Solve.- 6x^2 + 6 - 2x = xChoose 1 answer:

The correct equation is:  5/6 - 1/6 = 4/6

A number line is a visual representation of numbers, ordered from left to right, where each point on the line corresponds to a number. The number line can be used to represent a wide range of numbers, including integers, fractions, decimals, and even negative numbers.

On a basic number line, 0 is located in the center, with positive numbers to the right and negative numbers to the left. The numbers are usually evenly spaced, with tick marks or dots indicating each value. The distance between any two points on the number line represents the difference between the corresponding numbers.

According to question Option D is correct

This is because starting at 5/6 and ending at 1/6 involves moving in the negative direction on the number line. To find the distance between these two points, we need to subtract the smaller number (1/6) from the larger number (5/6).

So, 5/6 - 1/6 = 4/6, which simplifies to 2/3. This means that the distance between 5/6 and 1/6 on the number line is 2/3.

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Answer:

20m/s

Step-by-step explanation:

Given, s=400m

t=20s

Required, v=?

v=s/t

=400m/20s

=20m/s

Answer: C:800.B:1200.T:1600

Step-by-step explanation: If the ratio is proportional to the time spent on the marketing competition, then we can add the hours up: 4+6+8=18. Total amount divded by total hours -> 3600/18=200. So each hour worked is 200 dollars. Christine worked 4 hours, 4*200=800, Bianca worked 6 hours, 6*200=1,200, and Travis worked 8 hours, 8*200=1,600.

Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

The surface area of the square pyramid is 89.4 ft² as the lateral area is  80.4 ft².

The surface area of a square pyramid is calculated by the formula

SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.

In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.

The slant height of a square pyramid is calculated by the formula

s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.

In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is

s = √(3² + (3/2)²)

= √(9 + 2.25)

= √11.25

= 3.35 ft.

The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is

4ℓ = 4 x 3.35 ft x 6 ft

= 80.4 ft².

The surface area of the square pyramid is then

SA = B + 4ℓ

= 9 ft² + 80.4 ft²

= 89.4 ft².

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Answer: 45

Step-by-step explanation:

The solution to the system of equation y + 2x² = 14 , y = 3x² - 6 is as follows:

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation by substitution method.

Therefore,

y + 2x² = 14

y = 3x² - 6

Therefore, using substitution method,

3x² - 6 + 2x² = 14

5x² - 6  = 14

5x² = 14 + 6

5x² = 20

x² = 20 / 5

x² = 4

x = √4

x = 2

Therefore, let's find the value of y using y = 3x² - 6.

y = 3x² - 6

y = 3(2)² - 6

y = 12 - 6

y = 6

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The area and the circumference of the circle are 530.93 square ft and 81.68 ft. If fertilizer will be applied to the lawn. Then the area is used. If the lawn will be surrounded by tape. Then the circumference is used.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The figure below shows a circular lawn. Its diameter is 26 ft.

Then the area of the circle will be

\(\rm A = \dfrac{\pi }{4} d^2\\\\A = \dfrac{\pi }{4} \times 26^2\\\\A = 530.93 \ \ ft^2\)

Then the circumference of the circle will be

Circumference = π d

Circumference = π × 26

Circumference = 81.68 ft

If fertilizer will be applied to the lawn. Then the area is used.

If the lawn will be surrounded by tape. Then the circumference is used.

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Answer:

Solution:

x = how long the journey take

60x = 555

60x/60 = 555/60

x = 555/60  (divide)

x = 9.25 hours

Answer: -3

Step-by-step explanation:

First let's start with A

All the sides in a hexagon add up to 720

do 720/6

720/6=120

A=120

Each angle in that hexagon adds up to 120

Then B

The triangle is equilateral, so 180/3=60

B would be 60

C would also be 60

D is = to a, so D=120

A:120

B:60

C:60

D:120

Answer: 22

Step-by-step explanation:

3 times 5 then add 7

Answer:

-84+(-11)= -95

-84 + (-11) = -84 - 11 = -95

By the commutative property, adding a negative number is the same as subtracting that number as a positive; therefore, something + (-11) = something - 11. After changing the equation from -84 + (-11) to -84 - 11, we use regular addition properties, adding the tens place and ones place to get -95.

Answer:

69

Step-by-step explanation:

just plug in 5 for all the x in the equation and mulitply

Answer:

jejeiriiririrurur7urur

Answer:

Image of proof attached

Step-by-step explanation:

So it is given that ∠1 ≅ ∠4 and we have to find that ∠3 ≅ ∠2.

I am going to show one way to prove this, but there are likely many more ways to prove this.

I hope this helps. Happy studying.

Matrices are a type of data structure that can be used to represent and manipulate data in a variety of ways.

One way to use matrices to represent data is to store the data in the form of a matrix. For example, a matrix could be used to represent a table of values, where each row represents a different data point and each column represents a different attribute or feature of the data.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

Overall, matrices are a powerful tool for representing and manipulating data in a variety of contexts, and they are widely used in a range of fields including mathematics, computer science, engineering, and data analysis.

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Matrices are a type of data structure that can be used in a variety of ways to represent and manipulate data.

One method for utilizing grids to address information is to store the information as a framework. A table of values, for instance, could be represented by a matrix, with each row representing a distinct data point and each column representing a distinct attribute or feature of the data.

The plural form of a matrix, a rectangular array or table in which numbers or elements are arranged in rows and columns, is referred to as a matrices. They can have as many columns and rows as you want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.

When performing these matrix operations, certain rules must be followed. For example, they can only be multiplied if the first and second columns are exactly the same, and they can only be added or subtracted if they have the same number of rows and columns.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

In general, matrices are extensively utilized in a variety of fields, including mathematics, computer science, engineering, and data analysis. They are a powerful tool for representing and manipulating data in a variety of contexts.

Hence the matrices be used to represent and manipulate data.

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The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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The type of angle in which angle 3 and angle 6 are, is that they are alternate interior angles ( option C)

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Since line c and line b are parallel to each other and line a is the transversal that cut through both of them the angle on line a and line b will have the following characteristics;

They can be;

supplementary

alternate exterior

alternate interior

vertically opposite

and corresponding

The property between angle 3 and angle 6 is that they are alternate interior to each other.

Therefore angle 3 and angle 6 are alternate interior angles.

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Answer:

a=9

Step-by-step explanation:

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

a + 3a -3 = 6 + 3a

a - 3 = 6

a = 6 + 3

a = 9

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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The expression with the greatest value when a = 5 is:

a + 9 × 8 ÷ 7, with 9 in the first box, 8 in the second box, and 7 in the third box.

To create the expression with the greatest value when a = 5, we want to choose the largest possible numbers to fill in the missing parts.

Since each whole number can only be used once, we should choose the three largest numbers from 1 to 9.

The three largest numbers from 1 to 9 are 9, 8, and 7. So we can fill in the expression as follows:

a + 9 × 8 ÷ 7

When a = 5, this expression evaluates to:

5 + 9 × 8 ÷ 7 = 5 + 72 ÷ 7 = 15.2857...

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Answer:

x= 6, -4

Step-by-step explanation:

x^2 - 2x - 24 = 0

(x-6) (x+4) = 0

x = 6, x= -4

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Hi

add "x" with "x" and numbers with numbers

5x+3x+2+4 = 8x+6

Answer: \(8x+6\)

Add

\(5x+3x=8x\\2+4=6\\8x+6\)