Solve the trig equation on the interval [tex]0 \leqslant theta \: \ \textless \ 2\pi[/tex][tex]3 sec \: \: theta \: - 2 \sqrt{3 } = 0[/tex]
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Answers
Answer:
pi/6 and 11pi/6
Explanation
Given the trigonometry equation:
[tex]\begin{gathered} 3\text{sec}\theta\text{ - 2}\sqrt[]{3}=0 \\ \end{gathered}[/tex]Add 2\sqrt[3] to both sides as shown;
[tex]\begin{gathered} 3\sec \theta-2\sqrt[]{3}=0+2\sqrt[]{3} \\ 3\sec \theta\text{ = 2}\sqrt[]{3} \\ \sec \text{ }\theta\text{ = }\frac{2\sqrt[]{3}}{3} \\ \frac{1}{\cos \theta}=\frac{2\sqrt[]{3}}{3} \\ \cos \theta\text{ =}\frac{3}{2\sqrt[]{3}} \\ \cos \text{ }\theta\text{ = }\frac{3\sqrt[]{3}}{2\cdot3} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the cos inverse of both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=30^0 \end{gathered}[/tex]Since theta is between 0 and 2pi
theta = 360 - 30
theta = 330^0
Convert to radians
180^0 = pi rad
30^0 = x
180x = 30pi
x = 30pi/180
x = pi/6
Similarly;
180^0 = pi rad
330^0 = x
180x = 330pi
x = 330pi/180
x = 11pi/6
Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6
Related Questions
Draw a slope triangle, from point B, whose horizontal leg is along the x-axis. What are the lengths of the vertical and horizontal legs of your slope triangle?
Answers
Horizontal leg = 6 units
Vertical leg is 4 units
Lets Represent the diagonal as line AB where A and B are the endpoints of the line segment
The coordinates of point A is ( 12,4)
The coordinates of point B is ( 6,0)
Slope = ( Y2 - Y1 ) / (X2 -X1) = (0 - 4) / ( 6 - 12) = -4 / -6 = 2/3
or simply.
slope = rise / run = vertical leg/ horizontal leg = 4/6 = 2/3
ANSWER
Horizontal leg = 6 units
Vertical leg is 4 units
Slope = 2/3
Emilio borrows $1200 from a bank with 8% simple interest per year.How much will he have to pay back total in 2 years
Answers
The amount of money that Emilio will pay back in two years is $1392.00.
What is the accrued amount of the loan?The accrued amount includes principal plus interest.
Simple interest formula can be expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is rate and t is time elapsed.
Given the data in the question;
Principal P = $1200Simple interest rate r = 8%Time t = 2 yearsAccrued amount A = ?First, converting percent to decimal.
Rate r = 8% = 8/100 = 0.08
Now, plug the given values into the above formula and solve for the accrued amount.
A = P( 1 + rt )
A = $1200( 1 + 0.08 × 2 )
A = $1200( 1 + 0.16 )
A = $1200( 1.16 )
A = $1392.00
Therefore, the accrued amount is $1392.00.
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Use BIMDAS to calculate my fortnightly earnings.
I have two part-time jobs.
3 days per week I work for 6 hours each day and I earn $20.00 per hour. For 2 days per week, I earn $25.00 per hour, working an 8-hour day.
Answers
Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520
How to find the earnings?First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)
= (3 x 6 x 20)
The find out how much you earn in the second part-time job:
= (Number of days per week x Number of hours per day x Pay per hour)
= (2 x 8 x 25)
In a fortnight (two weeks), your earnings would be:
= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
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Fortnightly earnings would be $1,520 based on previous earnings.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that there are two part time jobs.
For first part time
3 days per week I work for 6 hours each day and I earn $20.00 per hour
(3 x 6 x 20)
=360
Second part time
2 days per week, I earn $25.00 per hour, working an 8-hour day.
=2×25×8
=400
Now we need to calculate, the total fortnightly earnings.
= (2 weeks x360) + (2 weeks x 400)
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
Hence $1520 is the fortnightly earnings.
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yesterday han drove 1 hour longer than ian at an average speed 5 miles per hour faster than ian. jan drove 2 hours longer than ian at an average speed 10 miles per hour faster than ian. han drove 70 miles more than ian. how many more miles did jan drive than ian?
Answers
Total 150 miles Jan drove than Ian.
Set the time Ian traveled as I, and set Han's speed as H.
Therefore, Jan's speed is H+5.
We get the following equation for how much Han is ahead of Ian;
H + 5I = 70.
The expression for how much Jan is ahead of Ian is; 2 (H + 5) + 10I
This simplifies to: 2H + 10 + 10I
However, this is just 2(H + 5I) + 10
Substitute, from the first equation, H + 5I as 70
Therefore, the answer is 140 + 10, which is 150.
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Rewrite the following calculation so it involves addition only and then determine the result. Show your work.
-3+1-7- (-4)+10
URGENT PLEASE HELP FOR HW
Answers
The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.
According to the question,
We have the following expression:
-3+1-7- (-4)+10
Now, we have to remove all the negative signs from this expression.
So, we will first solve this expression to the step where we have only addition.
Now, we know that the multiplication of two negative integers is always positive.
-3+1-7+4+10
Adding the numbers with the negative sign:
-10+10+1+4
1+4
5
Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.
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Leo wants to buy two pairs of shoes. He found the shoes at two different stores at different prices and discounts. Store X is offering 10% off the price of the shoes. Store Y is offering $6 off the price of the shoes. For each shoe price listed in the table, indicate which store offers the lowest discounted price. Select the correct answer in each row.
Answers
The correct option regarding the discounts is given as follows:
Store Z has the best sale price of $28.
How to calculate the discount?The discount can be a percentage or an amount off, and the calculations are explained as follows:
Percentage: the original price is multiplied by the subtraction of one and the equivalent decimal of the discount.Amount off: the equivalent amount is given by the original amount subtracted by the amount off. ($6 off, the amount is subtracted by $6).Considering the discount plans and the original price of $35, the discounted prices in this problem are as follows:
Store X: 0.85 x 35 = $29.75.Store Y: 35 - 5 = $30.Store Z: 4/5 x 35 = 0.8 x 35 = $28.Hence the correct statement is given as follows:
Store Z has the best sale price of $28.
Missing information
The complete problem is:
Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale:
Store X is offering 15% off the price of the shoes.Store Y is offering $5 off the price of the shoes.Store Z is offering a ⅕ discount off the price of the shoes.Which statement about the sale price of these shoes is true?
Store X has the best sale price of $20.Store Z has the best sale price of $28.Store Y has the best sale price of $30.More can be learned about discounts at https://brainly.com/question/7459025
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Write a multiplication problem with two fractions that has a simplified product of 4/5.
Answers
A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
What is a fraction in mathematics?A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.
The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;
let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]
The multiplication product is therefore;
[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]
The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5
Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]
The multiplication problem is therefore;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
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please help thank you, due soon
Answers
Answer:
8.1
Step-by-step explanation:
just calculate 45 of 18%
a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error. the sample standard deviation. the estimated standard error. the population mean. the population standard deviation.
Answers
A parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is the population mean.
What is meant by population mean?The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The μ sign stands for the population mean.
The average calculated from the entire group, distribution, or population is known as the population mean. It is calculated by dividing the sum of all population variables by the total population of variables. Here, μ exists the population mean. ∑X exists the sum of all the observations in the population.
The population mean is a quantity that expresses the population's overall degree of individual variation, which is often unknown.
Therefore, the correct answer is option c) the population mean.
The complete question is:
a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error.
a) the sample standard deviation.
b) the estimated standard error.
c) the population mean.
d) the population standard deviation.
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a newsletter publisher believes that 60`% of their readers own a laptop. is there sufficient evidence at the 0.050.05 level to refute the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answers
The null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
What is null and alternative hypothesis?
The null hypothesis is that the statement that researchers usually aim to disprove by performing tests of significance on the dataset. the most purpose of the null hypothesis is to help disprove a hypothesis or nullify it in favor of the alternate hypothesis that the researchers want to prove.
Let the percentage of readers who own a laptop be [tex]x.[/tex]
As newsletter publisher believes that [tex]60[/tex]`% of their readers own a laptop.
Therefore the null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
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5. Which equation is solved for the height of the cone based on theinformation given below?The equation V = 1 r represents the volume of a cone, where is the radius of the cone andh is the height of the coneh=V - Tr?h= } #r?VB3V - #r2 = h3Vha?D
Answers
We need to make h the subject of formula:
[tex]\begin{gathered} All\text{ the variables on the right are multiplied together.} \\ \text{First we get rid of the 1/3 by multiplying both sides by 3:} \\ 3(V)\text{ =3( }\frac{1}{3}\pi r^{2}h) \\ 3V\text{ = }\pi r^{2}h \end{gathered}[/tex][tex]\begin{gathered} \text{For h to stand alone on the right side, we divide both sides by }\pi r^2h \\ We\text{ apply division beause all the variables were ultiplied together} \\ So\text{ to undo it, we divide} \\ \frac{3V}{\pi r^{2}}=\text{ }\frac{\pi r^{2}h}{\pi r^{2}} \\ \frac{3V}{\pi r^2}=\text{ }h \end{gathered}[/tex][tex]h\text{ = }\frac{3V}{\pi r^{2}}\text{ (option D)}[/tex]the heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches. (a) if 10 men are selected at random, what is the probability their average height is above 72 inches? (b) if exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) what is the 80th percentile for the average height of 10 men? (d) what is the probability the average height of 10 men is between 70 and 71 inches?
Answers
a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.
b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.
c) The 80th percentile for the average height of 10 men is 0.0097%.
d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.
Mean = 69.7 inches
Standard Deviation = 2.8 inches
a) Using normal distribution,
P(Y > 72) = P(Y - mean > 72 - mean)
P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))
P(Y > 72) = P(Z > 2.25)
P(Y > 72) = 1 - P(Z ≤ 2.25)
P(Y > 72) = 0.0122
b) P(man's height is above 72 inches) = 0.0122
c) (80 × 0.0122) ÷ 100
= 0.0097%
d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)
P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))
P( 70 > Y > 71) = P(0.107 > Z > 0.464)
P( 70 > Y > 71) = 0.13607
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a marksman has a probability of 0.268 for hitting a certain long-range target. what is the probability that it takes 5 shots for the marksman to hit the long-range target? (round your answer to three decimal places, if necessary.)
Answers
The probability of the marksman hitting the long-range target in 5 shots is 0.1429.
The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.
P = 0.268
x = 5
Use the geometric probability mass function below to calculate the probability:
P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P
P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268
P(X = x) = 0.1429
The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.
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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be:
Answers
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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Round 34,582 to the nearest thousand.
Answers
Answer:
35000
Step-by-step explanation:
So the number is 34582
now look at the hundreds
if it is 5 or over then we add a thousand to and subtract what ever the lower than thosand
and in this case it is 5 so we round UP
and now we have 35000
The answer is 35,000.
To round to the nearest thousand, we look at the last three digits. If these digits are 500 or greater, then we round the thousands digit up, and if they are less than 500, then we round down, keeping the thousand's digit the same.
Since in this case the last three digit consists of 582 which is greater than 500 so we round the thousands digit up i.e. from 4 to 5 in this case.
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The temperature is −4°F. What will the temperature be if the temperature rises 20°F?
Answers
Answer:
16°F
Step-by-step explanation:
The temperature is −4°F. What will the temperature be if the temperature rises 20°F?
-4 + 20 = 16
so:
16°F
What is 4x + y = -3?
Answers
Answer:x=
−1/4y+ −3/4
Step-by-step explanation
If a and b are two events defined on the same sample space, given that p(a) = 0.28 and p(aub) = 0.51, find the p(b) such that a and b are mutually exclusive
Answers
P(B) such that a and b are mutually exclusive is 0.23
A group of potential results from a specific experiment is an event. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events.
Given: P(A) =0.28
P(AUB) = 0.51
We know,
P(AUB) = P(A) + P(B) - P(A∩B)
Since A and B are mutually exclusive events, they cannot happen together.
So, P(A∩B) = 0
Then,
P(AUB) = P(A) + P(B)
0.51 = 0.28+ P(B)
P(B) = 0.51 - 0.28 = 0.23.
Hence, P(B) = 0.23
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solve by graphing 6X + 3y equals 12 x + 4y equals 24
Answers
The system of equations is:
[tex]\begin{gathered} 6x+3y=12 \\ 8x+4y=24 \end{gathered}[/tex]To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:
[tex]\begin{gathered} \text{Solving the first equation for y:} \\ 6x+3y=12 \\ 3x=-6x+12 \\ y=-2x+4 \\ \text{Solving the second equation for y:} \\ 8x+4y=24 \\ 4y=-8x+24 \\ y=-2x+6 \end{gathered}[/tex]We have two equations to graph:
[tex]\begin{gathered} y=-2x+4 \\ y=-2x+6 \end{gathered}[/tex]Comparing with the slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.
The graph of the two equations is shown in the following image:
Where the green line is the first equation, and the red line is the second equation.
There is no solution to this system of equations because the lines do not intersect each other.
If f(x)=−13, find x.
Select one:
a. −3
b. −27
c. −51
d. −72
Answers
Two or more expressions with an Equal sign is called as Equation. x=-3 for function f(x)=−13.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We know that f(x) = -13. This means that:
f(x)= -13 = 2x-7
-13= 2x-7
Now we all need to do is solve this equation. First add 7 to both sides
-13 + 7= 2x
-6=2x
Divide by 2 on both sides.
-6 ÷ 2= x
x= -3
Hence x=-3 for function f(x)=−13.
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A scientist has 2 3rd liter of solution. He uses 1 halfof the solution for an experiment. Howmuch solution does the scientist use forthe experiment?
Answers
SOLUTION
The total amout of solution given is
[tex]\frac{2}{3}\text{liter}[/tex]From thequestion, 1/2 of the solution is used, then the amount of solution used for the experiment will be
[tex]\frac{2}{3}\times\frac{1}{2}=\frac{2\times1}{3\times2}=\frac{2}{6}=\frac{1}{3}\text{liters }[/tex]Hence
The amount of solution the scientist use is 1/3 litres
answer pls
1. A surfer paddles out past breaking waves, rides a
wave, paddles back out past the breaking waves,
rides another wave back to the beach. Draw a sketch
of a graph (with labels) that shows the surfer’s
possible distance from the beach over time.
2. For the table, identify the independent and
dependent variables, Represent the relationship
using words, an equation and a graph.
# of cases of
bottled
water, c
# of bottles
of water,
b
1 24
2 48
5 120
10 240
20 480
for this one i only need the graph cannot find it out
3. Sketch a graph of the function shown by the table. Is
its linear or nonlinear?
x y
1 0
2 1
3 8
4 20
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway
Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
7. Tell whether the relation is a function. Explain your
reasoning. find graph below
Describe the pattern in the sequence. Find the next
two terms of the difference.
-2, -5, -8, -11,
the graph for 7
Answers
Answer:
V = 243 - 0.2s
Step-by-step explanation:
See attached document for questions 1 - 3.
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway.
Volume Remaining (V) = Initial - Used
Volume Remaining (V) = 243 ft^3 - (0.2 ft^3/shovel)(s shovels)
V = 243 - 0.2s
6. Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
This is not a function. When x = 8, it results in more than one output.
7. Pattern:
-2
-5
-8
-11
Each step decreases by 3
-14
-17
8.
combine the like terms to create an equivalent expression -4r - 2r + 5
Answers
Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2
good luck
Step-by-step explanation:
X AND Y (PLEASE HELP)
Answers
Answer:
HERE YOU GO HOPE IT HELPS
FREE BRAINlIEST IF CORRECT: Find an equation of the perpendicular bisector of the segment AB with endpoints A(1, 2) and B(–3, 4). If the perpendicular bisector of AB intersects the x‑axis at point P, what are the lengths of PA and PB ?
Answers
The lengths of PA and PB are 3.1622 units if the point is P (0, 5).
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of the distance between two points exists P(x₁, y₁) and Q(x₂, y₂) is given by:
d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
The given points exists A(1, 2) and B(–3, 4).
The perpendicular bisector of AB will pass through the midpoint of AB.
Now the perpendicular bisector of AB will meet the Y-axis at P(0, y).
∴ AP = BP
Applying the distance formula, we get4
⇒ PA² = PB²
⇒ (x₁ – 0)² + (y₁ – y)² = (x₂ – 0)² + (y₂ – y)²
⇒ (1 – 0)² + (2 – y)² = (–3 – 0)² + (4 – y)²
After solving, we get y = 5
Therefore, the point is P (0, 5).
Now calculating the lengths of PA and PB
PA = √(1 – 0)² + (2 – 5)² = 3.1622
PB = √(-3 – 0)² + (4 – 5)² = 3.1622
Therefore, the lengths of PA and PB are 3.1622 units.
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One month Ivan rented 8 movies and 3 video games for a total of $43. The next month he rented 2 movies and 5 video games for a total of $32. Find the rental cost for each movie and each video game.
Answers
Given
Let's represent movies with M
Let's represent video with V
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ 2m+5v=32\ldots\text{Equation 2} \end{gathered}[/tex]Solution
Using substitution method
I will solve your system by substitution.
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ \text{Make M the subject of the formula} \\ 8m=43-3v \\ \text{Divide both sides by 8} \\ m=\frac{43-3v}{8}\ldots\text{Equation 3} \end{gathered}[/tex]Substitute for m in Equation 2
[tex]\begin{gathered} 2(\frac{43-3v}{8})+5v=32 \\ \\ \frac{43-3v}{4}+5v=32 \\ \end{gathered}[/tex]To clear the fraction multiply all through by 4
[tex]\begin{gathered} \frac{43-3v}{4}\times4+5v\times4=32\times4 \\ \\ \\ 43-3v+20v=128 \end{gathered}[/tex]Separate the similar term
[tex]\begin{gathered} -3v+20v=128-43 \\ 17v=85 \\ \text{Divide both sides by 17} \\ \frac{17v}{17}=\frac{85}{17} \\ \\ v=5 \end{gathered}[/tex]Substitute for v =5 in equation 3
[tex]\begin{gathered} m=\frac{43-3v}{8}\ldots\text{Equation 3} \\ m=\frac{43-3(5)}{8} \\ m=\frac{43-15}{8} \\ \\ m=\frac{28}{8} \\ \\ m=\frac{7}{2}=3.5 \end{gathered}[/tex]The rental cost for each movie
[tex]m=\text{ \$}3.50[/tex]The rental cost for each video game.
[tex]v=\text{ \$5}[/tex]For each sequence, determine whether it appears to be arithmetic. If it does, find the common difference.
Answers
We are to determin if the following sequence are arithmetic and also fin their common difference if they are arithmetic.
(1) -3, -9, -27, -81, ................
This sequence is not an arithmetic sequence because theere is no common difference.
-9 - -3 = -27 - -9
-9 + 3 = -27 + 9
-6 ≠ -18
Therefore is not an arithmetic sequcence.
(2) 13, 17, 21, 25, ......................
This sequence is an arithmetic sequence.
It has a commdon difference of 4
17 - 13 = 21 - 17
4 = 4
Therefore, the sequence is an arithmetic sequence.
(3) -6, -2, 2, 6, .........................
This sequence is an arithmetic sequence.
It has a common difference of 4
-2 - -6 = 2 - -2
-2 + 6 = 2 + 2
4 = 4
Therefore, the sequence is an arithmetic sequence
x+6x-5x=x+114 Please help.
Answers
"Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answers
The slope of the line = rise of the line / run of the line = 2/2 = 1.
How to Find the Slope of a Line?The slope (m) of a line can be determined by finding the ratio of the rise of the line to the run of the line, which is, the change in y over the change in x.
Referring to the image attached below, the blue line in the given graph shows the rise of the line while the red line shows the run of the line.
Therefore:
Rise of the line = 2 units
Run of the line = 2 units
Slope of the line (m) = rise/run = 2 units/2 units
Slope of the line (m) = 1
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Pls pls help due tomorrow!
Answers
If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
The equation is
y = -x
The slope intercept form
y = mx+b
Where m is the slope of the line
Comparing the slope intercept form and the given equation
Slope of the line m = -1
The line is passing through the points (-8,2)
The point slope form of the line
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-2 = -1(x-(-8))
y-2 = -1(x+8)
y-2 = -x-8
y = -x-8+2
y = -x-6
Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
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