Draw triangle PQR with vertices P(1,2),Q(3, 3),R(2,6).find PQ.
Answers
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 1~~)^2 + (~~3 - 2~~)^2} \implies PQ=\sqrt{( 2 )^2 + ( 1 )^2} \\\\\\ \implies PQ=\sqrt{ 4 + 1 } \implies PQ=\sqrt{ 5 }\implies PQ\approx 2.24[/tex]
Related Questions
How would I do this one
Answers
Answer/Step-by-step explanation:
y = -x - 3
m = slope = (-1/1)
b = y-intercept = -3 or (0, -3)
Point 1: (0, -3)
Point 2: (-1, -2)
Point 3: (1, -4)
I hope this helps!
Answer:
Step-by-step explanation:
y=-x-3
x | -3 | 0 |
y | 0 | -3|
1) x=-3
y=-(-3)-3
y=3-3
y=0
Thus, (-3,0)
2) x=0
y=-0-3
y=-3
Thus, (0,-3)
What is the rate of change for this table?
Answers
———-
X2 - X1
M= 18 - 21
————-
-2 - -4
M = -3
——-
2
Rate of change (slope) = -3/2
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The value of the inequality expression given as –3(2x – 5) < 5(2 – x) are x < 5 and number line (4)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
–3(2x – 5) < 5(2 – x)
Open the brackets
So, we have
-6x + 15 > 10 - 5x
Collect the like terms
So, we have
5x -6x > 10- 15
Evaluate the like terms
So, we have
-x > -5
This gives
x < 5
When represented on a number line, it can be represented as the number line in option (4)
Hence, the equivalents of the inequality are x < 5 and number line (4)
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una tuberia tiene 7 tramos iguales de 0.75 m. ¿cual es la longitud de la tuberia?
Answers
Answer: la respuesta es 5.25
Step-by-step explanation: 0.75 x 7 = 5.25
Determine whether the table represents a linear or nonlinear function.
Answers
Answer:
Linear Function
Step-by-step explanation:
A linear function has constant slope
That means the ratio of y differences to x differences must be the same throughout the function. In other words the rate of change of the function y value is the same throughout the function
IF we look at the table we see that as x increases by 1, y decreases by 15
For example at x = 0, y = 20 and at x = 1, y = 5
So change in y/change in x = 0 = (5-20)/(1-0) = -15/1 = -15
If we look at another pair of points, say x = 1, y=5 and x = 2, y = -10
we get the rate of change = (-10 - 5)/(2-1) = -15/1 = -15
This is the same for any two x, y pair of values
So it is a linear function
WHAT IF? You need a mean score of at least 85 points to advance to the next round of the touch-screen trivia game.
A banner titled, Trivia Challenge shows your scores. The score with remarks are as follows. Game 1: 95, Very impressive. Game 2: 91, Good job. Game 3: 77, You can do better. Game 4: 89, Nice work.
Which scores in the fifth game will allow you to advance?
Answers
The mean score in the fifth game that will allow you to advance is 73.
What is the mean score that will allow you to advance?
The mean score in the fifth game that will allow you to advance can be gotten this way:
Assign the mean score, the variable, and x.
Compute the scores with remarks as follows:
95 + 91 + 77 + 89 + x ≥ 85
5
352 + x ≥ 85
5
85 × 5 = 425
352 + x ≥ 425
x = 425 - 352
x = 73.
So, the score in the fifth game that will allow you to advance will be 73.
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Last year you mowed grass and shoveled snow for 12 houses. You earned $225 for each lawn you mowed
and $200 for each house you shoveled for a total of $2600. How many lawns did you mow? How many
driveways did you shovel?
Answers
1800 lawns were mowed. 800 driveways were shoveled.
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Given Data
Let mowed grass be x
Let shoveled snow be y
Last year you mowed grass and shoveled snow for 12 houses
x + y = 12
y = 12 -x
You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.
225x + 200y = 2600
Equating value of y
225x + 200(12-x) = 2600
225x + 2400 - 200x = 2600
225x - 200x = 2600 - 2400
25x = 200
x = 8
For value of y,
y= 12 -x
y = 12 - 8
y = 4
Lawn mowed = 225(8)
Lawn mowed = 1800
Shoveled snow = 200(4)
Shoveled snow = 800
1800 lawns were mowed. 800 driveways were shoveled.
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The Marianas Trench in the Pacific Ocean is the deepest part of the ocean. It's depth is 6.85 miles. Sound
travels 4700 feet in one second under water. Find the time, to the nearest tenth of a second, it takes sound to
travel from the surface of the ocean to the bottom of the Marianas Trench and back.
Answers
6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second. The Time takes to travel the sound is 7.69.
Given that,
The deepest area in the ocean is the Marianas Trench in the Pacific Ocean. 6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second.
We have to calculate the time it takes for sound to travel from the ocean's surface to the Marianas Trench's depths and back, to the nearest tenth of a second.
We know the Distance formula is
Distance =rate×times
Time=Distance/rate
We convert 4700 feet to miles
We get,
4700 feet =0.89 miles
Now,
Time=6.85/0.89
Time=7.69
Therefore, the Time takes to travel the sound is 7.69.
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If I bought a scooter and it dropped by 24% in the FIRST year and after every year it drops by 13% for 7 years. I payed £850. How much is it worth now
Answers
Step-by-step explanation:
850÷100=17/2=8.5
8.5×24=204
850-204=646
646÷100=6.46
6.46×13=83.98 1st
646-83.98=562.02
562.02÷100=5.6202 2nd
5.6202×13=73.0626
562.02-73.0626=488.9574
488.9574÷100=4.889574 3rd
4.889574×13=63.564462
4.889574×13=63.564462
488.9574-63.564462=425.392938
425.392938÷100=4.25392938 4th
4.25392938×13=55.30108194
425.392938-55.30108194=370.0918561
370.0918561÷100=3.700918561 5th
3.700918561×13=48.11194129
370.0918561-48.11194129=321.9799148
321.9799148÷100=3.219799148 6th
3.219799148×13=41.85738893
321.9799148-41.85738893=280.1225259
280.1225259÷100=2.801225259 7th
2.801225259×13=36.41592836
280.1225259-36.41592836=243.7065975
I spent waaaaay to much time typing this
answer out I swear if it is incorrect I am done
£243.71
Solve for x (6x+5) 86
Answers
Answer:
x = -5/6
Step-by-step explanation:
First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.
PLEASE HELP Which equation is equivalent to -2a + 6b = -8c + 16? A. a=-4b-10c+14 B. a=-3b+2c+8 C. a=3b+4c-8 D. a=4b-10c+14
Answers
Answer: a= 3b + 4c -8
Step-by-step explanation:
a= 3b + 4c -8
-2a + 6b = -8c + 16
-6b from the left the isolate a
-2a = -6b - 8c + 16
then divide by -2 to cancel it out
a = 3b + 4c -8
The equation is equivalent to -2a + 6b = -8c + 16 will be a= 3b + 4c -8
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given the linear equation;
a= 3b + 4c -8
-2a + 6b = -8c + 16
-6b from the left the isolate a
-2a = -6b - 8c + 16
Then divide by -2 to cancel it out;
a = 3b + 4c -8
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Explain how you can represent a proportional relationship using an equation.
Answers
The proportional relationship can be represented by using an equation y = kx
Proportional relationship defined as the relationships between two variables where their ratios are equivalent. We can say that , in a proportional relationship, one variable is always a constant value times the other. That constant is called as the "constant of proportionality"
Consider y and x are in direct proportional relationship
y ∝ x
We can write this proportional relationship as
y = kx
Where y and x are the two variables
K is the constant of proportionality
In this equation we can see that the variable y is a constant value times the other variable x
Hence, the proportional relationship can be represented by using an equation y = kx
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7x-15= where x=3
[tex]222[/tex]
Answers
HELPPPPPP
You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end of the day you made $150. Let x represent the number of hotdogs sold and y represent the number of sodas sold. Write an equation that can be used to find the number of hotdogs and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the number of hot dogs and sodas sold.
Answers
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sol
Maybe sorry if i got it wrong
ANSWER QUICK PLEASE ILL GIVE BRAINLY AND POINTS
Answers
Answer:
x = -11
Step-by-step explanation:
JL + LM = JK + KM
x + 2 + 2x + 27 = 9 + 7
x + 2x + 22 + 27 = 9 + 7
Combine like terms,
3x + 49 = 16
Subtract 49 from both sides,
3x = 16 - 49
3x = -33
Divide both sides by 3,
x = -33/3
x = -11
OMG ITS DUE TMR HELP ME
Answers
Based on the points given for the line in the table, the equation in slope intercept form is y = -1/2 + 1
How to find the equation of the line?To find the equation of a line, you first need to find the slope of the line as:
= Change in y / Change in x
= (0 - 1) / (2 - 0)
= -1 / 2
= - 1/2
Using the slope, find the y-intercept:
y = slope(x) + y-intercept
0 = -1/2(2) + y-intercept
y-intercept = 0 + 1
y-intercept = 1
The equation in slope-intercept form is:
y = -1/2 + 1
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. (4, 9) and (1, 6) the slope between the two points
Answers
Answer: the slope is 1
Step-by-step explanation:
Is the relation represented in this table a function?
Is the relation in this set of points a function?
Answers
Answer:
the relation in the table is a function
the relation in the set of points is not a function
Step-by-step explanation:
the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.
F = G(m1m2/d2)
Solve for m1
Answers
Answer:
[tex]m_1=\frac{Fd^2}{Gm_2}[/tex]
Step-by-step explanation:
[tex]F=G \left(\frac{m_1 m_2}{d^2} \right) \\ \\ \frac{F}{G}=\frac{m_1 m_2}{d^2} \\ \\ \frac{Fd^2}{G}=m_1 m_2 \\ \\ m_1=\frac{Fd^2}{Gm_2}[/tex]
you repeatedly roll a fair six-sided die until you roll a 1 (and then you stop). every time you roll a 3, you win a points, and every time you roll a 6, you lose b points. you do not win or lose any points if you roll a 2, 4 or a 5. what is the expected number of points (as a function of a and b) you will have when you stop?
Answers
The expected number of points as a function of a and b is C = b+a.
In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.
x1 = roll a 1 -> P1 = 1/6
x2 = roll a 2 -> P2 = 1/6
x3 = roll a 6 -> P3 = 1/6
x4 = roll a 1, 4 or 5 -> P4 = 1/2
E = P1*x1 + P2*x2 + P3*x2 + P4*x4
x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)
C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)
1/6*C = 1/6*b + 1/6a
Solving for C
C = b+a
Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability) that are the results that are going to affect your game.
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Please answer the question in the photo
Answers
Answer: 40
Step-by-step explanation:
There are 9 cogs on the outside, and the circumference of a circle is 360 degrees. Dividing 360 by 9 yields 40 degrees.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
D
Step-by-step explanation:
There are 25 students competing in a volleyball tournament.
They are all wearing school colors. There are 4 students with blue shirts, 11 students with white shirts, and 10 students with yellow shirts.
A student is selected at random to be the captain. Match each probability to an outcome.
The captain has a blue shirt
The captain has a red shirt
The captain has a blue or white shirt.
impossible unlikely
neither unlikely nor likely
likely certain
Answers
Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.
The total number of students is 15.
4 students are wearing blue shirt.
11 students are wearing white shirt.
10 students are wearing yellow shirt.
Only any one student can be captain.
The total outcomes are 25.
Probability that the student has blue shirt B is,
Total favorable outcomes = 4
P(B) = 1/25.
Probability that the student has red shirt R is,
Total favorable outcomes = 0
P(B) = 0/25.
P(B) = 0
Probability that the student has blue or white shirt B and W is,
Total favorable outcomes = 15
P(B&W) = 15/25.
P(B&W) = 3/5.
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Model Real Life Tours of a space
center can have no more than
7 guests. There are 31 guests in line to
tour the space center. Complete the
statements.
tours are full.
tours are needed.
guests are in the last tour.
Answers
The number of centers that will be needed to contain the guests is 5.
How to calculate the value?It should be noted that the question isn't well written but will be answered based on the information given.
From the information, a space center can have at most 7 guests and there are 31 guests. In this case, the number of space centers needed will be calculated by dividing the number of guests by the numbers that are contained in each center.
This will be:
= Number of guests / Number contained by each center
= 31 / 7
= 4 3/7
In this case, since there's a remainder of 3, this implies that we will need an extra space center. Therefore,the total space centre will be:
= 4 + 1
= 5
In this case, the value of 5 that's gotten simply shows the number of space centers that will be needed.
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i need help! please is expression equivalent
Answers
No the value of functions are not same .
What is function in math?
A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.A function is a type of rule that generates one output for a single output. This is represented by the equation y=x2. Any inputs for x result in an output for y. Given that x is the input value, we would state that y is a result of x.- 5 × ( -5)⁻⁹ = -5 × 1/-5⁹ ⇒ 1/5⁸ = 1/390625
[ -5 × (-5)]⁻⁹ = [25]⁻⁹ = 1/25⁹ = 1/3814697265625
No the value of functions are not same .
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27 ÷ 9 = 3, therefore 27 ÷ 0.9 = 30.
True
False
Answers
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
please help me fasttt need to find the equation
Answers
The equation of the linear graph is expressed in slope intercept form as; y = 20x
What is the equation of the Linear Graph?The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept (which is the point where the line crosses the y-axis)
From the graph given we can see that the line crosses the y-axis at 0. Thus; c = 0
Now, we can pick two coordinates to find the slope;
Slope = (y2 - y1)/(x2 - x1)
Slope = (40 - 20)/(2 - 1)
Slope = 20
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Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2
Answers
Answer:
y = -3(x + 2)^2 + 10.
Step-by-step explanation:
y = –3x2 – 12x – 2
Divide first 2 terms by -3:
y = -3(x^2 + 4x) - 2 Now complete the square on x^2 + 4x:-
y = -3(x^2 + 4x + 4 - 4) - 2
y = -3[(x + 2)^2 - 4] - 2
y = -3(x + 2)^2 + 12 - 2
y = -3(x + 2)^2 + 10.
Prime Factorization *Student A stated that the PRIME FACTORIZATION of 96 is 2x3x5x5. *Student B said that the PRIME FACTORIZATION of 96 is 2x2x2x2x2x3. Mr. Hrenko asks three students to find the PRIME FACTORIZATION of 96. *Student C stated that the PRIME FACTORIZATION of 96 is 2x2x3x3x5. Which student is correct? Prove your answer by making a factor tree. O Student B Studnet C O None of the students are correct O Student A
Answers
The student that is correct with regards to the prime factorization of 956 is student B.
Which student is correct?A factor is a number that divides another number without leaving any remainder. For example, 10 is a factor of 100. A prime number is a number that is perfectly divisible by 1 and that number only.
For example, a prime number is 7. A prime factor is the factor of a number that is a prime number. For example, a prime factor of 28 is 2.
In order to determine the prime factorization of a number, express the number as its prime factors.
Prime factors of 92 = 2 x 2 x 2 x 2 x 2 x 3
Thus, it is only student B that is correct. 5 is not a factor of 96.
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The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toys car to Pete, they each owned an equal number of toy cars. How many toy cars did they have altogether?
Answers
Answer:
5:2
5x-30 = 2x+30
3x = 60
x = 20
total cars:
5(20)+2(20)
=100+40
=140cars