Bob has $2,500 invested in a bank that pays 4 nnually. how long will it take for his funds to double?

Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

To learn more about : positive root

https://brainly.com/question/31512158

#SPJ8

The solution to the system of linear equations is:

x = 26/17

y = -28/17

To solve the system of linear equations using the elimination method, we'll eliminate the variable y by adding the two equations together. Here are the steps:

Write down the two equations:

2x - 3y = 8 ...(Equation 1)

5x + y = 6 ...(Equation 2)

Multiply Equation 2 by 3 to make the coefficients of y in both equations cancel each other out:

3 × (5x + y) = 3 × 6

15x + 3y = 18 ...(Equation 3)

Add Equation 1 and Equation 3 together to eliminate y:

(2x - 3y) + (15x + 3y) = 8 + 18

2x + 15x - 3y + 3y = 26

17x = 26

Solve for x by dividing both sides of the equation by 17:

17x/17 = 26/17

x = 26/17

Substitute the value of x back into one of the original equations to solve for y.

Let's use Equation 2:

5(26/17) + y = 6

130/17 + y = 6

Solve for y by subtracting 130/17 from both sides of the equation:

y = 6 - 130/17

Simplify the right side of the equation:

y = -28/17

So, the solution to the system of linear equations is:

x = 26/17

y = -28/17

Learn more about system of linear equations click;

https://brainly.com/question/20379472

#SPJ1

The first step to conducting a statistical study is to clearly define the research question or problem.

This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.

It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.

To know more about statistical study:

https://brainly.com/question/23276495

#SPJ4

Answer: 26.6 repeating number or 26 2/3

Step-by-step explanation:

the remainder is - 1

when (x ³ - 7x + 5) is divided by (x + 3) the remindeer is f( -3 )

x + 3 = 0 => x = - 3

f(-3) = (-3)³ - 7(-3) + 5

= - 27 + 21 + 5

= - 1

Answer:

b is the lowest and d is the highest y axis

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

(2,7)

Step-by-step explanation:

y=6x-5

y=x+5

Since they are both equal to y, set them equal to each other

6x-5 = x+5

Subtract x from each side

6x-x-5 = x+5-x

5x-5 = 5

Add 5 to each side

5x-5 +5 = 5+5

5x=10

Divide by 5

5x/5 = 10/5

x=2

y = x+5

y = 2+5

y =7

Answer:

Choice C: (2,7)

Step-by-step explanation:

Using substitution method let y = x + 5

We have x + 5 = 6x - 5

Get let’s get rid of the 6x, so -5x + 5 = -5

Get rid of the 5 by subtracting by 5, so -5x = -10

Divide -5 on both sides and you get x = 2

Input 2 for x in y = x + 5, we get y = 2 + 5, which equals 7.

So (2,7)

Please mark BRAINLIEST!

The Mean Value Theorem applies over the interval (-5, 5) and (5, ∞).

To determine the interval(s) where the Mean Value Theorem (MVT) applies for the function y=√(x^2-25), we need to ensure that the function is continuous and differentiable on the given interval.

1. The function is continuous when the expression under the square root is non-negative, which means x^2-25≥0. Solving for x, we get x≥5 or x≤-5. In interval notation, the domain for continuity is (-∞,-5] U [5,∞).

2. To check for differentiability, we need to find the derivative of the function. The derivative of y=√(x^2-25) is:

y' = (1/2)(x^2-25)^(-1/2) * 2x
y' = x/√(x^2-25)

Now, we need to ensure that the derivative is defined on the given interval. Since x=5 or x=-5 makes the denominator zero, we should exclude these points. Hence, the interval for differentiability is (-∞,-5) U (5,∞).

Since the MVT requires both continuity and differentiability, the applicable interval(s) for the Mean Value Theorem are (-∞,-5) U (5,∞).

To learn more about Mean value theorem : brainly.com/question/30403137

#SPJ11

Answer:

60x + 30 = y | Honestly not sure if it's right but I wanted to help anyways!

Step-by-step explanation:

On solving the provided question, we can say that sum of all angles of a triangle is 180, angle 1 = 103, angle 2 = 47 and angle 3 = 22

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in the given triangle

sum of all angles of a triangle is 180.

5x - 7 +2x +3 +x = 180

8x = 176

x = 22

angle 1 = 103

angle 2 = 47

angle 3 = 22

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer: \(f^{-1}(x)=-\frac{2}{3}x+\frac{7}{3}\)

Step-by-step explanation:

To find the inverse of a function, you want to replace x with y and y with x. Then, you solve for y.

\(y=-\frac{3}{2}x+\frac{7}{2}\)                       [replace y with x and x with y]

\(x=-\frac{3}{2}y+\frac{7}{2}\)                       [subtract both sides by 7/2]

\(x-\frac{7}{2} =-\frac{3}{2}y\)                       [multiply both sides by -2/3]

\(-\frac{2}{3} (x-\frac{7}{2} )=y\)                     [distribute]

\(y=-\frac{2}{3}x+\frac{7}{3}\)

Now, we have our inverse function.

\(f^-^1(x)=-\frac{2}{3}x+\frac{7}{3}\)

1) 2/1

2) 0

3)1/2

............

Answer:

10 and 7

Step-by-step explanation:

First you can list out numbers 1-10 and find thngs that equal 3 when subtracted. Then after you do that see if when you multiply y x 3 subtracted from x if it equals -11.

10-7 =3

10 - (7x3)

10 - 21

-11

Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

Answer: 1.No, 2.Yes, 3.No, 4.22, 25, 28, 5.-29, -34, -39, 6. 9/10, 1, 1 and 1/10,  For the last three you are on your own. Good luck :)

Step-by-step explanation:

Answer:

10.5.

Step-by-step explanation:

By similar  triangles:

IJ / 21 = 8 /(8+8) = 1/2

IJ / 21 = 1/2

IJ = 1/2 * 21

= 10.5.

Answer:

bottom: 12 x 12 = 144

1st triangle: (12 x 8)/2 = 48

2nd triangle: 48

3rd triangle: 48

4th triangle: 48

144 + 48 + 48 + 48 + 48 = 336 cm squared

Answer:

1364

Step-by-step explanation:

use the calculator

Kate bought $23.40 worth of two types of bird seed. Thistle bird seed sells for $1.60 per pound and sold bird seen sells for $0.95 per pound. The standard form 1.60x + 0.95y = $23.40.

Standard form, also known as scientific notation, is a way of writing a number that is a product of a number between 1 and 10 and a power of 10.Standard form is useful for expressing very large or very small numbers in a more manageable and easily comparable form. It is often used in scientific and engineering fields, such as physics and chemistry, where very large or very small numbers are common.

Let x be the number of pounds of thistle birdseed and y be the number of pounds of sunflower birdseed.

We know that:

1.60x + 0.95y = $23.40 (the total cost of the birdseed)

This equation is already in standard form, with the variables on one side and the constant on the other side, and the coefficients being the prices per pound of each type of birdseed.

To know more about number visit:

https://brainly.com/question/29766862

#SPJ1

Answer:

i don't understand

Step-by-step explanation:

the question is 11 divided 2and2over 3

\(=\frac{x^{3}(4x^{2} -25) }{2x-5} \\=\frac{x^{3} (2x+5)(2x-5)}{2x-5} \\=x^{3} (2x+5)\\=2x^{4}+5x^{3}\)

⇒Note there was a 2x-5 in the numerator and a 2x-5 in the denominator so they canceled each other. Leaving the above expression.

Answer:

D

Step-by-step explanation:

A system of equations with no solution means the lines are parallel and never intersect.

The only graph showing a possible set of parallel lines is D

Answer:

The answers that should go in the 108 box are as follows,

The answers that should go in 96 are, a

Answer:

she must let out the string when the kite is 700 ft away from her at 20 ft/s

Explanation:

given information:

a = the distance between the girl

b = the length of the string

a = 300

da/dt = 20 ft/s

c =500 ft, dc/dt = ?

Answer:

4 times

Step-by-step explanation:

1. 16 cups in a gallon

2. 16 total cups divided by 4 available cups in water bottle equals 4 times

Answer:

1/4x is basically x divided by 4/multiplied by 1/4

this can be applied in examples such as:

1/4(2) = 0.5

etc.

Step-by-step explanation:

i hope this helped, if not, please leave a comment specifically requiring what exactly you are stuck with.

Answer:

 1/8x+1/8x

Step-by-step explanation:

If you are considering speed regardless of direction, the average speed is:

(24 + 16) / 2 = 40 / 2 = 20mph

Although if direction matters, then one number has to be negative since the directions are opposite:

(24 - 16) / 2 = 8 / 2 = 4mph (in the positive direction)

The required surface area of the sphere with radius 10 feet is given by option a. 1,256 ft².

Let us consider 'r' be the radius of the sphere.

Radius of the sphere 'r' = 10 feet

Surface area of the sphere = 4 π r²

Substitute the value of radius in the formula we get,

⇒ Surface area of the sphere = 4 π × ( 10 )²

Substitute value of π is equal to 3.14 we get

⇒ Surface area of the sphere = 4 × 3.14 × ( 10 )²

⇒ Surface area of the sphere =  12.56 × 100

⇒ Surface area of the sphere = 1,256 square feet.

Therefore, the surface area of the sphere is equal to option a. 1,256 ft².

learn more about sphere here

brainly.com/question/12390313

#SPJ4

Answer:

We have the equation of the line as : 4x+2y=12

Step-by-step explanation:

Now 4x+2y=12

=> 2y = 12 - 4x

=> y = 6 - 2x

A line with a slope m and y-intercept c can be written as y = mx + c

In the case of y = -2x -...