Answers
Answer:
x = -1/3+3
slope = -1/3
Step-by-step explanation:
Related Questions
Solve the equation for all solutions in the interval. Write each answer in radians.
Answers
We are given a problem regarding trigonometric identities and asked to resolve for theta.
\(4\sec \theta-\sqrt[]{3}=\sqrt[]{3}+7\sec \theta\)Recall that:
\(\sec \theta=\frac{1}{\cos \theta}\)Therefore, we have:
\(\begin{gathered} \frac{4}{\cos\theta}-\sqrt[]{3}=\sqrt[]{3}+\frac{7}{\cos\theta} \\ \text{ We add }\sqrt[]{3}\text{ and subtract }\frac{7}{\cos\theta}\text{ from both sides to get:} \\ \frac{4}{\cos\theta}-\frac{7}{\cos\theta}=2\sqrt[]{3} \\ -\frac{3}{\cos\theta}=2\sqrt[]{3} \\ \text{Multiply both sides by }\cos \theta\text{ and divide both sides by }2\sqrt[]{3}\text{ to get:} \\ \cos \theta=-\frac{3}{2\sqrt[]{3}}=-\frac{\sqrt[]{3}}{2} \\ \theta=\cos ^{-1}(-\frac{\sqrt[]{3}}{2})=150^o \\ \end{gathered}\)In radians, we have:
\(\frac{150\pi}{180}=\frac{5\pi}{6}\)y=8-x
2x^2 + xy= -16
this is A simultaneous equation
Answers
Answer:
y=8-x→y+x=8
2x²+xy=-16→x²+xy=-x²-16
→x(x+y)=-x²-16→8x=-x²-16→x²+8x+16=0
→(x+4)²=0→x=-4→y=12
Given f(x) = x^2 + 2x and g(x) = 6 − x2 find (f + g)(x)
A.) (f + g)(x) = 2x + 6
B.) (f + g)(2x) + 2x + 6
C.) (f + g)(x) = 2x^2 + 8x
D.) (f + g)(x) = 2x^2 + 6
Answers
Hope it helps
find the reference angle for q= 7p/5
Answers
The reference angle for q = 7π/5 is -2π/5 radians.
To find the reference angle for an angle q given in radians, we need to determine the acute angle formed between the terminal side of q and the x-axis.
In this case, we are given q = 7π/5.
First, let's identify the quadrant in which the terminal side of q lies. To do this, we can compare the value of q to the angle measures of the quadrantal angles (0°, 90°, 180°, 270°, 360°) or the special angles in radians (0, π/2, π, 3π/2, 2π).
Since 7π/5 is greater than π (180°) but less than 3π/2 (270°), we can conclude that the terminal side of q lies in the third quadrant.
To find the reference angle, we consider the distance between the terminal side and the x-axis, measured in a counterclockwise direction.
The reference angle is formed by the terminal side and a line parallel to the x-axis that passes through the nearest x-axis intersection point (also known as the x-intercept) of the terminal side.
Since the terminal side of q lies in the third quadrant, the x-intercept is to the left of the origin.
To calculate the reference angle, we can subtract the absolute value of q from π (180°):
Reference angle = π - |q| = π - |7π/5| = π - (7π/5) = 5π/5 - 7π/5 = -2π/5
Given the angle q = 7π/5, we can determine the reference angle by finding the acute angle formed between the terminal side of q and the x-axis. By identifying the quadrant in which the terminal side lies, we establish that it is in the third quadrant. Subtracting the absolute value of q from π (180°), we find that the reference angle is -2π/5 radians.
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The price of a house DECREASED from $82500 to $77500. Calculate the PERCENTAGE DECREASE
with steps please and thank you
Answers
Answer:
6.06%
Step-by-step explanation:
\(percentage \: decrease \\ \\ = \frac{82500 - 77500}{82500} \times 100 \\ \\ = \frac{5000 \times 100}{82500} \\ \\ = \frac{500000}{82500} \\ \\ = 6.06060606 \\ \\ = 6.06 \%\)
how to find the number of solutions to a system of equations
Answers
Which of the following describes the idea of the Laffer Curve as it is expressed mathematically?
The ratios show the relationship between the federal income tax rates and revenue
To analyze how economic policies may affect growth and stability
Aggregate supply increases when production costs decrease.
reduce the government's role in the economy
Answers
The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.
The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.
Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.
