Hello!
This is a problem about relating values of the Unit Circle.
First, we need to figure out the specific "points" of each angle measure of 30 and 60.
For the angle measure 30, the point will be [tex](\frac{\sqrt{3}}{2},\frac{1}{2})[/tex].
For the angle measure 60, the point will be [tex](\frac{1}{2},\frac{\sqrt{3}}{2})[/tex].
The tangent value of a point will be its [tex]y[/tex] value over its [tex]x[/tex] value.
[tex]\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}*\frac{2}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
The cotangent value of a point will be the reciprocal of the tangent value, which we found previously.
[tex]\frac{3}{\sqrt{3}}=\frac{3\sqrt{3}}{3}=\sqrt{3}[/tex]
The sine value of a point will be the [tex]y[/tex] value of the point.
[tex]\frac{\sqrt{3}}{2}[/tex]
So the values we have so far are [tex]\frac{\sqrt{3}}{3}+\sqrt{3}+\frac{\sqrt{3}}{2}[/tex]
Now we have to find the LCD to add these together, which in this case would be 6.
[tex]\frac{2\sqrt{3}}{6}+\frac{6\sqrt{3}}{6}+\frac{3\sqrt{3}}{6}[/tex]
Which adds up to [tex]\frac{11\sqrt{3}}{6}[/tex], which is in simplest radical form.
Hope this helps!
Find the distance.
a. 9.7
b. 11.7
c. 10.7
d. 12.7
Answer:
b) 11.7
Step-by-step explanation:
Pls answer quickly will mark brainlest
Answer:
25
Step-by-step explanation:
That is the answer, 25
The measures of the exterior angles of a hexagon are x°x°, 2x°2x°, 5x°5x°, 6x°6x°, 7x°7x°, and 9x°9x°. Solve for x.
Answer:
x = 12°
Step-by-step explanation:
The measures of the exterior angles of a hexagon are x°, 2x°, 5x°, 6x°, 7x°, and 9x°. Solve for x.
The sum of the exterior angles of a polygon sums up to 360
An hexagon is a 6 - sided polygon
(x + 2x + 5x + 6x + 7x + 9x) = 360
30x = 360
Divide both sides by 30
x = 360 / 30
x = 12
Hence, x = 12°
question on picture:
Answer:
Formula for tan is opposite over adjacent, so do arctan of 150/100 to get 56.30993247 :))
Step-by-step explanation:
Answer:
B. 34
Step-by-step explanation:
sohcahtoa
tan x = 100/150
tan x = .667
x = 33.7
PLS HELP PLS PLS PLS For #1-2, determine if the sequence is arithmetic or geometric. Then find its common difference or ratio.
1.
1/2, 1, 2, 4…
2. -5, 1, 7, 13 …
Answer:
#1 is Geometric
the common ratio is 2
#2 is Arithmetic
the common difference is 6
Please help me with this kahn assignment!
Thank you
Answer:
[tex]7^{8}[/tex]
Step-by-step explanation:
When you multiply exponential numbers with the same base number, you have to add the exponents. So add 2 and 6 because the numbers share 7 as base.
please give brainliest if it helped:)
HELPPPPPP: Simplify - {- [- (-8) ] }
Answer:
[tex]-8[/tex]
Step-by-step explanation:
Just take away parentheses.
The cracker manufacturer is trying to determine the best dimensions for the boxes to hold their product so that they use the least amount of cardboard.
A rectangular prism with length of 6 inches, width of 4 inches, and height of 12 inches. A rectangular prism with length of 7 inches, width of 6 inches, and height of 9 inches.
Which box uses less cardboard, and how much less cardboard does it use?
A. The box on the right uses 30 inches squared less cardboard.
B. The box on the left uses 30 inches squared less cardboard.
C. The box on the right uses 90 inches squared less cardboard.
D. The box on the left uses 90 inches squared less cardboard.
Answer:
B, the box on the left used 30 in square units less cardboard.
Step-by-step explanation:
I took this question on my quiz and got it right.
Answer:
Step-by-step explanation:
Please help, I will give brainliest to whoever helps!
Does the graph represent a function?
yes or no
Answer:
no
Step-by-step explanation:
I need help right now !
