James borrows $300 at an interest rate of 8% and takes 5 years to pay it off. How much does he pay? Question 2 options: $420 $120 $240 $600

Consider

2x – y = 7

y = 2x + 3

Subst. 2x+3 for y in the first equation: 2x - (2x + 3) = 7

This boils down to 0 + 3 = 7, which simply is not true and can never be true.

Thus, this system of equations has no solution.

Answer:

The system of x and y is no solutions.

C is correct

Step-by-step explanation:

Given: System of equation

[tex]2x-y=7[/tex]

[tex]y=2x+3[/tex]

We have system of equation and to solve for x

Using substitution method to solve for x and y

Substitute y=2x+33 into 2x-y=7

[tex]2x-(2x+33)=7[/tex]

[tex]2x-2x-33=7[/tex]

[tex]-33\neq 7[/tex]

-33 is not equal to 7.

We didn't get the value of x.

No solution for x and y

Hence, The system of x and y is no solutions.

F (x) = axe ^ bx

F ‘ (x) = d/dx (axe ^ bx)

= a (d/dx) (xe ^ bx)

= a [(d/dx * x) e ^ bx + (x * d/dx * e ^ bx)]

= a [e ^ bx + bxe ^ bx]

= a [1 + bx] e ^ bx

For critical points, set f ‘ (x) = 0 and solve for x

a [1 + bx] e ^ bx = 0

= 1 + bx = 0

= bx = -1

X = -1/b

Given that f (x) has local max at 1/5, critical point x = 1/5

-1/5 = -1/b

Therefore b = -5

F(x) = axe ^ -5x

F(1/5) = a/5 e ^-1

1 = a/5e

Therefore, a = 5e

Answer:

The value of a and b is [tex]5e[/tex] and [tex]-5[/tex], respectively.

Step-by-step explanation:

The given function is [tex]f(x)=axe^{bx}[/tex].

The value of function at [tex]x=\dfrac{1}{5}[/tex] is [tex]f(\dfrac{1}{5})=1[/tex] and the function has a local maxima at  [tex]x=\dfrac{1}{5}[/tex].

So, the first derivative of the function at [tex]x=\dfrac{1}{5}[/tex] will be zero.

Now, calculating for a and b.

[tex]f(x)=axe^{bx}\\f(\dfrac{1}{5})=a\left (\dfrac{1}{5}\right )e^{b\dfrac{1}{5}}\\1=\left (\dfrac{a}{5}\right )e^{\dfrac{b}{5}}[/tex]

Differentiate the function,

[tex]f(x)=axe^{bx}\\f'(x)=abxe^{bx}+ae^{bx}\\f'(1/5)=\dfrac{ab}{5}e^{\dfrac{b}{5}}+ae^{\dfrac{b}{5}}=0\\b=-5[/tex]

Solving for a as,

[tex]1=\left (\dfrac{a}{5}\right )e^{\dfrac{b}{5}}\\a=5e[/tex]

Therefore, the value of a and b is [tex]5e[/tex] and [tex]-5[/tex], respectively.

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The equation of the line passing through the point A (2, 0) that is parallel to the line y = 3x - 5 is y = 3x - 6.

To find the equation of a line parallel to the line y = 3x - 5 and passing through point A (2, 0), we can use the fact that parallel lines have the same slope.

The given line has a slope of m = 3. Therefore, any line parallel to it will also have a slope of m = 3.

Now, using the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where m is the slope of the line and [tex](x_1, y_1)[/tex] is a point on the line, we can substitute the values we know:

For point A (2, 0):

[tex]x_1[/tex] = 2

[tex]y_1[/tex] = 0

Slope m = 3

The equation becomes:

y - 0 = 3 (x - 2)

y = 3x - 6

This line has the same slope as the given line, y = 3x - 5, and passes through the point A (2, 0). Therefore, it is parallel to the given line and passes through the given point.

Answer:

It took 2 hours and 15 minutes for the airplane to travel 1,991.25 Km

Step-by-step explanation:

In order to find the time, you need to use the fact that average speed = distance traveled/time taken, the problem gives you that the distance traveled is equal to 1,991.25 Km and the average speed is 885 Km/h.

So, you use these values to find the time taken as follows:

[tex]time = \frac{distance}{speed}=\frac{1991.25 km}{885 \frac{km}{h}} = 2.25 h[/tex]

2.25 is a number made by two parts: integer-part and fractional-part.

The integer-part is equal to 2 hours.

The 0.25 is the fractional-part and corresponds to the minutes. 0.25 in fraction is [tex]0.25 = \frac{1}{4}[/tex], the hour has 60 minutes, so when you divided by  [tex]\frac{1}{4}[/tex] you the get 15 minutes.

Answer:

[tex](24\sqrt{3}+72)\text{ square unit}[/tex]

Step-by-step explanation:

Since, the area of a regular hexagon is,

[tex]A=\frac{3\sqrt{3}}{2}a^2[/tex]

Where, a is the side of the hexagon,

Here, the base of the pyramid is a regular hexagon having side length,

a = 4 unit,

Thus, the base area of the pyramid is,

[tex]A_B=\frac{3\sqrt{3}}{2}(4)^2[/tex]

[tex]=\frac{48\sqrt{3}}{2}[/tex]

[tex]=24\sqrt{3}\text{ square unit}[/tex]

Now, the lateral face of the pyramid is a triangle having base = 4 unit and height = 6 unit,

Also, a hexagonal pyramid has 6 triangular faces,

So, the total lateral area of the pyramid is,

[tex]A_L=6\times \frac{1}{2}\times 4\times 6[/tex]

[tex]=\frac{144}{2}[/tex]

[tex]=72\text{ square unit}[/tex]

Hence, the total area of the pyramid is,

[tex]T.A.=A_B+A_L[/tex]

[tex]=(24\sqrt{3}+72)\text{ square unit}[/tex]

Answer:

[tex]24\sqrt3+72[/tex] Square units

Step-by-step explanation:

We are given that a pyramid which has a regular hexagonal base.

Side length of hexagonal base=Base of triangular face=4 units

Height of triangle=6 units

We have to find total area of the pyramid.

The total area of pyramid=[tex]A_B+A_L[/tex]

Where [tex]A_B[/tex]=Base area

[tex]A_L[/tex]=Lateral area

Area of hexagonal base=[tex]\frac{3\sqrt3}{2}a^2[/tex]

Where a= Side length

Now, area of hexagonal  base=[tex]\frac{3\sqrt3}{2}(4)^2=24\sqrt3[/tex] square units

Area of triangular face=[tex]\frac{1}{2}\times base\times height=\frac{1}{2}\times 6\times 4=12[/tex] square units

In pyramid , there are 6 triangular faces.

Therefore, lateral area of pyramid=[tex]6\times 12=72[/tex] square units

Substitute the values in the given formula then, we get

Total lateral area of given pyramid=[tex]24\sqrt3+72[/tex] Square units

Answer:A

Step-by-step explanation:

12 is divisble by 4

The perimeter is equal to 60 feet and has the formula:

Perimeter = 2 l + 2 w

60 = 2 l + 2 w

The area is equal to 200 square feet and has the formula:

Area = l w

200 = l w

Rewriting area in terms of l:

l = 200 / w

Combining this with the perimeter formula:

60 = 2 (200 / w) + 2 w

60 = 400 / w + 2 w

Multiplying all by w:

60 w = 400 + 2 w^2

Dividing by 2 and rearranging:

w^2 – 30 w = - 200

Completing the square:

(w – 15)^2 = - 200 + (-15)^2

(w – 15)^2 = 25

w – 15 = ±5

w = 10, 20

Hence the dimensions of the garden is 10 feet by 20 feet

The width and length of the rectangular garden, given an area of 200 square feet and a total available perimeter of 60 feet, are 10 feet and 20 feet respectively.

To solve this problem, we can use the formula for the area of a rectangle, which is length × width = area, and the perimeter of a rectangle, which is 2(length + width) = perimeter. We know the total perimeter available (which is the ornamental fencing) is 60 feet and the area is 200 square feet.

Let's denote the length of the rectangle as L and the width as W. We can then set up these two equations:

We can simplify the first equation to get L + W = 30 and then isolate either L or W to substitute into the area equation. Let's isolate L to get L = 30 - W.

We then substitute this into the area equation to get: (30 - W)W = 200. Solving this quadratic equation, the possible solutions are W=10 and W=20. However, if W=20, that would leave 0 feet for the length, which is not possible. Therefore, we have W=10 and L=20.

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Answer:

your answer is: A

Step-by-step explanation:

corresponding angles theorem.

Answer:

d.) Line AE

Step-by-step explanation:

We have been given a diagram. We are asked to find the intersection of planes ADE and BEA.

Upon looking at our given diagram, we can see that both planes intersect only at two points that are point A and E respectively.

We can also see that the line AE is a common side of both planes, therefore, line AE is the intersection of planes ADE and BEA.

Answer:

[tex]3b^2+2b\geq 56[/tex]

Step-by-step explanation:

Here, b represents the number of boxes she purchased for this upcoming school year,

Also,  The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year.

⇒ The number of marker in each box = 3b+2

Now, the total number of marker = Number of boxes × Number of marker in each box

[tex]=b\times (3b+2)[/tex]

[tex]=3b^2+2b[/tex]

Since, she plan to use at least 56 marker in the upcoming year,

That is, the total number of marker ≥ 56

[tex]\implies 3b^2+2b\geq 56[/tex]

Which is the required inequality that shows the given situation.

hardness        is the answer for sure

Answer:c

Step-by-step explanation:

The answer is the square root of terms separated by addition and subtraction cannot be calculated individually.

To find expression cannot be rewritten as during the next step and explain.

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

The statement that best explains why the expression cannot be rewritten as during the next step is that the square root of terms separated by addition and subtraction cannot be calculated individually.

So, the square root of terms separated by addition and subtraction cannot be calculated individually.

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Answer:

a^5b^4, -a^5b^4, 9a^5b&4

Step-by-step explanation:

The scientific notation of  0.00000003937  is 3.397 x [tex]10^{-8}[/tex]

A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less. So, we utilise scientific notation to clearly describe extremely large or extremely small integers.

Given  number:

0.00000003937

Now, to make the number in standard form we have to write the number in 10 raise to power.

So, 0.00000003937

= 3.397 x [tex]10^{-8}[/tex]

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Answer:

the other person is correct

Step-by-step explanation: