Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.

A′(−4, −1), B′(0, 1), C′(−2, −4)
A′(−4, 7), B′(0, 9), C′(−2, 4)
A′(0, 3), B′(4, 4), C′(3, 0)
A′(−8, 7), B′(−4, 9), C′(−6, 4)

Answer:

-cd+3c+8d

Step-by-step explanation:

4cd - 5cd + 3c + 8d

Combine like terms

(4cd - 5cd) + 3c + 8d

-cd+3c+8d

Answer:

3c + 8d - cd

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 4cd - 5cd + 3c + 8d

Let's simplify the expression,

→ 4cd - 5cd + 3c + 8d

→ 3c + 8d + 4cd - 5cd

→ (3c) + (8d) + (4cd - 5cd)

→ 3c + 8d + (-cd)

→ 3c + 8d - cd

Hence, answer is 3c + 8d - cd.

The length of the shadow of the second pole is 75 meters, was solved by using the concept of similar triangles.

The concept of similar triangles is based on the idea that if two triangles have the same shape but different sizes, they are called similar triangles. This means that their corresponding angles are equal and their corresponding sides are in proportion.

A triangle is a 2-dimensional geometric shape with three sides, three angles, and three vertices. It is one of the basic shapes in geometry and is used to describe many real-world objects and phenomena.

In the given question,

Length of shadow of first pole / Height of first pole = Length of shadow of second pole / Height of second pole

Substituting the given values, we get:

20√3 / 20 = x / 25√3

Simplifying, we get:

x = (20√3 / 20) * 25√3

x = 25*3

x = 75

Therefore, the length of the shadow of the second pole is 75 meters.

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The calculated value of the angle x is 58 degrees

from the question, we have the following parameters that can be used in our computation:

The triangle

Using the sum of opposite external angles, we have the following equation

114 = 56 + x

When the like terms are evaluated, we have

x = 114 - 56

Evaluate

x = 58

Hence, the value of x is 58

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Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.

An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.

Proof:

Since mXOY = mWOV, we can form the following equations:

m--YZ = m--ZW (Given)

Subtract both sides of the equation by m to get:

YZ = ZW

Then, multiply both sides of the equation by X to get:

XZ = XW

Now, substitute Y for V and W for V in the equation to get:

XZ = ZV

Finally, subtract both sides of the equation by m to get:

m--XZ = m--ZV

Therefore, m--XZ = m--ZV.

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the speed of the car was 5.33 meters per second. Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places) .

a. To find the speed of the car, we use the formula

Speed = Distance / Time

If the car raced 8 meters in 1.5 seconds, we can substitute these values in the formula to get:

Speed = 8 / 1.5 = 5.33 meters per second (rounded to two decimal places)

Therefore, the speed of the car was 5.33 meters per second.

b. The record time of 10 meters in 2.32 seconds gives us a speed of:

Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places)

Comparing this to the speed of the car that raced 8 meters in 1.5 seconds, we see that the car that raced 8 meters was faster, with a speed of 5.33 meters per second compared to the record time of 4.31 meters per second. This suggests that the car that raced 8 meters was well-designed and well-built, and was able to travel a greater distance in a shorter amount of time.            

It is important to note, however, that one data point is not enough to draw a firm conclusion about the superiority of one car over another. It is possible that the car that raced 8 meters had a lucky run, or that the car that set the record had a mechanical issue or was not driven to its full potential. To truly compare the performance of different cars, we would need to collect data from multiple trials and multiple cars, and analyze the data using statistical methods to determine which cars consistently perform better.

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Answer:

First, we need to calculate the daily interest rate on the credit card. We can do this by dividing the annual percentage rate (APR) by the number of days in a year:

Daily interest rate = APR / 365

Daily interest rate = 0.2445 / 365

Daily interest rate = 0.00067 or 0.067%

Next, we can calculate the interest that will accrue over the course of one month, which is approximately 30 days:

Interest = Balance * Daily interest rate * Number of days

Interest = $1,359 * 0.00067 * 30

Interest = $27.42

Adding the interest to the outstanding balance, we get:

Balance after one month = $1,359 + $27.42

Balance after one month = $1,386.42

Therefore, the balance on the credit card after one month will be approximately $1,386.42.

The expression that best represents the total cost of the charter bus for the field trip is 12n + 50

The total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.

If n represents the number of students going on the field trip, then the expression for the total cost can be written as:

Total cost = 12n + 50

This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.

The fixed cost of $50 is added to the variable cost to give the total cost.

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Answer:

The answer to your problem is 53 in ^2

Hope it helps

Answer:

“change” or “the change”

Step-by-step explanation:

Answer:

infinitely many solutions

Step-by-step explanation:

When you put the equations in desmos, the lines are the same therefore it has infinitely many solutions.

Answer:

✔️ c) infinitely many

Step-by-step explanation:

Answer:

1 ft per 4 seconds

120 seconds

72 seconds

Step-by-step explanation:

Answer:

negative linear association

Step-by-step explanation:

The best description of the association between life expectancy and infant mortality rate in the given graph is option B. Countries with higher infant mortality rates tended to have shorter life expectancies.

The negative linear association between life expectancy and infant mortality rate in the attached graph,

Life Expectancy,

Life expectancy refers to the average number of years a person is expected to live from birth.

In the graph, life expectancy is represented on the vertical axis (y-axis).

Infant Mortality Rate,

Infant mortality rate refers to the number of deaths of infants under one year of age per 1,000 live births.

In the graph, the infant mortality rate is represented on the horizontal axis (x-axis).

Negative Linear Association,

A negative linear association means that as one variable increases, the other variable tends to decrease at a consistent rate.

here, as the infant mortality rate increases (moving right on the x-axis), the life expectancy tends to decrease (moving down on the y-axis).

Interpretation,

Looking at the graph, we can see that countries with higher infant mortality rates are positioned towards the right side of the graph,

and they tend to have shorter life expectancies, which are positioned towards the bottom of the graph.

Conversely, countries with lower infant mortality rates are positioned towards the left side of the graph, and they tend to have longer life expectancies,

which are positioned towards the top of the graph.

Implication,

The negative linear association in the graph indicates that countries with higher rates of infant mortality are likely to have lower life expectancies.

This is because higher infant mortality rates often indicate poorer healthcare systems, lower living standards,

and other factors that can impact life expectancy negatively.

Therefore, based on the graph's trend, we can conclude that the statement B is the best description of the association between life expectancy and infant mortality rate.

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The above question is incomplete , the complete question is :

The Graph Below Shows The Relationship Between Life Expectancy And Infant Mortality Rate In A Random Sample Of Countries.

Which statement is the best description of the association between these variables? Choose all that apply.

A. Countries with higher infant mortality rates tended to have longer life expectancies.

B. Countries with higher infant mortality rates tended to have shorter life expectancies.

C. There is no clear relationship between infant mortality rates and life expectancy.

Attached graph.

Answer:

126305.622 is the town's population after 2 years on percentage  7.4.

Step-by-step explanation:

Answer:

you will asume this rate is constant. so put it into y=mx+b form y=1.74*2+109,500

Step-by-step explanation:

The value of any number raised to the power of 0 is always 1, irrespective of the value of x, as long as x is not 0. So, x^0 = 1.

From the given information provided, the value of fog(3) and fog(4) is 0.971 and 27/40 respectively.

a) To find fog(3), we first need to find g(3) and then evaluate f(g(3)).

To find g(3), we substitute x=3 into the formula for g(x):

g(3) = (5(3) - 2)/(3 + 2) = 13/5

Now, we can evaluate f(g(3)) by substituting g(3) into the formula for f(x):

f(g(3)) = f(13/5) = 3(13/5)² / (4(13/5)² + 4) = 0.971

Therefore, fog(3) = 0.971.

b) To find fog(4), we follow the same process. First, we find g(4):

g(4) = (5(4) - 2)/(4 + 2) = 18/6 = 3

Now, we can evaluate f(g(4)) by substituting g(4) into the formula for f(x):

f(g(4)) = f(3) = 3(3)² / (4(3)² + 4) = 27/40

Therefore, fog(4) = 27/40.

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The intersection points of the two conics are therefore[tex](1 + √14, -1 + √14)[/tex]and [tex](1 - √14, -1 - √14).[/tex]Hence, the two conics intersect at two points.

The point or points of intersection and the number of places the following 2 conic intersect is to be determined. The system over the real numbers for [tex]x² + y² = 34 and 3x - 3y = 6[/tex] is to be solved.

To determine how many points the following 2 conic intersect at, the two equations must be solved simultaneously. The points of intersection can then be determined by substituting the value of x or y into the other equation and solving for the remaining variable.The equation 3x - 3y = 6 is the equation of a straight line. Solving the equation for y, [tex]y = x - 2[/tex].

So the line passes through the point (0, -2) and (2, 0) on the x-axis. Now, substitute the value of y into the equation x² + y² = 34 to get[tex]x² + (x - 2)² = 34[/tex], expanding this gives 2x² - 4x - 26 = 0, which simplifies to x² - 2x - 13 = 0.The solution to the quadratic equation [tex]x² - 2x - 13 = 0[/tex] is given as[tex]x = 1 + √14, 1 - √14[/tex]. The corresponding value of y for each x can be calculated by substituting the value of x into the equation y = x - 2.

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It will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.

The container has 6 cups of oatmeal and Stella eats 1/4 cup every day for breakfast.

To find the number of days it will take Stella to finish all the oatmeal, we can use the formula:

Total amount of oatmeal in the container = 6 cups

Amount of oatmeal consumed by Stella per day = 1/4 cup

Therefore, it will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.

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The action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.

Part D: When the membrane potential of a neuron begins returning to normal, resting levels, the cell membrane experiences hyperpolarization.

During hyperpolarization, the membrane potential becomes more negative than the resting potential, making it more difficult to trigger an action potential.

Part E: Saltatory conduction allows for faster and more efficient conduction because action potentials are confined to the Nodes of Ranvier.

The Nodes of Ranvier are small gaps in the myelin sheath that covers the axon of some neurons. Because the myelin sheath insulates the axon, action potentials can only occur at the nodes, where the membrane is exposed. This means that the action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.

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Step-by-step explanation:

Lets assume this is a right triangle.

If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.

If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)

we get the length of the slide is 21.2 meters.

The percentage of rents between $1,300 and $1,720 is 34.13%.

To calculate this, we need to use the z-score formula to convert the rent range into a z-score range. The z-score formula is (x-μ)/σ, where x is the rent range, μ is the mean rent and σ is the standard deviation.

To calculate the lower z-score, the formula becomes (1300-1510)/210 = -1.19.

To calculate the higher z-score, the formula becomes (1720-1510)/210 = 1.14. The z-score of -1.19 to 1.14 corresponds to 34.13% according to the z-table. Therefore, 34.13% of rents are between $1,300 and $1,720.

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Answer:

[tex]y=3cos(3\pi x)+4[/tex]

Step-by-step explanation:

[tex]f(x)=cos(x)\\[/tex]

[tex]A(f(Bx+C)+D)[/tex]

The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.

[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]

[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]

I hope this helps

Answer:

(-2,-3)  

Step-by-step explanation:

3x+y=-9                      

-3x    -3x

y=-3x-9

5x-3(-3x-9)=-1

14x+ 27= -1

-27      -27

14x= -28

/14    /14

x=-2

plug in x    

3(-2)+y=-9  

    -6+y=-9

     +6    +6

          y=-3

The lines which are parallel are given below :

Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.

Line b is parallel to line f  because they both have a pair of alternate angles that are congruent which is 89.5 degrees and 90.5 degrees.

Line b is parallel to line d because they both have a pair of alternate angles that are congruent at 89.5 degrees.

Line c is parallel to line e because they both have a pair of alternate angles that are congruent at 91.5 degrees.

Line c is parallel to line d because they both have a pair of alternate angles that are congruent: 89.5 degrees.

Line d is parallel to line f since they have corresponding angles of 89.5 degrees and 90.5 degrees, respectively

Therefore, the correct answer is :

Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.

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Answer:14

Step-by-step explanation: I added 3 + 5 + 2 + 4 + 1 which gave me 15 and her daughter took 1 fruit so it is 14 fruits left

An American rapper, is known for his poetic, and complex lyrical style.

Kendrick Lamar is a highly talented storyteller, however, some people may not like his music when he raps quickly as it can be unpleasant.What are the aspects of Kendrick Lamar's music?

An American rapper, is known for his highly poetic, socially conscious, and complex lyrical style.

However, his musical talent has been highly praised by critics and   audiences alike.

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The set of ordered pairs (2,1), (3,3), (4,6), (2,3) is NOT a function because the input value of 2 corresponds to both the output values of 1 and 3.

For a set of ordered pairs to be a function, each input (x-value) must correspond to only one output (y-value). Therefore, if there exists an input (x-value) that corresponds to more than one output (y-value), then the set of ordered pairs is NOT a function.

Let's check each set of ordered pairs:

Therefore, the set of ordered pairs that is NOT a function is (2,1), (3,3), (4,6), (2,3).

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The distance from point A to point B is approximately 1363.7 feet.

Using slope concept:

tan(θ1) = h/d

tan(θ2) = h/(d+x), where x is the distance from point A to the boat when Dominic measured the angle of depression at point B.

We can rearrange these equations to solve for h and x:

h = d*tan(θ1)

h = (d+x)*tan(θ2)

d*tan(θ1) = (d+x)*tan(θ2)

d*(tan(θ1)-tan(θ2)) = x*tan(θ2)

d = x*tan(θ2)/(tan(θ1)-tan(θ2))

Substituting the given values, we get:

d = x*tan(32°)/(tan(6°)-tan(32°))

Using a calculator, we can evaluate this expression to get:

d ≈ 1363.7 feet

Therefore, the distance from point A to point B is approximately 1363.7 feet.

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This is impossible because the third column does not depend on the first two columns.

The third column's values are linear combination of the first two columns. the third column of the matrix as a linear combination of the first two columns, This can be seen by the fact that the third column has values which don't fit the pattern of the first two columns. For example, the first value in the third column (21) is not equal to an any linear combination of the first two columns. Thus, it is impossible to write the third column as a linear combination of the first two columns.

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Unpacking the expression we have,

[tex](\sqrt{x})(\sqrt[4]{x})[/tex]

Its better to work with this in terms of exponents so we rewrite the expression as [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}[/tex]. (cause [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]) This can be a little tricky when learning it for the first time.

Then by the exponent sum rule  [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}=x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex] (more straightforward, you probably know this from class).

I assume this is what you mean by rational exponent form. But you could also write it as [tex]\sqrt[4]{x^3}[/tex].

The probability that the arborist will break a saw chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking is 0.007

We are given the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw.

The time that he spends on each saw are 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking.

Let us find the probability that he will break a chain when he uses the small climbing saw.

P(small climbing saw) = 1/2P(Break a chain using small climbing saw) = 0.004

Using the medium limbing saw: P(medium limbing saw) = 3/8P(Break a chain using medium limbing saw) = 0.008

Using the large felling and bucking saw: P(large felling and bucking saw) = 1/8P(Break a chain using large felling and bucking saw) = 0.04

Now, to find the probability that he will break a chain on a day, we use the weighted average. Probability is a weighted average because the probability of breaking the saw chain is different for each saw that he uses.

Hence, the probability that he breaks a saw chain when he uses each saw is weighted according to how much time he spends on that saw.

P = P(small climbing saw)* P(Break a chain using small climbing saw) + P(medium limbing saw) * P(Break a chain using medium limbing saw) + P(large felling and bucking saw) * P(Break a chain using large felling and bucking saw)P = (1/2 * 0.004) + (3/8 * 0.008) + (1/8 * 0.04)P = 0.007

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