Recall that
tan²(x) + 1 = sec²(x)
for all x ≠ (2n + 1) 90°, where n is any integer. (That is, whenever x isn't an angle that is an odd multiple of 90°.)
Then
tan²(Φ) + sec²(Φ) = 3
tan²(Φ) + (tan²(Φ) + 1) = 3
2 tan²(Φ) + 1 = 3
2 tan²(Φ) = 2
tan²(Φ) = 1
tan(Φ) = ±√1
tan(Φ) = 1 or tan(Φ) = -1
Φ = tan⁻¹(1) + n 180° or Φ = tan⁻¹(-1) + n 180°
Φ = 45° + n 180° or Φ = -45° + n 180°
The first family of solution is the set of angles
{…, -315°, -135°, 45°, 225°, 405°, …}
and the second family is the set
{…, -405°, -225°, -45°, 135°, 315°, …}
(showing the solutions for n = -2 to n = 2)
You can condense the solution set into one family by noticing each angle is 45° plus some multiple of 90°, so that
Φ = 45° + n 90°
If you're looking for solutions in a given range, such as 0 ≤ Φ < 360°, then
Φ = 45°, 135°, 225° or 315°
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 12 B, and 48 C. Show the frequency and relative frequency distributions.
Answer:
CLASS FREQUENCIES RELATIVE FREQUENCIES
A 60 0.5
B 12 0.1
C 48 0.4
TOTAL 120 1
Step-by-step explanation:
Given that;
the frequencies of there alternatives are;
Frequency A = 60
Frequency B = 12
Frequency C = 48
Total = 60 + 12 + 48 = 120
Now to determine our relative frequency, we divide each frequency by the total sum of the given frequencies;
Relative Frequency A = Frequency A / total = 60 / 120 = 0.5
Relative Frequency B = Frequency B / total = 12 / 120 = 0.1
Relative Frequency C = Frequency C / total = 48 / 120 = 0.4
therefore;
CLASS FREQUENCIES RELATIVE FREQUENCIES
A 60 0.5
B 12 0.1
C 48 0.4
TOTAL 120 1
What is the missing number in this pattern?
2.704 * 10 = 27,04
2.704 * 100 = 270,4
2.704 * 1,000 = ???
Answer:
Step-by-step explain:
2.704 * 10 = 27,04
2.704 * 100 = 270,4
2.704 * 1,000 = 2,704
In equation form. What goes through the points (0, 4) and (2, 7)?
Answer:y=1.5x+4
Step-by-step explanation:
A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/15 for blue, 1/25 for green, 1/5 for pink, and 1/20 for black. What is the probability of pulling a black or pink card, written as a reduced fraction?
Answer:
Step-by-step explanation:
DAM I JUST STARTED LEARNING ABOut that
simplify:
[tex] \frac{ \sqrt{4} }{ \sqrt[3]{4} } [/tex]
choices:
[tex]4 \frac{5}{6} [/tex]
[tex]4 \frac{1}{6} [/tex]
[tex]4 \frac{3}{2} [/tex]
[tex]4 \frac{1}{3} [/tex]
Step-by-step explanation:
= 4^1/2 /4^1/3
=4^1/2-1/3
=4^1/6
There are a total of 168 hockey games in the season and 7 are played at night. The season is played for 14 months. How many games were played each month if each month has the same number of games?
Answer: 8
Step-by-step explanation: I added 7+14 then whatever i got i divied that by 168 so 168 by 21 which equals 8 but don’t hate if it’s wrong i’m only in the grade 5
2 + (3 + 5)2 ÷ 4 ⋅ 1 over 2 whole to the power of 4
Answer:
2 + (3 + 5)2 ÷ 4 ⋅ 1 over 2 whole to the power of 4
Step-by-step explanation:
Answer:
nauini
Step-by-step explanation:
Solve for x.
9 - 2x = 4x - 9
Answer: x = 3
Step-by-step explanation:
9 - 2x = 4x - 9
18 -2x = 4x
18 = 6x
x = 3
Answer:
1/3
Step-by-step explanation:
you add the 2x onto the 4x to get 6x on one side on the other side you add on the nine so now you have 18=6x then you divide by 18 to get 6/18 or simplified 1/3 also 33.3 as a decimal
A line passes through the point (-8,-5) and has a slope of 3/4. Write an equation in slope intercept form for this line.
