Answers
For the first pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
For the second pair of points: the first point has a tangent value of -sqrt(3), while the second has a tangent value of -1/sqrt(3), so these are not identical.
For the third pair of points: the first point has a tangent value of sqrt(3), while the second also has a tangent value of sqrt(3), so these have the same reference angle.
For the fourth pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
So the only correct answer is the third choice.
Related Questions
(0.2,3),(0.4,6) what is the slope? 10,15,20,25
HELP PLEASE
Answers
Answer:
15
Step-by-step explanation:
Use the slope formula to find the slope m.
m= y2-y1 / x2-x1
m= 6-3/0.4-0.2
m=15
Find the simple interest. $7,064 at 6.5% for 8 months
Answers
Simple Interest can be calculated using the formula I=Pr t
Here I= interest earned ,P= Principal ,R= rate of interest ,t= time in years.
It is given Principal P=$7,064
Rate r=6.5% =0.065
Time t= 8 months =[tex] \frac{8}{12} =\frac{2}{3} [/tex] years
Substituting these values in I = P r t
I =(7064)(0.065)([tex] \frac{2}{3} [/tex])
Solving for I
I=306.11
interest earned on $7,064 at 6.5% for 8 months is $306.11
A roped off area of width x is created around a 4-foot by 6-foot rectangular museum of display of Native American artifacts. The combined area of the display and the roped-off is 120 square feet. Find the width.
Answers
x----------> width a roped off area
we know that
(4+2x)*(6+2x)=120
then
4*6+4*2x+2x*6+2x*2x=120 ---> 24+8x+12x+4x²=120 -------> 4x²+20x+24=120
4x²+20x-96=0
using a graph tool---------> to calculate the quadratic equation
see the attached figure
the solution is
x=3 ft
the answer is
the width a roped off area is 3 ft
The width of the roped off area around the museum display is 4 feet.
To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:
Area of display + Area of roped-off region = Total Area
(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120
24 + (24 + 4x + 12x + 4x2) - 24 = 120
Simplifying, we get:
4x² + 16x - 96 = 0
Divide by 4:
x² + 4x - 24 = 0
Factor the quadratic equation:
(x + 6)(x - 4) = 0
Setting each factor equal to zero gives us two potential solutions:
x + 6 = 0
or
x - 4 = 0
Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:
x = 4 feet
The width of the roped-off area is 4 feet.
Find the zeros of the function. f(x)=9x^2-12x-5
Answers
You can use the quadratic formula or you can do any method that your teacher teaches you (box, etc.)
Explanation:
1) Set the given function equal to 0: 9x^2 - 12x - 5 = 0
2) make 9x^2 = (3x)^2 and 12x = 4(3x)
=> (3x)^2 - 4(3x) - 5 = 0
3) Factor the polynomial:
(3x - )(3x + ) first stept of factoring.
Now find two numbers that sum - 4 and their product of - 5, those are -5 and + 1: =>
(3x - 5) (3x + 1) = 0
4) Set the two factors equal to 0:
3x - 5 = 0 => 3x = 5 => x = 5/3 ↔ one root
3x + 1 = 0 => 3x = - 1 => x = - 1/3 ↔ the other root.
How many real number solutions does the equation have?
0=5x^2+2x-12
A- one solution
B- two solution
C-infinity many solutions
D-no solutions
Answers
x=(-b+sqrt(b^2-4ac))/2a and x=(-b-sqrt(b^2-4ac))/2a
Substituting using the equation 0=5x^2+2x-12
x=(-2+sqrt(2^2-4(5)(-12)))/(2(5)) and x=(-2+sqrt(2^2-4(5)(-12)))/(2(5))
Since the sqrt(244) is a real number, there are two real solutions.
75 less than twice a number
Answers
Will mark brainliest ⭐️⭐️⭐️⭐️⭐️
Answers
is a hope this helped
Answer:
answer is d
Step-by-step explanation:
Suppose that a system has 5000 grasshoppers. how many hawks would be expected?
Answers
What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.
Answers
Final answer:
The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.
Explanation:
The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.
Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.
−1
−0.75
−0.5
−0.25,
Answers
AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
=[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
= [tex] \sqrt{4+49} [/tex] =
= √53
- Hence, we know that the distance between point A and the point C to be found is:
AC = √53 / 4
- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:
y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4
This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)
- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
=[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
=[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
=[tex] \sqrt{(53/4) x^{2} } [/tex] =
=+/-(√53/2)x
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)
Since point C is towards point B, we have to take the negative answer:
x = -(1/2)
- Therefore the correct answer is C: -0.5
Phil is a commercial fisherman. He keeps 5 salmon for every 8 cod he catches. If Phil keeps 15 salmon, how many cod will he keep?
Answers
3 * 8 = 24 cod
What is 5% in a decimal and a fraction?
Answers
That is, 5% means 5/100. This is your fraction. It can be reduced to 1/20.
As a decimal, of course, 5/100 = .05, a number with 5 in the hundredths place.
which do you think would seat more people a 4ft by 6 ft rectangular table or a circular table with a diameter of 6 ft? How many people would sit at each table? Explain your reasoning.
Answers
For the rectangle, you will find the perimeter:
P = 2l + 2w
2 x 6 + 2 x 4
P = 20 feet
For the circle you will find the circumference:
C = pi x d
3.14 x 6
C = 18.84 feet
The rectangle would seat more people because the distance around the table is longer.
You would be able to fit about 7-8 people around the rectangular table and 6-7 people around the circular table.
Final answer:
Comparing a 4ft by 6ft rectangular table and a circular table with a 6ft diameter, the circular table can seat more people (approximately 9) due to more efficient use of its perimeter, compared to the rectangular table which can seat 6 people.
Explanation:
The question asks which table would seat more people: a 4ft by 6ft rectangular table or a circular table with a diameter of 6ft. To answer this, we need to compare the arrangements and sizes of the two tables.
The rectangular table measures 4 feet by 6 feet. Typically, a person needs about 2 feet of space at a dining table to sit comfortably. Therefore, on the longer sides (6 feet), you can seat 3 people on each side, for a total of 6. On the shorter sides (4 feet), it's not practical to seat anyone due to space constraints and leg room. So, the rectangular table can seat 6 people.
The circular table has a diameter of 6 feet. Placing chairs around a circle often allows for more efficient use of space. If we assume each person requires the same 2 feet of space, roughly, the circumference of the table (which is π * diameter) dictates how many people can sit around it. The circumference of a 6-foot diameter table is about 18.85 feet (π * 6). Dividing this by 2 feet per person, you can seat approximately 9 people around the circular table.
In conclusion, a circular table with a diameter of 6 ft would seat more people, approximately 9, compared to a 4ft by 6ft rectangular table, which would seat 6 people. This is due to the circular table's ability to more efficiently use the perimeter for seating.
Which fraction is NOT equivalent to 8 1/2 ? A) 2 3 B) 24 36 C) 4 6 D) 6 10
What is 5 x 2/3?
A) 3 1/3
B) 3 2/5
C) 5 2/3
D) 10/15
Answers
The answer for the second question is A. 3 1/3. 5/1 x 2/3 =10/3 10/3=3 1/3
5 times the sum of p and r
A.5(p+r)
B.5p+r
C.5pr
D.5+p+r
Answers
Option: A is the correct answer.
The mathematical representation of the given statement is:
[tex]5(p+r)[/tex]
Step-by-step explanation:We are asked to represent the given expression in words to numerical expression.
The statement is:
5 times the sum of p and r
The sum of p and r is: (p+r)
and now 5 times the sum of p and r i.e. 5 is multiplied to the sum of p and r.
i.e.
[tex]5(p+r)[/tex]
Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2 . What is the value of x?
Answers
Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:
24/(x-2) = 20/5
Cross multiply:
24*5 = 20(x-2)
Use the distributive property:
120 = 20x - 40
Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x
Divide both sides by 20:
160/20 = 20x/20
8 = x
A $50,000 investment earns 18% annually. If B represents the balance and t represents the number of years, determine an expression that gives the account balance, B, after t years. Also, determine an equivalent expression that displays the effective monthly interest rate.
Answers
FV=P(1+r/100)^t
FV is the future value
P is the principle
r is the rate
t is the time
the formula that gives the account balance after t years will be:
FV=50000(1+18/100)^t
FV=50000(1.18)^t
The formula for effective monthly interest rate will be:
monthly interest rate=(annual rate)/(number of months)
annual rate=18%
number of months in a year=12 months
rate=18/12=1.5%
Answer:
usa test prep its B
Step-by-step explanation:
Justin lives in saint paul and goes to school in minneapolis. in the morning, he has 333 transportation options (bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home. if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?
Answers
Answer:
2/9
Step-by-step explanation:
TRUST ME THIS GUY ABOVE ME IS A DING DONG
Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.
Answers
x = the number of years that Shannon has had the bracelet
Replace x with 5 to find the total number of charms after 5 years
2*5 + 4 = 14 charms after 5 years.
Please explain it and tell me how u got the answer
Thx
Answers
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
___
The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1
Please help me please
Answers
_____
The other selections are nonsense.
Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa
Answers
How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?
Answers
The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;
to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.
A system of linear equations can be solved by three major methods which are;
- Elimination method
- Substitution method
- Graph method
Now, in this question we want to know how substitution method is done.
Let us say we have two simultaneous equations which are;
2x + 3y = 8 ----(eq 1)
x + 5y = 11 ----(eq 2)
Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.
In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;
x = 11 - 5y
In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.
Read more at;https://brainly.com/question/19770914
What context clue in the paragraph best helps in understanding the meaning of the word native?
Question 2 options:
"much in America"
"lived in Nantes, France"
"first in France"
"born in Louisiana"
Answers
What needs to happen before you can use the reason CPCTC?
Answers
Explanation:
1) CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.
2) Therefore, to use that reason you first need to prove that the the triangles are congruent.
3) Once, it has been stated that the triangles are congruent, then you can use the reason to state the the corresponding segments are congruent which will let you to state the length of any side of one triangle known the corresponding side of the other triangle, because they are congruent (have the same length).
If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)
A. $10.59
B. $8.76
C. $10.80
D. $18.25
Answers
find the area of the circle .Leave your answer in terms of pie (3.14) the area is 4.1m .I need help on this question
Answers
Answer:
Area of the circle = 1.3π m²
Step-by-step explanation:
Area of the circle is given by the formula A = πr²
It is given that area of the circle is 4.1 m² and we have to convert it in the terms of π.
Now to convert the area in terms of π we will multiply the area by π and divide the area by 3.14.
⇒ Area×π / 3.14 = 4.1 × π/3.14 = 1.30π
Therefore answer is area of the circle = 1.30π m²
Perform the indicated operation. (r + s)(r2 - rs + s2)
Answers
The operation in the equation, (r + s)(r2 - rs + s2), is solved by distributing the multiplication of the binomial across each term in the trinomial. When the multiplications are complete and the terms are added, the resulting solution is r3 + s3.
Explanation:The indicated operation in the question is the multiplication of the binomial, (r + s), and the trinomial, (r2 - rs + s2). This can be performed by using the distributed property of multiplication over addition. In this case, you would multiply each term in the binomial by each term in the trinomial, then add the products. So the solution will be:
r3 - r2s + rs2 + r2s - rs2 + s3 = r3 + s3
Note: the terms -r2s and r2s cancel each other out, as do the terms rs2 and -rs2, which is why the final result is r3 + s3.
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Ben walks at a rate of 3 miles per hour. he runs at a rate of 6 miles per hour. in one week, the combined distance that he walks and runs is 210 miles.
b. (using 3x + 6y = 210 with x representing walk and y representing run) ben runs for 25 hours. for how many hours does he walk?
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PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER!
Answers
Our expression is 5/x^-2y^5
The first thing we notice is that we have a negative exponent in the denominator. This is easily solved if we switch the term with the negative exponent into the numerator.
Our expression now looks like this: 5x^2/y^5
Now, there aren't any other terms that cancel out, so our simplified expression is 5x^2/y^5.