The statement(s) that are true is that the measure of the reference angle is 45°.
What is the conversion of radians to degrees?The conversion of an angle in radian to a degree can be determined by the multiplication of the given angle in radian by 180/π.
From the given information:
[tex]\mathbf{\theta = \dfrac{7 \pi}{4}}[/tex]
To degrees, we have:
[tex]\mathbf{\theta = \dfrac{7 \pi}{4} \times \dfrac{180}{\pi}}[/tex]
[tex]\mathbf{\theta =315^0}[/tex]
A reference angle is an angle that measures the remaining distance (called the terminal distance) to the x-axis.
315° is in the 4th quadrant, i.e.
= 360° - 315°
= 45°
Therefore, the statement(s) that is true is:
The measure of the reference angle is 45°.Learn more about the conversion of radians to degrees here:
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Answer:
sin(0)=-√2/2
tan(0) = -1
The measure of the reference angle is 45°
Step-by-step explanation:
I took the test
Version B
We have worked with Ferris Wheels above
ground, but what if a portion of it went
underground and traveled in a clockwise
direction?
Details;
The Ferris Wheel has a diameter of 80
ft
The Ferris Wheel center is 20 feet
below the ground
The Ferris Wheel rotates in a clockwise
direction
The rider enters on ground level on
the right side of the wheel.
It takes 1 minute for 1 ½ rotations.
Your task:
Sketch a diagram that showcases this
scenario with labels and
measurements.
Determine the angular speed.
Develop an equation for the height of
the rider while on the ride.
Construct a graph (height vs. time).
Make sure both axes are labeled with
all landmark points.
Provide a statement, explaining the
relationship between your graph and
the rider's position on the wheel.
When will they be above ground and
below?
Calculate the rider's total distance
traveled from the moment they get on
at ground level on the right to the
other point on ground level on the left
where they get off.
An example of how to sketch the Ferris Wheel diagram is given in the image attached.
What is the angular speed about?To solve for the angular speed, you can use the formula of"
Given that the diameter is 80 feet, so we know the radius will be 40 feet.
The Ferris wheel bottom is 20 feet high, so we add the radius we get that the middle of the Ferris wheel is 60 feet high.
Finally, the Ferris wheel completes 1 ½ rotation (2π radians) in 1 minutes. So we say that the Ferris wheel is said to spins at π rad/min.
Angular velocity ( 1 ½ rev/1min)( 1min/60 sec)
C = 2π(60)
C ≈ 377.04 feet
540 revolution (1 ½ rotations) is 60 seconds, the speed is then
s = d/t
s = 377.06 ft / 60 sec
s = 6.28 ft/sec
To plot the graph, the final equation will be h(t) = 40sin(πt + π/2) + 60.
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The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w.
the force on a sail with area an area of 500 ft2 is 64. 8 pounds when the wind speed is 18 mph. what
would be the force for a sail with an area of 250 ft? with a wind speed of 35 mph.
how would you solve this problem? what would your answer be?
response:
Answer:
122.5 lbs
Step-by-step explanation:
The relation between force, wind speed, and area can be written ...
f = ks²a
for some wind speed s and area a.
__
The constant of proportionality, k, can be found from the given data.
64.8 = k(18²)(500) . . . force in pounds, area in square feet, speed in mph
k = 64.8/(324×500) = 0.0004
__
Using the equation with the second set of data, we have ...
f = 0.0004(35²)(250) = 122.5 . . . . pounds
The force on the 250 square foot sail would be 122.5 pounds.
QUICK PLEEEASEEEEEEEEE
Answer:
c) 2
Step-by-step explanation:
By definition The mode is the most repeated number in the data-set.
can someone help me with this
Step-by-step explanation:
[tex]2p + 2p + 2p + 60 = 360 \\ 6p = 360 - 60 \\ 6p = 300 \\ p = \frac{300}{6} \\ p = 50[/tex]
The probability of spinning blue, flipping heads, then spinning a 1 is
.
Answer:
[tex] \sqrt{32 \div 2 = } 82 \\ [/tex]
[tex]10/7 + 2/20 + 7-4[/tex]
[tex]\dfrac{10} 7 + \dfrac 2{20} +7 - 4\\\\\\=\dfrac{20(10)+7(2)}{140}+3\\\\\\=\dfrac{200+14+140(3)}{140}\\\\\\=\dfrac{634}{140}\\\\\\=\dfrac{317}{70}[/tex]
if you subtract 13 from my number and multiply the difference by -4, the result is -40, what is the number?
Answer:
23
Step-by-step explanation:
let the number = X
subtracting 13 from X = X -13
multiplying the difference by -4= (X -13)×-4
the result is -40 means (X-13)×-4=-40
(X- 13)×-4 = -40
-4 X +52 = -40
collect like term
-4 X = -40-52
- 4X = -92
dividing bothsides by -4
-4 X /-4 = -92/-4
X = 23
Convert the into millimetres.
A. 234cm
B. 15m
C. 25km
A. 234 cm
multiply the given length value ( 234 ) by 10.
[tex]234 \times 10[/tex]
[tex] = 2340 \: mm[/tex]
B. 15m
multiply the given length value ( 15 ) by 1000.
[tex]15 \times 1000[/tex]
[tex] = 15000 \: mm[/tex]
C. 25km
multiply the length value ( 25 ) by 1000000.
[tex]25 \times 1000000[/tex]
[tex] = 25000000 \: mm[/tex]
a)
234 × 10
= 2340 millimeters
b)
15 × 1000
= 15000 millimeters
c)
25 × 1000000
= 25000000 millimeters
Which is the slope-intercept form of the equation of the line with a slope
of 2 and a y-intercept of 5?
Oy-5=2(x-0)
Oy=2x-2
O y = 2x+5
Oy-0=2(x - 5)
Two friends each had an auto loan of $20,000. One was repaid at
8% in 3 years at about $625 per month, and the other at 8% in 5
Years at about $405 per month. The total of the payments for the 5-year loan is how much more than the total for the 3-year loan?
Answer:
1,800 more
Step-by-step explanation:
12 × 3 = 36 months
$625 × 36 = $22,500
12 × 5 = 60 months
$405 × 60 = $24,300
$24,300 - $22,500 = $1,800
the interest is paid per month, so we first need to convert the years to months. after that we calculate the total amount of money paid over the specified years. and then we subtract the one from the other to get the difference.
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 28 2-by-4s laid side by side. Simplify your answer
Work Shown:
3 1/2 inches = 3.5 inches
total width = 28*3.5 = 98 inches
The required total width of 28 2 - by -4s laid side by side is 98 inches.
Given,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. to determine the total width of 28 2-by-4s laid side by side.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches.
Now, the width of 28 2-by-4 woods laid side by side,
= 28 * 3 1 / 2
= 28 * 7 / 2
= 98
Thus, the required total width of 28 2 - by -4s laid side by side is 98 inches.
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solve for x in the triangle. Round to the nearest tenth
The sum of two numbers is 27 and their product is 50. Find the numbers.?
Answer:
a + b = 27
=> a = 27 - b
ab = 50
So, (27 - b) x b = 50
27b - b^2 = 50
b^2 - 27b + 50 = 0
Solving, b = 25, 2
Hence,
Case 1: b = 25, a = 2
Case 2, b = 2, a = 25
Answer:
2, 25
Step-by-step explanation:
Let the numbers be x and y :
x + y = 27xy = 50Rearrange the first equation so it is equal to one variable :
y = 27 - xSubstitute the value in the second equation :
x(27 - x) = 5027x - x² = 50x² - 27x + 50 = 0(x - 25)(x - 2) = 0x = 2, 25What is it called when your point is right on the Y axis?
Y Intercept
Slope- intercept
Answer:
y intercept
Step-by-step explanation:
What additional information do you need to prove the triangles are congruent by SSS
The information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side by side property which is written as SSS.
Now in the given figure, the side YD is similar and equal to the side OD so option C will be the correct answer.
Hence the information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.
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A box is 50 cm long. Which of these is the closet to the length of this box in feet ? (1 inch = 2.54cm)
Answer:
1ft 7.7in/1.64 ft
Step-by-step explanation:
50/2.54=19.69in
12in=1ft
so 1ft 7.7in
19.69/12=1.64
This is easy for other students in my class just not me lol
Answer:
65
Step-by-step explanation:
Angle FGH = x
Angle FGJ = 25
Angle JGH = 40
Angle FGH = Angle FGJ + Angle JGH
x = 25 + 40
x = 65
The value of x in the diagram is 65.
What is an angle?The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.
Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.
We have,
From the diagram,
∠JGH = 40
∠FGJ = 25
Now,
∠JGH + ∠FGJ = x
So,
40 + 25 = x
Solve for x.
x = 40 + 25
x = 65
Thus,
The value of x in the diagram is 65.
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2 similar rectangular pyramids have a similarity ratio of 4:5. What is the ratio of their volumes? Put your answer in the form a:b
Answer:
64:125
Step-by-step explanation:
When you go from a length ratio to an area ratio you need to square the numbers involved: [tex]4^{2} :5^{2}[/tex] = 16 : 25
By the same logic, if you want to go from length to volume you need to cube the numbers involved: [tex]4^{3} :5^{3}[/tex] = 64 : 125
Which is the apparent solution set of the system of equations graphed on the grid? a. {(0,0), (3,0)} b. {(0,-2), (1,0)} c. {(0,0), (1.5,2.25)} d. {(-1,-4), (2,2)}
The apparent solution set of the system of equations graphed on the grid is {(-1,-4), (2,2)}
How to determine the solution?The point of intersection of the curves or lines on a graph is the solution of the system of equations
From the complete question, the lines intersect at approximately
(-1,-4) and (2,2)
Hence, the apparent solution set on the grid is {(-1,-4), (2,2)}
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Answer:
D.
{(-1,-4), (2,2)}
Step-by-step explanation:
This should be the answer for Plato/Edmentum users. (Note: not all answers are in the same position. It might be d for me but the answer might be put under any other letter)
Find the surface area of the prism.
10 ft length
1 ft height
5 ft width
Answer:
Surface Area = 130 sq ft
Step-by-step explanation:
If you don't have a picture, draw a picture so you can see what's up. See image. Surface area is the area of all the faces of a 3d shape (a solid) all added up. This solid is a box. It has six faces. Each face is a rectangle. The top and bottom are the same. The front and back are the same. The left and right sides are the same. See image.
Area of a rectangle is:
A = l × w
Area of the top:
5 × 10 = 50
Area of the bottom also 50.
Area of the left side:
1 × 5 = 5
Area of the right side is also 5.
Area of the front:
1 × 10 =10
Area of the back is also 10.
ADD up all 6 areas:
50+50+5+5+10+10
Surface area = 130
Area has square units.
SA = 130 square ft
Given the function, f(x) = (-3x)2 , evaluate f(4)
Answer:
Step-by-step explanation:
(-3*4)^2 = (-12)^2 = 144
Write the standard form of the equation of the line described
through: (4,0) parallel to y=4
Answer:
y = 0.
Step-by-step explanation:
The line y = 4 is a horizontal line, parallel to the x-axis.
The point (4,0) is on the axis so the rquired equation is:
y = 0.
Someone help please.its really important
Answer: Angle Y is 90 degrees, angle X is 35.
Answer:x=35 and y=35
Step-by-step explanation:
Angle on straight line =180
so 180/2=90
90-55=35
and x and y opposite angle so are eqaul
please solve quickly
If a student is selected randomly, the probability that the student is a junior given that the student is male is 14%.
What is the probability?Probability determines the odds that an event would happen. The odds of the event happening lie between 0 and 1.
p (Junior | Males) = number of males that are junior / total number of males
2 / (4 + 6 + 2 + 2 ) = 2/14 x 100 = 14%
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PLEASE ANSWER ASAP
The sum of the first six terms of the geometric sequence 1, 2, 4, 8, ... is equal to the sum of
the first six terms of an arithmetic sequence that also has 1 as its first term. What is the
fifth term of the arithmetic sequence?
Answer:
FIND IT YOURSELF
Step-by-step explanation:
YOU ARE GIVEN QUESTIONS TO ANSWER FOR YOU, NOW DO IT YOURSELF.
The center of the circle below is at P. If the central angle < APB measures 88 °, and the length of arc AB = 10 cm., find the radius. (round to the nearest tenth)
If the measure of the arc of the circle is 10 cm. Then the measure of the length of the radius will be 6.51 cm.
What is the relationship between central angle and angle on circumference?Consider an arc of a circle.
Suppose it subtends θ angle on the rest of the part of the circumference (at any point). Then it subtends a 2θ angle on the center of that circle.
we know the formula
Are = θ/360 x 2πr
The center of the circle below is at P. If the central angle ∠APB measures 88° and the length of arc AB = 10 cm.
Then we have
10 = 88 / 360 x 2πr
40.91 = 2πr
r = 6.51 cm
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Hello, please help! I will be using this a lot within the next few days lol
Answer:
1/2
Step-by-step explanation:
1/3 + 1/6
LCM of 3 and 6 is 6.
therefore, multiple the fraction that doesn't have 6 as denominator with a fraction that makes the denominator equal to the LCM.
1/3 × 2/2 = 2/6
(we have used 2/2 because 3×2= 6)
so,
2/6+1/6 = 2+1/6
(2 + 1 whole divided by 6)
therefore we get,
3/6
on simplification,
3/6 = 1/2 = 0.5
hope it helps!!
PLEASE MARK BRAINLIEST..
Answer:
1/3 + 1/6 = 2/6 + 1/6 = 1/2 (simplified from 3/6)
Step-by-step explanation:
since 1/3 = 2/6 (to get the same denominator)
2/6 + 1/6 = 3/6 (or 1/2 simplified, when divided by 3/3)
so 2/6 + 1/6 = 3/6
2 is the first blank
1/2 is your answer. (second blank)
hope this helps:)
somebody please help me with this question!
Answers:
P(A) = 7/12
P(B) = 1/2
=====================================================
Explanation:
To see how I calculated P(A), check out this link to this very similar question
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--------------------
Now to calculate P(B)
If a number is divisible by 2, then the number is a multiple of 2.
In other words, the number is even.
Counting through the values in the table, you should find that there are 18 sums that are even (2, 4, 6, 8, 10 and 12). Refer to the dice chart below.
Here's a further breakdown
1 copy of "2"3 copies of "4"5 copies of "6"5 copies of "8"3 copies of "10"1 copy of 12Side note: We have nice symmetry going on.
There are 1+3+5+5+3+1 = 18 values total that are even numbers. The other half are odd numbers of course.
P(B) = 18/36 = (1*18)/(2*18) = 1/2
2 1/3 ÷ 1 3/4-2.6÷1.3
pls i rlly need help anything will help
Answer:
The answer is -2/3
Step-by-step explanation:
Multiply by the reciprocal:
7/3 / 1/4 x 2
Simplify expression:
7/3 x 4/7 -2
Calculate:
1/3 x 4 -2
4/3 - 2
= -2/3
answer these two questions asap!!
Answer:
Step-by-step explanation:
45 cm times 20 cm you find by by mutiply and divide