elizabeth divided one 3 yards piece of fabric into 1/4 yard pieces how many pieces of fabric does elizabeth have now

Answer:

Plot 3 points

Step-by-step explanation:

Let plot the vertex

\( - \frac{b}{2a} \)

\( - \frac{ - 2}{2} = 1\)

Plug this value in

\(y = {1}^{2} - 2 = - 1\)

So our minimum point is at (1,-1).

This also means our line of symmetry occurs about x=1.

Let use some point like 0.

\(0 = {0}^{2} - 0\)

So this means point (0,0) is a point. Since 1 is the line of symmetry, (2,0) is a point.

Answer:

y = 153/11

Step-by-step explanation:

The net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

We can use the Biot-Savart Law to calculate the magnetic field at point P due to each wire, and then add the two contributions vectorially to obtain the net magnetic field.

The magnetic field due to a current-carrying wire can be calculated using the formula:

d = μ₀/4π * Id × /r³

where d is the magnetic field contribution at a point due to a small element of current Id, is the vector pointing from the element to the point, r is the distance between them, and μ₀ is the permeability of free space.

Let's first consider the wire carrying current I₁ (in the positive X direction). The contribution to the magnetic field at point P from an element d located at position y on the wire is:

d₁ = μ₀/4π * I₁ d × ₁ /r₁³

where ₁ is the vector pointing from the element to P, and r₁ is the distance between them. Since the wire is infinitely long, we can assume that it extends from -∞ to +∞ along the X axis, and integrate over its length to find the total magnetic field at P:

B₁ = ∫d₁ = μ₀/4π * I₁ ∫d × ₁ /r₁³

For the given setup, the integrals simplify as follows:

∫d = I₁ L, where L is the length of the wire per unit length

d × ₁ = L dy (y - 1/2 L) j - x i

r₁ = sqrt(x² + (y - 1/2 L)²)

Substituting these expressions into the integral and evaluating it, we get:

B₁ = μ₀/4π * I₁ L ∫[-∞,+∞] (L dy (y - 1/2 L) j - x i) / (x² + (y - 1/2 L)²)^(3/2)

This integral can be evaluated using the substitution u = y - 1/2 L, which transforms it into a standard form that can be looked up in a table or computed using software. The result is:

B₁ = μ₀ I₁ / 4πd * (j - 2z k)

where d = 5 mm = 5×10^-3 m is the distance between the wires, and z is the coordinate along the Z axis.

Similarly, for the wire carrying current I₂ (in the negative X direction), we have:

B₂ = μ₀ I₂ / 4πd * (-j - 2z k)

Therefore, the net magnetic field at point P is:

B = B₁ + B₂ = μ₀ / 4πd * (I₁ - I₂) j + 2μ₀I₁ / 4πd * z k

Substituting the given values, we obtain:

B = (2×10^-7 Tm/A) / (4π×5×10^-3 m) * (30A - (-30A)) j + 2(2×10^-7 Tm/A) × 30A / (4π×5×10^-3 m) * (15×10^-2 m) k

which simplifies to:

B = (6e-5 j + 0.57 k) T

Therefore, the net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

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V = π(72 - 12) = 360π cm^3.

The volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis can be found using the formula V = π∫y^2 dx.

In this case, y = sqrt(36-x^2) and y = 0.

Substituting these values into the formula, we get V = π∫ (sqrt(36-x^2))^2 dx.

Integrating, we get V = π/3(36x - x^3/3) + C, where C is a constant.

We can solve for V by evaluating the integral from x = 0 to x = 6. Doing this gives us V = π(72 - 12) = 360π cm^3.

Therefore, the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis is 360π cm^3.

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The required equation based on the information given is y =0.433x + 24.493

It should be noted that one can simply copy and paste the data set into excel sheet

Then, use intercept and the slope formula to find slope and intercept. We will have

slope = SLOPE(y values, x values)

= 0.433

intercept = INTERCEPT(y values, x values)

= 24.493

Therefore, the required equation is y =0.433x + 24.493

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Answer:

160

Step-by-step explanation:

line AE is on the 160 degree line

Answer:

I'm pretty sure that A is right.

Step-by-step explanation:

They share a side, making them equal.  It is also shown that RQ and SR are equal.  This means that, for SAS, all you need is the angle in between them.

I hope this helps!

Answer:

70 , 84 , 105

Step-by-step explanation:

sum their ages , 10 + 12 + 15 = 37

divide the amount by this sum to find the value of one part of the ratio.

