find sin θ and cos θ if tan θ= 1/4 and sin 0>0.
Answer:
[tex]\displaystyle \sin(\theta)= \frac{\sqrt{17}}{17}[/tex]
[tex]\displaystyle \cos(\theta)= \frac{4 \sqrt {17} }{ 17 }[/tex]
Step-by-step explanation:
We want to find sin(θ) and cos(θ) given that tan(θ) = 1/4 and sin(θ) > 0.
First, since tan(θ) and sin(θ) are both positive, cos(θ) must be positive as well.
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the hypotenuse is:
[tex]h=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}[/tex]
So, with respect to θ, the opposite side is 1, the adjacent is 4, and the hypotenuse is √17.
Then it follows that:
[tex]\displaystyle \sin(\theta)=\frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17}[/tex]
And that:
[tex]\displaystyle \cos(\theta)= \frac{4}{\sqrt{17}} = \frac{4 \sqrt {17} }{ 17 }[/tex]
What is the y intercept of the graph of the inequality 2x + 3y > 12?
Answer:
-4 y>-2/3x-4
Step-by-step explanation:
-3y>2x+12 y> -2/3x-4
Margaret had 3/8 of a bag of chips. She ate 4/5 of it while watching TV. What fraction of the bag chips did Margaret eat?
Answer:
9/40
Step-by-step explanation:
3/8=15/40
4/5=24/40
15/40 x 24/40=360/1600
360/1600=9/40
What two numbers multiply to get -30 and add to get -7 ?
Answer:
3 and -10 to get 30
4 and -11 to get -7
Step-by-step explanation:
3 * -10 = -30
4 + (-11) = 4 - 11 = -7
Determine whether the ratios are equivalent 6 : 10 and 12 : 20 ?
Answer:
Yes, they are equivalent because 12 is divisible by 6 two times and 20 is divisible by ten two times.
Find the x and y intercepts of this line:
-5x+4y=-18
Answer:
Step-by-step explanation:
x- intercepts: ( 18/5,0)
y- intercepts: ( 0,-9/2)
What is the slope of the equation y- 5 = -3x?
Answer:
-3/1
Step-by-step explanation:
It's always the x value over the y value, so whatever's in the x
Answer:
-3
Step-by-step explanation:
the equation is y=-3x+5, so m=-3
Mhanifa please help I will mark brainliest
Answer:
36°90°Step-by-step explanation:
Question 1
x = 180° - 2*72° = 180° - 144° = 36°Question 2
x + 2(x/2) = 180°2x = 180°x = 90°Does anyone know the answer and could you explain how you got your answer? THANK YOUU
Answer:
This would be a 60% increase
Step-by-step explanation:
40-25 and divided by 25 times 100
you should get 15/25 multiply it by 100=60%
solve (3x-5)+(-4x+1)
Answer:
-x-4
Step-by-step explanation:
If Izzy has 43 minutes to do her work and her brother has 30 because he started before her how many minutes they would have together do you have to multiply to find it out
Answer:
you dont have to multiply
Step-by-step explanation:
because the keyword "Have together" in math indicates it is an adding problem
Will give brainliest
Answer:
Only Figure 4
Step-by-step explanation:
A regular polygon has all congruent sides and angles. Only Figure 4 has these qualities.
Figure 1 doesn't have congruent angles.
Figure 2 doesn't either.
Figure 3 doesn't have a congruent sides.
Polygon ABCD had the following vertices: A(-3,3), B(5,5), C(5,-4), and D(-3,-4)
ASAP PlEaSE
Answer:
I couldn't even understand the question
Step-by-step explanation:
A given field mouse population satisfies the differential equation dp/dt=.4p-450 where p is the number of mice and t is the time in months.
(a) Find the time at which the population becomes extinct if p(0)=1075
Round your answer to two decimal places in months.
(b) Find the initial population Po if the population is to become extinct in 1 year.
Round your answer to the nearest integer.
Po= mice
Answer:
a) 7.78 months
b) 1116
Step-by-step explanation:
Given -
[tex]\frac{dP}{dt} = 0.4p-450[/tex]
Integrating the above equation with respect to time, we get -
[tex]\int\ \frac{dP}{0.4p-450} = \int\ dt\\[/tex]
let us define new variable x
[tex]x = 0.4p - 450 \\dx = 0.4 dy[/tex]
substituting these values in above integral equation, we get -
[tex]\frac{1}{0.4} \int\ \frac{dx}{x} = \int\ dt\\ln x = 0.4 t + C\\x = ce^{0.4t}[/tex]
[tex]P (t) = \frac{C}{0.4} e^{0.4t} +1125\\[/tex]
at t = 0, P (0) = 1075, using this condition, we get -
[tex]\frac{c}{0.4} = -50\\P(t) = 50 e^{0.4t} +1125 \\t = 7.78\\P(0) = 1125 - \frac{1125}{e^{4.8}} = 1116[/tex]
Suppose that IQ scores have a bell-shaped distribution with a mean of 104
104 and a standard deviation of 17.Using the empirical rule, what percentage of IQ scores are between 70 and 138?
Answer:
68%
Step-by-step explanation:
The empirical rule basically states that 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviations from the mean, and 99.7% of the data falls within three standard deviations from the mean.
So to find the percentage of IQ scores between 70 and 138, you need to find how far each of these numbers is from the mean in terms of the standard deviation.
If you subtract the standard deviation from the mean, you receive 87, and if you add the standard deviation to the mean, you receive 121.
This means that both of these numbers are within one standard deviation from the mean meaning according to the empirical rule, that means 68% of the IQ scores are between 70 and 138.
good luck, i hope this helps :)
Answer:
99.7%
Step-by-step explanation:
According to the empirical rule, approximately 99.7% of data values lie within 3 standard deviations of the mean.
Pam has 24 marbles she put 3 fourth in a jar how many marbles does she have
Answer:
6 outside
18 in the jar
Step-by-step explanation:
-4+x=3x+12 (Pls explain how you got it)
Answer:
The answer is 8.
Step-by-step explanation:
I will explain in the comments
rate da fits 1-10 which is da best don't report dude/girl
Answer:
9-10
Step-by-step explanation:
nice lol
Natalie and Phil ran for 6th grade class president. The ratio of votes for Natalie to the votes for Phil is 16:12. Which statement is true? *
For every vote Phil received, Natalie received 4 votes.
For every vote Phil received, Natalie received 3 votes.
For very 4 votes Natalie received, Phil received 7 votes
For every 4 votes Natalie received, Phil received 3 votes.
Answer:
For every 4 votes Natalie received, Phil received 3 votes.
Step-by-step explanation:
Please help ASAP will give Brainlyest answer :M/5=2
Jade uses 28 inches of string to make bracelets. Each bracelet is 7 inches long. How many bracelets does Jade make?
Answer:
Jade made 4 bracelets
Step-by-step explanation:
If the string was 28inches and a bracelets requires 7inches 28÷7=4
Have a great day
I need help within the next 15 mins
Answer:30
Step-by-step explanation: LxW (length x Width) 3x10=30.... Hope this helps... if you break it down then you can write down (10) on your page but the answer is 30
Is 22,18,12 a right triangle
Answer:
Step-by-step explanation:
12²+18²=144+324=468
22²=484
468<484
12²+18²≠22²
it is not a right angled triangle.
The area of a rectangle is 48 m^2 the length is (x+2) and width is (x). What is the value of x?
Answer:
Please find attached pdf
Step-by-step explanation:
Ryan is trying to determine whether 2.7x – 5.9 is equivalent to 2.8x – 5.9. To test this, he substitutes 0 for x into both expressions. Explain why this will not give him the correct answer. send help ty
Answer:
Nggak tahu bahasa inggriis aku bang
Answer:
The coefficients of x are different in the expressions, but the constant values are the same. Zero times any value is zero, so both expressions will be equal to -5.9. If Ryan tried any other number, he would see that the expressions are not equivalent.
PUT THIS INTO YOUR OWN WORDS bc I just put what Edg said :)
100 point question. I attached a screenshot of the problem.
Answer:
Express the given function h as a composition of two functions f and g so that h (x )equals (f circle g )(x )commah(x)=(f g)(x), where one of the functions is 4 x minus 3.4x−3. h (x )equals (4 x minus 3 )Superscript 8h(x)=(4x−3)8 f (x )f(x)equals=4 x minus 3. See answer. zalinskyerin2976 is waiting for your help.
Step-by-step explanation:
this what f ;|
Answer:
x1=-1 ,x2=1
Step-by-step explanation:
what do i do with this
Answer: you should plot it a -3.2
Step-by-step explanation:
If x is to 8 as 15 is to 12, then x equals...
Answer:
12/8 = 6/4 = 3/2; 2/3 * 15 = 10
Step-by-step explanation:
A $230 suit is marked down by 30%. Find the sale price.
Answer:
161
Step-by-step explanation:
69 is 30% of 230 so 230-69=161 is the answer.
PLEASE HELP! PLEASE ALSO GIVE A GOOD EXPLANATION AND SHOW WORK! 45 points!!
Dalia is painting her room. After painting 1/10 of her room, Dalia has used 1/2 of a can of paint.
Select ALL of the true statements.
1. Painting 1/2 of Dalia's room requires 10 cans of paint.
2. Each can of paint will cover 1/20 of Dalia's room.
3. 3 cans of paint will cover 60% of Dalia's room.
4. Dalia's entire room requires 20 cans of paint.
5. Dalia's entire room requires 5 cans of paint.
Hence statement 3 and 5 are true from the equation given in question.
What is equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Types of Equations:
Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1.
Quadratic Equation: This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2.
Cubic Equation: A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3.
Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.
Number of cans used 1/10 part of room = 1/2
No. of cans paints used 1 part = 1/2 / 1/10 = 5
∵ 1/2 can paint is used = 1/10
∴ 1 can paint used = (1/10)*2 = 1/5
∴ 5 cans = 100%
3 cans used = (3/5)*100 = 60%
To know more about equation please visit:
brainly.com/question/10413253
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