Answer:
θ = 0°
θ = 30°
θ = 150°
θ = 180°
Step-by-step explanation:
2sin² θ = sin θ
Then
2sin² θ - sin θ = 0
Then
sin θ (2sin θ - 1) = 0
Then
sin θ = 0 or 2sin θ - 1 = 0
Then
sin θ = 0 or sin θ = 1/2
…………………………………………
We have sin θ = 0 and - 270° ≤ θ ≤180°
Then
θ = 0 or θ = π = 180°
On the other hand,
sin θ = 1/2 and - 270° ≤ θ ≤180°
Then
θ = π÷6 or θ = 5π÷6
π÷6 = 30° and 5π÷6 = 150°
If the population of
an alien race doubles
every two minutes,
how long will it take
for the population to
grow from 1,000 to 32,000 ?
It will take 32 minutes for the population to grow from 1,000 to 32,000.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If the population of an alien race doubles every two minutes,
1,000 x 32 = 32,000
Hence, It would take 32 minutes.
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What is the solution to
[tex] \sqrt{ - x} = \sqrt{x + 13} [/tex]
Answer: -6.5
Step-by-step explanation:
First, you take the values on both sides to the power of 2 to get:
-x = x + 13
Subtract x on both sides.
-2x = 13
Divide both sides by -2.
x = -6.5
Answer:
[tex]x=-\dfrac{13}2[/tex]
Step-by-step explanation:
[tex]~~~~~\sqrt{-x} = \sqrt{x+13}\\\\\implies -x= x+13~~~~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\implies -x -x = 13\\\\\implies -2x = 13\\\\\implies x = -\dfrac{13}2\\\\\text{Verify solution:}\\\\~~~~~~~\sqrt{-\left(- \dfrac{13} 2 \right)} = \sqrt{-\dfrac{13}2 +13}\\\\\\\implies \sqrt{\dfrac{13}2} = \sqrt{\dfrac{13}2}\\\\\text{Hence, the solution is}~ x=-\dfrac{13}2[/tex]
A group of students measured the lengths of their shoes. The lengths are listed in the table. Use the table to locate the incorrect data in the line plot.
I think the incorrect data is the second x to the left.
What is the ratio of the area of sector abc to the area of sector dbe? a. b. c. d. e.
The ratio of the area of sector abc to the area of sector dbe is 4/3
How to determine the ratio of the areas?For sector abc, we have:
Angle = x
Radius = 2r
For sector dbe, we have:
Angle = 3x
Radius = r
The area of a sector is:
[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]
So, we have:
[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]
Evaluate
[tex]ABC =\frac{x* \pi r^2}{90}[/tex]
For DBE, we have:
[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]
Evaluate
[tex]DBE =\frac{x}{120}* \pi r^2[/tex]
The ratio of both areas is:
[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]
Cancel out the common factors
[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]
Express as fraction
[tex]Ratio = \frac{120}{90}[/tex]
Divide
[tex]Ratio = \frac{4}{3}[/tex]
Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3
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4/3
its the answer edmentum
Write an equation in slope intercept form of the line that passes through the point (0,4) with slope 2
Answer:
y=2x+4
Step-by-step explanation:
From(0,4)
y intercept=b=4Equation in slope intercept form
y=mx+by=2x+4x+y=5
3x-y=7
solve this equation
9. Latoya's mom makes her a birthday cake in the shape of an "L". Latoya loves frosting,
so her mom covers the entire outside of the cake in frosting, even the bottom of the
cake.
4 in
12 in
2 in
9 in
How much space does Latoya's mom cover in frosting?
inches²
8 in
4 in
Answer:
223
Step-by-step explanation:
find the area for each side.
Which point is located at (3, -1)?
A. point A
B. point D
C. point E
D. point F
Answer:
i think its point D. So that means the answer is B. I think so because if the middle like going side to side is marked first then it must mean the positive is first and so it's point D
Use inductive reasoning to find the 10th term in the sequence 5, 8, 11, 14, ...
34
32
50
17
Answer: 32
Step-by-step explanation: this is arithmetic sequence
general formula = a+(n-1)d
nth term = 5+(n-1)3
=5+3n-3
=2+3n
10th term = 2+3(10)
=32
A pilot scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 10 minutes. Air traffic control approved a new flight plan that will allow her to arrive three times faster then she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
A. Y = 1/3x + 10
B. Y = 3x + 10
C. Y = 1/3x - 10
D. Y = 3x - 10
y = (1/3)x+10
=============================================================
Explanation:
x = number of minutes of the original flight
Because the pilot travels 3 times faster than before, it means she travels 1/3 of the original time. If she took x minutes on the original flight, then she will take (1/3)x minutes for the new faster flight.
Then add on the 10 minute delay to end up with (1/3)x+10
I need help please question is in the image
Select the correct answer. if a coin is flipped 10 times, what is the probability that it will show all heads or all tails? a. b. c. d. e.
Answer:
Step-by-step explanation:
1/2 chance for 1
1/4 for 2
1/8 for 3
1/16 for 4
1/32 for 5
1/64 for 6
1/128 for 7
1/256 for 8
1/512 for 9
1/1024 for 10
Determine the value of x. : A) B) 4 C) 4 D) 8
For an experiment, Sandra needs 20 grams of a 26% solution of salt. She has two large bottles of salt water: one contains a 20% solution, and the other contains 35% solution. How much of each must she use to make the solution she needs?
The amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.
Amount of gramsx grams of 20% and 20-x grams of 35%
Hence:
0.20x+0.35(20-x)=0.26×20
0.20x-0.35x+7=5.2
Collect like terms
-0.15x=-1.80
Divide both side by -0.15x
x=-1.80/-0.15
x=12 grams of 20% or 2.4 grams pure
20-x= (20-12) =8 grams of 35% or 2.8 grams pure
Therefore the amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.
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Consider triangle ABC. What is b?
7x<5x-16
It’s an inequality question
Answer:
7x <5x-16
Step-by-step explanation:
7x-5x < 5x -16 -5x
Drag the correct value into each box on the number line.
To identify the value that goes in each box, we must perform the corresponding operation and calculate the final result.
How to perform a mathematical operation?In mathematics there are procedures such as addition (+), subtraction (-), division (÷), and multiplication (×) to solve problems. These operations are the four basic operations of mathematics.
According to the above, what we must do is identify what operation we must perform with the given numbers and then identify the result and put it in the corresponding box.
Note: This question is missing because there is some information missing. Howeve i can answer it based on my general knowledge.
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Please answer its iready press the image below.
30 points btw
Answer:
alternate exterior angles
Step-by-step explanation:
<3 i hope this helps! sorry if it doesnt :)
Find the exact length of side a.
The exact length of a which is equivalent to BC is 7units
Cosine ruleA triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule
c² = a² + b² - 2abcosC
Given the following parameters
b = 2
c = 5√3
theta = 30 degrees
Substitute
c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2
c² = 79 - 30
c² = 49
c = 7 units
Hence the exact length of a which is equivalent to BC is 7units
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In circle O, ST is a diameter.
Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
What must be the value of x?
22.0
25.0
25.4
37.2
The value of x must be 25.0. The correct option is the second option- 25.0
Solving Linear equationsFrom the question, we are to determine the value of x
From the given diagram, we can write that
m ∠SOR + m ∠UOR + m ∠TOU = 180° (Sum of angles on a straight line)
∴ (2x +8)° + (3x - 14)° + (3x -14)° = 180°
2x° + 8° + 3x° -14° + 3x° -14° = 180°
Collect like terms
2x° + 3x° + 3x° + 8° - 14° -14° = 180°
8x° -20° = 180°
8x° = 180° + 20°
8x° = 200°
x = 200/8
x = 25.0
Hence, the value of x must be 25.0. The correct option is the second option- 25.0
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Answer:
25.0
Step-by-step explanation:
just took it
\
Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m 0.02 2.1m = –1.45 – 4.81m
Answer:
Pretty certain it's 100
chandra is constructing a weighted bookend for her shelf. it is a hollow rectangular prism, as shown, and she will fill it with sand to weigh it down
Since it is said to be a hollow rectangular prism, she will fill it with sand to weigh it about (573 + 9/2) cubic inches.
What is the prism about?
Note that the volume is said to be:
V = L x B x H
316 in = 6 √2 x 2 √3
The answer is 573 while the other part of the prison is 9√2 cubic inches.
Therefore, option A is correct.
See full question below
Chandra is constructing a weighted bookend for her shelf. It is a hollow rectangular prism, as shown, and she will fill it with sand to weigh it
down
6 √(2 in
316 in
2 √3 in
What is the volume of the bookend?
(Hint: The volume of a rectangular prism is the product of its length width and height.)
OA (573 + 9/2) cubic inches
B. 36/12 cubic inches
C 108 cubic inches
D. 216 cubic inches
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Help will name brainliest
[tex]\text{For angle N,}\\\\PQ= \text{Perpendicular.}\\\\QN = \text{Hypotenuse.}\\\\\text{Now,}\\\\\sin N = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\~~~~~~~=\dfrac{QP}{QN}[/tex]
Use mathematical induction to prove
[tex]Prove\ that\ the\ assumption \is \true for\ n=1\\1^3=\frac{1^2(1+1)^2}{4}\\ 1=\frac{4}{4}=1\\[/tex]
Formula works when n=1
Assume the formula also works, when n=k.
Prove that the formula works, when n=k+1
[tex]1^3+2^3+3^3...+k^3+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k+1)^2}{4}+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k^2+2k+1)}{4}+(k+1)^3=\frac{(k^2+2k+1)(k^2+4k+4)}{4} \\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+4k^3+4k^2+2k^3+8k^2+8k+k^2+4k+4}{4}\\\\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+2k^3+k^2}{4}+\frac{4k^3+12k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+6k^3+13k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\[/tex]
Since the formula has been proven with n=1 and n=k+1, it is true. [tex]\square[/tex]
14 + w is the same as which expression?
A
14w
B
14 - w
C
w + 14
D
w - 14
Answer:
C
Step-by-step explanation:
14 + w is the same as w + 14
Answer:
C. w + 14.
Step-by-step explanation:
The order does not matter when you are adding terms.
this is called the Commutative Property of Addition.
This Stem-and-Leaf Plot shows the scores of 10 students on a recent math test.
Which statistic is most affected by the lowest score?
A. the mean
B. the median
C. the mode
D. the mean and the median
The statistic that is most affected by the lowest score is A. the mean
How to determine the most affected statistic?The stem and leaf plot is missing from the question;
However, the question can be solved without it.
The lowest score on the stem and leaf plot is an outlier of the plot.
In statistics, outliers have huge effect on the mean of the dataset and they have little or no effect on the median and mode
This means that, the statistic that is most affected by the lowest score is A. the mean
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Drag the expressions to show the order of their quotients from least to greatest
Answer:
by solving the divisions
Step-by-step explanation:
8/9 ÷ 7/11 = 8/9 × 11/7 = 88/63 = 1.4019/12 ÷ 3/10 = 19/12 × 10/3 =190/36 = 5.2819/12 ÷ 1/15 = 19/12 × 15 = 285/12 = 23.758/9 ÷ 3/10 = 8/9 × 10/3 = 80/27 = 2.96.
now from the solutions you can get the least to greatest
1.40 , 2.96, 5.28 and 23.75
After getting answer in decimal form change it to fraction like how they set the question
The area A of a circle is the product of π and the radius r squared
i need written in a algebraic equation
Answer:
A=πr^2
Step-by-step explanation:
A=π*r^2
Where, A is area of circle
r is radius of circle
π is constant
.
Hope it's help and I think I have give brainleist answer
Answer:
πr^2
Step-by-step explanation:
it's just πr^2.
easy
Solve: -1/2 + c = 31/4
(1/2 and 31/4 are fractions)
[tex]~~~-\dfrac 12 + c = \dfrac{31}4\\\\\\\implies c = \dfrac{31}{4}+\dfrac 12\\\\\\\implies c = \dfrac{31}{4}+ \dfrac 24\\\\\\\implies c = \dfrac{31+2}{4}\\\\\\\implies c = \dfrac{33}4[/tex]
Calculate the volume of a cube of length 8 m
Answer:
V =512 m^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = 8^3
V =512 m^3