Volume of this triangular prism
21 mm base
38 mm
82 mm long
28 mm

For a one-tailed dependent samples t-Test with 30 participants at the p < .05 level, we need to overcome a specific critical value of 1.697.

This value can be obtained from a t-table or calculated using statistical software. It is important to note that the critical value may vary depending on the specific alpha level chosen and the study's degrees of freedom (df). However, for a one-tailed dependent samples t-Test with 30 participants at the p < .05 level, the critical value of 1.697 is appropriate. This critical value represents the minimum t-value that must be obtained to reject the null hypothesis and conclude that there is a significant difference between the two dependent groups being compared.

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The central angle is solved and wheel turns while the car travels 2 meters is 5.5556 radians, and while the car travels 5 meters, it is 13.8889 radians

Given data ,

To find the angle (in radians) that the wheel turns while the car travels a given distance, we can use the formula:

Angle (in radians) = Distance / Radius

a)

For a distance of 2 meters (200 cm):

Angle (in radians) = 200 cm / 36 cm

Angle (in radians) = 5.5556 radians

b)

For a distance of 5 meters:

Angle (in radians) = 500 cm / 36 cm

Angle (in radians) = 13.8889 radians

Hence , the angle (in radians) that the wheel turns while the car travels 2 meters is approximately 5.5556 radians, and while the car travels 5 meters, it is approximately 13.8889 radians

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The exact value of cos 30 degrees is √3/2.

The exact value of sin 45 degrees is 1/√2 or √2/2.

The exact value of tan 30 degrees is 1/√3 or √3/3.

We have,

The exact value of cos 30 can be found using the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane.

On the unit circle, the angle of 30 degrees is measured counterclockwise from the positive x-axis and intersects the circle at a point where the x-coordinate is √3/2 and the y-coordinate is 1/2.

Therefore, Cos 30 is equal to √3/2.

The exact value of sin 45 can also be found using the unit circle. In this case, the angle of 45 degrees intersects the unit circle at a point where both the x-coordinate and y-coordinate are 1/√2.

Therefore, Sin 45 is equal to 1/√2, which can be simplified to (√2)/2.

The exact value of tan 30 can be found using the relationship between tangent and sine/cosine: tan x = sin x / cos x.

Therefore, tan 30 = sin 30 / cos 30.

From the unit circle, we know that sin 30 is equal to 1/2 and cos 30 is equal to √3/2. Substituting these values into the formula, we get,

tan 30 = (1/2) / (√3/2) = 1/√3 = √3/3.

Thus,

The exact value of cos 30 degrees is √3/2.

The exact value of sin 45 degrees is 1/√2 or √2/2.

The exact value of tan 30 degrees is 1/√3 or √3/3.

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The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.

Exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,

Exponential model is a mathematical function which express in the form of a = [tex]e^{x}[/tex] where, x is power and the function is increasing exponentially.

[tex]y = ab^{x}[/tex]

Where,

a=1.067905095,

b=1.501755837,

y = [tex]1.067905095(1.501755837 )^{x}[/tex]

Thus, for finding the number of subscriptions in 2003,

x = 3,

Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is

y = [tex]1.067905095(1.501755837 )^{3}[/tex] = 4

The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.

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The given question is incomplete the complete question is :

Answer:4

Step-by-step explanation:

Both function have same y - intercept.

The two given functions are;

x:     -3    -2   -1   0   1   2

f(x):   9      4  -1   0   1    4

And, g(x) = 5 cos (3x) - 5

Since, We know that;

The y-intercept occurs when x=0.

Therefore,

⇒ f(x) has a y-intercept of 0

(from given tabular data).

And, g(x) has a y-intercept of at x = 0

 g(0) = 5 cos (0) - 5

        = 5 - 5

        = 0

Hence, Both function have same y - intercept.

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Answer:

= 30 square inches.

Step-by-step explanation:

This pic is blurry.

This is a parallelogram. The formula for area is base x height. From your question, I'm guessing the dimensions are 5 inches and 6 inches.

area = 5 x 6 = 30 square inches

By algebra properties, the simplified form of the expressions are listed below in the following four cases:

Case 1: 6

Case 2: 1 / 5

Case 3: √3

Case 4: - 3

In this problem we must simplify expressions involving powers and roots by algebra properties, mainly power and root properties. Now we proceed to show how each expression is simplified:

Case 1

[tex](1^{3}+2^{3}+ 3^{3})^{\frac {1}{2}}[/tex]

[tex](1 + 8 + 27)^{\frac{1}{2}}[/tex]

[tex]36^{\frac{1}{2}}[/tex]

√36

6

Case 2

[tex]\left[\left(625^{-\frac{1}{2}}\right)^{-\frac{1}{4}}\right]^{2}[/tex]

[tex]\left[\left[\left(625^{\frac{1}{2}}\right)^{-1}\right]^{-\frac {1}{4}}\right]^{2}[/tex]

[tex]\left[\left(\frac{1}{25}\right)^{\frac{1}{4}}\right]^{2}[/tex]

[tex]\left(\frac{1}{25} \right)^{\frac{1}{2}}[/tex]

√(1 / 25)

1 / 5

Case 3

[tex]\frac{9^{\frac{1}{2}}\times 27^{- \frac {1}{3}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}[/tex]

[tex]\frac{(3^{2})^{\frac{1}{2}}\times (3^{3})^{-\frac{1}{3}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}[/tex]

[tex]\frac{3\times 3^{- 1}}{3^{\frac{1}{6}}\times 3^{- \frac{2}{3}}}\\[/tex]

[tex]\frac{1}{3^{-\frac{1}{2}}}[/tex]

[tex]3^{\frac{1}{2}}[/tex]

√3

Case 4

[tex]64^{-\frac{1}{3}}\cdot \left[64^{\frac{1}{3}}-64^{\frac{2}{3}}\right][/tex]

[tex]64^{-\frac{1}{3}}\cdot 64^{\frac{1}{3}}-64^{-\frac{1}{3}}\cdot 64^{\frac{2}{3}}[/tex]

[tex]1 - 64^{ \frac{1}{3}}[/tex]

1 - ∛64

1 - 4

- 3

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The probability that a randomly selected point within the circle falls in the red-shaded square is: 0.50

The formula for the area of a circle is:

A = πr²

where:

A is area

r is radius

Thus:

A = π * 4²

A = 50.265 unit²

Area of square = side * side

Area = 5 * 5

Area = 25 unit²

Thus:

P(selected area falls in the read square) = 25/50.265

P(selected area falls in the read square) = 0.497 ≈ 0.50

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Answer:

The percentage equivalent of 21/70 can be found by dividing 21 by 70 and then multiplying by 100 to convert to a percentage.

In order to find a percentage just divide two numbers  which the numerator divided by the denominator x 100 = to answer%

(21/70) x 100 = 30%

Therefore, the answer is 30%.

Answer:

it's a triangle

Step-by-step explanation:

Game theory is a branch of mathematics that deals with the study of decision-making in situations where two or more individuals or groups are involved.

It aims to predict the outcomes of these decisions by analyzing the strategies and incentives of each player. In the context of oligopoly, game theory helps us understand how firms interact and compete with each other in a market. Oligopoly is a market structure where a small number of large firms dominate the market. In this situation, firms must take into account the actions and reactions of their competitors when making decisions about pricing, production, and advertising. Game theory provides a framework for analyzing the strategic behavior of firms in an oligopolistic market. It helps us understand how firms may collude or engage in strategic behavior to gain an advantage over their competitors. It also provides insights into how changes in market conditions or government regulations can affect the behavior of firms in an oligopoly. I can say that visual aids and real-world examples can be helpful in understanding complex concepts like game theory. Video clips can be a great way to illustrate key ideas and make them more accessible to a wider audience. However, it is important to remember that game theory is a highly technical field and may require a significant amount of study and practice to fully grasp its concepts and applications.

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When two data sets are both symmetric, then the appropriate measure of center to describe them would be the mean.

The mean, also known as the average, is calculated by adding up all the values in the data set and dividing by the total number of values. It represents the "center" of the data because it balances out the values on both sides of the distribution.

The mean is a good measure of center for symmetric data sets because it captures the balance of the distribution and provides a single value that summarizes the data.

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Which measure of center should you use to describe two data sets that are both symmetric?

Answer:

476 cm²

Step-by-step explanation:

area of top rectangle = 20 X 7 = 140.

area of bottom rectangle = 12 X (10 + 6) = 12 X 16 = 192.

area of small triangle = 1/2 X 6 X (20 - 12) = 1/2 X 6 X 8 = 24.

area of large triangle = 1/2 X 10 X 24 = 120.

area of the figure = 140 + 192 + 24 + 120 = 476 cm²

i) Null hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is equal to 2/3.

Alternative hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is different from 2/3.

ii) Null hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is less than or equal to 9%. Alternative hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is greater than 9%.

iii) Null hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is less than or equal to 106°F. Alternative hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is greater than 106°F.

In hypothesis testing, the null hypothesis is the default assumption, while the alternative hypothesis is what the researcher wants to prove.

The next step is to conduct a hypothesis test, where a test statistic is calculated, and its probability of occurrence is determined assuming that the null hypothesis is true.

If this probability is very small (usually less than 5%), then the null hypothesis is rejected in favor of the alternative hypothesis.

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Complete Question

1. For the following scenarios, state the null hypothesis and the alternative hypothesis to be used when a hypothesis test is performed.

Scenario i) After the Cold War, it was claimed that two of three Americans say that the chances of world peace are seriously threatened by the nuclear capabilities of other countries. Is there evidence that this proportion is actually different? To investigate this, a random sample of 400 Americans was taken, and it was found that only 248 hold this view.

Scenario ii) JP wants to test whether at least 9% of gaming headsets have manufacturing flaws that make game-play impossible. A sample of 150 headsets revealed that 12 contained a defect.

Scenario iii) The mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe should be no more than 106°F. Past experience has indicated that the standard deviation of temperature is 2°F. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 99°F

The reciprocal of 20.95 to 4 decimal places using the table of reciprocals is 0.0478.

To find the reciprocal of 20.95, we can look up the reciprocal of 20.9 or 21 in the table and then interpolate to get a more accurate value for 20.95.

To interpolate, we can calculate the difference between 20.95 and 20.9, which is 0.05, and the difference between the reciprocals of 20.95 and 20.9, which is 0.00009.

Then we can use the formula:

reciprocal of 20.95 = reciprocal of 20.9 + (difference / interval) x (reciprocal of 21 - reciprocal of 20.9)

where interval is the difference between the numbers in the table (which is 0.1 in this case).

Thus:

reciprocal of 20.95 = 0.04784 + (0.05 / 0.1) x (0.04762 - 0.04784)

= 0.04784 + 0.025 x (-0.00022)

= 0.04784 - 0.0000055

= 0.0478345

In other words, the reciprocal of 20.95 to 4 decimal places using the tables of reciprocals is 0.0478.

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The probability that the mean battery life would differ from the population mean by greater than 18.4 minutes is 0.0148. The formula for the standard error of the mean is  SE = σ/√n

To solve this problem, we need to use the Central Limit Theorem (CLT) which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

The formula for the standard error of the mean is:

SE = σ/√n

Where SE is the standard error, σ is the population standard deviation, and n is the sample size.

In this case, we are given that the population standard deviation (σ) is 62 minutes, the population mean is 606 minutes, and the sample size (n) is 99 batteries. Therefore, the standard error of the mean is:

SE = 62/√99 = 6.231

Next, we need to find the z-score associated with the difference between the sample mean and the population mean of 18.4 minutes. The formula for the z-score is:

z = (x - μ) / SE

Where x is the sample mean, μ is the population mean, and SE is the standard error.

Substituting the values we have:

z = (606 + 18.4 - 606) / 6.231 = 2.96

Using a standard normal distribution table, we find that the probability of getting a z-score greater than 2.96 is 0.0148. Therefore, the probability that the mean battery life would differ from the population mean by greater than 18.4 minutes in a sample of 99 batteries is 0.0148, or about 1.48%.

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a.  We are 95% confident that the true average porosity of the seam is between 4.25 and 5.45.

b. We are 98% confident that the true average porosity of the seam is between 3.68 and 5.44.

c. A sample size of at least 14 is necessary.

d. A sample size of at least 138 is necessary.

a. To compute a 95% confidence interval for the true average porosity of a certain seam, we use the formula:

CI = x ± tα/2 (s/√n)

where x is the sample average porosity, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with n-1 degrees of freedom and α/2 probability (0.025 for a 95% confidence interval).

Substituting the given values, we get:

CI = 4.85 ± 2.093 (0.75/√20)

= (4.25, 5.45)

Therefore, we are 95% confident that the true average porosity of the seam is between 4.25 and 5.45.

b. To compute a 98% confidence interval for the true average porosity of another seam, we use the same formula as in part (a), but with a different t-value (2.602 for a 98% confidence interval).

Substituting the given values, we get:

CI = 4.56 ± 2.602 (0.75/√16)

= (3.68, 5.44)

Therefore, we are 98% confident that the true average porosity of the seam is between 3.68 and 5.44.

c. To find the necessary sample size for a 95% confidence interval with a width of 0.40, we use the formula:

n = (tα/2 (s/width))^2

Substituting the given values and solving for n, we get:

n = (1.96 (0.75/0.40))^2

= 13.55

Therefore, a sample size of at least 14 is necessary.

d. To find the necessary sample size for a 99% confidence interval with a width of 0.2, we use the same formula as in part (c), but with a different t-value (2.576 for a 99% confidence interval).

Substituting the given values and solving for n, we get:

n = (2.576 (0.75/0.2))^2

= 137.68

Therefore, a sample size of at least 138 is necessary.

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The standard equation of a hyperbola with a vertical transverse axis, centered at the origin, and values of a = 9 and b = 4 is y^2/81 - x^2/16 = 1.

The standard equation of a hyperbola centered at the origin with a vertical transverse axis is given by (y^2/a^2) - (x^2/b^2) = 1. In this case, we are given that a = 9 and b = 4, so substituting these values into the equation, we get:

(y^2/81) - (x^2/16) = 1

This is the standard equation of the hyperbola in question. It tells us that the center of the hyperbola is at the origin (0,0), the transverse axis is vertical (parallel to the y-axis), and the distance from the center to the vertices is 9 units (which is the value of a).

The distance from the center to the foci is given by c = sqrt (a^2 + b^2), which in this case is sqrt (81 + 16) = sqrt (97). The asymptotes of the hyperbola are the lines y = (a/b) x and y = -(a/b) x, which in this case are y = (3/4) x and y = -(3/4) x.

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The nth term of this geometric sequence is simply 5.5, regardless of the value of n.

The nth term of a geometric sequence with first term a1 and common ratio r is given by the formula:

an = a1 * r^(n-1)

In this case, the first term a1 is given as 5.5 and the common ratio r is 3/3 = 1. Therefore, the formula becomes:

an = 5.5 * 1^(n-1) = 5.5 * 1 = 5.5

So, the nth term of this geometric sequence is simply 5.5, regardless of the value of n.

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Thus, the joint probability of x=1 and y=2 is used to calculate the probability of y=4 is 0.06.

To calculate the probability of y = 4, we need to use the fact that x and y are independent. This means that the probability of y taking a certain value is not affected by the value of x.

Therefore, we can use the marginal probability of y, which is the sum of the joint probabilities of all possible values of y.

Let's start by finding the marginal probability of y. We can do this by summing the joint probabilities of y taking all possible values:

p(y=1) = p(x=0, y=1) + p(x=1, y=1) + p(x=2, y=1) = 0 + 0.12 + 0 = 0.12
p(y=2) = p(x=0, y=2) + p(x=1, y=2) + p(x=2, y=2) = 0.06 + 0 + 0.18 = 0.24
p(y=3) = p(x=0, y=3) + p(x=1, y=3) + p(x=2, y=3) = 0 + 0.12 + 0.36 = 0.48
p(y=4) = p(x=0, y=4) + p(x=1, y=4) + p(x=2, y=4) = 0 + p(x=1, y=2) + 0 = 0.06

Therefore, the probability of y=4 is 0.06.

In summary, the joint probability of x=1 and y=2 is used to calculate the probability of y=4, by using the fact that x and y are independent and finding the marginal probability of y.

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A sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.

To calculate the sample size required for this scenario, we need to use the formula for the sample size for a mean:
n = (z² * s²) / E²

where:
n = sample size
z = z-score for desired confidence level (95% = 1.96)
s = standard deviation (12 minutes)
E = desired margin of error (2 minutes)

Substituting in the values given, we get:
n = (1.96^2 * 12^2) / 2^2
n = 138.2976

We round up to the nearest whole number to get:
n = 139

Therefore, a sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.

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(a) ab l 1 bc l = ab + bc

(b) cd l 1 db l = cd - db

(c) db l 2 ab l = 2ab + db

(d) dc l 1 ca l 1 ab = -ab + ca + dc

In each of the given combinations of vectors, we need to add or subtract the given vectors.

In case (a), the vectors are parallel and have the same direction, so we can simply add them to get the resultant vector: ab + bc = ac.

In case (b), the vectors are also parallel and have opposite directions, so we can subtract them to get the resultant vector: cd - db = cb.

In case (c), we need to double the vector db and subtract it from vector ab to get the resultant vector: ab - 2db = ab - db - db = ac - db.

In case (d), we need to add vector dc and subtract vectors ca and ab to get the resultant vector: dc - ca - ab = db. Therefore, the resultant vectors are: (a) ac, (b) cb, (c) ac - db, (d) db.

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If factor a has r levels and factor b has c levels in a two-way ANOVA, we have a r x c factorial design.

In statistics, a factorial design is a study design where all possible combinations of levels of two or more independent variables (factors) are studied. In a two-way ANOVA, two factors are considered, and each factor has multiple levels.

For example, a two-way ANOVA can be used to study the effect of fertilizer type and watering frequency on plant growth, where fertilizer type has three levels and watering frequency has two levels. The resulting design is a 3x2 factorial design.

The number of treatments (unique combinations of levels of factors) in a factorial design is equal to the product of the number of levels of each factor. The advantage of a factorial design is that it allows for the investigation of interactions between factors, which cannot be detected in a one-way ANOVA.

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After considering all the given options we conclude that the standard error of the mean is 1.80, which is Option A under the condition that the mean is x = 40.0 minutes and the standard deviation is s = 56.9 minutes.

The formula derived for standard error of the mean (SEM) is expressed as:

SEM = σ/√n

Here,

SEM = standard error of the sample,

σ = sample standard deviation

n = sample size.

For the given  case, we have x = 40.0 minutes and s = 56.9 minutes for a sample size of 1000 employed adults in Chicago. Therefore,

SEM = s/√n

   = 56.9/√1000

   ≈ 1.80

Therefore, the answer is A) 1.80.

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The complete question

A study of commuting times reports the travel times to work of a random sample of 1000 employed adults in Chicago. The mean is x = 40.0 minutes and the standard deviation is s = 56.9 minutes.

What is the standard error of the mean?

A) 1.80

B) 21.88

C) 6.99

D) 1.09

The painter can spend up to 4.5 hours painting each bedroom if he wants to finish painting the living room and both bedrooms within 16 hours.

If the painter has 16 hours in total, and he already spent 7 hours painting the living room, then he has 16 - 7 = 9 hours left to paint the two bedrooms.

If he wants to split his time equally between the two bedrooms, then he can spend x hours on each bedroom. Therefore, the total time spent painting the bedrooms would be 2x.

To find the maximum amount of time he can spend on each bedroom, we need to solve the following inequality:

2x ≤ 9

Dividing both sides by 2, we get:

x ≤ 4.5

Therefore, the painter can spend up to 4.5 hours painting each bedroom if he wants to finish painting the living room and both bedrooms within 16 hours.

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The slopes are not equal (7/6 ≠ 7/2), we can conclude that the segments CD and AB are not parallel in triangle ABCDE.

To verify that the segments CD and AB are parallel in triangle ABCDE, we need to show that the corresponding sides have the same slope.

Let's first find the slope of segment CD. Given that point C is the origin (0,0) and point D has coordinates (EC, ED) = (12, 14), the slope of CD can be calculated as follows:

slope_CD = (ED - 0) / (EC - 0)

= 14 / 12

= 7 / 6

Now, let's find the slope of segment AB. Given that point A is the origin (0,0) and point B has coordinates (CA, DB) = (4, 42/3), the slope of AB can be calculated as follows:

slope_AB = (DB - 0) / (CA - 0)

= (42/3) / 4

= (14/1) / (4/1)

= 14 / 4

= 7 / 2

If the slopes of CD and AB are equal, then the segments are parallel. Let's compare the slopes:

slope_CD = 7 / 6

slope_AB = 7 / 2

Since the slopes are not equal (7/6 ≠ 7/2), we can conclude that the segments CD and AB are not parallel in triangle ABCDE.

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The x and y intercept of the equation is (8,12)

A linear equation is an algebraic equation of the form y=mx+b. It involves only a constant and a first-order term, where m is the slope and b is the y-intercept.

For 3x +2y = 24

we need to put it to the standard form

2y = 24 - 3x

divide both sides by 2

y = 12 - 3/2x

Here b is 12 and m is -3/2

therefore the y intercept is 12

when y = 0

0 = 12 -3/2 x

3/2 x = 12

3x = 24

divide both sides by 3

x = 24/3 = 8

therefore the x intercept is 8

The x and y intercept of the equation is ( 8,12)

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Answer:

The lines are the same. (Infinite Solutions)

Step-by-step explanation:

To solve this, we need to get either x or y to cancel out and equal 0 first.

Let's look at our two equations.

4x-5y=(-2)

-8x+10y=4

I'm going to divide the -8x by 2. Remember when dividing to divide both sides of the equation, otherwise you will end up with something completely different than what you started out with.

-8x+10y=4 (divided by 2)

Our new equation is -4x+5y=2.

Now let's take our other equation. Please see the screenshot to see how this is solved.

Forgive the horrible handwriting, I'm on a computer :(