Answer:
cos θ = 1/2
Step-by-step explanation:
4 cos θ + 4 sin² θ = 5
Use Pythagorean identity.
4 cos θ + 4 (1 − cos² θ) = 5
4 cos θ + 4 − 4 cos² θ = 5
0 = 4 cos² θ − 4 cos θ + 1
0 = (2 cos θ − 1)²
0 = 2 cos θ − 1
cos θ = 1/2
Answer:
60° and 300°
Step-by-step explanation:
Before beginning to answer this question, you'll need a quick formula that will be very helpful trying to answer questions like this one:
[tex]sinx^2 + cosx^2 = 1[/tex]You'll see why this formula is useful soon.
Work:
[tex]4cosx+4sinx^2=5[/tex]
The way we want to go about answering this question is very similar to what we've learned in the past: factoring. In order to be able to factor though, we need to have only [tex]cosx[/tex] in our equation instead of both [tex]sinx[/tex] and [tex]cosx[/tex] like the above equation has. this is where the formula I showed earlier comes into play.Using the equation I showed earlier, we are going to get rid of the [tex]sinx[/tex].[tex]sinx^2+cosx^2=1[/tex]
We are going to isolate [tex]sinx^2[/tex] and then substitute what its equal to into the equation.[tex]sinx^2=-cosx^2+1[/tex]
Now Substitute this back into the original equation.[tex]4cosx+4(-cosx^2+1)=5[/tex]
Put this into standard form. Then we can factor.[tex]4cosx-4cosx^2+4=5[/tex]
[tex]-4cosx^2+4cosx+4=5[/tex]
[tex]4cosx^2-4cosx-4=-5[/tex]
[tex]4cosx^2-4cosx+1=0[/tex]
Let [tex]cosx[/tex] be [tex]u[/tex].[tex]4u^2-4u+1=0[/tex]
Look familiar? We could have factored before just the same, but this ensures there will be fewer mistakes while factoring.[tex](2u-1)^2=0[/tex]
Now let's change [tex]u[/tex] back to [tex]cosx[/tex][tex](2cosx-1)^2=0[/tex]
Set [tex]2cosx-1[/tex] equal to 0.[tex]2cosx-1=0[/tex]
[tex]2cosx=1[/tex]
[tex]cosx=1/2[/tex]
Hopefully if your teacher taught you unit circle properly, you will know that [tex]cosx=1/2[/tex] is asking for an angle. In this case, I know the angle because of memorization, but sadly the only way to learn this stuff is memorization, so I wont be able to show work for how I got my final answer. I'll have to just show calculator-wise how its done.[tex](cos^-^1)cosx=1/2(cos^-^1)[/tex]
[tex]x=60[/tex] [tex]x=300[/tex]
please help !!!!!!!!
Answer:
x = 65
Step-by-step explanation:
The triangle has 2 congruent sides and is therefore isosceles.
The base angles are congruent, both 25°
Subtract the sum of the base angles from 180° for vertex angle
vertex angle = 180° - (25 + 25)° = 180° - 50° = 130°
Hence x = 130° ÷ 2 = 65
A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm
Answer:
41.24 cm²
Step-by-step explanation:
Here is the complete question: A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?
Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]
Radius of circle is 4 cm.
We can find the area of shaded region by subtracting area of rectangle from area of circle.
First, lets find the area of rectangle
Formula; Area of rectangle= [tex]length\times width[/tex]
Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]
∴ Area of rectangle= 9 cm²
Now, finding the area of circle.
Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)
Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]
∴ Area of circle= 50.24 cm²
Next solving to find area of shaded region.
Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]
Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]
∴ Area of shaded region= 41.24 cm²
96
97
98
99 100
This number line
shows the numbers
between
95 and 101
85 and 96
O97 and 102
Answer:
This number line
shows the numbers
between 95 and 101.
Step-by-step explanation:
96, 97, 98, 99, and 100 all fall between 95 and 101.
97, 98, 99, and 100 are all greater than 96, so option 2 is incorrect.
96 is less than 97, so option 3 is incorrect.
A stone fell from the top of a cliff into the ocean.
In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?
Time taken by stone in air is 7 seconds and time taken by stone in water is 5 seconds
Solution:
Let "x" represents the time taken by stone in the air
Given that the stone's entire fall took 12 seconds
Thus, the total time taken by it in both air and water = 12 seconds
time taken by stone in the air = x
time taken by stone in water = 12 - x
In the air, it had an average speed of 16 m/s
average speed in air = 16 m/s
We know that,
distance = speed x time
distance covered by it in air = [tex]16 \times x = 16x[/tex]
distance covered in air = 16x
It had an average speed of 3 m/s before hitting the seabed
average speed in water = 3 m/s
distance covered by it in water = [tex]3 \times (12 - x) = 36 - 3x[/tex]
distance covered in water = 36 - 3x
Then,
Total distance covered = distance covered in air + distance covered in water
Total distance covered = 16x + 36 - 3x = 13x + 36
But, the total distance covered by it = 127 meters ( Given )
Therefore,
13x + 36 = 127
13x = 127 - 36
13x = 91
x = 7
Hence, the time taken by stone in air = x seconds = 7 seconds,
And, the time taken by it in water = 12 - x = 12 - 7 = 5 seconds
mystery question A=8+8 B= A-7 A=16 B=
Answer:
9.
Step-by-step explanation:
It's given that A = 16. It shows that B = A-7, so that would mean B is 16-7, which is 9.
Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. Explain the steps that Lana could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5, 2) into the point-slope formula. B) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. D) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula.
Answer:
A
Step-by-step explanation:
3x+2y=15
-3x
2y=15-3x
divide by 2
y=-3/2x+7.5
Parallel Line = Same Slope
y=-3/2x+b
substitute (5,2)
2=-3/2(5)+b
2=-7.5+b
+7.5
9.5=b
Final Equation: y=-3/2x+9.5
Lana needs to first convert the equation to slope-intercept form, and then use the parallel line's slope with the provided point in the point-slope formula to find her line's equation.
Explanation:The correct option for Lana to find an equation for a line that passes through the point (5, 2) and is parallel to the given equation 3x + 2y = 15, is option A.
First, Lana needs to write the given equation in slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept. To do this, she needs to rearrange the equation by subtracting 3x from both sides and dividing by 2, which gives y = -1.5x + 7.5.
Parallel lines have the same slope, so the slope, m, of Lana's line is -1.5. Now, she uses the point-slope form of a linear equation which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. Substituting the point (5, 2) and slope -1.5 into this equation, Lana gets y - 2 = -1.5x + 7.5.
She rearranges this to get her final equation.
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To describe a specific arithmetic sequence, Elijah wrote the recursive formula:
Write a linear equation that models this sequence using the sketchpad below.
Answer:
[tex]t_{n} = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........
Step-by-step explanation:
Given the arithmetic sequence in recursive formula.
f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)
Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}
Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44
And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51
and so on.
Therefore, the arithmetic sequence is 30, 37, 44, 51, .......
Therefore, the linear equation of this sequence is given by [tex]t_{n} = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........
(Answer)
20 points and I will mark you as brainliest
Answer:
Rock phosphate, insoluble phosphates in bone deposits, and dissolved phosphates available to plants
The ratio of girls to boys at a movie is 3:8. If there are 32 boys, how many girls are at the movie
Answer: 12 girls
Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's girls/boys.
Next, we set up our proportion. We know that at a movie there are 3 girls for every 8 boys so we have 3/8 and we are asked how many girls are at the movie if 32 boys are the movie so that's x/32.
Now we have the proportion 3/8 = x/32.
Notice that the 32 boys must go on the bottom of the second ratio because our unit ratio tells us that we put girls/boys.
