Find the measure of the reference angle for each given angle. Part 2
13. θ = -160°
14. θ = 345°
15. θ = =130°
Answers
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
Please see the attached pictures for full solution.
For negative angles, the arrow turns clockwise.
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
From a mathematical point of view, the reference angle is the smaller of α and (180°-α), where α = θ mod 180°.
That is, add or subtract multiples of 180° until the result is in the range 0–180°. Then choose the smaller of the angle and its supplement.
It is convenient to let a spreadsheet calculate these when you have a bunch of them.
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From a geometrical point of view, the reference angle is the positive angle between the terminal ray and the nearest x-axis.
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For the angles here, the reference angles (in degrees) are shown in the attachment.
Related Questions
What is the volume of the sphere?
Answers
Answer:
V = 523.5987756 Cubic in.
Step-by-step explanation:
The equation for the volume of a sphere is V = 4 * π * (r^3 / 3)
In this case: V = 4 * π * (41.6667)
V = 4 * 130.8996939
V = 523.5987756 cubic inches.
Hope this helps =)
Answer: C
Step-by-step explanation:
5 is the diameter so 2.5 has to be the radius.
The volume of sphere is v=4/3* π *r^3
v= 4/3 * 3.14 * 2.5^3
v= 65.4
i need these two questions!!!
Answers
Caleb’s puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian’s office, what is the percent increase in the puppy’s weight rounded to the nearest whole number? Enter your answer in the box.
Answers
Answer:
[tex]73\%[/tex]
Step-by-step explanation:
Given: Present weight of Caleb’s puppy = 2,250 grams
Puppy weighed 600 grams at his last visit to the veterinarian’s office.
To find: percent increase in the puppy’s weight rounded to the nearest whole number
Solution:
Increase in puppy's weight = 2250 - 600 = 1650 grams
Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]
[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]
I need this done please help in the picture
Answers
Answer
7.85
but I not sure JutMon21 know the problem
Answer:
I got 7.85
Step-by-step explanation:
First, I took the center angle which is 90 degrees in this case and divided by 360 and I got 0.25 Then, I multiplied that number by the radius which is 5 and I got 1.25. After that I multiplied 1.25 with 2π and the final answer that I got is 7.85
30 POINTS!!
find 10 rational numbers between -2/3 and 2/3
Answers
Answer:
Hey! Here is your answer. Hope it helps.
Find the slope and the y-intercept, then write the equation for the line in slope intercept form ?
Answers
Answer:
Slope: 1/3
Y-Intercept: (0,7)
Equation: y = 1/3x + 7
Step-by-step explanation:
If you find a point on the line, you can find the slope by counting the distance from the y-intercept.
Which expression is a difference of squares with a factor of 2x + 5
Answers
[tex]4x^2-25[/tex] is a difference of squares with a factor 2x+5
because when we factorize [tex]4x^2-25[/tex] we get [tex](2x-5)(2x+5)[/tex]
The expression is a difference of squares with a factor of 2x + 5 [tex]$4 x^{2}-25$[/tex].
What is the Difference of squares formula?Given:
2x + 5
To find:
The expression is a difference of squares with a factor of 2x + 5.
Step 1
The difference of squares formula is given by
[tex]$(a+b)(a-b)=a^{2}-b^{2}$$[/tex]
We have been given that one factor is 2x + 5.
Hence, [tex]$\mathbf{a}=\mathbf{2 x}, \mathbf{b}=\mathbf{5}$[/tex]
Step 2
It means that the other factor must be (a - b) = (2x - 5)
Hence, in order to expression, we can multiply the factors.
(2x + 5)(2x - 5)
Step 3
Using the difference of squares formula
(2x + 5)(2x - 5)
[tex]$&=(2 x)^{2}-5^{2} \\[/tex]
[tex]$&4 x^{2}-25[/tex]
The required expression exists [tex]$4 x^{2}-25$[/tex].
Therefore, the correct answer is [tex]$4 x^{2}-25$[/tex].
