Answer:
Step-by-step explanation:
When you list the trigonometic ratios for both acute angles in a right triangle, you notice some interesting developments.
Let's concentrate on sine and cosine:
Observation from the table above: notice1
In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B.
If ∠A and ∠B are the acute angles of a right triangle,
sin A = cos B
Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.
If we write, m∠B = 90º - m∠A (or m∠A = 90º - m∠B ), and we substitute into the original observation, we have:
notice4
If θ is substituted for m∠A , we establish the following relationship between sine and cosine:
sincosrule
The sine of any acute angle is equal to the cosine of its complement.
The cosine of any acute angle is equal to the sine of its complement.
Sine and cosine are called "cofunctions", where the sine (or cosine) function
of any acute angle equals its cofunction of the angle's complement.
FYI: What about tangent?
Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle. It is not, however, the same type of relationship that exists between sine and cosine.
The tangent of ∠A is the reciprocal (flip over) of the tangent of ∠B.
The angles being used in the following examples are acute angles.
ex1
If sin 30º = ½ and cos θ = ½,
find θ. Solution: Since both trig functions = ½,
30º and θ must be complementary.
θ = 60º
ex2
If sin(3x + 10)º = cos(x + 24)º,
find x. Solution: In order for the sine and cosine to be equal, the angles must be complementary.
3x + 10 + x + 24 = 90
4x + 34 = 90
4x = 56
x = 14
ex3
If sin(15º) = 0.26 and
cos (15º) = 0.97,
find sin(75º) and the cos(75º). Solution: The sine of an angle and the cosine of its complement are equal.
15º and 75º are complementary.
sin(75º) = cos(15º) = 0.97
cos(75º) = sin(15º) = 0.26
ex4
In right ΔABC, m∠C = 90º,
sin A = x + 0.1 and cos B = 2x - 0.4. Find x. Solution: If A and B are the acute angles of a right triangle, sin A = cos B.
x + 0.1 = 2x - 0.4
0.5 = x
Which of the following is square root of 0.000081?
(A) 0.9
(B) 0.09
(C) 0.009
(D) 9
Find the value of square root of 64/225?
(A) 8/17
(B) 8/15
(C) 13/8
(D) 8/11
Which number is not a perfect square?
(A) 4
(B) 9
(C) 111
(D) 81
Which of the following is square root of 1/25?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
What is square root of 36/49?
(A) 3/4
(B) 6/7
(C) 7/6
(D) 5/8
What is square root of 36/121?
(A) 6/11
(B) 3/5
(C) 2/3
(D) 6/121
Answer:
1. C) 0.009
2. B) 8/15
3. C) 111
4. D) 1/5
5. B) 6/7
6. A) 6/11
Hope this helps and have a nice day.
Write as a single exponent.
1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2
2. ( 1/10 x 1/10 x 1/10 )^3
3. ( 10 x 10 x 10 )^-2
Step-by-step explanation:
1. (1/10 × 1/10 × 1/10 × 1/10)^2
(10^-4)^2
10^-8
2. (1/10 × 1/10 × 1/10)^3
(10^-3)^3
10^-6
3. (10 × 10 × 10)^-2
(10^3)^-2
10^-6
Question
Write as a single exponent.
1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2
2. ( 1/10 x 1/10 x 1/10 )^3
3. ( 10 x 10 x 10 )^-2
Katarina wrote the standard form of a linear equation as 4x – 4 x minus StartFraction 2 Over 3 EndFraction y equals 8.Y = 8. Sofiya told her that the equation was not yet in standard form and gave her the right advice for how to fix it. What advice did Sofiya give to Katarina? Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24. Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12. Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 8. Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 4.
Answer:
Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.
Step-by-step explanation:
Katarina's equation
4x - 2/3y = 8
In order to convert Katrina's linear equation into standard form,
She should find the least common denominator
4x - 2/3y = 8
{4x(3) - 2y(1)} / 3 = 8
(12x - 2y) / 3 = 8
Multiply both sides by 3
(12x - 2y) / 3 × 3 = 8 × 3
12x - 2y = 24
Divide both sides by 2
(12x - 2y) / 2 = 24 / 2
6x - y = 12
The advice sofiya gave Katrina is to Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.
Answer:
B) Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.
Step-by-step explanation:
edg2020
A farm processes 6,000 gallons of milk every hour. Which equation represents the amount of milk, y, that the farm processes in x hours?
A. y=6,000+x
B. y=x6,000
C. y=6,000x
D. y=6,000x
can someone help me figure this out ?
