Notice that both sides of the equation have a similar form. If we ignore angle functions we end up with,
[tex]A+A\cdot B=B+B\cdot A[/tex]
That is true if condition [tex]A=B[/tex] is met.
Otherwise it is false.
Hope this helps.
r3t40
help!! asap!
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)
Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Answer:
A) A(p(t)) = 25πt²
B) 314 square units.
Step-by-step explanation:
Part A)
Flow of paint can be expressed by the function:
p(t) = 5t
Area of the pattern is expressed as:
A(p) = πp²
Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:
A(p(t)) = π (5t)²
A(p(t)) = 25πt²
Part B)
We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:
A(p(2)) = 25 x 3.14 x 4 = 314 square units.
Therefore, the area of spilled paint after 2 minutes will be 314 square units.
Choose a system of equations with the same solution as the following system: 6x + 2y = −6 3x − 4y = −18
Final answer:
To find a system with the same solution, multiply one of the original equations by a constant and/or add the two original equations together to derive a new equation. An example is the alternative system 6x - 8y = -36 and 9x - 2y = -24, which shares the same solution as the original.
Explanation:
To find a system of equations with the same solution as the given system:
6x + 2y = −6
3x − 4y = −18
We must ensure that the alternative system is equivalent, meaning they share the same solution. A common technique is to multiply both sides of one or both of the equations by a constant to create new equations that have the same solutions. For example, we could multiply the second equation by 2:
3x − 4y = −18 becomes 6x − 8y = −36 after multiplying by 2.
Then, to avoid having the same equation, we could add the original second equation to the first one to get a different second equation:
6x + 2y + (3x − 4y) = −6 + (−18) becomes 9x − 2y = −24.
So, the alternate system that shares the same solution as the original would be:
6x − 8y = −36
9x − 2y = −24
What is 12% of 4? Explain and Show your work
Answer:
0.48
Step-by-step explanation:
convert the percent to a decimal
12%=0.12
multiply 4 by 0.12
you're left with 0.48
you can check your math by dividing .48/.12, which will give you 4
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole
We want to know what is 12% of the number 4. This means 4 is the whole and the unknown (let's make this x) is the part.
[tex]\frac{x}{4} =\frac{12}{100}[/tex]
Now you must cross multiply
x*100 = 4*12
100x = 48
Now isolate x divide 100 to both sides
100x/100 = 48/100
0.48 = x
This means that 12% of 4is 0.48
Hope this helped!
~Just a girl in love with Shawn Mendes
10 - 4(2.4 • 3.5)2 + 0.12 10 - 4(8.4)2 + 0.12 10 - 4(70.56) + 0.12
Answer:
- 406.278
Step-by-step explanation:
10 - 4(2.4 • 3.5)2 + 0.12 10 - 4(8.4)2 + 0.12 10 - 4(70.56) + 0.12
Using BODMAS rule, first operation under bracket will be done. Then after Multiplication, addition and subtraction will be solved.
= 10 - 4 (8.4) 2 + 0.1210 - 4(8.4) 2 + 0.1210 - 4 (70.56) + 0.12
= 10 - 67.2 + 0.1210 - 67.2 + 0.1210 - 282.24 + 0.12
= - 406.278
If f(x) is a third degree polynomial function how many distinc complex rules are possible ?
Answer:
2
Step-by-step explanation:
According to the fundamental theorem of Algebra
A polynomial of degree 3 has 3 roots
However, complex roots occur in conjugate pairs, hence
There can only be 2 distinct complex roots.
Explain how System 1 becomes equivalent to System 2.
System 1:
AX + By = C
LX + My=N
System 2:
(A + L)X + (8 + M)y = C+N
AX + By = C
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
B.The first equation in System 2 is the difference of the equations in System 1. The second equation in System 2 is the first equation in System 1.
C.The first equation in System 1 is the sum of the equations in System 2. The second equation in System 1 is the second equation in System 2.
D.The first equation in System 1 is the difference of the equations in System 2. The second equation in System 1 is the second equation in System 2.
Answer:
[tex]\left\{\begin{array}{ccc}(A+L)x+(B+M)y=C+N\\Ax+By=C\end{array}\right[/tex]
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}Ax+By=C\\Lx+My=N\end{array}\right}\qquad\text{add both sides of the equations}\\(Ax+Lx)+(By+My)=C+N\qquad\text{distributive}\\(A+L)x+(B+M)y=C+N[/tex]
Equivalent expressions are expressions that have the same value.
The true statement is: (a) The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
The systems of equations are:
System 1
[tex]\mathbf{Ax + By = C}[/tex]
[tex]\mathbf{Lx + My = N}[/tex]
System 2
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
[tex]\mathbf{Ax + By = C}[/tex]
When the equations of system 1 are added, we have:
[tex]\mathbf{Ax + Lx + By + My = C + D}[/tex]
Factor out x and y
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
The above equation is the first equation of system 2.
While [tex]\mathbf{Ax + By = C}[/tex] is the second equation of the system
Hence, the true statement is (a)
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Evaluate sin-1(-1/2) for the angles between 0 and 360°
PLEASE HELP!!!!
Check the picture below, notice the angles encircled in purple.
Use the given area to find XY. A. 8 cm B. 12 cm C. 16 cm D. 24 cm
Answer:
A
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides = a : b
and ratio of areas = a² : b²
Here the ratio of areas = 7 : 28 = 1 : 4, hence
ratio of sides = [tex]\sqrt{1}[/tex] : [tex]\sqrt{4}[/tex] = 1 : 2
Hence
XY = 2 × DE = 2 × 4 = 8 cm
The answer is XY=2*DE=2*4=8cm, in summary, eight cenimeters.
the width of the credit card is 5.6 CM what is in millimeters
Answer: 56
Step-by-step explanation:
For this case we must make a conversion of centimeters to millimeters. By definition we have to:
1 cm equals 10 mm
By making a rule of three we have:
1 cm ---------> 10 mm
5.6 cm --------> x
Where "x" represents the quantity in millimeters.
[tex]x = \frac {5.6 * 10} {1} = 56[/tex]
Thus, we have that 5.6 centimeters equals 56 millimeters.
Answer:
56mm
which of the following is the quotient of the rational expressions shown below x-2/x+3 divided by 2/x
Answer:
2x^2+4x/3x-3
Step-by-step explanation:
ape.x
The quotient of (x-2)/(x+3) divided by 2/x is (x² - 2x)/(2x + 6), which corresponds to option D. This is achieved by multiplying the first fraction by the reciprocal of the second fraction and then simplifying.
To find the quotient of (x-2)/(x+3) divided by 2/x, we'll follow these steps:
Rewrite the division of fractions as multiplication by the reciprocal. This means:(x-2)/(x+3) ÷ (2/x) = (x-2)/(x+3) * (x/2)Multiply the numerators and multiply the denominators:((x-2) * x) / ((x+3) * 2) = (x(x-2)) / (2(x+3))Simplify the expression:(x² - 2x) / (2x + 6)Looking at the given options, the correct answer is: (x² - 2x) / (2x + 6) (Option D)
The complete question is
which of the following is the quotient of the rational expressions shown below x-2/x+3 divided by 2/x
A. (2x - 4)/(x ^ 2 + 3x)
B. (2x - 2)/(x ^ 2 + 3x)
C. x/(2x + 3)
D. (x² - 2x)/(2x + 6)
a train traveling at an average speed of 85 miles per hour. At this rate, how far will the train travel in 12 1/4 hours?
Answer:
1041.25 miles
Step-by-step explanation:
You just have to multiply 12.25 (which is equivalent to 12 1/4) by 85 and you'll get the answer 1041.25
Answer:
1041.248 miles
Step-by-step explanation:
Points to remember
Speed = Distance/Time
It is given that,a train traveling at an average speed of 85 miles per hour.
To find the speed of train
Speed = 85 miles/1
= 136.794 km/1 = 136.794 km/hr
To find the distance traveled in 12 1/4 hours
Distance = Speed * time
= 136.794 * 12 1/4
= 136.794 * 49/4
= 1675.7265
= 1041.248 miles
Built in 1599, the Globe Theatre was home to William Shakespeare and his performing company, The Lord Chamberlain’s Men. It was a circular amphitheater that stood 3-stories tall and had a diameter of 100 feet. What formula can you use to calculate the distance around the theatre?
Answer:
C = pi * d formula
C = 314 ft
Step-by-step explanation:
To find the distance around the theatre, we want to use circumference.
C= 2 * pi *r where r is the radius
or
C = pi * d where d is the diameter
C = pi *100
C = 100pi
Using 3.14 as an approximation for pi
C = 3.14*100
C = 314 ft
Here are the heights in inches of 10 professional basketball players: 66, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these heights is 77.6 inches. Does this set have an outlier and, if so, how does removing it affect the mean?
The set has 66 as an outlier and removing it decreases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it decreases the mean by about 6.6 inches.
The set has no outliers.
Question 5
Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 50 affect the mean?
The set has 50 as an outlier and removing it decreases the mean by about 10.
The set has 50 as an outlier and removing it decreases the mean by about 2.
The set has 50 as an outlier and removing it increases the mean by about 3.
The set has 50 as an outlier and removing it decreases the mean by about 6.
Answer:
Question 4: The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5: The set has 50 as an outlier and removing it increases the mean by about 3.
Step-by-step explanation:
Question 4:
Given heights are:
66, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is: 77.6 inches
Removing 66 will make the mean increase to 78.9
So,
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5:
50, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is 76.
We can clearly see that 50 is an outlier as it is quite less than the given data.
Calculating mean after removing 50 will give us mean equal to 78.9
So the correct answer is:
The set has 50 as an outlier and removing it increases the mean by about 3.
What is the solution to the equation fraction 1 over 6 x = 2?
x = fraction 1 over 12
x = fraction 1 over 3
x = 3
x = 12
Answer:
C=1/12
1/6x=2 so 1=12x
X=1/12
Step-by-step explanation:
Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
The solutions to the inequality x^2 + 3x - 4 > 0 are all real numbers where x is less than -4 or greater than 1, represented by the intervals (x < -4) or (x > 1).
To find the values that are solutions to the inequality x2 + 3x - 4 > 0, we first need to determine the roots of the quadratic equation x2 + 3x - 4 = 0. We can do this either by factoring, completing the square, or using the quadratic formula. In this case, factoring is the simplest approach:
x2 + 4x - x - 4 = 0
(x + 4)(x - 1) = 0
Therefore, the roots are x = -4 and x = 1. Since it is a parabola opening upwards (the coefficient of x2 being positive), the inequality x2 + 3x - 4 > 0 holds true when x is either less than -4 or greater than 1.
The solution set is thus all real numbers outside the interval [-4, 1], which can be written as (x < -4) or (x > 1).
A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the area of the circle.
a. 143
b. 400
c. 413
d. 314
Answer:
d. 314 in²
Step-by-step explanation:
Area of a circle=πr²where r is the radius of the circle.
A=πr²
=π×10²
=314.2 in²
Area of the circle is 314 in² to the nearest square inch.
ANSWER
d. 314
EXPLANATION
The area of a circle is calculated using the formula:
[tex]Area = \pi {r}^{2} [/tex]
It was given in the question that, the circle has radius r=10 units. We substitute this value and π=3.14 into the formula to get,
[tex]Area = 3.14 \times {10}^{2} [/tex]
[tex] \implies \: Area = 3.14 \times 100[/tex]
[tex]Area = 314 \: {in}^{2} [/tex]
The correct answer is D.
Simplify to create an equivalent expression. −y−3(−3y+5)
Answer:
[tex]\large\boxed{-y-3(-3y+5)=8y-15}[/tex]
Step-by-step explanation:
[tex]-y-3(-3y+5)\qquad\text{use the distributive porerty}\ a(b+c)=ab+ac\\\\=-y+(-3)(-3y)+(-3)(5)\\\\=-y+9y-15\qquad\text{combine like terms}\\\\=(-y+9y)-15\\\\=8y-15[/tex]
the simplified expression is 8y−15
To simplify the expression −y−3(−3y+5), we can start by distributing the negative sign to each term inside the parentheses.
This gives us −y+9y−15. Next, we can combine like terms by adding the coefficients of the y-terms, which gives us 8y.
Finally, we combine the constant terms to get −15.
Therefore, the simplified expression is 8y−15. We simplified the original expression by distributing the negative sign and then combining like terms to obtain a more concise and equivalent expression.
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What is 1(y), when y = -5/8
That's easy.
[tex]1\cdot-\dfrac{5}{8}=-\dfrac{5}{8}[/tex]
Hope this helps.
r3t40
Is BES - GES? If so, identify the similarity postulate or theorem that
applies
Answer:
A
Step-by-step explanation:
∠BES = ∠GES = 40°
∠BSE = ∠GSE = 90°
ΔBES and ΔGES are similar by the AA postulate → A
The given ΔBES and ΔGES are similar triangles according to the AA similarity postulate or theorem. Option A true.
What is the AA similarity postulate or theorem?The AA similarity postulate is that " If any two triangles have a pair of angles with equal measures then they are said to be similar triangles". If two angles are equal then the third one will also be equal in both the triangles.
Checking similarity in both the triangles:The given triangles are ΔBES and ΔGES
The ΔBES has dimensions as ∠BES=40° and ∠ESB=90° and the ΔGES has dimensions as ∠GES=40° and ∠ESG=90°
Thus, both the triangles have pair of angles with equal measures. I.e., ∠BES=∠GES=40° and ∠ESB=∠ESG=90°. So, they satisfy the AA similarity theorem.
Hence, the given triangles are said to be similar according to the AA similarity postulate or theorem. So, option A is true.
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Given EG = 16 and FH = 12, what is the length of one side
of the rhombus?
6 units
8 units
10 units
14 units
Answer: 10 units
Step-by-step explanation:
The length of one side of the given rhombus is; C: 10 units
What is the length of the rhombus?
The half diagonals of a rhombus are the legs of a right angle triangle with the hypotenuse being the side of the rhombus.
We see that EG and FH are the diagonals of the rhombus. This means that the half-diagonals measure 8 and 6.
Using Pythagoras theorem, we can find the hypotenuse which is the length of the side of the rhombus.
Thus;
8² + 6² = c²
64 + 36 = c²
100 = c²
c² = 100
c = 10
In conclusion, the length of one side of the rhombus is 10 units
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Solve the equation for the indicated variable
A = 8v for v
Answer:
A=8v
8v=A
8v/8=A/8
v=A/8 answer
Which of the following is the inverse of f(x)=-2x+3
The inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is [tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex].
To find the inverse of f(x) = -2x + 3 , you need to interchange x and y and solve for y .
Start with y = -2x + 3 .
Swap x and y to get x = -2y + 3 .
Solve this equation for y .
x = -2y + 3
First, subtract 3 from both sides:
x - 3 = -2y
Then, divide both sides by -2 :
[tex]\[ \frac{x - 3}{-2} = y \][/tex]
Thus, the inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex]
3 (x - 1) = 3x - ________
What would 3x be subtracted by
Answer:
3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
Use the distributive property:
3(x - 1)
= 3(x) + 3(-1)
= 3x - 3
PLEASE HELP FAST!!!!
A man goes fishing in a river and wants to know how long it will take him to get 10km upstream
to his favourite fishing location. The speed of the current is 3 km/hr and it takes his boat twice
as long to go 3km upstream as is does to go 4km downstream. How long will it take his boat to
get to his fishing spot?
Answer:
Time = 25/9 hr
Step-by-step explanation:
Let speed of boat in still water is x km/hr
then, speed in downstream equals to "x + 3"km/hr
and speed in upstream equals to "x - 3" km/hr
We also know that time taken to travel 3km in upstream is twice as time taken to travel 4km in downstream.
so, using time = distance/speed
3/x- 3 = 2 × (4/x + 3)
3x + 9 = 8x -24
5x = 33
x = 33/5 km/hr
Net speed in upstream = 33/5 - 3 = 18/5 km/hr
So, Time taken to travel 10km upstream = distance /speed
= (10 × 5) / 18 = 25/9 hr
Time = 25/9 hr
The boat speed in still water is determined to be 6.6 km/hr, and it will take around 2.78 hours to travel 10 km upstream.
To determine how long it will take the man to travel 10 km upstream to his favorite fishing location, let's first define the boat speed in still water as v km/hr.
From the problem, we know:
The speed of the current is 3 km/hr.
It takes twice as long to travel 3 km upstream as it does to travel 4 km downstream.
The speed of the boat upstream relative to the shore is v - 3 km/hr, and downstream it is:
→ v + 3 km/hr.
Let t be the time it takes to travel 4 km downstream. Then time to travel 3 km upstream is 2t.
We can set up the following equations using distance = speed x time:
→ For downstream: 4 = (v + 3)t
→ For upstream: 3 = (v - 3)2t
Solve these equations:
→ From 4 = (v + 3)t, we have t = 4/(v + 3)
Substitute t in 3 = (v - 3)2t: 3 = (v - 3)2(4/(v + 3))
→ Simplify: 3(v + 3) = 8(v - 3)
→ Expand and solve for v: 3v + 9 = 8v - 24
→ 33 = 5v
→ v = 33/5
= 6.6 km/hr
Now that we know the speed of the boat in still water is 6.6 km/hr, we can determine the time it takes to travel 10 km upstream:
→ The effective speed upstream is:
= 6.6 - 3
= 3.6 km/hr.
→ Time required to travel 10 km upstream is:
= 10 / 3.6
≈ 2.78 hours.
PLEASE HELP!!! ASAP!!!!!!
6 units right is the answer, since plugging in values(since it's asking for the translation you can ignore the -3) so your answer is:
The graph is translated 6 units RIGHT
Hope this helps!
plz brainliest
Help me with this question
Answer: Base.
The exponent is the 2, and the 5 is the base.
Answer:
Step-by-step explanation:
The five is the base. The two tells you what to do with the base.
5^2 = 5 * 5 = 25.
Notice what you are told. The 2 tells you to use two fives. The ^ in this case means multiply.
Which linear inequality is graphed with y>-x-2 to create the given solution set?
Answer
D
Step-by-step explanation:
just toke the test
Which of the following is the radical expression of a^4/9
For this case we must find an expression equivalent to:
[tex]a ^ {\frac {4} {9}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the expression we have:
[tex]\sqrt [9] {a ^ 4}[/tex]
Answer:
Option 4
Answer: OPTION 4.
Step-by-step explanation:
By definition, Radical expressions are those that use a root.
In this case you have this expression:
[tex]a^{\frac{4}{9}[/tex]
In order to find the radical expression of [tex]a^{\frac{4}{9}[/tex], it is important to remember that:
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
Therefore, once you apply this, you get:
[tex]a^{\frac{4}{9}=\sqrt[9]{a^4}[/tex]
You can observe that it matches with the expression provided in Option 4.
How many different 5-letter words can be created using the letters M, A, G, I, C without any letter being used more than once?
Answer:
You can spell only one word using the letters (M,A,G,I,C) the only word able to be made would be magic.
Step-by-step explanation:
Hope this helped you! :3
Answer:Meets,Abuzz,Glows,Inner,Creepy
Step-by-step explanation:
WILL MARK BRAINLIEST
PLEASE
Need NOW
a restraunt owner is going to panel a square portions of the restaurants ceiling. The portion to be paneled has an area of 185 ft^2. The owner plans to use square tin ceiling panels with a side length of 2 ft. What is the first steps in finding ouw whether the owner will be able to use a whole number of panels?
Answer: Dividing 185 by 4 is the first step in finding out whether the owner will be able to use a whole number of panels. Hope this helps!
Step-by-step explanation:
The owner will not be able to use a whole number of panels btw