To learn more about difference of squares formula
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What two numbers have a sum of 191 and a difference of 63? *Hint: Create a system where one equation represents the sum and one equation represents the difference. (smaller number) (bigger number)
Answers
Answer:
127 &64
Step-by-step explanation:
x+y=191 eq(1) & x-y=63 eq(2)
x=63+y then put in the eq(1)
63+y+y=191
2y=191-63
y=64 then put in the eq(2)
x-y=63
x= 63+y
x=63+64
x=127
Answer:
both numbers are 127 and 64
Step-by-step explanation:
x= one of the numbers
191-x= the other number
(191-x)-x=63
191-x-x=63 (combine like terms)
191-2x=63 (rearrange)
191-63-2x (simplify)
128=2x
64=x
(127 +64=191)
(127-64= 63)
Alexa has 2 hours of reading to complete over the weekend. She wants to break up her reading time into 1/2 hour blocks. How many times will she read over the weekend?
Answers
All we need to do is divide the amount of hours she needs to read by the time she wants to read each time.
1/2 = 0.5
Divide.
2 / 0.5 = 4
Therefore, Alexa will read 4 times over the weekend.
Best of Luck!
Answer:
4 times
Step-by-step explanation:
1 / 2 = 0.5
2 / 0.5 = 4
Tonya sells make-up part-time. She is paid a monthly commission. She receives 18% for the first $500 she sells and 22% for the balance. She made $356.42 in commission. How much did she sell in make-up?
Answers
Answer:
She sold $1,711 in make-up.
Step-by-step explanation:
She sold x.
For the first $500, she gets 18% = 0.18.
For the balance(x - 500), she gets 22% = 0.22.
So her total earnings can be modeled by the following equation:
[tex]E = 0.18*500 + 0.22*(x - 500)[/tex]
[tex]E = 90 + 0.22*(x - 500)[/tex]
She made $356.42 in commission. How much did she sell in make-up?
So
[tex]356.42 = 90 + 0.22*(x - 500)[/tex]
[tex]90 + 0.22x - 110 = 356.42[/tex]
[tex]0.22x = 356.42 + 20[/tex]
[tex]x = \frac{376.42}{0.22}[/tex]
[tex]x = 1711[/tex]
She sold $1,711 in make-up.
What is the value of x in the equation 3-2x=-1.5x?
оооо
-6
Answers
Answer:
x=6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x = 6
Step-by-step explanation:
In this equation, we are told to solve for the value of x. Thus, we must isolate the variable x (poor x... we're always trying to isolate it).
3 - 2x = -1.5x
(I'm going to swap sides to make it easier for me to solve. This doesn't change anything mathematically due to the associative laws. It's purely cosmetic.)
-1.5x = 3 - 2x
First, we can add 2x to both sides of the equation to get all algebraic expressions containing the variable x on one side of the equation alone.
0.5x = 3
For our next part here, let's convert 0.5 to a fraction to make life easier for us.
[tex]\frac{1}{2}[/tex]x = 3
When isolating x in this, we are trying to get rid of 1/2. How can we do this? We can multiply is by 2!
[tex]\frac{1}{2}[/tex]x · [tex]\frac{2}{1}[/tex] = 1x (or simply x)
What we do to one side we must do to another.
x = 3 · 2
x = 6
Our answer is x = 6. Woo!
A sphere has a radius of 6. Using 3.14 for pi, what is the volume?
Answers
Answer:
v= 904.78
Step-by-step explanation:
Answer:
904.77868423386 feet^3
Step-by-step explanation:
Step one the formula is 4/3 Pie R ^3
Step two you do 4/3 x PI x 6^3
Step three do exponents first so 6x6x6=216
Step four multiply 4/3 x 3.14 which equals 4.187
Step four finally you are going to multiply 216 by 4.187 to get 904.77868423386 feet^3
The owner of a car wash combines x gallons of a 2% liquid soap and 98% water mix with y gallons of a 7% liquid soap and 93% water mix to make 500 gallons of a 5% liquid soap and 95% water mix. Write a system of linear equations that represent the situation.
Answers
Not sure if it’s right or not!!!
Sofia is a helper for the kindergarten class and is in charge of picking a video for their end-of-year party. To choose which type of movie they would like best, she decided to survey every other child entering a matinee for a cartoon called, “Three Pretty Princesses.” The total number of children surveyed was 40. What is wrong with the way she selected her sample? Check all that apply. ill give brainliest to whoever answers
Answers
Answer:
a,c,d
Step-by-step explanation:
I did the quiz
Answer:
acd edge 2023
Step-by-step explanation:
Please help me it’s really important to me
Answers
2. e
3. a
4. c
5. d
6. f
7. g
8. h
hope this helps there is really no way of explaining you would have to study you theorems
If you answer a question put the number of the question in your answer. Thanks
Answers
Answer:
You'll find the answer below each.
Step-by-step explanation:
1-4 you can use this formula: [tex]V=l*h*w[/tex]
1.
[tex]V=l*w*h\\V=(6ft)(4ft)(1ft)\\V=24ft^3[/tex]
2.
[tex]V=l*h*w\\V=(2yd)(\frac{1}{2}yd )(2yd)\\V=2yd^3[/tex]
3.
[tex]V=l*h*w\\V=(12\frac{1}{2}mm)(3mm)(4mm)\\V=150mm^3[/tex]
4.
[tex]V=l*h*w\\V=(2cm)(8.5cm)(2cm)\\V=34cm^3[/tex]
5-7 you need these 2 formulas: [tex]A=\frac{bh}{2}[/tex] and [tex]V=Bh[/tex] or you can use one formula which is: [tex]V=\frac{bh}{2}*h[/tex]
Let me explain. The first formula is for finding the area of the base of the triangle and the second formula is for finding the volume of the prism using the area previously mentioned. The first h is with respect to the triangle and the second h is with respect to the prism.
5.
[tex]V=\frac{bh}{2}*h\\V=\frac{(8in)(6in)}{2}* 18in\\V=\frac{48in^2}{2}*18in\\ V=48in^2*9in\\V=432in^3[/tex]
6.
[tex]V=\frac{bh}{2}*h \\V=\frac{(11m)(5m)}{2}*35m \\V=\frac{55m^2}{2}*35m\\ V=\frac{1925m^3}{2}\\ V=962.50m^3[/tex]
7.
[tex]V=\frac{bh}{2}*h \\V=\frac{(5mm)(8mm)}{2}*12mm\\V=\frac{40mm^2}{2}*12mm\\ V=40mm^2*6mm\\V=240mm^3[/tex]
For the last one, we have a special case.
This formula is a bit odd and long.
[tex]V=\frac{1}{4}h(\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}[/tex]
a=8yd
b=15yd
c=17yd
h=11yd
[tex]V=\frac{1}{4}(11yd)(\sqrt{-(8yd)^4+2[(8yd)(15yd))]^2+2[(8yd)(17yd)]^2-(15yd)^4+2[(15yd)(17yd)]^2}[/tex][tex]-(17)^4[/tex]
As you can see this is long. I'll just jump to the answer.
Answer: [tex]660yd^3[/tex]
Answer:
He is correct
Step-by-step explanation:
The observed rabbit population on an island is given by the function p(t) =-4t^2+80t+1200, where t is the time, in years, since the teachers began observing the rabbits. According to this quadratic function, after how many years will the rabbit population reach its peak
Answers
Answer:
The rabbit population will reach its peak after 10 years.
Step-by-step explanation:
Suppose we have a quadratic function in the following format:
[tex]p(t) = at^{2} + bt + c[/tex]
The vertex of the function is the point:
[tex](t_{v}, p(t_{v})[/tex]
In which
[tex]t_{v} = -\frac{b}{2a}[/tex]
If a is negative, the vertex is a peak.
In this question:
[tex]p(t) = -4t^{2} + 80t + 1200[/tex]
So
[tex]a = -4, b = 80, c = 1200[/tex]
According to this quadratic function, after how many years will the rabbit population reach its peak
This is [tex]t_{v}[/tex]
[tex]t_{v} = -\frac{b}{2a} = -\frac{80}{2*(-4)} = 10[/tex]
The rabbit population will reach its peak after 10 years.
If two pyramids have the same heights what must be true of the pyramids for them to also have the same volume
Answers
Answer:
It is possible, but you must first measure the width.
Step-by-step explanation:
It is possible, but you must be sure.
Answer:
they whould need diffrent width and length
Step-by-step explanation:
imagen you have 2 glasses of watter, and they are both 6 inches high. But one glass has a longer width (aka how far backwords). Wich could hold more watter
help me fill this out thanks
Answers
Answer:
multiply
Step-by-step explanation:
Answer:
[tex]c = 4 \sqrt{3} [/tex]
[tex] \\ [/tex]
Step-by-step explanation:
[tex] \frac{4 \sqrt{3} }{ \sin(60) } = \frac{c}{ \sin(30) } \\ \frac{4 \sqrt{3} }{ \frac{1}{2} \sqrt{3} } = \frac{c}{ \frac{1}{2} } \\ c = \frac{4 \sqrt{3} \times \frac{1}{2} }{ \frac{1}{2} \sqrt{3} } \\ c = \frac{2 \sqrt{3} }{ \frac{1}{2} \sqrt{3} } \\ c = 4\sqrt{3} [/tex]
which one would you choose and please explain why
Answers
Please help I will give Brainliest please. Just tell what I need to do or solve I need help ASAP *image*
Answers
Answer:
Step-by-step explanation:
Hard to figure out huh
If f(x) = -2x + 3 and g(x) = 2x + 3; solve for f(3) + g(7)
Answers
Answer:
You just add the 2 equations together and fill in the 3 into the x where the f(x) equation is located and 7 into the x where the g(x) equation is located. I hope this helps. Have a great rest if your day!
The double number lines show the ratio of cups to gallons.
64
0
Cups 4+
Gallons +
0
4
How many cups are in 3 gallons?
cups
Answers
Answer:
Step-by-step explanation:
The answer is There are 3 gallons
Find the mean of the numbers below.
5, 10, 15, 20, 1, 2, 2, 1
Answers
Answer:
7
Step-by-step explanation:
used a calculator
a set of computers that are connected together so that they can share information
Answers
Answer:
A computer network
Step-by-step explanation:
What is the slope of the line with the equation:
6x + 2y = 8
Answers
Answer:
Using the slope-intercept form, the slope is 3 .
Step-by-step explanation:
In Circle T, TM is a radius. If TM=14.5, find CD. Find the diameter.
Answers
Answer:
29
Step-by-step explanation:
multiply by 2
What is the area of this composite figure?
Answers
Answer:
80
Step-by-step explanation:
i need help on this question
Answers
Answer:
the first one
Step-by-step explanation:
A gas company’s delivery truck has a cylindrical tank that is 14 feet in diameter and 40 feet long. How much gas, in cubic feet, can fit in the tank?
Answers
Answer:
[tex]6,157.5ft^3[/tex]
Step-by-step explanation:
We are looking for the volume of the tank which has a cylindrical shape.
The volume of a cylinder is given by:
[tex]V=\pi r^2 h[/tex]
where r is the radius of the circular base and h is the height.
In this case we have:
diameter: [tex]d=14 ft[/tex]
and since the radius is half of the diameter: [tex]r=14ft/2=7ft[/tex]
also the height is: [tex]h=40ft[/tex]
we substitute these values into the equation to find the volume:
[tex]V=(3.1516)(7ft)^2(40ft)[/tex]
solving the expression:
[tex]V=(3.1516)(7ft)^2(40ft)\\V=(3.1416)(49ft^2)(40ft\\V=6,157.5ft^3[/tex]
the tank can fit [tex]6,157.5ft^3[/tex] of gas
Amount of gas filled in tank is 6,154.4 feet³
Volume of cylinders:Given that;
Diameter of cylindrical tank = 14 feet
Length of cylindrical tank = 40 feet
Find:
Amount of gas filled in tank
Computation:
Diameter of cylindrical tank = 14 feet
Radius of cylindrical tank = 14 / 2 = 7 feet
Amount of gas filled in tank = Volume of tank
Amount of gas filled in tank = πr²h
Amount of gas filled in tank = (3.14)(7)²(40)
Amount of gas filled in tank = (3.14)(49)(40)
Amount of gas filled in tank = 6,154.4 feet³
Find out more information about 'Volume of tank'.
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