Answer:
7/3
Step-by-step explanation:
no brainlyest i see how it is -_-
Answer:
42.86%
Step-by-step explanation:
18 - 2n2 for n = 3
Need help
Answer:
Step-by-step explanation:
Here are some steps to help you
Step 1
18 - 2n2 We are gonna be evaluating
Step 2
18 - 2n^2 Substitute n for 3
18-2(3^2)
Step 3
18-2(3^2) simplify
0
So therefore, your answer is 0
Hope this helps
please show all work
Answer:
[tex]x=21.6[/tex]
Step-by-step explanation:
Use the Pythagorean theorem to solve this problem. The Pythagorean theorem states the following,
[tex]a^2 + b^c = c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle, and (c) is the hypotenuse or the side opposite the right angle.
Use the Pythagorean theorem in the right triangle with legs (15) and (18),
[tex](15)^2+(18)^2=c^2\\\\225 + 324=c^2\\\\549=c^2\\\\\sqrt{549}=c[/tex]
Use the Pythagorean theorem again in the right triangle with the legs (18) and (x)
[tex](x)^2+(18)^2=c^2\\\\\sqrt{x^2+324}=c[/tex]
Use the Pythagorean theorem one final time in the larger triangle,
[tex](\sqrt{x^2+324})^2+(\sqrt{549})^2=(x+15)^2\\[/tex]
Simplify, remember that anything to the power (2) is equal to the base (number under the exponent) times itself,
[tex]x^2+324+549=x^2+30x+225[/tex]
[tex]x^2+873=x^2+30x+225[/tex]
Inverse operations,
[tex]x^2+873=x^2+30x+225\\-x^2\\\\873=30x+225\\-225\\\\648=30x\\/30\\\\\frac{648}{30}=x\\\\21.6=x[/tex]
Find two consecutive even integers who's sum is 34.
Answer:
Step-by-step explanation:
Let the smaller integer be x
x+x+2 =34
2x+2=34
2x=32
x=16
Smaller even integer = 16
Larger even integer = 16+2 = 18
Answer = 16,18
Help me with this!!!!
Answer:
5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1 )^2 }[/tex]
with (x₁, y₁ ) = (6, 4) and (x₂, y₂ ) = (3, 8)
d = [tex]\sqrt{(3-6)^2+(8-4)^2}[/tex]
= [tex]\sqrt{(-3)^2+4^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
Answer:
5
Step-by-step explanation:
Luke surveyed his friends to see how many minutes it takes each of them to get to school in the moming. The results are in the list below.
6, 11, 14, 4, 8, 8, 10, 9, 14
What is the mean of the data? (Round to the nearest tenth if necessary)
Answer:
9.3
Step-by-step explanation:
The real answer is 9.33333 but I did as you said and rounded to the nearest tenth.
I got this answer by adding up 6, 11, 14, 4, 8, 8, 10, 9, 14 and I got 84. Then I divided 84 by 9 and got 9.33333.
Sorry if I'm wrong.
Please mark me as Brainliest.
The vertices of triangle ABC are A(−2, 3), B(4, 3), and C(−2, −4). The triangle is dilated with a scale factor of 2. Estimate the perimeter of the dilated figure to the nearest whole number.
Answer:
Use dynamic geometry software to draw any triangle and label it △ABC. a. Dilate △ABC using a scale factor of 2 and a center of dilation at the origin to form ... the scale factor is k = 3. —. 2 . So, the dilation is an enlargement. b. Because. CP′ ... Graph △ABC with vertices A(2, 1), B(4, 1), and C(4, −1) and its image after a.
Step-by-step explanation:
A third candle, in the shape of a right circular cone, has a volume of 16 cubic inches and a radius of 1.5 inches. What is the height, in inches, of the candle? Round your answer to the nearest inch.
Given:
Volume of a right circular cone = 16 cubic inches
Radius of the cone = 1.5 inches.
To find:
The height of the cone.
Solution:
The volume of a cone is:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Where, r is the radius and h is the height of the cone.
Putting [tex]V=16,r=1.5,\pi=3.14[/tex] in the above formula.
[tex]16=\dfrac{1}{3}(3.14)(1.5)^2h[/tex]
[tex]48=(3.14)(2.25)h[/tex]
[tex]48=7.065h[/tex]
Divide both sides by 7.065.
[tex]\dfrac{48}{7.065}=h[/tex]
[tex]6.794=h[/tex]
[tex]h\approx 7[/tex]
Therefore, the height of the cone is 7 inches.
Josh drinks 3 1/2 pints of milk a day. How much is this in cups?
Answer:
7 cups
Step-by-step explanation:
1 pint is 2 cups.
Just double the number of pints to get the amount of cups
Answer:
7
Step-by-step explanation:
PLZ HELP !! PICK ABC OR D
Answer:
C
Step-by-step explanation:
Don't use such phrases here, not cool! It hurts our feelings :(.
what is this i just asked a question and i get this.
Answer:
true
Step-by-step explanation:
Please Help!! 8th Grade
At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up 13% of total ice cream sales. This year, the same three ice creams made up 18.1% of ice cream sales. The percentage of rocky road sales doubled, the percentage of banana sales increased by 50%, and the percentage pumpkin sales increased by 20%. If the rocky road ice cream had one less percent of sales than the banana ice cream, find out the percentage of ice cream sales each individual ice cream made last year
Answer:
Banana made=3.22
Pumpkin made=7.86
Rocky road ice cream made=1.89
Step-by-step explanation:
From the question we are told that
1st year sales(banana, pumpkin, and rocky road ice cream) [tex]S_1= 13\%[/tex]
2nd year sales:[tex]S_2=18.1\%[/tex]
Rocky road sales doubled
Banana sales increased by 50%
Pumpkin sales increased by 20%
Rocky road ice cream had one less percent then banana
Let
Banana =x
Pumpkin=y
Rocky road ice cream=z
Generally the first year equation is given mathematically as
[tex]x+y+z=13......(1)[/tex]
Generally the second year equation is given mathematically as
100% increase in Rocky road ice cream sales()z i.e double
[tex]2*z=2z[/tex]
50% increase in banana ice cream sales()x
[tex]=>1*0.50=0.5\\=>0.5+1x=1.5x[/tex]
20% increase in pumpkin(y)
[tex]=>1*0.20=0.2\\=>0.2+1x=1.2y[/tex]
Therefore second year equation is given as
[tex]1.5x+1.27y+2z=18.1.....(2)[/tex]
Generally where rocky road ice cream had one less percent of sales than the banana ice cream the equation is given as
[tex]1.5x-2z=1........(3)[/tex]
Therefore combining the three equations
x+y+z=13
1.5x+1.27y+2z=18.1
1.5x-2z=1
matrix form
[tex]\begin {bmatrix}1 & 1& 1 & 13\\1.5 & 1.2 & 2 & 18.1\\1.5 & 0 & -2 & 1\end{bmatrix}[/tex]
Generally the determinant of the first three columns
[tex]\triangle=1.8[/tex]
Solving with Crammers Rule by solving Determinant when;
Column 4 replace column 1
[tex]\triangle_1=5.8[/tex]
Column 4 replace column 2
[tex]\triangle_2=14.15[/tex]
Column 4 replace column 3
[tex]\triangle_3=3.4[/tex]
Therefore x is given my
[tex]x=\frac{\triangle_1}{\triangle}[/tex]
[tex]x=\frac{5.8}{1.8}[/tex]
[tex]x=3.22[/tex]
Therefore y is given my
[tex]y=\frac{\triangle_2}{\triangle}[/tex]
[tex]y=\frac{14.15}{1.8}[/tex]
[tex]y=7.86[/tex]
Therefore z is given my
[tex]z=\frac{\triangle_3}{\triangle}[/tex]
[tex]z=\frac{3.4}{1.8}[/tex]
[tex]z=1.89[/tex]
Therefore
Banana made=3.22
Pumpkin made=7.86
Rocky road ice cream made=1.89
Marco’s Pizzeria is having a special: 5 pizzas for $25. What is the unit price?
Answer:
The unit price would be $5 per pizza
Step-by-step explanation:
Please help me find the answer for ABE ASAP plss!!
(Do not put links!!!)
Answer:
122
Step-by-step explanation:
The first thing to notice is that <EBC and <ABE form a straight line. This means they are a linear pair, also known as complementary. So, when they are added together they will equal 180 degrees. Therefore, to solve, set up and solve the algebraic equation, 180=58+x. When 58 is subtracted from both sides, you are left with x=122.
A restaurant wants to study how well its salads sell. The circle graph shows
the sales over the past few days. If 5 of the salads sold were garden
salads, how many total salads did the restaurant sell?
The restaurant sold salads over the past few days.
Answer:
20 total salads
Step-by-step explanation:
If garden salads make up 25%, and they sold 5 garden salads, you have to do 5 times 4 because 25% times 4 is 100% of the chart.
Irrational or rational -14.3
Answer:
It is an rational
Step-by-step explanation:
Can someone please help me out with this. I need this done by tomorrow. :(
Answer:
i got u its UMMMMMMMMMMMMMMMMMMMMM nvm
Step-by-step explanation:
Finding X in triangle
Answer:
x is 5 cm as the entire base is 10 cm, so 10/2 = 5
Can someone plz help me on this plz
