Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).
Step-by-step explanation:
Two lines are called perpendicular to each other if the product of their slope is -1.
Since, the slope of a line having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),
[tex]m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}[/tex]
While, The slope of line Joining points R(9, –6) and S(17, –5),
[tex]m_2=\frac{-5+6}{17-9}=\frac{1}{8}[/tex]
Since,
[tex]m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1[/tex]
Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).
70 is 25% of what number
What is the surface area of this design
Answer:
[tex]384\ in^{2} \\[/tex]
Step-by-step explanation:
Hello
according to the graph the figure is a cube, which has 6 square faces of 8 inches each side,the total area will be equal to the area of one of these faces multiplied by 6
Area of a square=side* side
Area of square= 8 in * 8 in
[tex]Area = 64\ in^{2} \\[/tex]
Now, the total area is
[tex]Tarea=6*64\ in^{2} \\Tarea=384\ in^{2}[/tex]
1 in= 1 inch = 2.54 cm
have a fantastic day
In algebra, why do you think that you are given many problems to solve that aren't really "real life" problems? For example, "Twice the sum of a number and 5 is 24. Find the number." ...?
Algebra problems may not seem like 'real-life' problems, but they help build a deeper understanding of mathematical concepts.
Explanation:Often, in algebra, you are given problems that may not seem like 'real-life' problems because they are designed to emphasize understanding the underlying concepts rather than simply executing a mathematical recipe. These problems aim to build a more meaningful understanding of the content by focusing on what the numbers represent and how they relate to each other. For example, in the problem 'Twice the sum of a number and 5 is 24. Find the number,' you can practice solving by setting up an equation and using algebraic manipulation to find the number.
equation for line parallel to 2x-3y+6=0, with the same y intercept
The number of private investigators is expected to increase from 52,000 in 2006 to 61,000 in 2016. If there are 648,982 police officers in 2006, how many police officers must there be in 2016 to have a greater percent increase than that of private investigators?
To have a greater percent increase than private investigators between 2006 to 2016, there must be approximately 760,945 police officers in 2016. This is found by applying the formula for percentage increase and adjusting it to find the required final number.
Explanation:The percent increase of private investigators from 2006 to 2016 is found by subtracting the initial number from the final number, then dividing by the initial number and multiplying by 100%. This formula gives us (61000 - 52000) / 52000 * 100 = 17.3%, rounded to the nearest tenth of a percent.
To have a greater increase in police officers than that of private investigators, the percent increase must be more than 17.3%. To find the required number of police officers in 2016, we first express 17.3% as a decimal, which is 0.173. Then we use the formula for percentage increase, which is (final number - initial number) / initial number = percentage increase. By rearranging the formula, we get the required final number = (initial number * percentage increase) + initial number. Substituting the given figures, we have (648982 * 0.173) + 648982 = 760945, rounded to the nearest whole number.
Therefore, there must be approximately 760,945 police officers in 2016 to have a greater percent increase than that of the private investigators.
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Is the number 53 a prime number or a composite number
Answer:
It's prime:)
Step-by-step explanation:
Which expression is equivalent to 3(x + 4y)?
6x + 16y
3x + 12y
8x + 24y
x + 4y
Jay earns $5.90 per hour working at the ice cream parlor after school. He needs at least $236 for a stereo system. Choose the inequality that describes how many hours Jay must work to buy the stereo system.
"Which ranges describe the cluster in the scatter plot?
Choose exactly two answers that are correct.
A.between 8 and 10 years of age
B.between 32 and 72 pages read
C.between 10 and 12 years of age
D.between 32 and 38 pages read"
Answer:
A and C
Step-by-step explanation:
A.between 8 and 10 years of age
C.between 10 and 12 years of age
Find the least residue of 7^5 mod 50 without using a calculator.
so far I have 7=7 mod 50 7^5 = 7^5 mod 50 7^2 = 49 7^3=343 since 7^2=(-1)mod50 and 7^3=(-43)mod50 it follows that 7^6=7^2 * 7^3 = (-1)(-43) = 43 feel like this is wrong though could somebody please explain where I have made an error?
a culture contains 1500 bacteria initially and doubles every 30 mins. a) find a function that models the number of bacteria at time t. b) find the number of bacteria after 2 hours. c) after how much time will there be 4000 bacteria ...?
solve for x
5(2x - 1) = 6
A)x=1/10
B)X=11/10
C)X=1/2
A triangle has side lengths of 12 cm, 35 cm, and 37 cm. Classify it as acute, obtuse, or right.
acute
obtuse
right
21 is 60 percent of what number
kenya picked 18 flowers from her garden. If 3/5 of flowers in her garden remain unpicked, how many flowers are still in her garden?
A side of the square is 4t. the area of the square is 400. what is the value of t?
The value of the variable 't' will be 5.
What is the area of the square?All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square.
Then the area of the square will be
Area of the square = a² square units
A side of the square is 4t. the area of the square is 400. Then the value of the variable 't' will be
400 = (4t)²
(4t)² - 20² = 0
(4t - 20)(4t + 20) = 0
t = -5, 5
Thus, the value of the variable 't' will be 5.
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change 50/16 into a mixed number .Reduce your answer to lowest terms a.48 3/16
b.3 1/25
c.3 1/8
d.4 7/8 ? ...?
What is 1 5/6 + 1/2 ?
a.
14/6
b.
17/12
c.
17/6
d.
25/12
which of the following is the sum of 3/18+2/18 reduced to lowest terms?
A submarine's elevation changes -657 feet over a period of 6 minutes. If the submarine descended at a constant rate, what is the approximate elevation change per minute?
-130 feet
-90 feet
-120 feet
-110 feet
The approximate elevation change per minute for the submarine is -109.5 feet.
Explanation:To find the approximate elevation change per minute, we need to divide the total elevation change by the total time taken. The submarine's elevation changes by -657 feet over a period of 6 minutes. So, we divide -657 by 6 to get the approximate elevation change per minute.
-657 / 6 = -109.5 feet
Therefore, the approximate elevation change per minute is approximately -109.5 feet.
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Which best describes the sides of any trapezoid?
A.
All sides are the same length.
B.
Only one pair of sides is parallel.
C.
Both pairs of opposite sides are parallel.
The answer is: only one pair of sides is parallel a.k.a b
Solve the system of equations below by graphing them with a pencil and paper. Choose the correct ordered pair (b, u).
u = -b + 21
u = -2b + 30 ...?
There are 132 people seated in the school auditorium for an assembly. There are 6 rows in the auditorium, each with the same number of seats. If the auditorium is completely filled, how many seats are there in each row?
What is the definition of percent??
Wren bought a baseball card last year for $2.25. this year the price dropped to $.45. what was the percent of decrease in the price of the card?
a. 80%
b. 400%
c. 500%
d. 120%
Answer:
a. 80%
Step-by-step explanation:
The percent of decrease can be calculated as:
[tex]Percentage Decrease = \frac{Initial price - Final Price}{ Initial Price}*100 [/tex]
Then, replacing initial price for $2.25 and final price for $.45 we get:
[tex]Percentage Decrease = \frac{2.25 - 0.45}{2.25} *100[/tex]
percentage of decrease = 80%
Finally the percentage of decrease in the price of the card is 80%
what does the 2 represent in 12.789
Make a mapping diagram for the relation.
{(–2, 2), (–1, –4), (0, –3), (2, 5)}
A basketball team averages 98 points in its first three games.How many points must it score in the next game in order to have 100 point average overall?
The basketball team must score 106 points in the next game to have a 100-point average overall.
To determine how many points the basketball team must score in the next game to have a 100-point average overall, we need to consider the total points scored in the first three games and the desired average.
The team has already played three games and has an average of 98 points. To find the total points scored in these three games, we multiply the average by the number of games:
Total points in the first three games = 98 points/game * 3 games = 294 points.
To have a 100-point average overall, the team needs to score a total of 100 points per game multiplied by the total number of games played, including the next game.
Let's represent the number of points needed in the next game as "x."
(294 points + x points) / (3 games + 1 game) = 100 points/game.
Simplifying the equation:
(294 + x) / 4 = 100.
Cross-multiplying and solving for "x":
294 + x = 400.
x = 400 - 294.
x = 106.
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What is 10 to the power of 3?
Help! Need help!
1. Justin is considering two websites for downloading music.The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+by=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Website 1:
Website 2:
2. Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=4x−4y=−4x+4
a. consistent b. consistent and coincident c. inconsistent