Rachel is designing a vegetable garden. Each plant will need 1/4 of a square foot of space. If she has 40 square feet of room in her garden, how many plants can she plant?
A: 10
B: 40
C: 80
D: 160

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

Learn more about function here:

https://brainly.com/question/2541698

#SPJ1

The equation that can be used to predict the number of times that she will roll a number that is greater than four is E(X) = np = 50 x 1/3 = 16.67

Let X be the number of times Teri rolls a number greater than four.

Since each roll of the cube is independent and has an equal probability of landing on each of the six numbers, we can model the number of rolls of a number greater than four as a binomial random variable with parameters

n = 50 and

p = 2/6 = 1/3 (since there are two numbers greater than four on the cube which is 5 and 6).

Therefore, the probability of rolling a number greater than four on any given roll is p = 1/3, and the expected number of rolls of a number greater than four in 50 rolls is given as

E(X) = np = 50 x 1/3 = 16.67

This expected value can be used to estimate the number of rolls of a number greater than four that Teri will achieve in her 50 rolls..

Learn more on probability on https://brainly.com/question/25870256

#SPJ1

Answer:

84 miles

Step-by-step explanation:

7+7=14

38-14=24

24/2=12

12 length

7 width

7x12=84

Answer: 8

please see below for work!

Answer:

133 m^2

Step-by-step explanation:

to find are of a circle it’s r^2 times pi

6^2 x pi

36 pi

113 m^2

Hopes this helps please mark brainliest

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 6m

Let us find the area of the circle.

A = πr²

A = 3.14 × 6 × 6

A = 113.04 m²

Approx. = 113m²

Answer:

104

Step-by-step explanation:

(5y) + (6x)

Let y = 13

x = y/2 = 13/2

(5*13) + (6*13/2)

65+39

104

Answer:

104

Step-by-step explanation:

See image below:)

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

Answer:

Step-by-step explanation:

10-5=5

The value of x does not exist.

What is Quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable of the form ax^{2} + bx + c = 0, where a, b, and c are constants and x is the variable. The highest exponent of the variable in a quadratic equation is 2, and the equation can be written in standard form, where the coefficient of the squared term (a) is not equal to zero.

The given expression is:

5x² - √3x + 2

This is a quadratic expression in the variable x, which means that it can be written in the form of ax² + bx + c, where a, b, and c are constants. In this case, we have:

a = 5

b = -√3

c = 2

We can use the quadratic formula to find the roots of this expression:

x = [-b ± √(b² - 4ac)] / 2a

Now, putting the values of a, b, and c, we get:

x = [-(-√3) ± √((-√3)² - 4(5)(2))] / 2(5)

Now, Simplifying the expression under the square root, we get:

x = [√3 ± √(-71)] / 10

Since the expression under the square root is negative, there are no real roots to this equation. Therefore, the expression 5x² - √3x + 2 has no real solutions.

To learn more about Quadratic equation, visit the link:

https://brainly.com/question/1214333

#SPJ1

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

Learn more about Matrix here:
https://brainly.com/question/29132693

#SPJ1

Answer:

69500

Step-by-step explanation:

695 x 100 = 69500

to check answer divided 69500 by 100

which is equals to 695

695 is a hundred times smaller than 69500

multiplication is a method of finding the product of two or more numbers.

We need to find the number which 695 is a hundred times smaller than

Six hundred ninety five times smaller than

Let us consider the number to be x.

Let us multiply 695 with 100 to  get the value or answer of the above question.

Six hundred ninety five into hundred is sixty nine thousand five hundred

695 x 100 = 69500

To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct

69500/100=695

Hence 695 is a hundred times smaller than 69500

To learn more on Multiplication click:

https://brainly.com/question/5992872

#SPJ2

Answer:

I think it is 4/7 I might be wrong

Answer:

11.06

Step-by-step explanation:

Answer:

C. from step 2 to step 3

Answer:

x = 13

Step-by-step explanation:

We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees

5x + x+12 + 90 = 180

Combine like terms.

6x+102=180

Subtract 102 from each side.

6x+102-102=180-102

6x = 78

Divide each side by 6

6x/6 = 78/6

x = 13

Answer:

x = 13

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

We know that,

→ The angle of right angle is 90°.

Forming the equation,

→ (x + 12)° + (5x)° = 90°

Then the value of x will be,

→ (x + 12)° + (5x)° = 90°

→ x + 12 + 5x = 90

→ (x + 5x) + 12 = 90

→ 6x + 12 = 90

→ 6x = 90 - 12

→ 6x = 78

→ x = 78 ÷ 6

→ [ x = 13 ]

Hence, the value of x is 13.

The weighted average length of a nail from the carpenter's box is 3.5 centimeters.

Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:

Short nail: 2.5 cm x 70.5%= 1.7625 cm

Medium nail: 5.0 cm x (19% = 0.95 cm

Long nail: 7.5 cm x 10.5% = 0.7875 cm

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

Learn more about the average in https://brainly.com/question/24057012

#SPJ1

Answer:

x+y= 136099

&'&**!;;#$*$*$$-%-%=-$*$&2=28%%"

Answer:

Step-by-step explanation: The smallest denominator between 54 and 38 would be 108.

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

To learn more about inverse function visit:

brainly.com/question/2541698

#SPJ1

Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

2

Step-by-step explanation:

2

Answer/Step-by-step explanation:

1. The figure is composed of a triangle and a rectangle.

Area of the triangle = ½*base*height

base = 4 ft

height = 12 - 8 = 4ft

Area of triangle = ½*4*4 = 8 ft²

Area of rectangle = length * width

Length = 8 ft

Width = 4 ft

Area of rectangle = 8*4 = 32 ft²

✔️Area of the figure = 8 + 32 = 40 ft²

2. The figure is composed of a semicircle and a triangle

Area of the semicircle = ½(πr²)

radius (r) = 3 cm

π = 3

Area = ½(3*3²) = 13.5 cm²

Area of triangle = ½*base*height

base = 3*2 = 6 cm

height = 6 cm

Area = ½*6*6 = 6 cm²

✔️Area of the figure = 13.5 + 6 = 19.5 cm²

Answer:

77 and 91

Step-by-step explanation:

So essentially, half 168 and half 14. You're left with 84 and 7. So, subtract 7 from 84 and add 7 to 84. You're left with 77 and 91. To verify, just add them both up and you'll see they equal 168. Then, subtract 77 from 91 and you'll see that 91 is 14 more than 77 :)

Answer:

29.575

Step-by-step explanation:

6.5(6.24-1.69)= 6.5(4.55) = 29.575

Answer:

\(6.5(6.24 - 1.69) \\ = 6.5 \times 4.55 \\ = 29.575\)

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

for more search question initially

https://brainly.com/question/28162977

#SPJ8

Answer:

a) The equation of the straight line passing through the origin and having slope m=-5

 y = -5x

b)  The equation of the straight line in slope-intercept form

 y = 2 x -1

Step-by-step explanation:

Step(i):-

We know that the equation of the straight line passing through the point (x₁, y₁) and having slope  'm'

y - y₁ = m(x-x₁)

a)

Given that the equation of the straight line passing through the origin and having slope m=-5

 y = -5x

Step(ii):-

b)

Given that the equation of the straight line in slope-intercept form

 y = m x +c

 y = 2 x -1

Answer:

\(\boxed{-2 < x\le1}\)

Representation on number line is in attached image.

Notice that -2 has an unfilled circle and 1 has a filled circle. Important

Step-by-step explanation:

The given inequality is

\(2 < 4x+10\le14\)

Subtract 10 throughout:

\(2-10 < 4x+10-10\le14-10\\\\)

\(-8 < 4x\le4\)

Divide throughout by 4:

\(-2 < x\le1\)

Answer:    \(\boxed{-2 < x\le1}\)

This is represented on the number line as follows: Notice the use of the

Answer: C) Closed circle at -5; shading to the left

The given inequality \(3x \le -15\) solves to \(x \le -5\) when we divide both sides by 3. The inequality sign does not change because we didn't divide both sides by a negative number.

The graph has a closed circle at -5 to include this value as part of the solution set. Shading is to the left to indicate values smaller than -5. Overall, the graph says "x can be -5 or smaller". If you wanted to exclude -5, you would say \(x < -5\) and use an open circle; but that's not the case here.

Answer:

C) Closed circle at -5; shading to the left

Step-by-step explanation:

Solution :

It is given that P(x) is said to be complete or proper probability distribution if it satisfies the following two ways :

1. \($P(x) \geq 0$\)

2. \($\sum_z P(x) = 1$\)

Now consider,

\($\sum_z P(x) = 1$\)

⇒ \($P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)=1$\)

⇒ \($0.61+T+0.14+0.01+0.01+0.03=1$\)

⇒ \($0.8+T=1$\)

⇒ \($T=1-0.8$\)

       = 0.2

Therefore, the value of T is 0.2

Thus, option (c) is correct.