Answer:
A = 4a² - 4ab + b²
Step-by-step explanation:
The area (A) of a square is calculated as
A = s² ( s is the side length ) , so
A = (2a - b)² ← expand using FOIL
= (2a)² - 2ab - 2ab + (- b)²
= 4a² - 4ab + b²
HELP? I WILL MARK BRAINIEST!!! Yuson must complete 15 hours of community service. She does 3 hours each day. Which linear equation represents the hours Yuson still has to work after x days?
Answer: y = 3x – 15
For the graph of the equation you wrote in Part A, what does the y-intercept represent?
A. Hours of community service completed each day
B. Hours of community service still to complete
C. Total hours of community service that must be completed
D. Days it takes to complete 15 hours of community service
Answer: C
Step-by-step explanation:
6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.
Answer:
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.
A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.
This means that:
[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]
Then
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_n = 17.5(0.7)^{n-1}[/tex]
First 5 terms:
[tex]a_1 = 17.5[/tex]
[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]
[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]
[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]
[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]
Find the total distance the ball has travelled after it hits the ground the 5th time.
[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
The average of 7 numbers is 45.If the last two numbers are 27 and 43 what is the average of the first five
Answer:
49
Step-by-step explanation:
The average is calculated as
average = [tex]\frac{sum}{count}[/tex] Given the average of 7 numbers is 45 , then
[tex]\frac{sum}{7}[/tex] = 45 ( multiply both sides by 7 )
sum of 7 numbers = 315
Subtract 27, 43 from the sum to obtain the sum of first 5 numbers
315 - (27 + 43) = 315 - 70 = 245 , then
average of first 5 numbers = [tex]\frac{245}{5}[/tex] = 49
Select the fraction greater than 7/9. a)4/5 b)2/3 c)13/18 d)3/5
Answer:
A)4/5
Step-by-step explanation:
7/9=0.778
so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.
a)4/5=0.8
b)2/3=0.667
c)13/18=0.722
d)3/5=0.6
The decimal that's greater than 0.778 is A=0.8 so that's the answer.
Solve for X
I’ll give BRAINLIEST to the correct answer
Answer: x = 19
Hi! I was studying for the NYC SHSAT when this exact problem came up a year ago. I will do my best to try to answer it correctly!
Step-by-step explanation:
To start, we have to notice the similar properties of the angles. They are alternate exterior angles (?). Therefore, I think that you just have to put the angles on opposite sides of the equation!
(6x + 6) = 120
-6 -6
6x/6 = 114/6
x = 19
The product of two integers is (-112).
If one of them is (-8), find the other.
[tex]\huge\bold{Given :}[/tex]
Product of two integers = - 112
One of the integer = -8
[tex]\huge\bold{To\:find :}[/tex]
The other integer.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\blue{The \:other \:integer\:is\: 14.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Let the other integer be [tex]x[/tex].
As per the question, we have
[tex]Product \: \: of \: \: two \: \: integers = - 112[/tex]
➼ [tex] \: - 8 \times x = - 112[/tex]
➼ [tex] \: x = \frac{ - 112}{ - 8} [/tex]
➼ [tex] \: x = 14[/tex]
[tex]\sf\purple{Therefore,\:the\:other\:integer\:x\:is\:14.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex] - 8 \times 14 = - 112[/tex]
➺ [tex] \: - 112 = - 112[/tex]
➺ L. H. S. = R. H. S
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
Answer:
If the product of two integers is -112 and one of them is -8, that means the value of the second integer would be 14.
Step-by-step explanation:
The product of two integers equals -112 means that there are two numbers that, when multiplied, were equivalent to -112. Since you know one of the integers is -8, you can infer that the second integer is both a positive number AND the remainder of [tex]\frac{-112}{-8}[/tex] or 14.
(x+1)^2 . (x^2+1) = 0
Answer:
[tex]x^4+2x^3+2x^2+2x+1[/tex]
Step-by-step explanation:
Given that,
[tex](x+1)^2 . (x^2+1) = 0[/tex]
We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]
So,
[tex](x+1)^2=x^2+1+2x[/tex]
So,
[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]
So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]
3
2
In the diagram above, Z3 = 40°.
Find the measure of Z2.
L2 = [?]°
Mr. Brown has a gate that measures 65 ft by 72 ft. He needs to reinforce the gate by placing a strip of wood on the diagonal of the fence. How long will the strip of wood need to be?
(5+6b^3)^2 expand and combine like terms
Answer:
[tex]( 5 + 6b^3)^2 = 36b^6 + 60b^3 + 25[/tex]
Step-by-step explanation:
[tex](a + b)^2 = a^2 + b^2 + 2ab[/tex]
So,
[tex](5 + 6b^3)^2 = (5)^2 + (6b^3)^2 + 2 (5)(6b^3)[/tex]
[tex]= 25 + 36b^6 + 60b^3[/tex]
What is the difference of the rational expressions below? 4/x^3 - 2x-1/3x
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{4}{x^3}[/tex] - [tex]\frac{2x-1}{3x}[/tex]
Multiplying the numerator/ denominator of the first fraction by 3 and the numerator/denominator of the second fraction by x² will ensure that the fractions have a common denominator.
= [tex]\frac{3(4)}{3x^3}[/tex] - [tex]\frac{x^2(2x-1)}{3x^3}[/tex]
= [tex]\frac{12}{3x^3}[/tex] - [tex]\frac{2x^3-x^2}{3x^3}[/tex] ← combine terms on numerator
= [tex]\frac{12-2x^3+x^2}{3x^3}[/tex]
= [tex]\frac{-2x^3+x^2+12}{3x^3}[/tex] → C
Select all the correct answers.
Which expressions are equivalent to the given expression?
Answer:
6√7=15.874507866387543=√252
Step-by-step explanation:
hope this is helpful
The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.
How to find equivalent expression?
Applying the surd rule,
√a = [tex]a^{\frac{1}{2} }[/tex]
Hence,
[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]
using surd rule, we can also decompose √252
Therefore,
√252 = √36 × 7 = 6√7
Hence, the equivalent expression of √252 are as follows:
[tex]252^{\frac{1}{2} }[/tex]6√7learn more on expression here: https://brainly.com/question/27768447
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Given: x+y=10
If x= -21, what is y?
Type a numerical answer in the space provided. Do not type spaces in your answer
Answer:31
Step-by-step explanation:
Answer:
y=31
Step-by-step explanation:
-21 + y= 10
-21 + y + 21 =10 + 21
y = 10+21
y = 31
HOPE THIS ANSWER HELPS YOU :)))
Write the equation in slope-intercept form from the graph
Answer:
[tex]1) y=\frac{1}{2} x+1[/tex]
[tex]2)y=-x-1[/tex]
[tex]3)y=-\frac{1}{2} -3[/tex]
Step-by-step explanation:
Hope this helps
I don't really understand it's due soon can someone please help me
Answer:
60
Step-by-step explanation:
Given: 1/2a + 2/3b =50
(Since b is equal to 30 we will automatically replace b with 30)
Step 1: Simplify both sides of the equation.
1/2a+20=50
Step 2: Subtract 20 from both sides.
1/2a=50-20
1/2a=30
Step 3: Multiply both sides by 2.
2(1/2a) 2(30)
a=60
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Answer:
a = 15
Step-by-step explanation:
1/2(a) + (2/3 x 30) = 50
2/3 x 30 = 20
1/2(a) + 20 = 50
Rearrange > 20 to -20
-20 + 50 = 30
1/2(a) = 30
Rearrange 1/2 to 2
2 > 30/2
30/2 = 15
a = 15
Hope this helps, and please let me know if it is correct or isn't.
Have a nice day
Line CD passes through points C(1,3) and D(4,-3). What is the equation of line CD in standard form?
Answer:
2x + y = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = C (1, 3) and (x₂, y₂ ) = D (4, - 3)
m = [tex]\frac{-3-3}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 3 )
3 = - 2 + c ⇒ c = 3 + 2 = 5
y = - 2x + 5 ← equation in slope- intercept form
Add 2x to both sides
2x + y = 5 ← equation in standard form
help help help help help
Answer:
y = 45
Step-by-step explanation:
y = 9x
input = 5
y = 9(5)
9(5) = 45
y = 45
Can somebody pls help !!
Answer:
$26.84
Step-by-step explanation:
We have to find 10% of 268.40. To do that, we multiply it by 0.10:
268.40 * 0.1 = 26.840, or $26.84
given that x^2+y^2=9 and xy=5, find the value of (x - y)^2.
Answer:
[tex](x -y)^2 = -1[/tex]
Step-by-step explanation:
[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]
[tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]
The binomial expansion of (x - y)² is
(x - y)² = x² - 2xy + y²
Substitute the given values to the equation
(x - y)² = x² - 2xy + y²
(x - y)² = x² + y² - 2xy
(x - y)² = 9 - 2(5)
(x - y)² = 9 - 10
(x - y)² = -1
Therefore the value of (x - y)² is -1.
#ILoveMath
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Second Number Cube
1
2.
3
4
5
6
First Number Cube
locN-
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
How many possible outcomes are there?
O 6
12
Answer:
36
Step-by-step explanation:
summation of all the outcome
There are 36 possible outcomes is shows in table for rolling two six - sided number cubes.
What is mean by Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The table shows all the possible outcomes for rolling two six - sided number cubes.
Now, We know that;
For rolling one six - sided number cubes,
There is 6 possible outcomes.
Hence, For two six - sided number cubes.
Number of possible outcomes = 6 × 6
= 36
Thus, There are 36 possible outcomes is shows in table for rolling two six - sided number cubes.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
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show the solution 3×(2÷3)^3+(2÷3)^2−20×2÷3+12
Answer with Step-by-step explanation:
We are given that
[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]
[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]
[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]
[tex]\frac{4-40}{3}+12[/tex]
[tex]-\frac{36}{3}+12[/tex]
[tex]-12+12[/tex]
[tex]=0[/tex]
In order for the parallelogram to be a
rhombus, x = [?].
(5x - 8°
(2x + 16)°
Answer:
8
Step-by-step explanation:
5x-8 = 2x+16
Move 2x to the left side and you get 3x-8 = 16
Move -8 to the right side and you get 3x = 24
Divide 3 on both sides and you get x = 8
Mary is making a recipe that calls for 3/4 teaspoon of cinnamon. Her only
measuring spoon holds 4/8 teaspoon. How many times will she need to fill
her measuring spoon to get enough cinnamon for the recipe?
Answer:
She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.
3/4 ÷ 4/8
=3/4 * 2/1
=6/4
=1.5
So, that much amount would be needed o be added to the recipe during the two times
How many quarters are there in 5 3/4?
Answer:
One quarter= 1/4
5 3/4= 23/4
Number of quarters in 5 3/4= 23/4 divided by 1/4
23/4 ÷ 1/4
= 23/4 × 4
=23
I hope this helps!
Answer:
23
Step-by-step explanation:
5x4 + 3
5 x 4 = 20
20 + 3 (3 Is the fraction part)
What they mean by 1/2? I mean I do know that 1/2 means half, but what they mean?
Step-by-step explanation:
See you know the area of rectangle that is base x perpendicular
When you cut half the area of rectangle, it becomes a triangle
That is why the formula is 1/2 x base x perpendicular
What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.
Answer:
Average rate of change = 0.6
Step-by-step explanation:
Average rate of change of a function between x = a and x = b is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the graph attached,
f(-5) = 0
f(0) = 3
Average rate of change of the graph between x = -5 and x = 0,
Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.
doe anyone know this
If f(1) = 2 and f(n) = f(n − 1)2 + 3 then find the value of f(3).
Answer:
52
Step-by-step explanation:
f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into
f(n-1)²+3 to get
f(1)²+3 = 2²+3 = 4+3=7
Thus, f(2) =7. Similarly,
f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52
Are the two triangles similar? How do you know? Explain your reasoning thoroughly.
Answer:
Yes, the triangles are similar ([tex]\triangle HMG \sim \triangle KMJ[/tex]).
Step-by-step explanation:
We're given that the two triangles share at least one angle, angles H and K. The two angles in the triangles at point M, [tex]\angle HMG[/tex] and [tex]\angle KMJ[/tex] are vertical angles, meaning they are on opposite sides of a point of intersection between two lines. Since vertical angles are always equal, these two angles are also equal.
If two triangles share two angles, they must share all three, because all triangles have a total sum of interior angles of 180 degrees. Therefore, the triangles share all 3 angles. AAA (Angle-Angle-Angle) is a proof of similarity, where two triangles share all three of their angles. Thus, the two triangles are similar.
Similarity statement (vertices should correspond):
[tex]\triangle HMG \sim \triangle KMJ[/tex]
Determine if the product of 2/18 • 3/3 is rational or irrational?
Explain your answer.
Answer:
Rational.
Step-by-step explanation:
2/18=0.1 repeating.
3/3 = 1
Multiplying these together get you 0.1 repeating.
There is only one rule that makes a number irrational.
This is a number that is not divisiable by two integers, and is not capable of being expressed as a fraction.
0.1, as we know, can be written as 2/18, or 1/9.
So it must be a rational number.
Something you may not know - Rational numbers CAN be infinitly repeating numbers.
For instance, 0.111 like shown above is repeating, and its rational.
However, pi is a repeating number...but its irrational.
This is not because its infinitly repeating, this is actually becuase it is not divisiable by two numbers, and cannot be put into fraction form.
Some people think infinitly repeating numbers are irrational, however this is not correct, for some fractions are actually repeating.
Hope this helps!