Answers
Answer:
[tex]\tan (A+B) =-\frac{680}{111}[/tex]
Step-by-step explanation:
[tex]\tan A=\frac{12}{5}[/tex]
[tex]\cos B=\frac{45}{53}\implies \sec B=\frac{53}{45}[/tex]
Now, by trigonometric identity:
[tex]\tan^2 B =\sec^2B-1[/tex]
[tex]\implies \tan^2 B =\bigg(\frac{53}{45}\bigg)^2-1[/tex]
[tex]\implies \tan^2 B =\frac{(53)^2-(45)^2}{(45)^2}[/tex]
[tex]\implies \tan^2 B =\frac{(28)^2}{(45)^2}[/tex]
[tex]\implies \tan B =\pm\sqrt{\frac{(28)^2}{(45)^2}}[/tex]
[tex]\implies \tan B =\pm\frac{28}{45}[/tex]
It is given that: Angles A and B are in quadrant I.
---------------------> Angles A and B would be positive.
[tex]\implies \tan B =\frac{28}{45}[/tex]
Next,
[tex]\tan (A+B) =\frac{\tan A +\tan B}{1-\tan A \tan B}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{12}{5} +\frac{28}{45}}{1-\bigg(\frac{12}{5}\bigg) \bigg(\frac{28}{45}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{108}{45} +\frac{28}{45}}{1-\bigg(\frac{336}{225}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\bigg(\frac{225-336}{225}\bigg)}[/tex]
[tex]\implies \tan (A+B) =\frac{\frac{136}{45}}{\frac{-111}{225}}[/tex]
[tex]\implies \tan (A+B) =-\frac{680}{111}[/tex]
Related Questions
120 90 x= i need help with thiss!!!
Answers
Answer:
60°
Step-by-step explanation:
Angles around a point sum to 360°360 - 90 - 120 - 90 = 240 - 180 = 60°Percent of discount is 40% sale price is 78 what’s the or
Answers
Answer:
124.8
Step-by-step explanation:
Answer: $130
Step-by-step explanation:
60% = 78
1% = 78/ 60
100% = 78/60 ×100
Discount is 40% = $52
The first five terms of an arithmetic sequence are given: $4,10,16,22,28, \\ldots$ What is the sixth term in the sequence
Answers
Answer:
34
Step-by-step explanation:
to find the number to add 4 which will increase it to 10 with them subtract 10 from 4 to find the number which is increasing termly
=> 10 - 4 = 6
increasing by 6
4 + 6 = 10
10 + 6 = 16
16 + 6 = 22-
22 + 6 = 28
28 + 6 = 34
6th term = 34
Consider the equation 3(x – 5)2
+ 6 = 54.
What value(s) of x makes the equation true? Enter one solution in each space
provided on your answer document. If there is only one solution, leave one space
blank
Answers
Answer:
if im not mistaken, x = 13!!
Help Please. I'm not that smart
Answers
Answer:
8580 yards
Step-by-step explanation:
[tex]4 \frac{7}{8}miles \times 1760 \frac{yards}{mile} = 8580yards[/tex]
The total will the friend's paddle combined is 51480 yards.
What is the unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor.
The Great Adventures Canoe and Kayak company offers 3 different options as shown in the table.
This afternoon a group of 6 friends is paddling the Adventure Mid Trip in individual kayaks.
The totals will the friends paddle combined is;
[tex]\rm = 4\dfrac{7}{8} \times 6\\\\=\dfrac{4\times 8+7}{8}\times 6\\\\=\dfrac{32+7}{8} \times 6\\\\ =\dfrac{39}{8} \times 6 \\\\=\dfrac{234}{8}\\\\= 29.25[/tex]
Here 1 mile = 1760 yards
The totals will the friends paddle combined is;
[tex]= 29.25 \times 1760\\\\=51480[/tex]
Hence, The total will the friend's paddle combined is 51480 yards.
Learn more about the unit conversation here;
https://brainly.com/question/2293461
#SPJ2
Which one does it simplify to? please
Answers
Answer:
[tex]1 + { \sin} \theta[/tex]
Step-by-step explanation:
[tex] \frac{ { \cos}^{2} \theta}{1 - \sin \theta} \\ \\ = \frac{ { \cos}^{2} \theta}{(1 - \sin \theta)} \times \frac{(1 + \sin \theta)}{(1 + \sin \theta)} \\ \\ = \frac{{ \cos}^{2} \theta(1 + { \sin} \theta)}{(1 - { \sin}^{2} \theta)} \\ \\ = \frac{{ \cancel{ \cos}^{2} \theta}(1 + { \sin} \theta)}{ \cancel{{ \cos}^{2} \theta}} \\ \\ = 1 + { \sin} \theta[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{cos^2\theta}{1-sin\theta}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1-sin^2\theta}{1-sin\theta}[/tex]
(a+b)(a-b)=a²-b²[tex]\\ \rm\Rrightarrow \dfrac{(1-sin\theta)(1+sin\theta)}{1-sin\theta}[/tex][/tex]
[tex]\\ \rm\Rrightarrow 1+sin\theta[/tex]
Option A
solve for x : -17 = -x - 7
Answers
Answer:
10
Step-by-step explanation:
-(-17)=17-7=10
Answer:
x = -119/16
Step-by-step explanation:
x/-17 = -x-7
x/-17 + x = -x-7+x
SIMPLIFY
16x/17 = -7
so x= -119/16
(I TRIED TO SOLVE THIS HOPE THIS HELPS).
Normal Distribution- Empirical Rule - please help
Answers
Solve the System of these Equations
Answers
Answer:
y=-9/2, x=7
Step-by-step explanation:
You can solve this via substitution. First solve for x in terms of y in one of the equations given. Lets use the first one:
25+4y=x
Now plug 25+4y in for x in the second equation
3(25+4y)-2y=30
75+12y-2y=30
75+10y=30
10y=-45
y=-9/2
Plug this into the first equation:
25-x=-4(-9/2)
25-x=18
x=7
Determine the equation of the line with the following characteristics.
Slope=3, passing through (-1, 10)
Answers
Answer:
y = 3x + 13
Step-by-step explanation:
The equation of a line is also known as slope-intercept form.
Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.
To put an equation in slope-intercept form, we need the slop and the y-intercept.
In this case, we already have the slope which is 3.
So far, we have y = 3x + b
Now, we need to find the y-intercept.
Since you already have a point, we can plug in the x and y values from the point, into the equation.
10 = 3(-1) + b
Now, we can solve for b.
10 = -3 + b
Add three on both sides so it becomes:
13 = b
13 is the y-intercept
y = 3x + 13
How to Convert 3,18km to M
Answers
Answer:
1.97596 miles
simplified
1.976 miles
The parabola in the image has its focus at (4,3).Its directrix is the line y=1.The point (8,6) is on the parabola.
Answers
The statements that are true for this parabola are:
C. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.
Option D.
Given the following data:
Vertex (h, k) = (4, 3).Point (x, y) = (8, 6).How to determine the equation of the directrix?Mathematically, the standard equation of the directrix line for a parabola is given by: y = a(x - h)² + 2.
Next, we would determine the distance where point (8, 6) lie on the parabola as follows:
y = a(x - h)² + 2
6 = a(8 - 4)² + 2
6 = a(4)² + 2
6 = 16a + 2
16a = 6 - 2
16a = 4
a = 4/16
a = 1/4.
Therefore, the parabolic equation becomes:
y = 1/4(x - 4)² + 2
When x = 2, we have:
y = 1/4(2 - 4)² + 2
y = 1/4(-2)² + 2
y = 1/4(4) + 2
y = 1 + 2
y = 3.
In conlusion, the statements that are true for this parabola in the image above include:
The point (8, 6) is the same distance from the point (4, 3) as it is from line (y = 1).The point (2, 3) is on the parabola.Read more on directrix here: https://brainly.com/question/2346582
#SPJ1
Mary had a 3-inch piece of ribbon. She cut it in half. How long were the new pieces?.
Answers
So 3/2=1.5
The pieces would each be 1.5 inches
3 inch.
to find:the length of the new pieces.
solution:to find the length of the new piece's you'll have to divide 3 by 2.
3/2
= 1.5 inch
so, the length of the new pieces is 1.5 inch.
how many sides does a quadrillateral have
Answers
Answer: 4
Step-by-step explanation:In geometry a quadrilateral is a four-sided polygon, having four edges and four corners. The word is derived from the Latin words quadri, a variant of four, and latus, meaning side
What is the total number of atoms in ammonium hydroxide, nh4oh ? 2 4 7 8
Answers
Answer:
7 total atoms.
Step-by-step explanation:
There's nothing written for N, so we assume there is one atom. There is 4 written for H, plus the other H at the end, making 5 hydrogen atoms. There is nothing written for O, so we assume there is one atom. 1+5+1=7 total
Answer:
7
Step-by-step explanation:
BABA BOI
which number is between 8.270 and 8.280
Answers
Answer:
8.275
Step-by-step explanation:
8.280 - 8.270 = 0.010
0.010/2 = 0.005
8.270 + 0.005 = 8.275
Henry is going to color a spinner with 16 equal-sized sections. Three of the sections will be orange,
and 13 of the sections will be black. Is this spinner fair? If so, explain why. If not, explain how to make
it a fair spinner.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. Yes. The spinner is fair because there are the same number of orange sections and black
sections.
OB. No. The spinner is not fair because there are more orange sections than black sections. A fair
spinner will have
orange section(s) and
black section(s).
(Type whole numbers.)
OC. No. The spinner is not fair because there are
more black sections than orange sections. A fair
black section(s).
spinner will have orange section(s) and
Click to select and enter your answer(s) and then click Check Answer
Clear All
Check Answer
All parts showing
Answers
Answer: C
Step-by-step explanation: Black shade will be 13/16 . That isn't fair at all. It has more Black
Can anyone please help answer this?
Answers
A = 45 inches!
11 + 7 = 18
12 + 5 = 17
6 + 4 = 10
18 + 17 = 35
35 + 10 = 45
y = 2x^2 + 3
im looking for how to find the axis of symmetry
Answers
Answer:
The axis of symmetry is simply 0
Step-by-step explanation:
When you enter that equation on the graph the axis of symmetary is the line that goes straight throught the middle of it.
I inserted an image so you could understand a littler better. Hope this helps!
The axis of symmetry of the quadratic equation y = 2x^2 + 3 is x = 0
How to determine the axis of symmetry?The equation is given as:
y = 2x^2 + 3
Differentiate the above equation with respect to x
y' = 4x + 0
This gives
y' = 4x
Set the equation to 0
4x = 0
Divide both sides by 4
x = 0
Hence, the axis of symmetry is x = 0
Read more about axis of symmetry at:
https://brainly.com/question/1349456
Calculate the length below labeled x
Image above
Please help me with this ill give you brainlist answer
Answers
Answer:
2√30
Step-by-step explanation:
Since we have a right triangle, we first need to find the base of the big triangle, which is also the hypo of the smaller triangle.
We apply A²+B²=C²
We plug values in that we have
15²+B²=19²
Simplify
B²=136
B=√136=√2x2x2x2x17=4√17
Now that we have the hypo for the small triangle we apply the same formula to get X
4²+X²=√136
16+X²=136
X²=120
X=√120=√2x2x2x3x5=2√30
Answer:
11.0 mm (3sf)
Step-by-step explanation:
Let length of hypotenuse of smaller triangle be H mm. (this is referring to the only unlabelled length in the picture)
by the Pythagorean theorem (larger triangle),
19² = 15² + H²
H² = 361 - 225
H² = 136
by the Pythagorean theorem (smaller triangle),
H² = 4² + x²
136 = 16 + x²
x² = 120
x = 11.0 mm (3sf)
hope this helps!
Julie invested $148,000 in a simple interest account. After 12 years and no additional deposits or withdrawals, the account balance was $210,160. Find the interest rate for the account.
Answers
If the invested price is $ 148,000 for 12 years with a return of $210,160. Then the rate of interest will be 11.83%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
Julie invested $148,000 in a simple interest account.
After 12 years and no additional deposits or withdrawals, the account balance was $210,160.
Then the interest rate will be
[tex]\rm A = \dfrac{PRT}{100}\\[/tex]
We have
A = $ 210,160
P = $148,000
T = 12 years
Then the interest rate will be
[tex]\begin{aligned} 210,160 &= \dfrac{148000 \times R \times 12}{100}\\\\R &= 11.83 \% \end{aligned}[/tex]
More about the simple interest link is given below.
https://brainly.com/question/2793278
#SPJ1
Answer: 3.5%
Step-by-step explanation:
The perimeter of a triangle is 42 yards. The first side is 5 yards shorter than the
second side, and the third side is 2 yards shorter than the first side. What is the length
of each side?
Answers
Answer: Is your question "What is the length of each side?"
Let x = the length of the second side
Let x - 5 = the length of the first side
Let (x - 5) - 2 = the length of the third side
P = a + b + c
x + x - 5 + x - 7 = 42
3x - 12 = 42
3x = 54
x = 18 yards
x - 5 = 13 yards
x - 7 = 11 yards
Step-by-step explanation:
Algebraic terms are separated by
Choose all that apply.
=
+
x
\
-
Answers
Marina has $145 to spend. She spends $68. 50 on jeans. T-shirts cost $12. 75. Write and solve an inequality to find the greatest number of t-shirts she can buy
Answers
Answer:
6
Step-by-step explanation:
145-68.50 = 76.50
76.20/12.75 = no of t-shirts she can buy
ans= 6
in a binomial experiemnt the probability of success is 0.16. what is the probability of two successes in seven trials
Answers
Answer:
0.2248307402
Step-by-step explanation:
Let 'success', p = 0.16,
and 'failure', q = 1 - 0.16 = 0.84
and the number of trials, n = 7
r = 2
[tex]P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} \\ P(X = 2) = \binom{7}{2} {(0.16)}^{2} {0.84}^{5 - 2} \\ = 0.2248307402[/tex]
A triangular prism has a volume of 360 in.³ the area of the base of the prism is 24 in.² what is the height of the prism?
Answers
Answer:
15 in
Step-by-step explanation:
Volume / Area = missing length
360 / 24 = 15 in
bro some one helpp lol
17 - q = 6
n-31/4 = 2
1 + 2r = 35
42 + 5t = 8t
4p - 3 = 17
Answers
Answer:
11
9.75
17
14
5
Step-by-step explanation:
q=17-6=11
4n-31=8
4n=31+8=39
n=9.75
2r=35-1=34
r=17
42=8t-5t=3t
t=14
4p=17+3=20
p=5
Find the image of the given point
under the given translation.
P(-9, -2)
T(x, y) = (x + 6, y − 4)
P' = ([?], [])
Answers
Explanation:
The notation [tex]T(x, y) = (x+6, y-4)[/tex] tells us to add 6 to the x coordinate and subtract 4 from the y coordinate.
An equivalent notation would be to write [tex](x,y) \to (x+6, y-4)[/tex]
Point P has the x coordinate of -9. Adding on 6 gets us the new x coordinate of -9+6 = -3
It also has the y coordinate of -2. Subtract off 4 to get -2-4 = -6
So,
[tex](x,y) \to (x+6, y-4)\\\\(-9, -2) \to (-9+6, -2-4)\\\\(-9, -2) \to (-3, -6)[/tex]
Answer:
P' (- 3, - 6 )
Step-by-step explanation:
the translation
(x, y ) → (x + 6, y - 4 )
means add 6 to the x- coordinate and subtract 4 from the y- coordinate , so
P (- 9, - 2 ) → P' (- 9 + 6, - 2 - 4 ) → P' (- 3, - 6 )
Find the surface area of the sphere if its radius is 13 inches. Round your answer to
nearest hundredth (two decimal places). Use 3.14 to approximate pi.
Answers
Answer: 530. 66
4*3.14*13^2
2122.64
Helpppppp plssss!!!!!!
Answers
Answer:
The answer is D or 180 degrees
Thank you Consider brainliest <3
Step-by-step explanation: