3.9+3.4+4.5+3.1+3.9+4.1+3.6+3.9

There are three possible cases for the number of solutions to an absolute value equation:

One solution: In this case, the absolute value of the expression equals a positive number. For example, the equation |x - 3| = 5 has one solution: x = 8 or x = -2.

Two solutions: In this case, the absolute value of the expression equals zero. For example, the equation |x - 3| = 0 has two solutions: x = 3.

No solution: In this case, the absolute value of the expression equals a negative number. However, the absolute value of any expression is always non-negative, so there can be no solutions. For example, the equation |x - 3| = -2 has no solutions.

The reason why there are differences in the number of solutions is because the absolute value function takes any input and returns a non-negative output. When we set an absolute value expression equal to a number, we are essentially splitting the equation into two parts: one where the expression is positive, and one where it is negative. Depending on the value that the absolute value expression is set equal to, we may get only one of these two parts (the positive part), both of them (the zero part), or none of them (the negative part).

For example, let's consider the absolute value equation |2x - 6| = 4. To solve this equation, we can split it into two cases:

Case 1: 2x - 6 = 4. Solving for "x", we get x = 5.

Case 2: -(2x - 6) = 4. Simplifying, we get -2x + 6 = 4, which gives us x = 1.

Therefore, the equation has two solutions: x = 1 and x = 5.

Answer:

Absolute value equations can have three possible cases based on the value within the absolute value brackets:

One solution: If the value within the absolute value brackets equals zero, there is only one solution. For example, |x| = 0 has the solution x = 0.

Two solutions: If the value within the absolute value brackets is positive, there are two solutions: one positive and one negative. For example, |x| = 3 has two solutions: x = 3 and x = -3.

No solutions: If the value within the absolute value brackets is negative, there are no solutions. For example, |x| = -2 has no solution because the absolute value of any real number is non-negative.

The differences in the number of solutions depend on the nature of the equation and the value within the absolute value brackets. If the value within the absolute value brackets equals zero, there is only one solution; if it is positive, there are two solutions; and if it is negative, there are no solutions.

For example, consider the absolute value equation |x - 5| = 7. If we subtract 5 from both sides, we get |x - 5| - 5 = 7 - 5, which simplifies to |x - 5| = 2.

Since the value within the absolute value brackets is positive, we know that there are two solutions. We can solve for both solutions by setting x - 5 equal to 2 and -2:

x - 5 = 2 => x = 7 x - 5 = -2 => x = 3

Therefore, the solutions to the absolute value equation |x - 5| = 7 are x = 3 and x = 7.

So to summarize, the number of solutions for an absolute value equation depends on the value within the absolute value brackets and can be one, two or zero, depending on the nature of the equation.

Answer:

a

Step-by-step explanation:

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Each of the value of x in the diagram above are as follows

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.

Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;

x = 141° (alternate interior angles theorem).

x = 39° (corresponding angles).

x + 169 = 180

x = 180 - 169 = 21°.

x = 88° (vertically opposite angles).

x = 180°- 82°

x = 98°

x + 41 = 180

x = 180 - 41 = 139°.

x + 117 = 180

x = 180 - 117 = 139°.

x = 102° (vertically opposite angles)

x + 130 = 180

x = 180 - 130 = 50°.

x + 14 = 180

x = 180 - 14 = 166°.

x + 18 = 180

x = 180 - 18 = 162°.

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A model to find a fraction equivalent to 1/4 is found to be 0.25.

The intervals among two integers are illustrated by the display of fractions on a number line, which also reveals the basic idea behind the generation of fractional numbers.

Now, for the given fraction 1/4.

To get the model of 1/4, draw number line and mark number starting from

0 to 4.

Divide in 4 equal part.

The first part shows the fraction 1/4 = 0.25.

Thus, a model to find a fraction equivalent to 1/4 is found to be 0.25.

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The value of log(27) is 1.431.

What is logarithm?

The power to which a number must be raised in order to obtain other numbers is referred to as a logarithm. The easiest method to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms.

We can use the property of logarithms that states that log a (b^c) = c log a (b) to evaluate log 27 using the given approximations:

log 27 = log (3³) = 3 log 3 ≈ 3(0.477) ≈ 1.431

Therefore, log 27 ≈ 1.431.

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The two-column proofs of the line segments are shown below

Given that

HI = 13

IJ = 13

IJ ≅ JH

The proof is as follows

Statement                                                Reason

HI = 13, IJ = 13, IJ ≅ JH                            Given

HI ≅ IJ                                                      Substitution property

HI ≅ JH                                                    Substitution property (proved)

Given that

AL = SK

The proof is as follows

Statement                                                Reason

AL = SK                                                    Given

AL + LS = AS                                            Point–line–plane postulate

LS + SK = LK                                            Point–line–plane postulate

LS + AL = LK                                            Substitution property

AS = LK                                                    Point–line–plane postulate

                                                                (proved)

Given that

DG = 11

GF = 11

GF ≅ EF

The proof is as follows

Statement                                                Reason

DG = 11, GF = 11, GF ≅ EF                        Given

DG ≅ GF                                                   Substitution property

DG ≅ EF                                                    Substitution property (proved)

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Volume of given two cylinders are 115.52π m³ and 350π in³

What is the formula for the volume of a cylinder?

[tex]V = π {r}^{2} h[/tex]

where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant approximately equal to 3.14.

4) Given, radius =3.8 m and height = 8 m

Substituting the given values into the formula, we get:

[tex]V = π × (3.8)^2 × 8 \\ V = 115.52\pi \: cubic \: meters[/tex]

Therefore, the volume of the cylinder is approximately 361.984 cubic meters.

5) Given, radius = 5 in and height = 14 in

Substituting the given values:

[tex]V = π(5²)(14) \\ V = π(25)(14) \\ V = 350π[/tex]

Therefore, the volume of the cylinder is 350π cubic in (or approximately 1099.56 cubic meters if you want to use a numerical approximation for π).

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The first statement given is not a random sample because athletes leaving practice are not representative of all athletes.

A random sample is a sample in which every member of the population being studied has an equal chance of being selected. In the given statement, the sample is not random because the athletes leaving practice are not representative of all athletes, as they may have different preferences or levels of skill in their favorite sport.

Additionally, the sample is not chosen through a random selection process, but rather through a convenience sampling method, in which participants are chosen based on their availability and willingness to participate.

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a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.

How to solve questions?

A. To estimate the standard deviation of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas, we can use the empirical rule for normal distribution. The empirical rule states that for a normally distributed random variable, about 68% of the values fall within one standard deviation of the mean, about 95% of the values fall within two standard deviations of the mean, and about 99.7% of the values fall within three standard deviations of the mean.

The range of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is 21 mpg to 26 mpg. We can estimate the mean by taking the average of the range:

Mean = (21 + 26) / 2 = 23.5 mpg

We can estimate the standard deviation by using the empirical rule. Since we know that about 68% of the values fall within one standard deviation of the mean, we can estimate the standard deviation as half the range that covers about 68% of the values:

Standard Deviation ≈ (26 - 21) / 4 = 1.25 mpg

B. To find the sample size needed to estimate the mean with 98% confidence and an error of 0.25 mpg, we can use the formula for the sample size:

n = (zα/2 * σ / E)²

where:

n is the sample size

zα/2 is the z-score corresponding to the desired confidence level, which is 2.33 for 98% confidence (from the standard normal distribution table)

σ is the population standard deviation, which we estimated in part A to be 1.25 mpg

E is the desired margin of error, which is 0.25 mpg

Substituting the values, we get:

n = (2.33 * 1.25 / 0.25)²

n = 72.96

Since we cannot have a fraction of a person in our sample, we round up to the next integer and get:

n = 73

Therefore, a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.

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The angles of the triangle are A=146.8°,B=22.3° and C=10.9°

The cosine rule states that for any triangle with sides of length a, b, and c and angles A, B, and C (with the side opposite each angle labeled with the corresponding lowercase letter), the following equation holds:

a² = b² + c²- 2bc cos(A)

b² = a² + c² - 2ac cos(B)

c² = a² + b² - 2ab cos(C)

Using the cosine rule,

a²=b²+c²-2bcCosA

2bcCosA=b²+c²-a²

A=cos⁻¹(b²+c²-a²/2bc)

A=cos⁻¹(18²+9²-26²/2×18×9)

A=cos⁻¹(-0.83642)=146.8°

Also from b²=a²+c²-2acCosB

B=cos⁻¹(a²+c²-b²/2ac)

B=cos⁻¹(26²+9²-18²/2×26×9)

B=cos⁻¹(0.925)=22.3°

The total angle of the triangle is 180°

A+B+C=180°

C=180°-146.8°+22.3°=10.9°

Thus, the angles of the triangle are A=146.8°,B=22.3° and C=10.9°

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The compelte question is;

Image is attached below

Answer:

k=0 or k=1/27

Step-by-step explanation:

3k-81k^2=0

3k(1-27k) =0

3k=0 or 1-27k=0

k=0 or -27k= -1

k= 1/27

there are 1,008 different computer systems possible, given the constraints provided.

what is constraints?

Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.

In the given question,

To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

So, for this problem, we have:

8 different choices for computers

7 different choices for monitors

9 different choices for printers

2 different choices for scanners

Using the multiplication principle, the total number of different computer systems possible is:

8 x 7 x 9 x 2 = 1,008

Therefore, there are 1,008 different computer systems possible, given the constraints provided.

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a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000

b. The present value of $100,000 when your child is born is $100,000.

Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.

a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:

[tex]FV = PMT*((1 + r)^n - 1)/r[/tex]

where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).

Plugging in the values, we get:

$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05

Solving for PMT, we get:

PMT = $3,436.76

Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.

b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:[tex]PV = FV/(1 + r)^n[/tex]

where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).

Plugging in the values, we get:

PV = $100,000/(1 + 0.05)^0

Solving for PV, we get:

PV = $100,000

Therefore, the present value of $100,000 when your child is born is $100,000.

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You would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.

The answer to this question depends on the dimensions of the wheelchair ramp and how much area needs to be covered with stain.

Assuming that the wheelchair ramp has an area of 100 square feet, and that the stain coverage is similar to the area covered by paint, then the amount of stain required can be estimated by using the following formula:

Amount of stain (in liters) = Area to be covered (in square feet) ÷ Coverage per liter (in square feet per liter)

If the stain coverage is 25 square feet per liter, then the amount of stain required to cover 100 square feet would be:

Amount of stain = 100 ÷ 25 = 4 liters

Therefore, you would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.

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The correct answer is option 2: if Lamont's sales are $2708.33, he earns $2290.63 with Plan B.

To determine which pay structure is better for Lamont, we need to compare the total amount of money he earns under each plan for different levels of sales. We can set up a system of equations to represent the two plans:

Plan A:

Total Pay = 1775 + 0.19S

where S is Lamont's total monthly sales

Plan B:

Total Pay = 2100 + 0.07S

To find the point at which the two plans yield the same result, we can set the two equations equal to each other and solve for S:

1775 + 0.19S = 2100 + 0.07S

0.12S = 325

S = 2708.33

If Lamont's monthly sales are exactly $2,708.33, then he earns the same amount of money under both plans - this is the break-even point.

However, for sales above this amount, Plan A becomes the better option as the commission rate is higher. Option 1 is incorrect because it assumes that Plan A is always better, whereas we know from the calculations that this is not the case. Option 3 is correct for sales above $2,708.33, but not for sales below this amount. Option 4 is also incorrect as we know that Plan B yields a slightly higher payout for sales exactly equal to the break-even point.

Therefore, option 2 is the correct answer as it accounts for the break-even point and accurately reflects the difference in total pay between Plan A and Plan B for Lamont's sales of $2,708.33.

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y= 2x+1 y = -3x-4

2x-y+1 = 0. 3x+y+4 = 0

a1 + b1 + c1 = 0 a2+ b2 + c2 = 0

x,y = b1c2- b2c1/ a1b2-a2b1 , a2c1-a1c2/a1b2-a2b1

x,y = -1×4 - 1×1 /2×1 - 3×-1 , 3×1-2×4 / 2×1 -3×-1

x,y = -5/-1 , -5/2

x,y= 5, 5/2

When the slope is an integer the best answer would be a. the rise number is one.

Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.

When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:

Therefore, the correct answer is a. the rise number is one.

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There is no logarithm base provided in the expression "log 5 + 2". Therefore, we assume that the base is 10, which is the default base for logarithms when no base is specified.

Using the logarithmic identity that states

"log a + log b = log(ab)",

we can combine the terms as follows:

log 5 + 2 = log(5) + log(10^2) [Note that 10^2 = 100]

Now, using the same identity, we can simplify this further:

log(5) + log(100) = log(5 * 100) = log(500)

Therefore, the expression "log 5 + 2" can be simplified as a single logarithm of "log 500" with base 10.

The bearing from A to F is 38

Answer:

  3 times the second equation, plus the first

Step-by-step explanation:

You want a strategy for eliminating x-terms in the system of equations ...

You can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.

Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...

Adding these two equations together will eliminate the x-terms:

  (9x -7y) +(-9x +15y) = (-3) +(27)

  8y = 24 . . . . . . . simplify; x-terms are gone

You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.

1. ∠EAD ≅ ∠EBC (Given) 2. ∠AEB ≅ ∠AEB (Common angle) 3. AD- ≅ BC- (Given) 4. ∆AED ≅ ∆BEC (AAS) 5. CE- ≅ DE- (CPCT)

According to the concept of corresponding parts of congruent triangles, or cpct, corresponding sides and corresponding angles of two congruent triangles are identical. The corresponding sides and angles of two triangles that are congruent to one another according to any of the following principles of congruency must be equal. When the corresponding sides and corresponding angles of two triangles are the same, two triangles are said to be congruent.

In the given figure given that, ∠EAD ≅ ∠EBC; AD- ≅ BC.

Thus,

1. ∠EAD ≅ ∠EBC (Given)

2. ∠AEB ≅ ∠AEB (Common angle)

3. AD- ≅ BC- (Given)

4. ∆AED ≅ ∆BEC (AAS)

5. CE- ≅ DE- (CPCT)

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Answer: Slope: 6y-intercept:(0,−1)

x= 0,1

y= -1,5

Step-by-step explanation:

Answer:

Yes, the data is an example of numerical data.

1. This is about data, which means information that we can measure and count.

2. There are two types of numerical data: continuous and discrete.

3. Continuous numbers CAN have fractions, like 3.5, 4.2, or 5.0. 4. like show sizes

4. Discrete data CANNOT have fraction. only whole numbers, like 0, 1, 2, 3, and so on. like number of students in a class

7. "range" formula used to find the difference between discrete & continuous numerical data

8.  "range" formula is largest value minus smallest value

Step-by-step explanation:

chatgpt

Answer: yes because it records the shoe sizes and you can calculate average, median, mode and range from this

Step-by-step explanation:

We can give the proof to class with certainty that 1+1=2 and not 11.

A statement that has been shown to be true based on a collection of axioms or presumptions is known as a theorem. This fact can be used to support other claims using mathematics. On the other hand, a proof is a logical argument that shows a theorem or claim to be true. In other terms, a proof is the procedure used to demonstrate a theorem's validity. A theorem may be true even in the absence of a proof, but it is not regarded as established until a proof is provided.

The basic properties of arithmetic can be used to prove 1 + 1 = 2.

The symbol "+" represents addition, thus 1 + 1 represents addition of 1 with 1 which is 2.

For 11 the 1 needs to be different place values which is not possible for 1 + 1.

Hence, we can give the proof to class with certainty that 1+1=2 and not 11.

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Mary Lou Mason's total taxes on her purchase would be $1.37.

Taxes are mandatory payments to the government that are used to fund public services such as infrastructure, education, and health care. Taxes can be direct, such as income taxes, or indirect, such as sales taxes.

Mary Lou Mason's total purchase was $19.14.

To calculate the total taxes for her purchase, we can use the following formula:

Tax = (State Sales Tax %) x (Total Purchase) + (County Tax %) x (Total Purchase)

Therefore, the total taxes for Mary Lou Mason's purchase would be:

Tax = (6.5%) x ($19.14) + (1.5%) x ($19.14)

Tax = (0.065 x 19.14) + (0.015 x 19.14)

Tax = 1.24 + 0.13

Tax = $1.37

Mary Lou Mason's total taxes on her purchase would be $1.37.

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The graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

What is graph?

A graph is a data structure consisting of a set of vertices (also called nodes or points) connected by edges (also called arcs or lines). It is used to represent relationships between objects or entities in a system or network. Graphs are commonly used in computer science, mathematics, and other fields where complex data structures need to be analyzed and visualized.

In a graph, each vertex may be connected to one or more other vertices by edges. The edges may be directed (pointing from one vertex to another) or undirected (connecting vertices without a specific direction). A graph can be represented mathematically as a set of vertices and a set of edges that connect them.

To find where the graph of the equation x²-x-2=y crosses the x-axis, we need to find the values of x when y=0.

So, let's set y=0 and solve for x, x²-x-2=0

We can factor this quadratic equation as (x-2)(x+1) = 0

So, the solutions are

x-2=0 or x+1=0

which give:

x=2 or x=-1

Therefore, the graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

So the answer is option D: (-1,0) and (2,0).

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