Answer: A and B
pi/3 and 2pi/3
=========================================
Work Shown:
2*sin(x) - sqrt(3) = 0
2sin(x) = sqrt(3)
sin(x) = sqrt(3)/2
Using the unit circle, we see that sin(theta) is equal to sqrt(3)/2 when theta is theta = pi/3 in quadrant I, and when theta = 2pi/3 in quadrant II.
So sin(pi/3) = sqrt(3)/2 and sin(2pi/3) = sqrt(3)/2
--------------------
You can check these answers by replacing x with the value in question and seeing if you get zero. Make sure your calculator is in radian mode
Plug in x = pi/3
2*sin(x) - sqrt(3) = 0
2*sin(pi/3) - sqrt(3) = 0
0 = 0 .................... this is a true equation, x = pi/3 is confirmed as a solution
Plug in x = 2pi/3
2*sin(x) - sqrt(3) = 0
2*sin(2pi/3) - sqrt(3) = 0
0 = 0 .................... true equation, x = 2pi/3 is confirmed as a solution
Plug in x = 4pi/3
2*sin(x) - sqrt(3) = 0
2*sin(4pi/3) - sqrt(3) = 0
-3.4641016 = 0 ............ false equation, x = 4pi/3 is a nonsolution
Plug in x = 5pi/3
2*sin(x) - sqrt(3) = 0
2*sin(5pi/3) - sqrt(3) = 0
-3.4641016 = 0 ............ false equation, x = 5pi/3 is a nonsolution
Final answer:
To solve the trigonometric equation 2 sin x - √(3) = 0 within the interval 0 ≤ x < 2π, we find that sin x = √(3)/2 at x = π/3 and 2π/3, which are the correct answer choices.
Explanation:
To solve for x in the given trigonometric equation 2 sin x - √(3) = 0, we first isolate the sine function by adding √3 to both sides and then divide by 2, giving us sin x = √(3)/2. Now, we seek the angles x within the interval 0 ≤ x < 2π (where π is pi) that satisfy this equation. We know that sin x is √(3)/2 at the angles π/3 and 2π/3 in the first and second quadrants, respectively. These are the two angles where the sine function takes the value of √(3)/2 between 0 and 2π. Therefore, the correct answer choices are π/3 and 2π/3.
It is important to consider that the sine function is positive in the first and second quadrants, and given the range for x, we don't need to consider the third or fourth quadrants where sine is negative. Additionally, the angles 4π/3 and 5π/3 correspond to a negative value of the sine function, thus they do not satisfy the equation.
Quadrilateral MATH is a square. If MA = 2x – 5 and AT = x + 10, find the perimeter of the square.
Answer:
Perimeter of the square MATH = 100.
Step-by-step explanation:
Given that MATH is a square, it means all sides would be equal to each other.
Given MA = 2x - 5 and AT = x + 10.
we know all sides are equal, so MA = AT.
2x - 5 = x + 10
2x = x + 10 + 5
2x = x + 15
2x - x = 15
x = 15
So, AT = x + 10 = 15 + 10 = 25.
Now the perimeter would be (MA + AT + TH + HM) = 4*AT = 4*25 = 100.
Hence, option D is the correct answer i.e. 100.
Answer:
100
Step-by-step explanation:
Sides of a square are congruent.
2x – 5 = x + 10
x = 15
Sides = 2(15) – 5 = 25
Perimeter = 25 + 25 + 25 + 25 = 100
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
Answer:
c
Step-by-step explanation:
How do you solve this problem?
What is the length of a radius of the circle represented by the equation x^2+y^2-4x+4y=0 ?
Will award brainliest for best explanation.
so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.
[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]
now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.
[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]
A salesperson had $240,000 in sales last year, which is 60% of the sales she had this year. Which equation could be used to determine x, the salesperson's total amount in sales, in dollars, for this year?
Answer:
$400,000
Step-by-step explanation:
We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other.
[tex]\frac{60}{100}=\frac{240000}{x}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
60x=100(240,000)
60x=24,000,000
y=400,000
Answer:
$400,000
Step-by-step explanation:
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, there were 1290 downloads of the song, for a total download size of 4403 MB. How many downloads of the high-quality version were there?
Answer:
770 high-quality songs were downloaded
Step-by-step explanation:
A web music store offerst two versions:
Standard Version = 2.1 MBHigh-Quality Version = 4.3MBThere were 1290 for a total download size of 4403MB.
According to the information above, we have the following system of equations:
A + B =1290
2.1A + 4.3B = 4403
Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.
Solving the sistem of equations we get that:
A + B =1290 ⇒ A = 1290 - B
2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403
⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770
Now, let's find the value of 'A':
A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.
Therefore, 770 high-quality songs were downloaded.
ASAP:::::: 75 POINTS TO THE BRAINLIEST!!!!!
Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together. Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.
Answer:
t = 6 4/25 hours
Step-by-step explanation:
The formula to find out how long it takes them to do the job is
1/m + 1/ a = 1 /t
where m is the time for Matthew to do the job
a is the time for Arianna to do the job
and t is the time for them to do the job together
m = 14 hours
a = 11 hours
Substituting what we know
1/14 + 1/11 = 1/t
Multiplying by 154t (14*11*t) so we can clear the fractions
154t*(1/14 + 1/11) = 1/t* 154t
11t + 14t = 154
Combine like terms
25t = 154
Divide by 25
t = 154/25
t = 6 4/25 hours
A baker pays $0.90 per pound for sugar and $2.75 per pound butter. How much will the baher spend if he puts 8 pounds of butter and 10 pounds of sugar?
A motorist traveled 250 miles on 11 gallons of gas. With the same vehicle, about how far could he go on 16 gallons of gas? Round to the nearest tenth.
Given:
A motorist traveled 250 miles on 11 gallons of gas.
To Find:
In the same vehicle, the distance that can be traveled in 16 gallons.
Answer:
Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.
Step-by-step explanation:
We first find the number of miles that can be traveled on 1 mile of gas.
We do this by using the unitary method.
Given that in 11 gallons, 250 miles can be traveled in a certain vehicle.
So in 1 gallon, 250 ÷ 11 miles can be traveled. This is roughly equal to 22.72.
Next we will calculate how much distance he can go in 16 gallons. We multiply the distance traveled in 1 gallon by 16.
That is, in 16 gallons, the number of miles that can be traveled is 22.72 x 16 = 363.52.
Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.
Answer:363.6miles
Step-by-step explanation:
Linnea's company's revenue in 20172017 is \dfrac{36}{25} 25 36 ? of its revenue in 20162016. What is Linnea's company's revenue in 20172017 as a percent of its revenue in 20162016 ?
Answer:
144%
Step-by-step explanation:
We are told that Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016..
To find the Linnea's company's revenue in 2017 as a percent of its revenue in 2016, we will have to figure out 36 is what percent of 25.
[tex]\text{Percent}=\frac{36}{25}\times 100[/tex]
[tex]\text{Percent}=36\times 4[/tex]
[tex]\text{Percent}=144[/tex]
Therefore, Linnea's company's revenue in 2017 is 144% of its revenue in 2017.
What store has the best deal? Tae Store:4 cans for $2.48, Be Cool Store:5 cans for $3.00 or Not Today Store:59 cents per can?
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
which of the following is the coefficient in the algebraic expression x2 +16y ?
A.2
B. Y
C. X
D.16
Answer:
16
D is correct.
Step-by-step explanation:
Coefficient: The coefficient is a number front of variable.
[tex]Expression: x^2+16y[/tex]
In the given expression there are two terms
x² and 16y
First term: x²
The coefficient of x² is 1
Second term: 16y
The coefficient of 16y is 16
Hence, The coefficient of 16 of the given expression.
When x = 12, y = 36. When x = 3, y = 9. What is the constant of proportionality? Enter your answer in the box.
Answer:
k = 3
Step-by-step explanation:
the equation relating x and y is
y = kx ← k is the constant of proportionality
to find use the given conditions
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{36}{12}[/tex] = [tex]\frac{9}{3}[/tex] = 3
50 points.
Right triangle ABC has its right angle at C.
AC=3 and BC=4.
Which trigonometric ratios are correct?
Select each correct answer.
1.) sinB= 3/5
2.) tanB= 4/3
3.) cosA= 4/5
4.) sinA= 4/5
5.) tanA= 4/3
sinB= 3/5 is correct
tanA= 4/3 is correct
and sinA= 4/5 is correct
hope this helps ^
Will someone please help me solve this? A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?
Answer:
104 boxes109 boxes218 boxesStep-by-step explanation:
Let b represent the number of boxes of cookies sold the first week. Then b+5 boxes were sold the second week, and 2(b+5) boxes were sold the third week. The total sold was ...
b +(b+5) +2(b+5) = 431
4b +15 = 431 . . . . . . simplify
b = (431 -15)/4 = 104 . . . . . subtract 15, divide by the coefficient of b
First week: b = 104
Second week: b+5 = 109
Third week: 2(b+5) = 218
This year the paradas had 127 floats . That was 34 fewer floats than last year how many floats were in the parade last year
Answer:
161
Step-by-step explanation:
We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.
127+34=161
Which term applies when using the method shown to determine if two ratios are proportions
Answer:
I think that there is a part of your question that is missing maybe? What is the method shown?
Step-by-step explanation:
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)
Image: ∆A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25), C' (2.25, −1.5)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
3/4
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]
B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]
C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]
Therefore, the scale factor of the dilation is 3/4.
You can buy 20 ounces of cereal for 4.40$ or 16 ounces of the same brand for 3.68$ which is the better buy?
To find the better buy, we can find how much they cost for an ounce and find it by comparison.
First option:
20/4.4
=$4.545454...
Second option:
16/3.68
=$4.3478...
As $4.3478..< $4.5454.., the second option is cheaper and therefore is the better buy.
Hope it helps!
The 20 ounces for $4.40 is the better deal at $0.22 per ounce, compared to the 16 ounces for $3.68 at $0.23 per ounce.
To determine which cereal is the better buy, we need to calculate the cost per ounce for each option. For the first option of 20 ounces at $4.40, the cost per ounce is:
[tex]\frac{0.44}{20} = 0.22 ~per ounce[/tex]
For the second option of 16 ounces at $3.68, the cost per ounce is:
[tex]\frac{3.68}{16} = 0.23[/tex]
Comparing these two costs per ounce, the 20 ounces for $4.40 is the better buy because it has a lower cost per ounce.
A bag contains 56 marbles 7 red , 8 green , 11 yellow , 17 brown and 13 blues if a marble is chosen at random what is the probability that the marble is green
Answer:
The probability is 1/7 or 14.29%
Step-by-step explanation:
In order to find this, divide the number of marbles that are green by the total number.
8/56 = 1/7 = 14.29%
PLEASE HELP ME!!! and if you could give me an explanation that would be good but if you can’t at least give me the answer please :(
Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C
=============================
Explanation:
Given roots: -2, 4, 4, 3
Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)
x = -2 leads to x+2 = 0, so (x+2) is one factor
x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor
x = 3 leads to x-3 = 0 so (x-3) is the last factor
Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)
Use the distributive property to expand everything out
g(x) = (x+2)(x-4)(x-4)(x-3)
g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )
g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )
g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )
g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96
g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96
which shows how I got choice C as the answer
What’s the area of PQSU? ______sq mi
Answer:
35 mi^2
Step-by-step explanation:
Area of parallelogram = base x height
7 x 5 = 35
Answer:
Area = 35 mi^2
Step-by-step explanation:
Area = b*h
The base is 7 mi
The height is 5 mi
Area = 7*5
Area = 35 mi^2
Rectangle R was dilated to form rectangle R' Which is the scale factor of the dilation? 5/4 , 2/1 5/2 5/1
Answer:
I'm not sure if those are the answer choices but your answer should be 5/2
Hope this helps
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
Describe the possible lengths of the third side of a triangle given that the lengths of the other two sides are 5 and 12 units long. Please express your response as a compound inequality.
Answer:
7<x<17
Step-by-step explanation:
a+b>x
5+12>x
17>x
5+x>12
x>7
12+x>5
x>-7 (ignore then since it is negative and you would use the one that makes the range smaller which is the one above)
Please help!!!
Which best explains the relationship between the two triangles below?
Answer:
1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]
Step-by-step explanation:
We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.
By angle sum property let us find measure of angle C of triangle ADC.
[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]
[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]
[tex]m\angle C+147.7^{o}=180^{o}[/tex]
[tex]m\angle C=180^{o}-147.7^{o}[/tex]
[tex]m\angle C=32.3^{o}[/tex]
Let us find measure of angle T of triangle RTS.
[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]
[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]
[tex]m\angle T+128.8^{o}=180^{o}[/tex]
[tex]m\angle T=180^{o}-128.8^{o}[/tex]
[tex]m\angle T=51.2^{o}[/tex]
We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.
what is the perimeter of a rectangle with a length of 3x + 3 and a width of x - 1
Answer:
P = 8x+4
Step-by-step explanation:
The perimeter of a rectangle is found by using the formula
P = 2(l+w)
We know l = 3x+3 and
w = x-1
Substitute these values in
P =2(3x+3 + x-1)
Combine like terms
P = 2(4x+2)
Distribute the 2
P = 8x+4
?Write the equation in standard form. Then factor the left side of the equation.? 2x2 = 28 – x A.) (2x + 7)(x – 4) = 0 B.) (2x – 7)(x + 4) = 0 C.) (2x + 4)(x + 7) = 0 D.) (2x – 4)(x + 7) = 0
2x² = 28 - x
2x²+x-28=0
2x²+8x-7x-28=0
2x(x+4)-7(x+4)=0
(x+4)(2x-7)=0
(2x-7)(x+4)=0
B.) (2x - 7)(x + 4) = 0
What is the probability that she would get heads two of the times?
There are 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Of these 4 have at least two heads. Assuming a fair coin, the probability of tossing at least two heads is 4/8 or 1/2. The Answer would probably be 3/8 though.
C) 3/8
Step-by-step explanation:The probability of heads is 1/2, so the probability of not-heads is 1/2.
Then the probability of 2 heads and a tails is (1/2)²·(1/2) = 1/8.
There are 3 choose 2 = (3·2)/(2·1) = 3 ways that the pair of heads may appear among the three tosses. Thus the probability of 2 heads in 3 tosses is ...
... 3·(1/8) = 3/8
_____
Or you can simply count the favorable outcomes among the possible outcomes:
TTT TTH THT THH HTT HTH HHT HHH . . . . 3 of 8 are favorable.
You and your friend are both saving your allowance for your summer vacation you have $48.50 in the bank
Answer:
B
Step-by-step explanation:
) The function g(x) = x^3 + (x + 1)^2
is used to create this table. Find the missing values. Must show work
for full credit.
Answer:
g(-1) = -1
g(1) =5
Step-by-step explanation:
g(x) = x^3 + (x + 1)^2
If x=-1 substitute this into the equation
g(-1) = (-1) ^3 + (-1+1)^2
g(-1) = 1+0 =-1
If x=1 substitute this into the equation
g(1) = (1)^3 + (1+1)^2 = 1+2^2 = 1+4 =5
Hi There!
--------------------------------------
Function: g(x) = x³ + (x + 1)²
Substitute: -1
Substitute: g(-1) = -1³ + (-1 + 1)²
Remember to follow PEMDAS.
Parenthese's: g(-1) = -1³ + (0)²
Exponents: g(-1) = -1 + 0
Simplify: g(-1) = -1
--------------------------------------
Function: g(x) = x³ + (x + 1)²
Substitute: 1
Substitute: g(1) = 1³ + (1 + 1)²
Remember to follow PEMDAS.
Parenthese's: g(1) = 1³ + (2)²
Exponents: g(1) = 1 + 4
Simplify: g(1) = 5
--------------------------------------
Hope This Helps :)