The coordinates of a triangle are P(1, 4), Q(3, 6), and R(5, 2). The triangle is reflected over a line and its image coordinates are P'(–1, 4), Q'(–3, 6), and R'(–5, Find the equation of the reflection line.
1. x = –1
2. y = –1
3. y = 0
4. x = 0

Answer:

(- 2, 5 )

Step-by-step explanation:

Given the 2 equations

3x + 4y = 14 → (1)

x = 2y - 12 → (2)

Substitute x = 2y - 12 into (1)

3(2y - 12) + 4y = 14 ← distribute and simplify left side

6y - 36 + 4y = 14

10y - 36 = 14 ( add 36 to both sides )

10y = 50 ( divide both sides by 10 )

y = 5

Substitute y = 5 into (2) for corresponding value of x

x = 2(5) - 12 = 10 - 12 = - 2

Solution is (- 2, 5 )

To find the point that satisfies both equations, substitute the value of x from the second equation into the first equation and solve for y. Then substitute the value of y into the second equation to find x. The point (-2, 5) satisfies both equations.

To find the point that satisfies both equations, we need to solve the system of equations:

3x + 4y = 14

x = 2y - 12

Substituting the value of x from the second equation into the first equation, we get:

3(2y - 12) + 4y = 14

6y - 36 + 4y = 14

10y = 50

y = 5

Substituting the value of y into the second equation, we get:

x = 2(5) - 12

x = 10 - 12

x = -2

Therefore, the point (-2, 5) satisfies both equations.

complete question given below:

3x+4y=14

x=2y-12

which point satisfies both equation

To divide 6 by 2 2/3, convert 2 2/3 to the improper fraction 8/3, then multiply 6 by the reciprocal of 8/3 (which is 3/8) to get 18/8. Simplifying this by dividing both numerator and denominator by 2 gives the result 9/4 or 2 1/4.

To divide and simplify 6 divided by 2 2/3, you first need to convert the mixed number to an improper fraction. The mixed number 2 2/3 can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, then adding the numerator of the fraction to that product. This gives you:

2 x 3 + 2 = 6 + 2 = 8

So, 2 2/3 as an improper fraction is 8/3. Now, to divide the number 6 by 8/3, you will multiply 6 by the reciprocal of 8/3, which is 3/8.

6 x (3/8) = 18/8

To simplify 18/8, you divide the numerator and the denominator by their greatest common divisor, which is 2. Therefore, you get:

18 / 2 = 9 and 8 / 2 = 4

So, the simplified result of 6 divided by 2 2/3 is 9/4 or 2 1/4.

Answer:

n=-2

Step-by-step explanation:

7/8+n/4=3/8

n/4=3/8-7/8

n/4=-4/8

-4/8=-1/2

n/4=-1/2

cross product

4*-1=2*n

-4=2n

n=-4/2

n=-2

Answer:

Step-by-step explanation:

7/8 +n/4 = 3/8

Multiply each term by 8

(8)7/8 +n/4(8) = 3/8(8)

7 + 2n = 3

2n = 3 - 7

2n = - 4

n = -4/2

n = -2

Answer:

w = 1.25[tex]\times[/tex] t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

Step-by-step explanation:

Water is running into a bathtub at a constant rate.

In 2 minutes , 2.5 gallons of water is filled in the tub. We are supposed to find the relation between the amount of water and the time taken and we also have to find the definition of the constant of proportionality.

Let w be the amount of water and t be the time taken in minutes.

The rate at which water is filled in the tub = [tex]\frac{2.5}{2}[/tex]

                                                                      = 1.25 gallons/minute

The water filled , w = 1.25[tex]\times[/tex] t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

Final answer:

The question asks for two equations representing the proportional relationship between water in a bathtub (w) and time (t), given a constant fill rate. We derived that water fills the tub at a rate of 1.25 gallons per minute, leading to two equations: w = 1.25t and t = w / 1.25, explaining both the fill rate and how to calculate time based on a certain water amount.

Explanation:

The question involves finding two equations for a proportional relationship between the amount of water (w, in gallons) in a bathtub and the time (t, in minutes) it takes for the water to fill up at a constant rate, given that 2.5 gallons of water fill the tub in 2 minutes. To build these equations, we will use the information provided to determine the constant of proportionality (k), which represents the rate at which the tub fills.

First, we find the constant of proportionality (k) by dividing the amount of water by the time:

k = w / t = 2.5 gallons / 2 minutes = 1.25 gallons per minute

This gives us two equations based on this scenario:

w = 1.25t (Equation 1)

t = w / 1.25 (Equation 2)

Equation 1 tells us the amount of water (w) in the bathtub after t minutes, showing that the bathtub fills at a rate of 1.25 gallons per minute. Equation 2 allows us to find the time (t) it takes to reach a certain amount of water (w) in the bathtub, by dividing the amount of water by the rate of 1.25 gallons per minute.

The constant of proportionality (1.25 gallons per minute) in both equations indicates the rate at which the tub fills with water. It tells us that for every minute that passes, an additional 1.25 gallons of water are added to the tub.

Answer:

The estimated taken to drive downtown using App is 38.4 minutes

Step-by-step explanation:

Given as :

The initial time taken to drive downtown = i = 48 minutes

The percentage error of time = r = 20%

Let The estimated time using app = t min

Let the time = 1 min

Now, according to question

The estimated time using app = The initial time taken to drive downtown × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, t minutes = i minutes × [tex](1-\dfrac{\textrm r}{100})^{\textrm 1}[/tex]

Or, t = 48 minutes × [tex](1-\dfrac{\textrm 20}{100})^{\textrm 1}[/tex]

Or,  t = 48 minutes × [tex]\dfrac{100-20}{100}[/tex]

Or,  t = 48 minutes × [tex]\dfrac{80}{100}[/tex]

∴ t = [tex]\dfrac{48\times 80}{100}[/tex] minutes

I.e t = 38.4 minutes

Or, The estimated time using app = t = 38.4 min

Hence, The estimated taken to drive downtown using App is 38.4 minutes Answer

Answer:

38.3

Step-by-step explanation:

38.3

Answer:

$8.50 per wk

Step-by-step explanation:

$8.50x6=$51.00+$24.00=$75.00.

Answer:

Manuel must save at least $ 8.5 each week ( 6x ≥ 75 - 24)

Step-by-step explanation:

He has to save more than $75 - $24 = $51 for the next 6 weeks to have enough money for class trip

X: the amount must save each week

6x ≥ 51   ... divide 3 both sides

2x ≥ 17

x ≥ 17/2

x ≥ 8 1/2

Answer:

The answer is "The order ended segregation in the military."

Step-by-step explanation:

President Harry S. Truman is the 33rd president of the United States of America. He assumed the President's role after the death of Franklin D. Roosevelt (the 32nd president of the USA). Under his leadership, he was able to abolish the issues concerning the discrimination according to race or religion in the USA's military force. This was backed by the "Executive Order 9981," which he issued in 1948.

The "Executive Order 9981" ended the segregation in the military. Before it was issued, the Black Americans were trained differently from the White Americans. The White Americans were given more priority than the Black ones. This means that the Black Americans have to wait and train longer before they became qualified. Later, it was found out that there was actually no sense in segregating both Americans, since they both performed well in the wartime.

Thus, this explains the answer.

Answer:

its A

Step-by-step explanation:

Answer:

y = -2x - 3

Step-by-step explanation:

The line has a slope of -2

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

Lets take another point (x, y) on the line,

Slope = change in y ÷ change in x

i.e slope = [tex]\frac{y - -1}{x - -1}[/tex] = -2

[tex]\frac{y + 1}{x + 1}[/tex] = -2

y + 1 = -2x - 2

y = -2x - 2 - 1

y = -2x - 3 (this is the equation of the line).

Answer:

6 ft

Step-by-step explanation:

Use the formula for area of a parallelogram A = bh

b is for base and h is for height. A is for area.

Substitute b for 8 1/4 ft² and A for 49 1/2 ft². Isolate "h" to find the height of the deck.

A = bh

49 1/2 ft² = (8 1/4 ft²)h    Divide both sides by 8 1/4 ft² to isolate h

(49 1/2 ft²) ÷ (8 1/4 ft²) = (8 1/4 ft²)h ÷ (8 1/4 ft²)

(49 1/2 ft²) ÷  (8 1/4 ft²) = h

h = 6ft

Therefore the height of the deck is 6 feet.

Hope it helps u.......

Answer:

C

Step-by-step explanation:

We have a linear equation in the form  y = mx

Where m is the slope

The slope is the change in y divided by change in x.

We can take any 2 points on the line and see the change in y and divide it by the change in x. We will get slope, m.

Lets take points (2,3) and (6,9).

The change in y is 9 - 3 = 6

The change in x is 6 - 2 = 4

So, the slope would be:

m = 6/4 = 3/2 = 1.5

So, the equation would be:

y = 1.5x

Correct answer is C.

[tex]5\frac{1}{3}[/tex] liters is the amount to be drained out and replaced

Solution:

40 % antifreeze solution in 16 liter radiator

Let "x" be the amount drained from radiation and replaced with pure antifreeze

To obtain a 60 % antifreeze solution

The original solution is 16 liter, 40% of which is antifreeze

You want the solution to be 60% antifreeze:

60 % x 16 = [tex]\frac{60}{100} \times 16 = 9.6[/tex]

You will remove x liters of the 40% solution and replace it with x liters pure (100%) antifreeze.

[tex]40 \% (16 - x) + 100 \% \times x = 60 \% \times 16[/tex]

Let us solve expression for "x"

[tex]\frac{40}{100} \times (16 - x) + \frac{100}{100} \times x = \frac{60}{100} \times 16\\\\0.4(16-x) + x = 0.6 \times 16\\\\6.4 - 0.4x + x = 9.6\\\\6.4 + 0.6x = 9.6\\\\0.6x = 3.2\\\\x = 5.33\\\\x = 5\frac{1}{3}[/tex]

Thus [tex]5\frac{1}{3}[/tex] liters is the amount to be drained out and replaced

Answer:

There are 32 pupils in the class

Step-by-step explanation:

Let's say there are N pupils in the class. Then each pupil must send N-1 cards - because it would make no sense to send one to themselves! So each of the N pupils send N-1 cards, which becomes 992 cards in total. In equation form, this is

[tex]N(N-1)=992\\N^2-N-992=0[/tex]

This is a second degree polynomial, which has the solutions

[tex]N=\frac{-b\pm \sqrt{b^2-4\cdot a \cdot c}}{2a}[/tex]

where [tex]a=1, b=-1, \text{and }c=-992[/tex]

If we insert these numbers in the equation,

[tex]N=\frac{-(-1)\pm \sqrt{1^2-4*1*(-992)}}{2*1}\\ = \frac{1\pm \sqrt{1+4*992}}{2}\\= \frac{1 \pm 63}{2}[/tex]

If we choose the solution with the minus sign, we get

N=-31

but this makes no sense! There can't be a negative number of pupils in the class!

So we choose the solution with the plus sign,

[tex]N=\frac{1+63}{2}\\ =\frac{64}{2}\\ =32[/tex]

So there are 32 pupils in the class

Answer:

number of pupils in the class = 32

Step-by-step explanation:

Let n be the number of students. So n-1 cards will be sent by each student.

n(n-1) =192

n² - n =192

n² - n - 192 = 0

n² - 32n + 31n - (31*32) = 0

n(n - 32) + 31 (n-32) = 0

(n-32)(n+31) = 0

n - 32 = 0    or n + 31 = 0

n = 32  or n = -31 is not possible because no. of students cannot be negative

n= 32

Answer:

$720

Step-by-step explanation:

$1,200 divided by 2 (600) equals how many vanilla cupcakes there were.

40 people times 24 cupcakes each person (960) equals how many total cupcakes there were.

The total amount of cupcakes minus the amount of vanilla cupcakes equals the amount of chocolate cupcakes (960-600=360).

360 chocolate cupcakes times the amount each cupcake was sold for equals the amount of money raised from the chocolate cupcakes (360x2=720).

Answer:

y= -x+2

Step-by-step explanation:

given that line m, passes through (2,-7) and (4,-9)

(refer to attached)

slope of line m,

= [(-7) - (-9)] / (2- 4)

= (-7 +9) / (2- 4)

= (2) / (-2)

= -1

recall that the general form of a linear equation is

y = mx + b, where m is the gradient.

in this case, we found that m = -1, so look for the answer where the x-term has -1 as a coefficient, i.e the x-term is "-x"

By observation, we see that the only answer that has "-x" as part of the equation is A

Answer:

C) -1/4

Step-by-step explanation:

slope=rise/run

The slope of the line between the points (-4, -3) and (4, 3) is 3/4. Therefore, the correct answer is C.

The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. A simple formula to find the slope is:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

In this case, we can use the points (-4, -3) and (4, 3) that are given on the graph. Plugging them into the formula, we get:

m = (3 - (-3)) / (4 - (-4))

Simplifying, we get:

m = 6 / 8

Reducing to the lowest terms, we get:

m = 3 / 4

Therefore, the slope of the line is 3/4. The correct answer is C).

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the true statements are:

- B. The difference in height between the pelican and the heron is 33 feet.

- C. The distance between the heights of the pelican and heron is 33 feet.

- E. The difference in height between the pelican and the trout is 40 feet.

- F. The distance between the heights of the pelican and the trout is 40 feet.

Let's calculate the differences and distances between the heights of the given objects.

Given heights:

- Heron: 50 feet above sea level

- Pelican: 17 feet above sea level

- Trout: 23 feet below sea level

Now, let's calculate the differences and distances:

A. The difference in height between the pelican and the heron is:

[tex]\[ \text{Difference} = \text{Height of pelican} - \text{Height of heron} \][/tex]

[tex]\[ \text{Difference} = 17 - 50 \][/tex]

[tex]\[ \text{Difference} = -33 \][/tex]

B. The difference in height between the pelican and the heron is:

[tex]\[ \text{Difference} = \text{Height of heron} - \text{Height of pelican} \][/tex]

[tex]\[ \text{Difference} = 50 - 17 \][/tex]

[tex]\[ \text{Difference} = 33 \][/tex]

C. The distance between the heights of the pelican and heron is the absolute value of their difference:

[tex]\[ \text{Distance} = |\text{Difference}| \][/tex]

[tex]\[ \text{Distance} = |-33| \][/tex]

[tex]\[ \text{Distance} = 33 \][/tex]

D. The difference in height between the pelican and the trout is:

[tex]\[ \text{Difference} = \text{Height of pelican} - \text{Height of trout} \][/tex]

[tex]\[ \text{Difference} = 17 - (-23) \][/tex]

[tex]\[ \text{Difference} = 17 + 23 \][/tex]

[tex]\[ \text{Difference} = 40 \][/tex]

E. The difference in height between the pelican and the trout is:

[tex]\[ \text{Difference} = \text{Height of trout} - \text{Height of pelican} \][/tex]

[tex]\[ \text{Difference} = -23 - 17 \][/tex]

[tex]\[ \text{Difference} = -40 \][/tex]

F. The distance between the heights of the pelican and the trout is the absolute value of their difference:

[tex]\[ \text{Distance} = |\text{Difference}| \][/tex]

[tex]\[ \text{Distance} = |-40| \][/tex]

[tex]\[ \text{Distance} = 40 \][/tex]

So, the true statements are:

- B. The difference in height between the pelican and the heron is 33 feet.

- C. The distance between the heights of the pelican and heron is 33 feet.

- E. The difference in height between the pelican and the trout is 40 feet.

- F. The distance between the heights of the pelican and the trout is 40 feet.

complete question given below:
A heron is perched in a tree 50 feet above sea level. Directly below the heron, a pelican is flying 17 feet above sea level. Directly below the birds is a trout, swimming 23 feet below sea level.

Select all the true statements.

A The difference in height between the pelican and the heron is -33 feet.The difference in height between the pelican and the heron is -33 feet.

B The difference in height between the pelican and the heron is 33 feet.The difference in height between the pelican and the heron is 33 feet.

C The distance between the heights of the pelican and heron is -33 feet.The distance between the heights of the pelican and heron is -33 feet.

D The difference in height between the pelican and the trout is -40 feet.The difference in height between the pelican and the trout is -40 feet.

E The difference in height between the pelican and the trout is 40 feet.The difference in height between the pelican and the trout is 40 feet.

F The distance between the heights of the pelican and the trout is 40 feet.

The given line has a slope of -1.

The slope of a perpendicular line is the negative reciprocal.

The slope of the new line would be positive 1.

Now using the point slope form, use the given pint to find the equation:

y -y1 = m(x -x1)

Replace x1 and y1 with the given point:

y - (-2) = 1(x -3)

Simplify:

y +2 = x -3

Subtract 2 from both sides:

y = x-5

Answer:

y = x-5

Step-by-step explanation:

Answer:

The number of hours did Sarah practice more than Leilani is [tex]\dfrac{11}{40}[/tex]  hours  .

Step-by-step explanation:

Given as :

The time for which Leilani practiced piano = [tex]\dfrac{3}{5}[/tex] hours

The time for which Sarah practiced piano = [tex]\dfrac{7}{8}[/tex] hours

Let the number of hours did Sarah practice more than Leilani = T hours

Now, According to question

The number of hours did Sarah practice more than Leilani = [tex]\dfrac{7}{8}[/tex] hours -  [tex]\dfrac{3}{5}[/tex] hours

Or, T =  [tex]\dfrac{35-24}{40}[/tex] hours

Or, T =  [tex]\dfrac{11}{40}[/tex] hours

So,The number of hours did Sarah practice more than Leilani = T =  [tex]\dfrac{11}{40}[/tex]  hours

Hence, The number of hours did Sarah practice more than Leilani is [tex]\dfrac{11}{40}[/tex]  hours  . Answer

Answer:

The center of the circle is c=50 and radius of the circle is [tex]r=\sqrt{3}[/tex]

Step-by-step explanation:

Given circle equation is

[tex]x^2-4x+y^2+14y=-50\hfill(1)[/tex]

Equation (1) can be written as [tex]x^2-4x+y^2+14y+50=0\hfill(2)[/tex]

we know that the equation of the circle is of the form

[tex]x^2+y^2+2gx+2fy+c=0\hfill(3)[/tex]

with centre (-g,-f) and radius=[tex]\sqrt{g^2+f^2-c}[/tex]

when, g,f and c are constants

Now comparing the (2) and (3) equations we get 2g=-4

                                                                          [tex]g=\frac{-4}{2}[/tex]

                                                                          [tex]g=-2[/tex]

                                                                          [tex]2fy=14[/tex]

                                                                          [tex]f=\frac{14}{2}[/tex]

                                                                          [tex]f=7[/tex]

                                                                 and  [tex]c=50[/tex]

Now to find the centre and radius of the given circle equation, substituting the values of g,f,c in the formulae of centre and radius

                  centre=(-g,-f)

                             =(-(-2),-7)

                  centre=(2,7)

                  Radius=[tex]\sqrt{g^2+f^2-c}[/tex]

                              =[tex]\sqrt{(-2)^2+(7)^2-50}[/tex]

                             =[tex]\sqrt{4+49-50}[/tex]

                            =[tex]53-50[/tex]

                   Radius=[tex]\srqt{3}[/tex]

The center of the circle is c=50 and the radius of the circle equation [tex]r=\sqrt{3}[/tex]

Answer:

(3, 6)

Step-by-step explanation:

D₃ means a dilation of 3, and R₁₈₀ means a rotation of 180°.

D₃ (-1, -2) = 3 (-1, -2) = (-3, -6)

R₁₈₀ (-3, -6) = (3, 6)

Answer:

217

Step-by-step explanation:

124%=x

36%=63

=>[tex]x=\dfrac{63\times 124}{36}=217[/tex]

Final answer:

To find 124% of the original number, we first determine that the number is 175 by dividing 63 by 0.36 (the equivalent of 36%). We then multiply 175 by 1.24 to arrive at 217, which is 124% of the original number.

Explanation:

To solve the student's question, we'll need to find the original number that 36% represents, and then calculate 124% of that number. If 36% of a number is 63, we would set up an equation to find 100% of that number (the whole number).

Let's call the unknown number 'x'. The equation would be 0.36x = 63. To solve for 'x', we would divide both sides of the equation by 0.36:

x = 63 ÷ 0.36

Once we've found the value for 'x', we then find 124% of that number by multiplying 'x' by 1.24 (since percent means 'per hundred' and 124% is equivalent to 1.24 when expressed as a decimal).

Now, calculating the values:

x = 63 ÷ 0.36 = 175

To find 124% of 175, we do the following calculation:

1.24 × 175 = 217

Therefore, 124% of the number is 217.

Answer:

y < (1/2)x + 2

Step-by-step explanation:

Recall that slope intercept form looks like

y = mx + b

we simply have to rearrange the given equation until it looks like the above

3x-6y>12   (subtract 3x from both sides and rearrange)

-6y > -3x + 12   (divide both sides by 6)

-y > (-3/6)x + (12/6)

-y > -(1/2)x + 2   (multiply both sides by -1, remember to flip the inequality)

y < (1/2)x + 2

Answer:

1 compounding every 2 years

Step-by-step explanation:

Compounded bi-annually in mathematics refers to calculating interest twice a year, where the interest earned in the first six months is used to calculate the interest for the second six months.

The term compounded bi-annually refers to a method of calculating interest where the interest is added to the principal amount twice a year or every six months. This means that the interest you earn after the first six months will also earn interest for the second six months of the year. For example, if you have $1000 with an annual interest rate of 10% compounded bi-annually, after six months, you'd earn 5% interest of $50 making your total $1050. In the next six months, the interest would be calculated on $1050, giving you an another 5% of $52.5 for a total of $1102.5 for the year.

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There are three congruence theorems for triangles and they are.

the assumptions made by the following theories are given below.

Step-by-step explanation:

  This theorem states that  triangles are congruent if any pair of corresponding sides and their angle are congruent.

    2. ASA theorem

  This theorem states that the triangles are congruent if any two angles and their sides are equal.

   3. SSS theorem

  This is the easiest among all three postulates. THIS theorem states that if all the sides of a triangle are congruent to the sides of the other triangle then the two triangles are congruent

A cell phone weighing 56 grams can be converted to kilograms by dividing by 1,000, resulting in a weight of 0.056 kilograms.

To convert the weight of a cell phone from grams to kilograms, one must utilize the metric system's conversion rate where 1 kilogram is equal to 1,000 grams.

Therefore, if a cell phone weighs 56 grams, to find the weight in kilograms, you would divide 56 by 1,000.

56 grams ÷ 1,000 = 0.056 kilograms.

Hence, the cell phone can weigh 0.056 kilograms.

It is important to note that in the metric system, expressing units in the most manageable form is advisable.

In this case, kilograms provide a more easily managed number for larger weights, whereas grams are suitable for smaller weights.

Answer:

THX

Step-by-step explanation:

now i know your student id number yes

Answer:

3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find LCM  for 10, 4.  LCM = 20

3/10 = 3*2/10*2 = 6/20

3/4 = 3*5/4*5 = 15/20

6/20 < 15/20

3/4 is greater

OR

3/10 = 0.3

3/4 = 0.75

3/4 is greater

Answer:

Step-by-step explanation:

Answer:

Vouch^ D on Edge

Step-by-step explanation:

If planet Y is twice the mean distance from the sun as planet X, the orbital period  is increased by the factor 2^3/2.

The Kepler's third law underscore the relationship between the orbital period T and the mean distance from the sun, A, in astronomical units, AU.

Mathematically, we can write; T^2 =A^3

Where;

T = orbital period

A =  mean distance from the sun

If planet Y is twice the mean distance from the sun as planet X, the orbital period  is increased by the factor 2^3/2.

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