Please help me! I'm having trouble solving this! In the △PQR, PQ = 39 in, PR = 17 in, and the height PN = 15 in. Find QR. Consider all possible cases.

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:

Step-by-step explanation:

Supplementary angles add up to 180°.

m∠VST = m∠VSW + m∠TSW

m∠VST = 180° → m∠VSW + m∠TSW = 180°

Answer:

supplementary

Step-by-step explanation:

acute= less then 90 degrees

straight=180 degrees

complementary= 2 angles that equal 90 degrees

supplementary=2 angles that equal 180 degrees

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

Answer:

57

Step-by-step explanation:

How I did this was 513 divided by 9 so the equation that I did was 513/9.

Answer:

57

Step-by-step explanation:  

you just need to divide=

513 divided by 9 = 57

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:

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:

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:

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

Weight of wire of 8.7 meters is 24.36 ounces

Solution:

Given that cable repair person has 8.7 meters of wire

Each meter of the wire weighs 2.8 ounces

To find: Weight of wire

From given information,

weight of 1 meter of wire = 2.8 ounces

Therefore weight of 8.7 meters of wire is found by multiplying weight of 1 meter of wire by 8.7

weight of 8.7 meter of wire = weight of 1 meter of wire x 8.7

weight of 8.7 meter of wire = 2.8 x 8.7 = 24.36

Therefore weight of wire of 8.7 meters is 24.36 ounces

The weight of the 8.7 meters of wire is 24.36 ounces.

To find the weight of the wire, we need to multiply the length of the wire by its weight per unit length. The student has 8.7 meters of wire, and each meter weighs 2.8 ounces.

Multiply the length of the wire in meters (8.7) by the weight per meter in ounces (2.8).

8.7 meters * 2.8 ounces/meter = 24.36 ounces.

Therefore, the total weight of the wire is 24.36 ounces.

Answer:

THX

Step-by-step explanation:

now i know your student id number yes

Answer: The inequality symbol is reversed

Step-by-step explanation:

Given : 3 > -6

If we we multiply both side by -3 , we will have

-3(3) < -6(-3)

-9 < 18

the inequality symbol  changes because , in the rule of inequalities , anytime we multiply or divide through by negative , the inequality symbol must change

Answer:

16

Step-by-step explanation:

Quotient means the answer to a division problem.

80 ÷ 5 = 16

In long division:

   16 R0

5∫80

   5  

   30

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.

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:

(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:

$25.5 per hour.

Step-by-step explanation:

The function C(x) = 25.50x + 50 ........ (1)  models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house.

Now, from the linear equation it is clear that the change in cost of cleaning from 3 hours and 9 hours are respectively  {From equation (1)}

C(3) = 25.5 × 3 + 50 = $126.5 and

C(9) = 25.5 × 9 + 50 = $279.5

Therefore, the average rate of change of the function between 3 hours and 9 hours will be = [tex]\frac{\textrm {Change in price of cleaning}}{\textrm {Change in hours}}[/tex]

= [tex]\frac{279.5 - 126.5}{9 - 3}[/tex]

= $25.5 per hour. (Answer)

Answer:

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

Step-by-step explanation:

Let

x ----> the number of jars of nuts worth $4

y ----> the number of jars of nuts worth $6

we know that

[tex]x+y=50[/tex] ----> equation A

[tex]4x+6y=4.80(50)[/tex]

[tex]4x+6y=240[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (30,20)

see the attached figure

therefore

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

The student has to mix 20 jars of $4 nuts with 30 jars of $6 nuts to end up with 50 jars of nuts each worth $4.80.

This question falls under a mathematical concept known as linear equations. Let's denote the number of $4 jars as X and the number of $6 jars as Y. According to the question, X + Y = 50 because the total number of jars is 50. We can also write another equation, which is 4X + 6Y = 50 * 4.8 ($4.80 is the average price of a jar, and there are 50 jars). Solving this system of linear equations gives us X = 20 and Y = 30. So, the student has to mix 20 jars of nuts worth $4 per jar with 30 jars of nuts worth $6 per jar to get 50 jars of nuts worth $4.80 per jar.

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Answer:

View image

Step-by-step explanation:

You treat inequality questions just like normal equation with an equal sign. You only have to worry about the inequality when you do the shading part.

Your first goal is to solve for y, which I did at the top.

And remember that when you divide/multiply by a negative number you have to flip the inequality sign.

So the first equation is already in term of y. (y < 2x + 4)

So you only have to solve for y for -3x - 2y ≥ 6.

I solved that and got y ≤ -3/2x - 3.

Now you have 2 equations. y < 2x + 4 and y ≤ -3/2x - 3

First you gotta treat it like a normal equation and graph them.

So i graphed y = 2x + 4 and y = -3/2x - 3. I assume you already know how do do that.

btw. < and > have dotted lines, while ≤ and ≥ have solid lines.

Now for the shading, you gotta look at the inequality sign.

y < 2x + 4 has a less than sign, so you have to shade everything underneath the line you graphed.

y ≤ -3/2x - 3 is also less than, so you have to shade everything underneath that line as well.

So in the future, you you get a > or ≥ then you have to shade above the graph.

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

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:

The true statements are : A, E & F

Step-by-step explanation:

In geometry symbols, ≅ means congruent to, equivalence of geometric shapes and size thus ∠B≅∠X

The symbol ~ means similarity, same shape not same size. Line segment AB~WX and line segment ZW ~ DA

Learn More

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Keywords :statements, true, similar, isosceles trapezoids

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Answer:

the first one and the last 2 are correct 8D

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.

Learn more about Kepler's law: https://brainly.com/question/1638294

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).

To learn more about slope

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Let x = the number of songs you can buy.

If you use company A at 0.79 dollars per song, your variable is 0.79x. If you use company B at 0.99 dollars per song, your variable is 0.99x. You are going to set both equal to 30.

Company A: 0.79x = 30

Company B: 0.99x = 30

When solving (though I know you didn't ask), do note that you cannot buy part of a song so you would need to round down to the nearest whole number.

So if you use company A, you divide both sides by 0.79 to isolate the variable x and satisfy the division principle of equality:

x = 30/0.79.

Simplify and your answer is 37.97, round down to 37 songs; you'd have 37 songs with company A and 77 cents left over in your account just sitting there because what really can you do with 77 cents on the App Store?

To model the song downloading situation with a budget of $30, we use the equations 0.79x <= 30 for Company A and 0.99x <= 30 for Company B, where x is the number of songs.

To model the situation where a student has $30 to spend on downloading songs, we can write two separate linear equations, one for each company. For Company A, which charges $0.79 per song, the equation will be:

0.79x ≤ 30

Where x represents the number of songs the student can download from Company A. For Company B, which charges $0.99 per song, the equation will be:

0.99x ≤ 30

Again, x represents the number of songs the student can download from Company B, but the cost per song is different, hence a different equation.

These equations are used to determine the maximum number of songs the student can download from each company without exceeding the $30 budget.

Answer:

I think I know this one. H is the answer. H is a reflection of A over the x-axis.

Answer:

The answer is EF

Step-by-step explanation:

Im smart

There are 21 nickels in carol bank

Solution:

Given that Carol's piggy bank consists of quarters and nickels

There are $ 4.55 in total

Let "a" be the number of nickels in bank

Let "b" be the number of quarters in bank

We know that,

1 quarter = $ 0.25

1 nickel = $ 0.05

Given that there are seven more nickels than quarters

Number of nickels = number of quarters + 7

a = b + 7 ---- eqn 1

From given question,

number of nickels in bank x value of 1 nickel + number of quarters in bank x value of 1 quarter = $ 4.55

[tex]a \times 0.05 + b \times 0.25 = 4.55\\\\(b + 7) \times 0.05 + b \times 0.25 = 4.55\\\\0.05b + 0.35 + 0.25b = 4.55\\\\0.3b = 4.55 - 0.35\\\\0.3b = 4.2\\\\b = 14[/tex]

Therefore from eqn 1

a = b + 7 = 14 + 7 = 21

a = 21

Thus there are 21 nickels in carol bank

Answer:

D

Step-by-step explanation:

Because B can be simplified to 3-4 ( which is the ratio needed)

therefor we know that Dis the answer

Answer:D.It is greater than the ratio of trumpets to clarinets.

First, you have to find the ratio flutes to violins. That is 9:12. Simplified, it is 3:4. Now, lets go down the list of options we have to pick

First option is A.It is the same ratio of violas to oboes. The ratio violas to oboes is 4:3. That is not the same as 3:4, so eliminate that option.

Second option is B.It is greater than the ratio of oboes to violas. The ratio oboes to violas is 3:4. This is the same as 3:4, so eliminate that option.

Third option is C.It is the same as the ratio of clarinets to trumpets. The ratio clarinets to trumpets is 6:2. That simplified is 3:1. This is not the same as 3:4. So lets eliminate that option. The only option left is option D, but how to check is down below.

Finally, the last option is D. It is greater than the ratio of trumpets to clarinets. The ratio trumpets to clarinets is 2:6. That simplified is 1:3. 3:4 is greater than 1:3, so D is the correct answer.

Answer:

Both answer shown

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7 [/tex]

Step-by-step explanation:

Given: Little confusion is in the question

e^ln7 x1

i.e [tex]e^{ln 7x}[/tex]

To Find:

[tex]e^{ln 7x}= ?[/tex]

Solution:

We know Logarithmic identity as

1. [tex]\ln e = 1[/tex]

2. [tex]\ln e^{x} = x[/tex]

Similarly,

3. [tex]e^{\ln x}=x[/tex]

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7\times 1=7 [/tex]

Answer:

7x

Step-by-step explanation: