Mathematics High School

MEDAL
True or false

The coefficient of x^k y^n-k in the expansion of (x+y)^n equals (n-k / k),

Answers

Answer 1
The statement The coefficient of x^k y^n-k in the expansion of (x+y)^n equals (n-k / k) is true.  This will show the standard formula and the expansion of it. We all know that it can still be expanded based on the power or degree of the terms.
Answer 2

Answer: the answer is FALSE. Just took this on a p e x

Step-by-step explanation:

Related Questions

Help me with this question please

Answers


We have consecutive odd numbers for the sides of a triangle, perimeter 201.  We could write an equation, but clearly the middle side is 201/3 = 67, so the other two sides are 65 and 69.

This is almost an equilateral triangle, angles around 60 degrees, so not obtuse, meaning one angle over 90 degrees.

Scalene means the sides are all different lengths; we didn't even have to solve the problem to know this is true.

Smallest side 61, false.

Largest side 69, true.

This last one doesn't make much sense to me.  What's a unit here?  Dilation of 1/3 means all the linear measures become 1/3 as big, including the perimeter.  It would decrease much more than 3 inches, since it would go from 201 inches to 67 inches.  If I have to answer I'd go with false.


Long division
3x+1/6x^6+5x^5+2x^4-9x^3+7x^2-10x+2

Answers

[tex](6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2) / (3x+1) [/tex]

We divide first number from first parenthesis with first number from second parenthesis. Then the resulting number we multiply by all numbers in second parenthesis and substract from first parenthesis.

[tex]6 x^{6}/3x = 2 x^{5} \\ \\ 6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2 - 6 x^{6} -2 x^{5} = 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2\\ [/tex]

We repeat previous steps until we run out of numbers:
[tex]3x^{5}/3x=x^{4} \\ \\ 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2-3x^{5}-x^{4}= \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2 \\ \\ \\ x^{4}/3x= \frac{1}{3} x^{3} \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2-x^{4}- \frac{1}{3} x^{3}= \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2 \\ \\ \\ - \frac{28}{3} x^{3}/3x= - \frac{28}{9} x^{2} \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2+ \frac{28}{3} x^{3}+ \frac{28}{9} x^{2} = \\ \\ \frac{91}{9} x^{2}-10x+2  [/tex]
[tex]\frac{91}{9} x^{2}/3x=\frac{91}{27} x \\ \\ \frac{91}{9} x^{2}-10x+2-\frac{91}{9} x^{2}-\frac{91}{27} x= \\ \\ -\frac{361}{27} x+2 \\ \\ \\ -\frac{361}{27} x/3x=-\frac{361}{81} \\ \\ -\frac{361}{27} x+2+\frac{361}{27}x+\frac{361}{27}= \\ \\ \frac{415}{27}[/tex]

We are left with a number that has no x inside. This is remainder.
The final solution is sum of all these solutions and remainder:
[tex](2 x^{5}+x^{4}+\frac{1}{3} x^{3} - \frac{28}{9} x^{2} +\frac{91}{27} x)+(-\frac{361}{81} )[/tex]

A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). what is the area of this triangle

Answers

A(7,0)
B(0,8)
C(20,10)   ⇒ A (ABC)= 1/2 | det( 7    0     1 ) |  = 
                                                     0   8      1
                                                    20  10    1
                                             
                                                     7      0    1
                                                     0     8      1
=  1/2 |7*8*1+0*10*1+20*0*1 -20*8*1-7*10*1-0*0*1 |=1/2*|-174|=1/2*174
A (ABC)=87 units

The missing number in the arithmetic sequence 60,51 blank , 33 is

Answers

Subtract 9 from each number to get the next number.
60 - 9 = 51
51 - 9 = 42
42 - 9 = 33

The number is 42.

Hope this helps =)
60-51=9
51-9=42
42-9=33
MISSING NUMBER IS 42

PLEASE HELP!!! i have no idea what i’m doing!!! your help would be GREATLY appreciated!!!

Answers

your answer should be 0.36

“The sum of 3 consecutive odd numbers is 69.” What is the third number in this sequence?

Answers

22,23,24
The third number would be 24
The 3 consecutive odd numbers i think are 25,27,29
So therefore the third number in his sequence is 29

If f(x) = x2 + 1 and g(x) =x-4, which value is equivalent to (f•g)(10)

Answers

the answer to your question is 37

Answer:

(f•g)(10)= 606

Step-by-step explanation:

We have been given that

[tex]f(x)=x^2+1\\\\g(x)=x-4[/tex]

We have to find the value of (f•g)(10)

We can write (f•g)(10) = f(10)•g(10)

Let us find the value of the functions at x = 10

[tex]f(10)=10^2+1\\\\f(10)=100+1\\\\f(10)=101[/tex]

And the value of g(10) is

[tex]g(10)=10-4\\\\g(10)=6[/tex]

Hence,

(f•g)(10)

= f(10)•g(10)

= 101×6

= 606

Therefore, (f•g)(10)= 606

A school spent $900 on new desk for the start of the year. that amount included a 6% sales tax . what was the original price of the desk. before tax

Answers

6% = 0.06

900 * 0.06 = 54

900 - 54 = 846

The original price of the desk before the tax was $846.00.

draw and label a parallelogram with a base twice as long as the height and an area less than 60 square inches. find the area

Answers

Answer: 5 cm by 10 cm gives an area of 50 cm^2

To do this draw a parallelogram and start by labeling the base as 10 cm. If 10 cm is the base, then the height needs to be 5 cm.

To find the area, multiply the base times height.

This will give you: 5 x 10 = 50 which is less than 60.

what are the values of x and y?

a) x= 136/15, y= 17/15
b) x= 64/15, y= 17/15
c) x= 8/15, y= 136/15
d) x= 64/15, y= 136/15

Answers

In the given figure, we have two right angled triangles:
1) Triangle ABC
2) Triangle CDB

Using pythagorean theorem, we can write equations for both triangles.

For triangle ABC:

[tex] (15+x)^{2}= 17^{2}+ y^{2} [/tex]

For triangle CDB:

[tex] y^{2}= 8^{2}+ x^{2} [/tex]

Using the value of y² in the first equation, we get:

[tex] (15+x)^{2}= 289 + 64 + x^{2} \\ \\ 225+30x+ x^{2} =353 + x^{2} \\ \\ 30x=128 \\ \\ x= \frac{128}{30} \\ \\ x= \frac{64}{15} [/tex]

[tex]y^{2}= 8^{2}+ x^{2} \\ \\ y^{2}=64+ ( \frac{64}{15} )^{2} \\ \\ y^{2}= \frac{18496}{25} \\ \\ y= \frac{136}{15} [/tex]

Thus the d option gives the correct values of x and y 

A square lawn has area 512 ft squared .ft. a sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. what is the radius of the​ circle?

Answers

The side length of the square is √512 ft = 16√2 ft. Then the radius of the circle is that distance divided by √2, so is 16 feet.

Answer:

Radius of circle = 16 ft

Step-by-step explanation:

Refer figure for the arrangement.

Area of square = 512 ft²

Side of square [tex]=\sqrt{512}=22.63ft[/tex]

From figure see that

      Diagonal of square = Diameter of circle

       [tex]\texttt{Diameter of circle}=\sqrt{22.63^2+22.63^2}=32ft[/tex]

     Radius of circle [tex]=\frac{32}{2}=16ft[/tex]

Convert this identity to one using sine term(s) only.
1-2cos(r)^2

Answers

Pythagorean identity:
sin²+cos²=1
Then cos²=1-sin²
Substitute:
1-2cos²
1-2(1-sin²)
1-2+2sin²
2sin²-1

The solution to system of inequalities is often an infinite set of points? TRUE OR FALSE :

The solution to a system of inequalities can be represented on a graph by shading the region on the graph? TRUE OR FALSE :

When you graph multiple inequalities on the same graph, the region is where the shading overlaps are the solution region? TRUE OR FALSE :

If the inequality is in the slope-intercept form it is easy to shade the solution region. For example, if it is y< ….. Will the shading be below the line? TRUE OR FALSE :

Answers

true
true
true (poor wording)
?? A question is not true or false. A statement is true or false. The answer to the question is, "yes."

Answer:

all of them are true

Joe plotted the points (2, 0.5), (1, 1), and (0.5, 2), and claimed that these points represent an inverse variation relationship. Which statement supports his claim?
xy = 1 for all points.
xy = for all points.
The graph of these points will be linear.
Inverse variation states that as one quantity increases, the other quantity also increases.

Answers

xy = 1 for all points.

 We are going to demonstrate this affirmation:
 (2) * (0.5) = 1
 (1) * (1) = 1
 (0.5) * (2) = 1
 Therefore, the relationship between the ordered pairs is inverse.
 The relationship between the ordered pairs is:
 y = 1 / x

 Answer: 
 xy = 1 for all points.

Answer:

xy = 1 for all points.

Step-by-step explanation:

Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5). (12, 18)

Answers

[tex]\text{The formula of the midpoint of segment AB:}\\\\\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right).\\\\\text{We have the points}\ H(5,\ 13)\ \text{and}\ K(7,\ 5).\ \text{Substitute:}\\\\x=\dfrac{5+7}{2}=\dfrac{12}{2}=6\\\\y=\dfrac{13+5}{2}=\dfrac{18}{2}=9\\\\Answer:\ \boxed{(6,\ 9)}[/tex]

20 Points! Please Help!

The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Please explain everything!

Answers

To solve this problem yo need to have the "x", the "y", and the radius. To find the radius since it is not given we use the formula.

sq rt(-3^2+1^2)

sq rt(9+1)

sq rt(10) would be the length of the radius in this case.

Then we use the sine cosine and tangent fractions

sin:y/r

cos:x/r

tan:y/x

With the values plugged in the equations are

SIN:1/sqrt(10) Since there can´t be a sq rt in hte denominator we change it to 1(sq rt(10))/10

COS:-3/sqrt(10) Since there can´t be a sq rt in the denominator we change it to -3(sq rt(10))/10

TAN:1/-3 This one can stay the same.

This would be the measures of SIN, COS, and TAN.

Answer:

Sin

Tan

Csc

Cot

Step-by-step explanation:

I just did it on edg

1.Write and exponent . (-4)(-4)
is it -4^2 i am so bad at this and i cannot wrap my head around it , can someone show me how to do it,

Answers

Yes, it is. Exponent is a notation for the number of times something is multiplied. It is same as multiplication is a notation for the number of times something is added. a+a+a+a+a = 5*a Similarly, a*a*a*a*a = a^5 Hence, -4*-4 = (-4)^2

Joanie ran in 6 races last month. Each race was 360 feet long. What was the total distance that Joanie ran in the races?

Answers

1 race = 360 feet
6 races = 360 x 6 = 2160 feet

---------------------------------------------------------------------------------
Answer: Total distance Joanie ran is 2160 feet
---------------------------------------------------------------------------------

k=1; f(x)=4x^3-2x^2+2x+4; Lower bound?

Answers

Given:
[tex]f(x) = 4x^{3} - 2x^{2} + 2x + 4[/tex]
and,
K = 1

We would require to do the synthetic division of the above problem in order to know whether K=1 is a lower bound or not. Let's do it!

Steps of Synthetic Division:

1. Write the coefficients of the equation, and before that write 1. Like,

1 ║ 4   -2   2   4

As you can see, the coefficients of the equation are seperated by ║.

2. Drop down the first value after ║as it is. Like:
1 ║ 4   -2   2   4
        :
----------------------
       4

3. Multiply 4 with 1 and then  place the resultant value under -2 and then add that resultant value with -2. Like
1 ║ 4   -2   2   4
        :    4
----------------------
       4   2

4. Repeat Step 3 until you're done.

1 ║ 4   -2   2   4
        :    4   2   
----------------------
       4   2    4   

1 ║ 4   -2   2   4
        :    4   2   4
----------------------
       4   2    4   8


Now every value, +4, +2, +4, +8, under the bar(---------) is positive; therefore, it means that K=1 is the upper bound, NOT lower bound.

Ans: K=1 is NOT a lower bound.
-i

helppppppppppppppppppppppppp

Answers

A. csc x=-5/2. sin x=1/csc x=-2/5. Since pi<x<3/2pi, this angle is in the third quadrant. cos x must also be negative, we can narrow the answer choices down to A and D. cos x=-\sqrt(1-sin^2 x)=-\sqrt(21)/5. tan x=(-2/5)/(-\sqrt(21)/5)=2/\sqrt(21), so the answer is A.

guys this Question is about system of equation word problem

please assist me !

Answers

Let f and s represent the weights of the first and second objects, respectively.
.. f - s = 200 . . . . . . . . the first is 200 lb heavier than the second
.. s = (1/3)f . . . . . . . . . . the second was 1/3 the weight of the first

In augmented matrix form, the equations can be written
.. f - s = 200
.. f - 3s = 0

The solution is
.. f = 300
.. s = 100
Their total weight is 400 lb, not enough to kill Mr. Boddy. The physics-loving professor is apparently innocent.

If triangle DEF is translated 5 units down, what will be the coordinates of point E ′ in the image?


Answers

Answer:  The correct option is

(B) (4, -2).

Step-by-step explanation:  Given that the triangle DEF is translated  units down.

We are to find the co-ordinates of point E' in the image.

From the graph, we note that

the co-ordinates of the vertices of triangle DEF are D(1, 2), E(4, 3) and F(3, 1).

We know that

if a point (x, y) is translated 5 units down, then its co-ordinates becomes

(x, y)  →  (x, y-5).

Therefore, after translation, the co-ordinates of the vertex E' in the image are

E(4, 3)  →   E'(4, 3-5) = E'(4, -2).

Thus, (B) is the correct option.

Answer:

(4 ,-2)

Step-by-step explanation:

Please help if your a Expert,Ace, or Genius if you are lower you can type the answer in but I might not take your answer as if it was correct.

Answers

They ones in the box are already right!!!!!!!!!!!

Examine the system of equations.
−3x + y = 4
−9x + 5y = −1
What is the solution?
( _ , _ )

Answers

the first one would be -3.5 and the second will be -6.5

The value of x is -3.5 and y is 6.5 for the given equations.

What is an equation?

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The equations will be solved as:-

−3x + y = 4

−9x + 5y = −1

Multiply the first equation by 3 and subtract the second equation.

−15x + 5y = 20

9x - 5y = -1

--------------------

-6x =   21

  x = -3.5

Put x = -3.5 into first equation.

(-3x3.5) + y = 4

y = 6.5

Hence, the values are -3.5 and 6.5.

To know more about equations follow

https://brainly.com/question/2972832

#SPJ5

What is the equation of a line with a slope of 7 and a point (1, 8) on the line?

A) y = 7x + 1
B) y = 7x
C) y = 7x + 8
D) y = 7x – 56

Answers

Hi there,
the answer is option (A).
Hope it helps

Hello there!

We have the slope and a point.

We can use the point-slope formula:

y-y1=m(x-x1)

Plug the point and the slope:

y-8=7(x-1)

y-8=7x-7

y=7x-7+8

y=7x+1

So the answer is Option A

Hope this helps

~Just a gloomy gal

#CarryOnLearning

[tex]SilentNature[/tex]

In a diagram of a landscape plan, the scale is 1 cm = 10 ft. in the diagram, the trees are 4.3 cm apart. How far apart should the actual trees be planted?

43 ft

430 ft

1.3 ft

0.43 ft

Answers

the actual trees should be planted 43 ft apart

How many solutions exist for 3x^2 +4x + 2 = 0

Answers

There are two solutions for this problem because there are two solutions for all quadratics.

However, in this case, since the value of the discriminate (b^2 - 4ac) is negative, each of the answers are imaginary. So while there are two answers, there are no real answers to the above equation.

Answer:

The given equation [tex]3x^2+4x+2=0[/tex] has exactly 2 solutions.

Step-by-step explanation:

Given :  Equation [tex]3x^2+4x+2=0[/tex]

We have to find the number of solutions of the given equation [tex]3x^2+4x+2=0[/tex]

Consider the given equation [tex]3x^2+4x+2=0[/tex]

Since, The highest degree of the given polynomial is 2.

For a polynomial, the highest degree gives the number of solution of that polynomial.

So, [tex]3x^2+4x+2=0[/tex] has 2 solutions.

The given equation [tex]3x^2+4x+2=0[/tex] has exactly 2 solutions.

Helpppppp. I’ll give brainlist

Answers

Question 15:
 We find the zero for:
 x = -3
 The quadratic equation of factored form is:
 p (x) = (x + 3) * (x + 3)

 Question 16: 
 We find the zero for:
 x = -2
 x = 3
 The quadratic equation of factored form is:
 p (x) = - (x + 2) * (x-3)
 Question 17:
 We find the zero for:
 x = -2
 x = 0.5
 The quadratic equation of factored form is:
 p (x) = (x + 2) * (2x-1)

A bag contains 4 green marbles and 5 white marbles. Suppose a marble is randomly selected. What are the odds in favor of picking a white marble ?

A. 4 to 5
B. 4 to 9
C. 5 to 4
D. 5 to 9

Answers

The odds in favor of picking a white marble from a bag of 4 green and 5 white marbles are 5 to 4.

To find the odds in favor of picking a white marble from a bag that contains 4 green marbles and 5 white marbles, first understand that 'odds in favor' are defined as the ratio of the number of ways the desired outcome can occur to the number of ways the desired outcome cannot occur. In this scenario, the desired outcome is drawing a white marble, and there are 5 white marbles. The number of ways the desired outcome can not occur is the number of non-white marbles, which is 4 green ones. Therefore, the odds in favor of drawing a white marble are 5 white marbles to 4 non-white marbles, or 5 to 4.

A steel reinforcing rod is 12 ft. long and 1" thick in diameter. If a cubic foot of steel weighs 490 lb., how much does the rod weigh (to the nearest pound)?

Answers

In cubic feet, the volume of the rod is given by the formula for the volume of a cylinder.
.. V = (π/4)*d^2*h
.. = (π/4)*(1/12 ft)^2*(12 ft)
.. = π/48 ft^3

Then the weight is
.. (490 lb/ft^3)*(π/48 ft^3) ≈ 32 lb

Answer:

32 pounds

Step-by-step explanation:

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