Answer:
The third term is [tex]24x^2y^2[/tex]
Step-by-step explanation:
The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem
The Binomial Theorem is:
[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]
In the given question x = 2x
a = y
n = 4
We have to find the third term, so value of k will be 2 as k starts from 0
Putting the values in the Binomial Theorem
[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]
[tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]
Putting the values:
[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]
So, the third term is [tex]24x^2y^2[/tex]
50.441−6.203=? help asap
Answer:
44.238
Step-by-step explanation:
50.441-6.203=44.238
Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation?
f(x) is the total number of hours overall that he has worked out.
x would be the number of weeks he works out.
You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).
Answer:
In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.
Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.
It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.
What are the coordinates of Z?
Answer:
The correct answer option is C. (0, c).
Step-by-step explanation:
We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.
Z is a point on the middle of one of the sides of the trapezoid.
Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.
Z (0, c)
==============================================
Explanation:
Note how the point (a,0) mirrors over the y axis to land on (-a,0)
A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.
The x coordinate changes from positive to negative. The y coordinate stays the same.
The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)
Apply the midpoint formula to find where Z is located.
Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0
Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c
So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.
Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
Answer: 84
Step-by-step explanation:
Set up a proportion as follows: [tex]\dfrac{\text{students that practice everyday}}{\text{total students}}[/tex]
[tex]\dfrac{7}{12}=\dfrac{x}{144}[/tex]
Cross multiply: 12x = 7 × 144
Divide by 12: x = 7 × 12
Simplify: x = 84
Which statements about the system are true? Check all that apply. y =1/3 x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line. The lines intersect.
ANSWER
The system consists of parallel lines. Both lines have the same slope.
EXPLANATION.
The first equation is
[tex]y = \frac{1}{3} x - 4[/tex]
This equation is in the slope-intercept form.
The second equation is
[tex]3y - x = - 7[/tex]
We write this one too in slope-intercept form so that we can make comparison.
[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]
We can see that both equations have slope
[tex]m = \frac{1}{3} [/tex]
This means the two lines are parallel.
The two lines have different y-intercepts.
Two parallel lines with different y-intercepts will never meet.
The lines will never intersect.
Answer:
The true statements are:
- The system consists of parallel lines
- Both lines have the same slope
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
where a is the coefficient of x , b is the coefficient of y and
c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
a is the coefficient of x , b is the coefficient of y and c is the
numerical term
* Lets solve the problem
∵ The system of equation is:
y = 1/3 x - 4 ⇒ (1)
3y - x = -7 ⇒ (2)
- Lets put equation (1) in the form of equation (2)
∵ y = 1/3 x - 4 ⇒ multiply both sides by 3
∴ 3y = x - 12 ⇒ subtract x from both sides
∴ 3y - x = -12
∴ Equation (1) is 3y - x = -12
∵ Equation (2) is 3y - x = -7
∵ The coefficients of x and y in the two equation are equal
∵ The numerical terms in the two equations are not equal
∴ The equations have no solution because their lines are parallel
∵ The parallel lines have same slope
* The true statements are
- The system consists of parallel lines
- Both lines have the same slope
Which graph correctly represents the equation y=−4x−3?
GUYS PLEASE HELP ME IAM NOT TRYING TO FAIL SUMMER SCHOOL and will offer 40 points for who ever helps me with the next 3 problems and will give brainlest
The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.
What is the slope of a line with two points?The slope of a line given by
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.
Calculation:The equation is y = -4x - 3
On comparing the equation with the slope-intercept form y = mx + c,
m = -4 and y-intercept c = -3.
Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.
Finding the slope for the points in the other two graphs:The graph at option 3 has a line with two points (2, 5) and (0, -3)
So, the slope is
m = [tex]\frac{-3-5}{0-2}[/tex]
= 4
Thus, it is not the same as the slope of the given equation.
The graph at option 4 has a line with two points (-2, 5) and (0, -3)
So, the slope is
m = [tex]\frac{-3-5}{0+2}[/tex]
= -4
Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.
Therefore, the graph at option 4 is the correct representation of the given equation.
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(05.05)On the coordinate plane below, what is the length of AB.
7 units
8 units
15 units
16 units
Each line on the graph is one unit.
