Solve the system of equations.

Answer:

18

Step-by-step explanation:

18 can be divided by 18 =1

54 divided by 18 = 3

The greatest common factor of numbers 18 and 54 is,

⇒ GCD = 18

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

We have to given that;

To find the greatest common factor of 18 and 54.

Now, We know that;

Greatest common factor of numbers are that highest number which divides exactly into two more numbers,  

Here, The numbers are,

⇒ 18 , 54

⇒ 18 = 18

⇒ 54 = 18 × 3

Hence, The greatest common factor of numbers 18 and 54 is,

⇒ GCD = 18

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Answer:

25 shaded tiles and 15 white tiles

Step-by-step explanation:

Added up these all make 40 tiles, making them the only answer. Hope this helps.

Answer:

y=(x-5)^2-1

Step-by-step explanation:

From the solid black graph to dashed red graph, you've shifted the graph right 5 units and down 1 unit.

Answer:

The correct answer is the one on the top right

Step-by-step explanation:

Answer:

\(-\frac{22}{91} = x\)

Step-by-step explanation:

To solve the equation \(3x - 23 = 94x - 1\), we'll follow these steps:

Start by simplifying the equation by combining like terms. In this case, we have terms with x on both sides, as well as constants:

\(3x - 23 = 94x - 1\)

To isolate the x terms, we can subtract 3x from both sides of the equation:

\(3x - 3x - 23 = 94x - 3x - 1\)

Simplifying further, we get:

\(-23 = 91x - 1\)

Next, we want to isolate the constant term on one side of the equation. We can do this by adding 1 to both sides:

\(-23 + 1 = 91x - 1 + 1\)

Simplifying further:

\(-22 = 91x\)

Finally, we can solve for x by dividing both sides of the equation by 91:

\(-\frac{22}{91}=\frac{91x}{91}\)

Simplifying further:

\(-\frac{22}{91} = x\)

Therefore, the solution to the equation \(3x - 23 = 94x - 1\) is \(-\frac{22}{91} = x\)

Answer:

Step-by-step explanation:

C equals x^2 plus 8x

Answer: 25%

Step-by-step explanation: The total number of city council is 80 and 20/80 is 1/4

The correct answer is option  b) AAS

According to the AAS congruence theorem, if two angles and the non-included side of one triangle are congruent with the corresponding components of another triangle, then the two triangles are congruent.

Therefore, option B is the correct answer.

"AAS congruence" theorem an be used to prove that the triangles are congruent .

The complete question is:

Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?

a) SSS

b) AAS

c) SAS

d) HL

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Answer:

10

Step-by-step explanation:

It's the $10 that is to be added to the cost for each produced item.

Answer: The first system is correct.

Step-by-step explanation:

The blue area to the left and below the dashed line is y < -2x +6

The area the yellow area to the right and below the solid line is y ≤ x + 2

The sentence "If it is a dog (d), it has fleas (f)" can be represented in symbolic form as d → f.

In symbolic logic, we represent the components of a sentence using letters or symbols. In this case, the given sentence has two components: "it is a dog" and "it has fleas." To represent these components, we assign the letter 'd' to "it is a dog" and the letter 'f' to "it has fleas."

The sentence "If it is a dog, it has fleas" implies a conditional relationship between the two components. It states that if something is a dog (d), then it has fleas (f). This can be symbolically represented as d → f, where the arrow (→) denotes the conditional relationship.

The given sentence, "If it is a dog (d), it has fleas (f)," can be represented in symbolic form as d → f. The arrow (→) in symbolic logic represents the conditional relationship. It indicates that if something is a dog (d), then it has fleas (f). In this symbolic representation, 'd' stands for "it is a dog," and 'f' represents "it has fleas."

The sentence is a conditional statement because it presents a hypothetical relationship between the two components. The truth value of the sentence depends on whether the antecedent (d) is true or false. If something is indeed a dog, then it implies that it has fleas. However, if it is not a dog, the statement does not make any specific claim about fleas.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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The domain of the following graph is equal to [-11. -3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-11, -3].

Range = [-5, 0].

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An interior angle of a polygon is an angle formed inside the two adjacent sides. In our case, an interior angle is the angle in red color:

In our case, there are 8 sides so our polygon is an octagon. So, the size of each interio angle is given by

Therefore, the answer is 135 degrees:

Answer: $31.55

Step-by-step explanation:

$25.75 + 37.80 - 32.00 = $31.55

Answer:

I believe the answer is 8th graders.

Step-by-step explanation:

Given that each bus ride is $3, and that assuming the takes the ride twice a day,

If he takes the ride in the same manner for 11 days,

Thus, he needs $66 to ride the bus twice for 11 days.

Since Clay has $50, he will not be able to ride the bus twice for 11 days.

Hence, the correct answer is False

Based on the slopes calculated, Sammy can conclude that quadrilateral EFHG is a rectangle.

To determine whether quadrilateral EFHG is a rectangle using coordinate geometry, Sammy can follow these steps:

1. Calculate the slopes of the opposite sides:

  - Slope of EF: mEF = (yF - yE) / (xF - xE)

  - Slope of HG: mHG = (yG - yH) / (xG - xH)

2. Calculate the slopes of the adjacent sides:

  - Slope of FG: mFG = (yG - yF) / (xG - xF)

  - Slope of EH: mEH = (yH - yE) / (xH - xE)

3. Check if the opposite sides have equal slopes:

  - If mEF = mHG and mFG = mEH, then EFHG is a parallelogram.

4. Check if the adjacent sides have perpendicular slopes:

  - If mEF * mFG = -1 and mHG * mEH = -1, then EFHG is a rectangle.

Let's calculate the slopes using the given coordinates:

mEF = (7 - 10) / (4 - 7) = 3 / -3 = -1

mHG = (5 - 8) / (6 - 9) = -3 / -3 = 1

mFG = (5 - 7) / (6 - 4) = -2 / 2 = -1

mEH = (8 - 10) / (9 - 7) = -2 / 2 = -1

Since mEF = mHG = -1 and mFG = mEH = -1, we have equal slopes for opposite sides and perpendicular slopes for adjacent sides.

Therefore, Sammy is able to determine that the quadrilateral EFHG is a rectangle based on the calculated slopes.

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The average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours.

Given the distance that an airplane covered in three different trips:

Hongkong-Manila: 1116 kilometers, Singapore-Manila: 2391 kilometers,

Korea-Manila: 2601 kilometers.

We are required to find the average distance traveled by the airplane in the three trips, the time it took in each trip if the speed of airplane is 760 km/h and the trip that took the longest time to travel.

Average distance that airplane travelled in the three trips=(1116+2391+2601)/3

=6108/3

=2036 kilometers

We know that speed=distance/time.

Time=Distance/speed

Time in trip from Hongkong to Manila=1116/760=1.468 hours

Time in trip from Singapore to Manila=2391/760=3.146 hours

Time in trip from Korea to Manila=2601/760=3.422 hours

We can observe that the trip from Korea to Manila took longest time to travel.

Hence the average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours and the trip from Korea to Manila took longest time to travel.

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The statement that is true about the segment connecting points B and C is D. The segment has a finite length that can be measured.

It should be noted that ieometry, a line segment is the part of a straight line bounded by two distinct end points, and contains every point on the line that is between its endpoints.

It should be noted that the length of a line segment is given by the Euclidean distance between its endpoints.

Therefore, in this case, the statement that is true about the segment connecting points B and C is that the segment has a finite length that can be measured.

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hope it helps

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#1

\(\\ \rm\rightarrowtail 3(a)(2)(b)=6ab\)

#2

\(\\ \rm\rightarrowtail c^5(c)=c^{5+1}=c^6\)

#3

\(\\ \rm\rightarrowtail 2y^4(5y^3)=10y^7\)

#4

\(\\ \rm\rightarrowtail 3gh^2(4g^3h^3)=12g^4h^5\)

For the actual number 3 and the predicted value 1.6 the residual  is equal to 1.4.

As given in the question,

The actual number is equal to 3

The predicted value is equal to 1.6

The residual is the difference between actual number and predicted value.

Formula for the residual is:

Residual = Actual number - Predicted value

Substitute the value of the actual number and the predicted value in the formula ,

⇒ Residual = 3 - 1.6

⇒ Residual = 1.4

Therefore, the residual for the given the actual number and the predicted value is given by 1.4.

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Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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The equation of the line is y + 1 = 3(x - 2).

The correct option is (3).

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

As per the given data:

The line passes through the point (2, -1)

slope of the given line is 3

By using the slope intercept form of line:

y = mx + c

where m is the slope

c is the y intercept

The line passes through the point (2, -1) so substituting the point in the equation also m = 3

y = 3x + c

-1 = 3(2) + c

c = -7

The equation of the line now can be written as:

y = 3x - 7

y + 1 = 3x - 7 + 1

y + 1 = 3(x - 2)

Hence, the equation of the line is y + 1 = 3(x - 2).

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If a person is chosen at random, and they are a heavy drinker, the probability of that person having a liver ailment is 0.053.

A random sample of 1,000 people,

7.4% have a liver ailment.

P(Have liver ailment) = 0.074

P(Have no liver ailment) = 1 - P(Have liver ailment)

P(Have no liver ailment) = 1 - 0.074

P(Have no liver ailment) = 0.926

Those who have a liver ailment, 9% are heavy drinkers.

P(Have liver ailment | Heavy drinkers) = 0.09

Those who have a liver ailment, 60% are moderate drinkers.

P(Have liver ailment | moderate drinkers) = 0.60

Those who have a liver ailment, 31% are nondrinkers.

P(Have liver ailment | nondrinkers) = 0.31

Those who do not have a liver ailment, 13% are heavy drinkers,

P(Have no liver ailment | Heavy drinkers) = 0.13

Those who do not have a liver ailment, 48% are moderate drinkers.

P(Have no liver ailment | moderate drinkers) = 0.48

Those who do not have a liver ailment, 39% are nondrinkers.

P(Have no liver ailment | nondrinkers) = 0.39

If a person is chosen at random, and they are a heavy drinker, then we have to determine the probability of that person having a liver ailment.

P(heavy drinker) = P(have liver ailment) × P(Have liver ailment | Heavy drinkers) + P(have no liver ailment) × P(Have no liver ailment | Heavy drinkers)

P(heavy drinker) = 0.074 × 0.09 + 0.926 × 0.13

P(heavy drinker) = 0.00670.1204

P(heavy drinker) = 0.1271

P(Have liver ailment| heavy drinker) = P(Have liver ailment) × P(Have liver ailment | Heavy drinkers)/P(heavy drinker)

P(Have liver ailment| heavy drinker) = (0.074 × 0.09)/0.1271

P(Have liver ailment| heavy drinker) = 0.0067/0.1271

P(Have liver ailment| heavy drinker) =0.053

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Given:

An exponential function goes through points (0, 14) and (4, 8750).

To find:

The function.

Solution:

The general form of an exponential function is

\(y=ab^x\)          ...(i)

It goes through points (0, 14) and (4, 8750). It means the the equation must be satisfied by these points.

Putting x=0 and y=14 in (i), we get

\(14=ab^0\)

\(14=a\)

The value of a is 14.

Putting a=14, x=4 and y=8750 in (i), we get

\(8750=14b^{4}\)

\(\dfrac{8750}{14}=b^{4}\)

\(625=b^{4}\)

It can be written as

\(5^4=b^{4}\)

\(5=b\)

The value of b is 5.

Putting a=14 and b=5 in (i), we get

\(y=14b^5\)

Therefore, the required exponential function is \(y=14b^5\).

Answer:

y=14(5)^x

Step-by-step explanation:

Answer:

1. m∠5 + m∠6 = 180° ...........Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property