Given :
Solve [0, 2π)
3cos(2x) = 5sin(x) - 1
To Find :
The value of x in range [0,2π).
Solution :
We know, cos(2x) = 1 - sin²x .
3( 1 - 2sin²x ) = 5sinx - 1
3 - 6sin²x = 5sinx - 1
6sin²x + 5sinx - 4 = 0
6sin²x + 8sinx - 3sinx - 4 = 0
2sinx( 3sinx + 4 ) - 1( 3sinx + 4) = 0
sin x = 1/2 and sin x = -4/3 .
Since, sin x ≤ 1.
So, sin x = 1/2 .
x = π/6 .
Therefore, value of x is π/6.
Hence, this is the required solution.
I estimated that the repairs to my car would cost $120. In fact, they cost $80. What was the percentage error?
Answer:
33.33% I am pretty sure
Step-by-step explanation:
Answer: 33%
Step-by-step explanation:
I need ur help please.....
Answer:
25 kg option bStep-by-step explanation:
let father s weight be 3x
son s weight be x
3x- x = 50
2x = 50
x =25
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. How high are the levels for the highest 2% of all children?
Answer: Read the following,
Step-by-step explanation:
1
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. What percentage of children have a cholesterol level above 200 mg/dl?Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in the bloodstream (in mg/dl) has approximate normal distribution with a mean of 38 mg/dland a standard deviation of 12. What proportion of these bears have between 27.5 and 67.5 mg/dl porphyrin in their bloodstream?A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution. What proportion of trees contains more than 150 cubic feet?GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. What proportion of freshman biology majors have GPA above 3.50?Mensa is an organization whose members possess IQs in the top 2% of the population. If the IQs are normally distributed with a mean of 100 and a standard deviation of 15, what is the minimum IQ necessary for admission?Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. A kitten isdesignated as dangerously underweight when, at 10 weeks, it weighs less than 10.0 oz. What proportion of healthy kittens will designated as dangerously underweight?
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2)
On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5).
On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Answer:On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Step-by-step explanation:
(f + g)(x) = -x² + 3x + 5 + x² + 2x = 5x + 5
=> y = 5x + 5
=> the slope is positive
the line crosses the x-axis at (-1;0) and the y-axis at (0;5)
Answer:
I think it is the last graph on Edge
Step-by-step explanation:
Sorry if I'm wrong ;-;
PLEASEEEE HELPPP!!
Which property is illustrated by the equation
3x – 6y = 3(x - 2y)?
1. associative
2.Commutative
3.distributive
4.closure
Answer:
3. Distributive
Step-by-step explanation:
In the equation 3(x - 2y) if you distribute the 3 to the x and the -2 you would get 3x-6y.
The property illustrated in the equation is 3)Distributive
What is the Distributive property?Distributive law, also called distributive property, in mathematics, the law relating the operations of multiplication and addition, stated symbolically as a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac.
Given here, 3x-6y=3(x-2y)
Thus clearly 3 is distributed over x and 2y
Hence, The property illustrated in the equation is 3)Distributive
Learn more about the distributive property here:
https://brainly.com/question/5637942
#SPJ2
Last season, a pair of jeans cost $42.95. This season, the price of the jeans increased by 25 percent. Later in the season, the jeans were put on sale for 25 percent off. First, guess. What do you think the sale price will be? Why? Then, calculate: How much did the jeans cost at the beginning of this season? What was their sale price? Did you get the sale price you were expecting? Why or why not? Consider what the jeans would cost if they had gone on sale by 25% first, and then had their price increased by 25%. First guess. What do you think the jeans will cost this time? Why? Then, calculate: How much will the jeans cost this time? Did you get the answer you were expecting? Why or why not?
Answer:
42.95 first price hiked 25%, then discounted by 25% : Final price = 40.28
42.95 first discounted by 25%, then price hiked by 25% : Final price = 40.27
Both are same (approx) because of same mathematical treatment
Step-by-step explanation:
If Jeans price first hiked price by 25%, then gone on sale by 25%Last season price = 42.95
This season increase in price = 25% of 42.95 = 10.73
Jeans price at beginning of this season = 53.68
Discount on sale price, this season = 25% of 53.68 = 13.42
Discounted jeans price this season = 53.68 - 13.42 = 40.28
If Jeans price first gone on sale by 25%, then price increased by 25%Last season price = 42.95
Discount on previous price = 25% of 42.95 = 10.73
Jeans price this season = 42.95 - 10.73 = 32.22
Price hike this season = 25% of 32.22 = 8.05
New jeans price this season = 32.22 + 8.05 = 40.27
The same answer is got in both cases. As, mathematically, they are same. 1st : 75% of (125% of 42.95) & 2nd : 125% of (75% of 42.95)What is 6/5 divided by 4/3
Answer:
9/10
Step-by-step explanation:
the diameter of a penny is 19.05 mm and it is 1.52 mm thick. what is the mass od the penny?
