Is it true that 7w + 4 = 5w + 12.
A. Write three more equations that you know are true based on this information.
B. Find the value of 2w.
C. Find the value of w.

A technique for solving an equation system is elimination.

2x + 8 = -y

-4x² + x - 7 = -y

Subtracting 2x + 8 from both sides:

-4x² - x + 15 = 0

(4x - 5)(x + 3) = 0

4x - 5 = 0

x = 5/4

x + 3 = 0

x = -3

Solutions:

x = 5/4 and x = -3

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The exponential growth model below that fits the points (0, 2720) and (8, 10,225) as  [tex]y = 2720 \times0.039^t.[/tex]

To find the exponential growth model that fits the points (0, 2720) and (8, 10,225), we need to find the values of the constants k and y0 in the equation [tex]y = y_0e^(kx)[/tex]. We can do this by substituting the coordinates of the two points into the equation and solving for the constants.

First, we substitute the coordinates of the first point into the equation:

[tex]2720 = y_0e^(k\times0)[/tex]

We can simplify this expression by substituting 1 for e⁰: 2720 = y⁰ˣ¹

This equation tells us that y0 = 2720.

Next, we substitute the coordinates of the second point into the equation: [tex]10,225 = y_0e^(k\times8)[/tex]

Substituting the value of y0 that we found above, we get: [tex]10,225 = 2720e^(k\times8)[/tex]

To solve for k, we divide both sides of the equation by 2720: [tex]\dfrac {10,225}{2720} = e^(k\times8)[/tex]

We can take the natural logarithm of both sides to get: ln(10,225/2720) = k8

Dividing both sides of the equation by 8, we get: k = ln(10,225/2720)/8

We can approximate the value of k by using a calculator to evaluate the logarithm: k ≈ 0.039

We now have the values of the constants k and y0, so we can write the exponential growth model that fits the given points: [tex]y = 2720 \times0.039^t.[/tex]

This is the exponential growth model that fits the points (0, 2720) and (8, 10,225).

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Yes, One of them must be even and this is because Pigeonhole Principle.

What is Pigeonhole Principle?

According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.  As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

From series {1,2......2n},  we need to select 'n+1' integers.

Even integers series from above series is {2,4,6..........2(n-1), 2n}

Odd integers series from above series is {1,3,5......2(n-2), 2n-1}

We can choose only n odd integers from the series. Therefore, if we choose n+1 integers, at least one of them must have to be even integer.

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Answer:

1st answer is correct

Step-by-step explanation:

[tex]\sf \frac{1}{2} +\frac{2b}{3}[/tex]

Given that,

b = -5

To find the value of the above expression, replace b with -5.

[tex]\sf \frac{1}{2} +\frac{2b}{3}\\\\\sf \frac{1}{2} +\frac{2*(-5)}{3}\\\\\sf \frac{1}{2} +\frac{-10}{3}[/tex]

Now, to solve the above fractions, you have to make the denominator the same.

For that, multiply both the numerator and denominator of (1/2) & (-10/3) by 3 & 2 respectively.

Let us solve it now.

[tex]\sf \frac{1}{2} +\frac{-10}{3}\\\\\sf \frac{1}{2} -\frac{10}{3}\\\\\sf \frac{1*3}{2*3} -\frac{10*2}{3*2}\\\\\sf\frac{3}{6} -\frac{20}{6} \\\\\sf\frac{-17}{6}[/tex]

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Given two points, the slope is given by the change in y divided by the change in x, hence the slope of segment RS is given as follows:

m = (16 - 4)/(9 - 3) = 2.

When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of the perpendicular bisector is obtained as follows:

2m = -1

m = -1/2.

The midpoint of a segment is given by the mean of the coordinates, hence:

The perpendicular bisector is a linear function with slope of -1/2 going through the point (6,10), hence the intercept b is calculated as follows:

10 = -0.5(6) + b

b = 13.

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The required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1. which is the correct answer would be an option (A).

The equation of an ellipse with a vertical major axis and center at (h, k) is given by the formula (x - h)² / a² + (y - k)² / b² = 1, where a is the length of the major axis and b is the length of the minor axis.

As per the question, the ellipse has a vertical major axis and center at (1, -3), a = 7, and b = 5.

Substituting these values into the formula, we get:

(x - 1)² / 7² + (y + 3)² / 5² = 1

Simplifying this expression, we get:

(x - 1)² / 49 + (y + 3)² / 25 = 1

Thus, the required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1.

