Elliot has 4 1/3 candy bars. He gives 2/3 of a candy bar to Sara and 1/3 of a candy bar to Bill. How much does Elliot have left? (Work it out)

The factored expressions (x + 3)(x + 27), (x + 9)(x + 9),and (x - 3)(x + 27) can matched to the quadratic expressions x² + 30x + 81, x² + 18x + 81, and x² + 24x - 81 respectively.

Factor is a number or an expression that divides another without a remainder. That is if multiplying two expressions gives us a product, then the expressions we are multiplying are factors of the product.

(x + 3)(x + 27) = x² + 27x + 3x + 81

(x + 3)(x + 27) = x² + 30x + 81

(x + 9)(x + 9) = x² + 9x + 9x + 81

(x + 9)(x + 9) = x² + 18x + 81

(x - 3)(x + 27) = x² + 27x - 3x - 81

(x - 3)(x + 27) = x² + 24x - 81

Therefore, the factored expressions (x + 3)(x + 27), (x + 9)(x + 9),and (x - 3)(x + 27) can matched to the quadratic expressions x² + 30x + 81, x² + 18x + 81, and x² + 24x + 81 respectively.

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The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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The length of time that it will take for each of the workout sessions would be: Plan A = 1.5 hours, and Plan B =  0.5 hours.

The length of the sessions can be obtained by first obtaining drawing a system of equations for the two cases. On Wednesday, we can represent the sessions as follows:

2A + 12B = 9 hours

On Thursday, we would have

5A + 3B = 9 hours

2A + 12B = 9  Eqn 1

5A + 3B = 9   Eqn 2

Multiply equation 2 by -4

2A + 12B = 9

-20A - 12B = -36

2A - 20A = 9 -36

-18A = -27

Divide both sides by -18

A = 1.5 hours

For B, substitute A in the first equation

2(1.5) + 12B = 9

3 + 12B = 9

12B = 9 - 3

12B = 6

Divide both sides by 12

B = 0.5

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Complete Question:

Ann the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Ann trained her Wednesday clients for a total of 9 hours and her Thursday clients for a total of 9 hours. How long does each of the workout plans last?

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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Answer:

$5.86

Step-by-step explanation:

The total was $36.31

We were given the price of 1, which was $1.15

$36.31-$1.15 = $35.16 remaining

Since the other 6 friends ordered the same meal, they would have paid the same price, so we would divide by 6

$35.16/6 = $5.86

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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The coordinates of the points after  (x - 2, y - 1) and dilating by 3 is

(- 3, 6).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, Maddie plots point A (1, 3).

She then translates it using the rule (x - 2, y - 1) which now becomes

(1 - 2, 3 - 1)

= (-1, 2) and dilates the image centered at the origin with a scale factor of 3.

∴ The new coordinates are (-1×3, 2×3) = (- 3, 6).

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Answer:

575.8 cubic cm

Step-by-step explanation:

V(cone) = 1/3· π · r² · h

V = 1/3 · π · 25 · 12

V = 4(25)π or 100π = 314

V(half-sphere) = (4/3 · π r³)/2

V = (4/3π · 125) = 261.8

Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

Answer:

8 + w

The sum of 8 and w.

Answer:

X    |   y

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

-2   |   3

-1   |   0

0   |  -3

1   |  -6

Answer:

95%

Step-by-step explanation:

%Change from 800 to 40 = %Decrease

%Decrease = Old Value - New Value/Old Value × 100%

%Decrease = 800-40/800 × 100%

%Decrease = 760/800 × 100%

% Decrease = 95%(Answer)

The approximate height of the tree is feet.

The exact height of the tree cannot be determined without additional information. However, a rough estimate can be made using the following formula:

Height of Tree = Length of Shadow / Tan(Angle of Elevation of Sun)

In this case, the estimated height of the tree would be: Length of Shadow / Tan( ) = feet/tan( ).

The formula to calculate the height of a tree is:

Height of Tree = Length of Shadow * Tan(Angle of Elevation of the Sun)

In this case, Length of Shadow = feet and Angle of Elevation of the Sun

Therefore, the height of the tree can be calculated as follows:

Height of Tree = feet * Tan( )

Height of Tree = feet * 0.839

Height of Tree = feet

Therefore, By  the angle of elevation the approximate height of the tree is feet.

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Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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9514 1404 393

Answer:

  1 11/49 ≈ 1.224 miles

Step-by-step explanation:

Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.

The total for 7 days is ...

  7(3.5m) = 30

  m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles

Mia's morning walks are 1 11/49 miles, about 1.224 miles.

Answer:

less!

Step-by-step explanation:

billy = 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20 = 295

maria = 10, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25 = 360

soooooo that in mind! maria earned more than billy!

Answer:1/24

Step-by-step explanation:

7/8 - 5/6

multiply the denometers by each other

what you do to the bottom you do to the top

42/48 - 40/48

subtract

2/48

simplify

1/24

Answer:

1/24

Step-by-step explanation:

Simplify first 7/8 and then 5/6

The find the least common factors which the denominator is the left 8 and for right 6

7/8=21/24

5/6=20/24

21/24-20/24=1/24

or

7x3-(5x4)/24=1/24

Answer:

you can make 12 cans of them

The concept of isosceles triangle is presented in this answer.

An isosceles triangle is a type of triangle in which two sides are of equal length. These two sides are known as the legs of the triangle, and the third side is called the base. The angles opposite to the legs are also equal in measure. This makes the isosceles triangle a symmetrical shape, with two congruent sides and angles.

In an isosceles triangle, the height is perpendicular to the base and bisects it, dividing the base into two equal parts. The height is also an axis of symmetry of the triangle, which means that if the triangle is folded along the height, the two halves will be congruent.

The problem is incomplete, hence concepts of isosceles triangles are presentd.

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Answer:

We need the length to answer

Step-by-step explanation:

The solution of the composite function fog(x) = 3x + 3 at x > 2.

Let the two function f(x) and g(x) generate a new function h(x) using an operation.

The operation is composition of functions and h(x) is a composite function.

We have three piecewise function.

First we have to show that,

the composite function,

fog(x) at x > 2.

For that,

g(x) at x > 2 is,

g(x) = 3x.

Now, f(g(x)),

= f(3x)

= 3x + 3 at x > 2.

Therefore, the function is fog(x) = 3x + 3.

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The complete question:

Find the fog(x) at x > 2

This is a pre-algebra problem. I'll go through the steps with you. If you don't get it, don't be afraid to ask!

Step One - Cross Multiply

These are fractions, but that doesn't mean you have to add them. Fractions are just the numerator divided by the denominator. So to 'remove' the 9, multiply both sides by 9. To 'remove' the 6, multiply both sides by 6. (We multiply both sides of the equation by the same number because we need to make each side the same). Note that when you multiply both sides by 9 or 6, you have to multiply the whole part.

(2x+1)×6 = (1-1)×9

Distribute.

12x+6 = 9-9

Step Two - Solve the Equation

So we are left with this equation after cross multiplying:

12x+6 = 9-9

First, we can start by subtracting 9 from 9, because those are the same types of numbers.

12x+6 = 0

Now, we have to 'remove' the 6. We can do that by subtracting each side by 6.

(12x+6)-6 = 0-6

12x = -6

Now we are left this this.

We need to 'remove' the 12 now, so we can isolate the x. Since 12 is multiplied to x, we divide each side by 12.

(12x)÷12 = -6÷12

We get x = -1/2

x = -1/2 or -0.5

Hope this helped!

Answer:

4 cookies

Step-by-step explanation:

The remainder of (7x12)/5 is your answer.

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x