Answer: AAS
Step-by-step explanation:
Lets call the intersection point between AC and DE F.
I think he meant the two triangles AFE and DFC.
We know angle A is congruent to angle D.
We also know AE is congruent to DC.
There is also a hidden piece of evidence which is AFE is congruent to DFC due to vertical angles.
We know two angles and 1 side, so we can use AAS to figure out that the two smaller triangles are congruent.
Find the midpoint (-4,6) (5,-9)
The midpoint would be (1/2, -3/2). Hope this helps! Please mark brainliest:)
Identify the domain and range of each relation
whether the relation is a function.
1. {(3, 6), (5,7), (7.7) (8. 9)}
7/8 square foot in 1/4 hour
Answer:
2 1/2
Step-by-step explanation:
The unit rate for the given parameters is 3 1/2 square feet /hour.
Given that, 7/8 square feet in 1/4 hour.
We need to find the unit rate.
How to find unit rate?In a unit rate, the denominator is always 1. So, to find the unit rate, divide the denominator with the numerator in a way that the denominator becomes 1.
Now, unit rate = 7/8 ÷ 1/4
=7/8 × 4 =7/2
=3 1/2 square feet /hour
Therefore, the unit rate for the given parameters is 3 1/2 square feet /hour.
To learn more about a unit rate visit:
https://brainly.com/question/11258929.
#SPJ6
PLease help me(: !!!!!!!!!!!!!!!!!!!!
Answer:
should be 65
Step-by-step explanation:
if not then hmu
–8 ÷ 2 =
answer now and free r
Answer:
-4
Step-by-step explanation:
A sculptor is designing her new triangular masterpiece. In her scale drawing, the shortest side of the triangular piece to be made measures The longest side of the drawing measures The longest side of the actual triangular piece to be sculpted must be long. How long will the shortest side of this piece be?
Answer:
3.71 m
Step-by-step explanation:
Here is the complete question.
A sculptor is designing her new triangular masterpiece. In her scale drawing, the shortest side of the triangular piece to be made measures 7 cm. The longest side of the drawing measures 20 cm. The longest side of the actual triangular piece to be sculpted must be 10.6 m long. How long will the shortest side of this piece be?
Solution
This is a scale drawing question.
Since scale = Scaled size/Actual size, we need to find the scale ratio of the triangle.
Now, the longest side of the drawing measures 20 cm which is equal to the scaled size and the longest side of the actual triangular piece to be sculpted is 10.6 m long which is the actual size.
So, scale = 20 cm/10.6 m
= 0.2/10.6
= 1/53.
Since in the scale drawing, the shortest side of the triangular piece to be made measures 7 cm, this is the scaled size, so the actual size of the shortest side is gotten from
scale = Scaled size/Actual size.
So,
Actual size = Scaled size/scale
= 7 cm ÷ 1/53
= 53 ×7 cm
= 371 cm
= 3.71 m
Easy 1 through 3 ! 17 points
1. (1.) -24, (2.) 6, (3.) -3
2. Positive
3. Difference = Subtraction
Product = Multiplication
Quotient = Division
What is an equation of the line that passes through the points (3,3) and (-2,6)
F.y=-3/5x + 24/5
G.y=-3/5x - 24/5
H.y=3/5x + 24/5
J.y=3/5x - 24/5
Answer:
F
Step-by-step explanation:
x - x1/ x2-x1= y - y1/ y2 -y1
x - 3 / -2 -3= y -3/6-3
x-3/-5=y-3/3
3(x-3)= -5(y-3)
3x-9= -5y +15
5y = -3x +24
y= -3x/5 +24/5
In a sports competition, Alyssa was penalized -16 points. She received the same number of penalty points in each of the 4 events. How many points was she penalized each event?
Answer:
-64
Step-by-step explanation:
multiply -16 by 4 to get the total of -64
What is the value of x in the equation -6x-5x+22?
-22
-2
2
22
What is the answer
Answer:
theres no answer
Step-by-step explanation:
is there more?
Need help with this algebra problem 15 points will give brainiest if right
Answer:
b is the lowest and d is the highest y axis
Step-by-step explanation:
Please help! Will be marking brainliest!
Answer:
integer and rational
Step-by-step explanation:
Tell whether each number is divisible by 2, 3, 5, 6, 9, and/or 10.
a. 8,435
b. 981
Step-by-step explanation:
a. 8,435 is divisible by 5
b. 981 is divisible by 3 and 9
10. Points D, E, and F are non-collinear. How many lines can be drawn that pass through F and are perpendicular
to DE ? Use a diagram to illustrate your answer.
Given:
Points D, E, and F are non-collinear.
To find:
Number of lines that pass through F and are perpendicular to DE.
Solution:
Points D, E, and F are non-collinear. It means points D, E and F are not lie on a single straight line.
We know that, the number of perpendicular lines on a line from a particular point is 1.
So, number of lines that pass through F and are perpendicular to DE is 1 as shown in the below figure.
Write an expression equivalent to -4(-6m - 7).
Answer: 24m+28
Step-by-step explanation:
Distribute the negative four among the two terms.
Answer:
[tex](12*2)m+(-56/-2)[/tex]
I hope this helped :)
Find the area of the semicircle please .
Answer:
39.25
Step-by-step explanation:
the formula is a = (3.14 × [tex]r^{2}[/tex]) / 2
the equation is a = (3.14 ×[tex]5^{2}[/tex]) / 2
5 is the radius
1. [tex]5^{2}[/tex] = 25
2. 3.14 × 25 = 78.5
3. 78.5 / 2 = 39.25
I hope this helped! :)
Answer:
12.5π or 39.25
Step-by-step explanation:
10 is diameter, we first find the radius which is 10/2 = 5 and so we know the area formula of the circle is πr^2 so 5^2 is 25 and then there's a π at the end so 25π, but it's a semicircle so 25π/2 which is 12.5π, if it's in base 10 (decimal form) then simply do 12.5 x 3.14 = 39.25
If the measure of angle 1=4x-3 and the measure of angle 2=3x+8, find the value of x so that the measure of angle 1 is supplementary to the measure of angle 2.
Answer:
hujikmnjhu
Step-by-step explanation:
egyiru9epojgtur9iokejrue
I can’t.....help. I’m gay, I don’t understand math.
Answer:
i cant help i do not know answer
Answer:i-
Step-by-step explanation: good luck
What is an equation of the line that passes through the point (-6, -7) and is
perpendicular to the line 6x + 5y = 30?
Answer:
Step-by-step explanation:
Product of slope of perpendicular lines = -1
6x + 5y = 30
Write this equation in y = mx + b form
5y = -6x + 30
y = [tex]\frac{-6}{5}x+\frac{30}{5}[/tex]
[tex]y=\frac{-6}{5}x + 6[/tex]
Slope of this line m₁ = -6/5
m₁ * m₂ = -1
m₂ = -1÷m₁ = -1 * [tex]\frac{5}{-6}[/tex]
[tex]m_{2}=\frac{5}{6}[/tex] & (-6 , -7)
Equation of the required line: y - y₁ = m (x - x₁)
[tex]y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2[/tex]
Which inequalities are true? Check all that apply.
Answer:
1,2,3, and 5
Step-by-step explanation:
I plugged them all into a calculator
1. Which graphs could represent a proportional relationship?
A. A
B. B
C. C
D. D
Answer:
a
Step-by-step explanation:
proportional relationship start from the origin (0,0)
they also have a line that goes upwards in an even relationship
they also can make points
follows the slope
If m ZAEB = 88°, find m2AED.
Step-by-step explanation:
Hey there!
Here;
Given is; angle AEB = 88°
angle AEB + angle AED = 180° { being linear pair}
88° + angle AED = 180°
angle AED = 180° - 88°
Therefore, angle AED = 92°
Therefore, answer is Option C.
Hope it helps...
what is 6g-m/2 if g=4 and m=16
Answer:
I think the answer would be 16?
Step-by-step explanation:
if you plug in the given numbers that represent each letter it would be 6(4)-16/2 = 24-8= 16
Question 4 fast please
Answer:
X=-10
Step-by-step explanation:
Collinear points are points on the same line.
Use the equation of gradient to find the gradient. Then use the gradient to find X
[tex]\frac{Y2-Y1}{X2-X1}=Gradient of a slope[/tex]
[tex]\frac{2-(-4)}{3-0}=\frac{2+4}{3}=\frac{6}{3}=2[/tex]
[tex]\frac{x+4}{-3-0}=2[/tex]
Multiply both sides of the equation to get rid of the fraction.
[tex]\frac{x+4}{-3}*-3 =2*-3[/tex]
x+4=-6
x=-6-4
x=-10
Hugo began his science experiment with 22 grams of sugar crystals. During the experiment, the change in the mass of the sugar crystals was
–
6 grams.
What is the final mass of the sugar crystals?
Answer:
its actually 16
Step-by-step explanation:
Answer:
16
Step-by-step explanation: