Answer:
36
Step-by-step explanation:
40 % of 60 = 24
60-24=36
The functions f(x) and g(x) are shown on the graph.
The image shows two graphs. The first is f of x equals log base 3 of x and it is increasing from negative infinity in quadrant four as it goes along the y-axis and passes through 0 comma 1 to turn and increase to the right to positive infinity. The second is g of x and it is increasing from negative infinity in quadrant two as it goes along x equals negative 4 and passes through 0 comma negative 3 to turn and increase to the right to positive infinity.
Using f(x), what is the equation that represents g(x)?
g(x) = log3(x) – 4
g(x) = log3(x) + 4
g(x) = log3(x – 4)
g(x) = log3(x + 4)
Answer:
[tex]g(x)=\log_3(x+4)[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\log_3x[/tex]
From inspection of the graph:
The x-intercept of [tex]f(x)[/tex] is (1, 0)The x-intercept of [tex]g(x)[/tex] is (-3, 0)If there was a vertical translation, the end behaviors of both g(x) and f(x) would be the same in that the both functions would be increasing from -∞ in quadrant IV.
As the x-intercepts of both functions is different, and g(x) increases from -∞ in quadrant III, this indicates that there has been a horizontal translation of 4 units to the left.
Therefore:
[tex]g(x)=f(x+4)=\log_3(x+4)[/tex]
Further Proof
Logs of zero or negative numbers are undefined.
From inspection of the graph, [tex]x=-3[/tex] is part of the domain of g(x).
Therefore, input this value of x into the answer options:
[tex]g(-3)=\log_3(-3)-4\implies[/tex] undefined
[tex]g(-3)=\log_3(-3)+4\implies[/tex] undefined
[tex]g(-3)=\log_3(-3-4)=\log_3(-7)=\implies[/tex] undefined
[tex]g(-3)=\log_3(-3+4)=\log_3(1)=0[/tex]
Hence proving that [tex]g(x)=\log_3(x+4)[/tex]
The equation that represents g(x) is: [tex]g(x) = log_3(x + 4)[/tex]
The correct answer is: the fourth option:
[tex]g(x) = log_3(x + 4)[/tex].
Here, we have to find the equation that represents g(x) using f(x), we need to consider how the graph of g(x) is related to the graph of f(x).
The graph of f(x) = log base 3 of x starts from negative infinity in quadrant four, passes through (0, 1), and increases to positive infinity.
The graph of g(x) is increasing from negative infinity in quadrant two, passes through (0, -3), and increases to positive infinity.
So, we can see that the graph of g(x) is the graph of f(x) shifted 4 units to the left along the x-axis.
Therefore, the equation that represents g(x) is:
[tex]g(x) = log_3(x + 4)[/tex]
The correct answer is: the fourth option:
[tex]g(x) = log_3(x + 4)[/tex].
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A die is tossed. Find the odds against rolling a number greater than 4.
Reason:
There are 4 outcomes we don't want (rolling 1,2,3 or 4) and 2 outcomes we do want (rolling 5 or 6)
This gives the odds against ratio of 4:2 or 2:1
This can be written out as "2 to 1" or "two to one".
Having 2 to 1 odds means that we're twice as likely to get something we don't want vs something we do want.
Side note: the odds in favor will have us flip the ratio.
Two exterior angles of a triangle measure 135° and 100°. What are the measures of the interior angles of the triangle?
A.
45°, 65°, 80°
B.
45°, 65°, 70°
C.
45°, 55°, 80°
D.
55°, 75°, 50°
E.
80°, 50°, 50°
Answer:
its it a
Step-by-step explanation:
The pie chart below illustrates the future plans of 200members of St.Thomas graduating class.
a)How many graduates are planning to continue studying?
b)What is the measurement of the angle representing those who plan to work?
Answer:
a) approximately 133 graduatesb) approximately 120°Step-by-step explanation:
a) the number of graduates planning to continue studying :
= (37 1/2% + 12 1/2% + 16 2/3%) × 200
[tex]=\frac{\left( 37\frac{1}{2} +12\frac{1}{2} +16\frac{2}{3} \right) }{100} \times200[/tex]
= (37.5 + 12.5 + 16.666666666667)×2
= 133.333333333334
…………………………………
b) the measurement of the angle representing those who plan to work :
= (360× 33 1/2)÷100
= (360× 33.333333333333)÷100
=119.999999999999
Please help me it’s for Plato on edmentum! Algebra 1 Quadratic relationships Mastery test
The equation of the function g(x) will be g(x) = (1/2) x². Then the correct option is B.
The complete question is attached below.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be
g(x) = a · x²
Then the value of will be
From the graph, at x = 2, g(x) will be 2.
Then we have
2 = a · 2²
a = 1/2
Then the equation of the function g(x) will be g(x) = (1/2) x².
Then the correct option is B.
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1) FILL IN THE SPACES:
a. 2.5 liters (L) = ______ml
b. 1320g = ________kg
c. 1.2g = _________mg
d. 1025mcg =_______mg
and. 2TBS=_______tsp
F. 1 TBS =_______ml
g. 2 fl oz =_______ml
h. 75kg =________pounds (lb)
PROBLEMS
1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
2) Express the amount of 1.243 g as:
mg ________
kg ________
mcg _______
3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg?
At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering.
The probability that a student is a female or major in civil engineering is 62%
Complete questionAt a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?
How to determine the probability?Let A represent Female and B represents civil engineering.
The above representation means that the given parameters are:
P(A) = 49%P(B) = 21%P(A and B) = 8%The required probability is calculated as:
P(A or B) = P(A) + P(B) - P(A and B)
This gives
P(A or B) = 49% + 21% - 8%
Evaluate
P(A or B) = 62%
Hence, the probability that a student is a female or major in civil engineering is 62%
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Please help me for a treat lol
Step-by-step explanation:
a) Jill ended her scooter at her house
b) 2/3 or 0.67
c) The domain is [0,19] , The domain tell about the Elapsed Time of the Jill's scooter ride
d) The range is [2,6] , The range tell about the Distance travelled from Jill's House
I hope it helps you
Treat Please :)
The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?
Answer:
-7/2 or 2 are inputs that give 19 as output.
Step-by-step explanation:
The problem gives us a quadratic function [tex]\displaystyle \large{f(x)=2x^2+3x+5}[/tex]. When its output is 19, we want to know the input value(s).
Since an output which is f(x) = 19. Therefore:
[tex]\displaystyle \large{19=2x^2+3x+5}[/tex]
Rearrange the expression in quadratic equation.
[tex]\displaystyle \large{0=2x^2+3x+5-19}\\\\\displaystyle \large{0=2x^2+3x-14}\\\\\displaystyle \large{2x^2+3x-14=0}[/tex]
Factor the expression.
[tex]\displaystyle \large{(2x+7)(x-2)=0}[/tex]
Solve like linear equation which we get:
[tex]\displaystyle \large{x=-\dfrac{7}{2}, 2}[/tex]
If you input these x-values in the function, you will get 19 as the output which satisfies the condition.
Hence, inputs are -7/2, 2
Answer:
[tex]x=2, \quad x=-\dfrac{7}{2}[/tex]
Step-by-step explanation:
Set the function to 19:
[tex]\implies 2x^2+3x+5=19[/tex]
Subtract 19 from both sides:
[tex]\implies 2x^2+3x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]: 7 and -4
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2x^2-4x+7x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(x-2)+7(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (2x+7)(x-2)=0[/tex]
Therefore the function's input values that when evaluated give a value of 19 are:
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}[/tex]
[tex](x-2)=0 \implies x=2[/tex]
Help please! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC.
(file is posted below)
The measure of BD and BC are 7 and 7√2 respectively
Triangular altitude theoremA triangle is a shape with 3 sides and angles.
According to the theorem
CD/BD = BD/DA
From the given figure
CD = DA = 14/2
CD = DA = 7
Substitute
7/BD = BD/7
BD² = 7²
BD² = 49
BD = 7
Determine the measure of BC
sin 45 = BD/BC
sin45 = 7/BC
BC = 7/sin45
BC = 7√2
Hence the measure of BD and BC are 7 and 7√2 respectively
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im really not sure with my answer, please tell which is the correct choice.
Answer:
the orange one
Step-by-step explanation:
(10 + 10) : (5-3) =
20 : 2 =
10
Benjamin finds some nickels and quarters under the couch cushions. How many
coins does he have if he has 8 nickels and 12 quarters? How many coins does he have
if he has a nickels and y quarters?
Benjamin has 340 cents or $3.40.
What is Proportion?Proportion in Mathematics is an equation where two or more ratios are made to be equal.
If a : b = c : d, then we can write a/b = c/d
We know that,
1 nickel = 5 cents
8 nickel = x cents
Using ratio and proportion,
1 : 5 = 8 : x
x = 8 × 5 = 40 cents
Similarly,
1 quarter = 25 cents
12 quarters = 12 × 25 = 300 cents
Total cents Benjamin has = 300 + 40 = 340 cents = $3.40
Hence, Benjamin has a total of $3.40.
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6x¹⁸ divided by 9x⁶
please answer fast thanks!
Answer:
[tex]\frac{2}{3}x^{12}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6x^{18}}{9x^6}=\frac{6}{9}*\frac{x^{18}}{x^6}=\frac{2}{3}*x^{18-6}=\frac{2}{3}x^{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x^{18}}{9x^6}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{18-6}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2x^{12}}{3}[/tex]
Question 4
(Essay Worth 10 points)
(06.05 MC)
a Iris is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is
seeds she planted. The function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points) (2
Part C: Evaluate the composite function in Part A for 30 weeks. (4 points)
A) Composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks is f[s(w)] = 50w + 25.
B) The unit of measurement for the composite function is flowers.
C) Number of the flowers for 30 weeks will be 1525.
What is a composite function?A function is said to be a composite function when a function is written in another function. The composite function that represents the number of flowers is f[s(w)] = 50w + 25. and the number of flowers for 30 weeks is 1525.
Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks.
From the given data we will find the function for the number of flowers with time.
f(s) = 2s + 25
We have s(w) = 25w
f[(s(w)]=2s(w) + 25
f[(s(w)] = 2 x ( 25w ) +25
f[s(w)] = 50w + 25.
Part B: What are the units of measurement for the composite function in Part A
The expression f[s(w)] = 50w + 25 will give the number of the flowers blooming over a number of the weeks so the unit of measurement will be flowers.
Part C: Evaluate the composite function in Part A for 30 weeks.
The expression f[s(w)] = 50w + 25 will be used to find the number of flowers blooming in 30 weeks put the value w = 30 to get the number of the flowers.
f[s(w)] = 50w + 25.
f[s(w)] = (50 x 30) + 25.
f[s(w)] = 1525 flowers.
Therefore the composite function is f[s(w)] = 50w + 25. unit will be flowers and the number of flowers in 30 weeks will be 1525.
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Which of the following is a right triangle?
Answer:
B
Step-by-step explanation:
A right triangle must have one of its 3 angles equal to 90°
the only triangle with an angle of 90° is Triangle C
Answer:
B:Triangle
Step-by-step explanation:
What is the name of the expression under the radical symbol in a radical function?
An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.
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N(-2,-2) After a rotation 90 degrees counterclockwise
Answer: (2,-2)
Step-by-step explanation:
Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)
Is (2,11) a solution to the equation y = 3x - 2 ?
Answer:
No (2, 11) is not a solution.
Step-by-step explanation:
y = 3x - 2
Plug in the points:
11 = 3(2) - 2
Solve:
11 = 6 - 2
11 = 4
11 does not equal 4.
Hope this helps.
Answer:
(2,11) is not a solution
Step-by-step explanation:
Substitute the value of x and y in the equation.
y = 3x - 2
Substitute(2,11)
11= 3*2 -2
= 6 - 2
11 ≠ 4
(2,11) is not an solution of the equation
Sum of 1 OK. Now, think of two numbers with a sum of 1.
Answer:
0+1
Step-by-step explanat
Any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
What is sum?The result we get after adding some quantity is called the sum of the data.
Given we need to find two numbers whose sum is 1,
So, we can consider in this case two consecutive numbers of opposite sign the greater number should have a positive sign and the smaller number should have negative sign,
For example =
-4+5 = 1
-3+4 = 1
-2+3 = 1
-9+10 = 1
So, any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.
Hence, there can be many numbers which can give sum of 1.
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which equation has the correct sign on the product
The equation which has the correct sign on the product is 27(-5) = -135
Sign of product- × - = +
- × + = -
+ × - = -
+ × + = +
Given equations:
27(-5) = -135
(-4)(-4) = -16
(-61) (3) = 183
22 × 4 = -88
Correct equation:
27(-5) = -135
(-4)(-4) = 16
(-61) (3) = -183
22 × 4 = 88
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If x = -3, then x 2 - 7x + 10 equals
37
40
22
40
Step-by-step explanation:
[tex]{ \red{ \tt{given \: }}} \: :- \: { \green{ \tt{x = - 3}}}[/tex]
Then, Substitute the value of "x" in this below equation..
[tex]{ \orange{ \tt{ {x}^{2} - 7x + 10}}}[/tex]
[tex]{ \orange{ \tt{ {( - 3)}^{2} - 7( - 3) + 10}}}[/tex]
[tex]{ \orange{ \tt{9}}} \: + \: { \orange{ \tt{21}}} \: + \: { \orange{ \tt{10}}}[/tex]
[tex] = { \orange{ \tt{40}}}[/tex]
7th grade math
(Look at photo!)
Easy math
Answer:
he will buy 4 tickets
Step-by-step explanation:
firts u have to mutilpy 7.50 by a number and start at 1 and go up till u get 30
hope this helps:)!!
What ordered pair is closest to a local minimum of the function, f(x)?
A. (-1, -3)
B. (0, -2)
C. (1, 4)
D. (2, 1)
Reason:
See the screenshot below. I used GeoGebra to plot the points.
The sub group of points D, E, F form a bowl shaped region. Imagine a small parabola passing through these points. Point E is either the local min or very close to it. This is because point E is at the bottom of the bowl shape.
|2x+1|=-13
A. No Solution
B. X = -7
C. X = -14, 12
D. X = -7, 6
Answer:
No solution.
Step-by-step explanation:
[tex]|2x+1| = -13\\\\\text{No solution for}~ x\in \mathbb{R}~ \text{because absolute value cannot be negative.}[/tex]
Which of the following is an example of an exponential function?
A.)f(x) = 4x3 + 2x2 – 3x + 9
B.) g(x) = log2(x)3
C.) h of x equals the quantity x squared plus 2x minus 7 end quantity divided by the quantity x plus 1
D.) p(x) = 500(1.02)x
Answer: D
Step-by-step explanation:
An example of exponential function is p(x) = 500(1.02)x Option D
Which of the following is an example of an exponential function?An exponential function is a mathematical function of the form f(x) = [tex]a * b^x[/tex], where 'a' and 'b' are constants, and 'x' is the variable. The function p(x) = [tex]500(1.02)^x[/tex] is in this form
Where 'a' is 500, 'b' is 1.02, and 'x' is the variable.
The variable 'x' is an exponent, which makes it an exponential function. Option D
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How to find the average collection period
Answer:
dividing a company's yearly accounts receivable balance by its yearly total net sales
Cameron purchased an electric guitar for 1,875. The value of the guitar depreciates by 20% each year. In how many years Will the guitar be valued at $768?
Answer:
4 years
Step-by-step explanation:
Each year the guitar is worth 80% of its previous worth
1875 ( .80)^n = 768 where n = years
n=4
Determine the length of side QS.
A) 1.9
B) 3.4
C) 2.4
D) 5.7
Answer: C) 2.4
Given one opposite angle, two known sides and one missing side.
Hence use cosine rule:
[tex]\sf c = \sqrt{a^2 + b^2- 2ab \ cos\theta}[/tex]
insert values
[tex]\sf c = \sqrt{1.2^2 + 1.4^2- 2(1.2)(1.4) \ cos(134)}[/tex]
simplify
[tex]\sf c = 2.3945 \quad \approx \quad 2.4[/tex]
Please help
Use absolute value to find the distance between 3 and -3 on a number line.
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
How much money would you have in your savings balance after 3 years if you initially invested $900 and had an interest rate of 1%?
$
assuming simple interest
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ t=years\dotfill &3 \end{cases} \\\\\\ A=900[1+(0.01)(3)]\implies A=900(1.03)\implies A=927[/tex]