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Answer:

n = -8 , n = -12

Step-by-step explanation:

First we factorise the quadratic using the factorisation method :

n²+8n+12n+96 = 0

n(n+8)+12(n+8) = 0

(n+12)(n+8) = 0

Now we equate each bracket to 0 :

Either

n + 12 = 0  

n = -12

OR

n + 8 = 0

n = -8

So the real solutions for that equation is

n = -8 , n = -12

The five types of infinitives are full infinitives, bare infinitives, split infinitives, continuous infinitives , and perfect continuous infinitive.

Explanation:

Types of infinitives:

Five types of infinitives are as follow:

To hear : full infinitives changes to split infinitives : to slowly hear.

Example : to be missing

Example : to have seen

Therefore, there are are five types of infinitives .

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There are six methods to solve linear equations;

Given,

Solving Linear equations;

To find a linear equation's solution is to solve a linear equation. Here, the techniques for solving the three primary forms of linear equations—linear equations with one variable, linear equations with two variables, and linear equations with three variables—are described.

We have to find the methods to solve linear equations;

There are six methods to solve linear equations;

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False. All economists do not believe that predatory pricing is a profitable business strategy.

What does "predatory pricing" mean?

A dominant company will often use predatory pricing as a deliberate strategy to drive out rivals by setting exceptionally cheap prices or supplying products for less than the company would otherwise have to spend on manufacturing (often equated for practical purposes with average variable costs).

Predatory pricing, sometimes referred to as undercutting, is a pricing strategy in which a good or service is offered at an extremely low cost with the goal of driving out rivals or establishing barriers to entry for potential new competitors.

If a competitor was selling a TV for $100 and you were offering the same TV for $80, you would be using predatory pricing.

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Answer:

  B Isosceles

Step-by-step explanation:

You want to know the classification of ∆MNP when ∠M = 37° and ∠P = 106°.

The third angle of the triangle can be found using the fact that the sum of angles is 180°.

  ∠N = 180° -37° -106° = 37°

This tells us angles M and N have the same measure (37°), so ...

  the triangle is isosceles.

The volume of pyramid with square base is 15466.67 cm³.

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Given, the pyramid has square base.

And the side of square is 40 cm

And the height is 29cm.

The volume of the pyramid with square base

V  = base area x height/3

V = (40 x40) x 29/3

V = 15466.67 cm³

Therefore, the volume of pyramid with square base is 15466.67 cm³.

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The statement that best describes how income levels have changed in the United States is given as follows:

C. High-income earners are making more, but most people have only seen limited gains.

Recently, in the entire world, an especially in the United States, inflation has been a problem, and thus people's income has not followed the pattern, staying mostly stagnant while inflation happens. This has happened even though the economy has improved from the 2008 global crisis.

However, high-income earners are making more, as the number of millionaires and billionaires increase, increasing the gap between high and low income earners. Thus option C is the correct option.

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Answer:

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

The dependent variable in this hypothesis is test performance.

What is a dependent variable?

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).

The outcome of this hypothesis is the dependent variable.

Hence, the dependent variable in this hypothesis is test performance.

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Answer:

To find the percentage of roses in the garden, we first need to determine the total number of flowers in the garden. We can do this by adding the number of roses and lilies, and then multiplying that number by the ratio of roses to lilies. For example, if there are 3 roses and 2 lilies in the garden, the total number of flowers would be 5 (3 + 2 = 5). To determine the percentage of roses, we would then divide the number of roses by the total number of flowers, and multiply by 100. In this case, the percentage of roses would be 60% (3 / 5 * 100 = 60).

The inequality for the statement negative three eighths is at most the product of a number and negative five sevenths is negative 3 over 8 ≤ negative 5 over 7w which is option A.

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

negative three eighths = -3/8

negative five sevenths = -5/7

At most for inequality symbol = [tex]\leq[/tex]

mathematically

-3/8 [tex]\leq[/tex] -5/7w

which is negative 3 over 8 ≤ negative 5 over 7w

In conclusion the inequality for the statement is negative 3 over 8 ≤ negative 5 over 7w

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Answer:

1) Median

2) Mode

3) Mean

(Hope this is correct :D )

Step-by-step explanation:

Mode is the number that is most repeated in the data set, and it would best describe the center of the data for the second one.

The first one has an outlier of 50 at the start, so the median would be most appropriate for this.

The last one is basically equal for each value, so the mean would best describe the center for this one.

Answer:

Here you go

Step-by-step explanation:

The increase in amount is $351.00 ($5400 x 0.065 = $351). The amount in the account at the end of the year was $5751.00 ($5400 + $351 = $5751).

The slope of the tangent line to the given polar curve at the point specified by the value of theta is m= 1/√3.

A straight line that just touches a plane curve at a particular location is referred to as the tangent line (or tangent) to the curve in geometry. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another. A line passes through the point (c, f(c)) on the curve and has a slope of f'(c), where f' is the derivative of f. This is more properly referred to as being a tangent of the curve y = f(x) at a point x = c. Curves in n-dimensional Euclidean space and curves in space have a comparable definition.

The tangent line is "passing" through the point of tangency—the intersection of the tangent line and the curve as it travels.

Given,

r=6cosθ

f'(θ)=-6sinθ

θ=π/3

dy/dx=(f'(θ)sinθ+f(θ)cosθ)/(f'(θ)cosθ-f(θ)sinθ)

dy/dx=( -6sinθsinθ+6cosθcosθ)/(-6sinθcosθ-6cosθsinθ)

=(6cos²θ-6sin²θ)/-12 sinθcosθ

=6(cos²θ-sin²θ)/-6(2sinθcosθ)

=6cos2θ/-6sin2θ

=-cos2θ/sin2θ

=-cot2θ

Slope of the given polar curve at θ=π/3 is

m=dy/dx

m= -cot(2(π/3))

m = cot(-2π/3)

m= 1/√3

Therefore, the slope of the tangent line to the given polar curve at the point specified by the value of theta is

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Answer:

5 to the second power

Step-by-step explanation:

5 to the power of 4 is 625

5 to the power of 3 is 125

5 to the power of 5 is 3,125

So the expression is now 625 x 125/ 3,125

625 x 125 = 78,125

78,125/3,125= 25

5 to the second power equals 25

For a 0.48 liter solution, Samantha will use 0.16 liters of water.

Given that

she can make a certain solution by mixing 0.04 liters of chemical a with 0.02 liters of water

she wants to make a total of 0.48 liters of this new solution.

a quantity 0.48/0.06 = 8 times greater than that produced by one recipe.

Water in the amount of 0.02 liters is required.

Samantha will require 0.16 liters of water, or 8 times as much water, to create the solution.

For a 0.48 liter solution, Samantha will use 0.16 liters of water.

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The equation in point-slope form of the line passing through [tex](1,2)[/tex] and  [tex](2,5)[/tex] is [tex]y=3x-1[/tex]

To find the slope of the line is

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-2}{2-1} \\m=\frac{3}{1} \\m=3[/tex]

The equation of the line is given by

[tex]y=mx+c.........(1)[/tex]

We have to use one point form to find the equation

The point [tex](1,2)[/tex] satisfies the equation

plug in the value of m, the equation becomes

[tex]2=3(1)+c\\2=3+c\\c=2-3\\c=-1[/tex]

Put the value of m,c in (1) equation

[tex]y=3x-1[/tex]

The equation of the line is [tex]y=3x-1[/tex].

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Surface area of any figure is the area that the outer surface of any figure covers.

If we look at the different figures we find that these figures if placed somewhere or if we need to cover the figures with some kind of material then in order to find the the dimensions of the material we will need to find out the area that the overall surface of the figure will cover. This will reduce the time and complication of the calculations of every part of the shape. For example, If there is a need to find the surface area of the cylinder then we use the formula for its curved surface area as

S = 2πrh where r is the radius and h is the height of cylinder

Also, the total surface area will be expressed as

T = 2πr(r + h) where r is the radius and h is the height.

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Answer:

read below :)

Step-by-step explanation:

SSS is the side side side theorem.

It states that if the three sides of a triangle are equal in length to the three sides of another triangle, they must be congruent.

278.5 if im not wrong

Step-by-step explanation:

75 x 15 1125 ten percent of that is 133.5 take 1125 - 133.5 =1011.5 take that add 210 get 1221.5 -1500 and you have 278.5

Answer:  [tex]H = -16s(s-6)[/tex]

Work Shown:

[tex]H = -16s^2+96s\\\\H = -16s*s+16s*6\\\\H = -16s(s-6)\\\\[/tex]

The answer can be confirmed by using the distributive rule to multiply -16s by each term inside the parenthesis. You should get [tex]-16s^2+96s[/tex] after distributing.

Each game starts every hour then 28 games will be occurred in 28 hours and therefore the tournament will take 28 hours for completion.

Given, there are total 8 players playing the tournament of world tic-tac-toe championship.

Also, new game start each hour.

We have to find the number of hours the tournament will take to complete.

Total games occurred be,

we will use the concept of A.P. to find the total number of games

First player will play with 7 players, second player will play with 6 players and so on.

Total games =  8/2[14 + 7×(-1)]

Total games =  4×7

Total games =  28

Now, if each game start every hour then 28 games will occurred in 28 hours and therefore the tournament will take 28 hours for completion.

Hence, the tournament will take 28 hours for completion.

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