6 Find the mistakel Circle the mistake below and explain why it is wrong: Label all consecutive Interior angles below then give its Explanation: characteristics. Consecutive interior angles are equal.
PLEASE HELP!!!!
Answer:
Step-by-step explanation:
I can't help u
x –12 = -8x + 6 a.x = 2 b.x = -2 c.x = 3 d.x = -3
Answer:
(a) x = 2
Step-by-step explanation:
x - 12 = -8x + 6
First, move all the like terms to one side of the equation. We will move all the x's to the left, and the rest to the right in this equation. (Don't forget to pay attention to the signs of the numbers as you move them over the equal sign.)
x - 12 + 8x = 6
x + 8x = 6 + 12
9x = 18
Next, solve for x by isolating it to one side of the equation. Here, we'll have to divide 18 by 9 (do the opposite of what 9 is doing with x; instead of multiplying it with 18 like it currently is with x, divide 18 by it.)
x = [tex]\frac{18}{9}[/tex]
x = 2
Therefore, your answer is (a), since x = 2.
I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!
what are two numbers that multiply to the value of 27and add to the value of -12
Answer:
[tex]-9[/tex] and [tex]-3[/tex]
Every workday, Zoe bikes 2.6 miles to work along city streets. On the way back, she likes to take a shortcut through a park, so she only bikes 0.9 times that far. How many miles does Zoe bike to work and back in a 5-day workweek?
Answer:
24.7
Step-by-step explanation:
16r - 8 factored if it can not be factored write prime
Answer:
Algebra 1 questions and answers - Get algebra 1 help with questions involving ratios, proportions, equations with 2 variables, monomials, polynomials, factoring, inequalities, absolute value, graphing, lines, x-intercept, y-intercept, slope, parabolas, functions, roots, radicals, quadratic equations, the quadratic formula and more.
Step-by-step explanation:
A 3-column table with 4 rows. Column 1 is labeled Rectangle with entries A, B, C, D. Column 2 is labeled Width with entries 3 feet, 6 feet, 15 feet, 60 feet. Column 3 is labeled Length with entries 5 feet, 10 feet, 25 feet, 90 feet. Which rectangle is not an enlargement of rectangle A? A B C D
Answer:
The answer is d
Step-by-step explanation:
Answer:
it D
Step-by-step explanation:
hope it helps
Please please help hope you have a great day
5x+2y=29
x+4y =13
i don’t know that answer
Answer:
x=71/9, y= -47/9
Step-by-step explanation:
5x+2y=29
x+4y=13 subtract 4y from both sides
x= -4y+13 substitute on the first one
5( -4y+13) + 2y = 29 distribute in parenthesis
-20y - 65 +2y =29 add 65 to both sides
-20y +2y = 29+65 combine like terms
-18y = 94 divide by -18 both sides
y= 94/-18= -47/9
substitute y =-47/9 in x=-4y+13
x=-4(-47/9)+13=(188/9)+13=188+117/9=71/9
The graph shows:
Positive Slope
Negative Slope
No Slope
This is an arrow. This is not slope
Answer:
Negative slope.
Step-by-step explanation:
Answer:
It is a negative slope
Step-by-step explanation:
the line it going down
hope this helps :3
HELPPPPPPP ASAPPPPPP PLEASEEEEEE
Answer:
C.) The amount of money she saved before attending lessons.
Which point will correspond to the rightmost point of the reflected figure?
Answer:
i need help with this question tooo
Step-by-step explanation:
2 variable inequalities from their graphs . Please answer. Ty!
Answer:
y≤[tex]\frac{1}{3} x+1[/tex]
Step-by-step explanation:
Since the graph is facing down, We know the equation is y<mx+b
Since slope is rise/run the slope is 1/3.
Since the y intercept (The point where the line hits y) is 1, the equation is
y<1/3x+1
BUT WAIT!
The line is solid meaning that we have to include the line as part of the values. This will make the new equation
y≤[tex]\frac{1}{3} x+1[/tex]
HELP PLEASE ITS DUE TOMMOROW AND I HAVE 2 TESTS TO TAKE TODAY D:
Directions: Find the value of each variable (x and/or y)
Answer:
x=25
x=47
y=25 x=10
y=20
Step-by-step explanation:
2x+10=60
-10 -10
2x=50
2x/2=50/2
x=25
2x+6=100
-6 -6
2x=94
2x/2=94/2
x=47
5y-25=100
+25 +25
5y=125
5y/5=125/5
y=25
11x-30+100=180
11x+70=180
-70 -70
11x=110
11x/11=110/11
x=10
7y-10=3y+70
+10 +10
7y=3y+80
-3y-3y
4y=80
4y/4=80/4
y=20
hopefully this helps :)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the GCF of the given polynomial. 16a^4b^4 + 32a^3b^5 - 48a^2b^6
Answer:
[tex]16a^2b^4[/tex]
Step-by-step explanation:
GCF= Greatest Common Factor
Given a polynomial, the GCF is the largest polynomial that will divide evenly into that polynomial.
The polynomial is
[tex]16a^4b^4 + 32a^3b^5 - 48a^2b^6[/tex]
First, we find the GCF of the coefficients:
16, 32, 48
Since 32 and 48 are multiples of 16, 16 is the GCF of the coefficients.
Now we select all the repeating variables with their smallest exponent:
[tex]a^4, a^3, a^2.\ GCF= a^2[/tex]
[tex]b^4, b^5, b^6.\ GCF=b^4[/tex]
The GCF of the polynomial is
[tex]\boxed{16a^2b^4}[/tex]
What is the slope of the line passing through (-3, 5) and (5, -3)?
no slope
slope = 0
slope = 1
slope = -1
Answer:
The Slope = -1
Help me with this please
Answer:
x = 14
I am sure of the answer :)
Prove that Triangle abc and Triangle edc are similar
The corresponding sides have equal ratios, so the triangles are similar triangles.
From the question, we have:
In triangle ABC, AB = 3, BC = 5 and AC = 4
In triangle EDC, ED = 9, DC = 15 and EC = 12
For the triangles to be similar, then the corresponding sides must have an equivalent ratio.
This is calculated as:
[tex]\mathbf{Ratio = \frac{ED}{AB} = \frac{DC}{BC} = \frac{EC}{AC}}[/tex]
So, we have:
[tex]\mathbf{Ratio = \frac{9}{3} = \frac{15}{5} = \frac{12}{4}}[/tex]
[tex]\mathbf{Ratio =3 = 3 = 3}[/tex]
[tex]\mathbf{Ratio =3}[/tex]
Because the corresponding sides have equal ratios, then the triangles are similar.
Read more about similar triangles at:
https://brainly.com/question/19738610
Hector has 10 cups of flour which equation shows how to determine the number of 2/5 of a cup serving where there are in the 10 cups of flour
A. 10 divide by 2/5 equals 25
B. 10x 2/5 equals 4
C. 2/5 divide by 10 equals 1/25
D. 5/2 divide by 10 equals 1/4
HELP!!!!!!!!
Answer:
10/(2/5)
Step-by-step explanation:
At what point does the graph of the line y=2x−6 cross the y-axis?
a.(2, −6)
b.(0, 2)
c. (0, −6)
d. I don't know.
Which equation is written in standard form?
6x - 4y = 13
4y + 10 = 2x
8x=-2y - 9
2/3x – 9y = 13
Answer: D
Step-by-step explanation:
Answer:
Answer= D
Step-by-step explanation:
Which distributive property gives the same answer as 7(99)?
7(99+9)
o 7(99-9)
. 7(100+1)
7(100-1)
Answer:
7(100-1)
Step-by-step explanation:
That's it right there
7. If a hardboiled egg is cracked, the cracked egg shells could be an
example of *
-the core
-tectonic plates
-the mantle
-the atmopshere
Answer:
The tectonic plates.
Step-by-step explanation:
If you look at a diagram of Earth on Google, you'll see there's the crust, the mantle, the core...etc. If the tectonic plates are apart of the crust- which is the Earth's surface, then it's safe to assume the shell of the egg is the tectonic plates.