Use the scale to help you solve the equation and find the value of x?

8. The center and radius of the circle given the following equation:

(x + 4)^2 + (y - 2) ^ 2 = 5 is

9. The  equation for the circle is

10. The length of arc AB is

Information given in the question

a circle whose equation is (x + 4)^2 + (y - 2) ^ 2 = 5

Equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where

r = radius

h and k are coordinates of the center

x and y is the coordinate of point on the circumference

The equation of the circle is compared with the given equation and this shows that

Using the graph the centers are (-5, -2) and the radius is 3, this will give equation  (x + 5)² + (y + 2)² = 3²

If angle ACB = 60 deg and the radius is 12 cm,  length of arc

= 60 / 360 * 2 * π * 12

= 4π

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In economics, business, and notably cost accounting, the break-even point (BEP) is the point at which total costs and total revenues are equal, or "even" and we need to sell a total of 1967 tires at the price of $89 to break even.

The break-even point (BEP) is the point at which total costs and total revenues are equal, or "even," in economics, business, and particularly cost accounting.

Although opportunity costs have been paid and capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

In other words, all necessary expenses are covered, and neither a profit nor a loss is realized.

So, for the break-even:

= 175000/89

= 1,966.29

Rounding off: 1967

Therefore, we need to sell a total of 1967 tires at the price of $89 to break even.

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Correct question:

Your factory makes tires. It costs you $175,000 to pay for the lease each year. The cost to make a tire includes labor and materials, but comes to $53 per tire. How many times do you need to sell to break even if you sell them for $89 per tire?

The midpoint and length of the sides of the triangle can be presented  follows

22 Part A

Midpoint of [tex]\overline{AB}[/tex] = (3, 5)

Midpoint of [tex]\overline{BC}[/tex] = (6, 4)

23 Part B

Length of [tex]\overline{AC}[/tex] is 2·√(10)

Slope of [tex]\overline{AC}[/tex] is -1/3

25 Part D

According to the midsegment theorem, Darlene is correct

The midpoint of a segment divides the segment into two same length segments.

22 Part A

The midpoint, ([tex]x_m[/tex], [tex]y_m[/tex]) between points (x₁, y₁), (x₂, y₂) of a segment can be found as follows;

[tex]x_m[/tex] = (x₁ + x₂)/2, [tex]y_m[/tex] = (y₁ + y₂)/2

The coordinates of the points in the triangle are; A(2, 2), B(4, 8), and C(8, 0)

23 Part B

The length of a segment with boundary points (x₁, y₁), (x₂, y₂) is the distance between the points (x₁, y₁), (x₂, y₂), which is found using the following distance formula for finding the distance, d, between points;

The length of the segment [tex]\overline{AC}[/tex] is the distance between the points A(2, 2), and C(8, 0), which is found as follows;

Where;

(x₁, y₁) = (2, 2) and (x₂, y₂) = (8, 0), we get;

Length of [tex]\overline{AC}[/tex] = √((8 - 2)² + (0 - 2)²) = √(6² + (-2)²) = √(40)

The slope of a line, m = (y₂ - y₁)/(x₂ - x₁)

25 Part D

The length of the line segment connecting the midpoint can be found using the distance formula as follows;

Therefore;

Length of the line segment connecting the midpoint = √((6 - 3)² + (4 - 5)²) = √(10)

The line segment connecting the midpoint is half the length of [tex]\overline{AC}[/tex], which is stated in the midsegment theorem

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The formula of the area of the trapezium as subject to x is,

x = 2A/h - y.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

The area of the trapezium,

A = (1/2)h(x + y)

To make x the subject of the equation:

2A/h = (x + y)

2A/h - y = x

x = 2A/h - y

Therefore, the formula is x = 2A/h - y.

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Answer:

Step-by-step explanation: In this situation, mean would be the most appropriate statistic to show the increase in the size of the offensive line of the football team. The mean is a measure of central tendency that takes into account all the values in a set and calculates the average, giving a good representation of the general trend of the data. The mean size of the offensive line can be calculated by adding up the size of all the players and dividing by the number of players. This would give a good idea of the overall increase in the size of the offensive line.

Answer:

0

Step-by-step explanation:

surface of ocean = sea level = elevation of zero

Answer:

Step-by-step explanation:

Statistical questions are questions that can be answered by collecting, analyzing, and summarizing numerical data. The data can then be used to make inferences, predictions, and draw conclusions.

In the context of statistical analysis, numerical data refers to data that can be measured and expressed as a number. For example, the number of hours someone spends practicing a musical instrument each week, or the number of books a student reads each month.

On the other hand, questions such as "Who is your favorite cartoon character?" cannot be answered with a number and therefore are not statistical questions. The answer to this type of question is qualitative or categorical data and can not be analyzed numerically.

It's important to note that while the questions that result in numerical data are often statistical questions, not all questions that result in numerical data are necessarily statistical questions. For example, the number of letters in someone's first name is a numerical piece of information, but it does not involve collecting and analyzing data to make inferences or draw conclusions.

Answer:2)How many hours do you practice your musical instrument each week.

Step-by-step explanation:

"How many hours do you practice your musical instrument each week?" is a statistical question that can result in numerical data.

This is a statistical question because it involves a numerical variable ("hours practiced per week"), which can be measured and quantified.

Answer:

1

Step-by-step explanation:

f(x) = 3x^3+kx+9, and the remainder when f(x) is divided by x+2 is -17, then what is the value of k=1

The distinct points are (1, 15), (2, 14) and (3, 13)

The slope implies that as the length increases by 1, the width decreases by 1

From the question, we have the following parameters that can be used in our computation:

2x + 2y = 32

Divide by 2

So, we have the following representation

x + y = 16

Make y the subject

y = 16 - x

Set x = 1, 2 and 3

So, we have

y = 16 - 1 = 15

y = 16 - 2 = 14

y = 16 - 3 = 13

So, the points are (1, 15), (2, 14) and (3, 13)

The slope is calculated as

y = mx + c

Where m = slope

When compared, we have

slope = -1

This means that as x increases, y decreases

The graph is attached

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Answer:

So Gary ran the longest

Step-by-step explanation:

Gary ran for 22 minutes + 7 minutes = 29 minutes.

Herbert ran for 29 minutes - 12 minutes = 17 minutes.

So Gary ran the longest, followed by Sandy and then Herbert.

A) If the change in b results in a smaller feasible region, then the optimal objective value will either remain the same or increase.

B)  If the change in b results in a larger feasible region, then the optimal objective value may remain the same or decrease.

In linear programming, the objective is to minimize or maximize an objective function subject to certain constraints. One common constraint is that the solution must be in the feasible region, which is defined by the set of all solutions that satisfy the constraints.

Recall that the constraints are given by Ax >= b, where A is a matrix of coefficients and x is a vector of variables. If we increase one component of b, say bi, then the set of solutions that satisfy the constraints will change. Specifically, any solution that previously satisfied Ax >= b may no longer satisfy the constraints, since the left-hand side of the inequality is fixed while the right-hand side has increased. In other words, the feasible region may shrink or shift in response to the change in b.

Now let's consider the effect on the optimal objective value. Recall that the objective function is given by cx, where c is a vector of coefficients. The optimal objective value is the minimum (or maximum) value of cx over all solutions in the feasible region. If we increase one component of b, then the optimal objective value may or may not change, depending on the specifics of the problem.

To see why, let's think about what happens to the feasible region. As we noted above, the feasible region may shrink or shift in response to the change in b. If the optimal solution was previously at the boundary of the feasible region, then it may no longer be feasible, and the optimal objective value will increase. On the other hand, if the optimal solution was previously in the interior of the feasible region, then it may still be feasible, and the optimal objective value will remain the same.

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The equation of the function shown in the table is y=2x +1, the correct option is B.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We are given that;

The x and y of the function

Input x: -2 -1 0 1 2

Output y: -3 -1 1 3 5

Now,

The general equation of line

y=mx+c

Here, m= 5-3/2-1

m=2

Substituting the value of m in general equation.

y=2x +1

Therefore, the equation of line will be y=2x +1

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Answer:

see explanation

Step-by-step explanation:

(a)

there is a common difference between consecutive terms, that is

10 - 12 = 8 - 10 = 6 - 8 = 4 - 6 = - 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 12 and d = - 2 , then

[tex]a_{n}[/tex] = 12 - 2(n - 1) = 12 - 2n + 2 = 14 - 2n

(b)

similarly this is an arithmetic sequence

with a₁ = 25 and d = 20 - 25 = 15 - 20 = 10 - 15 = 5 - 10 = - 5

[tex]a_{n}[/tex] = 25 - 5(n - 1) = 25 - 5n + 5 = 30 - 5n

find derivative of e^(e^x)

use chain rule to find d/dx of e^x is e^x.

so chain rule finds the value e^(e^x) d/dx = e^(e^x) x e^x

simplify to e^[(e^x)+x]

The yellow arches of a big M is not an example of a quadratic equation in real life.

What is quadratic equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0

where c is constant.

A quadratic equation is an equation in which the highest power of the variable is 2. In real life, many phenomena can be modeled by quadratic equations, such as the curve of hanging electrical wires, the path of a boat, the path of a tennis ball, and the path of a human cannonball.

However, the yellow arches of a big M is not a mathematical equation or a physical phenomenon that can be described by a quadratic equation. The arches are simply a design element of the McDonald's logo.

Therefore, The yellow arches of a big M is not an example of a quadratic equation in real life.

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In the experiment in which researcher randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention, this type of experiment design is a randomized block design where the pet types (dogs and cats) are the blocks.

Randomized block design is a type of experimental design that is used to control for the effects of extraneous variables. It involves dividing the subjects or treatments into groups, or blocks, that are similar with respect to the extraneous variable.

These blocks are then randomly assigned to the treatments being tested. By controlling for the extraneous variable in this way, the randomized block design can reduce error and increase the accuracy of the results.

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Answer:

answer B (Khan)

Step-by-step explanation:

A randomized block design where the pet types (dogs and cats) are the blocks

The perimeter of the trapezoid is 49.4.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

From the graph,

Height = 12 units

Parallel sides = 9 units and 15 units

Now,

Another side = x

Using Pythagorean theorem.

x² = 6² + 12²

x² = 36 + 144

x² = 180

x = √180

x = 13.42

Now,

The perimeter of the trapezoid.

= 12 + 13.42 + 9 + 15

= 49.42

= 49.4

Thus,

49.4 is the perimeter of the trapezoid.

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The congruence theorem that justifies the congruence of the two triangles is given as follows:

A. SSS.

The Side-Side-Side (SSS) congruence theorem states that three sides of a triangle are equivalent to the corresponding three sides of the another triangle, then the two triangles are said to be congruent by SSS rule.

In this problem, we have that:

Hence the triangles are congruent by the SSS postulate and the correct option is given by option A.

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La velocidad promedio del motociclista es 128km/h, entonces si, supera el limite de velocidad previsto.

Sabemos que podemos definir la velocidad como el cociente entre distancia y tiempo, en este caso sabemos que:

distancia = 320km

tiempo = 2.5 h.

Entonces la velocidad será:

v = 320km/2.5 h = 128 km/h

Podemos ver que claramente, el motociclista supera el limite de velocidad previsto.

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Answer:

Step-by-step explanation:

TEP 1: Find an interest by using the formula , I=P.i.t  where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this examplee P = $2700, i = 6.25% and t = 3 years, so

I=506.25

STEP 2: Find an amount by using the formula . A= P+I

Since P = $2700 and I = $506.25 we have,

A=I+P

A=3206.25

The values are a = 16.69, c=16.68 ad m∠C = 22.07°.

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find

sin68° = a/18

18 sin 68° = a

Using a calculator, we can find that sin 68° is approximately 0.9272. Multiplying 18 by 0.9272 gives us:

a ≈ 16.69

Therefore, a is approximately 16.69.

cos68° = c/18

18 cos 68° = c

Using a calculator, we can find that cos 68° is approximately 0.3714. Multiplying 18 by 0.3714 gives us:

c ≈ 6.68

Now

sinC = c/18

[tex]C = sin^{-1}(\frac{6.68}{18})\\\\C = sin^{-1}(0.3714)\\\\C = 22.07\degree[/tex]

Hence, the values are a = 16.69, c=16.68 ad m∠C = 22.07°.

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Answer:

Step-by-step explanation:Base on the diagram, and the following question, the following are the answers to your question.

#1 Congruent Angle

#2 Congruent Sides

#3 Side Angle Side

I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification

Answer:

Step-by-step explanation:

There is 3/4 of a gallon of bubble solution in the big bottle.

What is an equation?

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equal sign (=). An equation contains one or more variables, which are symbols that represent unknown values, and may also contain constants, coefficients, and arithmetic operations such as addition, subtraction, multiplication, and division.

Let's use "x" to represent the amount of bubble solution in the big bottle, in gallons.

According to the problem, the big bottle was divided equally among 6 small bottles, and each small bottle holds 1/8 of a gallon of bubble solution. Therefore, the total amount of bubble solution in the big bottle is equal to the sum of the amounts in the 6 small bottles:

x = 6 * (1/8)

Simplifying the right-hand side of the equation, we get:

x = 3/4

Therefore, there is 3/4 of a gallon of bubble solution in the big bottle.

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The solution is Option D.

The median of the data is A = 20 and the mean of the data is M = 22.7

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the data be represented as M

Let the median of the data be represented as A

Now , the equation will be

The list of donations is represented as set D

Set D = { 10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55 }

Now , the mean M is = 10 + 10 + 10 + 10 + 15 + 15 + 15 + 19 + 20 + 20 + 20 + 25 + 25 + 25 + 30 + 30 + 55 + 55 / 18

The mean M = 409 / 18

On simplifying the equation , we get

The mean M = 22.722

Now , the median of the data is A = 20

Hence , the mean is 22.7

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The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

Answer: 38

Step-by-step explanation:

4 x 9.5 can also be seen as 2 (2 x 4.75)

To solve this,

1) 2 x 2 = 4

2) 2 x 4.75 = 9.5

4 x 9.5 = 38.

Simple ways without distributive property is just 4 x 9.5 which is equal to 38.

If it is like 4(9.5) then the answer would be 4 * 9.5 which is 38. But if you were asking about this, 4(9 + 5) then these would be the steps.

So, distributive property is A(B + C) so A = 4 and B = 9 and C = 5.

So the setup would be 4(9 + 5).

And in order to solve this we have to distribute the 4 to 9 and 5. And after that, we remove the parenthesis. So, we get 36 + 20. And that would equal 56. So,

or

The solution is, the equation of the line is y = 2x/3 + 2, that is, The correct option is A.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept(This is the point where the line cut across the y axis.

The first step is to find the slope. The formula is

Slope, m = (y2 - y1)/(x2 - x1)

From the given points on the graph,

when x1 = 0, y1 = 2

when x2 = 3, y2 = 4

m = (4 - 2)/(3 - 0)

m = 2/3

Looking at the graph, at the point where the line cuts the y axis, y = 2. Thus, c = 2

We would substitute m = 2/3 and c = 2 into the slope intercept equation. Thus, the equation of the line is

y = 2x/3 + 2

The correct option is A.

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Answer:

Given value is Rational. The value is 2.06

Step-by-step explanation:

Answer: Rational.

Step-by-step explanation:

An irrational number is one that terminates forever, and cannot be expressed as a fraction. 68/33 is a fraction, therefore it's rational. Irrational can be values like pi, which do not have a ratio form (e.g. fraction).

The length of the ladder needed to reach the window to the nearest tenth of a foot is option (a). 17.0 feet.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given,

Length of the moat = 8 feet

Height of the window from the ground = 15 feet

Using the concept of right triangle, from the figure, length of the moat is the base and height of the window is the altitude.

Length of the ladder is the hypotenuse.

By Pythagoras theorem,

Length of the ladder = [tex]\sqrt{8^{2}+15^2 }[/tex] = [tex]\sqrt{289}[/tex] = 17

Hence the length of the ladder is 17.0 feet to the nearest tenth of a foot.

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