The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;
f(x) = x² - 9 does not have an inverse.
What is the inverse of a function?An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.
A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements
A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence
The function in the question f(x) = x² - 9
Making x the subject of the function to verify if it has an inverse gives;
x² = f(x) + 9
[tex]x = \pm\sqrt{f(x) +9}[/tex]
Putting x = f⁻¹(x) gives;
[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]
Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.
The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.
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HELP 50 POINT MATH QUESTION MIDDLE SCHOOL
In the proportional relationship table, x would represent distance and y, weight.
The complete table is given in the explanation below.
What is a Proportional Relationship?If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.
x represents distance (cm)
y represents weight (newtons).
Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:
k = y/x = 28/20
k = 1.4
The equation would be y = 1.4x.
Use the equation to complete the table by substituting the value of each missing variables:
Row 2, when x = 55:
y = 1.4(55)
y = 77
Row 3, when y = 140:
140 = 1.4x
140/1.4 = x
100 = x
x = 100
Row 4, when x = 1:
y = 1.4(1)
y = 1.4
The table would be:
Distance (cm) Weight (newtons)
Row 1 20 28
Row 2 55 77
Row 3 100 140
Row 4 1 1.4
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A scientist mixes water (containing no salt) with a solution that contains 20% salt. she wants to obtain 120 ounces of the mixture that is 15 % salt. How many ounces of water and how many ounces of the 20% salt solution should she use?
Answer:Say w= the amount of water in oz, then the 60% of the solution is 250 - w
Set up the equation:
Use distributive property first
0.60(250-w) = 0.15 x 250
Isolate to solve for w
150- 0.60w= 37.5
-0.60w= 37.5-150
0.60w= -112.5
w= 187.5 ounces
250-187.5= 62.5 ounces salt solution
Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.
Hope this helps!
Step-by-step explanation:
In Alex's drawer she has 10 pairs of socks, 8 of which are white, and 9 tee shirts, 2 of which are white.
The probability of choosing a white pair of socks is
The probability of choosing a white tee shirt is
The probability of both being white is
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total socks= 10
White socks= 8
Total T- shirts= 9
White T- shirts = 2
Now, The probability of choosing a white pair of socks is
= 8/10
= 4/5
and, The probability of choosing a white tee shirt is
= 2/9
and, The probability of both being white is
= 4/5 x 2/9
= 8/45
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6 books weigh 1.260 kg. How many books will weigh 3.150 kg?
Answer: 15 books
Step-by-step explanation:
Given that the weight of 6 books is 1.260 kg
⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg
Let the number of books that will weigh 3.150 kg be x
as we know that
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15
The number of books is 15
15 books will weigh 3.150 kg.
Given the weight of 6 books is 1.260 kg
⟹ weight of each book is
1.260/6
=0.210 kg
Let x be the total number of books that weigh 3.150 kg.
as we are aware
weight of x books is 0.210x kg
⟹0.210x=3.150
⟹x= 3.150/0.210
=15
So, the number of books is 15.
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A small rectangle has a width of 5cm and a length of 7cm. using the same ratio, what will be the length of a bigger rectangle it its width is 90cm?
Factor: 64x³ + 125y³
64x³+125y³
= (4x+5y)( 16x²-20xy+25y²)
a³ + b³ = ( a + b )( a² - ab + b² )
64x³ + 125y³
= ( 4x )³ + ( 5y )³
= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]
= (4x+5y)( 16x²-20xy+25y² )
8.7% increase of 525 what is answer
Answer:
Step-by-step explanation:
570.675
Simplify the variable expression by evaluating its numerical part, and enter
your answer below.
g- 16/4 +2
simplification of expression will be g - 2
Our expression is g - 16/4 + 2
16/4 = 4
so we c will write it as
g - 4 + 2
which can be further simplified to
g - 2
Therefore, our simplified expression comes out to be g - 2.
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Consider the equation and the following ordered pairs: (−3,y) and (x,2). y=−3x−1 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation. Answer Keyboard Shortcuts Complete the table below. x y row 1−3 Answer row 2 Answer 2
Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.
How to Compute Missing Values that Satisfies an Equation?An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.
Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:
y = -3(-3) - 1
y = 9 - 1
y = 8
The missing value in the ordered pair is: (-3, 8).
To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:
2 = -3x - 1
2 + 1 = -3x
3 = -3x
3/-3 = x
x = -1
The missing value is (-1, 2).
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A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?
Use I=PRT
p=12,000
r=4%
t=3year
find I
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]
Please help me verify. I am stuck.
The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.
Proving the identityThe identity is presented as follows:
[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]
Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:
[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]
The following identity relates the square of the secant and of the tangent:
[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]
Hence:
[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]
Thus the remaining expression is:
[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]
The equations of the cotangent, secant and tangent are given as follows:
Cotangent: cosine/sine.Secant: 1/cosine.Tangent: sine/cosine.Hence:
[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]
One divided by the sine is the cosecant, as follows:
[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]
Hence the simplified expression is:
[tex]\csc{\beta} + 1[/tex]
Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.
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What Did the Baby Porcupine Say
When It Backed Into a Cactus?
each
Answer:
As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give call to its mother.
Step-by-step explanation
He said hi Ma.
Fewer than %97 of adults have a cell phone. In a reputable poll of 1160 adults, %88
said that they have a cell phone. Find the value of the test statistic
The value of the test statistic of the hypotheses is; -17.969
How to find the test statistic?
The test statistic is defined as a number, calculated from a statistical test, which is used to find if your data could have occurred under the null hypothesis.
We are given;
Sample size; n = 1160
Sample proportion; p^ = 88% = 0.88
Population proportion; p = 97% = 0.97
The claim is about the population proportion (p) in the hypotheses. Since we are told that fewer than 97% of adults have a cell phone, then the claim is; p < 0.97
The null hypothesis is expressed as;
H₀: p = 0.97
The alternative hypothesis is expressed as;
Hₐ: p < 0.97
The value of the test-statistic is gotten from the formula;
z = (p^ - p)/(√(p(1 - p)/n))
z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))
z = -17.969
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For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 6 or greater than 9.
The probability that the sum will be less than 6 or greater than 9 is
The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).
What is the likelihood of rolling two dice together?The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.
I am assuming that you are rolling two dice.
Probability of even: 18 "evens" out of 36 total outcomes = 18/36
→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)
Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36
→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)
Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36
→(4,6), (5,5), (6,4), (6,6)
evens OR >9s NOT both
18/36 + 6/8 - 4/36 = 20/36 = 5/9.
The probability that the sum is 5/9.
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Represent the following expressions as a power of the number a where a ≠ 0: (a^3)^-2. PLEASE ANSWER I WILL GIVE BRAINLYEST
Answer:
a^-6 or 1/a^6
Step-by-step explanation:
(a³)-²
=a^-6
=1/a^6
there are 32 steps in one floor of a tower max lives .he climbs 6 floors of his building. if he clims 6 floor every day , how many steps does he climb every week
Answer:
1,344
Step-by-step explanation:
First, find how many steps he climbs every day
32*6=192
Now, multiply that by 7 to see how many he climbs in a week
192*7=1,344
determine the degree, leading coefficient and constant term or each polynomial
1. x+5
degree:______
leading coefficient:_____
constant term:____
For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.
What are polynomials?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The given polynomial is x+5.
(1) The degree is the highest power of the polynomial.
Degree = 1
(2) The leading coefficient is 1.
(3) The constant term is 5
Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 220 numerical entries from the file and r = 52 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.
(i) Test the claim that p is less than 0.301. Use = 0.05.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p < 0.301; H1: p = 0.301
H0: p = 0.301; H1: p ≠ 0.301
H0: p = 0.301; H1: p > 0.301
H0: p = 0.301; H1: p < 0.301
Correct: Your answer is correct.
(b) What sampling distribution will you use?
The Student's t, since np > 5 and nq > 5.
The standard normal, since np > 5 and nq > 5.
The Student's t, since np < 5 and nq < 5.
The standard normal, since np < 5 and nq < 5.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
The hypothesis are given as follows:
H0: p = 0.301; H1: p ≠ 0.301.
a) The level of significance is of 0.05.
b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.
The test statistic is of: z = -2.09.
c) The p-value is of: 0.0366.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:
[tex]H_0: p = 0.301[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:
[tex]H_1: p \neq 0.301[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
The parameters of the equation are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters for this test are:
[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]
Hence the value of the test statistic is of:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]
z = -2.09.
What is the p-value?We have a two-tailed test, as we are testing if the proportion is different of a value.
Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.
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The table below shows a proportional relationship between h and j.
h
18
27
48
j
6
9
16
Find the constant of proportionality from h to j. Express
your answer as a fraction in reduced terms.
As per the proportional relationship, the constant of the proportionality is 1/3
Proportional relationship
A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.
The standard form of proportional relationship is written as.
y = k x
where k refers the constant of proportionality.
Given,
The table shows the proportional relationship between h and j.
Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.
We know that the standard form of the proportionality is written as,
y = k x
So, here y takes the value of j and x takes the values of h.
Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,
=> 6 = k (18)
Here we need the value of k, so move the number to the other side then we get,
=> k = 6/18
When we reduce this, then we get,
=> k = 1/3
Therefore, the constant of proportionality is 1/3.
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2. Determine if the diagram is a function.
Why or why not?
