11. Given: 17 - 3(w + 5) = 6(w + 5) - 2w;
Prove: w = -4
Statements
Reasons
11.17-3(3+5)=6(W+5)-2W
2.17-30-15= 60 +30 -2W
3.-3W +2 = 4W+30
4. -7W +2=30
5. -W=28
1. W= -4

Answer:

vanilla thickshake = $5

fruit juice = $3

USING ELIMINATION METHOD

Let the price of vanilla thickshake = x

Let the price of fruit juice = y

Given that a vanilla thickshake is $2 more than a fruit juice.

so

Given that If 3 vanilla thickshakes and 5 fruit juices cost $30.

So the system of equations

\(x = 2+y\)

\(3x+5y = 30\)

Arrange equation variables for elimination

\(\begin{bmatrix}x-y=2\\ 3x+5y=30\end{bmatrix}\)

\(\mathrm{Multiply\:}x-y=2\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:3x-3y=6\)

\(\begin{bmatrix}3x-3y=6\\ 3x+5y=30\end{bmatrix}\)

so

\(3x+5y=30\)

\(-\)

\(\underline{3x-3y=6}\)

\(8y=24\)

so the system of equations becomes

\(\begin{bmatrix}3x-3y=6\\ 8y=24\end{bmatrix}\)

solve 8y = 24 for y

\(8y=24\)

Divide both sides by 2

\(\frac{8y}{8}=\frac{24}{8}\)

\(y=3\)

\(\mathrm{For\:}3x-3y=6\mathrm{\:plug\:in\:}y=3\)

\(3x-3\cdot \:3=6\)

\(3x-9=6\)

\(3x=15\)

Divide both sides by 3

\(\frac{3x}{3}=\frac{15}{3}\)

\(x=5\)

Therefore,

                                              2ND METHOD

Step-by-step explanation:

As a vanilla thickshake is $2 more than a fruit juice.

Given that 3 vanilla thickshakes and 5 fruit juices cost $30.

3(Vanilla thickshakes) + 5(fruit juice) = 30

3(x+2) + 5x = 30

3x+6+5x=30

8x+6=30

8x=30-6

8x=24

x = 3

Thus,

The equations Verdita could use to represent the data sets include the following:

A. Data Set A: y = 4x-2

Data Set B: y = x +4

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of data set A;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 6)/(1 + 1)

Slope (m) = 8/2

Slope (m) = 4

At data point (1, 2) and a slope of 4, a linear equation for data set A can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4(x - 1)

y = 4x - 2

At data point (0, 4) and a slope of 1, a linear equation for data set B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = 1(x - 0)

y = x + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: B

Step-by-step explanation:

1+4/x                       x + 4

------------   =            -------------  

1-16 x^2           x(-4x + 1) (4x + 1)

hope this helps, it probs won't but-

Answer: \(\frac{x+{4} }{x - 16x^{3} }\)

Steps:

Sorry about the delay. Hope this helps!

Answer:

x= 1/27

Step-by-step explanation:

the correct answer is : X = 1/27

Answer:

- 1/2

Step-by-step explanation:

To solve for x in the equation 3^2x = 1/3, we can start by taking the logarithm of both sides with base 3:

log3 (3^2x) = log3 (1/3)

Using the logarithmic property logb (a^n) = n * logb (a), we can simplify the left side:

2x * log3 (3) = log3 (1/3)

Since log3 (3) = 1, we can simplify further:

2x = log3 (1/3)

To find the value of the logarithm on the right side, we can use the definition of logarithms: logb (a) = c if and only if b^c = a. Since 1/3 = 3^-1, we have:

2x = log3 (3^-1) = -1

Finally, to solve for x, we divide both sides of the equation by 2:

x = -1/2

So the solution to the equation 3^2x = 1/3 is x = -1/2.

Answer:

See below picture.

Explanation:

y=2 has a y-intercept of 2, so we start graphing there. with most equations, we would follow the slope starting from that point, but y=2 doesn't have a slope. The 2 stays going all the way "across" for all x-values. I used demos to graph.

After using the formula for the area of the triangle, we know that the area is 200 cm² when the height is 25 cm and the base is 16 cm respectively.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The easiest approach I've found to know for sure if an angle is 90 degrees is to use the 3:4:5 triangle.

According to this criterion, a triangle is a right triangle if the diagonal between its two points measures 5, even though one of its sides measures 3 and the other measures 4.

So, the formula for the area of the triangle is:

A = 1/2 *  base  *  height

Now, calculate the area by inserting the values as follows:\

A = 1/2 *  base  *  height

A = 1/2 *  16 *  25

A = 8 * 25

A = 200 cm²

Therefore, after using the formula for the area of the triangle, we know that the area is 200 cm² when the height is 25 cm and the base is 16 cm respectively.

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hdhdbbdnfnbrndjjrhrhrhrhbdbd

The probability

a) All three cards are aces is: P(all three cards are aces) = 4/22,100 ≈ 0.000181

b)  All three cards are black is: P(all three cards are black) = 2,600/22,100 ≈ 0.117647

c) all three cards are spades is:  P(all three cards are spades) = 286/22,100 ≈ 0.012959

(a) To find the probability that all three cards are aces, we need to divide the number of ways in which we can select three aces by the total number of ways to select any three cards from the deck. There are 4 aces in the deck, so the number of ways to select three aces is given by:

C(4,3) = 4

where C(n,r) denotes the number of combinations of r objects chosen from a set of n distinct objects.

The total number of ways to select any three cards is given by:

C(52,3) = (52 * 51 * 50) / (3 * 2 * 1) = 22,100

Therefore, the probability that all three cards are aces is:

P(all three cards are aces) = 4/22,100 ≈ 0.000181

(b) To find the probability that all three cards are black, we need to divide the number of ways in which we can select three black cards by the total number of ways to select any three cards from the deck. There are 26 black cards in the deck (13 clubs and 13 spades), so the number of ways to select three black cards is given by:

C(26,3) = (26 * 25 * 24) / (3 * 2 * 1) = 2,600

Therefore, the probability that all three cards are black is:

P(all three cards are black) = 2,600/22,100 ≈ 0.117647

(c) To find the probability that all three cards are spades, we need to divide the number of ways in which we can select three spades by the total number of ways to select any three cards from the deck. There are 13 spades in the deck, so the number of ways to select three spades is given by:

C(13,3) = (13 * 12 * 11) / (3 * 2 * 1) = 286

Therefore, the probability that all three cards are spades is:

P(all three cards are spades) = 286/22,100 ≈ 0.012959

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Answer: 2.12 miles.

Step-by-step explanation: To find the width of Hardee County, we need to determine the length of one of its sides. We can use the fact that the area of a rectangle is equal to its length times its width to find the length of one of its sides.

The area of Hardee County is 637 square miles, and we know that its width is 30 miles. We can use this information to write the following equation: 637 square miles = 30 miles * length

We can solve this equation for the length by dividing both sides by 30: 637 square miles / 30 miles = length

This simplifies to: 21.2 square miles = length

Since the length of a rectangle is one of its sides, the width of Hardee County is 21.2 miles.

a) the study has been done by controlling the groups hence it is an experiment.

b) The persons are assigned randomly o each group hence it is a randomized design.

c) the explanatory and response variables. are:

Effect of listening to music by Mozart

IQ of the person

What are an experiment and observational study?

In observational research, participants are measured or surveyed without any attempt to influence them. In a controlled experiment, participants or objects are divided into groups, and one group is given treatment while the other is not.

What are randomized or block designs?

An experimental design known as a randomized block design divides the experimental units into units known as blocks. The experimental units inside each block are assigned the treatments at random. We have a fully randomised block design when each block has at least one instance of each treatment.

a. Is this an experiment or an observational study?

Since the study has been done by controlling the groups hence it is an experiment

b. If it is an experiment, is it randomized or block design?

Since the persons are assigned randomly o each group hence it is a randomized design

c. If it is an experiment, identify the explanatory and response variables.

explanatory variable = effect of listening to music by Mozart

response variable =  IQ of the person

(d)Three levels of the treatment  effect of listening to music by Mozart

level 1: listen to Mozart's music

level 2: told to relax

level 3: no instructions

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Answer:

4(x + 1/4) ≤ 9 + 2x

Step-by-step explanation:

Answer:

it not clear maybe you can take an other pohto

sorry

Step-by-step explanation:

Answer:

(0,3) (-1,0) im sorry if this is incorrect

Step-by-step explanation:

Answer:

yeah, im not sure

Step-by-step explanation:

The inverse of the function f(x) = 2x+1 is (x-1)/2.

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

Given;

Function, f(x) = 2x + 1.

To find the inverse of the function:

First, let y = f(x)

That is,

y = 2x +1

Then, make x the subject of the equation

y = 2x + 1

To make x the subject of this equation:

First, subtract 1 from both sides

We get

y -1 = 2x

Now, divide both sides by 2.

x = (y-1)/2

Now, rewrite as f⁻¹(x) by replacing y by x.

That is,

f⁻¹(x)  =  (x-1)/2

Therefore, the inverse of the function f(x) is (x-1)/2.

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True.An example of a variable input on a college campus would indeed be the number of instructors needed.

The number of instructors required can vary based on factors such as the number of courses being offered, the size of the student population, class sizes, faculty-student ratios, and other factors that affect the teaching workload and staffing needs of the institution.

The number of instructors needed is a variable input because it can change over time and in response to different circumstances. For example, at the beginning of a semester, when a college campus experiences high enrollment, more instructors may be required to meet the demand for teaching courses. On the other hand, during summer or holiday breaks when fewer courses are offered or when the student population is reduced, fewer instructors may be needed.

The number of instructors needed is an important consideration for colleges and universities to ensure the smooth functioning of academic programs and the provision of quality education. It plays a crucial role in determining the faculty-student ratio, class sizes, course availability, and overall academic experience for students.

In terms of solution, determining the number of instructors needed involves careful planning and analysis by the college administration or academic departments. They need to consider various factors, such as the number of courses being offered, the size and nature of the courses, the expertise required for specific subjects, and any contractual or workload obligations of the instructors.

The process typically involves forecasting student enrollments, analyzing historical data on course registrations, and considering factors such as class sizes, faculty workload policies, and teaching responsibilities. The administration may use mathematical models, scheduling software, or historical data analysis to estimate the number of instructors required for each semester or academic year.

Based on this analysis, the college can make decisions about hiring new instructors, assigning existing faculty members to courses, or adjusting course offerings to ensure that the staffing needs are met. It is crucial to strike a balance between the number of instructors and the workload to ensure that instructors have a manageable teaching load while meeting the needs and expectations of students.

In conclusion, the number of instructors needed is a variable input on a college campus. It can fluctuate based on factors such as student enrollments, course offerings, class sizes, and other factors. Determining the appropriate number of instructors requires careful planning, analysis, and consideration of various factors to ensure the effective functioning of academic programs and the provision of quality education to students.

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Answer:

answer of the above given question is (c) 1/2(10*6)=30,as we know the area of the triangle is 1/2*base*height.So,we can directly find the area of the triangle.

1. The normal force in this case is 78.4 N. Since the box is lying on a table, the gravitational force acting downwards on the box is 8 kg x 9.8 m/s² = 78.4 N. Since the box is at rest, the normal force acting upwards on the box must be equal to this force.

The vertical force acting upwards on the box due to the person pulling up is not relevant in calculating the normal force.2. The normal force in this case is 98 N. Since the box is lying on a table,

the gravitational force acting downwards on the box is 6 kg x 9.8 m/s² = 58.8 N. Since someone is pushing down on the box with a force of 50 N, the normal force acting upwards on the box must be equal to the sum of the gravitational force and the pushing force: 58.8 N + 50 N = 108.8 N.3.

The normal force in this case is 53 N. Since the box is lying on a table, the gravitational force acting downwards on the box is 3 kg x 9.8 m/s² = 29.4 N. Since someone is pulling up on the box with a force of 50 N, the normal force acting upwards on the box must be equal to the difference between the upward pulling force and the gravitational force: 50 N - 29.4 N = 20.6 N.

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We are asked to determine the equation of an ellipse that has a base of 40 feet and a height of 18 feet. This can be visualized in the following diagram:

The general form of the equation of an ellipse is:

We have set the origin of the coordinate system to be in the middle of the ellipse. The value of "a" is the x-intercept of the ellipse and the value of "b" is the y-intercept of the ellipse. Therefore, the equation is:

Now, we solve the squares:

And thus we have determined the equation of the ellipse.

Answer:

t(x) = 948(0.955)^x

Step-by-step explanation:

I had this for a warm up

Answer: (x) 948(0.955)

Answer:

<M=32 degrees

Step-by-step explanation:

triangle equals 180 degrees total

76+72=148

180-148= 32

<M= 32

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Based on the rate given, in four years it is expected to have 21,104 subscribers.

It is known the number of subscribers will decrease by 7% or 0.07, based on this let's calculate the change every year.

First year:

28,215 x 0.07 =  1,975

28,215 - 1,975 = 26,239

Second year:

26,239 x 0.07 =  1,836

26,239 - 1,836 = 24,402

Third year:

24,402 x 0.07 =  1,708

24,402 - 1,708 = 22,693

Fourth year:

22,693 x 0.07 =  1,588

22,693 - 1,588 = 21,104

Based on this, by the fourth year, the number of subscribers will be 21,104

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There are 924 ways in which an advertising agency can promote 12 items, taking 6 items at a time, during a 12-minute period of TV time.

This is because the question refers to a combination problem where the order of the items doesn't matter.

To solve this problem, we can use the combination formula, which is:

nCr = n!/r!(n-r)!

Where n is the total number of items, r is the number of items being chosen at a time, and ! denotes the factorial operation.

Using this formula, we can substitute n=12 and r=6 to get:

12C6 = 12!/6!(12-6)!

= (12x11x10x9x8x7)/(6x5x4x3x2x1)

= 924

Therefore, there are 924 ways in which an advertising agency can promote 12 items, taking 6 items at a time, during a 12-minute period of TV time. This means that they have a variety of options to choose from when deciding how to promote their products within the given time frame.

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Answer:

Step-by-step explanation:

weight = (volume of block - volume of slots) x density of block

           = (30 * 20 * 9) - (2 x (10 * 8 * 9)) x 1.7

            = (5400 - 1440) x 1.7

           = 8,568

Volume is a three-dimensional scalar quantity. The correct option is D, 8568 grams.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the complete block is,

Volume = 36 cm x 20 cm x 9 cm = 6480 cm³

The volume of the opening is,

Volume of the opening = 2 × 10 cm x 8 cm × 9cm = 1440 cm³

Therefore, the weight of the cement block to the nearest gram is,

Weight = (6480 -1440)cm³ × 1.7 gram/cm³

            = 8568 grams

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To answer this question, we will use the trigonometric function tangent. Recall that in a right triangle:

In the given triangle, θ=25°, adjacent leg=x, and opposite leg=10, therefore:

Solving the above equation for x, we get:

Simplifying the above result we get:

Answer:

Answer:

No real roots, two complex roots

Step-by-step explanation:

By calculating the discriminant:

\(D=b^2-4ac=5^2-4(5)(21)=25-420=-395 < 0\), then there will be no real zeroes. However, there will be two complex roots.

Answer:

FD = 25.9

Step-by-step explanation:

13x - 16 = 4x + 11

9x = 27

x = 3

using Pythagorean theorem:

FD²  = 12² + [4(3) + 11]²

FD² = 144 + 23² = 144 + 529 = 673

FD = 25.94