What is the total amount that Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually? TA= P (1+i)^t

The displacement is 18.03 steps, and the direction is 47.25°

We know that displacement is the difference between the final position and the initial position.

We assume the initial position (0, 0). Let's define the positive x-axis as the east and the positive y-axis as the north.

First, the student moves 8 steps east, so she is at:

(0 + 8, 0)

Then she moves 6 steps northeast, so the new position is:

(6*cos(45°) + 8,  6*cos(45°))

Finally, she moves 9 steps due north, so we have:

(6*cos(45°) + 8,  6*cos(45°) + 9)

Then the final position is:

(12.24, 13.24)

So the displacement is:

D = (12.24, 13.24) - (0, 0) =  (12.24, 13.24)

The magnitude of the displacement is:

[tex]|D| = \sqrt{12.24^2 + 13.24^2} = 18.03[/tex]

So the magnitude is 18.03 steps.

And the direction is given by the arctangent of the quotient between the y-component and the x-component:

[tex]\theta = Arctg(13.24/12.24) = 47.25 \°[/tex]

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Answer:

I believe its C , i took this class

Step-by-step explanation:

A cylinder is a three-dimensional structure formed by two parallel circular bases connected. The height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Given the volume of the cylinder is 1250 cm³, and the radius of the cylinder is 8 cm. Therefore, the volume of the cylinder can be written as,

[tex]\text{Volume of the cylinder} = \pi r^2h[/tex]

[tex]1250 = \pi \times (8)^2 \times h\\\\h = 6.217\rm\ cm[/tex]

Hence, the height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

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Answer:

NO!!! Megabytes AREN'T bigger than Gigabytes!

Step-by-step explanation:

Here's the table!

1 Kilobyte = 1,024 Bytes

1 Megabyte = 1,024 Kilobytes

1 Gigabyte = 1,024 Megabytes

1 Terabyte = 1,024 Gigabytes

Answer:

  16.6°

Step-by-step explanation:

The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.

__

We choose to use a=10, b=4, C=29°.

  c² = a² +b² -2ab·cos(C) . . . . . law of cosines

  c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304

  c ≈ √46.0304 ≈ 6.78457

Then angle B (opposite side b) is ...

  sin(B)/b = sin(C)/c . . . . . . . . . law of sines

  sin(B)/4 = sin(29°)/6.78457

  B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°

The missing acute angle is about 16.6°.

The equivalent ratio of the given ratio of 8:2 is 4:1. Hence, the ratio of 8 to 2 is equivalent to the ratio of 4:1.

When we compare ratios, equivalent ratios are the ones that are the same. To see if two or more ratios are equivalent, they can be compared to one another.

Given information:

As we know that the equivalent ratio is defined as the ratio which is having the same proportion as the given ratio.

Now, using the division property of the ratio, We will divide the given ratio with the same number on both sides:

Hence, by dividing the given ratio by 2 we get the ratio as 4:1.

Therefore, the equivalent ratio of the given ratio of 8:2 is 4:1. Hence, the ratio of 8 to 2 is equivalent to the ratio of 4:1.

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Answer:

B

Step-by-step explanation:

let me know if you need an explanation, I'll add one :D

Based on the calculations, the length of LM is equal to 1.10 units.

Given the following data:

Scale factor = 0.5.

Length of AB = 2.20 units.

In Mathematics, there are different types of transformation and these include the following:

Since polygon A'B'C'D'E' is dilated by using a scale factor of 0.5 about D', so as to form polygon LMNOP. Thus, the length of LM is given by:

LM = A'B' × scale factor

LM = 2.20 × 0.5

LM = 1.10 units.

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The width of the rectangular box with  volume of 150 cubic inches is: 5 inches.

Volume of a box = (length)(width)(height).

Given the following:

150 = (w + 10)(w)(2)

2w² + 20w - 150 = 0

Factorize

(w - 5)(w + 15) = 0

w = 5, w = -15

The width cannot be negative, therefore, the width of the box is: 5 inches.

