I guess you have to find
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}[/tex]
given that [tex]\tan\theta=\frac8{15}[/tex].
We can immediately solve for [tex]\sec\theta[/tex]:
[tex]\sec^2\theta=1+\tan^2\theta\implies\sec\theta=\pm\dfrac{17}{15}[/tex]
(without knowing anything else about [tex]\theta[/tex], we cannot determine the sign)
Then we get [tex]\cos\theta[/tex] for free:
[tex]\cos\theta=\dfrac1{\sec\theta}=\pm\dfrac{15}{17}[/tex]
and we can now solve for [tex]\sin\theta[/tex]:
[tex]\sin^2\theta+\cos^2\theta=1\implies \sin\theta=\pm\dfrac8{17}[/tex]
Notice that we have 2*2 = 4 possible choices of sign for either sin or cos.
• If both are positive, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{90}[/tex]
• If both are negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{480}[/tex]
• If sin is positive and cos is negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{480}[/tex]
• If cos is positive and sin is negative, then
[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{30}[/tex]
The string is 30 centermeters long how long is string in inches
Answer:
11.811 inches
Step-by-step explanation:
every inch is 2.54 centimeters
Answer:
11.811 inches
Step-by-step explanation:
divide the length value by 2.54
If f(x) = 22 – 4x – 5, find the following:
a. f(-2)
b. f (10)
.c. f(0)
Answer:
a.25
b.-23
c.17
Step-by-step explanation:
Plug each value in for x and solve
The gift box is 10 cm x 12 cm x 3 cm what is the volume of the box
Answer:
volume = L*B*H
Step-by-step explanation:
SO,
Volume of the box = L*B*H
OR, Volume of the box = 10*12*3
thus, Volume of the box =360
The regular price of a color tv is 559.45. during a sale, hill tv is selling the tv for 457.41. Determine the percent decrease in the price of the tv.
Answer:
478
Step-by-step explanation:
559.45-457.41=102.04
102.04/559.45*100
approximately 478
Identify the binomial
Step-by-step explanation:
where are the numbers?
Find the value of x in each case:
Answer:
KLP=54, LPM=18, PMN=108
Step-by-step explanation:
x+3x+2x+72=180
6x=108
x=18
3x=54
x=18
2x+72=108
Round 3528003 to the nearest million
Answer:
it would be rounded to about 4028003
Step-by-step explanation:
Answer:
4,000,000
Step-by-step explanation:
Solve the equation 7 minus 2X equals 19
Answer: x=-6
Step-by-step explanation:
Answer:
x=-6
Step-by-step explanation:
Put it in an equation,
7-2x=19
Solve for x
Subtract 9 on both sides
-2x=12
Divide -2 on both sides
x=-6
What does the grid represent
Answer:
0.030
Step-by-step explanation:
I don't really know how to explain this one, sorry.
Hope this helps! (✿◕‿◕✿)
[tex]\tt Step-by-step~explanation:[/tex]
We have to find out what the shaded regions represent. We can count up ten rectangles in total, and three of them are shaded. We take the amount of shaded rectangles over the total amount to get [tex]\tt \frac{3}{10}[/tex] as a fraction, and 0.3 as a decimal.
[tex]\tt First~option:[/tex]
The first choice is 0.300. The zeroes at the end of the number do not mean anything, so we can simplify it to 0.3. 0.3 is equal to 0.3, so this is not the answer.
[tex]\tt Second~ option:[/tex]
The second choice is 0.30. Again, we can simplify it to 0.3. We can see that it is equivalent to 0.3, so this is not the answer, either.
[tex]\tt Third~option:[/tex]
Our third choice is 0.3. 0.3 = 0.3, so this is not our answer either.
[tex]\tt Fourth ~option:[/tex]
Our final choice is 0.030. Take out the last zero to get 0.03. 0.03 is equal to [tex]\tt \frac{3}{100}[/tex], so this is our answer, since it is not 0.3.
[tex]\large\boxed{\tt Our ~final~answer:~Last~option:~0.030}[/tex]
At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same
Answer: $7.50
Step 1: Divide.
10 ÷ 4 = 2.50
Step 2: Multiply.
2.50 × 3 = 7.50
The answer is 7.50
2 ton of rocks cost $2,920.00. What is the price per pound?
Answer:
$0.73 per pound
Step-by-step explanation:
2920 divided by 4000 (2 tons is 4000 pounds) equals 0.73
a(x+y)-a(x-y) simplified .
Answer:
2ay
Step-by-step explanation:
a(x+y)-a(x-y)
Distribute
ax +ay - ax + ay
Combine like terms
2ay
Work Shown:
a(x+y)-a(x-y)
ax+ay-ax+ay
(ax-ax)+(ay+ay)
(0ax)+(2ay)
0+2ay
2ay
Question 5 (1 point)
A rectangle has a length of x + 7 and a width of x - 2. Write an
equation that describes the area, A, of the rectangle in terms of
Ob
A = 2x + 5
A = x2
+ 9x - 14
A = 2x + 9
ос
Od
A=x²+.
= x + 5x – 14
Answer:
A = x^2 + 5x - 14
Step-by-step explanation:
A = L × W
A = (x+7) × (x-2)
A = x^2 + 7x - 2x - 14
Answer the following question. What is 6x-7-12x+3?
Answer:
-6x-4
Step-by-step explanation:
Combine 6x and −12x to get −6x.
−6x−7+3
Add −7 and 3 to get −4.
−6x−4
Answer:
-6x-4
Step-by-step explanation:
6x-12x
-6x
-7+3
-4
-6x-4
Please help quick
Divide polynomials using long division
(13q–91)÷(q–7)
Answer:
13
Step-by-step explanation:
q-7 can go into 13q-91 thirteen times.
Set up the long division sign with the q-7 on the outside and the 13q-91 inside.
Then, notice that to get to 13, you multiply the q and 7 by 13. This gets both terms to 13q and 91, which cancel out the numbers inside the long division sign.
Tim read 70% of his book containing 230 pages how many pages does he have left
69 Pages are left to read by Tim.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total pages= 230
Percentage of reading = 70%
So, number of Pages Tim reads
= 70 /100 x 230
= 161 pages
Hence, number of pages left = 230- 161 = 69 pages
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NEED HELP GIVING 20 POINTS
Answer:
-5
Step-by-step explanation:
Just substitute the values and use a calculator to solve.
Determina la ecuación de recta de una recta en su forma estándar, tal que contiene al
punto(3,-4) y es paralela a la recta que pasa por (0,2) & (3,1).
-5(x+2)+3x= Which expression can be written in the box on the other side of the equation
Answer:
O-2(x+5)
Step-by-step explanation:
I have to much time on my hands
Answer:
-2x-10
Step-by-step explanation:
-5(x+2)+3x=
Distribute
-5x-10 +3x
Combine like terms
-2x-10
Janice is roller skating at a constant speed away from her house. The first half of the street is flat, but the second half has a steep upward hill. Janice moves more slowly as she skates up the hill.
Which graph shows Janice's position as she roller skates away from her house?
A. Z
B. X
C. W
D. Y
Answer:
It's Z.
Step-by-step explanation:
Because the road is straight at first, then it gets steep.
which means that the road goes down,
kinda like a drop off.
Answer:
Y moving quicker, then moving slower rate
Circle YES or NO The terms -5x and 5x are like terms.
Answer:
YES
Step-by-step explanation:
Answer:
yes!
Step-by-step explanation:
x are still the same term whether they are negative or not! Good Luck!
which number line represents the solution to -2X equals 4
Answer:
It is B
Step-by-step explanation:
67 times a number minus 65 is equal to -4 less than the number
Answer:
Translation is 67x-65=x-4, you can use any variable for the number.
Step-by-step explanation:
Simplify (x^2/7)^3/4
Answer:
(x^2)^(3/4)/7^(3/4)
Step-by-step explanation:
help help help help help help
Answer:
no, its an acute triangle
Step-by-step explanation:
Answer:
This is not a right triangle
Step-by-step explanation:
The reason as to why this is a right triangle is because I used the equation a2 + b2 = c2. * = 2
24* + 42*= 2340
26*= 676
2340 is not the same as 676
Therefore the triangle is not a right triangle
True statement about parallelogram
All four sides are congruent.
Answer:
a parallelogram is a simple non-self-intersecting quadrilateral with two pairs of parallel sides.
Step-by-step explanation:
sin θ=√5/3, cos θ=2/3
3/2
2√5/5
√5/2
3√5/5
9514 1404 393
Answer:
cos θ = 2/3
Step-by-step explanation:
We presume you want the value of the cosine for
sin θ = √5/3 ≈ 0.745356
__
There are several possible approaches you can take to this problem.
1) Using the trig identity:
cos = √(1 -sin²)
cos θ = √(1 -(√5/3)²) = √(1 -5/9) = √(4/9)
cos θ = 2/3
__
2) Another approach you can take is to use a calculator to find the angle, then use the calculator to find the cosine of the angle.
cos θ = cos(arcsin(√5/3)) = cos(arcsin(0.745356)) = cos(48.19°) ≈ 0.666667
cos θ = 2/3
__
3) Yet another approach is to check the answer choices for reasonableness.
You are given sin θ = 0.745356. This is more than 0.707107, the value where sine and cosine are equal, so the cosine value must be less than 0.707. The answer choices are ...
2/3 ≈ 0.667
3/2 . . . greater than 1; not a viable cosine value
2√5/5 ≈ 0.894 . . . too large
√5/2 . . . greater than 1; not a viable cosine value
3√5/5 . . . greater than 1; not a viable cosine value
So, just looking at the values of the offered answer choices, you can choose the correct one. It is the only value with the appropriate magnitude.
cos θ = 2/3
10.2 is 21.25% of what number?
Answer: 48
Step-by-step explanation: Using proportions
48 is the number whose 21.5 percent is 10.2 .
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100.
How to convert a percentage into a number?Divide the given percentage by hundred to convert it into a number.
Let x be a number whose 21.5% is 10.2.
Therefore,
[tex]\frac{21.25}{100} (x) = 10.2[/tex]
⇒ [tex]21.25x = 10.2(100)[/tex]
⇒[tex]21.25x = 1020[/tex]
⇒[tex]x = \frac{1020}{21.25}[/tex]
⇒[tex]x = 48[/tex]
Hence, 48 is the number whose 21.5 percent is 10.2.
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Solve for a. 3(a+3)+6=30
Answer:
a = 5
General Formulas and Concepts:
Order of Operations: BPEMDAS
Properties: Distributive, etc.
Step-by-step explanation:
Step 1: Write equation
3(a + 3) + 6 = 30
Step 2: Solve for a
Distribute 3: 3a + 9 + 6 = 30Combine like terms: 3a + 15 = 30Subtract 15 on both sides: 3a = 15Divide 3 on both sides: a = 5Step 3: Check
Plug in a to verify it's a solution.
Substitute: 3(5 + 3) + 6 = 30Add: 3(8) + 6 = 30Multiply: 24 + 6 = 30Add: 30 = 30Suppose the dimensions of your dining room are 12 feet by 14 feet. You purchase a rectangular table that is 7 feet by 9 feet. After you put the table in the dining room, how much space is left in the dining room (in square feet)?
7 x 9 = 63
12 x 14 = 274
add them together and you gey the total space left