The transformed function is y = 1/3(log(x/3 + 4)) + 1
How to transform the logarithmic function?The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
The transformation of function f(x)We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is [tex]-\infty < f(x) < \infty[/tex]
In the domain, we have:
x < 5
This means that the interval of decrease is [tex]-\infty < x < 5[/tex]
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
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someone help for easy points
Answer:
First one
Step-by-step explanation:
First one ....pick a point ....say C for 'x' add 8 for y subtract 3 and you will be at C'
What is the quadratic function of this graph. Any form is fine!
Answer:
y=-0.012x(x-200).
Step-by-step explanation:
1) the given parabola has two zeros: 0 and 200. It means, the required equation is: y=ax(x-200), where a - unknown number;
2) according to the given graph the vertex is (100; 120). It is possible to substitute the coordinates of it into the equation y=ax(x-200) and calculate the value of 'a':
120=a*100(100-200); ⇒ a=-0.012.
3) finally, the required equation is:
[tex]y=-0.012x(x-200).[/tex]
[tex]\frac{n}{4} =\frac{k}{x} / n = 15/ k = 60[/tex]
Using proportions, the value of x is given as follows: x = 16
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We are given this following proportion:
[tex]\frac{n}{4} = \frac{k}{x}[/tex]
In this problem, we have that n = 15 and k = 60, hence:
[tex]\frac{15}{4} = \frac{60}{x}[/tex]
Applying cross multiplication:
15x = 60 x 4
Simplifying by 15:
x = 4 x 4
x = 16.
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can you please help me with this question? thank you
Answer:
A. Coffee 4C below the freezing point
Step-by-step explanation:
Negative temperature when talking about water means below the freezing point (below 0). Look up number line. Negative 4 is below 0 whereas positive 4 is above 0. Thus, option A is the best answer
Answer:
A
Step-by-step explanation:
This is because negative number start below zero and since water freezes at zero degrees celsius, Mia's iced coffee is below the freezing point.
please please in a survey it was found that the ratio of people who like arithmetic and algebra is 9:8 if 25% like both 80% like none of these and 20% like arithmetic only find the number of people who participate in the survey
Answer:
200
Step-by-step explanation:
it was found that the ratio of people who liked Arithmetic and Algebra is 9 : 8. If 25% liked the both, 80 liked none of these and 20% liked arithmetic only, find the total number of people participated in the survey. Ans: 200
Which expression equals 24? Group of answer choices (2 + 4)(3) (4 x 2)(3) (4 - 2) + 3 (4 + 3) - 2
The expression which equals 24 is (4 + 2) (3) . Option B
How to determine the expressionGiven the following expression
Let's evaluate each of them. we have
(2 + 4)(3) = 6× 3 = 18
(4 x 2)(3) = 8 × 3 = 24
(4 - 2) + 3 (4 + 3) - 2 = 2 + 3(7) -2 = 2 + 21 - 2 = 23 -2 = 21
Thus, the expression which equals 24 is (4 + 2) (3) . Option B
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Geometry
What the perimeter and area of the shape?
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
During one shift, the express lane clerk recorded how many times customers violated the "10 items or less"
rule for his lane. In particular, he recorded how many items over the limit each violator placed on the
conveyor belt. This data is summarized in the histogram below. NOTE: The last class actually represents "7
or more items," not just 7 items.
What is the most frequent number of over-the-limit items for this data set?
What is the frequency of the most frequent number of over-the-limit items?
The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5 and the frequency of the most frequent number of over-the-limit items is 14
What is the most frequent number of over-the-limit items for this data set?The most frequent number of over-the-limit items for this data set is the dataset that has the highest frequency.
This is represented by the class that has the highest bar on the histogram
To do this, we simply check the class that has the highest bar on the histogram.
From the attached histogram the class that has the highest bar on the histogram is 3.5 - 4.5
Hence, the most frequent number of over-the-limit items for this dataset is 3.5 - 4.5
What is the frequency of the most frequent number of over-the-limit items?In (a), we have:
The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5
Next, we check the frequency of the most frequent number of over-the-limit items for this dataset
According to the histogram, the most frequent number of over-the-limit items for this dataset has a frequency of 14
Hence, the frequency of the most frequent number of over-the-limit items is 14
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The number is between 8,500 and 8,800.
When multiplied by 8, the result is a whole number.
The digit in the hundreds place is ¾ the digit in the thousands place.
The sum of all digits in the number is 26.
The digit in the hundredths place is 200% of the digit in the tenths place.
There are no zeros in the decimal places.
Your first job is to post at least two numbers that do NOT work.
Explain why they do not work.
Post your best guess for a number that works (or a number that almost works)
A pair of dice are tossed twice.Find the probability that both rolls give at most a sum of 8.
the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
How to find the probability?The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:
36*36 = 1,296
Now if we define the outcomes as:
{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }
The outcomes that give at most a sum of 8 are:
{1, 1, 1, 1}
{2, 1, 1, 1} ( 3 permutations)
{2, 2, 1, 1} ( 6 permutations).
{2, 2, 2, 1} ( 3 permutations)
{3, 1, 1, 1} ( 3 permutations)
{3, 2, 1, 1} ( 12 permutations)
{3, 3, 1, 1} (6 permutations)
{4, 1, 1, 1} (3 permutations)
{4, 2, 1, 1} (6 permutations)
{5, 1, 1 , 1} (3 permutations)
{2, 2, 2, 2}
These are all the outcomes that give a sum of, at most, 8.
If we add all the outcomes we get 47 outcomes.
Then the probability that in bot rolls we have a sum of, at most, 8, is:
P = 47/ 1,296 = 0.036
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a student was given the following daigram and asked to prove that <1= <2 what would be the reason for the final step in the proof given line A and Line B are parallel prove <1=<2
The correct option based on the paralel line given is that the corresponding angles are congruent.
How to illustrate the information?Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.
We are to find the reason for the second step in the following proof. Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3
Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.
And, therefore we get ∠1 ≅ ∠2.
Thus, the reason in the second step will be angles 1 and 3 are corresponding angles and corresponding angles are congruent.
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The sum of a number and 6 is at least 15.???
Answer:
x + 6 ≥ 15
Step-by-step explanation:
Add any number greater than equal to 9 to the number 6 and you get a result of at least 12. Any number less than 9 produces a result that is not at least 15.
Just saying the question was not that descriptive so I don't know if this is what you asked for... Sorry!
Pls answer problem is in the image give a explanation pls not just a answer I’ll give brainiest
Total cards left
52-12=40Total hearts left
13-3=10Probability
P(Heart)=10/40=1/4Option B
Answer:
[tex]\sf F. \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
A deck of 52 playing cards contains 13 hearts.
If Sara has 12 cards from this deck in her hand and 3 of them are hearts, then:
Total cards remaining in the deck
= total deck - cards Sara has
= 52 - 12
= 40
Total hearts left in the remaining deck
= total heart cards - heart cards Sara has
= 13 - 3
= 10
So there are 40 cards in the deck and 10 of them are hearts.
Probability Formula[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore, the probability that a card drawn at random from the remainder of the deck will be a heart is:
[tex]\begin{aligned}\implies \sf P(heart) & =\dfrac{\textsf{number of hearts in remaining deck}}{\textsf{total cards in remaining deck}}\\\\ & =\dfrac{10}{40}\\ \\& =\dfrac{1}{4}\end{aligned}[/tex]
can you show me how can i solve sin(pi/2-x)=1/2??
By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and
[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].
What are trigonometric Identities?Trigonometric Identities exist as the equivalencies that apply trigonometry operations and have true for all the values of variables shown in the equation. There exist different trigonometric identities concerning the side length as nicely as the angle of a triangle.
How to simplify the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]?
Given:
[tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]
General solution for [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]
then from the general equation, we get
[tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] and
[tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]
Solve [tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] then [tex]$x= -2n\pi +\frac{\pi}{3}[/tex]
Solve [tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]then [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Therefore, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Radians, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]
Degree, [tex]$x = 60 \degrees- 360\degree n[/tex], [tex]$x = -60\degree- 360\degree n[/tex]
By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and
[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].
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I need help with question 30 please! :)
Answer:
B ∩ (A ∪ C)'
Step-by-step explanation:
It's the B part excluding A and C union. Hence,
(A ∪ C)' ∩ B
50 POINTS, I NEED IT QUICK PLSS
The thing that's wrong with the equation is that 2 shouldn't be multiplied by 4 but should have been added.
How to illustrate the information?From the information given, it can be seen that the equation is:
(3x²)(-2x⁴) = 3(-2)x² × x⁴ = 6x^8
Based on the information above, this calculation is incorrect. The correct calculation will be:
(3x²)(-2x⁴) = 3(-2)x² × x⁴
= -6x^6
Therefore, the multiplication should be an addition of the power.
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The highest point on land on Earth is the top of Mt. Everest in the Himalayas, at an elevation of 29,028 feet above sea level. The lowest point on land is the Dead Sea, between Israel and Jordan, at 1319 feet below sea level. Find the difference in elevations.
Final answer:
The difference of the elevations is 30347 feet.
Step-by-step explanation:
Step 1
The highest elevation is 29028 feet.
Step 2
The lowest elevation is -1319 because it is below the sea level.
Step 3
The difference of the elevations is:
29028 - (-1319)
Step 4
Evaluate the value of expression:
29028 - (-1319) = 30347
For the function q(x) =10 times rootindex 5 startroot x minus 2 endroot, what is the inverse function?
Hence, the inverse of the given function is [tex]{(\frac{x}{10})}^5 - 2[/tex]
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.
How to solve?given function,
q(x) = 10[tex]\sqrt[5]{x-2}[/tex]
say y=q(x)
now we have,
y = 10[tex]\sqrt[5]{x-2}[/tex]
[tex]\frac{y}{10}[/tex] = [tex]\sqrt[5]{x-2}[/tex]
raising to 5th power on both sides,
[tex](\frac{y}{10})^5[/tex] = x - 2
x = [tex](\frac{y}{10})^5[/tex] + 2
[tex]q^{-1}(x) =[/tex] [tex]{(\frac{x}{10})}^5 - 2[/tex]
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What is the definition of quantum physics?
Answer:
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.
Dante wrote several equations and determined that only one of the equations has infinitely many solutions. which of these equations has infinitely many solutions? 6 (x 3) x = 7 x 2 1 6 (x 3) x = 7 x 5 6 (x 3) x = 6 x 3 15 6 (x 3) x = 7 x 9 9
Among all the given equations 6(x+3)+x=7x+9+9 is having many solutions.
Given Equations :
6(x+3)+x=7x+2+1
6(x+3)+3=7x+5
6(x+3)+x=6x+3+15
6(x+3)+x=7x+9+9
We have to find the equation having many solutions.
The equation whose both sides are equal to each other is supposed to have many solutions. For determining all equations needs to be solved.
Equation 1
6(x+3)+x=7x+2+1
6x+18=7x+3
No the above equation is not having many solutions.
Equation 2
6(x+3)+3=7x+5
6x+18+3=7x+5
6x+21=7x+5
No the above equation is not having many solutions.
Equation 3
6(x+3)+x=6x+3+15
6x+18+x=6x+18
7x+18=6x+18
No the above equation is not having many solutions.
Equation 4
6(x+3)+x=7x+9+9
6x+18+x=7x+18
7x+18=7x+18
Yes the above equation is having many solutions.
Hence the equation which is having many solutions is 6(x+3)+x=7x+9+9.
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The options given in the question are wrong and the correct options are as under:
1) 6(x+3)+x=7x+2+1
2)6(x+3)+x=7x+5
3)6(x+3)+x=6x+3+15
4) 6(x+3)+x=7x+9+9
what are the coordinates of the point hat is 2/3 of the way from A to B?
Answer:
A. (2,3)
It is rather simple the 9 points between a and B 2/3 of that is 6
please helpppppppppp thanks!
Answer:
First one is false. (You are correct)Second is true. (a will be greater than 0)Third is also false. (a can't be equal to 0)Hope it helps!!
Answer:
[tex]a < 0[/tex] False
[tex]|a| > 0[/tex] True
[tex]|a|=0[/tex] False
________________________________________________
a is on the right side of 0,
which means a is positive.
The absolute value is the distance to zero (always positive)
Which means the absolute value of a is also positive.
[tex]a < 0[/tex] is wrong because a is positive
[tex]|a| > 0[/tex] is correct because a is larger than 0
[tex]|a|=0[/tex] is wrong because [tex]a[/tex] ≠ [tex]0[/tex]
________________________________________________
Hope this helps :)
please help asap, thanks so much
The system of inequalities that represent the graph is
y ≤ -x +4
y < 3x-1
The correct option is the third option
Graph of InequalitiesFrom the question, we are to determine the system of inequalities that represents the graph
The equation of the solid line is y = -x +4
Since the lower part of the graph was shaded
Then,
The inequality that represents the solid line is
y ≤ -x +4
The equation of the dotted line is y = 3x -1
Since the lower part of the graph was shaded,
Then,
The inequality that represents the solid line is
y < 3x-1
Hence, the system of inequalities that represent the graph is
y ≤ -x +4
y < 3x-1
The correct option is the third option
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First accurate answer gets brainliest
Answer:
B i think
Step-by-step explanation:
Given: AD ~ BC and AD
BC
Prove: ABCD is a parallelogram.
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
.
Step-by-step explanation:
A parallelogram has two pairs of parallel lines so if AD // BC and that AD//BC, Then it is indeed a parallelogram
Erica earned a total of $15,450 last year from her two jobs. the amount she earned from her job at the store was $1250 more than four times the amount you earn from her job at the college how much. how much does he earn from her job at the college
If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.
Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.
Amount from store forms an equation.
let the amount earned from college is x.
According to question:
Amount earned from store=4x+1250
Amount earned from college=x
Total amount earned=4x+1250+x
5x+1250=15450
5x=15450-1250
5x=14200
x=14200/5
x=2840
Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.
Hence the amount earned by Erica from college is $2840.
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( a^2x^3 -5x+3a).(-2a^3x)
The product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x
How to evaluate the expression?The expression is given as:
(a^2x^3 -5x+3a).(-2a^3x)
Open the bracket
-2a^3x * a^2x^3 -2a^3x * - 5x -2a^3x * 3a
Evaluate the products
-2a^5x^4 + 10a^3x^2 - 6a^4x
Hence, the product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x
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. Describe the transformation of the function, y = x + 4, from y = x.
There are two interpretations we could go for:
Adding 4 to the end means we add 4 to each y coordinate (since y = x). This shifts the entire line 4 units upReplacing x with x+4 means the xy axis is shifted 4 units to the right. If the line y = x is held completely still while the axis moves, then it gives the illusion the line is moving 4 units to the leftCheck out the diagram below.
Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.
Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.
(3,0) and (4,4)
equation
The equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.
The given coordinates are (3,0) and (4,4).
What is the formula to find the slope of an equation?The formula to find the slope of an equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
Now, slope[tex]=\frac{4-0}{4-3} =4[/tex].
The equation of the line is [tex](y-y_{1} )=m(x-x_{1} )[/tex]
⇒(y-3)=4(x-0)
⇒y-3=4x
⇒4x-y+3=0
Therefore, the equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.
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help i dont know how to do this
By evaluating in x = π/3, we conclude that the correct option is C.
Which is the graphed function?
By looking at the graph, we can see that the function becomes zero when:
x = π/3
Now, this is really trivial.
Just evaluate the four options in x = π/3, and see which ones become equal to zero, and discard the others.
By doing that, you will see that the only option that becomes zero when evaluated in x = π/3 is option C.
[tex]y = 3*sin(2(x - \frac{\pi}{3} ))[/tex]
Then we conclude that it is the only option that can be the correct one.
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