What is the length of the hypotenuse of the triangle below?
45°
h
5V2
45°
90°
52

Answer:

angle MON = 57 degree

Step-by-step explanation:

Angle LOM + Angle MON =90 degree (being perpendicular)

3x- 15+5x -23 = 90

8x -38 = 90

8x = 90 + 38

8x = 128

x = 128/8

x = 16

Angle MON

5x - 23

5*16 - 23

80 - 23

57 degree

Angle LOM

3x - 15

3*16 - 15

48 - 15

33 degree

Answer:

3.141

Step-by-step explanation:

3 decimals is .xxx, and you round the last digit up, so it becomes 3.141

Answer:

3.141

Step-by-step explanation:

since the forth number behind the decimal place is bigger than 5 we round up the third number.

I hope this helps in anyway.

The solution is : x = 19 is the extraneous solution Li Juan obtained.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, we have,

The given equation is 13 - 2w = w + 6.

We need to solve the equation by squaring both sides of the equation.

Now,  13 - 2w = w + 6 squaring both sides of the equation.

That is, (13-2w)²= 169 - 52w + 4w²

(w+6)²= w²+ 12w + 36

Setting them equal, we get

169 - 52w + 4w² = w² + 12w + 36

⇒3w²- 64w + 133 = 0

Now, using the quadratic formula, we get

x = (64±√(64² - 4×3×133))/6

⇒x = (64±√2500)/6.

⇒x = (64±√50)/6.

⇒x = 19 or 14/6 = 7/3.

Solving the original equation, we get

7 = 3w⇒w = 7/3

Therefore, x = 19 is the extraneous solution Li Juan obtained.

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complete question:

Li Juan solves the equation below by first squaring both sides of the equation.

13 - 2w = w + 6

What extraneous solution does Li Juan obtain?

9514 1404 393

Answer:

  R32.15

Step-by-step explanation:

Let x and y represent the original price of a loaf of bread and a liter of drink, respectively. The two relations given by the problem statement are ...

  10x +12y = 138.90

  10(1.2x) +12(1.1y) = 159.54

Multiplying the first equation by 1.2 and subtracting the second gives ...

  1.2(10x +12y) -(10(1.2x) +12(1.1y)) = 1.2(138.90) -(159.54)

  1.2y = 7.14 . . . . collect terms

  y = 5.95 . . . . . divide by 1.2

The value of x can be found from the first equation.

  10x + 12(5.95) = 138.90

  10x = 67.50 . . . . . . . . . . . subtract 71.40

  x = 6.75 . . . . divide by 10

Then the value of 3x+2y is ...

  3(6.75) +2(5.95) = 32.15

The original price of 3 loaves and 2 liters is R31.15.

Answer:

here is your answer

Step-by-step explanation:

here is your answer

Answer:

73

Step-by-step explanation:

-9+84+(-2) =

-9+82 =

= 73

Hope this helps

9514 1404 393

Answer:

  a4 = 132,499

Step-by-step explanation:

Use the recursive relation repeatedly.

  a1 = 4

  a2 = (a1)² +3 = 4² +3 = 19

  a3 = 19² +3 = 364

  a4 = 364² +3 = 132,499

Answer:

Step-by-step explanation:

make it 1 triangle and trapezium

1) 1/2 x 7 x 8 = 28 in2

Answer:

56 in^2

Step-by-step explanation:

A = b* h

A = (8) * (7)

A = 56

A = 56 in ^2

Hope this helps!

Answer:

hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and

9514 1404 393

Explanation:

This is a self-answering question: you solve it by graphing the equations.

The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.

__

The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.

Answer:

A

Step-by-step explanation: When you multiply a coordinate in the complex plane it doesn't just magically rotate. It works the exact same way a normal coordinate would. Therefore, the answer is A

When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a scalar of the complex number.

The correct answer is an option (A)

"It is number of the form [tex]x+iy[/tex] where the first part (x) is called real part and the second part ([tex]iy[/tex]) is called as imaginary part and [tex]i=\sqrt{-1}[/tex]"

"It is a combination of rational and irrational numbers, including positive and negative whole numbers, integers, decimals, fractions"

For given example,

The product of a complex number and a real number.

Let, [tex]u[/tex] be any real number and [tex]x+iy[/tex] be any complex number.

The product of 'u' and 'x + iy' is,

[tex]\Rightarrow u\times(x+iy)=(u\times x)+i(u\times y)\\\\\Rightarrow u(x+iy)=ux+i(uy)[/tex]

Let [tex]2+3i[/tex] be a complex number.

For [tex]u=4[/tex],

[tex]\Rightarrow 4\times(2+3i)=8+12i[/tex]

Let [tex]u=-2[/tex],

[tex]\Rightarrow -2\times(2+3i)=-4-6i[/tex]

We can observe that, the product is a scalar of the complex number.

Therefore, when 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a scalar of the complex number.

The correct answer is an option (A)

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Answer:

3x + 3

Step-by-step explanation:

First, the 2 must be distributed. This leaves us with x + 2x + 2 + 1. x and 2x are like terms, as are 2 and 1. They can be combined, giving us 3x + 3. 3x + 3 cannot be simplified any further, so it is the final answer.

Question: X + 2 (x + 1) + 1 in the simplest form

Answer: 3x+3

Answer: Graph B

=====================================================

Explanation:

Point A appears to be at (2.5, -1)

If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5

If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3

Overall, the point A(2.5, -1) moves to A'(-3.5, 3)

Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.

Answer:

Is 32,13

Step-by-step explanation:

Because one is not bigger than five so it disappears.

See the graph in the attached image.

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]

Answer:

C 8

Step-by-step explanation:

the number cube has six sides and the coin has 2 sides

Answer:

There are more females dropping than males each year and that there are more females than males

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x=10

Giving brainiest would be appreciated! :D

Answer:

A

Step-by-step explanation:

f has zero means that f(x)=0

if f(x)=0 we have to look intersection point or points in the graph on the x-axis.

for A

y=0

x=-3, x=4

for B

y=0

x=-4, x=3

for C

y=0

x=-4, x=-3

for D

y=0

x=3, x=4

Answer:

dvide 54 by 6 then the answer you get  subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer

Step-by-step explanation:

remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first  ( btw your answer is   ( 3 )

Answer:

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

5-x=13

5-5=0

13-5=8

x stays because its a variable

x=8

one solution

Answer:

Step-by-step explanation:

The problem told you what all the variables represent, so all we have to do it fill them in accordingly and solve:

[tex]V=6440e^{(.068)(8)}[/tex] and

[tex]V=6440e^{.544}[/tex] and

V = 6440(1.7228846) so

V = $11,095.38

Answer:

remember that:

a*i + b*j + c*k can be written as a vector: (a, b, c)

We know the acceleration of the particle, and we want to find the velocity of the particle, so we just need to integrate two times.

a(t) = (8*t, sin(t), cos(2*t))

integrating that, we get:

V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + v0

where v0 is the vector that defines the velocity at t = 0

in the question you wrote:

V(0) = i

so i suppose that this is:

V(0) = (1, 0, 0)

Then the velocity equation gives:

V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + (1, 0, 0)

V(t) = (4*t^2 + 1, -cos(t), sin(2*t)/2)

Now to get the position equation, we integrate it again

r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + r0

where r0 is the initial position, in the question you wrote:

r(0) = j

so we get:

r(0) = (0, 1, 0)

replacing that we get:

r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + (0, 1, 0)

r(t) = ((4/3)*t^3 + t, -sin(t) + 1, -cos(2*t)/4)

Writing this in the same notation than in the question, we get:

r(t) = [(4/3)*t^3 + t}*i + [-sin(t) + 1]*j + [-cos(2*t)/4]*k

b) Now we want to graph this:

The image isn't really good but can be used to understand the motion of the particle.

Answer:

120 free throws

Step-by-step explanation:

If she misses 15% of her free throws, that means she makes 85% of them.

Find how many she attempted by dividing 102 by 0.85:

102/0.85

= 120

So, she attempted 120 free throws

The number of free throws that were attempted is 120 free throws.

Since the basketball player missed 15% of her free throws, This means that the percentage scored will be:

= 100% - 15% = 85%

Therefore, 85% of x = 102

0.85x = 102

x = 102/0.85.

x = 120

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Answer:

2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)

Step-by-step explanation:

Proved case for n

2+4+6+...+2n = n(n+1) ................(1)

for n = k + 1, we replace n by k and add n = k+1 on both sides (

2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))

rearrange by factoring the right-hand-side

2+4+6+...+2k+2(k+1) = (k+1)(k+2)

which if we substitute n=k+1, we get back

2+4+6+...+2(n-1) + 2(n) = n(n+1)  ...............(2)

This means that equation (1) is applicable to case n+1, and the proof by induction is completed.