5. Triangle PQR has vertices P(-3,-1). Q(-1,7), and R(3, 3), and points A and B are midpoints of PQ and RQ, respectively.Use coordinate geometry to prove that AB is parallel to PR, and is half the length of PR. (6 pts]
Answers
This is a graph of the three initial points. Now we are going to graph the midpoints A and B.
But, first let's calculate the midpoints.
To calculate the average points we will use the following formula
\(\begin{gathered} P=(\frac{x1+x2}{2},\frac{y1+y2}{2}) \\ \end{gathered}\)For A
\(\begin{gathered} A=(\frac{-3-1}{2},\frac{-1+7}{2}) \\ A=(\frac{-4}{2},\frac{6}{2}) \\ A=(-2,3) \end{gathered}\)For B
\(\begin{gathered} B=(\frac{3-1}{2},\frac{3+7}{2}) \\ B=(\frac{2}{2},\frac{10}{2}) \\ B=(1,5) \\ \end{gathered}\)The graph shows the midpoints and the originals.
Visually we can check that the lines of those points are parallel. However, we are going to calculate the slopes of the points to prove it.
To calculate the slopes we will use the following formula
\(m=\frac{y2-y1}{x2-x1}\)Slope AB
\(\begin{gathered} m=\frac{5-3}{1-(-2)} \\ m=\frac{2}{3} \\ \end{gathered}\)Slope PR
\(\begin{gathered} m=\frac{3-(-1)}{3-(-3)} \\ m=\frac{4}{6} \\ m=\frac{2}{3} \end{gathered}\)As the slopes are equal we can conclude that the two segments are parallel.
Finally, we will calculate the length of each of the segments.
To calculate the length of the segments we will use the following formula
\(d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}\)For AB
\(\begin{gathered} d_{AB}=\sqrt[]{(1-(-2)^2+(5-3)^2} \\ d_{AB}=\sqrt[]{3^2+2^2} \\ d_{AB}=\sqrt[]{9+4} \\ d_{AB}=\sqrt[]{13} \end{gathered}\)For PR
\(\begin{gathered} d_{PR}=\sqrt[]{(3-(-1))^2+(3-(-3))^2} \\ d_{PR}=\sqrt[]{4^2+6^2} \\ d_{PR}=\sqrt[]{16+36} \\ d_{PR}=\sqrt[]{52} \\ d_{PR}=2\sqrt[]{13} \end{gathered}\)Now we can see that the PR segment is twice the AB segment
Related Questions
When Lauren left her house in the morning her cell phone battery was partially charged the charge remaining in Lawrence battery as a percentage can be modelled by the equation B equal 63 - 70where T is the number of hours since Lauren left her house what is the X intercept of the equation and what is its interpretation in the context of the problem
Answers
Answer: Intercept of the equation = (9,0)
Charge remaining in Lauren's battery is 0 after 9 hours( since Lauren left her house)
Step-by-step explanation:
Given: When t= the number of hours since Lauren left her house, the charge remaining in Lauren's battery, as a percentage, can be modeled by the equation B=63-7t .
To find the x-intercept, put B =0 (as x denoted the independent variable , here independent variable is 't')
Hence, the x-intercept of the equation = (9,0)
i.e. Charge remaining in Lauren's battery is 0 after 9 hours( since Lauren left her house)
Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answers
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
Help me pls this is due tomorrow I need help !!
Answers
Answer:
it's B.
Step-by-step explanation:
manuel knows that doubling either the width or length of a rectangle will double its area
On the first day of Middle School, the students ate 3/4 of the available ice cream. of the ice cream the students ate, 2/5 of it was fudge bars. What fraction of the available ice cream was fudge bars?
Answers
3/10
Explanation:Amount of icecream they ate = 3/4
Fraction of fudge bars = 2/5
Fraction of the available ice cream was fudge bars = 2/5 of 3/4
\(\begin{gathered} of\text{ means multiplication} \\ \frac{2}{5}\times\frac{3}{4} \end{gathered}\)\(\begin{gathered} =\frac{6}{20} \\ =\frac{3}{10} \end{gathered}\)Fraction of the available ice cream that was fudge bars = 3/10
Jason and his three friends went bowling. They bowled all afternoon and each paid $3.25 per game. Jason had a coupon for one free game. Three of his friends paid $2.75 each to rent shoes. Using this information, Jason writes the expression 3.25\left(g-1\right)+2.75\left(3\right). What does Jason’s expression represent? the number of friends who bowled the number of friends who bowled the number of games Jason and his friends bowled the number of games Jason and his friends bowled the amount of money Jason saved using the coupon the amount of money Jason saved using the coupon the amount of money Jason and his friends spent that afternoon
Answers
The expression 3.25(g-1) + 2.75(3) by Jason and his friends is a linear expression
The number of friends who bowled is 3The number of games Jason and his friends bowled is gThe amount of money Jason saved using the coupon is 3.25 The amount of money Jason and his friends spent that afternoon is 3.25(g-1) + 2.75(3)How to interpret the expression?The expression is given as:
3.25(g-1) + 2.75(3)
The above expression means that:
-1 represents the coupon on one free game3.25 represents the amount paid per game2.75 represents the amount paid to rent a shoe3 represesents the number of shoes they rentRead more about linear expressions at:
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PLEASE HELP ITS DUE TODAY!!
Answers
3. choice a (work shown in attached image)
4. Choice a (work shown in attached image)
Answer:
3a and 4a
Step-by-step explanation:
3. v = \(\pi r^{2} h\)
v = 3.14 x 4.1^2 x 5
v = 263.917 or 263.92
4. v = 4/3\(\pi r^{3}\)
v = 4/3 x 3.12 x 3.65^3
v = 203.59
Five thousand dollars is deposited into a savings account at 2.5% interest compounded continuously.
a. What is the formula for A(t), the balance after t years?
b. What differential equation is satisfied by A(t), the balance after t years?
c. How much money will be in the account after 5 years? (Do not round until your final answer. Round your final
answer to the nearest cent as needed.
d. When will the balance reach $7,000? (Do not round until your final answer. Round your final answer to the
nearest tenth as needed.)
Answers
Answer:
A). A(t) = P(1+r/n)^(nt)
B). DA/Dt = np(1+r/n)^(t)
C). A(5) =$ 5664.0
D).t = approximately 13.5 years
Step-by-step explanation:
A(t) = P(1+r/n)^(nt)
P = $5000
n= t
r= 2.5%
After five years t = 5
A(t) = P(1+r/n)^(nt)
A(5) = 5000(1+0.025/5)^(5*5)
A(5) = 5000(1+0.005)^(25)
A(5)= 5000(1.005)^(25)
A(5) = 5000(1.132795575)
A(5) = 5663.977875
A(5) =$ 5664.0
When the balance A= $7000
A(t) = P(1+r/n)^(nt)
7000= 5000(1+0.025/n)^(nt)
But n= t
7000= 5000(1+0.025/t)^(t²)
7000/5000= (1+0.025/t)^(t²)
1.4= (1+0.025/t)^(t²)
Using trial and error
t = approximately 13.5 years
12. Which of the following represents the linear equation 3(x + 2) = 12 - 2y in standard \ A|y=-3/2x+3 [B] y = 3/2x-3 3x - 2y = 10 D 3x + 2y = 6
Answers
Answer: The answer is D. 3x+2y=6, please mark me as brainliest, I want my brainliest back and I want very helpful for good!!!
Step-by-step explanation:
Which expression shows the first step in dividing 5x + 3 by x?
o 5x/ + 3/3
o 5x/x + 3/x
o 5x/5 + 3/5x
o 5x/5x + 3/5x
Answers
Answer:
second
Step-by-step explanation:
(5x+3)/x=
5x/x + 3/x=
5+3/x
Find the mean median mode and standard deviation with this frequency table
Answers
The mean and the standard deviation, from the frequency table, are given as follows:
Mean: 1.73.Standard deviation: 0.73.How to obtain the mean and the standard deviation for a frequency table?The frequency table gives the number of times that each observation appears.
The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:
Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.
The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:
Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.
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Wyatt was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 19%. What number should he multiply the cost of the meal by to find the total plus tip in one step?
Answers
Answer:
The cost of the meal should be multiplied by 1.19.---------------------------------------
Let the cost of the meal be x.
Adding a tip of 19%:
x + 19% = x + 0.19x = x (1 + 0.19) = 1.19xAnswer:
Wyatt should multiply with 1.19.
Step-by-step explanation:
Forming the expression,
→ 1 + (19% of 1)
Now the required number is,
→ 1 + (19% of 1)
→ 1 + ((19/100) × 1)
→ 1 + (19/100)
→ 1 + 0.19 = 1.19
Hence, required number is 1.19.
what answer? here, can you answer that? thankyou
Answers
It should be noted that the number of sample size based on the information will be 300.
How to explain the sampleIn order to calculate the sample size, we can use the following formula:
n = z² * p * (1-p) / E²
n = 1.96² * 0.5 * (1-0.5) / 0.05²
= 300
A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.
In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".
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Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a jfunction in terms of a for the balance of her savings account if she doesn't notice the monthly fee.
Answers
Answer:
see below
Step-by-step explanation:
balance = 200 - 5 m where m = number of months
A competitor moved into your area in late April this year. Based on percent change, which location's volume has been most negatively impacted?
Location 21
Location 34
Location 57
Location 63
Answers
The location's volume has been most negatively impacted is Location 63: option D
What is volume of returns?The volume of returns display low extreme correlation, meaning that a stock market crash or a stock market boom can be associated with both large and small volumes.
The given table shows
Volume over time
Locations May April May
last year This year this year
location 21 296 278 248
location 34 376 324 336
location57 354 328 314
location 63 226 186 198
Totals 1252 1116 1096
Based on this table, the volume of returns from last year may to this year April, the location that has least volume is location 63 option D
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Which table represents a linear function
Answers
Answer:
First table
Step-by-step explanation:
find b and round to the nearest tenth... (geometry) plz help fast i’m behind
Answers
Answer:
5.51 cm
Step-by-step explanation:
Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
Answers
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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If m
101, what is the value of x to
the nearest whole number?
Answers
Answer:
vp chop go go go go go go go go go
The ratio of girls to boys in a grade is 6 to 5. If there are 24 girls in the grade, how many students are there altogether?
Answers
Answer:
44
Step-by-step explanation:
24/4=6
5x4 = 20
20+24=44
What percentage of growth is needed annually to reach 400,000 in 3 years if today I have 200,000
Answers
Answer:
approx 26%
Step-by-step explanation:
you try find the multiplier
200000 * 1. ???? ^3= 400000
rearrange equation
\(\sqrt[3]{\frac{400000}{200000} }\) = multiplier
1.25992105
subract one
0.25992105
multiply by 100 to get percentage
25.9%
rounded to whole number = 26%
Which of these equations is linear
A. -3x+y=8
B. y=x²-3
C. 4y-2x³=0
D. 3=xy+9
Answers
Answer:
a) -3x + y = 8
Step-by-step explanation:
Now we have to,
→ find which of these equations is linear.
Format of linear equation,
→ Ax + By = C
Then the linear equation is,
→ Ax + By = C
→ -3x + y = 8
Hence, answer is -3x + y = 8.
Answer:
A. -3x + y = 8
Step-by-step explanation:
Definition of a Linear Equation:
A linear equation is an equation for a straight line.The highest power of its variables is always one.Each variable is multiplied by a constant only.A. -3x + y = 8This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.
B. y = x² - 3This is not a linear equation as the highest power of the term in x is 2.
C. 4y - 2x³ = 0This is not a linear equation as the highest power of the term in x is 3.
D. 3 = xy + 9This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.
What is the surface area of this shape?
Answers
Answer:
88 square cm
Step-by-step explanation:
Surface area of combined solids:Surface area of down rectangular prism:
l = 6cm ; w = 3 cm & h = 2 cm
\(\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}\)
= 2*(6*3 + 3*2 + 2*6)
= 2* (18 + 6 + 12)
= 2 * 36
= 72 cm²
Lateral surface area of the top rectangular prism:
l = 3 cm
w = 1 cm
h = 4 - 2 = 2 cm
LSA = 2h( l + w)
= 2*2 *( 3 + 1)
= 4 * 4
= 16 cm²
Surface area of the shape = 72 + 16
= 88 cm²
Answer:
a = 88 cm2
Step-by-step explanation:
\(a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15\)
\(a=88cm^{2}\)
Hope this helps
PLEASE HELP 2 QUESTONS ALL MY POINTS RIGHT ANSWER GETS BRAINLY PLEASE HELP I NEED ANSWERS NOW
Answers
Answer:
set 1 is 40
Step-by-step explanation:
In need of help for questions 2 and 3 please and thank you
Answers
The value of n from the given informal histogram is 11.7649.
What is data table?A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis.
2) The given data is
2 6 4 4 3 6 7 5 4 8
4 5 8 3 5 5 7 6 1 4
a) Ascending order of data 1 2 3 3 4 4 4 4 4 5 5 5 5 6 6 6 7 7 8 8
So, the frequency distribution table
Number Frequency
1 1
2 1
3 2
4 5
5 4
6 3
7 2
8 2
b) Here, n=20
3)
a) From the give graph n=1+3+3+4+2+1
n= 14
b) ∑x= (1×1+2×3+3×3+4×4+5×2+6×1)/14
= 48/14
= 3.43
c) ∑x²= 3.43²
= 11.7649
Therefore, the value of n from the given informal histogram is 11.7649.
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HOCKEY Andrew went to the hockey game. He paid $13.50 for admission. He bought a program for $4.75, a bag of a popcorn for $3.50, and a large drink for $3.35. How much did he spend in all ?
Answers
Answer:
$25.10
Step-by-step explanation:
We can find the total amount Andrew spent at the hockey game by finding the sum of each individual cost, including the costs for admission, the program, the popcorn, and the large drink
Total amount spent = 13.50 + 4.75 + 3.50 + 3.35
Total amount spend = $25.10
3/2 inches snow fell in 3/4 of an hour which two statements are true
Answers
Answer:
I don't see the two statements
Step-by-step explanation:
Answer:
A and E Usa test prep
Step-by-step explanation:
I know it might be late by now but this is for the people who are searching for the answer for the future
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
10.7
Step-by-step explanation:
Since this is a right triangle, we can use trig functions to calculate the hypotenuse.
We know the opposite side from the angle labeled 59 degrees.
sin 59 = opp side / hypotenuse
sin 59 = 9.2/x
x = 9.2/ sin 59
x = 10.733
the dice was thrown 35 times and following numbers were obtained prepare frequency table51423266142545361526254132141626333
Answers
This table shows the frequency of each number obtained after throwing the die 35 times
How to prepare frequency tableTo prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.
Numbers: 1, 2, 3, 4, 5, 6
Frequency: 5, 14, 6, 4, 5, 1
Based on the given numbers, the frequency table would look like this:
Number | Frequency
1 5
2 14
3 6
4 4
5 5
6 1
This table shows the frequency of each number obtained after throwing the die 35 times.
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PLEASE HELP NOW ITS DUE IN 5 MIN ONLY ANSWER S4 PLEASEEE
Answers
Answer:
R1 subtraction R2 distrivution S4 9x=61 R5 division
Step-by-step explanation:
Use the information to answer the question.
Miranda is making a vegetable salad. She adds 2 cups of cucumbers, 4 cups of carrots, and some cherry tomatoes. Then, Miranda puts all of the
salad into 5 bowls. She puts cups into each bowl.
How many cups of cherry tomatoes did Miranda put in the vegetable salad? Enter the answer in the box.
cups
Answers
Answer:
Step-by-step explanation:
The equation is poorly written and I cannot unfortunately solve it.