"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis ⇒ 3rd answer
Step-by-step explanation:
The form of the exponential function is [tex]f(x)=a(b)^{x}[/tex], where
a is the initial value (value f(x) at x = 0)b is the growth/decay factorThe domain of the function is {x : x ∈ R} (all real numbers)The range of the function is {y : y > 0} (all positive real numbers)∵ [tex]f(x)=2(\frac{1}{4})^{x}[/tex]
- Compare it with the form above
∴ a = 2 ⇒ initial value
∴ b = [tex]\frac{1}{4}[/tex] ⇒ decay factor because its between 0 and 1
∵ The domain of the function is the values of x
∴ The domain of the function is {x : x ∈ R} ⇒ all real numbers
∵ The range of the function is values of y
∴ The range of the function is {y : y > 0}
∵ Reflection over the y-axis change the sign of x
∴ The image of f(x) is [tex]y=2(\frac{1}{4})^{-x}[/tex]
- That means, all x-coordinates of the points on the graph
opposite in signs, but that does not effect the domain
because the domain is all real numbers
∵ There is no change of the sign of y
- That means reflection over y-axis does not effect the range
∴ The range of the function after reflection is the same as the
range of f(x)
∴ The range of the image of f(x) is {y : y > 0}
"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis
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Answer:
C
Step-by-step explanation:
edge 2020
Write the inequality shown in the graph below:
Solve the quadratic equation for x. What is one of the roots?
2x2 + 9x − 5 = 0
A) −
1
2
B) −
1
5
C)
1
2
D)
1
5
Final answer:
To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.
Explanation:
To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.
Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.
Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:
x1 = (-9 + 11) / 4 = 2 / 4 = 0.5 or 1/2x2 = (-9 - 11) / 4 = -20 / 4 = -5Thus, one of the roots of the equation is 1/2, which corresponds to option C.
What is an example of a situation that you might not be able to use an equation with a single unknown to understand?
Answer:
An example of a situation that you might not be able to use an equation with a single unknown is
[tex]x = \ln{e^x}[/tex]
Step-by-step explanation:
An example of a situation that you might not be able to use an equation with a single unknown is
[tex]x = \ln{e^x}[/tex]
The identity on both sides which results in 1 = 1 and thus the equation is not usable.
A situation where an equation with a single unknown cannot be effectively used is when you need to explore or solve multiple variables or dimensions, like best represented by physics-related problems. The number of unknowns should not exceed the number of equations for correct problem-solving. Equations with a single unknown may not always suffice, especially for problems involving various dimensions or variables.
Explanation:An example of a situation where you may not be able to use an equation with a single unknown to understand is a problem that involves multiple elements or dimensions needing exploration. For instance, in physics, if you're calculating an object's motion, you may need to take into account various forces acting on it, its initial velocity, its acceleration, and the time. No single equation with just one unknown can solve this problem; you would need multiple equations to represent each of these dimensions.
Remember that the number of unknowns should not be larger than the number of equations. Otherwise, the problem can't be solved. Therefore, the complexity of your problem can sometimes make it impossible to use an equation with a single unknown. Physics is often an area where this is true, due largely to the dimensional consistency of equations.
Nevertheless, equations with a single unknown can often be combined together or manipulated to solve specific problem-solving strategies. Overall, while an equation with a single unknown is a powerful tool, it may not always be sufficient to understand every situation, especially those involving multiple dimensions or variables.
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Solve for x 2x+6>20 please help
Answer:
x>7
Step-by-step explanation:
2x+6>20
2x>20-6
2x>14
x>14/2
x>7
What are the dimensions of a rectangular wall that can be constructed with 400 feet of brick that will maximize the area enclosed by that brick
Answer:
The dimensions of the wall are 100 ft x 100 ft
Step-by-step explanation:
we know that
The perimeter of a rectangular wall is
[tex]P=2(x+y)[/tex]
where
x is the length
y is the width
we have
[tex]P=400\ ft[/tex]
so
[tex]400=2(x+y)[/tex]
simplify
[tex]200=x+y[/tex]
[tex]y=200-x[/tex] ----> equation A
The area of a rectangular wall is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-x)\\A=-x^2+200x[/tex]
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
Convert the quadratic equation in vertex form
[tex]A=-x^2+200x[/tex]
Factor -1
[tex]A=-(x^2-200x)[/tex]
Complete the square
[tex]A=-(x^2-200x+100^2)+100^2[/tex]
[tex]A=-(x^2-200x+10,000)+10,000[/tex]
Rewrite as perfect squares
[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form
The vertex is the point (100,10,000)
The x-coordinate of the vertex represent the length of the wall for a maximum area
so
[tex]x=100\ ft[/tex]
Find the value of y
equation A
[tex]y=200-(100)=100\ ft[/tex]
therefore
The dimensions of the wall are 100 ft x 100 ft
To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.
Explanation:To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,
which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.
solve each inequality, graph the solution on the number line, and write the solution in interval notation
3x− 2 > 4 or 5x− 3 ≤ 7
Answer:
[tex](-\infty,+\infty)[/tex]
Step-by-step explanation:
The given inequality is 3x-2>4 or [tex]5x-3\leq 7[/tex]
We group similar terms to obtain: 3x>4+2 or [tex]5x\le7+3[/tex]
Simplify to get:
3x>6 or [tex]5x\le10[/tex]
x>2 or [tex]x\le 2[/tex]
This implies that the solution set is all real numbers.
The solution in interval notation is [tex](-\infty,+\infty)[/tex]
Which expression is not a polynomial?
x-1
4+p
5x² - x
8x - z3
The given question have mistake.
Question:
Which expression is not a polynomial?
(1) x – 1
(2) 4 + p
(3) [tex]5x^2-\sqrt x[/tex]
(4) [tex]8x-z^3[/tex]
Answer:
[tex]5x^2-\sqrt x[/tex] : Not a polynomial
Solution:
Definition of polynomial:
A polynomial can have constants, variables and exponents.
Constants = 2, 5
Variables = x, y, z
Exponents = [tex]x^2[/tex]
Not a polynomial:
Roots, fractions in power, negative powers and dividing by a variable are not polynomials.
Given expressions:
(1) x – 1 : Polynomial
(2) 4 + p : Polynomial
(3) [tex]5x^2-\sqrt x[/tex] : Not a polynomial
(4) [tex]8x-z^3[/tex] : Polynomial
Hence in the given expressions [tex]5x^2-\sqrt x[/tex] is not a polynomial.
If you are convicted of DUI, your fine and jail time will be increased if _____.(FLVS)
Conviction of DUI results in increased fines and jail time if aggravating factors such as high alcohol levels or prior offenses are present.
If you are convicted of DUI (driving under the influence), your fine and jail time will typically be increased if certain aggravating factors are present. These can include having a high blood alcohol content, previous DUI convictions, causing an accident while DUI, especially if injury or death occurred, having minors in the vehicle, and others. The penalties are enhanced due to the increased risk and harm these factors represent.
Anyone know this.
What is the negation of the following statement?
A triangle cannot contain two obtuse angles.
A. A triangle can contain two obtuse angles.
B. A triangle does not contain two obtuse angles.
Answer:
it's B
Step-by-step explanation:
a triangle cannot two obtuse angles
A traingle does not contain two obtuse angles. Option B is correct.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
Here,
A triangle cannot contain two obtuse angles.
A triangle cannot have the two obtuse angle, becaue for a triangle sum of the iternal angle must not exceeds 180°
Thus, A traingle does not contain two obtuse angles. Option B is correct.
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(1 point)
10. A sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g. Construct a 95% confidence interval estimate of the mean weight of all the coins.
a) 7.6675g
b) 8.0518g
c) 8.0447g
d) 8.0329g
Answer:
Step-by-step explanation:
i think its b or c
The confidence interval of the mean weight of all the coins is 8.0518g. The correct option is B.
What is a confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.
Given that a sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g.
The confidence interval is calculated by the formula:-
CI = X ± z (S / √n)
CI = 8.0710 ± [ (1.96 x 0.0411) / √20 ]
CI = 8.0710 - 0.018
CI = 8.053 g
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1.4x - y = -3
1. {-2x + y = 5
Answer:
look at shown picture.
Answer:
The answer is 4
Step-by-step explanation:
Why?...Because this is a site where everything is fake and incorrect.
If there are 46 scores in a set of data, in which position will the lower quartile lie
Answer:
Position 12.
Step-by-step explanation:
It will be n the center of the bottom 23 numbers ( when the data is arranged in ascending order).
That is in position 12.
The quotient of a number and -5, decreased by 9, is 2
Hello there n ÷ 5 - 9 = 2!
Here's how i solved it:
The quotient of a number and -5, decreased by 9, is 2
"is 2" means the result is 2, so we can have one side of the equation set up to look like this: = 2.
The quotient of a number and -5, decreased by 9, is 2
This looks like: n ÷ 5
The quotient of a number and -5, decreased by 9, is 2
We are taking 9 away from the previous expression, so n ÷ 5 - 9
Putting it all together, we have: n ÷ 5 - 9 = 2
The algebraic mathematical problem is to solve the equation x/-5 - 9 = 2. Simplifying this equation through a series of algebraic steps gives the result x=-55.
Explanation:The subject of your question is algebra, a branch of mathematics. You are looking for a number which, when divided by -5 and then decreased by 9, equals 2. The equation that represents this problem is x/-5 - 9 = 2.
To solve for x, we would first get rid of the -9 from the left side of the equation. We do this by adding 9 to both sides of the equation. We then have x/-5 = 2 + 9, which simplifies to x/-5 = 11.
Next, we isolate x by multiplying both sides of the equation by -5. We now get x= -5*11, which gives x = -55. Thus, the number x that satisfies this equation is -55.
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What is the value of x in the proportion (x-1)/5=(4x+3)/35
Answer:
x = 10/3
Step-by-step explanation:
(x - 1)/5*35 = (4x + 3)/35*35
7(x - 1) = 4x + 3
7x - 7 - 4x + 7 = 4x + 3 - 4x + 7
3x/3 = 10/3
x = 10/3
If three workers paint a house in 12 hours how long will it take 5 painters to paint the same house
Answer:
60 hours
Step-by-step explanation:
you multiply 5×12 and then you get 60
Referring to the figure, evaluate the expression shown.
a. (-3) b. 7 c. -3 d. 3
Answer:
d
step-by-step explanation:
find the zeros/roots of k(x)=x^3+5x^2+9x+45
Answer:
k(x)=x^3+9x+5x^2+45
Step-by-step explanation:
k(x)=x^3+5x^2+9x+45
k(x)=x^2(x+5)+9(x+5)
K(x)=(x+5)(x^2+9)
k(x)=x^3+9x+5x^2+45
Solve using sublimation
3x+4y=-17
y=-6*-1
Answer:17
Step-by-step explanation:trust me use mathaway;) mathaway dot com
Answer:
x=-41/3, y=6 (-41/3, 6).
Step-by-step explanation:
3x+4y=-17
y=-6*-1
-------------------
3x+4y=-17
y=6
3x+4(6)=-17
3x+24=-17
3x=-17-24
3x=-41
x=-41/3
Find the area of the following geometric figure.
Find the area of a triangle with base of 6 m and altitude of 4 m.
Area =
m2
What is angle A? 313 degrees 133 degrees 143 degrees 147 degrees
133 is the Answer bc that is a supplementary angle and supplementary angles always sum up to 180 hope this helps please mark brainliest
Step-by-step explanation:
Write an equation that has variables on each side and has a solution of -2.
Answer:
2(x+4)=6+x
Step-by-step explanation:
Let x be our variable.
We want to write about equation using x that gives us -2 as solution.
We can write many of such equation.
An example is:
[tex]2( x + 4) = 6 + x[/tex]We cross check.
Let us expand:
[tex]2x + 8 = 6 + x[/tex]
Group similar terms:
[tex]2x - x = 6 - 8[/tex]
Combine similar terms:
[tex]x = - 2[/tex]
How many solutions does the system of equations have 4x+2y=-8 2x+y=4 explain your answer
Answer:
x=-y/2
Step-by-step explanation:
1. The value of a variable that makes an equation true.
2. In chemistry, a solution is a homogeneous mixture composed of only one phase
Can someone help me plzzzz!
8.2is the answer
Step-by-step explanation:
|CB|+8
20. Coin Collecting The value of Gerald's coins is the
value of his brother's coins. Gerald's coins are worth $14.
What is the value of his brother's coins? Write and solve
an equation.
Answer:
$14
Step-by-step explanation:
if Gerald's coins have the same value as his brothers, then that means they have exactly the same amount
What is 2/2 simplified
Answer:1
Step-by-step explanation:just divide numerator by denominator
helllllpppp please!!!
Do you do Accelus Online School?
I do that too!
Sorry i'd totally answer this question but i'm struggling toooo
The angle of depression from the top of a cruise ship to the top of a sailboat is 22. Sitting above water, the cruise ship is 236 feet tall while the sailboat is 27 feet tall. Find the distance between the cruise ship and the sailboat.
Answer:
The distance between the cruise ship and the sail boat is 517 feet.
Step-by-step explanation:
The cruise ship is 236 feet tall, and the sailboat is 236 tall; this means the distance between the top of the cruise ship and the top of the sail boat is
236 feet - 27 feet = 209 feet.
We also know that the angel of depression from the top of the cruise ship to the bottom of the cruise ship is 22°. This forms a right triangle as shown in the figure attached.
Now from trigonometry we get:
[tex]tan \: \theta = \dfrac{209}{d}[/tex]
[tex]d= \dfrac{209}{tan\:\theta }[/tex]
[tex]\boxed{d=517ft}[/tex]
The distance between the cruise ship and the sailboat is 517 feet.
Final answer:
To calculate the horizontal distance between the cruise ship and the sailboat, we subtract the sailboat's height from the cruise ship's height to get 209 feet, use the angle of depression and tangent function, and find that the distance between them is approximately 517.57 feet.
Explanation:
To find the distance between the cruise ship and the sailboat, we need to apply trigonometry. First, we determine the difference in height between the two, which is the cruise ship's height above the water subtracted by the sailboat's height. This will be 236 feet - 27 feet = 209 feet. Since the angle of depression from the cruise ship to the sailboat is 22 degrees, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.
The opposite side, in this case, is the difference in height (209 feet), and the adjacent side is the horizontal distance between the ships, which we're trying to find. Thus:
tangent(22 degrees) = opposite/adjacent
adjacent = opposite/tangent(22 degrees)
= 209 feet / tangent(22 degrees)
Now we calculate the tangent of 22 degrees and then divide 209 feet by this amount to find the distance between the two vessels.
Using a calculator, tangent(22 degrees) ≈ 0.4040, so:
adjacent ≈ 209 feet / 0.4040 ≈ 517.57 feet
Therefore, the horizontal distance between the cruise ship and the sailboat is approximately 517.57 feet.
(-4-3n).-8
Need help
In the diagram above which two red lines are parallel.!?
Answer:L F and K G
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The answer is not A because:
lines gk and kg are the same line
The answer is not B because:
lines il and gk are perpendicular if they were to touch
The answer is not C because:
line fl and il are perpendicular
The answer IS D because:
lines fl and gk are parallel because they will never touch
10 POINTS
Choose the polynomial that is written in standard form.
A:−3x5 + 4x3 + 10x2
B:−8x + 4x4 + 3x3
C:x4 + 4x3 + 10x4
D:x6 + 4x3 + 10x7
Answer:
A
Step-by-step explanation:
-3×5+4×3+10×2
=-15+12+20
=17
Answer:
A: 3x5 + 4x3 +10x2
Step-by-step explanation: