Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2

The total cost of 2 burgers and 3 fries, considering a system of equations, is given as follows:

$17.

The costs are obtained by a system of equations, for which the variables are given as follows:

3 burgers and 6 fries, which cost $30, hence:

3x + 6y = 30

x + 2y = 10

x = 10 - 2y.

3 burgers and 2 fries, which cost $18 in total, hence:

3x + 2y = 18

1.5x + y = 9

Replacing the first equation into the second, the value of y is given as follows:

1.5(10 - 2y) + y = 9

2y = 6

y = 3.

Then the value of x is given as follows:

1.5x + 3 = 9

x = 6/1.5

x = 4.

Then the cost, in dollars, of 2 burgers and 3 fries, is given as follows:

2 x 4 + 3 x 3 = $17.

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The 95% confidence interval for the mean SAT scores is CI = (526.2, 549.8)

It is a statistical tool used in inferential statistics to estimate the unknown population parameter based on the sample data.

To find the 95% confidence interval for the mean SAT scores, we can use the formula: CI

where:

sample mean (538)

population standard deviation (96)

n = sample size (250)

z = z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96)

Plugging in the values, we get:

CI = 538 ± 1.96*(96/√250)

Simplifying, we get:

CI = 538 ± 11.8

Rounding to the nearest tenth, the 95% confidence interval for the mean SAT scores is:

CI = (526.2, 549.8)

For example, a 95% confidence interval for a population mean means that if we were to repeat the sampling process multiple times and calculate a 95% confidence interval each time, about 95% of the intervals would contain the true population mean.

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to follow the order of operations or PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction) to ensure that we get the correct answer. [tex]231 3/25 \times 0.75 = 4348.5 / 75.[/tex]

To solve this multiplication problem, we can first convert the mixed number 231 3/25 to an improper fraction:

[tex]231 3/25 = (25 \times 231 + 3) / 25 = 5778/25[/tex]

Then, we can multiply this fraction by 0.75:

[tex]5778/25 \times 0.75 = (5778 \times 0.75) / 25[/tex]

To simplify this fraction, we can multiply the numerator and denominator by 3:

[tex](5778 \times 0.75 \times 3) / (25 \times 3) = 4348.5 / 75[/tex]

Therefore, [tex]231 3/25 x\times 0.75 = 4348.5 / 75.[/tex]

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The number of girls in the gym must be: g ≥ 16

Let's define the variable "g" to be a representation of the number of girls in the gym.

We know that there are 30 students in total. Therefore, the number of boys in the gym will be:

b = 30 - g

We also know that there are at least 16 girls in the gym. So, we can write the inequality:

g ≥ 16

This inequality means that the number of girls in the gym must be greater than or equal to 16.

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The independent variable and the dependent variable are the number of dollars spent and the number of tickets bought

Given that we have the following statement:

The independent variable is the input value

i.e. the number of dollars spent

Similarly, the dependent variable is the output value

i.e. the number of tickets bought

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The derivative of f(x) = 3·x² + 7·x + 6, at x = 4, f'(4) is presented as follows;

f'(4) is the limit as x → 4 of the expression 6·x + 7.

The value of this limit is 31

The equation of the tangent line to the parabola y = 3·x² + 7·x + 6 at the point (4, 82) is y = 31·x - 42

The derivative of a function is a measure of how much the output values of the function changes as the input value is changed. The derivative is the limit of the difference quotient as the change in input approaches zero. The limit is the instantaneous rate of change of the function at a specified input variable value.

The value of f'(4) using the definition of derivative, can be obtained using the following definition;

f'(x) = lim(h → 0)[f(x + h) - f(x)]/h

Plugging in x = 4, and f(x) = 3·x² + 7·x + 6, we get;

f'(4) = lim(h → 0)[f(4 + h) - f(4)]/h

f'(4) = lim(h → 0)[3·(4 + h)² + 7·(4 + h) + 6 - (3·(4)² + 7·(4) + 6)]/h

f'(4) = lim(h → 0)[(3·h + 31)·h]/h

f'(4) = lim(h → 0)[(3·h + 31)]

Therefore;

f'(4) = lim(h → 0)[(3·h + 31)] = 31

f'(4) = 31

Therefore; f'(4) is the limit as x → 4 of the expression 6·x + 7, therefore. The value of this limit is 31

The point-slope form of the equation of a line can be used to find the equation of the parabola as follows;

y - y₁ = m·(x - x₁)

The point (x₁, y₁) and the slope of the line is m

The point on the parabola of the tangent is; (4, 82)

The slope of the tangent line at x = 4, f'(4) = 31

The tangent equation is therefore;

y - 82 = 31·(x - 4)

y =  31·(x - 4) + 82 = 31·x - 42

The equation of the tangent line to the parabola, y = 3·x² + 7·x + 6, at the point (4, 82) is; y = 31·x - 42

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Answer:

Volume =

Step-by-step explanation:

Volume = length x width x depth

Volume = (6.5 x 3 x 1.6)m

Volume = 31.2m

The missing numbered angle is  80 degrees.

In the given diagram, we can see that angles A and B form a linear pair (they are adjacent angles whose sum is 180 degrees). So we can write:

A + B = 180 degrees

Substituting the given value of angle A, we get:

(3x + 10) + B = 180 degrees

Simplifying this equation, we get:

3x + B = 170 degrees

We are also given that angle C is a complementary angle to angle B, which means that angle C + angle B = 90 degrees. We can substitute the value of angle B from the above equation to get:

C + (3x + B) = 90 degrees

Simplifying this equation, we get:

C + (3x + 170 - 3x) = 90 degrees

Simplifying further, we get:

C + 170 = 90 degrees

Subtracting 170 from both sides, we get:

C = 80 degrees

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The resulting graph should have a period of 4, an amplitude of 3, a midline of y=-1, and no reflection over the x-axis.

What are the period and amplitude of a graph?

The period of a function is the smallest distance over which the function repeats itself. In other words, it is the length of one complete cycle of the function. For a sine or cosine function of the form f(x) = a sin(bx) or f(x) = a cos(bx), the period is given by 2π/b.

The most simple sine function considered the parent function, is:

  y = sin(x)

That function has:

Midline, also known as rest or equilibrium position: y = 0

Minimum: - 1

Maximum: 1

Amplitude: the distance between a minimum or a maximum and the midline = 1

period: the interval of repetition of the function = 2π

The more general sine function is:

 y = Asin(Bx + C) + D            

That function has:

Midline: y = D (it is a vertical shift from the parent function)

Minimum: - A + D

Maximum: A + D

Amplitude: A

period: 2π/B

phase shift: C (it is a horizontal shift of from the parent function)

Now, you have to draw the sine function with the given key features:

Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2

Amplitude, A = 3

midline y = - 1 ⇒ D = - 1

y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

y = 3sin(2x/π + C) -1

Substitute (0, -1)

-1 = 3sin(2(0)/π + C) -1

3sin(C) = 0

sin(C) = 0

C = 0

Hence, the function to graph is:

             y = 3sin(2x/π ) -1

To draw that function use this:

Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)

Minima: 3(-1) - 1 = - 3 - 1 = -4

y-intercept: (0, - 1)

x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1

first point of the midline: (0, -1) it is the same y-intercept

Hence, the resulting graph should have a period of 4, an amplitude of 3, a midline of y=-1, and no reflection over the x-axis.

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Answer:

Answer is option  D

Step-by-step explanation:

Hope this helps:)

we can simplify |x+3| to x+3 when x is greater than 5. This is the final answer.The absolute value of a number is the distance of the number from zero on a number line, regardless of whether the number is positive or negative.

For example, the absolute value of -5 is 5, because 5 is the distance of -5 from zero on the number line.

In this problem, we are asked to simplify the expression |x+3| without using the absolute value symbol. We are also given the condition that x is greater than 5.

When x is greater than 5, we know that x+3 is also greater than 5+3=8. This is because x is already greater than 5, and adding 3 to it makes it even larger. So, we can say that x+3 is positive when x is greater than 5.

Now, let's consider what the absolute value of x+3 means in this context. Since x+3 is positive when x is greater than 5, the absolute value of x+3 is just x+3 itself. This is because the absolute value of a positive number is just the number itself.

Therefore, we can simplify |x+3| to x+3 when x is greater than 5. This is the final answer.

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Answer:

f(x) = 4+10/x

Step-by-step explanation:

f(x)x-5 = 4x+5

add 5 to both sides

f(x)x = 4x+10

divide both sides by x

f(x) = 4+10/x

still not sure if its the right problem...

Option D is correct. The Standard Deviation of the number of residents in the sample who were born in colorado is 7.75

How to find Standard Deviation of a given sample ?

Let x be the standard deviation for the sample, n =250

p = probability of success, q = probability of failure = 1 - p

q = 1 - 0.40 = 0.60

[tex]x = \sqrt{n \times p \times q}\\= \sqrt{250 \times 0.40 \times 0.60}\\= \sqrt{60}\\=7.75[/tex]

Therefore, Option D is correct. Standard Deviation is 7.75.

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option (d) the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.

The standard deviation of a binomial distribution is given by the formula:

σ = √(np(1-p))

binomial distribution with parameters n = 250 and p = 0.4—where n is the sample size and p is the probability of success—can be used to approximate the distribution of the number of Colorado residents who were born in Colorado in a sample of 250 residents.

Substituting n = 250 and p = 0.4, we get:

σ = √(250 x 0.4 x 0.6) ≈ 7.75

Therefore, the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.

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The value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010 is approximately -2.326.

With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution. When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.

To find the value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010, we can use a t-table or a calculator. Using a calculator, we can use the inverse t-distribution function. The inverse t-distribution function gives us the value of t for a given probability and degrees of freedom.

Using this function, we have:

t = invT(0.010, 45) ≈ -2.326

Rounding this to three decimal places gives us the answer:

t ≈ -2.326

Therefore, the value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010 is approximately -2.326.

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The product of the values can be obtained by multiplying as follows:

1. 8 * 15 * 19 = 2280

2. 7 * -4 * 12 =  -41

To find a product simply means to multiply the figures in order to arrive at a value. The question asks that we get the product of some values. To get these values, we are to multiply the numbers given to arrive at the answers.

It is possible to multiply two, three, or more values at the same time. So, another word that is used in place of multiplication is "product" as is the case in the question given.

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Step-by-step explanation:

angle c = 180 -19 - 139 = 22 degrees   (  interior angles of a triangle sum to 180 degrees)

Now you can use law of sines to find the missing  side lengths

12 / sin 22  =  DC /sin19

DC = sin 19 * 12 / sin 22  = 10.4 units

12/sin 22 = BC / sin 132

BC =  sin132 * 12 / sin 22 =  23.8 units

These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex] is[tex]x = 3 + 3i or x = 3 - 3i[/tex].

A linear formalism is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or explain the whole situation, this is known as an equation.

The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 consists of the two numbers 3x + 5 and 14, which are separated by the 'equal' sign.

we have a = 1, b = -6, and c = 18

[tex]x = (-(-6) +- \sqrt{-6^{2} } - 4(1)(18))) / 2(1)[/tex]

[tex]x = (6 +/- \sqrt{36-72} / 2[/tex]

[tex]x = (6 +/- \sqrt{36} / 2[/tex]

[tex]\sqrt{-36} = \sqrt{36} * \sqrt{-1} = 6i[/tex]

Therefore, the solutions are:

[tex]x = (6 + 6i) / 2 or x = (6 - 6i) / 2[/tex]

Simplifying:

[tex]x = 3 + 3i or x = 3 - 3i[/tex]

These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex].

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Answer:

The slope of this line is 2.

Step-by-step explanation:

Start at (1, 0). Go up 4 units, then right 2 units. You will end at (3, 4). The slope of this line is 2.

Answer:

yes

Step-by-step explanation:

4p+ 3p= 7p

7p+7n=14pn

To solve for z, we can subtract 7 from both sides to get -5/z = -6. Finally, we can multiply both sides by -1 to get z = -7. Therefore, the solution to this equation is z = -7.

A logarithm is an equation that expresses the relationship between an exponent and its base. In this equation, we have two logarithms, ln (-5z) and ln [tex](z^2-7z)[/tex], which are both equal to each other. To solve this equation, we can use the properties of logarithms to isolate the variable. First, we can rewrite the equation as ln (-5z) - ln [tex](z^2-7z)[/tex]= 0, which can then be simplified to ln (-5/z+7) = 0. We can then take the inverse of both sides to get -5/z+7 = 1. To solve for z, we can subtract 7 from both sides to get -5/z = -6. Finally, we can multiply both sides by -1 to get z = -7. Therefore, the solution to this equation is z = -7.

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Answer:

[tex]225 \: {m}^{2} [/tex]

Step-by-step explanation:

I added a photo of my notes

This figure is formed from a rectangle and a trapezoid

Since the opposite sides of a rectangle are equal, we can find the its area:

A (rectangle) = 9 × 17 = 153 m^2

In order to find the area of a trapezoid, we have to know the length of its altitude:

H = 15 - 9 = 6 m

We know the lengths of both bases, now we can find the area:

A (trapezoid) = 0,5(7 + 17) × 6 = 0,5 × 24 × 6 = 12 × 6 = 72 m^2

Now add these two areas together and we'll get the total area of this figure:

A = 153 + 72 = 225 m^2

1.The equation that represents the proportional relationship is y = 4x + 3.

2. The corresponding equation that represents a proportional relationship is y = (1/5)x.

3. y = 7/2x.

4. when y = 21 is x = 6.

5. y = 8 is x = 3.33.

The slope of a function is the rate of change in the function's output (y-value) relative to the change in its input (x-value).

The equation that represents a proportional relationship is y = mx + b, where m is the slope of the equation.

In this equation, x and y are in direct proportion.

1.The equation that represents the proportional relationship is y = 4x + 3. This equation is in the form of y = mx + b, with m being the coefficient of x, which is 4, and b being the constant, which is 3.

2. The corresponding equation that represents a proportional relationship is y = (1/5)x.

This equation is in the form of y = mx + b, with m being the coefficient of x, which is 1/5, and b being the constant, which is 0.

3. The equation that represents this relationship is y = 7/2x.

This equation is in the form of y = mx + b, with m being the coefficient of x, which is 7/2, and b being the constant, which is 0.

4. The value of x when y = 21 is x = 6.

This is because the equation representing the proportional relationship is y = 7/2x, and

when y = 21, 21 = 7/2x,

so x = 6.

5. The value of x when y = 8 is x = 3.33.

This is because the equation representing the proportional relationship is y = 12/5x, and when y = 8, 8 = 12/5x, so x = 3.33.

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Answer:

x=14

Step-by-step explanation:

80+58=138

180-138=42

42÷3=x

14=x

Answer:

x= 14

Step-by-step explanation:

80 + 58 = 138°

A triangle has 180°

180-138= 42°

Put into equation

42=3x

42/3=14

X=14

Answer:

Therefore, the shuffleboard disk will travel a distance of 4.71 meters before coming to a stop, which is less than the length of the court (14.3 meters).

Step-by-step explanation:

We can start by using the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. In this case, we can assume that the initial kinetic energy of the disk is entirely converted to work done by friction, which causes the disk to come to a stop. The equation can be written as:

Work done by friction = Change in kinetic energy

The work done by friction can be calculated using the formula:

Work = force x distance

The force of friction can be found using the formula:

Force of friction = coefficient of friction x normal force

The normal force is equal to the weight of the disk, which can be found using the formula:

Weight = mass x gravity

Substituting the values given in the problem, we get:

Weight = mass x gravity = 0.75 kg x 9.81 m/s^2 = 7.3575 N

Force of friction = coefficient of friction x normal force = 0.34 x 7.3575 N = 2.4985 N

Work done by friction = Force of friction x distance

We can solve for the distance by rearranging the equation as:

Distance = Work done by friction / Force of friction

The initial kinetic energy of the disk can be found using the formula:

Kinetic energy = 0.5 x mass x velocity^2

Substituting the values given in the problem, we get:

Kinetic energy = 0.5 x 0.75 kg x (5.6 m/s)^2 = 11.76 J

Using the work-energy principle, we know that the work done by friction is equal to the change in kinetic energy, which is:

Work done by friction = Kinetic energy = 11.76 J

Substituting this value and the force of friction into the distance formula, we get:

Distance = Work done by friction / Force of friction = 11.76 J / 2.4985 N = 4.71 m

Therefore, the shuffleboard disk will travel a distance of 4.71 meters before coming to a stop, which is less than the length of the court (14.3 meters).

Polynomials are functions that are constructed from a sum of powers of the independent variable x, multiplied by coefficients. In this case, we have powers of x from 0 to 3, and the coefficients are 3, 5, -11, and 3.

To evaluate the function for a particular value of x, we substitute that value in place of x and perform the necessary arithmetic. For example, to find f(2), we substitute x = 2 in the expression for f(x):

f(2) = 3(2)^3 + 5(2)^2 - 11(2) + 3

= 24 + 20 - 22 + 3

= 25

Therefore, f(2) = 25. We can similarly evaluate the function for other values of x.

Step-by-step explanation:

So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...

Vertex at   60,90   <=====given

 Vertex form   y = a (x-h) ^2 + k

                        y = a ( x -60)^2 + 90    to find 'a' substitute in a point on the parabola...I'll use   0,0

                       0 = a ( 0-60)^2 + 90    shows a = - 1/40

so the equation is   y =  -1/40 ( x -60)^2 + 90  

           (  or expanded to y=   -1/40 x^2 + 3x )

Solve for 'x' when y = 6 ft  ( to keep from hitting your head)

      6 = -1/40x^2 +3x

      0 = -1/40 x^2 + 3x - 6      Use Quadratic Formula to find x = ~ 2 feet

The volume of the figure is 76 ft³.

In geometry, a prism is a three-dimensional solid object that has two parallel bases that are congruent polygons, and rectangular faces connecting the bases. The rectangular faces are also called lateral faces or sides, and the edges where the bases and lateral faces meet are called lateral edges. The number of sides in the bases and the shape of the bases determine the name of the prism.

To find the volume of the figure, we can break it down into two rectangular prisms and add their volumes.

The first rectangular prism has dimensions 6 ft x 2 ft x 3 ft, so its volume is:

V1 = 6 ft x 2 ft x 3 ft = 36 ft³

The second rectangular prism has dimensions 4 ft x 2 ft x 5 ft (8 ft - 3 ft), so its volume is:

V2 = 4 ft x 2 ft x 5 ft = 40 ft³

The total volume of the figure is the sum of these volumes:

V = V1 + V2 = 36 ft³ + 40 ft³ = 76 ft³

Therefore, the volume of the figure is 76 ft³.

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Answer:

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (- 11, - 13 ) , then

y - (- 13) = - [tex]\frac{2}{3}[/tex] (x - (- 11) ) , that is

y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)

Answer: 16.642

Step-by-step explanation:

I hope this helped you! A brainilist is highly appreciated and helpful! <3

Answer: 16.642

Step-by-step explanation:

10 + 6.034 = 16.034

16.034 + 0.608 = 16.642

Answer:

k=-4

Step-by-step explanation:

k+7=3

take way 7 from both sides

k=-4