The exact measure of the angle is 45°.
How to get the angle?
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
[tex]1 = \sqrt{( \frac{\sqrt{2} }{2} )^2 + y^2} \\\\1^2 = \frac{2}{4} + y^2\\1 - 1/2 = y^2\\\\1/\sqrt{2} = y[/tex]
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
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AABC is similar to ADEF. The measure of AC = 10, the measure of DE=8, the measure of BC = 6, and the measure of DF = 20.
Find the measures of AB and EF.
The measure of AB and EF for the similar triangle ABC and DEF are 4 and 12 respectively.
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
In similar triangles, corresponding sides are always in the same ratio. The angles are congruent.
ΔABC is similar to ΔDEF. Therefore, the sides will form a ratio.
AC / DF = BC / EF = AB/DE
AC = 10
DF = 20
DE = 8
BC = 6
Hence,
10 / 20 = AB / 8
cross multiply
20AB = 80
AB = 80 / 20
AB = 4
Hence,
10 / 20 = 6 / EF
10EF = 120
EF = 120 / 10
EF = 12
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please help
Answer: Please send more, is that all??
Step-by-step explanation:
I need more clarification, what are you trying to answer?
12. m is inversely proportional to the square of (p-1) when p=4,m=5.
Find m when p = 6.
You spent 1/5 of your birthday money on 2 video games.If each video game cost the same amount.what fraction of your birthday money did each video game cost
Answer: 2/5
Step-by-step explanation: 1/5 divided by 2You do 1/5, then the 2 is a whole number so you have to always put a denominator under a whole number. The denominator will be 1.in this case you will do KCF or KFC KEEP, CHANGE FLIP.1/5 you will keep
you will CHANGE the division sign to multiplication, never change when it is multiplication.
1/5 X 1/2
You will FLIP 2/1 into 1/2. Now multiply numerator x numerator, denominator x denominator.
1/5 X 1/2= 2/5
Now you have gotten your answer but for the future, the numerator should never be greater than the denominator, if it is, divide.
Are 1/2(6x - 2) and 3 - x equivalent?
I really need help!
Answer:
No
Step-by-step explanation:
So, you can use the distributive property.
1/2(6x)=3x
1/2(-2)=-1
It is 3x-1, not 3-x
What percent of 96 is 367
Answer:
96 is what percent of 367? = 26.16
Step-by-step explanation:
line h is parallel to line 0; ∠13 = ∠8 use the image of the protractor to find the angle measure of angle 1 then compute all the missing angle measure
Answer: Below
Step-by-step explanation:
Angles 1, 3, 5, 7 are 120 degrees.
Angles 4, 2, 8, 6 are 60 degrees.
angles 10, 12, 13, 15 are 70 degrees.
Angles 9, 11, 16, 14, are 110 degrees.
angle 17 is 50 degrees.
what is [( 2+ 75.5) - 3] x 2
Simplify the expression.
149x
hope this is what your looking for
220,000 population grows 8%. What will population be in 7 years
Answer:
the population will be 1,540,000 in 7 yrs
Answer: 377041.34
Step-by-step explanation: if it is growing 8 percent then you will add 8 percent to 100 which will equal 108 percent
Plug that into a calculator with the starting number so it wil look like 108% 220,000 and if you do that seven times you will get the answer.
Each side of a square is increased by 10%
By what percentage is the area increased?
Answer:
21%
Step-by-step explanation:
If it is correct pls mark me as brainliest and learn we
Calculator
A group of students is painting a background piece for the school play, What is the area of the part that is painted blue? Enter your answerint
40 ft
30 ft
5 ft
3 ft
2 ft
3 ft
20 ft
Answer:
479 ft^2
Step-by-step explanation:
Area of the bottom rectangle = 30 X 20 = 600 sq ft
then subtract the areas of the window and the door
600 - (5x3) - (2x3) = 579 ft^2
Then add the triangular top area
1/2 (20)(10) = 100
579 - 100 = 479 ft^2
giving brainliest! 5 (4m +2)
[tex]5(4m+2)\\\\=20m+10[/tex]
What is the equation of the circle?
Answer:
○ [tex]\displaystyle (x - 4)^2 + (y + 2)^2 = 25[/tex]
Explanation:
Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:
Pythagorean Theorem
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 4^2 + 3^2 = r^2 \hookrightarrow 16 + 9 = r^2 \hookrightarrow \sqrt{25} = \sqrt{r^2} \\ \\ \boxed{5 = r}[/tex]
Sinse we are dealing with length, we only desire the NON-NEGATIVE root.
Distanse Equation
[tex] \displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-7 + 4]^2 + [-2 - 2]^2} = r \hookrightarrow \sqrt{[-3]^2 + [-4]^2} = r \hookrightarrow \sqrt{9 + 16} = r; \sqrt{25} = r \\ \\ \boxed{5 = r}[/tex]
Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.
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Find the area of a rectangle that measures 3 1/4 yd long and 2 1/2 yd wide???
Answer:
Area of rectangle = 65/8 yd²
Step-by-step explanation:
The area of the rectangle is the length multiplied by the width. In this case, we are given the length 3 1/4 yd and the width 2 1/2 yd wide. Therefore,
⇒ Area of rectangle = (L × B) = (3 1/4 × 2 1/2) yd²
It is suggested to convert the terms in the expression (3 1/4 × 2 1/2) to improper fraction. Therefore,
⇒ Area of rectangle = [(3 × 4) + 1]/4 × [(2 × 2) + 1]/2 yd²
⇒ Area of rectangle = [(12) + 1]/4 × [(4) + 1]/2 yd²
⇒ Area of rectangle = [13]/4 × [5]/2 yd²
⇒ Area of rectangle = 13/4 × 5/2 yd²
Simplify the expression on the right hand side to determine the area.
⇒ Area of rectangle = 65/8 yd²
Thus, the area of the rectangle is 65/8 yd².
Зу – 15 = y +1
I need the answer
y=8
Solution:First, move the y's to the left:3y-y-15=1Now, add 15 to both sides:3y-y=1+15Combine Like Terms:2y=16Divide both sides by 2:y=8Hope it helps.
Do comment if you have any query.
Answer:
y = 8
Step-by-step explanation:
Given equation: Зу - 15 = y + 1
Subtract "y" both sides:
→ Зу - 15 = y + 1→ 3y - y - 15 = y - y + 1→ 2y - 15 = 1Add 15 both sides:
→ 2y - 15 = 1→ 2y - 15 + 15 = 1 + 15→ 2y = 16Divide 2 both sides:
→ 2y/2 = 16/2→ y = 8What is the inverse relation of the function f(x) = -12 +4?
O y= x - 14
O y(x) = - +14
O y=-x+
O y= {c -
f(x)=7x+12
Put y in place of f(x).
y=7x+12
Switch x and y.
x=7y+12
Solve for y.
x-12=7y
(x-12)/7=y
Put in the f^-1(x) notation.
f^-1(x)=(x-12)/7
What is the first step in which the student made an error?
o Step 1, because the student should have written a compound statement with "and"
o Step 2, because the student should have graphed the inequalities Y1 SX-4 andy, 51
o Step 3, because the values for x for which yn Sy2 also include values between 3 and 5
Step 4, because the solution is one continuous interval
The first step where the student made an error is in step 4 because the solution is one continuous interval.
What is r continuous interval?A function can be continuous in nature on an interval and this is said to be the time when the function is said to be seen at all point on that given interval and does not get any interruptions or breaks.
Note that in step 3, the values for x for which y₁ ≤ y₂ is x = 3 or x= 5. and in step 4 , the error is here when it state the solution is one continuous interval because there are more than one interval which is (∞, 3) ∪ (5, ∞)
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Subtract the matrices.
What number fills in [?] ?
А
B
2 -9 8
-5 3 2
4 2-1
1 4 -8
-5 -3 7
7 -2 5
4 8 -4
-35-2
A-B =
7 -12 6
3 [?] 7
-12 -1 2
7 3-2
Answer:
[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]
Explanation:
[tex]\Longrightarrow \ \sf Give n \ A = \sf \bold{\begin{pmatrix}2&-9&8\\ 4&2&-1\\ -5&-3&7\\ 4&8&-4\end{pmatrix}}[/tex]
[tex]\Longrightarrow \ \sf Given \ B = \bold{\begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}}[/tex]
Solve:
[tex]\sf A - B = \begin{pmatrix}2&-9&8\\ \:4&2&-1\\ \:-5&-3&7\\ \:4&8&-4\end{pmatrix}- \begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}[/tex]
subtract the elements in matching positions
[tex]\sf A - B = \begin{pmatrix}2-\left(-5\right)&\left(-9\right)-3&8-2\\ 4-1&2-4&\left(-1\right)-\left(-8\right)\\ \left(-5\right)-7&\left(-3\right)-\left(-2\right)&7-5\\ 4-\left(-3\right)&8-5&\left(-4\right)-\left(-2\right)\end{pmatrix}[/tex]
Final Outcome
[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]
Describe the end behavior for f (x) = x^2 − 4x + 6
Answer:
as x approaches ∞, y is positive
as x approaches -∞, y is positive
Step-by-Step Explanation:
you need to graph the equation and look at what happens
how many calories of energy are in 165 g of bananas if there ae 100 c in 110 bananas
What function equation is represented by the graph? f(x)= 3 exponent x+4 4 exponent x 5 4 exponent x +4 3 exponent x +5
Answer:
LAST OPTION
Step-by-step explanation:
F(X)
[tex]f(x) = {3}^{x} + 5[/tex]
is the required function
Hint:FOR finding these types of question just Substitute and check values with the options
What is the difference in length between the longest meteor and the shortest meteor? (4 points)
Answer:
13 / 8 in
Step-by-step explanation:
Longest ( 1 7/8) - shortest ( 2/8) = 13/8 in
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
39⁰
Step-by-step explanation:
WE KNOW THAT,
SUM OF ALL ANGLES OF A TRIANGLE IS EQUAL TO 180⁰
P+Q+R=180⁰
2x⁰-9⁰+x⁰+33⁰+x⁰=180⁰
4x⁰+24⁰=180⁰
4x=180⁰-24⁰=156⁰
x=39⁰
In a bag there are six red marbles, four blue marbles, and eigint green marbles. What is the probability that you will draw a green marble? 1. 1/3 2. 4/9 3. 1/18 4. 4/5
Answer:4/9 We know, Probability = Favorable Outcome / Total Outcome
Here, Favorable Outcome (Number of Green Marbles) = 8
Total Outcome = 6 + 4 + 8 = 18
P = 8 /18 = 4/9
In short, Your Answer would be 4/9 or 0.44
Hope this helps!
The growth of bacteria makes it necessary to time-date some food products so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product the number of bacteria present is given by f(t)=600e0.1t, where t is time in days and the value of f(t) is in millions. Find the number of bacteria present at each time. (a) 2 days (b) 3 days (c) 1 week
a) Substitute t = 2 into the formula
= 600e^0.1(2)
= 600e^0.2
= 732.84 million
Therefore, 732.84 million bacteria are present after 2 days
b) Substituting t = 4 days we get
= 600e^0.1(4)
= 600e0.4
= 895.09 million
Hence, 895.09 million bacteria are present after 4 days
c) 2 weeks = 14 days
Substituting t = 14 days we get
= 600e^0.1(14)
= 600e^0.4
= 2433.12 million
Thus, 2433.12 million bacteria are present after 2 weeks
Sara and her friends go to a football game and get snacks from the concessions. She uses various pictures to show what they ordered. Which of the following expressions best represents their order
F. 4d + h + 2f
G. 4d + 2h + 2f
H. h + 2f + 5d
J. 2h + 4f + 3d
Choose the figure that does NOT belong with the other three figures?
8
11
24
14
The 11 figures do NOT belong with the other three figures. Then the correct option is B.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
If all the sides of the polygon are congruent, then the polygon will be known as a regular polygon.
In a trapezoid, the length of all the sides is not congruent. Then the trapezoid (11) figures do NOT belong with the other three figures.
Then the correct option is B.
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Use the example above and determine the fraction of total interest owed. After the fifth month of a 12-month loan: the numerator is: {(n + ) + (n + ) + (n + ) + (n + ) + (n + )} = , and the denominator is: {(n) + (n + 1) + ... + (n + )} = . Therefore, the fraction is numerator/denominator (to the nearest tenth) = %.
The fraction of total interest owed after the fifth month of a 12-month loan is 64.1%
How to determine the fraction of interest owed?From the question, we have the following parameters
The numerator is given as: {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)}The denominator is given as: {(n)+(n+1)+...+(n+11)}After the fifth month, the equation of the numerator is:
Numerator = (1+11)+(1+10)+(1+9)+(1+8)+(1+7)
Numerator = 50
The equation of the denominator is:
Denominator = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12
Denominator = 78
The fraction of total interest is then calculated using:
Fraction = Numerator/Denominator
This gives
Fraction = 50/78
Express as percentage
Fraction = 64.1%
Hence, the fraction of total interest owed after the fifth month of a 12-month loan is 64.1%
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Answer:
D. Point D
Step-by-step explanation:
4.82 is close to 5 so D is right A and B are not even close. C is a little to close to 4.5 to be 4.82. But D looks like it could be 4.82 to though so D is right.