Write an equation for the line perpendicular to 2x−3y = 5 and containing (−2, 1).

To solve this problem, we have to manually solve for the value of x for each choices or equations. The correct equation will give a value of -1 since the linear equations intersects at point (-1, -4).

1st: 7x + 3 = x + 3

7x – x = 3 – 3

6x = 0

x = 0                (FALSE)

2nd: 7x − 3 = x – 3

7x – x = 3 – 3

6x = 0

x = 0                (FALSE)

3rd: 7x + 3 = x − 3

7x – x = - 3 – 3

6x = -6

x = -1               (TRUE)

4th: 7x − 3 = x + 3

7x – x = 3 + 3

6x = 6

x = 1                (FALSE)

Therefore the answer is:

7x + 3 = x − 3

In this exercise, we are going to solve using our knowledge of systems and in this way we will find that the equation that satisfies the points.

As we know that the equation that will satisfy will have to have the values ​​of X=-1, we will solve each one of the alternatives as:

[tex]7x + 3 = x + 3\\6x = 0\\x = 0[/tex]

We realize that the value of x is not what we want so it doesn't satisfy us.

[tex]7x - 3 = x - 3\\7x- x = 3- 3\\6x = 0\\x = 0[/tex]

We realize that the value of x is not what we want so it doesn't satisfy us.

[tex]7x + 3 = x − 3\\6x = -6\\x = -1[/tex]

[tex]7x − 3 = x + 3\\7x – x = 3 + 3\\6x = 6\\x = 1[/tex]

We realize that the value of x is not what we want so it doesn't satisfy us.

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The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:

width = 51,047

length = 51,055

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Here, we have,

given that,

A fence is to be installed around a rectangular field.

the​ field's perimeter is 204204 feet.

now, we have,

204204 - 16 = 204188

we get,

204188 / 4 = 51,047

so, we get,

width = 51,047

length = 51,055

Hence, The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:

width = 51,047

length = 51,055

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Answer:

The correct answer is B. 110.

The cost to rent each chair is $5, and the cost to rent each table is also $5.

This problem can be solved using the method of substitution in solving systems of linear equations. We can set up two equations based on the information given: 5C + 3T = 25 and 2C + 6T = 40 where C represents the rental cost of each chair and T represents the rental cost of each table.

When we simplify the second equation, we get C + 3T = 20. We can then substitute this into the first equation, which gives us 5(C + 3T) = £25. Solving these equations gives us the cost to rent each chair (C) as $5 and each table (T) as $5.

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To find the area of the region completely bounded by the curve y=-x^2+x+6, you can integrate the equation with respect to x and evaluate it between the x-values where the curve intersects the x-axis. By solving the quadratic equation -x^2+x+6=0, you can determine the x-values. Then, evaluate the definite integral between these x-values to find the area.

The area of the region completely bounded by the curve y=-x^2+x+6 can be found by integrating the equation with respect to x and evaluating it between the appropriate bounds. The integral of the given equation is ∫(-x^2+x+6) dx. To find the area, we need to find the definite integral between the x-values where the curve intersects the x-axis. First, set the equation equal to zero and solve for x:

-x^2+x+6=0

This quadratic equation can be factored as: (x-2)(x+3). Therefore, the curve intersects the x-axis at x=2 and x=-3.

By evaluating the definite integral between x=-3 and x=2, we can find the area of the region:

Area = ∫-32 (-x^2+x+6) dx

Integrating this equation will give you the area of the region bounded by the curve y=-x^2+x+6.

The dimes are 28 dimes

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

total coins = 57

So,

D + Q = 57

D= 57 - Q....(1)

0.10D + 0.25 Q = 10.05

Using (1), we get

0.10(57 - Q) + 0.25Q= 10.05

5.7 - 0.10Q + 0.25Q = 10.05

0.15Q = 4.35

Q= 29

So, dimes = 57- 29= 28 dimes

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Answer:

x = + 0.85 , -0.85

Step-by-step explanation:

Given : 11x² = 8.

To find : use any method to solve the equation. If necessary, round to the nearest hundredth.

Solution : We have given that : 11x² = 8.

First we divide both sides by 11,

x² = [tex]\frac{8}{11}[/tex].

Now taking square root both sides .

x = [tex]\sqrt{\frac{8}{11}}[/tex].

x =± 0.8528.

Therefore, x = + 0.85 , -0.85

Answer:

Step-by-step explanation:

option b

Given a polynomial with rational coefficients, if √3 is a root, its irrational conjugate -√3 must also be a root due to the Irrational Conjugates Theorem, ensuring that the polynomial maintains rational coefficients.

The subject of this question is a polynomial function with rational coefficients, which is encountered in mathematics, particularly in algebra. When a polynomial has rational coefficients and one of its roots is an irrational number, such as the square root of 3 (√3), the Irrational Conjugates Theorem states that its conjugate, in this case, the negative square root of 3 (-√3), must also be a root of the polynomial. Therefore, the polynomial function in question must include both √3 and -√3 as roots to have rational coefficients.

Given that the function already has -2 as a root, we know that (x + 2) is a factor of the polynomial. Additionally, because √3 is a root, the factors (x - √3) and (x + √3) will also be part of the polynomial. To find the roots of a quadratic equation or higher-order polynomials, one can set the function equal to zero and solve for x, either by factoring, applying the quadratic formula, or other algebraic methods.

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This problem states that the sum of 3 consecutive integers is 63 and it asks us to find the largest integer.

Three consecutive integers can be represented as followed.

X → first integer

X + 1 → second integer

X + 2 → third integer

Since the sum of our three consecutive integers is 24, we can write an equation.

X + X + 1 + X + 2 = 63

We can simplify our equation on the left and it will read...

Answer:

81^1/12

HAVE A GREAT DAY

The expression ''4 square root of 81³'' can be rewritten as,

⇒ [tex]81^{\frac{3}{4} }[/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression to write is,

⇒ 4 square root of 81³

Now, It can be written as;

⇒ 4 square root of 81³

⇒ [tex]\sqrt[4]{81^{3} }[/tex]

By rule of exponent we get;

⇒  [tex]81^{\frac{3}{4} }[/tex]

Thus, The expression ''4 square root of 81³'' can be rewritten as,

⇒ [tex]81^{\frac{3}{4} }[/tex]

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Answer:

4 deaths per hour

Step-by-step explanation:

We have been given that approximately 31,000 citizens of the country died in automobile accident in 2015.

Since we know that 1 year = 365 days,

1 day = 24 hours

In one year there are total hours = 365 × 24 = 8,760 hours

Death per hour = [tex]\frac{31000}{8760}[/tex] = 3.5388 ≈ 4

Therefore, the toll in deaths per hour is approximately 4 in 2015.

Answer:

3:1 or 3/1

Step-by-step explanation:

We have the next information:

Gallons of Milk             Cost

           2                  ⇒     $6

dividing both quantities by two, we get the price for a single gallon of milk:

Gallons of Milk             Cost

           1                  ⇒     $3

We are asked for the ratio of dollars to gallons of milk (the order is important since dollars go first than gallons) so we will have the following:

dollars:gallons or dollars/gallons

and since $3 dollars pay for 1 gallon of milk, the ratio is:

3:1 or 3/1

Final answer:

To determine where the tangent line to a function is horizontal, find the derivative of the function, set it equal to zero, and solve for 'x'. This value of 'x' is where the slope is zero, indicating a horizontal tangent line.

Explanation:

How to Find Where the Tangent Line is Horizontal

To find where the tangent line to a curve is horizontal, you need to determine where the slope of the tangent (which is the derivative of the function) is zero. This involves calculating the derivative of the given function and solving for the value of 'x' where this derivative equals zero.

For example, if we have a function y = 4x - x², we first find its derivative: dy/dx = 4 - 2x. Setting this derivative equal to zero gives us 4 - 2x = 0. Solving for x gives us x = 2. This is the value of x where the tangent line is horizontal.

If we are given a graph, like in a velocity-time graph, a horizontal tangent indicates a moment where the velocity is zero, signifying a change in direction of the particle. At such points, we can see that the slope of the tangent line is zero, meaning it is a horizontal tangent.

area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

Answer: area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

radius = diameter/2

so 28/2=14

 using 3.14 for PI

2*3.14*14 = 87.92 = 88 inches

Answer:

b and c

Step-by-step explanation:

2020 edge assignment

Final answer:

The given equation has no solution, as simplifying both sides leads to the false statement -6 = -11. The number of solutions is zero, and the Distributive Property was used to solve the equation.

Explanation:

To solve the equation 4x + 2(x – 3) = 4x + 2x – 11, follow these steps:

Expand the left side of the equation: 4x + 2x - 6.

Combine like terms: 6x - 6.

Since the left and right side both have 4x, we can cancel out 4x from both sides, leaving 2x - 6 = 2x - 11.

Subtract 2x from both sides to get -6 = -11, which is a contradiction.

There is no solution to this equation because we arrived at a false statement. Therefore, the number of solutions is zero.

Part B: The property I used to solve this equation is the Distributive Property when expanding 2(x - 3).