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The cone is a three dimensional shape, and the value of the height of the cone is 27 inches

The given parameters are:

The volume of the cone is calculated using:

[tex]V = \frac13 Bh[/tex]

So, we have:

[tex]45 = \frac13 * 5 * h[/tex]

Divide both sides by 5

[tex]9 = \frac13 * h[/tex]

Multiply both sides by 3

h = 27

Hence, the value of the height of the cone is 27 inches

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Answer:

108

Step-by-step explanation:

Volume of a Square Pyramid :

Solving :

Answer: Volume = 108 cm ³

Explanation:

For a square pyramid, the volume can be calculated as follows:

Volume =  * area of base * height

Volume =  * side² * height

We have:

side length = 6 cm

height = 9 cm

Therefore:

Volume =  * 36 * 9 = 108 cm ³

Hope this helps :)

Answer:

2.5 > 2 2/5

Step-by-step explanation:

2 2/5 = 2.4

2.4 is less than 2.5

Answer:

8 in is the answer

Step-by-step explanation:

Answer:

qa no.4 do cross muntiply

Answer:

[tex](x - 3) \: (x - 8)[/tex]

Step-by-step explanation:

We were given the equation:

[tex] {x}^{2} - 11x + 24 = 0[/tex]

Therefore in order to factorize we first need to find the numbers that add to be equal to -11 and multiply to be equal to 24. The two numbers are:

[tex] - 8 \: and \: - 3 \\ \\ - 8 + ( - 3) = - 11 \\ - 8 \times - 3 = 24[/tex]

So the new equation is

[tex]{x}^{2} - 8x - 3x + 24 = 0 \\ \\ factorize: ( {x}^{2} - 8x) \: ( - 3x + 24) = 0 \\ \\ x(x - 8) \: - 3(x - 8) \\ \\ therefore : (x - 3) \: ( x - 8) = 0[/tex]

Answer:

Step-by-step explanation:

Comment

There are a lot of choices. Luckily the middle term is minus and the third term is plus, so you don't have to juggle minus signs around. Both factors are minus when put together with x.

-3 - 8

-4 - 6

-2 -12

-1 - 14

I think these are all the possible factors.

-4 + - 6 = - 10  Not the answer. It needs to be - 11

-2 + -12 = -14  Not the answer. It needs to be - 11

-1 + - 24 = -25 Just about as far away as you can get. Not the answer

So A must be right

-3 + -8 = - 11

That's what it should be. So the factors are

Answer:

(x -3)(x - 8)= x^2 - 11x + 24

Answer:

The product of the functions f(x) = x2 and g(x) = x - 8 is f(x).

Perpendicular Line: y = 3x - 10

[tex]\sf {Given:} \ y = -\dfrac{1}{3} x-4[/tex]

Comparing it with slope intercept formula:  [tex]\bf y = mx + b[/tex]

Identify the slope for this particular function:

[tex]\star \ \ \sf slope = -\dfrac{1}{3}[/tex]

Now given that the line passes perpendicularly, then the slope shall be negatively inverse of the parallel slope.

[tex]\implies \sf \ perpendicular \ slope : \ -(\dfrac{1}{m} ) \ = \ -(\dfrac{1}{-1/3} ) \ = \ 3[/tex]

Now, find the equation:

[tex]y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]     given points : (6, 8)

equation:

[tex]\rightarrow \sf y - 8 = 3(x-6)[/tex]

[tex]\rightarrow \sf y = 3x-18+8[/tex]

[tex]\rightarrow \sf y = 3x-10[/tex]

On comparing to y=mX+b

Perpendicular lines have slopes negative reciprocal to each other

Slope of perpendicular line

Equation in point slope form

Answer:

  (b)  16^(3/2)

Step-by-step explanation:

Your calculator is a good source of information about the values of numerical expressions.

__

Here, all of the expressions have a value of 16 except 16^(3/2). That has the greatest value.

_____

Additional comment

Assuming you're familiar with powers of 2 and the rules of exponents, you can evaluate these without a calculator:

  ∛(64²) = ∛(2^6)² = (2^12)^(1/3) = 2^4

  16^(3/2) = (2^4)^(3/2) = 2^6 . . . . . has the greatest value

  √(16²) = ((2^4)^2)^(1/2) = 2^(4·2/2) = 2^4

  ∛(8^4) = ((2^3)^4)^(1/3) = 2^(3·4/3) = 2^4

__

8= 2^3; 16 = 2^4; 64 = 2^6

(a^b)^c = a^(bc)

A root is equivalent to a fractional power. The cube root is the 1/3 power, for example.

Answer:

Step-by-step explanation:

perimeter of a rectangle P= 2(L+W)

L= length

W= width

48=2(L+W)---------------(1)

twice the length= 2×L= 3L

decreased by three= 2L-3

three times the width= 3×W= 3W

twice the length decreased by three is equal to three times the width

2L-3= 3W-------------------(2)

solving equation one and two simultaneously

from equation (2)

3W= 2L-3

W=2L/3-3/3

W= 2L/3 - 1----------(3)

substitute equation (3) into equation (1)

48=2(L+2L/3-1)

48=2L+4L/3-2

48×3=6L+4L-6

144=10L-6

10L=144+6

10L=150

dividing bothsides by 10

L= 15

substitute L= 15 into equation (2)

2L-3=3W

2(15)-3=3W

30-3 = 3W

27= 3W

3W= 27

dividing bothsides sides 3

3W=27/3

W=9

Answer:

y= -x to the power of 2

so the answer is the first one!

Hope this helps!!

Answer:

Step-by-step explanation:

1,)

3x+y=4 <-Equation 1

2x-y=6 <-Equation 2

Step 1 Eliminating Y Multiply negative both side

-[3x +y = 4 ] -

-3x-y = -4 <-Equation 3

Equation 2 to Equation 3

2x-y=6

-

-3x-y = -4

= 5x = 10

x =2

Substituting X to Equation 1

3x+y=4

3(2) + y =4

6 + y = 4

y = -2

Therefore x =2 and y = -2

Answer:

y intercept = 3

Step-by-step explanation:

y = 1/3x + 3

y = mx + b

where b represents the y intercept

y intercept = 3

[tex]area = l \times w \\ area = 34 \times 17 \\ area = \: 578 {mm}^{2} [/tex]

[tex]Area \: of \: the \: triangle = ½× width×height. \\ area \: = \frac{1}{2} \times 34 \times 6 \\ area = 34 \times \frac{ {\cancel6} {}^{ \: \: 3} }{ \cancel2} \\ area = 34 \times 3 \: {mm}^{2} \\ area = 102 {mm}^{2} [/tex]

[tex]volume \: = area \: \times length \\ vol = 102 \times 17 \: \: {mm}^{3} \\ vol \: = 1734{mm}^{3} [/tex]

Answer:

1734 mm² = volume

[tex] \\ \\ \\ \\ [/tex]

The graph of the system of inequalities can be seen at the end of the answer.

Here we have two inequalities:

x < 2

y ≥ - 3

To graph the first one, we need to shade all the region at the left of the line x = 2, such that the line must be dashed, because the points on the line are not solutions.

For the second inequality, we need to shade all the regions above the line y = -3, this time the line must be solid, because the points on the line are solutions.

Then the graph of the inequalities is the one you can see below. The intersection of the shaded regions is the solution of the system of inequalities.

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Explanation:

Turn the irrational numbers into decimals, so it is easy to understand and point on the number line graph.

Numbers provided:

√13 = 3.605551275 ≈ 3.61

√17 = 4.123105625 ≈ 4.12

Step by Step Solving:

Plot the points (circled area's):