259 ÷ 37 = 7 ← value of 1 part of the ratio , then

10 parts = 10 × 7 = 70 euros ← Tom's share

12 parts = 12 × 7 = 84 euros ← Mary's share

15 parts = 15 × 7 = 105 euros ← Bill's share

Answer:

8

Step-by-step explanation:

\(P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8\)

Answer:

See below ~

Step-by-step explanation:

Question 4

Finding the lateral area :

⇒ Lateral area = 2πrh

⇒ Lateral area = 2π(8)(20)

⇒ Lateral area = 320π cm²

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

Finding the surface area :

⇒ Surface area = Lateral area + 2 × area of the circle

⇒ Surface area = 320π + 2 × π(8)²

⇒ Surface area = 320π + 128π

⇒ Surface area = 448π cm²

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

Question 5

⇒ In this scenario, the part that is painted is the lateral area

⇒ Area painted = 6 × 4 × 170

⇒ Area painted = 24 x 170

⇒ Area painted = 4,080 mm³

Answer: y=20x+45

Step-by-step explanation:

y=total cost to hire the organizer

x=number of hours you are hiring the organizer

Answer:

b = 2√3

a = 4

Step-by-step explanation:

Here taking 60 as reference angle

so

tan60 = p/b

\(\sqrt{3}\)    = p/2

so p = 2√3

so

b = 2√3

so

\(h^2 = p^2 + b^2\\h^2 = (2\sqrt{3})^2 + 2^2\\h^2 = 12 + 4\\h^2 = 16\\h = \sqrt{16} \\h = 4\)

a = 4

Answer:A

Step-by-step explanation:  divide both by 5 and you get 3/4 because 15 divided by 5 = 3 and 20 divided by 5 =4

Hi there! :)

Infinite solutions.

2x + 8 = 2(x + 4)

Distribute the 2 with the terms inside of the parenthesis:

2x + 8 = 2(x) + 2(4)

Simplify:

2x + 8 = 2x + 8

Subtract 2x from both sides:

2x - 2x + 8 = 2x - 2x + 8

0 + 8 = 8

Subtract 8 from both sides:

0 + 8 - 8 = 8 - 8

0 = 0

Therefore, there are infinite solutions.

Answer:

all real numbers

Step-by-step explanation:

2x+8=2(x+4)

First you need to distribute the numbers inside the parenthesis:

2(x+4)

=2*x+2*4

=2x+8

Next, look at the new, simplified equation

2x+8=2x+8

Since both sides are equal the solution is all real numbers

All real numbers means that x can be any number

Answer:23.4$

Step-by-step explanation:

The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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Answer:

If a is positive, the parabola will open to the right, so the answer is C

Step-by-step explanation:

Answer:

5 miles: $10

8 miles: $16

20 miles: $40

Step-by-step explanation:

Since each mile costs $2 and that it asks you to figure out the price for 5 miles, 8 miles and 20 miles, you multiply 2 with the amount of miles travelled

Answer:

6

Step-by-step explanation:

All it is asking is what value should you plug in for x to make the equation true.

Lets solve it:

x - 11 = -5

Solve by adding 11 to both sides to isolate the x:

x = 6

✪According to question:-

Ben is 6 years older than Ishaan

So :-

put supposed values

Original Ages :-

✪Verification :

1st condition:-

put original ages

LHS=RHS

Hence verified !

Ben's age = 8 years

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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Step-by-step explanation:

7x6=42. 7+35=42. The numbers are 7 and 42.

The mean amount for the three bills is  $100  .

In the question ,

it is given that

the electricity bill for June is = $75

the electricity bill for July is = $75

the electricity bill for August is = $150

Sum of the electricity for three months = 75 + 75 + 150 = 300

number of months =  3

The mean of the three months can be calculated using the formula ,

mean = (sum of bill for three months )/( number of months)

Substituting , the  values

we get

mean = 300/3

= 100

Therefore , the mean amount is $100 .

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Answer:

16 cans per minute

Step-by-step explanation:

Its simple 80 divided by 5 is 16 so ever minute 16 cans are packed.

The ratio of the cans to minutes is 80 : 5 or 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign: between the numbers.

A machine can pack 80 cans in 5 minutes.

let's denote the number of cans with X and

Time with T

So we have to find the value of X : T

X = 80 and

T = 5 minutes

X : T = 80 : 5  or

X : T = 16 : 1   (divide by 5 on both sides)

It means the machine can pack 16 cans per minute.

Thus, the ratio of the cans to minutes is 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.

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Answer:

Step-by-step explanation:

f(x) = x² + 2x - 15

0=x² + 2x - 15

a+b = 2

a*b = -15

0 = (x-5)(x-3)

x+5 = 0

x - 3 = 0

x = -5, 3

vertex = -b/2a

-(2)/2(1)

-2/2

x = -1

(-1)² + 2(-1) - 15

-16

vertex = (-1, -16)

vertex is point of minimum as a is positive.

Answer:

I don't get what to answer because this is not a proper question?

Step-by-step explanation:

Why do you hate your life. It can't be that bad.

Answer:

$530

Step-by-step explanation:

6% of 500 is 30. Add 500 and 30.

Answer:

  d.  102°

Step-by-step explanation:

We can use the relations ...

to write equations that let us find x and all of the angles in ∆PQR.

The congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...

  ∠P = ∠A

  8x +4 = 5x +16

  3x = 12 . . . . . . . . . subtract (5x+4)

  x = 4 . . . . . . . . . divide by 3

Then the measure of angle P is ...

  ∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees

Angle Q in ∆PQR is given as ...

  ∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees

Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...

  ∠R = 180° -36° -42° = 102°

Angle R is 102°.

__

In summary: