Using the relation between the sine and the cosine of an angle, it is found that:
[tex]\cos{\theta} = -\frac{2\sqrt{2}}{3}[/tex]
What is the relation between the sine and the cosine of an angle?The sine squared of an angle, plus the cosine squared of the same angle, is equals to one, hence:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, we have that the sine is given by:
[tex]\sin{\theta} = -\frac{1}{3}[/tex]
Hence:
[tex]\left(-\frac{1}{3}\right) + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]
[tex]\cos^2{\theta} = \frac{8}{9}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]
We have that pi < theta < 1.5pi, hence the angle is in the third quadrant, where the cosine is negative, thus:
[tex]\cos{\theta} = -\frac{2\sqrt{2}}{3}[/tex]
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Given the regular square pyramid with RS = 6 and PX = 4, then XY=3.
True
False
Evaluate without using a calculator by using ratios in a reference triangle.
cos 5pi/3
Answer:
The answer is 1 /2
Step-by-step explanation:
Cos, tan and sin are all positive in the first quadrant, but depends on the direction of the angle. Reference angle here we are looking for is the one in relation to the quadrant cos 5pi/3.
Any multiples of cos outside 2nd quadrant will give a positive value.
cos 5pi/3 is located in the 4th quadrant, while, cos pi/3 is located in the 1st quadrant, where the cos ratio has a positive value.
In terms of cosine, anytime the angle falls on the first or fourth quadrant it will always produce a positive graph.
For cos 5pi/3, cos pi/3 and cos 7pi/3 will give the same answer as "1/2" or "0.5" because, cos pi/3 will give 60 degrees which fall in the first quadrant
If "R" is a real number, for all R multiplied by pi/3, the new value gives an angle in the first or fourth quadrant, the angle will be 0.5
The exact value of cos 5 ( π /3 ) is 1 /2 .
The function h(x) = x + 1 is formed by adding two functions, f(x) and g(x). The function j(x) = 3x – 6 is formed by multiplying the same functions. Which could be true of f(x) and g(x)? Check all that apply.
Both functions must be linear functions.
Both functions must have a positive rate of change.
The rate of change of both f(x) and g(x) must be less than 3.
The y-intercept for one function must be positive, while the y-intercept for the other function must be negative.
The y-intercepts of f(x) and g(x) must be between –6 and 1.
Answer: this is the right answer Both functions must be linear functions. And The y-intercept for one function must be positive, while the y-intercept for the other function must be negative.
Step-by-step explanation:
The true statements about the functions f(x) and g(x) are (a), (c) and (d)
How to determine the true statement?The functions are given as:
h(x) = x + 1
j(x) = 3x - 6
From the question, we have:
h(x) = f(x) + g(x)
j(x) = f(x) * g(x)
Expand the function j(x)
j(x) = f(x) * g(x) = 3 * (x - 2)
By comparison, we have:
f(x) = 3
g(x) = x - 2
f(x) + g(x) = 3 + x - 2
f(x) + g(x) = x + 1
This gives
h(x) = x + 1
By analyzing the functions f(x) = 3 and g(x) = x - 2, we can see that:
Both functions are linear functionsThe rates of change of the functions are less than 3The y-intercept for one function must be positive, while the y-intercept for the other function must be negative.Hence, the true statements are (a), (c) and (d)
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If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Giving Brainliest to teh right answer! Come quick!
Answer:
x=65
Step-by-step explanation:
145 and 2x+15 are vertical angles meaning that they are congruent to each other. Subtract 15 from both sides, and divide by 2 giving x=65.
Hope this helps!
x=?? will give brainliest
Answer:
I think its a right angled triangle
and so x= 90°
A used book sale charged $7.50 for hardcovers and $1.25 for paperbacks. During the sale, 15 hardcovers were sold and the sale earned $166.25. Write and solve an equation to determine the number of paperbacks, p, that were sold.
20 points i think
Answer:
43 paperback books
Step-by-step explanation:
7.50(15) + 1.25x = 166.25
112.50 + 1.25x = 166.25
Subtract 112.50 from both sides
(112.50 - 112.50) + 1.25x = (166.25 - 112.50)
1.25x = 53.75
Divide 1.25 from both sides
x = 43
PLEASE HALP!!!!
Carlos wants to get an average of 86% in his science class. The science
teacher has given 5 tests. Carlos's scores on 4 of the tests have been 85%,
89%, 90%, and 82%. What score does Carlos need to get on the 5th test to
get a mean score of 86%?
O A) 81
OB) 84
OC) 86
OD) 92
Answer:
The answer is B
Step-by-step explanation:
Answer:
B. 84
(85+89+90+82+x)/5=86
so x=84
does anyone know thisss
Answer:
Step-by-step explanation:
area of sector = angle/360 * pi * r^2
59.4 = angle/360 * 3.142 * 17.9^2
angle = 21.24
Answer:
21.24°
Step-by-step explanation:
I hope it helps:)
Find the volume of the planets
Answer:
can you show the planets. or do you want real planets volumes?
If it is 5 degrees outside, and the temperature will drop 12
degrees in the next six hours, what will the temperature be in six
hours?
Answer:
-7 degrees
Step-by-step explanation:
Dropping 12 degrees means that it will get colder by 12 degrees. The colder it gets, the lower the temperature. 5 degrees - the current temperature, is going to be dropped by 12 degrees. To calculate this: 5-12 = -7 (degrees)
a) Which of these numbers is 6 less than -11?
A) -5
B) -17
С) 17
D) 5
b) Which of these numbers is 34 less than -7?
A) -27
B) 27
C) -41
D) 41
Answer:
For the first on it is A) 17
For the second one it is B) 41 I hope cause I haven't done these in along time
Step-by-step explanation:
For the first on it's going to 17 because if you turn the less than sign into a minus sign you're going to get 6 - -11. You turn the two signs into a plus sign you get 6 + 11 and you add them you get 17
For the second one your going to the same thing you add 34 + 7 and you get 41
Set up as equal rates and solve. The distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. How many miles is it from Pensacola to Miami if the distance on the map measures 27 inches?
We have been given that the distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. We are asked to find the actual distance from Pensacola to Miami if the distance on the map measures 27 inches.
We will use proportions to solve our given problem as proportion states that ratio between two proportional quantities is similar.
[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{27 inches}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{27 inches}}\times \text{27 inches}=\frac{200\text{ miles}}{\text{8 inches}}\times \text{27 inches}[/tex]
[tex]\text{Actual distance}=\frac{25\text{ miles}}{1}\times 27[/tex]
[tex]\text{Actual distance}=675\text{ miles}[/tex]
Therefore, the actual distance from Pensacola to Miami is 675 miles.
When solving a word problem why is it important to check if the final answer makes sense for the problem?
This circle is circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
The value of x is 56°
Step-by-step explanation:
Given that opposite angles in a cyclic quadrilateral is add up to 180°. So in order to find x, you have to write an expression in terms of x :
[tex]97 + x + 27 = 180[/tex]
[tex]x + 124 = 180[/tex]
Next you have to solve it by substracting 124 to both sides :
[tex]x + 124 - 124 = 180 - 124[/tex]
[tex]x = 56[/tex]
Anna runs a 5k in 20 minutes. What is her speed in kilometers per hour?
Answer:
15kmh
Step-by-step explanation:
Answer:
15k
Step-by-step explanation:
There is 60 mins in an hour. Since she runs 5k in 20 mins you would multiply 20 by 3 because it would equal 60. Also you would multiply 5k by 3 also.
i hoped that made sense ;-;
Which of the following functions has the largest value when x= 3? Show your work.
p(x) = 2x^2 + 4x + 11
h(x) = 4x
s(x)=10x
Answer:
p(x)
Step-by-step explanation:
Substitute x = 3 into each function and calculate the value.
p(3) = 2(3)² + 4(3) + 11 = 2(9) + 12 + 11 = 18 + 12 + 11 = 41
h(3) = 4(3) = 12
s(3) = 10(3) = 30
Thus p(x) = 41 is the largest value when x = 3
What is an equation of the line that passes through the point (4, -3) and is
perpendicular to the line
4x +y = 3?
Answer:
y = 1/4x - 4
Step-by-step explanation:
If you put the equation in slope-intercept form y=mx+b, then you have y=-4x+3, so the slope is -4. Then take the negative reciprocal of that so you have the perpendicular slope 1/4. Plug in x, y, and, m into the equation and solve for b.
-3 = 1/4(4) + b
-3 = 1 + b
-4 = b, then rewrite the equation with the new slope and the b you found.
y = 1/4x - 4
The point (5, -2) is rotated 90° about the origin. Its image is
(-2, 5)
(2, 5)
(-5, 2)
Answer:
(2,5)
Step-by-step explanation:
The rule to 90 degrees about the origin is (x,y) to (-y,x). You basically switch the values of y and x but remember the value of y is negative. The value of y is -2 so -2 is now 2 since the rule changed the sign (-2×-y=2) and 5 isnt affected except it is the x value. Just know that since they r switched, x is now 2 and y is 5 when rotated 90 degrees about the origin.
Answer:
(2,5)
Step-by-step explanation:
can someone helpp ??
Answer:
21.24°
Step-by-step explanation:
I hope it helps :)
John is creating a shed in his backyard he wants to use brick for the front side with the door using the given brick how many will he need to cover the front of the shed
Answer:
180 bricks.
Step-by-step explanation:
The dimensions of the front of the shed are 30 x 12.
30 x 12 = 360
The dimensions of the brick are 2 x 1.
2 x 1 = 2.
360/2 = 180.
Which is the graph of f(x) = x2 – 2x + 3?
Answer:
Step-by-step explanation:
We cannot factor this function out which tells us that there are no zeros. The graph backs this up because we can see that there are none. The easiest way to graph this would start by plugging in points and making a table for yourself.
Lets start by plugging in -1.
(-1)^2-2(-1)+3 =6, this means we have a point at (-1,6).
Now lets plug in 0.
(0)^2-2(0)+3= 3 (0,3)
For plugging in 1
(1)^2-2(1)+3=2 (1,2) (this happens to be the vertex)
And lastly lets plug in 2
(2)^2-2(2)+3=3 (2,3)
Depending on how many points are needed, keep plugging in numbers like we did above.
Answer:
A
Step-by-step explanation:
Edge 2021
Can someone help me on this one.
Answers:
a) 6km/hour
b) 10 minutes
Step-by-step explanation:
a) after 30 minutes, Jo had walked 3km which means that after 1 hour
(30mins x 2), Jo would have walked 6km (3km x 2).
∴ Jo walks 6km/hour for the first 30 minutes
b) after 30 minutes, there is a flat line on the graph that stretches from 30 minutes to 40 minutes. The flat line indicates that Jo covered NO distance and was therefore taking a break. from 30 mins to 40 mins is 10 mins
∴ Jo's rest was 10 mins long
Hope this helps :-)
Which is a solution for the equation 2x - 3 = 33?
O n = 12
On = 13
On = 18
On = 19
Answer:
x = 18 hope this helps
(33+3=36)
(36÷2=18)
Given the points (0,−3) and (5,-6) and on a line, find its equation in the form
y=mx+b
Answer:
Step-by-step explanation:
y=mx+b
b=-3 (y intercept)
Use equation y2-y1/x2-x1
-3/5= m
y=-3/5x-3
Picture attached
A 15
B 41
C 20
D 30
Step-by-step explanation:
Find the distance between the line segments XY & YZ
XY = 4 units
YZ = 5 units
Use the following equation to solve for the hypotenuse of the triangle:
Hypotenuse = √(a² + b²)
Let: a = XY
b = YZ
Hypotenuse = √(4² + 5²)
Remember to follow PEMDAS. Solve the parenthesis first, and the powers first before adding:
Hypotenuse = √(16 + 25)
Hypotenuse = √(41)
B) 41 is your answer, if you keep it as c². However, if it is not, then none of your answer choices work, as the answer would be √41.
~
Could i get some help on this please?
Answer:
27, 12, 9, 6, 4, 3
Step-by-step explanation:
please vote me brainliest
A pitcher can hold 8 times as much as a glass. The pitcher holds 64 ounces.
Which model shows this comparison?
54 ounces
Glass ?
Pitcher ??????
Glass ?| ?| ?| ?| ?| ?| ?| ?
Pitcher ?
54 ounces
3 ounces
Glass ????
Preher ????
Glass
Pitcher
54 ounces
84 ounces
Answer:
Im guessing this i might be wrong
54 ounces
3 ounces
Step-by-step explanation:
Answer:
To be honest i think 54 ounces and 3 ounces
Step-by-step explanation:
i was going to say 54 and 84 but i said to myself that didn't make any sense if it is 84 let me know plz
Hope this helpsHope this is rightFind the area of the sector.
Answer:
Step-by-step explanation:
Area of sector = angle/360 * pi * r^2
r is 19m
37/360 * 22/7 * 19 * 19
Area = 116.61 m^2
Multiply
(2x + 4)(2x - 4)
Answer:
4x^2 -16
Step-by-step explanation:
(2x + 4)(2x - 4)
FOIL
first:2x*2x = 4x^2
outer: -4 *2x = -8x
inner: 4*2x = 8x
last: -4*4 = -16
Add them together
4x^2 -8x+8x =-16
4x^2 -16
The multiplication of the expression (2x + 4)(2x - 4) is 4x² - 16.
What is the simplified form of the expression?Given the expression in the question:
(2x + 4)(2x - 4)
We can multiply the expression (2x + 4)(2x - 4) using the distributive property and the FOIL method.
(2x + 4)(2x - 4)
Apply the FOIL method:
2x( 2x - 4 ) + 4( 2x - 4 )
Apply distributive property:
2x × 2x + 2x × - 4 + 4 × 2x 4 × - 4
Multiply the terms:
4x² - 8x + 8x - 16
Collect and add like terms:
4x² - 16
Therefore, the simplified form is 4x² - 16.
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