part 1. Find the value of the trig function indicated, use the Pythagorean Theorem to find the 3rd side if you need it
Answers
Answer: [tex]\bold {1)\ \cos\ \theta}=\dfrac{\sqrt2}{2}\qquad 2)\ \tan \theta =\dfrac{1}{3}\qquad 3)\ \cos\ \theta=\dfrac{3\sqrt{13}}{13}\qquad 4)\ \cos\ \theta = \dfrac{2\sqrt5}{5}}[/tex]
Step-by-step explanation:
Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse
[tex]1)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt2}\quad =\large\boxed{\dfrac{\sqrt2}{2}}[/tex]
Note: 2² + 2² = hypotenuse² → hypotenuse = 2√2
[tex]2)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{2}{2\sqrt2}\quad =\dfrac{5}{15}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
Note: hypotenuse not needed for tan θ
[tex]3)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3}{\sqrt{13}}\quad =\large\boxed{\dfrac{3\sqrt{13}}{13}}[/tex]
Note: 2² + 3² = hypotenuse² → hypotenuse = √13
[tex]4)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{2\sqrt5}\quad =\large\boxed{\dfrac{2\sqrt5}{5}}[/tex]
Note: hypotenuse given in problem
Related Questions
factorize x^2/16+xy+4y^2
Answers
Answer:
[tex]\frac{x^2}{16} +xy+4y^2[/tex] can be factored out as: [tex](\frac{x}{4} +2\,y)^2[/tex]
Step-by-step explanation:
Recall the formula for the perfect square of a binomial :
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Now, let's try to identify the values of [tex]a[/tex] and [tex]b[/tex] in the given trinomial.
Notice that the first term and the last term are perfect squares:
[tex]\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2[/tex]
so, we can investigate what the middle term would be considering our [tex]a=\frac{x}{4}[/tex], and [tex]b=2y[/tex]:
[tex]2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y[/tex]
Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:
[tex](\frac{x}{4} +2\,y)^2[/tex]
What is the inverse of g(x) =
X +8
Answers
Answer:
The inverse is x-8
Step-by-step explanation:
g(x) = x+8
y = x+8
To find the inverse, exchange x and y
x = y+8
Solve for y
Subtract 8 from each side
x-8 = y+8-8
x-8 = y
The inverse is x-8
HELP TIMED! WILL MARK BRAINLIEST! What are the domain and range of the piecewise function below? Graph and answer choices are attached.
Answers
Answer:
Its the second choice.
Step-by-step explanation:
x does not have a value of -2 so is not in the domain
The range does not have values greater than 1 and less than or equal to 4.
A basket has at most 150 applies in it. Then the number of apples in the basket if the number of apples satisfy the following conditions If counted in pairs, one remains; If counted in threes, two remains; If counted in fourss, three remains; If counted in fives, four remains; If counted in sixes, five remains; If counted in sevens, nothing remains; (A) 116 (B) 117 (C) 118 (D) 119
Answers
Answer:
Number of apple = 119
Step-by-step explanation:
Given
[tex]Max_{Apple} = 150[/tex]
Required
Find the actual number of apples;
When counted in any numbers, the number being counted is the divisor;
Take for instance, when counted in pairs, the divisor is 2
When counted in threes, the divisor is 3
and so on...
So; from the question, we understand that; when the apple is counted in 2s,3s,4s,5s, and 6s; what's left is always one less than the divisor
This means that the number of apple must satisfy the following conditions
Less than 1501 less than the Common Multiple of 2,3,..,6Divisible by 7The common multiple of 2,3,..6 are 60, 120 ,180,240.....
Recall that, these multiples must satisfy the three conditions above;
1. Less than 150: Only 60 and 120 satisfy condition.
At this point, we'll discard other numbers (180,240,300.....)
2. 1 less than the Common Multiple of 2,3,..,6:
1 less than 60: 60 - 1 = 59
1 less than 120: 120 - 1 = 119
3. Divisible by 7
At this point, we'll divide 59 and 119 by 7 to see if they satisfy this condition;
[tex]\frac{59}{7} = 8.42857142857[/tex]
[tex]\frac{119}{7}=17[/tex]
The results of these division shows that 59 is not divisible by 7;
Hence, the actual number of apple is 119
Number of apple = 119
-1 1/8 - 5/8 answer plz
Answers
Answer:
-1 6/8
Step-by-step explanation:
Answer:
-2 answer this is 100% correct
Step-by-step explanation:
Which word describes a triangle with three angles, if each angle measures less than 90°? Please help
Answers
Answer:
acute triangle
Step-by-step explanation:
If an angle measures less than 90 degrees it is an acute angle
A triangle with all acute angles is an acute triangle
What is a rigid motion?
Answers
Answer:
Rigid motion is otherwise known as a rigid transformation and occurs when a point or object is moved, but the size and shape remain the same. This differs from non-rigid motion, like a dilation, where the size of the object can increase or decrease.
Step-by-step explanation:
what is the estimate of 14.8(20.7)
Answers
Answer:
306.36 is the answer
Step-by-step explanation:
Answer:
306.36
Step-by-step explanation:
hope it helps! x
A rectangle with a length of x + 5 has a perimeter of 4x + 14.
1. Write the expression for the width of the rectangle in terms of x.
Help plsss
Answers
Answer:
hope this helps you
Please help! Correct answer only, please!
Given matrix A and B both have dimensions 2 x 2 and are the inverse of one another what should be the following product?
A · B
A.
B.
C.
D.
Answers
Answer:
B)
Step-by-step explanation:
If two square matrix, with same dimensions, are inverse of one another, their product will always be the identity matrix with the same dimensions.
The matrix A and B are 2x2, so the result of the product A * B is a 2x2 identity matrix, that is represented as follows:
I = [1 0 ; 0 1]
(First line: 1 0, second line: 0 1)
So the correct option is B)
What is the range of the function 2x + y = 7
if the domain is {-4, -2,0, 5, 7)?
Answers
Answer| range: {15, 11, 7, -3, -7}
Step-by-step explanation:
Plug in the domain to find the range:
x = 4
2(-4) + y = 7
-8 + y = 7
y = 15
x = -2
2(-2) + y = 7
-4 + y = 7
y = 11
x = 0
2(0) + y = 7
0 + y = 7
y = 7
x = 5
2(5) + y = 7
10 + y = 7
y = -3
x = 7
2(7) + y = 7
14 + y = 7
y = -7
A chemist bought 2390 test tubes and beakers.1034 of them were test tubes and the rest were beakers.How many more beakers did the chemist buy than test tubes?
Answers
Answer:
322
Step-by-step explanation:
The question explains that the total of both test tubes and beakers were
= 2390.
If 1034 of them were test tubes, then the number of beakers bought,
= 2390 - 1034
= 1356.
The question requires the answer to how many more beakers than test tubes were bought, and this would mean subtracting the number of beakers from the number of test tubes.
= 1356 - 1034
= 322
Therefore, 322 more beakers than test tubes were bought.
Order the simplification steps of the expression below using the properties of rational exponents. [tex]\sqrt[3]{7}=7^{\frac{1}{3}}[/tex]
A.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}}\cdot ^{\frac{1}{3}}\cdot ^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7\\[/tex]
B.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7\cdot 7^{\frac{1}{3}}=3\cdot \frac{1}{3}\cdot 7=1\cdot 7=7[/tex]
C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}}+\:^{\frac{1}{3}}+\:^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
D.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7\cdot \left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)=7\cdot \frac{3}{3}=7\cdot 1=7[/tex]
Answers
The answer is C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
what you plug in for calculator
\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7
WILL give brainliest, I need these for my grade :c. 1.Find the Slope 2.Find the Slope 3. Find the midpoint
Answers
Answer:
Hard to calculate first one is -1/2
Next one is 2.5/1.5 or 2 its hard to tell because of line (not clear)
Next one is -1/2 I think the numbers are small.
You can sign up for Khan academy for clear answers
What is the solution to the division problem below? (You can use long division
or synthetic division.)
2x - 3x2 -5x - 12
X-3
A. 2x2 + x + 4
B. 2x2 + 3x + 4
C. 2x2 + 7x + 4
O D. 2x2 + 5x + 4
SUBMIT
Answers
Answer:
I would say B.
Step-by-step explanation:
I used synthetic division for this, so I'm unsure if this is right. I have yet to learn exponents with it. Here's how I wrote it : 3] 2 -3 -5 -12. I bring down the 2 and multiply it by three to get six. After that, I multiply the sum of it (3) and got 9. I do the same, get -4 and multiply it another time, getting positive 12. I add the twelves together, get zero, and put it together as 2x^2+3x+4.
Hope this helps!
which 3 sticks should he use (there’s a picture of the problem)
Answers
Answer:
The answer is number three
Step-by-step explanation:
I know this because the formula for pythageon theorm is. (A)squared + (B)squared = (C)squared so if you substitude the value of number three into the therom it would be equal to this 6x6+8x8=10x10
then if you simplify it would equal 36 + 64 = 100 and so this would satisfy the therom.
Can the polynomial in the numerator of the expression x^2-5x+7/x-9 be factored to derive (x − 9) as a factor
Answers
Answer:
Step-by-step explanation:
We can find out by using synthetic division and the fact that x - 9 Might be a 0. If x = 9 is a 0 of that polynomial, then we will get no remainder when we divide the polynomial by 9:
9 | 1 -5 7
____________
First thing to do is bring down the 1 and multiply it by the 9 and put that product up under the -5:
9 | 1 -5 7
______9____
1
Now add down the column to get:
9 | 1 -5 7
_____9____
1 4
Now multiply 4 by 9 and put that product up under the 7:
9 | 1 -5 7
______9__36
1 4
Now add to see what the remainder is:
9 | 1 -5 7
_______9_36
1 4 R43
we have a remainder of 43. Since it is not a 0, then the polynomial is not evenly divisible by x - 9.
So the answer is No.
-5/3 x(-1/8)weurEzzrtx
Answers
Answer:
-5/3 x (-1/8 )= 5/24 = 0.2083333
Step-by-step explanation:
Susie heard a traffic report that 495 was jammed. She then decided to find an alternate route home. This is an example of ??? reasoning Converse Deductive Inductive Indirect
Answers
Answer:
The correct option is;
Deductive
Step-by-step explanation:
Deductive reasoning or logic is the basic reasoning process that begins with a premise, hypothesis or general statement that is taken as being correct or true and continues with the consideration of the likelihoods or possibilities to come to a conclusion which is logically certain
In deductive reasoning a top to down reasoning approach is applied to link a premise with a conclusion.
If x = 4 and y = 8 , evaluate the following expression: x/y Give your answer as a fraction in its simplest form.
Answers
Answer:
X/Y = 4/8= 1/2
Step-by-step explanation:
This is the answer of this question
Which is the first step in simplifying the expression 2(x + 3) + 5?
Answers
Answer:
Step-by-step explanation:
Feel pleasure to help you.
plz, help. plzzzzzzzzzzzzz
Answers
Answer:
[tex]Area = 26.75 \:units^2[/tex]
Step-by-step explanation:
[tex]Area =\:\frac{\left(3.5\right)\left(2+2+5\right)}{2}+\frac{\left(2\right)\left(2\right)}{2}+\left(2\cdot 2\right)+\frac{\left(2\right)\left(5\right)}{2}\\\\=26.75[/tex]
Which regression equation best fits these data?
Answers
[tex]the \: right \: answer \: is \: of \: option \: a \\ y = - 0.32 {x}^{2} - 1.26x + 15.81 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Simplify the radical expression.
Answers
Answer:
x^4y^9, the second option.
Step-by-step explanation:
A radical sign over an expression also means the expression is to the power of 1/2. In other words, the square root of n=n^1/2
(x^8y^18)^1/2
You divide the powers by 2
x^4y^9 is the answer
Answer:
b
Step-by-step explanation:
6. What is the slope of a line perpendicular to the line whose equation is y = 2x -5?*
1) -2
2) 2
3) 1/2
4) -1/2
Answers
Answer: -1/2
You get y = 2x - 5, so the slope is 2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is -1/2.
hlp me hlp me hlp me hlp me
Answers
The unit rate would be points per game.
To find the points per game, divide both numbers by 6:
288/6 = 48
the unit rate would be 48 points / 1 game.
The answer is the first choice.
Answer:
[tex]\frac{288 points}{6 games}[/tex] ÷ [tex]\frac{6}{6} =\frac{48 points}{1 game}[/tex] or the 1st option
Step-by-step explanation:
[tex]\frac{288 points}{6 games}[/tex] ÷ [tex]\frac{6}{6} =\frac{48 points}{1 game}[/tex]
We get this answer because to find the unit rate, we need to get however many points over one game.
Calving works totally for 3 hours in weekdays and 5 hours in weekends. How many hours does he works in 4 weeks?
A. 36 hours
B. 32 hours
C. 20 hours
D. 12 hours
Answers
Answer:
B. 32
Step-by-step explanation:
5+3=8
8×4=32
// have a great day //
The junior class sells tickets to a talent show to raise money. Each ticket sells for $8. How much money do they raise?
Answers
Answer:
unsolvable
Step-by-step explanation:
you need to know how many people bought a ticket
Which of the following is a function?
Click on the graph until the correct graph appears.
Answers
Answer:
The correct graph should have x values that have no more than one y value.
Step-by-step explanation:
A the inputs (x values) of a function can have no more than one y value. This is a "fact" for functions. So you should click on the graph until you see a graph where every x value has exactly 0 or 1 y value.
What is mzABC?
75°
Om ABC = 15°
Om ABC = 45°
135
С
Om ABC = 60°
Om ABC = 75°
B
D
Answers
Answer:
D
Step-by-step explanation:
I got it on the test
The measure of ∠ABC in the triangle below is 60°
Triangle
Triangle is a polygon with three sides and three angles. The sum of angles in a triangle is 180°.
∠ACB + 135 = 180° (Sum of angles in a straight line)
∠ACB = 45°
In triangle ABC:
∠ABC + ∠ACB + ∠CAB = 180° (Sum of angle in a triangle)
∠ABC + 75 + 45 = 180
∠ABC = 60°
The measure of ∠ABC in the triangle below is 60°
Find out more on Triangle at: https://brainly.com/question/23945265