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Melanie saves $20 every month in her savings account. She withdrew $60 one time to go shopping. She now has $280 in her account. write and solve an equation to determine how many months she has been saving up
Answers
Answer:
20x-60=280
Equation
So x for unknown amount of months, since 20 dollar each month 20x
-60 becuase she withdraws 60 one time
=280 becuase thats what she has left
Now solve
add 60 on both sides
20x=340
Divide 20 on both sides
x=17
17 months
9+g+6g–3
a
n
s
w
e
r
p
l
e
a
s
e
Answers
Answer:
6+7g
Step-by-step explanation:
9+g+6g-3=9-3+g+6g=6+g+6g=6+7g
how do you find circumstance of a circle using the area? please help!
Answers
Answer:
Step-by-step explanation:
The formula C = 2√πA is designed to find a circle's circumference using the area (A). Alternatively, you can solve the equation A = πR2 in reverse to find R, then plug R into the circumference equation.
7
Oliver makes a plan to be healthier, starting with exercising more often. He signs up for a karate class, thinking this will be a cool way to get active.After three weeks, Oliver finds himself dreading karate class. He would much rather stay home and play RPG with his friends. Since Oliver has already made the decision, what is the BEST path for him to take?
Answers
It a because i told the tese
The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty members are there at the college?
Answers
Answer:
111
Step-by-step explanation:
It is given that the student to faculty ratio at a small college is 17:3.
Let number of students and faculty members are 17x and 3x respectively.
It is given that total number of students and faculty is 740.
\(17x+3x=740\)
\(20x=740\)
Divide both sides by 20.
\(x=37\)
Number of student \(=17\times 37=629\)
Number of faculty members \(=3\times 37=111\)
Therefore, there are 111 faculty members at the college.
Answer:
102(D.)
Step-by-step explanation:
In a clinical trial to test a vaccine's effectiveness, the researchers report a slight reduction in the percentage of those catching the virus in comparison to those in a control group, and publish a p-value of 0.23. What is the best interpretation of this value
Answers
A p-value of 0.23 in the context of a clinical trial testing a vaccine's effectiveness suggests that the observed reduction in the percentage of individuals catching the virus, when comparing the vaccine group to the control group, is not statistically significant at conventional levels of significance (such as 0.05 or 0.01).
The p-value represents the probability of obtaining the observed data, or data more extreme, under the assumption that the null hypothesis is true.
In this case, the null hypothesis would typically state that there is no difference in the percentage of virus cases between the vaccine and control groups. A p-value of 0.23 indicates that there is a 23% chance of observing the reported reduction in cases or an even more substantial reduction if the null hypothesis were true.
Therefore, based solely on the p-value of 0.23, the best interpretation is that the observed reduction in virus cases could plausibly be due to random variation or chance, rather than a true effect of the vaccine. However, it is important to consider other factors, such as the study design, sample size, and clinical significance of the observed reduction, before drawing final conclusions about the vaccine's effectiveness.
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when a cold drink is taken from a refrigerator, its temperature is 5°c. after 25 minutes in a 20°c room its temperature has increased to 10°c. (round your answers to two decimal places.) (a) what is the temperature of the drink after 50 minutes?
Answers
The temperature of the drink after 50 minutes is -15°C. The temperature of the drink after 50 minutes can be calculated by using the concept of thermal equilibrium. The rate of temperature change is proportional to the temperature difference between the drink and the surrounding room.
After 25 minutes, the drink's temperature has increased from 5°C to 10°C. To calculate the temperature difference, subtract the room temperature (20°C) from the drink's temperature after 25 minutes (10°C). The temperature difference is -10°C (rounded to two decimal places).
Next, we can determine the rate of temperature change per minute. Divide the temperature difference (-10°C) by the time in minutes (25 minutes). The rate of temperature change per minute is -0.4°C/minute (rounded to two decimal places).
Now, we can calculate the change in temperature after 50 minutes. Multiply the rate of temperature change per minute (-0.4°C/minute) by the number of minutes (50 minutes). The change in temperature is -20°C (rounded to two decimal places).
Finally, add the change in temperature to the initial temperature of the drink (5°C) to find the temperature after 50 minutes. The temperature of the drink after 50 minutes is -15°C (rounded to two decimal places).
Therefore, the temperature of the drink after 50 minutes is -15°C.
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what is the constant of proportionality for the line on the graph below?
Answers
Answer:
you add then you multiply the number that you have and then whatever you get thats your answer
Step-by-step explanation:
hopes this help :)
a researcher conducts a study in which the same participants are observed across each level of the independent variable. if there are only two levels of the independent variable, then what type of t test is appropriate for this study?
Answers
One type of t test that is suitable for this study is the related one-sample t test.
What is a t-test?The T-test provides insight into whether the difference between the means of two groups is due to chance or is reliable (ie would be found again in another measurement from the same population).
What are the uses of t test?t test is used for following purposes :
1. Testing significance between hypothetical mean of sample and population mean.
2. Testing significance between mean of 2 different samples.
3. Testing significance between mean of sample post and prior to a stimuli or operation.
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Your friend says that the quotient 3/8 divided by 1/8 is 1/3 what is the correct quotient? What mistake did you friend likely make?
Answers
Answer:
its 1/8
Step-by-step explanation:
he said 1/3 it does not match the other 2 numbers hope its right ;-; also helpfull
What term is defined by the formula?
Answers
Olivia and Sam will randomly select mints from a jar that contains 7 blue mints and 3 orange mints.
Olivia selected a blue mint, replaced it back in the jar, and then selected an orange mint.
Sam selected a blue mint, did not replace it back in the jar, and then selected an orange mint.
Who had the highest probability?
Sam had the highest probability at 70%
Sam had the highest probability at 23.3%
Olivia had the highest probability at 70%
Olivia had the highest probability at 23.3%
Answers
The person with the highest probability is Sam with the highest probability at 23.3%
How to calculate the probability?From the information, Olivia and Sam will randomly select mints from a jar that contains 7 blue mints and 3 orange mints.
Olivia selected a blue mint, replaced it back in the jar, and then selected an orange mint. The probability will be:
= 7/10 × 3/10
= 21/100
= 21%
Sam selected a blue mint, did not replace it back in the jar, and then selected an orange mint. The probability will be:
= 7/10 × 3/9
= 21/90
= 23.3%
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Corresponding angles?
Helo im trying to pass
Answers
Answer:
Corresponding angles are
1 and 3
or 5 and 7
or 2 and 4
or 6 and 8
Step-by-step explanation:
month and a utility bill of $250 a month? 8. there are 52 weeks in a year, and you work 40 hours a week how much do you need to make an hour to make $60,000 a year?
Answers
We need to make approximately $28.85 an hour to make $60,000 a year, working 40 hours a week for 52 weeks.
To determine how much you need to make an hour to earn $60,000 a year, follow these steps:
1. Calculate the total hours worked in a year:
There are 52 weeks in a year, and you work 40 hours a week.
Multiply these values to find the total hours worked annually :
52 weeks * 40 hours/week = 2080 hours.
2. Divide the desired annual salary by the total hours worked:
To make $60,000 a year, divide this amount by the total hours worked (2080 hours):
$60,000 / 2080 hours = $28.85/hour.
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What is the slope of the line? Choose 1 answer:
A. 0
B. 1
C. 6
D. undefined
Answers
Answer:
D. undefined
Step-by-step explanation:
Since, line is perpendicular to x-axis, so it's slope would be undefined.
Hope it helps you in your learning process.
Desmos "Shelley the Snail"
Answers
The linear function in the context of this problem is defined as follows:
y = 18 - 2x.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.When the input is of zero, the output is of 18, hence the intercept b is given as follows:
b = 18.
When the input increases by one, the output decreases by two, hence the slope m is given as follows:
m = -2.
Then the function is given as follows:
y = 18 - 2x.
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True or false, the two triangles are congruent by ASA.
Answers
The two angles are not Congruent by ASA so it is false.
What are Congruent angles?Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
The two triangles are congruent but not by the ASA rule because only one angle is equal in both triangles and there are two corresponding equal sides in the both triangle so the correct rule is SAS.
In conclusion it is false that the two triangles are congruent by ASA.
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help me with this step by step
Answers
Answer:
C
Step-by-step explanation:
Elevation of the plane is y.
y =
The airplane starts at an elevation of 8500 feet
y = 8500
It is said that the plane loses elevation at a rate of 150 feet per minute.
y = 8500 - 150
We don't know how many minutes the plane has been losing elevation so we use m
y = 8500 - 150m
does 3/4x+x-5=10 + 2x have infinite solutions, one solution or no solutions
Answers
Answer:
x = 5; so basically one solution
how far does alex swim
Answers
Answer:
24 meters
Step-by-step explanation:
Tim needs a new car while he attends college in the United States for the next three years. The car he would like has a MSRP of $15,000. A local dealer can get him a 3-year loan with a 7% interest rate if Tim can give them a $1,500 down payment.
The same dealer offers the same car to lease with a money factor of 0.00271 and a residual value of 75%. The lease requires an additional fee of $1,250 to cover Tim’s security deposit and the acquisition and documentation fees for the car.
Tim is looking to drive the car home with the smallest initial out-of-pocket cost. Which of the following statements is true?
a.
The initial out-of-pocket cost is less for the lease.
b.
The initial out-of-pocket cost is less for the loan.
c.
The initial out-of-pocket cost is the same for the lease and loan.
d.
The initial out-of-pocket cost for a lease is not comparable to that of a loan.
Answers
Answer:
Its A. The initial out-of-pocket cost is less for the lease.
Step-by-step explanation:
I just got it right:)
Tim needs a new car when he is in college for 3 years. The car is like a $15,000 a local dealer got him a deal of 7% of interest worth a 3 year loan. If Tim can give him $1500 as a down payment.
Same dealers offer the very same car at a lease of 0.00271. and give a residual value of 75%. Tim is looking to drive the car back home with a small amount of cost from his pocket.He needs initially make out of the pocket costs less when taking the lease.
Hence the option A is correct.Learn more about the while he attends college in the United States.
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write each of the following base 10 number in base 2, base 4, and base 8.
a.137=
b.6243=
Answers
a) 137 in binary representation in base 2 is 10001001, in base 4 is 2021, and in base 8 is 211.
To convert 137 to base 2 (binary), we divide it by 2 repeatedly and record the remainders. The remainders, read in reverse order, give us the binary representation.
137 ÷ 2 = 68 remainder 1
68 ÷ 2 = 34 remainder 0
34 ÷ 2 = 17 remainder 0
17 ÷ 2 = 8 remainder 1
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Reading the remainders in reverse order, we get 10001001 as the binary representation of 137.
To convert 137 to base 4, we divide it by 4 repeatedly and record the remainders.
137 ÷ 4 = 34 remainder 1
34 ÷ 4 = 8 remainder 2
8 ÷ 4 = 2 remainder 0
2 ÷ 4 = 0 remainder 2
Reading the remainders in reverse order, we get 2011 as the base 4 representation of 137.
To convert 137 to base 8 (octal), we divide it by 8 repeatedly and record the remainders.
137 ÷ 8 = 17 remainder 1
17 ÷ 8 = 2 remainder 1
2 ÷ 8 = 0 remainder 2
Reading the remainders in reverse order, we get 211 as the octal representation of 137.
b) 6243 in base 2 is 1100001011011, in base 4 is 30223, and in base 8 is 14633.
To convert 6243 to base 2, we divide it by 2 repeatedly and record the remainders.
6243 ÷ 2 = 3121 remainder 1
3121 ÷ 2 = 1560 remainder 1
1560 ÷ 2 = 780 remainder 0
780 ÷ 2 = 390 remainder 0
390 ÷ 2 = 195 remainder 1
195 ÷ 2 = 97 remainder 1
97 ÷ 2 = 48 remainder 0
48 ÷ 2 = 24 remainder 0
24 ÷ 2 = 12 remainder 0
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading the remainders in reverse order, we get 1100001011011 as the binary representation of 6243.
To convert 6243 to base 4, we divide it by 4 repeatedly and record the remainders.
6243 ÷ 4 = 1560 remainder 3
1560 ÷ 4 = 390 remainder 0
390 ÷ 4 = 97 remainder 2
97 ÷ 4 = 24 remainder 1
24 ÷ 4 = 6 remainder 0
6 ÷ 4 = 1 remainder 2
1 ÷ 4 = 0 remainder 1
Reading the remainders in reverse order, we get 301203 as the base 4 representation of 6243.
To convert 6243 to base 8, we divide it by 8 repeatedly and record the remainders.
6243 ÷ 8 = 780 remainder 3
780 ÷ 8 = 97 remainder 4
97 ÷ 8 = 12 remainder 1
12 ÷ 8 = 1 remainder 4
1 ÷ 8 = 0 remainder 1
Reading the remainders in reverse order, we get 14633 as the octal representation of 6243.
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A spinner has 9 equal sections labeled A, B, C, D, E, F, G, H, and I. What is P(not A)? 89 23 13 19
Answers
Answer:
P(not A) = 8/9
Step-by-step explanation:
To write a simple probability, write a fraction. The bottom is all the possibilities, here there are 9. So put a 9 on the bottom. Then on top write how many ways the event can happen. There are 8 ways you can land on "Not A" (that is: B, C, D, E, F, G, H, I) So 8 goes on top. Simplify if possible. 8/9 cannot be simplified.
P(not A) = 8/9
As per the probability of an event, the value of P(not A) is 8/9.
What is the probability of an event?The probability of an event is the chance of happening that particular event.
Given, total number of events in the sample space = 9.
Number of favorable events in that sample space is = 1.
Therefore, the probability P(A) = 1/9.
Now, P(not A)
= 1 - P(A)
= 1 - 1/9
= 8/9
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