AB = 15 units long
Answer:
15 units
Step-by-step explanation:
Since A and B are along the same horizontal line, we count count the number of units to determine the distance
The horizontal distance from A to B is 15 units
División de polinomios(a²+3a+2)÷(a+1)
Answer:
a + 2
Step-by-step explanation:
Given
[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator
= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]
Cancel the factor (a + 1) on the numerator/denominator
= a + 2 ← quotient
Charlene's parents deposit $500 in an account on the day she is born. The account earns a high interest rate of 9.2% compounded quarterly because Charlene is not allowed to access the money until her 22nd birthday. How much money will Charlene have on her 22nd birthday?
Answer:
about A+=+2000%281%2B+0.023%2F1%29%5E%281%2A18%29+=+2000%2A1.023%5E18= $3,011.56 thats my math
Step-by-step explanation:
Answer:
$3,698.50
Step-by-step explanation:
When making a compound interest rate this means that the interests generated are taken into consideration when creating new interests in the next period, now there are 4 quarterly periods on a year, this means there are 88 periods in the 22 years that the account will grow, you just have to do the math:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where n is the number of cycles per year and nt is the number of cycles over the years.
We just have to put the values into the formula:
[tex]A=500(1+\frac{.092}{4})^{22*4}[/tex]
[tex]A=500(1+\frac{.092}{4})^{88}[/tex]
[tex]A=$3,698.50[/tex]
(3,0),(-11,-15) slope
Slope formula: y2-y1/x2-x1
Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope
For this case we have by definition, the slope of a line can be found by the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Two points are needed through which the line passes.
According to the data we have:
[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]
Substituting we have:
[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]
ANswer:
The slope is [tex]\frac {15} {14}[/tex]
Hernando ate 2/8 of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told them to share it equally
Answer:
umm his friends each got 1/8
Step-by-step explanation:
hernando ate 2/8 meaning 8-2=6= 6/8
6/8 / 6 = 1/8
:D
I guess this what you want
After Hernando ate [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with [tex]\frac{1}{8}[/tex] of the pizza
Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6
First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:
[tex]1- \frac{1}{4} =\frac{4-1}{4} = \frac{3}{4}[/tex]
The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:
[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]
Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.
If a graph of y=-3x+ 5 were changed to a graph of y = 2x + 5, how would the
slope change?
A. The slope of the new graph would become less steep.
B. More information is needed to determine the change.
C. The slope would remain the same.
D. The slope of the new graph would become steeper.
Alright (so what I did was type this into desmos and it was the exact same line but it was the other way around so it is) C
Changing from y = -3x + 5 to y = 2x + 5 would make the slope steeper.
The slope of the new graph would become steeper.
When changing from y = -3x + 5 to y = 2x + 5, the original slope of -3 increases to 2, making the new graph steeper.
Therefore, the correct answer is D. The slope of the new graph would become steeper.
Need help fast as soon as possible!!!
Answer:C 13/2
Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2
Answer:
[tex]\frac{13}{2}[/tex]
Step-by-step explanation:
When you have a whole number, you gotta add a denominator, so just add 1 underneath:
[tex]\frac{13}{1}[/tex]
Then you have
[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]
Multiply straight across and you get
[tex]\frac{13}{2}[/tex]
What is -2^2? I've been getting mixed results from people against calculators.
Answer:
-4
Step-by-step explanation:
Technically, the negative sign is treated as multiplying by -1, which is then separate from the 2. This equation can also be rewritten as [tex]-1 * 2^2[/tex], which would be simplified to [tex]-1 * 4[/tex] and then [tex]-4[/tex].
It depends on how the parenthesis is like. -(2)^2 will equal -4 while (-2)^2 equals 4. But the answer will most likely be 4 because they tend to make sure to put parenthesis if they want the answer to be -4. (Calculators are programmed differently which is why you're getting mixed answers.)
Perform the computation and write the result in scientific notation:
5.27 x 10 exponent 5 power
________________
8.7 x 10 exponent -5 power
Express your answer rounded correctly to the proper number of significant figures.
Answer:
6.06 x [tex]10^{9}[/tex]
Step-by-step explanation:
(5.25 x [tex]10^{5}[/tex] ) / (8.7 x [tex]10^{-5}[/tex] )
= (5.25 x [tex]10^{5}[/tex] ) x( [tex]10^{5}[/tex] )/ (8.7 )
= (5.25 x [tex]10^{5 + 5}[/tex] )/ (8.7 )
= 0.606 x [tex]10^{10}[/tex]
= 6.06 x [tex]10^{9}[/tex]
What is the area of the rhombus shown below?
EG = 20
FD = 15
To find the area of a rhombus, multiply the two diagonals together then divide by 2.
Area = 20 *15 = 300 / 2 = 150 sq. units.
Evaluate the expression below for
x= -4
6(x + 15)
Answer:
66
Step-by-step explanation:
We know x = -4. To solve, we just need to plug in -4 for x.
6 (-4 + 15) =
6 (11) =
66
Answer:
66
Step-by-step explanation:
x= -4
6(x + 15)
Substitute x =-4 into the second equation
6(-4+15)
6(11)
66
Which of the following is a trinomial?
O c2 + C + 6
o c2 - 16
0-80
O c3 + 402 – 120 + 7
Graph the function y = x3 + 3x2 – x – 3. Which lists all of the turning points of the graph?
Answer:
(-1, 0)
Step-by-step explanation:
Jim, please use the symbol " ^ " to indicate exponentiation:
y = x^3 + 3x^2 – x – 3. Thanks.
A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa). To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.
Given y = x^3 + 3x^2 – x – 3,
dy/dx = 3x^2 + 6x - 1
d²y
------ = 6x + 6 and this is zero at x = -1.
dx²
We can easily show that the 2nd derivative changes sign at x = -1.
Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).
Answer: (-2,3) and (0,-3)
Step-by-step explanation:
Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4?
y – = (x – 4)
y – = (x – 4)
y – = 4(x – 3/4)
y – 4 = (x – 1/3)
Answer:
y - 1/3 = 3/4(x - 4)
Step-by-step explanation:
We know that the general equation of a line is the following:
y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.
Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)
For this case we have that by definition, the slope-intersection equation of a line is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
They tell us as data that:
[tex]m = \frac {3} {4}[/tex]
Now the equation is:
[tex]y = \frac {3} {4} x + b[/tex]
We substitute the point to find "b":
[tex](4, \frac {1} {3})[/tex]
[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]
[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]
Finally the equation is:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
In point-slope form the equation is:
[tex]y- \frac {1} {3} = \frac {3} {4} (x-4)[/tex]
Answer:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
According to the synthetic division below which of the following statements are true? Check all that apply.
Answer:
A and D
Step-by-step explanation:
The remainder after division is 8, that is the 8 at the end of 2 - 4 8
Given f(x) divided by (x + h)
Then if (x + h) is a factor the remainder = 0
Hence (x + 7) is not a factor since remainder is 8
and f(- h) = remainder
that is f(- 7) = 8 → D
A and D are the correct statements.
How to know which are the following statements are true?We know that when f(x) is divided by (x - h) then f(h) is the remainder.In option A f(-7) is the remainder which gives the value 8.
So, option A is correct.
Here the value x = 7 does not satisfy the function.When we put x = 7 in the function it is coming 99
So, option B and C are wrong.
On putting x = -7 in the function we are getting 8So options D is correct
Again, the value of f(7) is 99.So, (x - 7) when divides the given function, 8 is not the remainder.So, option E is wrong.
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Can someone help me plz
Answer:
- (- 10)
Step-by-step explanation:
Point A is positioned at - 10 on the number line.
The opposite is the negative of the value
That is the opposite of - 10 is - (- 10)
-9x -5+6=19 simplify
Answer:
[tex]{\huge \boxed{x=-2}[/tex]
Step-by-step explanation:
First you do is add and subtracting numbers from left to right.
-5+6=1
-9x+1=19
Then subtract by 1 from both sides of equation.
-9x+1-1=19-1
Simplify.
-9x=18
Divide by -9 from both sides of equation.
-9x/-9=18/-9
Simplify, to find the answer.
18÷-9=-2
x=-2 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
x=-2
Step-by-step explanation:
-9x -5+6=19
Combine like terms
-9x +1 = 19
Subtract 1 from each side
-9x +1-1 = 19-1
-9x = 18
Divide by -9
-9x/-9 = 18/-9
x = -2
Given right angle abc, what is the value of tan(A)
Answer:
C
Step-by-step explanation:
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]
Using the quadratic formula to solve x2 = 5 – x, what are the values of x?
Answer:
x^2=5-x
x^2+x-5=0
x=-1± √(1)^2-4(1)(-5) /2(1)
-1± √21 /2
Step-by-step explanation:
Answer:
The answer will be A. -1± √21 /2
Step-by-step explanation:
I hope it helps
Match each vocabulary word to its correct definition:
1.
Cubic Polynomial--
A cubic polynomial is a polynomial of degree three.
2.
End behavior--
The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.
3.
Irreducible--
A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.
4.
Leading coefficient--
It is the coefficient of the highest degree term existing in the expression.
5.
Leading term--
It is the term with the highest degree.
6.
quartic polynomial-
A quadratic polynomial is a polynomial of degree 4.
7.
Zeros of polynomial--
The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.
A gardener makes a new circular flower bed. The bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answer:
The circumference is:
[tex]C = 43.98\ ft[/tex]
The area is:
[tex]A=153.94\ ft^2[/tex]
Step-by-step explanation:
The circumference of a circle is calculated using the following formula
[tex]C = \pi d[/tex]
Where C is the circumference and d is the diameter of the circle.
In this case we know that
[tex]d = 14\ ft[/tex]
Therefore the circumference is:
[tex]C = \pi *14[/tex]
[tex]C = 43.98\ ft[/tex]
The area of a circle is calculated using the following formula
[tex]A=\pi(\frac{d}{2})^2[/tex]
Where d is the diameter of the circle.
Then
[tex]A=\pi(\frac{14}{2})^2[/tex]
[tex]A=\pi(7)^2[/tex]
[tex]A=49\pi[/tex]
[tex]A=153.94\ ft^2[/tex]
The circumference of the flower bed is approximately 43.96 feet and the area is approximately 153.86 square feet.
Explanation:The gardener's circular flower bed has a diameter of 14 feet. The formula to calculate the circumference of a circle is C=πd where 'd' represents the diameter. Therefore, by substituting the given diameter, we get C = 3.14 * 14 = 43.96 feet approximately.
The area of the circle can be calculated by using the formula A=πr², where 'r' represents the radius of the circle. The radius is half of the diameter, that is 14/2 = 7 feet. So, A = 3.14 * 7² = 153.86 square feet approximately.
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What’s the total power in a circuit with a current of 4A and a resistance of 12 ohm?
Power = Current *Voltage
You already have the current, but not the voltage.
But you are given resistance, and you know that
Voltage=Current*Resistance
Therefore
V=I*R=4*12=48V
So you have 48V
Now you can figure out the Power
P=I*V=4*48=192W
Therefore you have 192W.
hope this helps
The total power in a circuit is 192W.
PowerPower exists at the time rate of excess or absorbing energy. The power delivered or absorbed by an element exists as the product of the current flowing through the component and the voltage across the element. Power exists estimated in watts. If the power exists positive then it exists absorbed by the component and if it exists negative then it is supplied by the element.
Power = Current [tex]*[/tex] Voltage
We have the current, but not the voltage.
But you are given resistance, and you know that
Voltage = Current [tex]*[/tex] Resistance
Therefore,
[tex]V=I*R=4*12=48V[/tex]
So you have 48V
Thus, we get the Power
[tex]P=I*V=4*48=192W[/tex]
Therefore, the total power in a circuit is 192W.
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Which of the following is the result of flipping the graph of the function shown
below over the line y - x?
Answer:
See attachment
Step-by-step explanation:
When the graph of the given function is flipped over the line [tex]y=x[/tex], the coordinates will swap.
The mapping for a reflection in the line [tex]y=x[/tex] is [tex](x,y)\to(y,x)[/tex].
We can observe that one portion of the graph is in the first quadrant [tex](x,y)[/tex]. When we flip this part we will get [tex](y,x)[/tex], which is still in the first quadrant.
Also, when we flip the portion of the graph in the second quadrant (-x,y), we will obtain (y,-x), which is standing for all coordinates in the fourth quadrant.
The image is shown in the attachment.
Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.

Which equation models the motion of the ball?
y = –17(x)(x – 4)
y = –16(x)(x – 4)
y = –16(x – 2)2 + 68
y = –17(x – 2)2 + 68
y = –16(x – 2)² + 68 is the equation which models the motion of the ball.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Ryan throws a tennis ball straight up into the air.
The ball reaches its maximum height at 2 seconds.
The approximate height of the ball x seconds after being thrown is shown in the table.
We need to find the equation of the motion of the ball.
Let us take a point (0, 4) from the table.
The right equation is the point in which the equation satisfies.
y=-17(0)(0-4)
4=0
So y = –17(x)(x – 4) is false.
y = –16(x – 2)² + 68
4=-16(4)+68
The point (0, 4 ) satisfies the equation y = –16(x – 2)² + 68
Hence, y = –16(x – 2)² + 68 is the equation which models the motion of the ball.
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