Choose (two) statements (the original conditional statement and converse)
that could form the biconditional "An object measures 12 inches if and only if it is 1 foot long."

A. If an object is 1 foot long, then it measures 12 inches.
B. If an object does not measure 12 inches, then it is not 1 foot long.
C. An object is not 1 foot long if it does not measure 12 inches.
D. If an object measures 12 inches, then it is 1 foot long.

PLEASE HELP !!

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.

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:

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:

Is 32,13

Step-by-step explanation:

Because one is not bigger than five so it disappears.

Answer:

here is your answer

Step-by-step explanation:

here is your answer

Answer:

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

Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

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:

hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and

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:

60

[tex]2^{2} * 3 * 5[/tex]

Step-by-step explanation:

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?

Given:

Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.

To find:

The volume of rectangular prism.

Solution:

The volume of a cuboid or rectangular prism is:

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth and h is height of the prism.

The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:

[tex]V=3.4\times 0.8\times 0.6[/tex]

[tex]V=1.632[/tex]

Therefore, the volume of the rectangular prism is 1.632 cubic feet ​.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

-9+84+(-2) =

-9+82 =

= 73

Hope this helps

Answer:

[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Step-by-step explanation:

Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]

Length [tex]l=8cm[/tex]

Height [tex]H=15cm[/tex]

Water level [tex]L_w= 4cm[/tex]

Generally the equation for relationship b/w h and a is mathematically given by

Since by the properties of similar triangles

 [tex]k=\frac{h}{1/2}[/tex]

Let

 [tex]h=15cm \\\\a=8cm[/tex]

 [tex]k=\frac{h}{1/2a}[/tex]

 [tex]k=\frac{15}{4}[/tex]

Therefore

 [tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]

 [tex]a=\frac{8h}{15}[/tex]

Generally the equation for volume of Pyramid is mathematically given by

 [tex]V=\frac{1}{3}ah^2h[/tex]

Subsitute a

 [tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]

Therefore

 [tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]

 [tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

Since

 [tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]

Therefore

 [tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

 [tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]

 [tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

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.

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:

x=6.25 and y=1.5

Step-by-step explanation:

Given equation

2x+5y=20

y=0.4x-1

Putting the value of y in above equation

2x+5(0.4x-1)=20

2x+2x-5=20

4x-5=20

4x=20+5

4x=25

x=6.25

Now,

y=0.4x-1( Given)

Putting the value of x=6.25 in above equation y

y=0.4(6.25)-1

y=2.5-1

y=1.5

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:

1205.76 m^3

Step-by-step explanation:

given:

radius = 8m

height = 18 m

volume of a cone = πr2h/3

=3.14 * (8)^2 * 18/3

=3.14 *64 *18/3

=3617.28/3

=1205.76 m^3

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:

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.

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.

See the graph in the attached image.

Answer:

Height A = [tex]12\frac{3}{4}[/tex] inches

Step-by-step explanation:

Height A = Sum of widths of all sections of the cabinet + thickness of the wood

Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]

               = [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]

               = [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]

               = [tex]11+\frac{7}{4}[/tex]

               = [tex]11+1\frac{3}{4}[/tex]

               = [tex]11+1+\frac{3}{4}[/tex]

               = [tex]12\frac{3}{4}[/tex] inches

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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