Determine the slope and y-intercept of the line.
y = -69x - 346

Answer:

13.76ft²

Step-by-step explanation:

Side of square: d=8ft

Area of board: Sb=d×d=64ft²

Area of circle: Sc=pi×r²=pi×(d/2)²=pi×d²/4=pi×64/4= 16×pi=50.24ft²

Remainin area: Sb-Sc=64-50.24=13.76ft²

Answer:

Area of remaining board is 13.728 feet²

Step-by-step explanation:

Given; Square side length = 8 feet

Therefore, the diameter of the cut out circle = 8 feet, then Radius = 4 feet

The approximate area, in square feet, of the remaining board will be the are of the square minus the ares of the cut out circle.

Area of the square =  S²

                                = (8 feet)²

                                = 64 feet²

Area of the cut circle = π(4 feet)²

                                   = 3.142 x 16 feet²

                                   = 50.272 feet²

Area of remaining board = Area of the square - Area of the cut circle

Area of remaining board = 64 feet² - 50.272 feet²

Area of remaining board = 13.728 feet²

Answer:

?

Step-by-step explanation:

The -1 inside the parenthesis is an x value and the blank is a y value.

f(x) = y

Replace x in the equation with -1 to solve for y:

-2(-1) + 3 = 2+ 3 = 5

The answer is 5

Answer:

[tex]\displaystyle y'' = \frac{-75}{16y^7}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y^4 + 5x = 21[/tex]

Step 2: Find 1st Derivative

Step 3: Find 2nd Derivative

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Step-by-step explanation:

The question above is answered below.

Consecutive numbers are set of numbers that follow one another in ascending or descending order, e.g. 1, 2, 3, 4, 5....

The sum of three consecutive numbers = 72

Let the unknown consecutive numbers be represented by x+1, x+2 and x+3 such that:

[tex](x + 1) + (x + 2) + (x + 3) = 72[/tex]

Remove the brackets

[tex]x + 1 + x + 2 + x + 3 = 72[/tex]

Collect like terms and simplify

[tex] x + x + x + 1 + 2 + 3 = 72[/tex]

[tex]3x + 6 = 72[/tex]

Make 3x subject of formula by subtracting 6 from both sides

[tex]3x + 6 - 6 = 72 - 6[/tex]

[tex]3x = 66[/tex]

To obtain the value of x, divide through by the coefficient of x, which is 3. Hence;

[tex] \frac{3x}{3} = \frac{66}{3} [/tex]

[tex]x = 22[/tex]

Since x = 22,

[tex]x + 1 = 22 + 1 = 23[/tex]

[tex]x + 2 = 22 + 2 = 24[/tex]

[tex]x + 3 = 22 + 3 = 25[/tex]

The smallest of these numbers is 23.

Check,

23 + 24 + 25 = 72

Answer:

B) x = 11

Step-by-step explanation:

Add 4 to both sides

x - 4 + 4 = 7 + 4

x = 11

Steps to solve:

x - 4 = 7

~Add 4 to both sides

x - 4 + 4 = 7 + 4

~Simplify

x = 11 (Option B)

Best of Luck!

Answer:

B

Step-by-step explanation:

Multiply each term by -10

The matrix in Option B is the value of the given expression.

'In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.'

According to the given problem,

Given matrix = [tex]\left[\begin{array}{ccc}23&-38\\17&-6\\\end{array}\right] \left[/tex]

On multiplying -10 with this,

Matrix = [tex]\left[\begin{array}{ccc}(23*(-10))&(-38*(-10))\\(17*(-10))&(-6*(-10))\\\end{array}\right][/tex]

          = [tex]\left[\begin{array}{ccc}-230&380\\-170&60\\\end{array}\right][/tex]

Hence, we can conclude the matrix  [tex]\left[\begin{array}{ccc}-230&380\\-170&60\\\end{array}\right][/tex]  after multiplying -10 to    [tex]\left[\begin{array}{ccc}23&-38\\17&-6\\\end{array}\right] \left[/tex].

Learn more about matrices here:

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Answer:

3(3x+2)

Step-by-step explanation:

Answer:

3(3x+2)

Step-by-step explanation:

take out LCF of 3

Answer:

28

Step-by-step explanation:

divide 35 by 5 and multiply the product by 4

35 ÷ 5 = 7

7 × 4 = 28

Answer:

Thirty-one increased by fourteen OR

31 + 14 is 45

Step-by-step explanation:

First- Line up the numbers

When you add, you want to line up the numbers. It makes it easier to add up.

[tex]\left\begin{array}{ccc}31\\&+\\14\end{array}\right\\---[/tex]

Second - Add the numbers

You want to do the ones side first

31 = Three tens and one

14 = One ten and four ones

So you do 1+4 first

[tex]1+4=5\\\\\mathrm{To\:check...}\:\\5-1=4\\5-1=4\\\\\mathrm{Fact\:Family!}\:[/tex]

Then you go on the tens side

Like I said before...

