12. Triangle ABC is shown on the coordinate plane. If it is translated 4 units to the left and 3
units up, what are the coordinates of the vertices of the image?


A. A (1.1), B'(6,0), C (1.4)
B. A'(-1,1), B'(0,6), C (-4,-1)
C. A' (1.-1), B'(6,0). C'(-4,1)
D. A'(-1,-1), B'(0.6), C'(4-1)

Answer: 40 degrees

Step-by-step explanation:

Answer:

A'(-8,6)

B'(6,4)

C'(-8,0)

Step-by-step explanation:

 Since this transformation is a violation we can we can use the skill factor to multiply both the x-coordinate and the Y And the Y coordinate of the Of the point to make sure that everything is consistent and that the figures stay similar.

No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

Learn more about no solution equation at https://brainly.com/question/14603452.

#SPJ4

Step-by-step explanation:

Step-by-step explanation:

25 (divided by 5) 5

__ = __

40 (divided by 5) 8

\(|\Omega|=25+15=40\\|A|=25\\\\P(A)=\dfrac{25}{40}=\dfrac{5}{8}=62.5\%\)

Answer:

put a dot on the following points ( -1, -3) (0, -2) (1, -1) and (2, 0)

Step-by-step explanation:

Two ratios are equivalent if they have the same value. Therefore, 16:36 is equivalent to 2:4, 8:18, and 4:9 since all three have the same value of 0.4444 when expressed as a decimal or 4/9 when expressed as a fraction.

A ratio is a mathematical expression that compares two values. It is expressed as a fraction in the form of a:b, where a and b are the two values being compared. The ratio 16:36 is equivalent to 2:4, 8:18, and 4:9.The ratio 16:36 can be expressed as a fraction as 16/36. This fraction can be simplified by dividing both the numerator and denominator by 4, resulting in 4/9.Since every ratio can be expressed as a fraction, it can also be expressed as a decimal. A decimal is a way of representing a fraction in a base ten system. To convert the fraction 16/36 to a decimal, divide 16 by 36. This result is 0.4444, which can be expressed as 4/9.Finally, two ratios are equivalent if they have the same value. Therefore, 16:36 is equivalent to 2:4, 8:18, and 4:9 since all three have the same value of 0.4444 when expressed as a decimal or 4/9 when expressed as a fraction.Finally, we can use the concept of equivalent fractions to find another equivalent ratio. Since 16:36 is a fraction, we can find an equivalent fraction by multiplying both terms by the same number. For example, if we multiply both terms by 3, our new ratio is 48:108, which is equivalent to 16:36. In summary, three equivalent ratios to 16:36 are 4:9, 32:18, and 48:108.1. 16:36 = 8:18

Divide each side by 8:

16/8 = 2

36/8 = 4.5

Ratio = 2:4.5

2. 16:36 = 4:9

Divide each side by 4:

16/4 = 4

36/4 = 9

Ratio = 4:9

3. 16:36 = 2:4.5

Divide each side by 2:

16/2 = 8

36/2 = 18

Ratio = 8:18

Learn more about ratio here:

https://brainly.com/question/29467965

#SPJ1

Step-by-step explanation:

(9.16 * -30)= -27.48

(5.5 x 160)° 880

Hey there! :)

Answer:

x = 12.

Step-by-step explanation:

Given:

\(\frac{3}{5} = \frac{x}{20}\)

Cross multiply to solve for x:

3 · 20 = 5 · x

60 = 5x

Divide by 5:

12 = x.

Answer:

so x=12

Step-by-step explanation:

\(\frac{3}{5}=\frac{x}{20}\\ by cross multiplication\)

3×20=5×x

60=5x

dividing 5 on both sides

60/5=5x/5

x=12

i hope this will help you :)

Step-by-step explanation:

if x and y vary directly, they are defined as

y = kx

with k being a constant for all x.

now, if they vary inversely, they are defined as

y = k/x

so,

6/5 = k/4

24/5 = k

y = f(x) = 24/5 / x = 24/(5x)

f(7) = 24/(5×7) = 24/35

when x = 7, y = 24/35

When x and y vary inversely, their product is always a constant, k. In this case, we know that x = 4 and y = 6/5, so we can use this information to find the value of k:

k = xy = (4)(6/5) = 24/5

The function that models this inverse variation is:

xy = k

We can find y when x = 7 by substituting this value into the equation and solving for y:

xy = k

(7)y = 24/5

y = 24/5*(1/7)

y=24/35

So when x = 7, y = 24/35.

To learn more about inverse variation:

brainly.com/question/11592410

Answer:

Just multiply the exponents of the numbers

So this is the order from top to below and I'll mark as 1 to 5

2

1

4

5

3

Answer:

1 ton=2,000 pounds so 6,700 pounds

Step-by-step explanation:

The 7th term of the sequence is 48.

Sequence is an ordered arrangement of elements. It is often used to refer to a series of related events, or occurrences, which take place in a logical order. This order can be used to describe a process, a set of instructions, or a mathematical pattern. In mathematics, a sequence is a collection of numbers or other objects that follow a certain pattern or order. Common examples of sequences include the Fibonacci sequence, the prime numbers, and the geometric sequence.

This can be found by calculating the difference between each pair of terms, which is 6, and then adding 6 to each successive term.

Therefore, the 7th term is 27 + 6 = 33, and 33 + 6 = 39, and 39 + 6 = 45, and 45 + 6 = 51, and 51 + 6 = 57, and 57 + 6 = 63, and 63 + 6 = 69. Rounded to the nearest integer, the 7th term is 48.

To know more about sequence click-
https://brainly.com/question/6561461
#SPJ1

Answer:

There will be 24 boys, 32 -8 = 24

Step-by-step explanation:

In the class there is 20 boys.

All these are alzebraic expressions. A monomial consists of only one term, binomial contains two terms and a polynomial is when the number of terms is two or more than two.

In the given question

There are 8 more boys than girls in a class of total 32 students

let the number of girls be x according to the given data boys will be (x + 8)

∴ {x + (x+8)} = 32

 2x + 8 = 32

 2x = 24

   x = 12

∴ the no. of girls = 12 and no. of boys = 12+8 = 20.

Learn more about Polynomials here :

https://brainly.com/question/4420925

#SPJ5

For the hole in the above triangular, the area that we need is the area of the rectangular hole i.e length times breadth that is 3 × 2 = 6

Hence, 6 sq. ft. carpet will be needed

Answer:

the answer is 9 inches

360/10=36

36*.25 =9

Answer:

6.148

Step-by-step explanation:

Answer:

See graph below

Step-by-step explanation:

The equation r=5cosθ basically means the graph is going to be a circle with a radius of 5/2=2.5 to the right on the horizontal axis since it's cosine.

To graph the function r=5cosθ, we graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ and a radius of 2.5

The function is given as:

r=5cosθ

The above means that, we want to graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ.

The radius r is calculated using;

r = 5/2

r = 2.5

Hence, the graph of r=5cosθ has a radius of 2.5

Read more about polar curves at:

https://brainly.com/question/9363127

The critical value for the left-tailed test is −2.0537.

For a left-tailed test, when α=0.02, the critical z-value is the value on the horizontal axis of the z- or standard normal distribution curve such that the area under the curve to the left of this critical value is 0.02.

Using a standard normal distribution table,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

There are two z-score tables which are:

Now 0.5-α=0.5-0.02

=0.48

So 0.48 is closest in z score table is z=2.05

The left-tailed critical value always negative(-).

So, the value is -2.05.

For more such questions on normal distribution table

https://brainly.com/question/23864730

#SPJ4

The repairs have indeed changed the nature of the output of the machine, with an overall improvement in the quality of the parts produced.

To determine if the repairs have changed the nature of the output of the machine, we can compare the percentages of excellent, good, and unacceptable parts before and after the repairs.

Before repairs:
- 80% excellent
- 16% good
- 4% unacceptable

After repairs, we can calculate the percentages based on the sample of 200 parts:
- 157 excellent parts: (157/200) * 100 = 78.5% excellent
- 42 good parts: (42/200) * 100 = 21% good
- 1 unacceptable part: (1/200) * 100 = 0.5% unacceptable

Comparing these percentages, we can see that the output has changed after the repairs:
- Excellent parts decreased from 80% to 78.5%
- Good parts increased from 16% to 21%
- Unacceptable parts decreased from 4% to 0.5%

Learn more about percentage:

https://brainly.com/question/24877689

#SPJ11

Answer:

B

Step-by-step explanation:

As per the given conditions the probability of having exactly one head in all the flips is 7/8.

To find the probability of exactly one head in all the flips, we need to consider the possible outcomes and calculate their probabilities.

There are two cases to consider:

Case 1: The first coin flip results in heads (H).

In this case, two additional coins are flipped, and we want exactly one head among the three flips. The possible outcomes are  HHT, HTH, and THH. Each outcome has a probability of \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{8}\)

So, the probability of exactly one head in this case is \(3*\frac{1}{8}= \frac{3}{8}\).

Case 2: The first coin flip results in tails (T).

In this case, only one additional coin is flipped, and we want exactly one head among the two flips. The possible outcomes are TH and HT. Each outcome has a probability of \(\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\)

So, the probability of exactly one head in this case is  \(2 * \frac{1}{4}=\frac{1}{2}\).

To find the overall probability, we sum the probabilities from both cases:

\(P(exactly\: one \:head) = P(Case 1) + P(Case 2) =\frac{3}{8} + \frac{1}{2}= 7/8\).

Therefore, the probability of having exactly one head in all the flips is 7/8.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

As a decimal rounded to the nearest thousandth, the probability is approximately 0.111. So, P(number that is divisible by 4, number that is divisible by 4) = 0.111

To determine the theoretical probability of rolling a number that is divisible by 4 two times in a row, we can first find the probability of rolling a number divisible by 4 in a single roll, and then square it.

In a single roll of a standard six-sided die, there are 2 numbers that are divisible by 4 (4 and 8). Since there are 6 possible outcomes in each roll, the probability of rolling a number divisible by 4 is 2/6, which simplifies to 1/3.

Now, to find the probability of rolling a number divisible by 4 two times in a row, we can square the probability from a single roll: (1/3) * (1/3) = 1/9.

To learn more about : decimal rounded

https://brainly.com/question/29123526

#SPJ11

Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

\(d = \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1 })^{2} }\)

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

Answer:

x=4/7

Step-by-step explanation:

Change mixed fractions to improper fractions

2 1/4 = 9/4

1 2/7 =9/7

Therefore, we have

9/4=9/7÷x

9/7÷x is 9/7×1/x=9/7x

Then, we have

9/4=9/7x

Cross multipy

9×7x=9×4

63x=36

Make x the subject of the formula, we have

x=36/63

x=4/7

The given system of differential equations can be written using matrices as follows:

X' = AX + B,

where X = [x, y, z] is the vector of variables, X' represents the derivative of X with respect to some independent variable, A is the coefficient matrix, and B is the constant matrix.

In this case, the coefficient matrix A is [[1, 2, 0], [0, 0, 2], [4, -4, 0]], and the constant matrix B is [-2, 1, 52].

To solve the system, we can find the eigenvalues and eigenvectors of the coefficient matrix A.

These eigenvalues and eigenvectors help in diagonalizing the coefficient matrix, allowing us to solve the system using the diagonalized form.

Once we have the diagonalized form, we can solve each equation individually to obtain the solutions for x, y, and z. Finally, we combine these solutions using linear combinations to form the general solution for the system.

However, without specific eigenvalues, eigenvectors, or initial conditions, it is not possible to provide the numerical solution.

If you have the eigenvalues, eigenvectors, or initial conditions, please provide them, and I can assist you in solving the system using the given matrices.

To know more about differential equations refer here:

https://brainly.com/question/2273154#

#SPJ11

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

To know more about area,

https://brainly.com/question/31479047

#SPJ11

Answer:

B

Step-by-step explanation:

44/77

=0.55

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.

Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :

Number of Compressor Failures Probability (Relative Frequency)

0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.

We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.

As a result, there will be a total of 20 values of X, each representing a year's worth of data.

We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.

The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.

Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.

It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.

Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.

These results are then used to generate probability distributions of potential results.

In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.

1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.

2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.

3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable

4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.

5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.

6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.

After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Know more about probability, here:

https://brainly.com/question/31828911

#SPJ11