,7 ; x=3+4/tan(45)=5,469
Solve this im stuck please solve!
4. Steven drove from place A to place B at an average speed of 50 km/h. At the same
time, Joseph drove from place B to place A at an average speed of 60 km/h using
the same route. If the distance between A and B were 300 km, what is the distance
between Steven and Joseph after one and one half hours?
5.An owner jeep traveling at an average speed of 70 km/h left the town at 2:00 pm
If it arrived in another town at 6:00 p.m., how far are the two towns?
Answer:
1. 10 km
2.280 km
please mark my answer as brainliest answer.
the answer is surely correct
Bob's Gift Shop sold 650 cards for Mother's Day. One salesman, Scarlett, sold 10% of
the cards sold for Mother's Day. How many cards did Scarlett sell?
Answer:
65
Step-by-step explanation:
To find the amount of something given a percentage, we first must translate the percentage into a fraction or decimal. One way to do this is to divide the percentage by 100. In this case, we can divide 10% by 100 to get 0.1
We can then multiply the percent by the total, or 100%. In this case, we have 0.1 of 650, so we multiply the two to get 0.1 * 650 = 65 as 10% of 650, or how many cards Scarlett sold
Answer:
65
Step-by-step explanation:
650 x .10 (or 10%)=65
PLEASE help! I really appreciate it thanks!
Answer:
h=A-πr²÷2πr
Step-by-step explanation:
Making h subject
A=2πrh+πr²
A-πr²=2πrh
A-πr²÷2πr=h
h=A-πr²÷2πr
Answer:
The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Step-by-step explanation:
To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].
Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Type the correct answer in the box. Use numerals instead of words. Tony bought a new car at a cost of $20,000. The value of the car decreases by approximately 12% each year. Formulate the equation that gives the value, A(+), of the car xyears since Tony bought the car. A(t)-
9514 1404 393
Answer:
A(x) = 20000(0.88)^x
Step-by-step explanation:
The general form of these exponential equations is ...
A(x) = a·b^x
where 'a' is the initial value, and b is the annual growth factor. x is the elapsed time in years.
The growth factor is ...
growth factor = 1 + growth rate
Here, the growth rate per year is -12%, so the growth factor is ...
b = 1 -12% = 88% = 0.88
Of course, the initial value is a=20,000, so the equation is ...
A(x) = 20000(0.88)^x
All of the following statements have the same value except..?
1. six below zero
2. the opposite of six
3. negative six
4. the absolute value of six
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
Let's consider each of the statements.
1. Six below zero.
⟹ Any number below zero will be negative. So, the value will be [tex]\boxed{-6}[/tex]
____________________
2. The opposite of six.
⟹ The opposite of 6 wil be negative 6. The value again will be [tex]\boxed{-6}[/tex]
____________________
3. Negative six.
⟹ Negative six in numerical form is [tex]\boxed{-6}[/tex]
____________________
4. The absolute value of six.
⟹ Here they've asked the absolute value of 6 which will be [tex]\boxed{6}[/tex]
____________________
⏩ So, the statement which doesn't have the same value will be ⇻ [tex]\boxed{statement \ 4}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex]RainbowSalt2^{2}2^{2}[/tex]
can someone help me with this question
Answer:
D
Step-by-step explanation:
this answer is correct , i think if you think of it in logically
function travelSpeed = CalculateTravelSpeed(startX, startY, endX, endY, travelTime) % startX, startY: Starting coordinates % endX, endY: Ending coordinates % travelTime: Travel time in hours % Write an anonymous function to compute distance given two coordinates % Function name: EuclideanDist % Function inputs: x1, y1, x2, y2 % EuclideanDist = ... % Do not modify the statement below travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime; end
Answer:
The functions in Python is as follows:
from math import *
def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):
travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime
return travelSpeed
def EuclideanDist(startX, startY, endX, endY):
dist = sqrt((startX - endX)**2 + (startY - endY)**2)
return dist
Step-by-step explanation:
from math import *
This defines the CalculateTravelSpeed function
def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):
This calls the EuclideanDist function to calculate the distance; Next, the speed is calculated
travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime
This returns the calculated speed
return travelSpeed
This defines the EuclideanDist function
def EuclideanDist(startX, startY, endX, endY):
This calculates the distance from the given coordinates
dist = sqrt((startX - endX)**2 + (startY - endY)**2)
This returns the calculated distance
return dist
Help is very much needed!!
Answer:
DE = 24
Step-by-step explanation:
The midsegment DE is half the length of the third side AC , that is
DE = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 48 = 24
Here are the first three terms of a different sequence.
1
3
9
Write down two numbers that could be the 4th term and the 5th term of this sequence.
Give the rule you have used to get your numbers.
please helpp
Step-by-step explanation:
everything can be found in the picture
What is 2+2-35x62+88-1x675
[tex]\longrightarrow{\blue{ -2753}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]2 + 2 - 35 \times 62 + 88 - 1 \times 675[/tex]
[tex] = 2 + 2 - 2170 + 88 - 675[/tex]
[tex] = 92 - 2170 - 675[/tex]
[tex] = 92 - 2845[/tex]
[tex] = - 2753[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Find the y-coordinates of the points that are 10 units away from the point (-1,6) that have an x-coordinate of 7
Answer:
y = 0 or 12
Step-by-step explanation:
[tex]Let \ (x _ 1 , y _ 1) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ coordinates \ \\\\Distance \ between \ the \ points = \sqrt{(x_2 - x_1)^2 + (y_ 2 -y_1)^2}\\\\[/tex]
[tex]Given : distance = 10 \ units , (x_1 , y _ 1 ) = ( - 1 , 6 ) \ and \ (x_2 , y _ 2 ) = (7 , y )\\\\[/tex]
[tex]Substituting \ the \ values \ \\\\10 = \sqrt{(7 -(-1))^2 + (y - 6)^2}\\\\10 = \sqrt{(7 + 1)^2 + ( y - 6 )^2}\\\\10 = \sqrt{8^2 + ( y - 6)^2 }\\\\10 = \sqrt{64 + (y -6)^2 } \\\\Squaring \ both \ sides \\\\10^2 = (\sqrt{64 + (y -6)^2 })^2\\\\100 = 64 + ( y -6)^2\\\\100 - 6 4 = ( y -6)^2 \\\\36 = ( y - 6 )^2\\\\\sqrt{36} = y - 6\\\\\pm 6 = y - 6 \\\\So, \\\\\ y - 6 = 6 => y = 12\\\\\ \ \ \ y - 6 = - 6 => y = 0[/tex]
The y coordinate of the point is P ( 7 , 12 ) or P ( 7 , 0 ) where the distance of the point is 10 units from Q ( -1 , 6 )
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P ( 7 , y )
Let the second point be Q ( -1 , 6 )
Now , the distance between P and Q is D = 10 units
So , on simplifying the equation , we get
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
10 = √ [ ( 7 - ( - 1 ) )² + ( y - 6 )² ]
Squaring both sides of the equation , we get
100 = ( 8 )² + ( y - 6 )²
Subtracting 64 on both sides of the equation , we get
( y - 6 )² = 36
Taking square roots on both sides , we get
y - 6 = ±6
Adding 6 on both sides , we get
y = +6 + 6 = 12
or y = -6 + 6 = 0
So , the coordinates of the point P is P ( 7 , 12 ) or P ( 7 , 0 )
Hence , the distance formula is solved and coordinates of the point P is P ( 7 , 12 ) or P ( 7 , 0 )
To learn more about distance between 2 points click :
https://brainly.com/question/18234495
#SPJ2
Select the correct answer from each drop-down menu.
Some of the images in the diagram are images of polygon 1 from similarity transformations ?
Polygon and polygon are similar to polygon 1.
Answer: 3 and 4
Step-by-step explanation:
Complete equation describing how X and Y are related.
Answer:
[tex]2[/tex]
Step-by-step explanation:
Every time the x-value increases by 1, the y-value increases by 2. Therefore, the slope of the line must be equal to [tex]2/1=\boxed{2}[/tex] (rise/y-values over run/x-values). In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents the slope of the line, [tex]b[/tex] represents the y-intercept, and [tex](x,y)[/tex] represents any point the line passes through.
Since [tex]m[/tex] represents the slope of the line, the value of
While the question only asks for this value, it's good to note that the equation of the function is [tex]y=2x+7[/tex] (find 7 by substituting any ordered pair in the table with [tex]m=2[/tex]).
Answer:
y = 2x + 7
Step-by-step explanation:
y = mx + b
For every increase of 1 in x,
there is an increase of 2 in y
m = 2
When x is 0,
y is 7
b = 7
y = 2x + 7
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 14 cups of coffee, using 204 ounces of coffee, while collecting a total of $16.70. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answer:
Step-by-step explanation:
Lets assume that Kyle fill "a" 10-oz cups of coffee, "b" 14-oz cups of coffee and "c" 20 oz cups of coffee.
a + b + c = 16 (1)
10*a + 14*b + 20*c = 224 (2)
0.95*a + 1.15*b + 1.50*c = 18.60 (3)
Now, multiplying equation (1) by 10 and subtracting it from equation (2), we get
4b + 10c = 64 (4)
Again, multiplying equation (1) by 0.95 and substracting it from equation (3), we get,
0.2b + 0.55c = 3.4 (5)
Now,
Multiplying equation (5) by 20 and subtracting it from equation (4), we get
-c = -4,
Hence, c= 4
Putting this value in equation (4),
4b + 40 = 64
Hence, 4b = 24
So, b = 6
Again, putting the values of b and c in equation (1),
a + 6 + 4 = 16
Thus,
a = 6
Hence, the solution is
a = 6, 10oz cups of coffee
b = 6, 14 oz cups of coffee
c = 4, 20 oz cups of coffee
Pls help as fast as u can pls...
Answer:
226=2×113
321=3×107
305=5×61
133=7×19
Classify the questions as statistical or not statistical.
How many houseplants
does each house on my
block have?
How many hours did Ryan
study last Saturday?
How many hours do students
in my class study every day?
How many cars does each
person in my neighborhood
own?
How many bags do I own?
How many students in my
class own 2 bags?
Answer:
1- statistical
2- statistical
4 - statistical
remaining others are non statistical in my opinion
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
Check explanation
Step-by-step explanation:
I'll give you my way of solving it and you can figure it out from there.
<CEA = <DEB due to vertical angles
AE = ED due to midpoint theorem
<CAD = <ADB due to alternating angles theorem
thus two triangles congruent due to ASA
1. My number has two digits.
2. Double my number is less than 150.
Follo
ther
3. I am not divisible by 12.
4. My digits are different from each other.
5. The second digit in my number is divisible
by an odd number.
6. My first digit is less than my second digit.
7. My digits add up to 14.
way.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
1. My number has two digits.
59 is a two-digit number. ✔2. Double my number is less than 150.
Double of 59 is 118, which is less than 150. ✔3. I am not divisible by 12.
Since 59 is an odd number, hence it is not divisible by 12. ✔4. My digits are different from each other.
The digits 5 and 9 are different. ✔5. The second digit in my number is divisible by an odd number.
9 is divisible by an odd number, i.e. 3. ✔6. My first digit is less than my second digit.
5 is less than 9. ✔7. My digits add up to 14.
5 + 9 gives us 14. ✔Therefore, the required number is [tex]\sf\pink{59}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
59
Step-by-step explanation:
two digits, 59=118, unable to divide by twelve since its an odd number, 9÷3=3, 5<9, 5+9=14