I need help with cancelling units please

Answer:

d. $343.33

Step-by-step explanation:

We use the equation

A = P(1 + r)^t

P = $1287

r = 6% = 0.06

t = 4 years

Let's solve

A = 1287( 1 + 0.06)^4

A = 1287(1.06)^4

A = $1630.33

$1630.33 - $1287 = $343.33

So, the answer is D

The length of each of Rosie's jumps, given that she overshoots the 120 - step mark by 6 steps, is 21 steps.

Rosie is involved in the 120 - step contest and when she took 6 jumps, she overshot the 120 - step mark by 6 steps. This simply meant that she took 6 more steps over the 120 mark, thanks to her jump length.

The number of steps she took in total is therefore :

= 120 + 6

= 126 steps

This then means that the length of each jump was :

= Number of steps in total / Number of jumps

= 126 / 6

= 21 steps

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The rational expression that simplifies to 5 square root of 3 is given as follows:

C. [tex]\sqrt{75}[/tex]

A rational expression is a term that involves a root in the expression.

The simplified rational expression for this problem is given as follows:

[tex]5\sqrt{3}[/tex]

The original expression, from which the simplified expression was obtained, can be obtained moving the number 5 back to the square root.

The number is moved back into the square root with an exponent of 2, hence the original expression is obtained as follows:

[tex]\sqrt{3 \times 5^2} = \sqrt{75}[/tex]

Which is the original expression, meaning that the correct option regarding which expression simplifies to five times the square root of three is given by option C.

The problem is given by the image presented at the end of the answer.

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To find the perpendicular distance between two lines in 3D, you can use the dot product of the vector joining the two lines and the cross product of the direction vectors of the two lines, divided by the length of the cross product vector.

To find the perpendicular distance between two lines in 3D, you can use the following method:

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Answer:

Step-by-step explanation:

x+y=56

x+12=y

2x+12=56

2x=44

x=22

y=56-22

y=34

x=22

hope this helps

Answer:

34 and 22

Step-by-step explanation:

x + y = 56   Add the two equations together

x - y = 12

2x     = 56  Divide both sides by 2

x = 34

substitute 34 for x in either of the two original equations to solve for y

x + y = 56

34 + y = 56   Subtract 34 from both sides

y = 22

Check:

x + y = 56

34 + 22 = 56  Checks

x - y = 12

34 - 22 = 12

12 = 12  Checks

Answer:8-b=13

Step-by-step explanation:

8-b=13

-b=13-8

-b=5

b=-5

Therefore , the solution of the given problem of equation comes out to be 1225 boats registrations done in year 2013.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Let x be the number of boats:

t is number of years

In 1996 and 1997

=> 797 -751 = 46 boats increased

In 1997 and 1998

=> 806 -797 = 9 boats increased

So ,

the equation which can signify  the given information :

=> 2002 + t = 923 +x

So ,At 2013

=> 2013 = 1225 boats registrations done.

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a) The system of equations to find Fred and Natalie's ages are:

b) Solving the system of equations shows that their respective ages are:

A system of equations is two or more equations simultaneously or concurrently solved.

We call this a system of equations or simultaneous equations because they are solved at the same time.

Let Natalie's age = x

Let Fred's age = y

The total ages of Natalie and Fred = 38

x + y = 38

Let Natalie's age = 3x

Let Fred's age = y

The total ages of Natalie and Fred = 66

3x + y = 66

Subtract Equation 1 from Equation 2:

3x + y = 66

-

x + y = 38

2x = 28

x = 14

y = 38 - 14

y = 24

Thus, Fred is 24 years old while Natalie is 14 years.

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Answer:

Step-by-step explanation:

Yes 7/8= 0.875. 2/5 is equal to 0.40

The integer value of both values is 10 and -4.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

A positive integer and a negative integer cannot be multiplied. A pair of positive integers have a positive product. Two negative integers add up to a positive number. A positive integer and a negative integer do not add up to a positive number.

Positive and negative numbers are used differently in everyday life. Although positive numbers are frequently employed everywhere, negative integers are also used to measure temperature because it is possible for a city's temperature to be either -4°C or -10°C.