Please
Answer:
IT IS A FUNCTION
It is specifically a Surjective/ onto Mapping/function
Step-by-step explanation:
surjective or onto function is when y has an image in x
Answer:
The graph is a function
Step-by-step explanation:
-For every input (x) there is only one output value (y)
Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.
Ex.
X: 2, 4, 7 , 2, 5 This is not a function. More than one input for each output.
Y: 1, 2, 4, -3, 7
Ex.
X: 5, 6, -5, 8 this is a function. Exactly one input for every output.
Y: 1, 4, 5, 9
need help with this asap first answer will get brainliest
Answer:
x° = 34°
Step-by-step explanation:
First, find the interior angle supplementary to the given exterior angle 124°.
I will label it y.
124° + y° = 180°
y° = 180° - 124°
y° = 56°
Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.
x° + y° + 90° = 180°
x° + y° = 90°
x° + 56° = 90°
x° = 90° - 56°
x° = 34°
Answer:
x = 34---------------------------
Exterior angle in the triangle is the sum of remote interior angles124 = x + 90x = 124 - 90x = 34Two buses leave a station at the same time and travel in opposite directions. On bus travels 17 km/h faster than the other. If the two buses are 836 kilometers apart after 4 hours, what is the rate of each bus
Step-by-step explanation:
speed = distance / time
to get distance, we have to multiply by time.
the speed the 2 busses are moving seat from each other is
x + (x + 17) = 2x + 17
x = the speed of one bus
x + 17 = the speed of the other bus.
so, after 4 hours the distance between them is
(2x + 17) × 4 = 836
2x + 17 = 209
2x = 192
x = 96 km/h
bus 1 travels at 96 km/h.
bus 2 travels at 96+17 = 113 km/h.
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6
How to determine the correct statementInformation given in the question
f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity
This is written as (x + 6) / ( x² - 9x + 18 )
factorizing the denominator gives
(x + 6) / {( x - 6)( x - 3)}
In the denominator
At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:
f(x) is decreasing for all x < 6: contains x = 3 and result to a higher value
f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing
f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4
Therefore the correct option is f(x) is increasing for all x > 6
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Describe the graph of g?
The given points gives us a line with constant slope of -2.
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
The points are in the form of ( x, y) , where y= g(x)
Plot these points on the graph and join the points through a line.
Refer to the attachment for the graph.
The slope is constant.
consider any 2 points:
(x,y) = (0,7)
(m,n) =(2,3)
Slope = change in y values/ change in x values
= (7-3)/(0-2) = 4/-2 = -2
The given points gives us a line with constant slope of -2.
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Solve 2x-7 = 3x-2(x+8) for x
Answer:
x = -11
Step-by-step explanation:
2x - 7 = 3x - 2x - 18
2x - 7 = x - 18
collect like terms
2x - x = 7 - 18
x = -11
A fish tank has a capacity of 154L.
What is the volume of the fish tank?
The volume of the fish tank required = 0.154 m^3.
A fish tank has a capacity = 154L.
Capacity of fish tank in Litre = Volume of the fish tank in meter cube
So the volume of the fish tank required in cubic meter.
For the volume we required a conversion of litre into meter cube.
Cubic meters and liters are two common metric units of volume.
1 cubic meter is 1000 liters.
To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.
1L = 0.001 m^3
So 154L = 0.154 m^3
So the volume of the fish tank required = 0.154 m^3.
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4.
Consider the following diagram:
What is the value of m?
56°
m
68°
According to the solving the Angle m = 124
What is the name for a straight angle?An angle with something like a vertex point at 180 degrees is considered to be a straight angle in geometry. Basically, it produces a straight line with sides that are turned away from the vertex. "Flat angles" is another term for it.
How do you see a straight angle?A straight line appears to have a straight angle. Here's an illustration of a straight angle. a straight line that has a half circle in the middle and at the top to symbolize a straight angle.
According to the given data:The sum of all angles in triangle = 180.
Angle A = 56
Angle B = 68
Angle C =
A + B + C = 180
56 + 68 + C = 180
124 + C = 180
C = 180 - 124
C = 56
if Angle C = 56
so we know the property of straight angle:
= Angle m + 56 = 180
Angle m = 180 - 56
Angle m = 124
According to the solving the Angle m = 124
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Given that capital is fixed, what do you figure is the marginal cost or additional cost of producing another:
haircut
sandwich
Ferris Wheel ride
The marginal cost is the labor utilized in order to provide an additional cost of a haircut.
What is the marginal cost?The marginal cost is the extra cost of generating one additional unit of output.
The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.
Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.
Change in cost / Change in quantity Equals Marginal cost.
The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.
Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.
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HELP PLEASE QUICKLY!!!!
The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).
What is the expression?The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.
Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.
7(3y - 1/11)
= 7 x (3y - 1/11)
= 21y - 7/11
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