A wheel of radius 10 cm is turning at a rate of 5 revolutions Calculate: the distance moved by a point on the rim in 2 seconds

The coordinates of the new rectangle formed after transformation are; A'(3, -1); B'(6, -1); C'(6, 4); D'(3, 4)

We are told that the original rectangle which I labelled ABCD in the attached image is rotated 90° clockwise about the origin.

Now, from the translation of Rectangle ABCD into A'B'C'D' using the transformation rule in the question, the new coordinates are;

A'(3, -1)

B'(6, -1)

C'(6, 4)

D'(3, 4)

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Answer:

B. No Solution

Step-by-step explanation:

\(13-2(v-2)=-3-2v\\\\12-2v+4=-3-2v\\\\16-2v=-3-2v\\\\16\neq -3\)

Answer:

Step-by-step explanation:This particular answer works out to be undefined because it is a straight line and there is no slope and no equation for it. I will show you how to work it out though so you will know how to do it with other problems. We will still be using the y = mx + b formula. First step is to find m. In order to find the slope we would use the equation:

m = (y2 - y1) / (x2 - x1) Note: The number behind the letter designates which x or y value you will use of the 2 (x, y) plots

m = (-5 - 2) / (3 - 3)

m = -7 / 0 Note: A number divided by 0 is undefined which means your slope is undefined

Since your slope is undefined your equation would be x = 3 because your x values are both 3.

Now let's assume your second (x, y) plot was actually (-3, -5).

m = (-5 - 2) / (-3 - 3)

m = -7 / - 6 Note: A negative divided by a negative is a positive. The negatives cancel each other out.

m = 7/6

Okay now back to our slope-intercept formula.

y = 7/6x + b

Now in order to figure out what b is, we will again take the plot point and plug the values into the equation. You can use either point because either way the answer will come out the same. In this case we will use (3, 2).

2 = 7/6(3) + b

2 = 21/6 + b Note: The easiest way to do the next part is to make the 2 into a fraction over 6

12/6 - 21/6 = b

-9/6 = b or -3/2

So now all we have to do is plug this value into our equation.

y = 7/6x - 3/2

By using the quadratic formula, the roots of the quadratic equation are x = -7 and x = -3.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph with a maximum exponent of two (2).

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is represented by this mathematical equation:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)

For the given quadratic equation x² + 10x + 21 = 0, we have:

\(x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{100 - 84}}{2}\\\\x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{16}}{2}\\\\x = \frac{-(10)\; \pm \;4}{2}\)

x = (-10 - 4)/2 = -14/2 = -7

x = (-10 + 4)/2 = -6/2 = -3

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Answer:

25%

Step-by-step explanation:

18.1x4=72.4

Answer:

$18.10/  $72.40 * 100  

=25%

Step-by-step explanation:

Answer:

the answer is g(x)=18x

Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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9514 1404 393

Answer:

  D) $304.47

Step-by-step explanation:

The value of the account is found using the compound interest formula:

  A = P(1 +r/n)^(nt)

where interest rate r compounded n times per year for t years is applied to principal P.

  A = $300(1 +0.0148/365)^(365·1) ≈ $304.47

Answer:

D

Step-by-step explanation:

After exchanging all the $100 bills, the cashier will receive 250 $10 bills. To determine the number of $10 bills the cashier receives after exchanging all the $100 bills, we can follow these steps.

Since $2,500 consists of 100 $100 bills, we need to calculate how many $10 bills are equivalent to $2,500.

1. Calculate the total value of $100 bills: $2,500.

2. Divide the total value by the value of each $10 bill: $2,500 / $10 = 250.

3. The result is 250, which means the cashier will receive 250 $10 bills.

Therefore, after exchanging all the $100 bills, the cashier will receive 250 $10 bills.

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The general solution of the system is: x = x (free parameter), y = (7/2)x, and z = -(3/2)x. This represents the set of all solutions to the system of equations.

To find the general solution of the system represented by the augmented matrix, we can perform row operations to bring the matrix to its reduced row-echelon form (RREF). The RREF will reveal the solution of the system.

Let's work through the row operations step by step:

Row 2 = Row 2 - 2 × Row 1

Row 3 = Row 3 - 4 × Row 1

The new augmented matrix after the first row operation:

[ 2 -7 3 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Next, divide Row 1 by 2:

Row 1 = Row 1 / 2

The updated augmented matrix:

[ 1 -7/2 3/2 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Now, we can see that the second and third rows consist of all zeros. This indicates that the system has infinitely many solutions.

To express the general solution, we can assign a parameter to one of the variables (let's choose x):

x = Free parameter

Then, we can express the other variables in terms of x:

y = (7/2)x

z = - (3/2)x

Therefore, the general solution of the system is:

x = x (free parameter)

y = (7/2)x

z = -(3/2)x

This represents the set of all solutions to the system of equations. By assigning different values to the parameter x, we can obtain infinitely many solutions.

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Answer:

a) \(y=\frac{1}{3} \sqrt{x+4}\)

b) \(y=4 \sqrt{x}+3\)

c) \(y=\sqrt{2x}-6\)

Step-by-step explanation:

Part a is the green curve

Part b is the purple curve

Part c is the red curve

The black curve is the equation of the graph \(y=\sqrt{x}\)

just for reference

Answer:

Carl lives seven blocks away from Ann

Step-by-step explanation:

You start at Ann's house ( 0 ) 0+5+2=7

Beth is five blocks from Ann ( 5 )

Carl lives two blocks from Beth ( 2 )

Answer:

carl can be at 4 or 2

Step-by-step explanation:

Ava's age is 8 years old, and Charlie, being two years older, is 10 years old.

If the product of Ava's and Charlie's ages is 80 and Charlie is the older of the two, their ages must be two even integers that multiply to 80. Let's denote Ava's age as 'a' and Charlie's age as 'a + 2' (since they are consecutive even numbers).

From the problem, we know that:

a * (a + 2) = 80

This equation simplifies to:

a^2 + 2a - 80 = 0

This is a quadratic equation, and we can factor it:

(a - 8)(a + 10) = 0

Setting each factor equal to zero gives the solutions a = 8 and a = -10. Since age cannot be negative, we discard a = -10.

So, Ava's age is 8 years old, and Charlie, being two years older, is 10 years old.

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Answer:

128°

Step-by-step explanation:

Adjacent angles on a straight line must add up to 180°

Using the angle measures given,

(5x−28)° + 8x° = 180°

5x - 28 + 8x = 180

13x - 28 = 180

13x  = 180 + 28

13x = 208

x = 208/13 = 16

Therefore second angle = 8x° = 8(16)° = 128°

Answer:

\(y=x-1\)

Step-by-step explanation:

The line of symmetry of an isosceles triangle is perpendicular to its base.

Given vertices of the isosceles triangle:

By sketching the triangle with the given points, we can see that AB is its base.  (See attached graph).

To find the equation for the line of symmetry, first find the slope of the line AB.  To do this, use the coordinates of points A and B and the slope formula.

Define the points:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1\)

As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.

Therefore, the slope of the line of symmetry = 1.

The line of symmetry will pass through point C (4, 3).

Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-3=1(x-4)\)

\(\implies y-3=x-4\)

\(\implies y=x-1\)

Therefore, the equation of the given isosceles triangle's axis of symmetry is:

\(y = x - 1\)

If we graph the points

then we will get AC=CB

That means C is the point from where the axis of symmetry passes

Foot of perpendicular is midpoint of AB

Midpoint of AB

Find equation of C and foot of perpendicular

Slope

Equation

Answer:

24x+48

Step-by-step explanation:

(3x+6)(8)

=8(3x+6)

=(8*3x)+(8*6)

=24x+48

Answer: 24x + 48

Step-by-step explanation:

The formula to find the are of a rectangle is A=LW. A being the total area, W being the width, or the value on the bottom (8), and L being length how tall the object is (3x+6).

First you must replace L and W, for their given values.

A= (L) (W)

A= (3x+6) (8)

Then, simply simplify by multiplying 3x+6 by 8

You would end up getting 24x + 48

Answer:

12.5 L of grape juice is needed in 5L of cranberry juice.

Step by step explanation:

We can solve this situation by using proportional relationships:

Now, solve for x:

Step-by-step explanation:

l = 3 + 2w

P= 2w t 2l

= 2w+2(3+2w)

=2w+6+4w

=6w+6 = 54

6w=48

w=8

divide 6 both side

l=3+2(8)=3+16=19

answer

width 8feet and length 19 feet

Set (X, Y) Unif([0, 1] x [-1,0]). This means that (X, Y) is a uniform random point on the rectangular [0, 1] x [-1,0] then X and Y are independent.

Since the area of this region is 1, we have:

f(X,Y) = 1

Now we need to find the marginal PDFs of X and Y. In order to find fX(X), we integrate f(X,Y) over all possible values of Y:

fX(X) = ∫ f(X,Y) dy

= ∫ 1 dy (since f(X,Y) = 1)

= 1

Similarly, to find f_Y(Y), we integrate f(X,Y) over all possible values of X:

f_Y(Y) = ∫ f(X,Y) dx

= ∫ 1 dx (since f(X,Y) = 1)

= 1

Therefore, we have: f(X,Y) = fX(X) * fY(Y) which shows that X and Y are independent.

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Answer:

a constant

Step-by-step explanation:

k is an example of a constant

Answer:

D. A Variable

Step-by-step explanation:

A variable is a letter or symbol used to represent an unknown number.

Hope I was able to help you!

When 4 < a < 5 and 5 < b < 8, the option that best describes a-b is B) between -4 and 0. This illustrates the equation.

From the information illustrated, 4 < a < 5. In this case, a can be 4.5. This implies that a is greater than 4.

Also, 5 < b < 8. In this case, b can be 7.5. Therefore, the difference between the values can be:

a - b

= 4.5 - 7.5

= -3

This number is between -4 and 0. In conclusion, the correct option is B.

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If given inequalities are 4 < a < 5 and 5 < b < 8, then a-b lies between -4 and 0. So Option B is correct.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let us consider a inequality

4 < a < 5

By this inequality we have

a<5

a>4

So value of a lies between 4 and 5 which is a= 4.5.

5<b<8

b<8 and b>5

So values of b will be 6, 6.5 , 7 and 7.5.

Let us consider value 6.5 as b.

a-b

=4.5-6.5

=-2

This number a-b is between -4 and 0.

Hence if 4 < a < 5 and 5 < b < 8, then a-b lies between -4 and 0.

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The coordinates of the point after dilation is P' = (-10, 15)

Given,

Point of P (-4,6) was dilated by a scale factor of 2.5.

To find the coordinates of P'

Dilation with Scale Factor:

The center of dilation is a fixed point in the plane. Based on the scale factor and the center of dilation, the dilation transformation is defined. If the scale factor is more than 1, then the image stretches. If the scale factor is between 0 and 1, then the image shrinks.

Now, According to the question:

Point of P is  (-4,6)

and, Scale Factor is 2.5

The coordinates of the point after dilation :

P' = -4 x 2.5 , 6 x 2.5

P' = (-10, 15)

Hence, The coordinates of the point after dilation is P' = (-10, 15)

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The value of x from the given equation is 3/4

Linear equations are equation that has a leading degree of 1. Given the expression below

-7/2(x+2/3)=5+2x

We are to determine the value of x as shown;

-7/2x -(7/2)(2/3) = 5 + 2x

-7/2x - 7/3 = 5 + 2x

Collect the like terms

-7/2x - 2x = 5 + 7/3

-7x-4x/2 = 5 + 7/3

-11x/2 = 22/3

Cross multiply

-33x = 44

-3x = 4

Divide both sides by -3

-3x/-3 = 4/-3

x = -3/4

Hence the value of x from the given equation is 3/4

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Answer:

brooo you dummm lol 4

Step-by-step explanation:

Answer:

4 :P hava gud day

Step-by-step explanation:

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

nth number:  74+(n-1)*(-16)

Step-by-step explanation:

Angles XWY and VWY are supplementary, so the angle measure of XWY is (180 - 6x)°.

Similarly, angles XYW and ZYW are also supplementary, so the measure of XYW is (180 - 4x)°.

The interior angles of any triangle sum to 180°. Triangle XYW is a right triangle, so we have

(180 - 6x)° + (180 - 4x)° + 90° = 180°

Solve for x :

(180 - 6x) + (180 - 4x) + 90 = 180

450 - 10x = 180

270 = 10x

x = 27

Answer:

m<D = 108

Step-by-step explanation:

m<ACD = 28 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent.

m<CAD = 44 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent. (Same reasoning.)

Now, since the sum of all angles in a triangle is 180 degrees, we can use the two angles that we know as well as angle D to add up to 180 and figure out how much D is. (All of the angles in triangle ADC)

<CAD + <ACD + <D = 180

Substitute the values in.

44 + 28 + <D = 180

72 + <D = 180

Subtract on both sides

<D = 108

The measure of angle D is 108 degrees.