Answer:
its all of them except for A cuz i got it wrong with the other answer.
Step-by-step explanation:
A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.
What is a pentagon?A pentagon is a polygon that has five sides and five angles. A regular pentagon is a pentagon in which all the sides are equal. A line of symmetry is a line that cuts a shape exactly in half.
A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.
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What is a requirement of supplementary angles?
Answer:
Two Angles are Supplementary when they add up to 180 degrees.
Step-by-step explanation:
Notice that together they make a straight angle.
Solve 2x-3/5=x+6 ASAP
Answer:
Problem 1: [tex]\frac{2x-3}{5}=x+6[/tex] gives x=-11
Problem 2: [tex]2x-\frac{3}{5}=x+6[/tex] gives x=33/5
Step-by-step explanation:
I will do it both ways:
Problem 1:
[tex]\frac{2x-3}{5}=x+6[/tex]
I don't like the fraction so I'm going to clear by multiplying both sides by 5:
[tex]2x-3=5(x+6)[/tex]
Distribute:
[tex]2x-3=5x+30[/tex]
Subtract 2x on both sides:
[tex]-3=3x+30[/tex]
Subtract 30 on both sides:
[tex]-33=3x[/tex]
Divide both sides by 3:
[tex]-11=x[/tex]
Problem 2:
[tex]2x-\frac{3}{5}=x+6[/tex]
Clear the fraction by multiplying both sides by 5:
[tex]5(2x-\frac{3}{5})=5(x+6)[/tex]
Distribute:
[tex]10x-3=5x+30[/tex]
Subtract 5x on both sides:
[tex]5x-3=30[/tex]
Add 3 on both sides:
[tex]5x=33[/tex]
Divide both sides by 5:
[tex]x=\frac{33}{5}[/tex]
For this case we must solve the following equation:
[tex]\frac {2x-3} {5} = x + 6[/tex]
Multiplying by 5 on both sides we have:
[tex]2x-3 = 5 (x + 6)\\2x-3 = 5x + 30[/tex]
We add 3 to both sides of the equation:
[tex]2x = 5x + 30 + 3\\2x = 5x + 33[/tex]
Subtracting 5x on both sides:
[tex]2x-5x = 33\\-3x = 33[/tex]
Dividing between -3 on both sides:
[tex]x = \frac {33} {- 3}\\x = -11[/tex]
Answer:
-11
A normal distribution has a mean of 50 and standard deviation of 5. Which value produces a negative z-score?
Answer:
[tex]x\:<\:50[/tex].
Step-by-step explanation:
The z-score for a normal distribution is calculated using the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex].
From the question, the distribution has a mean of 50.
[tex]\implies \mu=50[/tex] and the standard deviation is [tex]\sigma=5[/tex].
For a z-score to be negative, then, [tex]\frac{x-\mu}{\sigma}\:<\:0[/tex].
[tex]\frac{x-50}{5}\:<\:0[/tex].
[tex]x-50\:<\:0\times 5[/tex].
[tex]x-50\:<\:0[/tex].
[tex]x\:<\:0+50[/tex].
[tex]\therefore x\:<\:50[/tex].
Any value less than 50 will produce a negative z-score
Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges?
square pyramid
triangular prism
rectangular prism
triangular pyramid
Rectangular prism: 6 faces (4 lateral, 2 bases), 8 vertices, 12 edges, meeting all criteria specified.
let's break down the characteristics of each of the options provided:
1. **Square Pyramid**:
- Faces: A square pyramid has five faces. It has a square base and four triangular faces.
- Vertices: A square pyramid has five vertices.
- Edges: A square pyramid has eight edges (the base square has four edges, and each triangular face has one edge).
2. **Triangular Prism**:
- Faces: A triangular prism has five faces. It has two triangular bases and three rectangular lateral faces.
- Vertices: A triangular prism has six vertices.
- Edges: A triangular prism has nine edges (three on each base triangle and three connecting the lateral faces).
3. **Rectangular Prism**:
- Faces: A rectangular prism has six faces. It has two rectangular bases and four rectangular lateral faces.
- Vertices: A rectangular prism has eight vertices.
- Edges: A rectangular prism has 12 edges (four on each base rectangle and four connecting the lateral faces).
4. **Triangular Pyramid**:
- Faces: A triangular pyramid has four faces. It has a triangular base and three triangular lateral faces.
- Vertices: A triangular pyramid has four vertices.
- Edges: A triangular pyramid has six edges (three on the base triangle and three connecting the lateral faces).
Given the characteristics you provided: six faces, four lateral faces, two bases, eight vertices, and 12 edges, we can eliminate the options of square pyramid and triangular pyramid because they don't fit all the criteria.
Now let's look at the remaining options:
- **Triangular Prism** has five faces, six vertices, and nine edges. It doesn't match the given criteria.
- **Rectangular Prism** has six faces (two bases and four lateral faces), eight vertices, and 12 edges, which perfectly matches all the provided characteristics.
Therefore, the correct answer is the **Rectangular Prism**.
Cecilia correctly solved this inequality.
3x > 102
X> 34
Which graph matches the inequality?
28 29 30 31 32 33 34 35 36 37 38 39 40
28 29 30 31 32 33 34 35 36 37 38 39 40
The graph of the inequality x > 34 is graphed
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Given the inequality:
3x > 102
Divide the inequality by 3:
x > 34
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Which angle is coternal with 130 degrees?
Answer:
- 230°
Step-by-step explanation:
A coterminal angle is the given angle ± 360n ( where n is an integer )
Given 130°
Then a coterminal angle = 130° - 360° = - 230°
OR 130° + 360° = 490°
which function results after applying the sequence of transformations to f(x) = x^5
This is the final function f(x) = (-2(x-2))^5 after a horizontal shrink, reflection, and shift.
To determine which function results after applying a given sequence of transformations to the original function f(x) = x^5, we need to apply each transformation in the correct order. Transformations affect the graph and the function's formula. Here is how you would apply the transformations in the correct order:
f(2x): Multiply the independent variable by 2, which shrinks the graph horizontally by half. The function becomes f(x) = (2x)^5.
f(-2x): Negate the independent variable x, which flips the graph across the y-axis. The function becomes f(x) = (-2x)^5.
f(-2x-2): Subtract 2 from the result of -2x. This is incorrect as the sequence of operations should reflect transformations applied directly to the independent variable x. Instead, it should be f(x-2) after step (ii), which translates the graph to the right by 2 units.
If we were to correct the third operation and apply the transformations properly, the resulting function after applying a horizontal shrink, reflection across the y-axis, and horizontal shift would be f(x) = (-2(x-2))^5.
The Outlanders Club keeps track of the mean and median ages of its members. The ages of the six members are 26, 18, 42, 22, 38,
and 34. Which will increase more, the mean or the median, when a new member who is 65 years old joins?
A translation is shown on the grid below.
Which are true statements about the translation?
1 The sides of the image and preimage are congruent.
2 The image is turned 90 degrees.
3 The angles in the image are different from the angles in the pre-image
4 The image is a slide of the preimage.
5 The image has a different shape than the pre-image
6 Each point has moved in a different direction.
7 Each point has moved the same number of units.
Answer:
The correct options are 1, 4 and 7.
Step-by-step explanation:
From the given figure it is clear that the vertices of preimage are A(-4,2), B(-4,-2) and C(-1,-2).
The vertices of image are A'(1,5), B'(1,1) and C'(4,1).
The relation between vertices of preimage and image is defined by the rule
[tex](x,y)\rightarrow (x+5,y+3)[/tex]
It means the figure ABC translated 5 units right and 3 units up.
Translations a rigid transformation. It means the size and shape of image and preimage are same.
We can say that,
(a) The sides of the image and preimage are congruent.
(b) The angles in the image and angles in the pre-image are same.
(c) The image is a slide of the preimage.
(d) The image and pre-image have same shape.
(e) Each point has moved in same direction.
(f) Each point has moved the same number of units.
Therefore the correct options are 1, 4 and 7.
May someone plz help me
Answer:
y = -1/2 x +5
10 weeks
Step-by-step explanation:
The y intercept is 5 ( That is is the point where x=0)
Our slope is rise over run or 1 lb /2 weeks
We know this is negative because the cat is losing the weight
slope = -1/2
The equation in slope intercept form is
y= mx + b where m is the slope and b is the y intercept
y = -1/2 x +5
We need to determine when y=0 to find when the cat loses all 5 lbs
0 = -1/2 x +5
Subtract 5 from each side
0-5 = -1/2x +5-5
-5 = -1/2x
Multiply each side by -2 to get x alone
-5 *-2 = -1/2x * -2
10 = x
It will take 10 weeks
Answer:
y = -1/2x + 5
It will take 10 weeks for the cat to lose 5 pounds.
Step-by-step explanation:
Find slope
Take 2 points (2,4) (6,2)
y2 - y1/x2 - x12 - 4/6 - 2slope = -1/2
y-intercept
(0,5)
y = mx + b form
m represents slope
b represents y-intercept
y = -1/2x + 5
Find the number of weeks it will the cat to lose 5 pounds
Set y = to 0, to find when the cat loses weight
0 = -1/2x + 5
Subtract 5 in both sides
-5 = -1/2x
Isolate the variable by getting rid of the denominator
-1/2x * 2 = -x
2 * - 5 = -10
Simplify
-x = -10
Divide both sides by -1
-x/-1 = x
-10/-1 = 10
Simplify
x = 10
Answer
It will take 10 weeks for the cat to lose 5 pounds
According to the rational root theorem what are all the potential rational roots of f(x)=9x^4-2x^2-3x+4
Answer:
+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....
Step-by-step explanation:
The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the leading coefficient of the function
Given: f(x)= 9x^4-2x^2-3x+4
Factors of q (leading coefficient) are: +/-9, +/-3, +/-1
Factors of p (constant term) are: +/-4 , +/-2, +/- 1
According to the theorem we write the roots in p/q form:
Therefore,
p/q =+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....
Caleb took his sled to the top of the hill. The snow was pure and white. He jumped on the sled and whizzed down the hill. He was so excited. Winter was his favorite season. He went down the hill three times. Each time he traveled ninety feet. How far did he travel on his sled?
Help summer Homework
Which inequality is not true? -7/8 > -0.50 -7/8 < -0.60 -7/8 < -1/4 -7/8 > -15/16
Shirley is drawing triangles that have the same area. the base of each triangle inversely with the heigh. what are the possible base and height of a second triangle if the first triangles base is 12 and its height is 8.
select one:
a. 120 and 80
b. 10 and 10
c. 60 and 36
b. 16 and 6
Answer:
A
Step-by-step explanation:
they're proportional
Answer: the answer is A
Step-by-step explanation:
have a good day
Find the tan θ when sin θ= -cos θ and θ is in quadrant IV
Answer:
Step-by-step explanation:
sin θ= - cos θ
if : cos θ ≠ 0
you have : tan θ = -1
tan θ = - tan π/4
tan θ = tan(- π/4 )
θ = - π/4 +kπ k ∈ Z
calculate: k when θ is in quadrant IV : 3π /2 ≤ θ ≤2π
3π /2 ≤ - π/4 +kπ ≤2π
add π/4: 3π /2 + π/4 ≤ - π/4 +kπ+π/4 ≤2π +π/4
7π/4 ≤ kπ ≤9π/4
7/4 ≤ k ≤9/4
1.75 ≤ k ≤ 2.25
k ∈ Z : k =2
so : θ = - π/4 +2π
θ = 7π/4
θ = 7(180°)/4 = 315°
You have a total of $1760 to invest. Account A pays 7% annual interest and account B pays 4% annual interest. How much should you invest in each account if you would like the investment to earn $ 95 at the end of one year? Let A represent the amount of money invested in the account that earns 7% annual interest and let B represent the amount of money invested in the account that earns 4% annual interest. Complete the system of linear equations to solve the problem.
Answer:
You should invest $820 in account A and $940 in account B
Step-by-step explanation:
* Lets use the system of linear equations to solve the problem
- Simple Interest Equation I = Prt , Where:
# P = Invested Amount
# I = Interest Amount
# r = Rate of Interest per year in decimal; r = R/100
# t = Time Period involved in months or years
* Lets solve the problem
- The total money invested is $1760
- Account A pays 7% annual interest
- Account B pays 4% annual interest
- Let A represent the amount of money invested in the account A
- Let B represent the amount of money invested in the account B
- You would like to earn $ 95 at the end of one year
∴ The interest from both accounts at the end of one year is $95
- Lets write the equations
# Account A :
∵ Account A has $A invested
∴ P = $A
∵ Account A pays 7% annual interest
∴ r = 7/100 = 0.07
∵ t = 1 year
∵ I = Prt
∴ I = A(0.07)(1) = 0.07A
# Account B :
∵ Account B has $B invested
∴ P = $B
∵ Account A pays 4% annual interest
∴ r = 4/100 = 0.04
∵ t = 1 year
∵ I = Prt
∴ I = B(0.04)(1) = 0.04B
- The total amount of interest from both accounts at the end of one
year is $95
∴ I from A + I from B = 95
∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100
∴ 7A + 4B = 9500 ⇒ (1)
- The total money to invest in both accounts is $1760
∵ Account A has $A invested
∵ Account B has $B invested
∴ A + B = 1760 ⇒ (2)
* Lets solve the system of equations to find the amount of money
invested in each account
- Multiply equation (2) by -4 to eliminate B
∵ A + B = 1760 ⇒ × -4
∴ -4A - 4B = -7040 ⇒ (3)
- Add equation (1) and (3)
∵ 7A + 4B = 9500 ⇒ (1)
∵ -4A - 4B = -7040 ⇒ (3)
∴ 7A - 4A = 9500 - 7040
∴ 3A = 2460 ⇒ divide both side by 3
∴ A = 820
- Substitute the value of A in equation (1) or (2)
∵ A + B = 1760 ⇒ (2)
∴ 820 + B = 1760 ⇒ subtract 820 from both sides
∴ B = 940
- From all above
* You should invest $820 in account A and $940 in account B
NEED HELP ASAP (RADICALS)
Order from least to greatest:
[tex]\sqrt{9}[/tex]
-6[tex]\sqrt{5}[/tex]
5[tex]\sqrt{3}[/tex]
-5[tex]\sqrt{6}[/tex]
plzzz hurry up and help me if A+B=45
prove that
(1+tanA)(1+tanB)=2
Answer:
see explanation
Step-by-step explanation:
If A +B = 45° then tan(A+B) = tan45° = 1
Expanding (1 + tanA)(1 + tanB)
= 1 + tanA + tanB + tanAtanB → (1)
Using the Addition formula for tan(A + B)
tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above
Hence
tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )
tanA + tanB + tanAtanB = 1 ( add 1 to both sides )
1 + tanA + tanB + tanAtanB = 2
Then from (1)
(1 + tanA)(1 + tanB) = 2 ⇒ proven
Which polynomial represents the sum below (4x^2+1)+(4x^2+x+2)
Answer:
8x^2 + x + 3.
Step-by-step explanation:
(4x^2+1)+(4x^2+x+2)
= 8x^2 + x + 2 + 1
= 8x^2 + x + 3.
Answer:
The polynomial [tex]8x^2+x+3[/tex] represents the sum of given expression.
Step-by-step explanation:
The given expression is
[tex](4x^2+1)+(4x^2+x+2)[/tex]
We need to find the sum of given polynomials.
Open the brackets.
[tex]4x^2+1+4x^2+x+2[/tex]
Combine like terms.
[tex](4x^2+4x^2)+x+(1+2)[/tex]
On further simplification we get
[tex]8x^2+x+3[/tex]
Therefore the polynomial [tex]8x^2+x+3[/tex] represents the sum of given expression.
Solve the following system using the elimination method: 2x-4y=2 -4x+6y=-4
Answer:
(1, 0)
Step-by-step explanation:
Given the 2 equations
2x - 4y = 2 → (1)
- 4x + 6y = - 4 → (2)
Multiplying (1) by 2 and adding to (2) will eliminate the x- term
4x - 8y = 4 → (3)
Add (2) and (3) term by term
(- 4x + 4x) + (6y - 8y) = (- 4 + 4), simplifying gives
- 2y = 0 ⇒ y = 0
Substitute y = 0 in (1) or (2)
Substituting in (1) gives
2x - 0 = 2, that is
2x = 2 ( divide both sides by 2 )
x = 1
Solution is (1, 0 )
Find the value 7+3^2(-5+1)divided by 2
The expression 7 + 3^2(-5 + 1) divided by 2 equals -14.5, after calculating the exponent, solving the parenthesis, multiplying, adding to 7, and then dividing by 2.
Explanation:To find the value of the expression 7 + 32(-5 + 1) divided by 2, follow these steps:
Calculate the exponent: 32 = 9.Solve the parenthesis: (-5 + 1) = -4.Multiply the results from steps 1 and 2: 9 * -4 = -36.Add the result from step 3 to 7: 7 - 36 = -29.Finally, divide by 2: -29 / 2 = -14.5.The value of the expression is -14.5.
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help !! I can’t find the answer
Answer:
385/pi
Step-by-step explanation:
Circumference is given by
C= pi * d where d is the diameter
385 = pi *d
Divide each side by pi
385/pi = pi * d/pi
385/pi = d
The first number in a sequence is 8. If each number in the sequence is 10 less than three times the previous number, then what will the fourth term be?
The fourth term of the arithmetic series is 38.
Given that, the first number in arithmetic series (a)=8 and common difference (d) =10.
What is the nth term of the arithmetic series?The nth term of the arithmetic series is [tex]a_{n} =a+(n-1) \times d[/tex].
Now, the fourth term= [tex]a_{4} =8+(4-1) \times 10[/tex]
=8+30=38
Therefore, the fourth term of the arithmetic series is 38.
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What is the value of b in the equation below?
5^6/5^2=a^b
3
4
5
8
Answer:
b=4
Step-by-step explanation:
subtract the exponents
6-2=4
The value of b is 4.
What is exponent ?Exponent is a mathematical method to express large numbers in power form. It will describe how many times a number multiplied by itself.
Example : 7⁵ , where the number 7 multiplied 5 times by itself.
What is the required value of b ?Given, 5⁶/5² = 5ᵇ
We know that, in exponent, if [tex]a^{m}=a^{n}[/tex], then m=n
Here, 5⁶/5² = 5ᵇ
⇒ [tex]5^{6-2} =5^{b}[/tex]
⇒ [tex]5^{4} =5^{b}[/tex]
∴ By the above rule, b = 4
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What are the solutions to the equation 3(x-4)^2=27
Answer:
x=1, x=7
Step-by-step explanation:
Firstly, you can simplify by dividing both sides by 3, which will make the equation easier to simplify:
(x-4)^2=9
Next, you can take the square root of each side, which will cancel the square, and make the 9 even easier to work with:
(x-4)=(± )3
*Note the (± ) sign, this is because there is a positive and negative answer*
After this, you will basically have two equations:
(x-4)=3
and
(x-4)=-3
You are going to solve both to get both answers, but lets start with the positive first:
x-4=3 Add 4 to both sides to get an x= equation
x=7
And it's the same thing for the negative:
x-4=-3 Add 4 to both sides to get an x= equation
x=1
Hope this helps
Final answer:
To solve the equation 3(x-4)²=27, divide by 3 to get (x-4)²=9, then take the square root to find the solutions x=7 and x=1.
Explanation:
When we're tasked with solving a quadratic equation, such as 3(x-4)²=27, we first need to get it into the standard form of a quadratic equation, which is ax² + bx + c = 0. To do so in this case, we can divide both sides of the equation by 3 to isolate the squared term, yielding (x-4)²= 9. We then take the square root of both sides, giving us x - 4 =3. Solving for x results in two solutions: x = 4 + 3 and x = 4 - 3, which simplifies to x = 7 and x = 1 respectively. These are the solutions to the given equation.
To verify these solutions, you can substitute them back into the original equation to ensure that they satisfy the equation, which in this case, they will. This critical step confirms the accuracy of our solutions.
- 18
A scientist rolls two balls A and B down two different ramps. Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14
meters in the 3rd second, and so on. Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd
second, and so on. How many meters would each ball roll in 10 seconds?
Select one
a. A: 49 m: B: 305 m
b. A: 54 m; B: 33.5 m
CA: 59 m: B: 36.5 m
d. A: 85 m: B: 72 m
Answer:
a. A. 49m B 30.5 m
Step-by-step explanation:
If I have understood the question correctly:
Ball A:
After each second the total distance travelled increases by 5 meters.
Ball A: after 10 seconds it has rolled 4 + (10-1) * 5 = 49m
Ball B: after 10 seconds it has rolled 3.5 + (10-1)* 3 = 30.5 m.
Answer:
Option A. A: 49 m: B: 30.5 m
Step-by-step explanation:
Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14 meters in the 3rd second, and so on.
We can see that after each second the total distance traveled by ball increases by 5 meters.
So, we can solve this as an arithmetic sequence that is [tex]a+(n-1)d[/tex]
For ball A, a = 4 n = 10 d = 5
Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd second, and so on.
For ball B, a = 3.5 n = 10 d = 3
For ball A:
After 10 seconds, the distance will be [tex]4+(10-1)5[/tex]
= [tex]4+45[/tex] = 49 meters
For ball B:
After 10 seconds, distance covered will be [tex]3.5+(10-1)3[/tex]
= [tex]3.5+27[/tex] = 30.5 meters.
Hence, the answer is option A.
6 = 3x - 9
x + 4 < 1
x/2 + 3 = -5
Answer:
see explanation
Step-by-step explanation:
1
6 = 3x - 9 ( add 9 to both sides )
15 = 3x ( divide both sides by 3 )
5 = x
2
x + 4 < 1 ( subtract 4 from both sides )
x < - 3
3
[tex]\frac{x}{2}[/tex] + 3 = - 5
Multiply terms on both sides by 2
x + 6 = - 10 ( subtract 6 from both sides )
x = - 16
Which pair of points will determine a line
parallel to the x-axis?
(1) (2,3), (2,-5)
(2) (5, 4), (-1, 4)
(3) (2, 2), (-1, -1)
(4) (3, 4), (6,2)
Please help I don’t get it I’m stuck:(
Answer:
2) (5,4) and (-1,4)
These have the same y so this line will be horizontal making it parallel to the x-axis.
Step-by-step explanation:
All horizontal lines are parallel to each other. The x-axis is horizontal. So we are looking for a horizontal line. On a horizontal line, all the y-coordinates are the same; their equation is in the form y=a number after all.
Anyways we looking for a pair of points with the same y-coordinate.
1) (2,3) and (2,-5)
These have the same x-coordinate so this line is vertical. This would actually be perpendicular to the line given.
2) (5,4) and (-1,4)
These have the same y so this line will be horizontal making it parallel to the x-axis.
3) (2,2) and (-1,-1)
y's aren't the same so not horizontal
x's aren't the same so not vertical
4) (3,4) and (6,2)
y's aren't the same so not horizontal
x's aren't the same so not vertical
For a pair of points to be parallel to the x-axis, the points have to consist the same x-coordinates.
In this case, only (1) (2,3), (2,-5) have the same x-coordinates.
Therefore, the answer is (1) (2,3), (2,-5).
Hope it helps!
Solve sin2∅=sin∅ on the interval 0≤x< 2[tex]\pi[/tex] .
a. 0,[tex]\frac{\pi }{3}[/tex]
b. 0, [tex]\pi[/tex], [tex]\frac{\pi }{3}[/tex], [tex]\frac{5\pi }{3}[/tex]
c. 0, [tex]\pi[/tex], [tex]\frac{2\pi }{3}[/tex],[tex]\frac{4\pi }{3}[/tex]
d. [tex]\frac{3\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex],[tex]\frac{\pi }{6}[/tex], [tex]\frac{5\pi }{6}[/tex]
Answer:
[tex]\large\boxed{b.\ 0,\ \pi,\ \dfrac{\pi}{3},\ \dfrac{5\pi}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \sin2x=2\sin x\cos x\\\\\sin2\O=\sin\O\\\\2\sin\O\cos\O=\sin\O\qquad\text{subtract}\ \sin\O\ \text{from both sides}\\\\2\sin\O\cos\O-\sin\O=0\qquad\text{distribute}\\\\\sin\O(2\cos\O-1)=0\iff\sin\O=0\ \vee\ 2\cos\O-1=0[/tex]
[tex]\sin\O=0\iff\O=0\ \vee\ \O=\pi\\\\2\cos\O-1=0\qquad\text{add 1 to both sides}\\\\2\cos\O=1\qquad\text{divide both sides by 2}\\\\\cos\O=\dfrac{1}{2}\iff\O=\dfrac{\pi}{3}\ \vee\ \O=\dfrac{5\pi}{3}[/tex]
Jacob is calculating the amount of time it takes a rocket to get to the moom
Answer:
16 hours
Step-by-step explanation:
Speed=distance/time
Let S be speed, D be distance, and t be time.
Let's solve the speed equation for t since we are looking for time, t.
[tex]S=\frac{D}{t}[/tex]
Multiply both sides by t:
[tex]St=D[/tex]
Divide both sides by S:
[tex]t=\frac{D}{S}[/tex]
So our distance is 239000 and our speed is 250 so plug them in:
[tex]t=\frac{239000}{250}[/tex]
Putting into the calculator now:
t=956 minutes (I knew this was in minutes because the speed was 250 miles per minute)
We need to convert this to hours. 60 minutes=1 hour.
60 minutes=1 hour
956 minutes=x hours
You can setup a proportion if you don't know you just need to take 956 and divide it by 60. Like so:
[tex]\frac{60}{956}=\frac{1}{x}[/tex]
Cross multiply:
[tex]60x=956(1)[/tex]
[tex]60x=956[/tex]
Divide both sides by 60:
[tex]x=\frac{956}{60}[/tex]
Putting into calculator now:
x=15.9333333333333 which mean we have almost 16 hours