31 = Three tens and one

14 = One ten and four ones

So now we add 3+1

[tex]1+3=4\\\\\mathrm{To\:check...}\:\\4-3=1\\4-1=3\\\\\mathrm{Fact\:Family!}\:[/tex]

You add a 0 to the sum of the numbers because it is in the tens place...

So 4 becomes 40!

Finally - Add your sums up!

Now we add our 40 from our tens plus our 5from our ones and get

45!

So thirty-one increased by fourteen is...

45!

Hope this helps you!

Have a wonderful night!

Answer:

Step-by-step explanation:

[tex]5^5-5^4+5^3 \: \: \:by \:\:\:\:7\\common factor\\\\\frac{5^5-5^4+5^3}{7}\\\\\frac{5^3(5^2-5+1)}{7}\\\\\frac{5^3(5^2-4)}{7}\\\\\frac{5^3(25-4)}{7}\\\\\frac{5^3(21)}{7}\\ \\Simplify\\\\5^3(3)\\[/tex]

Answer: 10cm^3 equals density please give briainliest

Step-by-step explanation: formula D=M/V

so D=20/2

D=10cm^3

If that 'x' signifies multiplication, then,

[tex]2a * 7b^2 = (2*7)ab^2 = 14ab^2[/tex]

So,

[tex]2a*7b^2[/tex] simplifies to [tex]14ab^2[/tex]

Answer:

All functions have a dependent variable.

All functions have an independent variable.

A horizontal line is an example of a functional relationship.

Step-by-step explanation:

i did it n got it right yayyyyyyyy

Answer:

20/5=number in each group. It can also be S/5

Step-by-step explanation:

Answer:

I think its A

Step-by-step explanation:

sorry if im wrong but hope this helps :)

The problem discusses a circular puzzle of 20 inches in diameter. Without further information on the dimensions of the individual pieces, an exact number of pieces cannot be determined.

The subject of this question is Mathematics and it is relevant to a Middle School grade-level. It involves understanding the concept of a circular puzzle and its diameter. Although the information provided about the icosahedron, which is with 20 faces and 12 corners, is fascinating, it is not directly applicable to the question about the circular puzzle.  

To solve this problem, you need to consider the size of the typical puzzle piece. Since we don't have that information, we can't provide a precise number of pieces. For example, if each puzzle piece is 2 inches wide then there would be a different number of pieces than if each piece was 1 inch wide.

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Part a: The value of x is 33°

Part b: The measure of each base angle is 69°

Explanation:

It is given that the vertex angle of an isosceles triangle measures 42°.

The base angle in the triangle has a measure of [tex](2x+3)^{\circ}[/tex]

Part a: To determine the value of x

Since, in an isosceles triangle the base angles are always equal.

Thus, the three angles in an isosceles triangle add up to 180°

Hence, we have,

[tex]42+2x+3+2x+3=180[/tex]

              [tex]42+4x+6=180[/tex]

                     [tex]4x+48=180[/tex]

                             [tex]4x=132[/tex]

                               [tex]x=33^{\circ}[/tex]

Thus, the value of x is 33°

Part b: To find the measure of each base angle.

Base angle = [tex](2 x+3)^{\circ}[/tex]

Substituting [tex]x=33^{\circ}[/tex] , we get,

[tex]Base \ angle = (2(33)+3)^{\circ}[/tex]

                  [tex]=(66+3)^{\circ}[/tex]

                  [tex]=69^{\circ}[/tex]

Thus, the measure of each base angle is 69°

Answer:

33 and 69 lol funny number

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

2, 4, 6 = 3 composite numbers

There are six numbers. Count the number of composite numbers.

Write it as a fraction.

3/6

Then convert it to a percent.

3/6 converts to 50%

To solve the problem, let's start by understanding what a number cube is and what a composite number is.
A number cube is typically a six-sided die, with each side having one of the numbers 1, 2, 3, 4, 5, or 6. Each number has an equal chance of appearing on the top when the cube is rolled.
A composite number is a whole number that has more than two distinct positive divisors. In other words, it can be divided evenly by numbers other than 1 and itself. The smallest positive composite number is 4 because it can be divided by 1, 2, and 4.
Let's list all the positive composite numbers that are on a standard number cube:
- 4 can be divided by 1, 2, and 4.
- 6 can be divided by 1, 2, 3, and 6.
The numbers 2 and 3 are not considered composite numbers, even though they are divisible by numbers other than 1 and themselves; this is because they are prime numbers, having exactly two distinct positive divisors (1 and the number itself).
Now, let's determine the probabilities.
The probability (P) of an event is given by the number of favorable outcomes (f) divided by the total possible outcomes (t), or P = f / t.
For a number cube, the total possible outcomes when rolling the cube are 6 (since there are 6 sides).
The favorable outcomes for rolling a composite number on a number cube are the outcomes where the top number is either 4 or 6.
Thus, f (favorable outcomes for rolling a composite number) = 2 (just the numbers 4 and 6).
Now, we can calculate the probability:
P(composite number) = f / t = 2 / 6
We can simplify this fraction by dividing both the numerator and the denominator by 2:
P(composite number) = 1 / 3
Hence, the probability of rolling a composite number on a standard number cube is 1/3.

Answer:

25

Step-by-step explanation:

First: 125+72-150 is 47

Chairs: 125-47 is 78 chairs

Umbrellas: 72-47 is 25 umbrellas

Hence, there is 25 people rented umbrellas

Hope this helps!!!

Have a nice day:)

By applying the principle of inclusion-exclusion, we determined that the number of people who rent umbrellas is 97, after accounting for the overlap of customers who rent both chairs and umbrellas.

To solve this combinatorial problem, we can employ the principle of inclusion-exclusion. The principle is a way to count the number of elements of each collection, subtracting the overlaps (in this case, people who rent both chairs and umbrellas), and adding the elements that are in neither category if necessary.

Let's define the following terms:

According to the question:

C = 125 (chairs)

B = 72 (both chairs and umbrellas)

The total number of customers, T, is given by:

T = C + U - B

Since the total number of customers is 150, we have:

150 = 125 + U - 72

To find U (the number of people renting umbrellas), we just need to solve for U:

U = 150 - 125 + 72

U = 25 + 72

U = 97

Therefore, the number of people who rent umbrellas is 97.

The inequality to represent the number of hours when Kent has ridden more than 30 miles is y = 6x for x > 5, where x is the number of hours ridden and y is the distance in miles.

Step-by-step explanation:

Step 1:

First, we need to plot the coordinates of the line on the graph.

We plot the points that fall exactly on an x axis value and also on a y axis value.

There are three such points on the given graph; (5, 30), (10, 60) and (15, 90). These points fall exactly on the values of the x axis and the y axis.

Step 2:

Now, we establish a relationship between the values of x (the number of hours ridden) and y (distance in miles).

Here y is the dependent value and x is the independent value i.e. the value of y values according to the values of x.

In 5 hours, Kent rode 30 miles. In 10 hours, he rode 60 miles and in 15 hours he rode 90 miles.

Step 3;

So for every 5 hours, Kent rides another 30 miles.

So y = 6x for x>5 is the

When x = 10, y = 6 × 10 = 60 miles,

When x = 15, y = 6 × 15 = 90 miles.

Answer:

x = 5

Step-by-step explanation:

Given

2(x + 7) - 3(2x + 4) = - 18 ← distribute both parenthesis

2x + 14 - 6x - 12 = - 18, that is

- 4x + 2 = - 18 ( subtract 2 from both sides )

- 4x = - 20 ( divide both sides by - 4 )

x = 5

The original equation 2(x+7) - 3(2x+4) = -18 simplifies to -4x = -20, which leads to the solution x = 5. This is confirmed by substituting x back into the original equation, resulting in an identity (-18 = -18).

The equation to solve is 2(x+7) - 3(2x+4) = -18. To solve for x, we first expand the equation:

2x + 14 - 6x - 12 = -18

Combining like terms, we get:

-4x + 2 = -18

Subtracting 2 from both sides gives us:

-4x = -20

Dividing both sides by -4, we find that x = 5.

To verify the solution, plug x back into the original equation:

2(5+7) - 3(2*5+4) = -18

Which simplifies to:

24 - 30 = -18

This confirms that the solution x = 5 is correct as it results in an identity after substitution.

Answer:

16.64 units

Step-by-step explanation:

Use Pythagorean Theorem:

a^2+b^2=c^2

14^2+9^2=x^2

196+81=x^2

277=x^2

16.64=x

So the length is about 16.64 units

Answer:

y = -52

Step-by-step explanation:

Step 1:  Convert to Standard Form

y + 4 = -6(2 + 6)

y + 4 = -12 - 36

y + 4 - 4 = -48 - 4

y = -52

Answer: y = -52

Answer:

(¾ * -3) -2.5

equals (-9/4) -2.5

equals -4.75

Step-by-step explanation:

Answer:that's it

Step-by-step explanation:

Answer:

totalCost = 150 + 12x

$210

-3.25x + 4.1

40x-24y

4(x+5)

6(x+9)

Step-by-step explanation:

let x = day

foodCost = 100 + 5x

gameCost = 50+ 7x

totalCost = 100 + 50 + 7x + 5x

totalCost = 150 + 12x

5 days

150 +12(5) = 150 + 60 = 210

75x+6 -2.5x-1.9

-3.25x + 4.1

where are the answer choices?

Answer: Vehicle's color

Step-by-step explanation: took the quiz.

Answer:

Step-by-step explanation:

When dividing fractions, I use a method called Keep Change Flip. Let's use the example 1/2 divided by 3/4 as an example. First, you have to keep the first fraction the same. This is what you currently have: 1/2 / 3/4. Next, you have to change the divison sign into a multiplication symbol. Now, this is what it should look like: 1/2 x 3/4. Then, you have to flip the fraction 3/4 into 4/3. Now, you have 1/2 x 4/3. Multiply the fraction. If you don't know how to, multiply numerator by numerator, denominator by denominator. You should get 4/6. However, this isn't your final answer. You can simplify this by dividing by 2 to get 2/3. So, your answer is 2/3. Hope this helped you and let me know if you need more help! :D