Answer:
y = ¾x + 1
Step-by-step explanation:
Point-slope equation for line of slope ¾ that passes through (-8,-5):
y+5 = ¾(x+8)
Put into slope-intercept form:
y = ¾(x+8) - 5 = ¾x + 6 - 5 = ¾x + 1
Write the equation x2 + 6x + y2 – 8y = 19 in standard form.
Question 11 options:
1)
(x + 3)2 + (y – 4)2 = 44
2)
(x + 3)2 + (y – 4)2 =
3)
(x – 3)2 + (y – 4)2 =
4)
(x + 3)2 + (y + 4)2 = 44
Answer:
i think its 2
Step-by-step explanation:
The equation of x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44. Hence, Option A is the correct answer.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been given the equation as;
x² + 6x + y² - 8y = 19
We need to find the standard form of the equation.
Thus, we have,
(x² + 6x )+(y²- 8y) = 19
We shall complete the square for the term;
(x² + 6x + 9 - 9 ) + (y² + 4y + 16 - 16) = 19
Simplifying, we get,
(x² + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19
(x² + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19 + 9 + 16
Formula used :
x²+2xy+y² = (x+y)²
x²-2xy+y² = (x-y)²
Simplifying, we get,
(x + 3)² + ( y - 4)² = 44
Thus, the equation of x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44.
Hence, Option A is the correct answer.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ2
A bag of marbles contains 2 white, 3 black, 1 red and 4 blue marbles. Cate draws one marble from the bag, looks at it and then replaces it. What is the probability that she will draw a black marble and then a black marble?
A) 9/10
B) 9/100
C) 3/5
D) 1/25
Step-by-step explanation:
Number of black marbles = 3
Total number of marbles = 2 + 3 + 1 + 4 = 10
P(Drawing a black marble) = 3/10
Since the drawing is replaced,
they are considered independent events.
=> P(Black marble, following by black)
= [P(Drawing a black marble)]²
= (3/10)²
= 9/100. (B)
60 is it rocking horse has a weight limit of 60 pounds what percentage of the weight limit is 114 pounds
Answer:
86.4
Step-by-step explanation:
Choose all equations for which x=2 is a solution.
A:x+3=5
B:x+2=8
C:x+1=1
D:x-2=4
Ex-7=5-
Solve for x.
13(x-3) = 39
X=1
X=4
x=6
x=10
Click on the measure that is equivalent to 3 kilometers!
Answer:
3000
Step-by-step explanation:
Answer:3000
Step-by-step explanation:
why is it when you take a shower and you come out clean, how does the towel become dirty? This some real mathematics
okay. so, when you wash your hair, there is no way to get 100% of the shampoo/conditioner out of your hair, so the excess it rubbed onto the towel. Say you have no hair. The shower isn't germ-free, so even if you feel clean, the towel and yourself is still a harbor of germs, good and bad.
Which graph shows a proportional relationship between the number of hours of renting a camping tent and the total amounts back to work for camping tent?
Answer: Graph 2
Step-by-step explanation:
Which of the ratios below has a unit rate of 8? Select all that apply.
A) 40:5
B) 24:16
C) 96:12
D) 48:6
E) 2:24
A basketball player makes 145 out of 180 free throws. We would estimate the probability that the player makes the next throw to be
-4x + 12 = -6x
Step 1: Add 4x to both sides:
12 = -6x + 4x
Step 2: Combine like terms:
12 = -2x
uh- this is the correct way to answer the problem....
−4x+12=−6x
Step 1: Add 6x to both sides.
−4x+12+6x=−6x+6x
2x+12=0
Step 2: Subtract 12 from both sides.
2x+12−12=0−12
2x=−12
Step 3: Divide both sides by 2.
[tex]\frac{2x}{2}[/tex] = [tex]\frac{-12}{2}[/tex]
x=−6
What is the area of the region bounded by the lines x= 1 and y= 0 and the curve y=xe^x^2?
Answer:
A = 0.859
Step-by-step explanation:
We want to find the area of the region bounded by the lines x = 1 and y = 0 and the curve y = xe^(x²).
At y = 0, let's find x;
0 = xe^(x²)
Solving this leads to no solution because x is infinity. Thus we can say lower bound is x = 0.
So our upper band is x = 1
Thus,lets find the area;
A = ∫xe(x²) dx between 1 and 0
A = (e^(x²))/2 between 1 and 0
A = ((e¹)/2) - (e^(0))/2)
A = 1.359 - 0.5
A = 0.859
Solve 3a – 8= 5a + 12
Show your work. (please)
Answer:
a = - 10
Step-by-step explanation:
3a – 8 = 5a + 12
3a – 8 + 8 = 5a + 12 + 8
3a = 5a + 20
3a - 5a = 5a + 20 - 5a
- 2a = 20
[tex]\dfrac{-2a}{-2}=\dfrac{20}{-2}[/tex]
a = - 10
Max has 42 baseball cards. Jordan has b baseball cards. Max has 6 times as many baseball cards as Jordan Decide if each statement is correct. Choose Yes or No for each statement
Answer:
where are the statement?
Step-by-step explanation:
The length of a rectangle is 5 inches more than three times the width.The perimeter is 64 inches. Find the length and width.
Answer:
L=25.25 in
W= 6.75in
Step-by-step explanation:
Step one
Given data
Let the width be x
W= x
and length
L= 3x+5
Perimeter= 64 in
Step two:
we want to find the dimension of the rectangle
We know that perimeter is
P= 2W+2L
64= 2*x+2*(3x+5)
64= 2x+6x+10
collect like terms
64-10=8x
54= 8x
divide both sides by 8
x= 54/8
x= 6.75in
We know that the length is
L= 3x+5
L= 3*6.75+5
L= 20.25+5
L=25.25 in
A rectangular prism is a three-dimensional geometric figure, hollow or solid, contained by six rectangular sides that meet at right angles to form eight vertices. The maximum capacity of a rectangular prism is calculated with the formula,, where Volume and length, width, and height.
For a rectangular shaped box with a maximum capacity of 2.25 · 104 cubic meters, a length of 25 meters, a width of 2x meters and height of 1.5·102 meters, x =
meters.
Answer:B. C. D.
Step-by-step explanation:
what linear equation in slope intercept from does this graph represent?
Answer:
[tex]y = 16\frac{2}{3} x + 100[/tex] or [tex]y = \frac{50}{3} + 100[/tex]
Step-by-step explanation:
The equation of a line is [tex]y = mx + b[/tex], with [tex]m[/tex] being the slope and [tex]b[/tex] being the y-intercept.
We can see on the graph that the y-intercept, where the line crosses or touches the y-axis, is 100. So, our new equation is [tex]y = mx + 100[/tex].
Now we have to find the slope. Let's pick a point that's clearly on the graph. Perhaps (3, 150). And then we'll take the y-intercept point for convenience, (0, 100).
Then, we'll use [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1} }[/tex] to find the slope.
Let's substitute in our points.
[tex]\frac{150-100}{3-0}[/tex]
Simplify.
[tex]\frac{50}{3}[/tex]
Now, we can leave the slope like that or turn it into a mixed number. As a mixed number, your slope is [tex]16\frac{2}{3}[/tex].
We'll put that in our equation for a line and...bam!
[tex]y = 16\frac{2}{3} x + 100[/tex] or [tex]y = \frac{50}{3} + 100[/tex]
Given that R= 6x + 5y
Find y when x = 8 and R =20
Give your answer as an improper fraction in its simplest form
Answer:
-28/5=y
Step-by-step explanation:
20=6(8)+5y
20=48+5y
-28=5y
-28/5=y
help please. Find the measure of each angle
1. 139
2. 41
3. 139
4. 139
5. 41
6. 139
7. 41
how many times can 200 go into 487
A homeowner stays in a single location for an average of 20 years with a standard deviation of 5.7 years. What are the chances that someone lives in their home for 40 years or more?
Answer:
The Probability that someone lives in their home for 40 years or more
[tex]P(X\geq 40 ) = P( Z\geq3.50 )[/tex] = 0.0002
Step-by-step explanation:
Explanation:-
Given mean of the Population = 20 years
The standard deviation of the Population = 5.7 years
Let 'X' be the random variable in normal distribution
[tex]Z = \frac{x-mean }{S.D} = \frac{40-20}{5.7} = 3.508[/tex]
The Probability that someone lives in their home for 40 years or more
[tex]P(X\geq 40 ) = P( Z\geq3.50 )[/tex]
= 1 - P( Z< 3.50)
= 1 - ( 0.5 + A(3.50)
= 0.5 - 0.4998 ( from normal table )
= 0.0002