(+6)-(-3) (+1)

⇒ 6 + 3 + 1        [using rules of integers, (-)(-) yields (+)]

⇒ 9 + 1

⇒ 10

(-3)-(-7)-(+8)

⇒ -3 + 7 - 8       [using rules of integers, (-)(+) yields (-)]
⇒ -3 - 8 + 7

⇒ -11 + 7        

⇒   -4   [As -11 is greater than 7]

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Answer:

Step-by-step explanation:

2y+7=3x

-3x+2y=-7

1/2x+4y=6

x+8y=12

The triangle's third side will measure 6.71 units in length.

According to the Pythagorean theorem, two squares added together equal the square of the longest side.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length. Next, we have

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

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Answer:

48 centimeters

Step-by-step explanation:

This deals with the midline theorem.

The midline is defined by a seg that is joined by the midpoints of 2 sides.

The midline is half of the base, so if it is 10, the base is 20 cm.

You see that 26 cm is 1/2 of the hypotenuse because it is bisected, sot he whole thing is 26(2) or 52.

Now you have to solve for x using the Pythagorean theorem.

20^2 (400) + x^2  = 52^2 (2704)

Subtracted 400 from both sides to get x^2 by itself.

x^2 = 2304

Take the square root of both sides to isolate x (take the principle root)

x= 48 centimeters.

Hope this helps!

No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.

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Answer:

Step-by-step explanation:

Zero Angle (0° in Measure)

Acute Angle (0 to 90° in Measure)

Right Angle (90° in Measure)

Obtuse Angle (90 to 180° in Measure)

Straight Angle (180° in Measure)

Reflex Angle (180 to 360° in Measure)

Complete Angle (360° in Measure)

The correct solution is shows in below.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

1) 3/4 - 1/5 = 11/20

2) 3 1/3 - 4/7 = 2 16/21

3) 3 3/7 - 2 2/3 = 16/21

Now,

Simplify the fraction as;

1) 3/4 - 1/5 = 11/20

LHS;

⇒ 3/4 - 1/5

⇒ (15 - 4) / 20

⇒ 11/20

⇒ RHS

2) 3 1/3 - 4/7 = 2 16/21

⇒ 10/3 - 4/7

⇒ (70 - 12) / 21

⇒ 58 / 21

⇒ 2 16/21

⇒ RHS

3) 3 3/7 - 2 2/3 = 16/21

LHS;

⇒ 3 3/7 - 2 2/3

⇒ 24/7 - 8/3

⇒ (72 - 56)/21

⇒ 16/21

⇒ RHS

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Only in the absence of acceleration, S, is it precisely proportional to time. When there is no outside force acting on the item, its acceleration 'a decreases to zero, and the equation of motion changes to s= ut.

Subtract their x-coordinates to get the distance between them. The x-coordinate is the same for every point along a vertical line. Subtract their y-coordinates to calculate the distance between them. Below is a picture of the equation's graph, 2x+3y=6. In this location, the graph departs from the x-axis (3,0). The x-intercept is this particular location.

The point where the graph also deviates from the y-axis (0, 2). In the case of a speed vs time graph, where time is on the x-axis and speed is on the y-axis, the intercept's SI unit will be speed (m/s). x-intercept: You can find x by setting y=0 in the equation y=2x-6. 3.0 is the x-intercept. y-intercept: Enter x=0 in y = 2x - 6 and find x using the formula. It is -6 for the y-intercept.

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Answer: m = -1/2

Step-by-step explanation:

Bing bang boomarang i have no idea

The slope-intercept method is a way to graph a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. This method allows you to find the slope and y-intercept of the line and use that information to graph the line.

An explanation graph is what?

A graph shows how two variables that are typically measured along one of a pair of axes at right angles relate to one another.

To graph a linear equation using the slope-intercept method, you can follow these steps:

Identify the y-intercept by looking for the constant term (b) in the equation. The y-intercept is the point where the line crosses the y-axis, so it will have an x-coordinate of 0.

Plot the y-intercept on the coordinate plane.

Identify the slope of the line by looking for the coefficient of the x-term (m) in the equation. The slope represents the steepness and direction of the line.

Using the slope and the y-intercept, pick a point on the x-axis and use the slope to find the corresponding point on the y-axis.

Plot the point found in step 4.

Plot the two spots and then draw a straight line through them.

Note that this method will work for any linear equation where y = mx + b, and can help you graph a line quickly.

Also note that there is another method to graph a linear equation, it's called the point-slope method which is starting from any point on the line and use the slope to locate the additional line points.

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1. Add the same number to both sides.

2. Subtract the same number from both sides.

3. Multiply both sides by the same positive number.

4. Divide both sides by the same positive number.

5. Multiply both sides by the same negative number and reverse the sign.

Answer:

20:5

Step-by-step explanation:

There were 25 kids and 20 of them watched the movie, meaning only 5 people did not watch so it is 20:6.

Answer:

[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]

Step-by-step explanation:

Period: [tex]7\pi=\frac{2\pi}{b}\rightarrow b=\frac{2}{7}[/tex]

Phase Shift:

[tex]\displaystyle \frac{c}{b}=\frac{1}{5}\\\\\rightarrow\frac{c}{\frac{2}{7}}=\frac{1}{5}\\\\\rightarrow \frac{2}{7}=5c\\ \\\rightarrow \frac{2}{35}=c[/tex]

Final equation:

[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]

Answer: prime

Step-by-step explanation:

there is no greatest common factor (GCF) of the coefficients: 8 and -27. And the variables: c and d, are different so the polynomial is in its prime form.

So, on solving the provided question, we cans ay that new slope interest equation is y = 3x +c

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

given, x = 5, that is lope

coordinates = (1,0)

new slope interest equation is

y = 3x +c

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The correct question is -

Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?

Answer:

x= 92 degrees

Y=44 degrees

The total length of the flowers that Judy measures will be the 1 3/4 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, Judy measured the lengths of her flowers, in inches. The total length of the flowers will be the sum. This will be:

= 1/4 + 1/2 + 3/4 + 1/4

= 1 3/4 inches.

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Complete question

Judy measured the lengths of her flowers, in inches. The lengths are shown below.

1/4

1/2

3/4

1/4

What is the total length of the measurement?

Dilation and Stretch are non-rigid transformations.

Non - Rigid transformation:

Non-rigid transformations can change the size or shape of the archetype, or both size and shape. The two transformations Strain and Shear are not rigid. The resulting image of the transform is changed in size, shape, or both.

A non-rigid transformation is a transformation that changes the length or angle of a shape's sides. Nonrigid transformations are dilation and stretching.

All types of transformations except dilation are rigid transformations.

Dilation transformations are divided into two types

Therefore non-rigid transformations are Dilation and Stretching

Dilation:

Dilation (usually denoted by ⊕) is one of the fundamental operations in mathematical morphology. Originally developed for binary images, it was expanded first to grayscale images and then to full meshes. Stretch operations typically use a structuring element to examine and expand the shapes contained in the input image.

Strechting:

A non-rigid transformation changes the size or shape of an object. Resizing (stretching horizontally, vertically, or both) is a non-rigid transformation.

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Answer:

13.29x

Step-by-step explanation:

1.97x - 4.83x = -2.86x

-2.86x + 7.95x = 5.09x

5.09x + 11.83x = 16.92x

16.92x - 3.63x = 13.29x

The partial fraction decomposition in terms of x for the given equation is:

3x + 9 = (a(x-5) + b(x+1))

To solve for a and b, we need to multiply both sides by (x+1)(x-5). This will give us:

3x² + 4x - 45 = ax - 5a + ax + b

Now we can move all the terms with an x to one side and all the terms without an x to the other side. This will give us:

3x² + 4x - ax + b = 45 - 5a - b

We can rearrange this equation to get the following:

3x² - ax + (4 + b) = (45 - 5a - b)

Now we can use the quadratic formula to solve for a and b:

a = (4 + b) + √(4²- 4×3×(45 - 5a - b))/ (2×3)

b = (45 - 5a - (3x² - ax)) / (4 + b)

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Answer:

It's C

Step-by-step explanation:

StartFraction 3 x + 9 Over (x + 1) (x minus 5) EndFraction = StartFraction negative 1 Over x + 1 EndFraction + StartFraction 4 Over x minus 5 EndFraction