Answer:
[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.
The longest side of the triangle is called the hypotenuse and the other two sides are the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The tangent ratio is defined as:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
The cotangent ratio is defined as:
[tex]\displaystyle \cot\theta=\frac{\text{adjacent leg}}{\text{opposite leg}}[/tex]
As shown above, the tangent and the cotangent are the ratios of the two legs in any possible order.
If the triangle has angles of 30°, 60°, and 90°, then we can take one of the acute angles and find the tangent and cotangent to know the required ratios:
Let's take for example the 30° angle:
[tex]\displaystyle \text{ratio of legs: }\tan 30^\circ=\frac{\sqrt{3}}{3}[/tex]
[tex]\displaystyle \text{ratio of legs: }\cot 30^\circ=\sqrt{3}[/tex]
Thus the possible ratios from the list are:
[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]
The reciprocals of those ratios are also applicable
Find the cost with sales tax for an item with a purchase price of $7. Assume that the sales tax is 8%, or 0.08 times the price.
Group of answer choices
Answer:
$7.56
Step-by-step explanation:
$7(.08) = .56 in tax
$7 item cost + .56 in tax
josh earned $30,000 last year if the tax rate was 15%,how much money can he keep after taxes
Answer:
25500
Step-by-step explanation:
15% of 30000 is (multiply 30000 by .15 to get this) 4500
Subtract 4500 from 30000 and you got the answer
pls help me whats 5x4
HELP PLEASE
classify the triangle
Answer:
I believe it would be an acute triangle.
Round 59..166 to the nearest tenth
Answer:
59.2
Step-by-step explanation:
so each number placement after the decimal is different.
it goes tenths place, hundredths place, thousandths place, ten thousandths place and so forth
Answer:
59.2
Step-by-step explanation:
the tenth place is the 1st place on the right side of the dwecimal. so this rounded to the nearest tenth woul be 59.2, since 6 is enough to make 1 round up one more
Resolver esta ecuación
Answer:
Step-by-step explanation:
f(x)/g(x) = (x+6)/[(x+6)(x-6)]
Cancel (x+6)
Answer is 1/(x-6)
ellie is preheating her oven before using it to bake. the initial temperature of the oven is 65° and the temperature will increase the rate of 10° per minute after being turned on what is the temperature of the oven six minutes after being turned on what is the temperature of the oven t minutes after being turned on
Answer:
The temperature six minutes after being turned on is 125°.
T(t)= 65° + t * 10°
Step-by-step explanation:
Linear Equations
Ellie sets the temperature of the oven to 65°. The oven will increase the temperature at 10° per minute after being turned on.
After the first minute, the temperature of the oven is
65° + 10° = 75°
After the second minute, the temperature is:
65° + 2*10° = 65° + 20° = 85°
The same pattern goes on after minute 6, where the temperature is:
65° + 6*10° = 65° + 60° = 125°
The temperature six minutes after being turned on is 125°.
The general formula can be deducted for any time t as:
T(t)= 65° + t * 10°
The sum of two numbers is 8. The difference of the same two numbers is 4. What are the two numbers?
Answer:
2 and 6
Step-by-step explanation:
2+6=8. 6-2=4.
Answer:
2 and 6
Step-by-step explanation:
pls help me yes you help
Answer:
C
Step-by-step explanation:
Answer:
C) A car can travel 80 miles on 2 gallons of gasoline.
Step-by-step explanation:
They gave us the unit rate which is 40 mile/1 gallon of gasoline. With the unit rate, we can then simplify each answer choice.
Simplified version of answer a: 1 mile/40 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)
Simplified version of answer b: 41 mile/ 1 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)
Simplified version of answer c: 40 miles/1 gallon of gasoline (this one is the correct answer since it matched the unit rate.
Simplified version of answer d: 40 miles/ 20 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)
Hope this helped you : )
Which of the following results in the expression 0.22 x 86?
Answer:
18.92
Step-by-step explanation:
Im preatty sure this is right
Answer:
18.92
I multiplied 0.22 and 86
What is the midpoint of the line segment that has endpoints (3,8) and (1,−4) ?
Answer:
D
Step-by-step explanation:
Midpoint Formula:
[tex]\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}[/tex]
[tex]\frac{3+1}{2}[/tex] ⇒ [tex]\frac{4}{2}[/tex] ⇒ [tex]2[/tex]
[tex]\frac{8+-4}{2}[/tex] ⇒ [tex]\frac{8-4}{2}[/tex] ⇒ [tex]\frac{4}{2}[/tex] ⇒[tex]2[/tex]
[tex](2,2)[/tex]
Dan uses 340 grams of blueberries to make 24 fluid ounces of smoothie. last week he made 54 fluid ounces of smoothie. how many grams of blueberries did dan use last week?
Answer: He used 765 grams of blueberries.
Step-by-step explanation:
The quantity of blueberries is directly proportional to the quantity of smoothie.
Equation of direct variation : [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Substitute [tex]x_1=340\text{ grams},\ \ \ y_1=24\text{ fluid ounces}[/tex]
[tex]y_2=54\text{ fluid ounces}[/tex]
To find : [tex]x_2[/tex]
[tex]\dfrac{340}{24}=\dfrac{x_2}{54}[/tex]
[tex]\Rightarrow\ x_2=\dfrac{340}{24}\times54\\\\\Rightarrow\ x_2=765[/tex]
Hence, he used 765 grams of blueberries.
find y when y = 3x^2 -2x+5 and x = -1
Answer:
the answer is y=10
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1500. How much would the law firm charge the client daily if 9 associates and 4 partners were assigned to the case? How much would the law firm charge the client daily if aa associates and pp partners were assigned to the case?
Answer:
$8700
Step-by-step explanation:
Associates cost $800 each, you have 9 associates, so multiply 800 by 9 which gives you: $800x 9= $7200.
Partners cost $1500 each, you have 4 partners, so multiply 1500 by 4 which gives you: $1500x 4=$6000.
Then add the two together like this: $7200+$1500= $8700.
Answer:8000
Associates cost $800 each, you have 9 associates, so multiply 800 by 9 which gives you: $800x 9= $7200.
Partners cost $1500 each, you have 4 partners, so multiply 1500 by 4 which gives you: $1500x 4=$6000.
Then add the two together like this: $7200+$1500= $8700.
• You have given an equal sided triangle with side length a. A straight line connects the center of the bottom side to the border of the triangle with an angle of α. Derive an expression for the enclosed area A(α) with respect to the angle (see drawing).
9514 1404 393
Answer:
[tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]
Step-by-step explanation:
If we place the bottom center at the origin and make the sides of the triangle 2 units, then the right side can be described by the equation ...
y = √3(1 -x)
and the terminal side of the angle α can be described by ...
y = tan(α)·x
We want the height of the shaded area, which is the y-coordinate of the point of intersection of these two lines.
y = √3(1 -y/tan(α)) . . . . substituting for x
y = √3·tan(α)/(√3 +tan(α)) . . . . solved for y
Since we have defined the base of the shaded area to be 1, the shaded area is half this value, or ...
A(α) = (√3/2)tan(α)/(√3 +tan(α))
Further manipulation can put this in the form ...
A(α) = (√3/4)sin(α)/sin(α+π/3) . . . . for α ≤ π/2, side length 2
__
For α > π/2, we need to subtract the area A(π-α) from the area of the whole triangle. This gives an area (after some rearranging) of ...
A(α) = √3(1 -sin(α)/(4·sin(α-π/3))) . . . . for α > π/2, side length 2
__
The problem statement defines the triangle as having a side length of 'a', so the final area formula will be a factor of (a/2)² times the above expressions. That is ...
[tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]
_____
The graph (second attachment) shows the area as a function of α (in degrees) for a unit triangle. There are inflection points in the curve at 30°, 90°, and 150°
I need help with this assignment
Answer:
1) 3x = 2x + 50
3x - 2x = 50
X= 50
2)6x = 2x + 44
6x - 2x = 44
4x = 44
divide both sides by 4
X = 11
3)8x = 2x + 36
8x - 2x = 36
4x = 36
divide both sides by 4
X = 9
4) 4x = X + 18
4x - X = 18
3x = 18
divide both sides by 3
X= 6
5) 7x + 10 = 3x + 120
collect like terms
7x - 3x = 120 - 10
4x = 110
divide both sides by 4
X = 27.5
6) 20 + 2x = X + 56
collect like terms
2x - X = 56 - 20
X = 36
7) already done
8)12x + 12 = 3x + 84
collect like terms
12x - 3x = 84 - 12
9x = 72
divide both sides by 9
X = 8
9) 3 + 6x = 2x + 27
collect like terms
6x - 2x = 27 - 3
4x = 24
divide both sides by the coefficient of X (4)
X = 6
10) 8x + 2 = 72 + X
collect like terms
8x - X = 72 - 2
7x = 70
divide both sides by the coefficient of X (7)
X = 10
11) 2x + 20 = X + 60
collect like terms
2x - X = 60 - 20
X = 40
12). 4x + 1 = 25 + 2x
collect like terms
4x - 2x = 25 - 1
2x = 24
divide both sides by the coefficient of X (2)
X = 12
I hope this helps
I would really appreciate it if sombody helped me please i suck at me math :(
if you need help with Math:)
Answer:
Thanks!
Step-by-step explanation:
I already have it on my phone tho lol
PLEASE HELP ASAP GIVING 15 POINTS AND MARKING BRAINLIEST THE FIRST PHOTO IS THE GRAPH THE SECOND IS THE ANSWER CHOICES PLEASE HELP!!!
What is the gfc of 24 and 36
Answer:
6 is the gfc
Step-by-step explanation:
hope this helped :-)
Answer:
it is -
Step-by-step explanation:
Which graph shows a linear function?
8(a+4)=___a+___ PLZ HELP IM STUCK ON THIS
Answer:
8(a+4)=8a+32
Step-by-step explanation:
Use the distributive property.
Use the distributive property to expand the following expression.
-2(2.1x+3y-1.8)
WILL MARK BRAINLYEST
A car can travel 264 miles on 11 gallons of gasoline. How far can it travel on 2
gallons?
Answer:
The answer is 48 miles.
My Logic
If you divide 264 into 11, then you will get 24. 24 is the cars MPG. Then you can Multiply 24 by 2 and you get the answer. Hope this is helpful!
Solve the proportion 4/5 equals X over 15
Write the algebraic notation for dilation with a scale factor of ½
Answer: (x, y) goes to (1/2x, 1/2y)
Step-by-step explanation:
y+4= 2/3 (x+3) written in standard form
One number is 2 less than a second number.twice the second number is 37 more than 5 times the first. Find more the two number
Answer:
The numbers are -11 and -9.
Step-by-step explanation:
The two numbers are x and y.
x = y - 2
2y = 5x + 37
2y = 5(y - 2) + 37
2y = 5y - 10 + 37
3y = - 27
y = -9
x = - 11
If a 150-pound teenager eats 5.5 pounds of food per day, is that proportional to a 250-pound panda eating 40 pounds of bamboo a day? Explain your answer.
Answer: No It's not proportional as the constant of proportionality for both of them.are different.
Step-by-step explanation:
For the first part of the question, a 150-pound teenager eats 5.5 pounds of food per day, we've to calculate the constant of proportionality. This will be:
y = kx
150 = 5.5k
k = 27.27
For the second part of the question, a 250-pound panda eats 40 pounds of bamboo a day. we've to calculate the constant of proportionality. This will be:
y = kx
250 = 40k
k = 250/40
k = 6.25
This shows that the 150-pound teenager eats 5.5 pounds of food per day, is not proportional to a 250-pound panda eating 40 pounds of bamboo a day because th e value of k are different.
Factor the Expression. 121x + 44 *
11(10x + 4)
21x + 4
11(11x + 44)
11(11x + 4)
i like chicken nuggets
Answer:
what the heck is this
Step-by-step explanation: