Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
H. Pete wants a new truck. The sale price is 15% lower than the original price. The sale price is $20,000. Write and evaluate an expression for the original price. Uses for sale price and p for original price.
100-15=85%=SP
[tex]\\ \sf\longmapsto 85\%\times x=20000[/tex]
[tex]\\ \sf\longmapsto \dfrac{85}{100}x=20000[/tex]
[tex]\\ \sf\longmapsto x=20000\times \dfrac{100}{85}[/tex]
[tex]\\ \sf\longmapsto x=235.2(100)[/tex]
[tex]\\ \sf\longmapsto CP=23520[/tex]
Aimee deposited $250 into a savings account with the simple interest of 6% per year.
After 4 years, how much money, in total, will she have in her account?
Answer:
Step-by-step explanation:
Interest=principal*rate*time/100
Interest=240$
Amount= principal + interest
Amount=$490
A rectangle has perimeter 66 cm and length 27 cm. What is its width?
(help pls it’s my hw)
Answer:
Step-by-step explanation:
A rectangle has the perimeter of 66cm, and since a rectangle has 2 lengths and 2 widths, we can tell that 2 widths = 66-27*2 = 12
so 1 width is half of 12 which is 6
Find the difference between temperatures of 17 degrees celcius above zero and 12 degrees celcius below zero
Answer:
29° C
Step-by-step explanation:
-17(-12)
=29
Hope this helps
Answer:
29C
Step-by-step explanation:
Above zero temperature = +17C
Below zero temperature = -12C
Difference= 17 - (-12C)
= 17 + 12 C
=29C
How can 863.141 be written in expanded form?
Answer:
800 + 60 + 3 + 0.1 + 0.04 + 0.001
4 The equation 5W + 3 = 4w + 9 is modeled below. w W 1 W W 1 1 W 1 1 W W 1 1 1 What value of w makes this equation true? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. MI - SI – PSA- S-
Answer:
w = 6.
Step-by-step explanation:
5w + 3 = 4w + 9
5w - 4w = 9 - 3
w = 6
Then, check your work!
5(6) + 3 = 4(6) + 9
30 + 3 = 24 + 9
33 = 33
So, w = 6 will be the correct answer.
Hope this helps!
4. Determine both the HCF and LCM of 25 and 200
Answer:
The LCM of 25 and 200 is 200.
Explanation:
Find the prime factorisation of 25
25 = 5 × 5
Find the prime factorisation of 200
200 = 2 × 2 × 2 × 5 × 5
Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:
LCM = 2 × 2 × 2 × 5 × 5
LCM = 200
Answer:
the HCF of 25 and 200 is 25 because it divides both of them and is maximum factor of them.
LCM of 25 and 200 is 200 because it can be divided by both 200 and 25
A clothing company buys t-shirts for $10 and sells them for $100. What is the percentage mark up on
t-shirts? Make sure you show at least one step of working
Answer:
900%
Step-by-step explanation:
Starting price : 10
End price: 100
100-10 = 90
90/10 = 9 = 900%
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the answer to the green box?
The bacteria increases 90% the formula adds the percentage, as a decimal to the 1.
The answer would be 0.90
How many solutions are there to the equation below?
145 = 10x - 8x
O A. infinitely many
O B. 2
O c. 1
Answer:
c. one solution
Step-by-step explanation:
[tex]145 = 10x - 8x \\ 2x = 145 \\ x = 72.5[/tex]
Answer:
C
Step-by-step explanation:
yes
this is the answer for sure
3/4x + 4/7y = 5/4x -1...solve for y
Answer:
[tex] \frac{3}{4} x + \frac{4}{7} y = \frac{5}{4} x - 1 \\ \frac{4}{7} y = \frac{5}{4} x - 1 - \frac{3}{4} x \\ \\ \frac{4}{7} y = \frac{5x - 4 - 3x}{4} \\ \frac{4}{7} y = \frac{2x - 4}{4} \\ \\ y = \frac{2x - 4}{4} \div \frac{4}{7} \\ y = \frac{2x - 4}{4} \times \frac{7}{4} \\ \\ y = \frac{14x - 28}{16} \\ \\ y = \frac{14x}{16} - \frac{28}{16} [/tex]
I hope I helped you^_^
someone help please :)
Answer:
its basically a Cross
the point they cross is p
and the 2 lines are AB and RS
I hope I'm correct.And yea
.hope it helps
Point B is on line segment AC. Given AB=4x-6, AC=2x+10, and BC=4, determine the numerical length of AC
Answer:
AC = 22
Step-by-step explanation:
AB + BC = AC , substitute values
4x - 6 + 4 = 2x + 10 , that is
4x - 2 = 2x + 10 ( subtract 2x from both sides )
2x - 2 = 10 ( add 2 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Then
AC = 2x + 10 = 2(6) + 10 = 12 + 10 = 22
f(x) = 3x2 – x
Find f(10)
Answer: f(10) = 290
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given expression
f(x) = 3x² - x
Substitute values into the expression
f(10) = 3(10)² - (10)
Simplify exponents
f(10) = 3(100) - (10)
Simplify by multiplication
f(10) = 300 - 10
Simplify by subtraction
f(10) = [tex]\boxed{290}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
which expression are equivalent to the given expression
y^-8 y^3 x^0 x^-2
Answer:
y^-24, x^-2 y^-5, 1/ y^24, x^2/y^11, x^2y^-11 and 1/ x^2y^5
ok i tried searching up the problem and how to solve it but didn`t come up with much.
i don`t know if this changes anything, but I noticed that some of these answers are opposites
ex (from the sequence you gave me in the comments below) : y^-24, x^-2, y^-5, y^24, x^2, y^5
maybe thats what it meant by matching the expressions?
again, sorry if this wasnt much help i have a small brain DD::
What is the solution of the equation?
-6x+5= 3-5x
Answer:
I think the answer is x = 2
Answer: 2
Step-by-step explanation:
-6x+5=3-5x
+5x +5x
-x +5=3
-5 -5
-x = -2
-2 -2
X=2
A car accelerates from stationary state to X kmj-1 in 10 minutes. If the acceleration of the car is 300 km h-2, find the value of X.
Step-by-step explanation:
X = Acceleration × time
=300× (10/60)
=50km/h
Tìm tập giá trị y = x² - căn 4 - x²
Answer:
0 and 2 s the answer
Using the numbers 2,7,13,11,5 can you get the total of 23? (You must use all numbers, no negatives, no using each number more than once, and only use Subtraction, Multiplication, addition, and division, you can also group numbers)
Answer:
(2-7)/5 + 13 + 11
Step-by-step explanation:
There's a lot of guess and check that needs to go into this to make this work, but here's what I got:
(2-7)/5 + 13 + 11
-5/5 + 13 + 11
-1 + 13 + 11
24 - 1
23
14>6>2 true or false
Answer:
I think this is if it is right then help me plz this is false ..
HELP PLEASEEEEEEEEEEE
Answer:
The answer you have selected is correct.
Step-by-step explanation:
Answer:
X^2 - 7xy + y^2 +2y
Step-by-step explanation:
For this, they are just trying to test if u know how to expand the brackets, especially for the one on the right, since that is a negative infront of the bracket, u would need to multiply negative to all the values in that bracket
100 POINTS + BRAINLIST IF RIGHT. GEOMETRY
In problems 13-15 is the bisector of AC
Please help 13-15 I’m struggling so hard :(
Hello! I'm happy to help!
Question 13: First, we will need to find the value of x. We know that AB and BC are equal.
So, we can subtract x from both sides.
2x-8
-x
x-8
So, we get AB as x-8
x+17
-x
17
and BC as 17. We know that these are equal, so we need to find which x value will make them that way. In this case, x=25 because 25-8=17. We can now add back the x we removed earlier.
17+25=42
Therefore, both AB and BC have a value of 42. and AC will be the combined total.
42+42=84
So, for question 13, x=25, AB=42, BC=42, and AC=84.
Question 14: This question is similar, but we have an expression for AB and AC, instead of AB and BC. We still know that AB=BC, so we can also say that BC=x+6 also. To find x, we need to find a second expression that is equal to AC. We can ad AB and BC together to get that. (x+6)+(x+6)=2x+12. This expression is equal to the AC expression, so we can compare them to find x.
2x+12=3x-31
We need to single out the x on one side, by changing things in the same way on both sides.
2x+12=3x-31
-2x -2x
12=x-31
+31 +31
43=x
Now that we know our x value, we need to plug it in!
43+6=49
We now know that both AB and BC have a value of 49. Let's plug in the value for AC.
(43·3)-31
129-31
98
After plugging in the values, we know that AC is equal to 98. You could have also added AB and BC together, giving you 98 also.
To Summarize Question 14: x=43, AB=49, BC=49, AC=98.
Question 15: This one is very similar to the last, with a little more complexity to the expressions. First, let's simplify the expressions on AB and AC.
AB=3(3x-1) AB=9x-3
AC=5(2x+2) AC=10x+10
Now that we have the simplified expressions, let's solve. We need to find an equivalent expression for AC. We know that AB and BC are equivalent, and also add up to AC. We can copy the expression from AB to BC, and then add them
(9x-3)+(9x-3)=18x-6=AC
We now compare the two expressions in an equation to find x.
10x+10=18x-6
Again, we have to single out x on one side.
10x-10=18x-6
-10x -10x
10=8x-6
+6 +6
16=8x
This time, we need to divide both sides to single out x.
[tex]\frac{16}{8}[/tex]=[tex]\frac{8x}{8}[/tex]
2=x
Now that we have x, we need to plug it in to finish solving.
(9·2)-3
18-3
15
AB=15 BC=15
From here, you can do one of two things, add AB and BC together (easy), or plug in x for AC.
15+15=30 (10·2)+10
AC=30 20+10=30
AC=30
To Summarize Question 15: x=2, AB=15, BC=15, AC=30.
I'm always happy to help, keep learning! :D
6) find HJ
8)find IK
Answer:
HJ = 17
IK = 30
Step-by-step explanation:
to find HI :
GH : 2
HI : ?
IJ : 12
GI : 7
HI = GI - GH
HI = 7- 2
HI = 5
HI + IJ = HJ
5 + 12 = HJ
17 = HJ
To find IK
IJ = ?
JK = 12
KL = ?
IL = 49
JL = 31
To find IK we need to find KL and IJ
KL = JL - JK
KL = 31 - 12
KL = 19
IJ = IL - (JK + KL)
IJ = 49 - 31
IJ = 18
IK = IJ + JK
IK = 18 + 12
IK = 30
Simplify each expression completely.
7[3+2(x-4)-6(x-4)]
Answer:
21 + 14x - 56 - 42x + 168
= 133 - 28x
Step-by-step explanation:
Answer:
19 - 4x
Step-by-step explanation:
[tex]3 + 2(x - 4) - 6(x - 4)[/tex]
[tex]3 + 2x - 8 - 6(x - 4)[/tex]
[tex]3 + 2x - 8 - 6x + 24[/tex]
[tex]19 + 2x - 6x[/tex]
[tex]19 - 4x[/tex]
1. Identify the terms in the expression
1.3x - 2.7x2
-
5.4x + 3
50 points whoever aswners it
Answer:
- and+
Step-by-step explanation:
Answer:
1.3x, -2.7, x^2 (x squared), -5.4x, +3 are the terms. hope this helps
Step-by-step explanation:
- Zombie
evaluate the expression (-2) - ( -5)
Answer:
The answer is 3
Step-by-step explanation:
(-2)+5=3
e) If the radede circle is 7em, then find the area of circle. al- (SSS. x at Solna -
Hi
area of circle, which is call in proper math terme circumference ( latin for going around) is given by this formula :
2 times radius x pi
As math is all about knowing your formula and training, I let you have a shot. You wont progress other wise.
Ask in comment section if you are still blocked.
Need help on how how to do the question step by step need help ASAP
Answer:
4
Step-by-step explanation:
64 = 4 × 4 × 4 = 4³ , then
[tex]\sqrt[3]{4^3}[/tex]
= 4
Helppp pleaseeeee
Which expression is equivalent to
Answer:
The second option
Step-by-step explanation:
First, simplify the bracket
[tex] \frac{4r {}^{3} s {}^{2} t {}^{4} }{2r {}^{4} st {}^{6} } [/tex]
Apply Quotient of Powers
[tex]2 {r}^{ - 1} s {t}^{ - 2} [/tex]
Which equals
[tex] \frac{2s}{rt {}^{2} } [/tex]
Raise this to the fifth power
[tex] \frac{32s {}^{5} }{ {r}^{5} t {}^{10} } [/tex]
Multiply by the outsides numbers(5^r^6 and t^4
[tex] \frac{160 {}^{} r {}^{6}s {}^{5} t {}^{4} }{r {}^{5} t {}^{10} } [/tex]
[tex]160r {}^{5} t {}^{ - 6} [/tex]
[tex] \frac{160r {}^{}s {}^{5} }{t {}^{6} } [/tex]
Can somebody please help? I been struggling to answer this!
Answer:
the first option is the answer. I am sure of this
Answer:
the first option is the answer