Solving from here, we use the means-extremes property to get 3 times 32 to get 96 = 8 times x or 8x. So we have 96 = 8x.
Dividing both sides by 8, we find that 12 = x.
This means that 12 girls are at the movie when 32 boys are at the movie.
write an equation for the line perpendicular to y=2x-5 through the point (8,-2)
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
We have the following equation of the line:
[tex]y = 2x-5[/tex]
Then [tex]m_ {1} = 2[/tex]
We find [tex]m_ {2}:[/tex]
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {2}\\m_ {2} = - \frac {1} {2}[/tex]
Thus, the perpendicular line will be of the form:
[tex]y = - \frac {1} {2} x + b[/tex]
We substitute the given point and find "b":
[tex]-2 = - \frac {1} {2} (8) + b[/tex]
[tex]-2 = -4 + b\\-2 + 4 = b\\b = 2[/tex]
Finally, the equation is of the form:
[tex]y = - \frac {1} {2} x + 2[/tex]
ANswer:
[tex]y = - \frac {1} {2} x + 2[/tex]
A circle of radius 10 is divided into four congruent sectors. One of these sectors is used to form the curved surface of a cone. What is the volume of this cone?
Answer:
V ≈ 63.4
Step-by-step explanation:
The arc length of the segment becomes the circumference of the cone's base. Therefore, we can find the radius of the cone:
s = C
(90/360) 2π (10) = 2π r
r = 2.5
The radius of the segment is the slant length of the cone. So we can use Pythagorean theorem to find the cone's height.
l² = r² + h²
10² = 2.5² + h²
h = √93.75
The volume of the cone is:
V = π/3 r² h
V = π/3 (2.5)² √93.75
V ≈ 63.4
mathematics help plz
Answer: 4, 6,7,10
Step-by-step explanation: since X is greater than 3, then X can assume all numbers great than 3.
Answer:
4, 6, 7, 10Step-by-step explanation:
x > 3 - we read: all numbers greater than number 3
Therefore:
#1: NOT, because -1 < 3 and -2 < 3
#2: NOT, because all numbers are less than 3
#3: NOT, because 3 is not greater than 3
#4: YES, because all numbers are greater than 3.
suppose your sat score is 2040 a college with an average sat score for admitted students of which of these would most likely be your best opinion
a. 1640
b. 2060
c. 1220
d. 1480
Answer:
1640.
Step-by-step explanation:
1640 would be your best option. As you are much higher than average. 2060 would not be a better option as you are below average in this case.
Answer:2060
Step-by-step explanation: your closest to 2060
Sybil grows and sells watermelons. The function C = 4n + 15 represents her cost, in
dollars, for producing n watermelons. Her revenue, or the amount she receives for
selling n watermelons, can be represented by the function R = 6n. Which function
represents Sybil's profit, P, for selling n watermelons?
Sybil's profit for selling n watermelons is represented by the function P = 2n - 15, which is the result of subtracting her cost function from her revenue function.
Explanation:The function that represents Sybil's profit, P, for selling n watermelons is found by calculating the difference between her revenue and her costs. The profit function, therefore, is the revenue function R = 6n minus the cost function C = 4n + 15. Executing the subtraction, we get:
P = R - C
P = 6n - (4n + 15)
P = 6n - 4n - 15
P = 2n - 15
This function represents the profit made on selling n watermelons.
Final answer:
The function representing Sybil's profit for selling n watermelons is P = 2n - 15.
Explanation:
Profit can be calculated by subtracting the total cost from the total revenue. In this case, the total revenue function is R = 6n and the total cost function is C = 4n + 15. To find the profit function, we subtract the total cost function from the total revenue function:
P = R - C
P = 6n - (4n + 15)
P = 2n - 15
Therefore, the function representing Sybil's profit for selling n watermelons is P = 2n - 15.
A company's stock was selling at
$16 a share. A month later, it was
selling at $20 a share. What is
the percent increase?
[?]%
old: $16
new: $20
percent increase
-> formula: (new-old / old) x 100
(20-16 / 16) x 100
4/16 x 100
0.25 x 100
answer: 25% increase
According to the question,
Old selling price,
$16New selling price,
$20We know the formula,
→ [tex]Percent \ increase = \frac{New \ selling \ price- Old \ selling \ price}{Old \ selling \ price}\times 100[/tex]
By putting the values,
[tex]= \frac{20-16}{16}\times 100[/tex]
[tex]= \frac{4}{16}\times 100[/tex]
[tex]= 0.25\times 100[/tex]
[tex]= 25[/tex] (%)
Thus the above approach is appropriate.
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A bought a car for Rs.100000 and spent Rs. 10000 on its repairs.He sold this car to B at a gain of 10% who later on sold to Close at a gain of 5%.what did C pay for the car?
Final answer:
C paid Rs. 127,050 for the car.
Explanation:
To find out what C paid for the car, we need to consider the gains made by A and B. A bought the car for Rs.100,000 and spent Rs. 10,000 on repairs. This means A's total cost is Rs. 110,000. A then sells the car to B at a gain of 10%, which means B buys the car for 110% of Rs. 110,000, or Rs. 121,000.
Now, B sells the car to C at a gain of 5%. To find out what C paid, we need to calculate 105% of Rs. 121,000, which gives us Rs. 127,050. Therefore, C paid Rs. 127,050 for the car.
In the 6,492.709 which number is in the 10th place?
I believe that the answer is 7 because it is in the tens place.
Sorry misunderstood the Question the other user is correct
originally had a 2
Answer:
7 because it is in the 0.1 (1/10 or tenth) place of the number
24,358 divided by 38
Answer:
641
Step-by-step explanation:
24,358 ÷ 38=641
Hope this helps!!
24,358 / 38 = 641
Use long division to find the answer :)
Hope this helps!
9. Using the diagram below, if < 2 = 107*. find each missing angle:
M24 =
m26 =
mZ8 =
m25 =
m27 =
Answer:
24
Step-by-step explanation:
Every year Aiden uses income from his job to pay for 75% of his college tuition. Next year’s tuition will be $720 more than this year’s, and Aiden will pay $2400. How much is this year’s tuition?
Answer:
$2,480
Step-by-step explanation:
Let $x be next year tuition. Aiden will pay $2,400, that is 75% of $x.
$x - 100%
$2,400 - 75%
Write a proportion:
[tex]\dfrac{x}{2,400}=\dfrac{100}{75}\\ \\75x=2,400\cdot 100\\ \\75x=240,000\\ \\x=3,200[/tex]
Next year’s tuition will be $720 more than this year’s, then this year tuition is
[tex]\$3,200-\$720=\$2,480[/tex]
8➗2(2+2)????????????
Answer:
16
Step-by-step explanation:
So according to PEMDAS we need to do the work in the parentheses first. 2 plus 2 is 4 so we will put 4 in the parentheses to replace 2 plus 2. Now we will divide 8 by 2 which is 4. since 4 is right next to the parentheses, we need to multiply the 4 by the 4 in the parentheses. 4 times 4 is 16.
What is the quotient when 4x3 + 2x + 7 is divided by x + 3?
Final answer:
The quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.
Explanation:
To find the quotient when 4x^3 + 2x + 7 is divided by x + 3, we can use long division. Divide the first term, 4x^3, by x which gives 4x^2. Multiply x + 3 by 4x^2 to get 4x^3 + 12x^2. Subtract this from the original expression to get -10x^2 + 2x + 7. Then, divide -10x^2 by x which gives -10x. Multiply x + 3 by -10x to get -10x^2 - 30x. Subtract this from the previous result to get 32x + 7. Finally, divide 32x by x which gives 32. Multiply x + 3 by 32 to get 32x + 96. Subtract this from the previous result to get -89. Therefore, the quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.
Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
=
Answer: 14ft > 4 1/2 yd
Step-by-step explanation:
Determine the sign of cos pi divided by seven
Answer:
As π/7 is in first quadrant and all trig functions are positive there,
so, cos pi/7 is positive.
Step-by-step explanation:
In 1st quadrant, all trigonometric functions are positive. Measure of Angle Ф is from 0 to π/2, and measure of reference angle is Ф.In 2nd quadrant, sinФ and cosecФ are positive. Measure of Angle Ф is from π/2 to π, and measure of reference angle is π - Ф.In 3rd quadrant, tanФ and cotФ are positive. Measure of Angle Ф is from π to 3π/2, and measure of reference angle is Ф - π.In 4th quadrant, cosФ and secФ are positive. Measure of Angle Ф is from 3π/2 to 2π, and measure of reference angle is 2π - Ф.Please check the attached figure a.
As π/7 is in first quadrant and all trig functions are positive there,
so, cos pi/7 is positive.
Keywords: trigonometric function, cos π
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Can anyone answer this? I will give brainliest to whoever answers the fastest and correctly!
Answer:
-1
Step-by-step explanation:
The answer is minus one. The third quadrant only has all negative numbers therefore the answer is -1. All the other answers in the selection is positive.
Answer:
A. -1
Step-by-step explanation:
In the third quadrant, the x-coordinate and the y-coordinate are negative.
The x-coordinate must be a negative number.
Answer: A. -1
The daughter is 36 years younger than her mother. How many years ago was the mother 5 times the daughters age, if she is 50 years old now?
Answer:
The answer is 5 years ago.
Step-by-step explanation:
5 years ago the age of the mother was 5 times the daughter's age.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Suppose the current age of the daughter is D while the mother is M.
As per the given, The daughter is 36 years younger than her mother.
D = M - 36
And , M = 50
D = 50 - 36 = 14
Let's say x year age the mother was 5 times the daughter's age.
(M - x) = 5(D - x)
(50 - x) = 5(14 - x)
50 - x = 70 - 5x
-x + 5x = 70 - 50
4x = 20
x = 5
Hence "5 years ago the age of the mother was 5 times the daughter's age".
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which is a slope intercept form of an equation for the line containing (0,5) slope -3
Answer:
y=-3x+5
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-0)
y-5=-3(x)
y-5=-3x
y=-3x+5
Will give brainliest! 20 Points!
Hi! Some help with these problems would be great thank you!
Answer:
Question 1:
Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.
Question 2:
A). y = 1.2x - 6
Question 3:
J). y = [tex]\frac{9}{4}x - 81[/tex]
Question 4:
F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*
Step-by-step explanation:
Question 2:
The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8
For parallel lines, their values of slope is the same.
So our line, that passes through point (5, 0), also has a slope of 1.2
Taking another point (x, y) on our line;
Slope = change in y ÷ change in x
1.2 = [tex]\frac{y - 0}{x - 5}[/tex]
y = 1.2x - 1.2(5)
y = 1.2x - 6
Question 3:
The line passes x-axis at point (36, 0)
The line is perpendicular to another line whose equation is y = -[tex]\frac{4}{9}x[/tex] + 5
For perpendicular lines, the product of their slopes = -1
Let's say the slope of our unknown line is a ;
Given: The slope of our second line is -4/9
So,
a × -4/9 = -1
a = -1 × -9/4 = 9/4
Taking another point (x, y) on our unknown line;
Slope = change in y ÷ change in x
9/4 = [tex]\frac{y - 0}{x - 36}[/tex]
Cross-multiplying that you get;
y = [tex]\frac{9}{4}x - 81[/tex]
Question 4:
The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6
Two points are located at (2,3) and (8,-5) complete the equations below to show how you can use the pythagorean theorem to find the distance between these two points
Answer:
3
Step-by-step explanation:
-2(x+5)^2=50 solve using square root
Answer:
x = -5 + 5i, -5 - 5i
Step-by-step explanation: