Answer:
a) rational
b) rational
c)exponential
d) power function
e) polynomial function of degree 6
f) trig function
Step-by-step explanation:
Functions can be classified by the operations they contain. Remember the following functions:
Power function has as its main operation of an exponent on the variable.Root function has as its main operation a radical.Log function has as its main operation a log.Trig function has as its main operation sine, cosine, tangent, etc.Rational exponent has as its main function division by a variable.Exponential function has as its main operation a variable as an exponent.Polynomial function is similar to a power function. It has as its main function an exponent of 2 or greater on the variable.Below is listed each function. The bolded choice is the correct type of function:
(a) y = x − 3 / x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3
(b) y = x + x2 / x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function
(c) y = 5^x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function
(d) y = x^5 trigonometric function power function exponential function root function logarithmic function
(e) y = 7t^6 + t^4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6
(f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
The functions (a) y = x − 3 / x + 3 is a rational function, (b) y = x + x2 / x − 2 is a rational function, (c) y = 5ˣ is an exponential function, (d) y = x⁵ is a power function, (e) y = 7t⁶ + t⁴ − π is a polynomial function, (f) y = cos(θ) + sin(θ) is a trigonometric function.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
(a) y = x − 3 / x + 3 is a rational function, as the terms are rational.
(b) y = x + x2 / x − 2 is a rational function, as the terms are rational.
(c) y = 5ˣ is an exponential function as the x is in the power.
(d) y = x⁵ is a power function, as 5 is the power.
(e) y = 7t⁶ + t⁴ − π is a polynomial function of degree 6 as the highest degree is 6.
(f) y = cos(θ) + sin(θ) is a trigonometric function, as the cos and sin are trigonometric functions.
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Solve the equation (linear equation)
[tex]4^{x-7}[/tex] × [tex]8^{2x-3} =\frac{32}{2^{x-9} }[/tex]
Answer: [tex]x=\frac{37}{9}[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
[tex](m^n)(m^l)=m^{(n+l)}[/tex]
Rewrite 4, 8 and 32 as following:
4=2²
8=2³
32=2⁵
Rewrite the expression:
[tex](2^2)^{(x-7)}*(2^3)^{(2x-3)}=\frac{32}{2^{(x-9)}}[/tex]
Keeping on mind the exponents properties, you have:
[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=32(2^{-(x-9)}[/tex]
[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=(2^5)(2^{-(x-9)})\\\\(2)^{(2x-14)}*(2)^{(6x-9)}=(2^5)(2^{(-x+9)})\\\\2^{((2x-14)+(6x-9))}=2^{(5+(-x+9))}[/tex]
As the bases are equal, then:
[tex](2x-14)+(6x-9)=5+(-x+9)\\\\2x-14+6x-9=5-x+9\\\\8x-23=14-x\\9x=37[/tex]
[tex]x=\frac{37}{9}[/tex]
Answer:
[tex]x=4\frac{1}{9}[/tex]
Step-by-step explanation:
We are given the following linear equation and we are to solve it:
[tex] 4 ^ { x - 7 } \times 8 ^ { 2x - 3 } = \frac { 32 } { x ^ { x - 8 } } [/tex]
Changing the constants to the same base to make it easier to solve:
[tex] 2 ^ { 2 ( x - 7 ) } \times 2^ { 3 ( 2x - 3 ) } = \frac { 2 ^ 5 } { 2 ^ { x - 9 } } [/tex]
[tex]2^{2x-14} \times 2^{6x-9} = 2^{5}(2^{-x+9})[/tex]
[tex] 2 ^ { 2x - 14 + 6x - 9 } = 2 ^ { 5 - x + 9 } [/tex]
[tex] 2 x + 6x - 14 - 9 = 5 - x + 9 [/tex]
[tex]8x+x=14+9+5+9[/tex]
[tex]9x=37[/tex]
[tex]x=4\frac{1}{9}[/tex]
How do the expressions 72 / 9 and -72/ (-9) compare when they are evaluated?
A. They have different values and are different signs.
B. They have different values but are the same sign.
C. They have the same value but are different signs.
D. They have the same value and the same sign.
Answer:
D. They have the same value and the same sign.
Step-by-step explanation:
72 / 9 and -72/ (-9)
Answer:
D
Step-by-step explanation:
just took the test
Each bottle of lemonade costs the local soccer team $0.75 they have $437.25 in their treasury to buy as many bottles of lemonade as possible to sell for a profit at their soccer games. How many bottles can they afford to buy.
$437.25 ÷ $0.75 = 583 bottles of lemonade
Hope this helps :)
State the domain and range of the graph in interval notation.
Answer:
The domain is the interval [tex][-6,6][/tex]
The range is the interval [tex][-2,2][/tex]
Step-by-step explanation:
we know that
Observing the graph
The domain is the interval [tex][-6,6][/tex]
All real numbers greater than or equal to -6 and less than or equal to 6
The range is the interval [tex][-2,2][/tex]
All real numbers greater than or equal to -2 and less than or equal to 2
The graph's domain spans from -6 to 6, and the range extends from -2 to 2. In summary, the domain is [-6, 6], and the range is [-2, 2].
In the given graph, the domain represents all possible input values, and it spans from -6 to 6, inclusive. This is because the graph includes every real number greater than or equal to -6 and less than or equal to 6 along the horizontal axis.
The range, on the other hand, corresponds to the output values of the function and extends from -2 to 2, inclusive. This is derived from the observation that the graph encompasses all real numbers greater than or equal to -2 and less than or equal to 2 along the vertical axis.
The domain is [-6, 6], indicating all real numbers between -6 and 6, and the range is [-2, 2], signifying all real numbers between -2 and 2. The graph visually illustrates these intervals as the inclusive bounds for both domain and range.
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The ratio of boys to girls in a group is 5:3. If there are 16 more boys than girls, work out how many people there are in total.
We find that there are 24 girls and 40 boys, leading to a total of 64 people in the group.
To solve for the total number of people in the group given the ratio of boys to girls and the information that there are 16 more boys than girls, we can set up a proportion based on the ratio 5:3. Let the number of girls be represented by x and the number of boys be represented by x + 16, as there are 16 more boys than girls. From the ratio 5:3, we know that for every 8 parts (5+3), there are 5 parts boys and 3 parts girls. This gives us two equations: 5/8 of the total is boys, and 3/8 of the total is girls.
From the information given:
(x + 16) / x = 5 / 3
Cross-multiplying gives us:
3(x + 16) = 5x
3x + 48 = 5x
48 = 5x - 3x
48 = 2x
x = 24
This means there are 24 girls. Since there are 16 more boys, this means there are 24 + 16 = 40 boys. Adding up the boys and girls gives us the total number of people in the group:
40 boys + 24 girls = 64 people in total.
will mark brainliest !!!!!!
The base of the middle triangle is 3 and the base of the larger one is 6, so the larger triangle is twice the size of the middle one.
Multiply the height of the middle one by 2 to get the height of the larger one, which is labeled n.
n = 5 x 2 = 10
Justin receives $15 $ 15 and puts it into his savings account. He adds $0.25 $ 0 . 25 to the account each day for a number of days, d , after that. He writes the expression 15+0.25(?1) 15 + 0 . 25 ( d - 1 ) to find the amount of money in his account after d days. Which statement about his expression is true?
Answer:
15.25
Step-by-step explanation:
Answer:
It is the sum of the initial amount and the additional amount after d days.
Step-by-step explanation:
It is the sum of the initial amount and the additional amount after d days.i have ttm
Which choice is equivalent to the product below? Square root Of 8 Times Square root 3
Answer:
The answer would be around 3.7
Step-by-step explanation:
Which expressions are equivalent to 5x-15?Check all that apply
5(x+15)
5(x-3)
4x+3y-15-3y+x
-7y-6x-8y+x
-20-3x+5+8x
Answer:
Step-by-step explanation:
4×+3Y-15-3y+×
The equivalent expressions to 5x-15 are 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x. These simplify to 5x-15 when combining like terms and distributing, matching the original expression.
The student is asking which expressions are equivalent to 5x-15. To find the equivalent expressions, we need to check each option to see if they simplify to the same form.
5(x+15) is not equivalent because when you distribute the 5, you get 5x + 75, which is not the same as 5x - 15.5(x-3) is equivalent because when you distribute the 5, you get 5x - 15, which matches the original expression exactly.4x+3y-15-3y+x is equivalent because when you combine like terms (4x + x and 3y - 3y), you get 5x - 15.-7y-6x-8y+x is not equivalent because even if you combine like terms, the x terms do not add up to 5x, nor do the constants add up to -15.-20-3x+5+8x is equivalent because when you combine like terms (-3x + 8x), you get 5x, and when combining constants (-20 + 5), you get -15; hence, it simplifies to 5x - 15.Therefore, the expressions 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x are equivalent to 5x - 15.
if the air temperature is 20°c and the relative humidity is 55 percent, will the dew point be reached if the temperature drops to 20°C?
Answer:
Your dew point would be at 10.
Step-by-step explanation:
35 POINTS HELP PLEASE! RUNNING OUT OF TIME!
Answer:
[tex]\large\boxed{9x^8,\ 25x^{12},\ 36x^{16}}[/tex]
Step-by-step explanation:
[tex]Use\\(\sqrt{s})^2=s\ for\ s\geq0\\(a^n)^m=a^{nm}\\(ab)^n=a^nb^n\\a^n\cdot a^m=a^{n+m}\\===========================\\6x^2=(\sqrt6)^2x^2=(x\sqrt6)^2\to\boxed{NOT}\\\\9x^8=3^2x^{4\cdot2}=3^2(x^4)^2=(3x^4)^2\to\boxed{YES}\\\\16x^9=4^2x^{8+1}=4^2x^{4\cdot2}\cdot x=4^2(x^4)^2x=(4x^4)^2x\to\boxed{NOT}\\\\25x^{12}=5^2x^{6\cdot2}=5^2(x^6)^2=(5x^6)^2\to\boxed{YES}\\\\36x^{16}=6^2x^{8\cdot2}=6^2(x^8)^2=(6x^8)^2\to\boxed{YES}[/tex]
Answer:
[verb] to allow someone to do; to allow something; to acquiesce on something; to concede something.
Ernestine deposited $6800 into a savings account that earns 3.5% simple interest each year calculate annually what is the future value of understands account to 16 years
Answer:
[tex]\$10,608[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=16\ years\\ P=\$6,800\\r=0.035[/tex]
substitute in the formula above
[tex]A=\$6,800(1+0.035*16)=\$10,608[/tex]
Quick does anyone know the answer to this algebra question? Will give brainiest
Reducing the equation, we get:
3^(3-3a) = 3^(-2a)
So 3-3a = -2a, a = 3.
The value of the variable 'a' will be 3. Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
[tex]7 + 42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a} + 7[/tex]
Simplify the equation, then we have
[tex]42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a}\\\\3^{2 - 3a} = \dfrac{1}{3} \cdot 3^{-2a}\\\\\left (3 \right )^{2 - 3a } } = (3)^{-1 - 2a}[/tex]
Compare the power of the number 3, then we have
- 1 - 2a = 2 - 3a
3a - 2a = 2 + 1
a = 3
The value of the variable 'a' will be 3. Then the correct option is C.
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(Q8) The graph of an exponential function is given. Which of the following is the correct equation of the function? (Picture Provided)
Answer:
b. [tex]y=3.9^x[/tex]
Step-by-step explanation:
Remember that the standard exponential function is [tex]y=ab^x[/tex]
where
[tex]a[/tex] is the coefficient
[tex]b[/tex] is the base
If [tex]b>0[/tex], the function is growing
If [tex]0<b<1[/tex] the graph is decaying
We can infer from the graph that the function is growing, so we can discard [tex]y=0.45^x[/tex] and [tex]y=0.73^x[/tex].
Now, to evaluate our tow remaining equations, we are using the test values [tex]x=0[/tex] and [tex]x=1[/tex]:
For [tex]y=1.8^x[/tex]
For [tex]x=0[/tex]
[tex]y=1.8^0[/tex]
[tex]y=0[/tex]
For [tex]x=1[/tex]
[tex]y=1.8^1[/tex]
[tex]y=1.8[/tex]
The graph passes through the points (0,1) and (1, 1.8)
For [tex]y=3.9^x[/tex]
[tex]x=0[/tex]
[tex]y=3.9^0[/tex]
[tex]y=0[/tex]
[tex]x=1[/tex]
[tex]y=3.9^1[/tex]
[tex]y=3.9[/tex]
The graph passes through the points (0,1) and (1, 3.9)
We can see in the graph when [tex]x=1[/tex], [tex]y[/tex] is almost 4, so we can conclude that the correct equation is [tex]y=3.9^x[/tex]
Myra invested $10,000 in an account earning a nominal 8% per year compounded continuously. How much was in the account at the end of one year? Round the answer to nearest dollar.
Answer:
[tex]\$10,833[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=1\ years\\ P=\$10,000\\ r=0.08[/tex]
substitute in the formula above
[tex]A=\$10,000(e)^{0.08*1}=\$10,833[/tex]
Compound interest computed continuously after one year on a principal sum of $10,000 with an 8% interest rate will yield $10,833, rounded to the nearest dollar.
Explanation:Your question relates to the mathematics topic of compound interest. When interest is compounded continuously, we use the formula A = P * e^(rt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
In your case, you are looking to find how much $10,000, invested at a nominal 8% per year compounded continuously, would amount to at the end of one year. Substituting the given values into the formula, we have:
A = $10,000 * e^(0.08*1).
The value of 'e' is approximately 2.71828. Therefore, we calculate:
A = $10,000 * 2.71828^0.08 = $10,833.
So, the amount in the account at the end of one year, rounded to the nearest dollar, would be $10,833.
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1.) 2x + y = 3 2.) x - 2y = -1 If equation 1 is multiplied by 2 and then the equations are added, the result is
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. What percent of students scored below Jake? Include a step by step description of the process you used to find that percentage. (Round your answer to the nearest whole number.)
Answer:
63 percent student scored below Jake.
Step-by-step explanation:
For finding the percentile
Step 1: Subtracting mean from Jake’s score
=520-500
=20
Step 2: Calculating z-score
The z-Score is found by dividing the difference obtained in step 1 by SD of the data
z-score= 20/60
z-score=0.333
Step 3: Converting the z-score to percentile
The z-score will be converted to percentile using the z-score to percentile conversion table, the value of percentile for 0.3333 is 63rd .
So, 63 percent students scored below Jake.
What is the value of X in the triangle below to the nearest degree? The triangle is not drawn to scale. I selected an answer but I’m not sure about it
Answer:
x = 25
Step-by-step explanation:
To find the value of x we use the formula:
tan x° = opposite side /adjacent side
Opposite Side = 8
Adjacent Side = 17
tan x° = 8/17
tan x° = 0.4705882352941
[tex]Tan^{-1}[/tex] of [tex]0.4705882352941[/tex]
x° = 25
in the symbol AB, the letter A represents a(n) ANSWERS : a.) segment b.) ray c.) point d.)plane
It would have to be C. point.
Since it says AB that marks two points and a line in between them. If only talking about A, it would be a point.
Option: C is the correct answer.
c.) Point
Step-by-step explanation:In the symbol AB:
AB represents a line segment which connects point A to point B.
If there would be an arrow over this with right arrow then it would represent a ray which originates at point A an it extends to infinity from the other direction.
Hence the letter A will represent a : Point.
What is the surface area of a box that is 237.7 in squared if it is scaled up by 10
Which expression best represents the product of two consecutive integers? CLEAR CHECK x?(2+x) x?(x+1) 2?(x+1) 2x+2
Answer:
The product of two consecutive integers:x · (x+1) = x(x + 1)Step-by-step explanation:
Consecutive integer:
... -2, -1, 0, 1, 2, 3, ...
Difference between two consecutive integers is equal to 1.
Therefore two consecutive integers is x and x + 1.
What is the sum of the series 3,---5,-13..........-229
ANSWER
[tex]S_{30}= - 3390[/tex]
EXPLANATION
The given sequence is
3,-5,-13,.....-229.
The first term of this sequence is
a_1=3
There is a common difference of
[tex]d = - 5 - 3 = - 8[/tex]
The last term of this sequence is -229.
The nth term of this sequence is given by:
[tex]a_n=a_1+d(n-1)[/tex]
We use the last term to determine the number of terms in the sequence.
[tex] - 229 = 3 + - 8(n - 1)[/tex]
[tex]- 229 - 3= - 8(n - 1)[/tex]
[tex]- 232= - 8(n - 1)[/tex]
Divide through by -8;
[tex]29= (n - 1)[/tex]
[tex]n = 30[/tex]
Hence there are thirty terms in the sequence.
The sum of the first n terms is given by:
[tex]S_n= \frac{n}{2} ( a_{1} + l)[/tex]
The sum of the first 30 terms is given by:
[tex]S_{30}= \frac{30}{2} ( 3 + - 229)[/tex]
[tex]S_{30}=15( - 226)[/tex]
[tex]S_{30}= - 3390[/tex]
Complete the statements describing investments by filling in the correct words. Different investments have different levels of and offer different rates of return. For example, investing in property than investing in bonds.
Answer:
Risk
More risky
Step-by-step explanation:
Got it right on edmunto
Different investments have different levels of - RISKS and offer different rates of return. For example, investing in property is MORE RISKY than investing in bonds.
The property rates can change drastically within a short period of time, while bonds are static in income. This is why investing in property is riskier than investing in bonds.
A warehouse worker moved 108 pallets in 4.5 hours. In minutes, what is the rate to move one pallet? The worker will be off the clock in 2 hours. How many pallets can he move before quitting time?
Number of pallets moved in 4.5 hours = 108
converting 4.5 hours in minutes we get,
4*60 + 0.5*60 = 240+30 = 270 minutes
So, 108 pallets were moved in = 270 minutes
1 pallet was moved in = [tex]\frac{270}{108}=2.5[/tex] minutes
As the tie will get over in 2 hours or 2*60 = 120 minutes, the number of pallets that can be moved will be = [tex]\frac{120}{2.5}= 48[/tex] pallets.
Hence, 48 pallets can be moved before quitting time.
Answer:
The answer is 2.5 minutes; 48 pallets
Step-by-step explanation:
Number of pallets worker moved in a warehouse = 108
Number of hours it takes to do so = 4.5
Rate at which they require to move one pallet is given by
Number of pallets worker moved in a warehouse = 108
Number of hours it takes to do so = 4.5
Rate at which they require to move one pallet is given by
4.5/108 x 60 minutes = 2.5 minutes
Now, if the worker will be off the clock in 2 hours ,
So, number of pallets he can move before quitting time is given by
In 4.5 hours, number of pallets they moved = 108
In 1 hour, number of pallets they moved = 108/4.5 = 24
In 2 hours, number of pallets they moved = 24 x 2 = 48
HELP PLEASE LAST QUESTION I NEED!!!!!!!!!!!!!!!!!
The question is a little blurry. I can't read it.
Answer:
I believe the answer is c.
Step-by-step explanation:
20 POINTS!!!!!!!!!
Which data sets could be used to create the box plot below?
4, 11, 8, 12, 1, 6, 14
10, 6, 9, 14, 1, 6, 12, 7
14, 10, 6, 9, 11, 8, 1
6, 8, 11, 1, 7, 14, 10
7, 9, 11, 1, 6, 7, 14, 8
Select more than one answer
4,12,16,22,32,45648383929282
Answer:
B.) 10, 6, 9, 14, 1, 6, 12, 7
&
D.) 6, 8, 11, 1, 7, 14, 10
Step-by-step explanation:
i got it right
In 2000 there were approximately 27 million people 18-24 years old in the United States.
Find the exact value of sine, cosine, and tangent of A and T for each triangle.
Answer:
See below
Step-by-step explanation:
19)
13² = 4² + AM²
169 = 16 + AM ²
AM ² = 153
AM =√153 = √(9× 17) = 3√17
sinA = MT /AT = 4/13
cosA = AM/AT = (3√17)/13
tanA = MT/AM = 4/(3√17) = (4√17)/51
sinT = AM/AT = (3√17)/13
cosT = MT/AT = 4/13
tanT = AM/MT = (3√17)/4
20)
10² = 5² + AJ²
100 = 25 + AJ²
AJ² = 75
AJ = √75 = √(25×3) = 5√3
sinA = JT/AT = 5/10 = ½
cosA = AJ/AT = (5√3)/10 = (√3)/2
tanA = AJ /AJ = 5/(5√3) = (√3)/3
sinT = AJ/AT = (5√3)/10 = (√3)/2
cosT = AJ/AT = 5/10 = ½
tanT = AJ/JT = (5√3)/5 = √3
Need Answer ASAP
What is the equation of a line that is parallel to y=47x−3 and passes through (14, 4) ?
PARALLEL slopes always have the same slope no matter what because they are parallel
Answer:
[tex]y=47x-654[/tex]
Step-by-step explanation:
To find the line parallel to the given linear equation, we have to use the same slope, because the condition of parallelism is that they must have the same slope.
So, the slope of the given line is [tex]m=47[/tex], because it's expressed in slope-intercept form, where the coefficient of the variable x is the slope.
Now, we know that they new parallel lines must have a slope equal to 47, and must pass through (14,4). Using this data, we apply the point-slope formula to find the equation of the new line:
[tex]y-y_{1}=m(x-x_{1})\\y-4=47(x-14)\\y=47x-658+4\\y=47x-654[/tex]
The image attached shows the parallelism.
Therefore, the answer is [tex]y=47x-654[/tex]
Please help me out if possible. :)
Answer:
R(c - a, b)Step-by-step explanation:
Look at the picture.
R(x, y)
y - is the same as second coordinate of the point Q → y = b
x - is first coordinate of the point S reduced by distance a → x = c - a