Answers
Answer:
2a) [tex]g(x)=3x-6[/tex]
2b) This is a show kind of answer. The showing of this in the explanation.
2c) I provided the graph. The lines should be a reflection through the y=x line. The points (a,b) on y=(1/3)x+2 or swapped to get the points (b,a) on y=3x-6. That is for, example the point (-3,1) is on y=(1/3)x+2 while (1,-3) is on y=3x-6.
Step-by-step explanation:
2a) The inverse of a function is you just swapping x and y around. You also almost always asked to remake y the subject after that though.
So anyways we have this equation [tex]y=\frac{1}{3}x+2[/tex] to represent that function you have there.
We want to swap x and y:
[tex]x=\frac{1}{3}y+2[/tex]
Now we want to solve for y.
Subtract 2 on both sides:
[tex]x-2=\frac{1}{3}y[/tex]
Multiply both sides by 3:
[tex]3(x-2)=y[/tex]
[tex]y=3(x-2)[/tex]
Distribute:
[tex]y=3x-6[/tex]
So they want us to name the inverse g(x).
[tex]g(x)=3x-6[/tex]
2b) We want to show by composition that these functions are inverses. That is we want to show f(g(x))=x and g(f(x))=x.
Let's do that:
f(g(x))
Replace g(x) with 3x-6 since g(x)=3x-6.
f(3x-6)
Replace the old input x with the new input (3x-6) in (1/3)x+2.
[tex]\frac{1}{3}(3x-6)+2[/tex]
Distribute:
[tex]\frac{3x}{3}-\frac{6}{3}+2[/tex]
Simplify:
[tex]x-2+2[/tex]
[tex]x-0[/tex]
[tex]x[/tex].
So we do have f(g(x))=x.
Now to show the other way:
g(f(x))
Replace f(x) with (1/3)x+2 since f(x)=(1/3)x+2.
g((1/3)x+2)
Replace the old input x with the new input (1/3)x+2 in 3x-6.
3((1/3)x+2)-6
Distribute:
[tex]3(\frac{1}{3})x+3(2)-6[/tex]
Simplify:
[tex]1x+6-6[/tex]
[tex]x+6-6[/tex]
[tex]x+0[/tex]
[tex]x[/tex]
So we do have g(f(x))=x.
We have confirmed that f and g are indeed inverses since f(g(x))=x and g(f(x))=x.
2c) Visually if two functions are inverses they should be reflections through the y=x line so that is what we should see since f and g are inverses.
I going to compare both equations to y=mx+b form to determine the y-intercept and the slope.
y=mx+b
y=(1/3)x+2 tells us the slope is 1/3 and the y-intercept is 2.
y=3x-6 tells us the slope is 3 and the y-intercept is -6.
I have color-coded the picture.
Related Questions
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?
Answers
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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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.
Answers
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.
According to the rational root theorem what are all the potential rational roots of f(x)=9x^4-2x^2-3x+4
Answers
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] ....
which function results after applying the sequence of transformations to f(x) = x^5
Answers
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.
a 15-foot telephone pole has a wire that extends from the top of the pole to the ground. The wire and the ground form a 42 degree angle. How long is the wire, and what is the distance from the base of the pole to the spot where the wire touches the ground.
Answers
Answer:
The length of the wire is 22.42 feet
The distance from the base of the pole to the spot where the wire touches the ground is 16.66 feet
Step-by-step explanation:
* Lets explain the situation in the problem
- The telephone pole , the wire and the ground formed a right triangle
- The wire is the hypotenuse of the triangle
- The height of the telephone pole and the distance from the base of
the pole to the spot where the wire touches the ground are the legs
of the triangle
- The angle between the wire and the ground is 42°
- The angle 42° is opposite to the height of the telephone pole
- The height of the telephone pole is 15 feet
* Lets use the trigonometry functions to find the length of the wire
(hypotenuse) and the distance from the base of the pole to the spot
where the wire touches the ground
∵ sin Ф = opposite/hypotenuse
∵ Ф = 42° and its opposite side = 15 feet
∴ sin 42 = 15/hypotenuse ⇒ by using cross multiplication
∴ sin 42° (hypotenuse) = 15 ⇒ divide both sides by sin 42
∴ hypotenuse = 15/sin 42° = 22.42 feet
∵ The length of the wire is the hypotenuse
∴ The length of the wire is 22.42 feet
∵ The distance from the base of the pole to the spot where the wire
touches the ground is the adjacent side to the angle 42°
∵ tan Ф = opposite/adjacent
∴ tan 42° = 15/adjacent ⇒ by using cross multiplication
∴ tan 42° (adjacent) = 15 ⇒ divide both sides by sin 42
∴ adjacent = 15/tan 42° = 16.66 feet
∵ The adjacent side is the distance from the base of the pole to the
spot where the wire touches the ground
∴ The distance from the base of the pole to the spot where the wire
touches the ground is 16.66 feet
The recipe for beef stew calls for 1/4 teaspoon of pepper
for every 3 potatoes. If 9 potatoes are used, how much
pepper is needed?
ģ to answer the question
Solve the proportion 3 -
Explain your steps
Answers
[tex]\bf \begin{array}{ccll} \stackrel{teaspoons}{pepper}&potatoes\\ \cline{1-2} \frac{1}{4}&3\\ x&9 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{3}{9}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{1}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{1}{3}\implies 3=4x\implies \cfrac{3}{4}=x[/tex]
Answer:
Since 9 is 3 times the denominator of the first ratio, multiply the numerator of the first ratio by 3 to get the numerator of the second ratio. The amount of pepper is 3/4 teaspoon.
Step-by-step explanation:
Which expression will help you find the surface area of this right triangular prism? Select all the apply
Answers
To find the surface area of a right triangular prism, we have to calculate the area of all its faces, which include the two triangular bases and the three rectangular faces.
1. **Triangular Bases:** If the right triangle base has sides of lengths `a`, `b`, where `b` is the base and `a` is the height of the triangle, then the area of one triangular base will be given by the formula:
\[\text{Area of one triangular base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times a \times b.\]
Since there are two identical triangular bases, we multiply this area by 2:
\[\text{Total area of triangular bases} = 2 \times \left( \frac{1}{2} \times a \times b \right) = a \times b.\]
2. **Rectangular Faces:** The three rectangular sides include two rectangles that are formed by the sides of the triangle (`a` and `b`) with the height (`h`) of the prism and one rectangle that is the width of the base `b` and the height of the prism. The areas of these rectangles will be:
- Rectangle with side `a` and height `h`: \[a \times h.\]
- Rectangle with base `b` and height `h`: \[b \times h.\]
- Rectangle with the side corresponding to the hypotenuse `c` of the base triangle and height `h`: \[c \times h.\]
Therefore, the total area of the three rectangles is the sum of the areas:
\[\text{Total area of rectangular faces} = a \times h + b \times h + c \times h = h \times (a + b + c).\]
Putting it all together, the formula for the total surface area (SA) of the right triangular prism is:
\[ SA = a \times b + h \times (a + b + c).\]
So, the expression that will help you find the surface area of a right triangular prism is the sum of the areas of the two triangles and the three rectangles as given by this formula.
Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges?
square pyramid
triangular prism
rectangular prism
triangular pyramid
Answers
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**.
A square image has a side length of 7 cm on a computer monitor. It is projected on a screen using an LCD projector. When projected, 1 cm of the image on the monitor represents 8 cm on the screen. Find the perimeter of the square in the projection.
answers are 392, 224, 448
Answers
Answer:
The perimeter of the square in the projection is [tex]224\ cm[/tex]
Step-by-step explanation:
we know that
1 cm of the image on the monitor represents 8 cm on the screen
so
using proportion
Find out how much represent on the screen 7 cm on a computer monitor
Let
x ----> the length side of the square image on the screen
[tex]\frac{1}{8}\frac{monitor}{screen} =\frac{7}{x}\frac{monitor}{screen} \\ \\x=8*7\\ \\x=56\ cm[/tex]
Find the perimeter of the image on the screen
the perimeter of a square is equal to
[tex]P=4b[/tex]
[tex]b=56\ cm[/tex]
substitute
[tex]P=4(56)=224\ cm[/tex]
Answer:
224cm
Step-by-step explanation:
The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm
square on the screen.
The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.
The side length of the square in the projection is the product of the side length of the preimage and the scale factor.
h=7(8)
cm
Simplify.
h=56
cm
The perimeter of the square is
P=4(56)
cm
Simplify.
P=224
cm
Therefore, the perimeter of the square in the projection is 224
cm.
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]
Answers
Which inequality is not true? -7/8 > -0.50 -7/8 < -0.60 -7/8 < -1/4 -7/8 > -15/16
Answers
Solve the following system using the elimination method: 2x-4y=2 -4x+6y=-4
Answers
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 )
What is the value of b in the equation below?
5^6/5^2=a^b
3
4
5
8
Answers
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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plzzz hurry up and help me if A+B=45
prove that
(1+tanA)(1+tanB)=2
Answers
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
The equations X-2Y=1, 3x-y=-1, x+2y=-1, and 3x+y=1 are shown on the graph below.
Which system of equations has a solution of approximately (0.6, –0.8)?
A. x+2y=-1 and 3x+y=1
B. x-2y=1 and 3x+y=1
C. x-2y=1 and 3x-y=-1
D. x+2y=-1 and 3x-y=-1
Answers
Answer:
When you graph all the equations into a graphing calculator, you find the answer is:
C. x-2y=1 and 3x-y=-1
The system of equations has a solution of approximately (0.6, –0.8) are;
x + 2 y = - 1 and 3 x + y = 1
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
From this information, it is clear that the green line and the Purple line intersect each other at an approximate point (0.6, -0.8).
Since, the green line passes through the x-intercept (-1,0) and y-intercept (0,-0.5).
Therefore, the equation of the green line will be;
⇒ x + 2y = - 1
Again, the purple line passes through the point (0,1) and has a negative slope thus, the equation of purple line will be;
3x + y = 1 {Since it has negative slope}
Therefore, the first option will be the answer.
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which of the following has 12 faces?
a.dodecahedron
b.octahedron
c.Icosahedron
d.terrahedron
help me PLEAS!!!!!! APEX
Answers
Answer:
Option a) dodecahedron
Step-by-step explanation:
we know that
case a) Dodecahedron
it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12). Each face has 5 edges (a pentagon)
case b) Octahedron
it is a polyhedron that has 8 faces (from Greek okto- meaning eight).
case c) Icosahedron
it is a polyhedron that has 20 faces (from Greek icos- meaning twenty).
case d) Terrahedron
it is a polyhedron composed of four triangular faces (from Greek tetra- meaning four).
therefore
The answer is dodecahedron
What is a requirement of supplementary angles?
Answers
Answer:
Two Angles are Supplementary when they add up to 180 degrees.
Step-by-step explanation:
Notice that together they make a straight angle.
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
Answers
He traveled 270 feet. (90 yards)
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
Answers
Answer:
A
Step-by-step explanation:
they're proportional
Answer: the answer is A
Step-by-step explanation:
have a good day
A normal distribution has a mean of 50 and standard deviation of 5. Which value produces a negative z-score?
Answers
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
Complete the equations of the line through (-8, - 2) and (-4, 6)
Answers
Answer:
y = 2x + 14
Step-by-step explanation:
As we move from (-8, - 2) to (-4, 6), x increases by 4 and y increases by 8.
Thus, the slope, m, equal to rise / run, is m = 8/4, or m = 2.
Use the slope-intercept form of the equatino of a straight line:
y = mx + b. This becomes 6 = 2(-4) + b, or 6 = -8 + b. Thus, b = 14, and the desired equation is y = 2x + 14.
6 = 3x - 9
x + 4 < 1
x/2 + 3 = -5
Answers
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
use the quadratic formula to find the solutions to the equation x^2-3x+1=0
Answers
Answer:
x = 3, plus or minus, radical 5 all over 2
Step-by-step explanation:
Cindy bought a car for $21,330. A few years later, she sold the car for $19,700. Find the percent of change in the value.
Answers
well, the difference is 21330 - 19700 = 1630.
now, if we take 21330 as the 100%, what is 1630 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 21330&100\\ 1630&x \end{array}\implies \cfrac{21330}{1630}=\cfrac{100}{x}\implies \cfrac{2133}{163}=\cfrac{100}{x} \\\\\\ 2133x = 16300\implies x=\cfrac{16300}{2133}\implies x \approx 7.64[/tex]
Answer:
Change in the price of the car was 7.64%
Step-by-step explanation:
Cindy bought a car for $21330.
After few years she sold the car for $19700.
Net loss she suffered = Selling price - Cost price
= 21330 - 19700
= $1630
Now the percent change in the value will be = [tex]\frac{\text{Difference in the price}}{\text{Cost price of the car}}\times 100[/tex]
= [tex]\frac{1630}{21330}\times 100[/tex]
= 7.64%
Therefore, change in the price of the car was 7.64%
Solve 2x-3/5=x+6 ASAP
Answers
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
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]
Answers
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]
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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
Answers
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.
help !! I can’t find the answer
Answers
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
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
Answers
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
Find out more on inequality at: https://brainly.com/question/24372553
What are the zeros of f(x) = x2 - x-30?
re the zeros
Answers
Answer:
x = 6 and x = -5
Step-by-step explanation:
The zeros are what 2 x-values makes this function equal to zero.
So we need to find [tex]x^2-x-30=0[/tex]
Now we need 2 numbers multiplied that gives us -30 (constant) and added gives us -1 (coefficient in front of x).
The two numbers are : -6, and 5
Now we can write:
[tex]x^2-x-30=0\\(x-6)(x+5)=0\\x=6, -5[/tex]
Hence the zeroes are x = 6 and x = -5
Final answer:
The zeros of the function f(x) = x^2 - x - 30 are found by factoring the quadratic equation. They are x = 6 and x = -5.
Explanation:
To find the zeros of the function f(x) = x2 - x - 30, we need to solve the equation for when f(x) equals zero. This means we have to solve x2 - x - 30 = 0. This is a quadratic equation, and we can attempt to factor it to find the solutions.
The factors of -30 that add up to -1 (the coefficient of x) are -6 and +5. Thus, we can rewrite the quadratic as (x - 6)(x + 5) = 0. Now, we can set each factor equal to zero to find the zeros of the function:
x - 6 = 0, which gives x = 6
x + 5 = 0, which gives x = -5
Therefore, the zeros of the function are x = 6 and x = -5.