On a coordinate plane, 2 right triangles are shown. The first triangle has points A (negative 1, 3), B (negative 1, 1), C (3, 1). The second triangle has points A prime (2, negative 2), B prime (2, negative 4), C prime (6, negative 4).
Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options.

The rule for the translation can be written as T–5, 3(x, y).
The rule for the translation can be written as T3, –5(x, y).
The rule for the translation can be written as
(x, y) → (x + 3, y – 3).
The rule for the translation can be written as
(x, y) → (x – 3, y – 3).
Triangle ABC has been translated 3 units to the right and 5 units down.

Answer:

this is true, I think so...

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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C. 0.42 I did this right before the pandemic

Answer:

Step-by-step explanation:

2(2x +4) - 2x = x + 18

4x +8 -2x = x +18

2x -x = 18-8

X = 10

Put the value of x in both side

Left side *+*+*+*+*+

2 ( 2*10+4)-2*10

48-20 = 28

Right side +*+*+*+*+*

X + 18

10+ 18 = 28

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Answer:

y = 4

Step-by-step explanation:

8(y + 4) - 2(y - 1) = 70 - 3y ← distribute parenthesis and simplify left side

8y + 32 - 2y + 2 = 70 - 3y

6y + 34 = 70 - 3y ( add 3y to both sides )

9y + 34 = 70 ( subtract 34 from both sides )

9y = 36 ( divide both sides by 9 )

y = 4

Answer: How do you find you four consecutive odd integers such as three times the sum of the first and the second is 15 less than the fourth?

Step-by-step explanation: So, the normal consecutive integers numbers are: 2,3,4,5. And the even consecutive integers numbers are: 2,4,6,8. And the odd consecutive integers are: 3,5,7,9. Consecutive integers formula are the algebraic representations of the consecutive integers. The formula to get a consecutive integer is n + 1.

Same as above, 7 is one of 4 consecutive integers, then the result is only 4 cases:

, 5, 6, 7

, 6, 7, 8

, 7, 8, 9

, 8, 9, 10

Hope this helps.

a) a minimum of 3 doctors required so that at least 70% of the arriving patients.

b) a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes

a) Minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately

Formula used:

The number of patients arriving in an hour: λ = 9

Treatment time: μ = 6 minutes

Per the Little’s law, the waiting time is proportional to the average number of patients present at any given time.

λ/μ is the average number of patients present at any given time.

If there are k servers present in the ER, the number of patients they can serve is given by kμ.

Hence, the percentage of patients who have to wait is given by:

Percentage of patients waiting = λ / (kμ + λ)

Percentage of patients receiving treatment immediately = kμ / (kμ + λ)

Thus, we can now form an equation as:

kμ / (kμ + λ) ≥ 0.7

=> kμ / (kμ + 9) ≥ 0.7

=> k ≥ 3 doctors (Approximately)

Therefore, a minimum of 3 doctors required so that at least 70% of the arriving patients can receive treatment immediately.

b) Minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised

The percentage of patients who have to wait = λ / (kμ + λ)

Again, let us use the Little's law to find the average time patients spend waiting in the queue, which is equal to

λ / (k(μ - λ/k)).

We are given that the waiting time should not be more than 30 minutes, which can be converted to 0.5 hours.

Thus:

λ / (k(μ - λ/k)) ≤ 0.5

=> 9 / (k(0.1 - 1/k)) ≤ 0.5

=> 18 ≤ k(0.1 - 1/k)

=> 0.1k - 1 ≤ 18/k

=> 0.1k² - k - 18 ≥ 0

Using the quadratic formula, the solution is k = 6.66, which is rounded up to 7, and k = 2.5, which is rounded up to 3.

Therefore, a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes as advertised and a minimum of 3 doctors are required so that the average time a patient waits for treatment is no more than 15 minutes.

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Open questions:

Closed questions:

Open questions allow individuals to express their thoughts, feelings, and opinions freely. These questions promote exploration and encourage the respondent to provide unique and personal insights.

Closed questions provide limited options for responses and are useful when seeking specific information or clarifying details. They are used in surveys, assessments etc.

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We have shown that both pairs of opposite sides are parallel, we can conclude that VWXT is a parallelogram.

A parallelogram is a geometric shape with two pairs of parallel sides. It is a quadrilateral, which means it has four sides, and its opposite sides are equal in length and parallel to each other. In a parallelogram, the opposite angles are also equal in measure. The area of a parallelogram can be found by multiplying the base (one of the sides) by the height (the perpendicular distance between the base and the opposite side). A special type of parallelogram is the rectangle, which has four right angles. Another type of parallelogram is the rhombus, which has four equal sides. The square is a special type of rhombus that has four equal sides and four right angles.

To prove that VWXT is a parallelogram, we need to show that both pairs of opposite sides are parallel.

Since T is the midpoint of VZ, we know that TV = TZ and TW = TX.

We are also given that TYZ is congruent to XYW. Congruent means that they have the same size and shape. So, TY = XY and YZ = WY.

Now, let's consider the two pairs of opposite sides:

VT and WX:

We know that TV = TZ and TY = XY. Therefore, VT + TY = TZ + XY. But TYZ is congruent to XYW, so YZ = WY. Thus, we have:

VT + TY = TZ + XY

VT + WY = TZ + XY

VT = TZ + XY - WY

Now, since TYZ and XYW are congruent, we know that the corresponding angles are congruent as well. In particular, angle YTX is congruent to angle WTV. Therefore, we have:

angle WTV = angle YTX

But we also know that angle TXW is congruent to angle TVY (since they are vertical angles). Therefore:

angle TXW = angle TVY

So we have two pairs of corresponding angles that are congruent, which means that VT is parallel to WX.

VW and TX:

We already know that TW = TX. We also know that YZ = WY, and since T is the midpoint of VZ, we have VY = ZT. Therefore:

VW = VY + YZ + ZT

VW = ZT + YZ + VY

VW = ZT + WY + VY

VW = TX + TW

So VW is equal to TX + TW, which means that VW is parallel to TX.

Since we have shown that both pairs of opposite sides are parallel, we can conclude that VWXT is a parallelogram.

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We have shown that both pairs of opposite sides are parallel, we can conclude that VWXT is a parallelogram.

A parallelogram is a geometric shape with two pairs of parallel sides. It is a quadrilateral, which means it has four sides, and its opposite sides are equal in length and parallel to each other. In a parallelogram, the opposite angles are also equal in measure. The area of a parallelogram can be found by multiplying the base (one of the sides) by the height (the perpendicular distance between the base and the opposite side). A special type of parallelogram is the rectangle, which has four right angles. Another type of parallelogram is the rhombus, which has four equal sides. The square is a special type of rhombus that has four equal sides and four right angles.

To prove that VWXT is a parallelogram, we need to show that both pairs of opposite sides are parallel.

Since T is the midpoint of VZ, we know that TV = TZ and TW = TX.

We are also given that TYZ is congruent to XYW. Congruent means that they have the same size and shape. So, TY = XY and YZ = WY.

Now, let's consider the two pairs of opposite sides:

VT and WX:

We know that TV = TZ and TY = XY. Therefore, VT + TY = TZ + XY. But TYZ is congruent to XYW, so YZ = WY. Thus, we have:

VT + TY = TZ + XY

VT + WY = TZ + XY

VT = TZ + XY - WY

Now, since TYZ and XYW are congruent, we know that the corresponding angles are congruent as well. In particular, angle YTX is congruent to angle WTV. Therefore, we have:

angle WTV = angle YTX

But we also know that angle TXW is congruent to angle TVY (since they are vertical angles). Therefore:

angle TXW = angle TVY

So we have two pairs of corresponding angles that are congruent, which means that VT is parallel to WX.

VW and TX:

We already know that TW = TX. We also know that YZ = WY, and since T is the midpoint of VZ, we have VY = ZT. Therefore:

VW = VY + YZ + ZT

VW = ZT + YZ + VY

VW = ZT + WY + VY

VW = TX + TW

So VW is equal to TX + TW, which means that VW is parallel to TX.

Since we have shown that both pairs of opposite sides are parallel, we can conclude that VWXT is a parallelogram.

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The complete question is:

The probability of the complement of A is 1 - P(A) = 1 - 0.25 = 0.75.
The answer is C. 0.75.

The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event "favorable outcomes".

Given that P(A) = 0.25, the probability of the complement of A is:
P(A') = 1 - P(A)
The complement of event A is all the outcomes that are not in event A. The probability of an event and its complement always add up to 1.
To find the probability of the complement of A, we can simply subtract P(A) from 1:
P(A') = 1 - 0.25 = 0.75
So, the correct answer is C. 0.75.

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The vector y is orthogonal to the vector u v.

Since y is orthogonal to both u and v, it implies that the dot product of y with each of u and v is zero. Let's denote the dot product as y · u and y · v, respectively.

Now, we need to determine if y is orthogonal to the vector u v, which is the sum of u and v. To prove this, we need to show that the dot product of y with u v is also zero, that is, y · (u v) = 0.

To verify this, we can expand the dot product y · (u v) using the distributive property: y · (u v) = y · u + y · v.

Since y is orthogonal to both u and v, we know that y · u = 0 and y · v = 0. Therefore, y · (u v) = 0 + 0 = 0.

The result y · (u v) = 0 confirms that the vector y is orthogonal to the vector u v, which is the sum of u and v.

Therefore, the statement holds true, and the vector y is indeed orthogonal to the vector u v.

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The length on the blueprint is approximately 0.2667 units.

To find the length on the blueprint, we can set up a proportion using the given information.

Let's denote the length on the blueprint as "x".

According to the blueprint, the width is 4 inches, and the actual length is 20 feet. We can set up the following proportion:

Width on Blueprint / Actual Width = Length on Blueprint / Actual Length

Plugging in the values:

4 inches / 20 feet = x / 16 feet

Now, we need to convert the units to be consistent. Since we have feet in the denominator on both sides, we can convert inches to feet by dividing by 12:

(4 inches / 12 feet) / 20 feet = x / 16 feet

Simplifying:

1/3 / 20 = x / 16

Now, we can cross multiply:

(1/3) × 16 = 20 ×x

Simplifying further:

16/3 = 20x

To solve for x, we can divide both sides by 20:

(16/3) / 20 = x

Simplifying:

16 / (3 × 20) = x

16 / 60 = x

Now, we can simplify the fraction:

4/15 = x

So, the length on the blueprint is 4/15 of a unit.

Alternatively, if you want to convert the fraction to decimal form, you can divide 4 by 15:

4 ÷ 15 ≈ 0.2667

Therefore, the length on the blueprint is approximately 0.2667 units.

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A value at the center or middle of a data set is a measure of center. It  is a statistical value that represents the central or average value of a dataset.

In statistics, a measure of center refers to a value that represents the central tendency or average of a data set. It provides a single value that summarizes the central or typical value of the data. The measure of center is used to understand the central position or location of the data points.

Common measures of center include the mean, median, and mode. The mean is calculated by summing all the values in the data set and dividing by the total number of values. The median is the middle value of a sorted data set, or the average of the two middle values if there is an even number of values. The mode represents the value that occurs most frequently in the data set.

These measures of center help in understanding the central tendency of the data and provide a representative value around which the data points are distributed. They are useful for summarizing and analyzing data sets, allowing for comparisons and making inferences about the data.

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There are 7 months in the year that have thirty-one days.

These months are January, March, May, July, August, October, and December.

There are seven months in the Gregorian calendar that have thirty-one days: January, March, May, July, August, October, and December.

This pattern of months with 31 days followed by months with fewer days repeats throughout the year.

This pattern was established by the Roman calendar, which had ten months totaling 304 days in a year.

The months of January and February were later added by King Numa Pompilius to align the calendar with the lunar year.

The months of January and February initially had 29 and 28 days respectively, but in 45 BC, Julius Caesar added one day to January and one day to August, which was originally a 30-day month, to make them both 31-day months.

In the Gregorian calendar, which is the most widely used calendar in the world, January, March, May, July, August, October, and December all have 31 days.

The remaining five months have fewer days, with February having 28 days most of the time, and 29 days in a leap year.

Knowing the number of days in each month is important for various reasons, such as planning events, scheduling appointments, and calculating pay periods.

There are several mnemonics used to remember the number of days in each month, such as "30 days hath September, April, June, and November, all the rest have 31, except February, with 28 days clear, and 29 in each leap year."

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Answer:

1 17/48

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

1 3/6÷8/5

Applying the fractions formula for division,

=1/3×5/6×8

=65/48

Simplifying 65/48, the answer is

=1 17/48

Answer:

4,641

Step-by-step explanation:

Answer: it would be 4641

Step-by-step explanation:

Because when you multiply 91 and 51 that’s the answer you get

Answer:

x=33

Step-by-step explanation:

The angles of a straight line always add up to 180°.

Hence, (x+13)+(4x+2)=180 we can then remove the parenthesis and we get x+13+4x+2. Adding the two, we get 5x+15=180--->x=33

The two angles:

46° and 134°

completing the steps in the image, you should choose supplementary in the drop-down. Supplementary means the angles add up to 180 degrees In the next blank, put 4x+2. In the last blank, put 180 degrees.

The temperature of steam at the exit of the turbine is 41.23°C. The minimum mass flow rate of steam through the turbine is 875.51 kg/s.

The enthalpy and entropy data at the turbine entrance and exit can be found by interpolating the steam tables. Using the following equations:\($$\Delta h = h_2 - h_1 = 3305.3 - 3473.3 = -168\ kJ/kg$$\)

\($$\Delta s = s_2 - s_1 = 6.8692 - 6.3827 = 0.4865\ kJ/kg.K$$\)

Using the steam tables, the properties of steam at the inlet and outlet are: Inlet: T = 380°C, P = 168 bar, v = 0.0465 m3/kg, h = 3473.3 kJ/kg, s = 6.3827 kJ/kg.K

Outlet: P = 0.06 bar, x = 0.9, v = 143.89 m3/kg, h = 3305.3 kJ/kg, s = 6.8692 kJ/kg.K

(a) To find the exit temperature of the steam:\($$\Delta h = C_p \Delta T$$\)

\($$T_2 - T_1 = \frac{\Delta h}{C_p} = \frac{\Delta h}{(C_p)_2}$$\)

At x = 0.9, v = 143.89 m3/kg, and h = 3305.3 kJ/kg; using the steam table, we can find the specific heat of the mixture as 2.012 kJ/kg.K.

Thus\(:$$T_2 = T_1 + \frac{\Delta h}{C_p} = 380 + \frac{-168 \times 10^3}{2.012 \times 10^3} = 41.23\ °C$$\)

Therefore, the temperature of steam at the exit of the turbine is 41.23°C.(b) To find the minimum mass flow rate of the steam:

\($$\dot{m}_{min} = \frac{P_t}{\Delta h/\eta_t} = \frac{160 \times 10^3}{(-168 \times 10^3/0.85)} = 875.51\ kg/s$$\)

Thus, the minimum mass flow rate of steam through the turbine is 875.51 kg/s.

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Normally the figure that is the original, It is always the figure without "prime" notation

For example

A,B, C is the

Answer:

__

0.45

__

__ means it's on-going, so 0.45454545

Angle 1 and 2 are equal because of correspondence angle

so , (78-2x) = (89-3x)

x = 89 - 78

x = 11

hence angle 1 = ( 78 - 2*11) = 56

and angle 2 = ( 89-3*11) = 56

So, both of angle is 56

hope it help and your day will full of happiness

The probability that the number of lost-time accidents occurring over a period of 8 days will be no more than 4 is 0.2027, or approximately 20.27%.

To solve this problem, we can use the Poisson distribution formula, which is as follows:

P(X ≤ 4) = ∑(k=0 to 4) [(e^-λ * λ^k) / k!]

where λ is the mean rate of lost-time accidents per day, and X is the number of lost-time accidents occurring over a period of 8 days.

Substituting the given values, we get:

λ = 0.7 * 8 = 5.6

P(X ≤ 4) = ∑(k=0 to 4) [(e^-5.6 * 5.6^k) / k!]

Using a calculator, we can evaluate this probability as:

P(X ≤ 4) = 0.2027 (rounded to four decimal places)

In conclusion, the Poisson distribution can be used to calculate the probability of a certain number of events occurring over a given time period, given the mean rate of occurrence per unit time.

In this case, we used the Poisson distribution to calculate the probability of a certain number of lost-time accidents occurring over an 8-day period, given the mean rate of lost-time accidents per day.

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Given the following relationship dQ = (∂T/∂E)_V dT + [(∂V/∂E)_T + P]dV

To prove the relationship between heat transfer (dQ) and changes in temperature (dT) and volume (dV) using the internal energy (E) as a function of state E(T, V), we need to differentiate E with respect to T and V.

The first step is to express the total differential of E using the chain rule:

dE = (∂E/∂T)_V dT + (∂E/∂V)_T dV

where (∂E/∂T)_V represents the partial derivative of E with respect to T at constant V, and (∂E/∂V)_T represents the partial derivative of E with respect to V at constant T.

Now, let's rearrange the equation to isolate dQ:

dQ = (∂E/∂T)_V dT + (∂E/∂V)_T dV

To relate dQ to the given partial derivatives, we need to consider the first law of thermodynamics:

dQ = dE + PdV

where P is the pressure.

Substituting dE + PdV into the equation above:

dQ = (∂E/∂T)_V dT + (∂E/∂V)_T dV + PdV

Now, we can rearrange the terms to match the desired relationship:

dQ = (∂E/∂T)_V dT + [(∂E/∂V)_T + P]dV

This matches the relationship stated:

dQ = (∂T/∂E)_V dT + [(∂V/∂E)_T + P]dV

Therefore, we have successfully proven the relationship between heat transfer (dQ) and changes in temperature (dT) and volume (dV) using the internal energy (E) as a function of state E(T, V).

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Answer:

Y= -1/2X+9

Step-by-step explanation:

Answer:

Y= -1/2X+9

Step-by-step explanation:

Answer:29.04

Step-by-step explanation:

3.79+20.25=24.04

24.04+5=29.04

The diagram demonstrates why the length of the third (3) side of a triangle cannot be less than the total of the lengths of any two (2) of its sides: B. by demonstrating the inability of two sides with lengths of 4 and 3 to come together to form a vertex.

A triangle is a geometric shape with only three (3) sides, three (3) vertices, and three (3) angles.

It is a two-dimensional shape.

the various triangle types.

According to the length of their sides, triangles can be divided into three (3) primary categories, which are as follows:

Triangle types:

triangle with equal sides.

Triangle in isosceles.

Scalene triangle - Scalene's triangle.

Triangle inequality theorem:

The Triangle Inequality Theorem asserts that the length of the third (2) side of a triangle must be bigger than the sum of any two (2) of its side lengths.

This finally means that, according to the Triangle Inequality Theorem, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle.

Therefore, the diagram demonstrates why the length of the third (3) side of a triangle cannot be less than the total of the lengths of any two (2) of its sides: B. by demonstrating the inability of two sides with lengths of 4 and 3 to come together to form a vertex.

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Answer:

b  ≥ 4

Step-by-step explanation:

12b + 12 ≥ 60

Subtract 12 from each side

12b + 12-12 ≥ 60-12

12b  ≥ 48

Divide each side by 12

12b/ 12 ≥ 48/12

b  ≥ 4

Close circle at 4  line to the right

Answer:

Step-by-step explanation:

12b + 12 ≥ 60

1) add -12 at both members

12b + 12-12 ≥ 60 -12

12b ≥ 48

2) divide both members by 12

12/12 b ≥ 48/12

b ≥ 4

for graph the solutions we have to draw two lines

the first one is an horizontal line that has as equation the right part of the inequality

y = 60

the second one is a line the that passes from the origin and interecpts the first line in (4;60). 4 is the the first number that can be a possible value of the inequality

Equation a line that passes for two points  A (0,0) , B (4,60)

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y - 60)/ (0 -60) = (x - 4) / (0-4)

(-y+60)/60 (-x+4)/4

-y + 60 = -15x + 60

y = 15x

the solutions of the inequality are all the points between the two lines with x≥4 and y≥60

The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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Part A. When we have two chords that intercept at one of the exterme points of a circle, like this:

Then the relationship between the minor arc and the interior angle of the chords is:

therefore, if we substitute according to the given circle we have:

Therefore, angle a is 85°.

Part B. The angle formed by a tangent and a chord of a circle is half the the arc that is formed:

We have that:

Now, we substitute:

Therefore, "b" is 105°.

Part C. Given the following configuration:

The following relationship holds:

Now, we substitute the values according to the given circle:

Now, we divide both sides by "c":

Therefore, the value of "c" is 13.5

Part D. In the following configuration:

The following relationship holds:

Now, we substitute the values:

Solving the operations:

therefore, the angle "d" is 80 degrees.

Answer:

-7x + 6

Step-by-step explanation: