Can anyone help me with these two true/false questions? :)
9. Determine whether the statement is always, sometimes, or never true.
A cubic function has an inverse.
a. always true
b. sometimes true
c. never true
10. Determine whether the statement is always, sometimes, or never true.
A linear function has an inverse relation.
a. always true
b. sometimes true
c. never true
___
Thanks!,
Answers
Answer:
9. b. sometimes true
10. a. always true
Explanation:
9. Any function will have an inverse relation. This question is not specific as to whether that inverse relation must be a function. We will assume that that is the intent.
The attached graph shows a cubic function with an inverse function (green), and another without (red).
A cubic function will have an inverse function sometimes.
____
10. As stated above, any function will have an inverse relation.
A linear function will have an inverse relation always.
__
The graph shows a linear function with an inverse function (green), and one that has an inverse relation, but not an inverse function (red).
Related Questions
The management of the unico department store has decided to enclose an 833 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)
Answers
To maximize area and minimize perimeter, you want a figure that is as close to equilateral as you can get. Therefore we take the square root of our area:
√833 = 28.9.
Dividing 833/28.9 we get 28.8.
We want to use the shorter side, 28.8, for the pine boards, as they cost more. 28.8*2*6 = 345.60.
The cost of the steel side is given by 28.9*2 = 57.80.
Together it costs 345.60+57.80 = 403.40.
If tan theta= 15/8, then:
A. sec theta = 17/8
B. cos theta = 15/17
C. cot theta = 8/15
D. csc theta = 17/15
There's potentially more than one answer.,
Answers
The only thing we have to do here is remember our trigonometric functions!
sin=y/r
cos=x/r
tan=y/x
sec=r/x
csc=r/y
cot=x/y
Knowing that tanᎾ=15/8, we know that y=15 and x=8
Now we need to look at the answer choices and see if they are correct.
A. secᎾ=17/8
Since secᎾ=r/x and r=17 and x=8, this is correct.
B. cosᎾ=15/17
Since cosᎾ=x/r and x=8 and r=17, this is wrong.
C. cotᎾ=8/15
Since cotᎾ=x/y and x=8 and y=15, this is also correct!
D. cscᎾ=17/15
Since cscᎾ=r/y and r=17 and y=15, this is right too.
I really hope this helps!
Best wishes :)
Answer:
secᎾ=17/8
cotᎾ=8/15
cscᎾ=17/15
Step-by-step explanation:
One of the sides of a parallelogram has the length of 5 in. can the lengths of the diagonals be: c 6 in and 7 in?
Answers
In a parallelogram, only the opposite sides of the parallelogram are congruent. All the sides don't have to be congruent. Therefore we can have different measurement for the diagonals.
In a square, all of the diagonals would have to be the same.
The dimensions of 5 inches for a side and diagonals of 6 inches and 7 inches for a parallelogram violate the Pythagorean theorem and therefore are not possible for any right-angled triangle, suggesting an error if considered for a parallelogram.
Explanation:The question is whether parallelogram sides can correspond to the dimensions given, with one side being 5 inches and the possible diagonals being 6 inches and 7 inches respectively. By applying the Pythagorean theorem, we can deduce that a parallelogram with such dimensions may not be possible due to the constraints of the theorem.
Given the Pythagorean theorem, expressed as a² + b² = c², the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. If we consider the diagonals and the side as parts of a right triangle, then 6² + 5² does not equal 7² (36 + 25 = 61, which is not equal to 49).
Therefore, it is not possible for a parallelogram to have side lengths and diagonal lengths as described in the question because the mathematically described conditions violate the rules of the Pythagorean theorem.
Stephanie is 20 years old and has a base annual premium of $930 and a rating factor of $1.30. What is her total premium?
A) $1,209
B) $100.75
C) $604.50
D) $1,032.65
Answers
Hope I help
Answer:
Her total premium would be $1,209.00
Other answer is incorrect.
19. How many 2-inch segments are there in 12 ft.? A. 24 B. 72 C. 10 D. 6
Answers
There are 24 2-inch segments in 12 ft.
State the property that justifies the statement:
If 3x = 6, then x = 2
a. Subtraction Property of Equality
b. Addition Property of Equality
c. Division Property of Equality
d. Multiplication Property of Equality
Given that AD and BC are parallel, find the value of x.
a. 15
b. 5
c. 12.5
d. 17.5
Answers
Convert the angle \theta=\dfrac{23\pi}{20}θ= 20 23π theta, equals, start fraction, 23, pi, divided by, 20, end fraction radians to degrees
Answers
For this case we have the following angle in radians:
[tex] theta = \frac{23\pi}{20} [/tex]
The first thing you should know to answer the question is the following conversion:
π radians = 180 degrees
Applying the conversion to the given angle we have:
[tex] theta = \frac{23\pi}{20}*\frac{180}{\pi} [/tex]
Rewriting we have:
[tex] theta = 207 [/tex]
Answer:
the angle measured in degrees, it is given by:
[tex] theta = 207 [/tex]
What is the specific name for a regular quadrilateral?
Answers
The specific name for a regular quadrilateral is a polygon
~cutie
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
Answers
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
cashews - 6.50 per pound * c pounds = 6.5c
the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)
to solve for p and c lets use simultaneous equations
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
The polygons below are similar. Find the value of y.
12
16
Guess: 16
Answers
Answer:
4.5
Step-by-step explanation:
In similar polygons, the ratios of corresponding sides is equal.
The only two corresponding sides we have measurements for are BC, with a measure of 8, and FG, with a measure of 6. This makes their ratio 8/6.
The other half of the proportion will be comparing AB, with a measure of 6, to EF, with a measure of y:
8/6= 6/y
Cross multiply:
8(y) = 6(6)
8y = 36
Divide both sides by 8:
8y/8 = 36/8
y = 4.5
The value of y will be 4.5.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The polygons are similar.
Now,
Since, The polygons are similar.
Hence, The proportional of corresponding sides are equal.
So, We can formulate;
⇒ 6 / y = 8 / 6
⇒ 6×6 / 8 = y
⇒ y = 36 / 8
⇒ y = 4.5
Thus, The value of y will be 4.5.
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In the year 1997 d takahashi and y kanada calculated pi to 51,539,600,000 decimal places. what type of computer did they use? where did they do the calculations
Answers
They used a computer called the HITACHI SR2201 which has 1024 processors. As an example most desktops in use now (by individuals such as you and I -- not by computer scientists doing research) have 1-2 processors with 2 cores each.
You are knitting a blanket. You want the area of the planet to be 24ft^2. You want the length of the blanket to be 2ft longer than it's worth. What should the dimensions of the blanket be?
Answers
length being longer than the width means that blanket is a rectangle
width of the blanket = x
length of blanket = x +2
area = length * width
area = x * (x+2)
= x² + 2x
since area = 24
x² + 2x = 24
x² + 2x - 24 = 0
we have a quadratic equation and we need to now solve for x
x² + 6x - 4x - 24 = 0
x (x + 6) - 4(x + 6) = 0
(x-4) (x+6) = 0
x-4 = 0 or x + 6 = 0
x = 4 or x = -6
x could be either 4 or -6. since dimensions cannot have negative values,
x ≠ -6
therefore x = 4
width = 4 ft
length = 6 ft
Solve for x
2/(7x) = 6/5
5/21
-21/5
21/5
I don't know
- 5/21
Answers
________________________________________
Given:
2/ (7x) = 6/5;
→ (6/5) * (7x) = 2 ;
42x / 5 = 2 ;
42x = 2*5 ;
42x = 10 ;
42x /42 = 10/42 ;
x = 10/42 = (10÷2) / (42÷2) = 5/21 ;
x = [tex] \frac{5}{21} [/tex] ;
→ which is: Answer choice: [A]: " [tex] \frac{5}{21} [/tex] " .
__________________________________________________
PLEASE HELP!
Fine Line Trucks rents an 18-ft truck for $42 per day plus 35¢ per mile. Judy needs a truck for one day to deliver a shipment of plants. However, she only has a budget of $70.
a) Set up an equation that models this information.
b) How many miles can Judy drive to stay within her budget?
Answers
She wants the truck for one day, which will cost $45. We don't know how far the truck is traveling so that is the variable. She cannot spend more than $70, since that is her budget.
b.) Solve for x using the above equation:
0.35x + 42 ≤ 70
0.35x ≤ 28
x ≤ 80
Judy can drive 80 miles
Tickets for a concert sold for $8 for floor seats and $6 for balcony seats. For one performance, 400 tickets were sold, bringing in $2,888. How many of each ticket were sold?
Answers
What is the measure of angle A?
Answers
180 - 43 = 137
So angle A is 137 degrees
what is the value of x will mark brain list 20 extra points
Answers
2x + 5 = 4x - 1
5 = 2x - 1
6 = 2x
3 = x
Do you get it?
A lawn mower uses 0.7 gallons of gas every 3 hours. the gas tank holds 2 gallons. how long can the mower run on a full tank?
Answers
[Divide by 0.7 through]
1 gallon = 4.286 hours
[Multiply by 2 through]
2 gallon = 4.286 x 2
2 gallon = 8.57 hours
The lawn mower can run for approximately 8 hours and 34 minutes on a full tank of gas.
Explanation:
To find out how long the lawn mower can run on a full tank, we can divide the total amount of gas in the tank by the amount of gas used per hour. The lawn mower uses 0.7 gallons of gas every 3 hours. So, it uses 0.7/3 = 0.2333 gallons of gas per hour. The gas tank holds 2 gallons, so the lawn mower can run for 2/0.2333 = 8.57 hours, which is approximately 8 hours and 34 minutes.
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What is the quotient in simplest form? State any restrictions on the variable.
(z^2 - 4)/(z - 3) divided by (z+2)/(z^2+z -12),
Answers
The first step to solve this problem is to completely factor the expressions first.
(z^2 - 4)/(z - 3) / (z+2)/(z^2+z -12)(z + 2)(z – 2)/(z – 3) / (z + 2)/(z +4)(z – 3)
When dividing two fractions, you have to reciprocate the denominator and do the multiplication:
(z + 2)(z – 2)/(z – 3) / (z +4)(z – 3)/(z + 2)
The expressions (z + 2) and (z – 3) will be cancelled. So the expression would become: (z – 2)(z + 4) = z^2 + 2z - 8
Final Answer:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
Explanation:
To find the quotient in simplest form when dividing two rational expressions, you need to multiply the first expression by the reciprocal of the second. The given expressions are:
Expression 1: [tex]\(\frac{z^2 - 4}{z - 3}\)[/tex]
Expression 2: [tex]\(\frac{z + 2}{z^2 + z - 12}\)[/tex]
Firstly, let's take the reciprocal of Expression 2, which is:
Reciprocal of Expression 2: [tex]\(\frac{z^2 + z - 12}{z + 2}\)[/tex]
Now, to find the quotient, multiply Expression 1 by the reciprocal of Expression 2:
Quotient: [tex]\(\frac{z^2 - 4}{z - 3} \cdot \frac{z^2 + z - 12}{z + 2}\)[/tex]
Before multiplying, it's helpful to factor where possible to simplify. Let's factor both the numerator and the denominator where applicable:
For the expression [tex]\(z^2 - 4\)[/tex] (the difference of squares), it factors into:
[tex]\(z^2 - 4 = (z - 2)(z + 2)\)[/tex]
For the quadratic expression [tex]\(z^2 + z - 12\)[/tex], we look for two numbers that multiply to -12 and add to +1. These numbers are +4 and -3.
So this expression factors into:
[tex]\(z^2 + z - 12 = (z - 3)(z + 4)\)[/tex]
Now substitute in these factorizations:
[tex]\(\frac{(z - 2)(z + 2)}{z - 3} \cdot \frac{(z - 3)(z + 4)}{z + 2}\)[/tex]
Next, we cancel out the common terms in the numerator and the denominator:
The z + 2 term in the numerator of the first fraction cancels with the z + 2 term in the denominator of the second fraction.
Similarly, the z - 3 term in the denominator of the first fraction cancels with the z - 3 term in the numerator of the second fraction.
What remains is:
Quotient: (z - 2)(z + 4)
Finally, you can expand this to get the simplest form of the quotient:
[tex]\(z^2 + 4z - 2z - 8\)[/tex]
Combine like terms:
[tex]\(z^2 + 2z - 8\)[/tex]
So the simplest form of the quotient is:
[tex]\(\frac{z^2 + 2z - 8}{1}\)[/tex]
or simply:
[tex]\(z^2 + 2z - 8\)[/tex]
Now let's consider the restrictions on the variable z. Before we canceled terms, the original expression had denominators of z - 3 and [tex]\(z^2 + z - 12\)[/tex]. Division by zero is undefined, which means we have restrictions where these denominators equal zero:
For z - 3 = 0, the restriction is [tex]\(z \neq 3\)[/tex].
For [tex]\(z^2 + z - 12 = 0\)[/tex], we had already factored this into (z - 3)(z + 4). From the factored form, we can find the restrictions by setting each factor equal to zero:
z - 3 = 0 gives z = 3 (which we already noted) and z + 4 = 0 gives z = -4.
Therefore, the restrictions on the variable z are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
To summarize:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
What is the simplest form of ^4 sqrt 81x^8y^5
Answers
ANSWER
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
EXPLANATION
We want to simplify:
[tex] \sqrt[4]{81 {x}^{8} {y}^{5} } [/tex]
We can split the radical sign to obtain:
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} } [/tex]
Or
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y} [/tex]
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
[tex]\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
Recall that:
[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]
[tex]{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y} [/tex]
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
Answer:
B!!!!!!!!!
Step-by-step explanation:
What is the solution to the system of equations?
{x + 3y + 2z = 8
{3x + y + 3z = -10
{-2x -2y - z = 10
A: (-10, -2, 6)
B: (10, 2, 6)
C: (-10, 2, 6)
D: (-10, 2, -6)
Answers
In order to convert from radians to degrees multiply the radians by...
Answers
what is the slope of the line that contains the points (-1,2) and (3,3)?
A. -1/4
B. 1/4
C. 4
D. -4
Answers
the slope of the line is letter B) 1/4....
The slope of the line that contains the points (-1,2) and (3,3) is calculated using a specific formula. After performing the calculation, the result is 1/4.
Explanation:The slope of a line is calculated using a specific formula based on line's points: (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of two distinct points on the line. In this case, the points given are (-1,2) and (3,3).
Let's substitute into the formula:
(3 - 2) / (3 - (-1)) = 1 / 4.
Therefore, the slope of the line that contains the points (-1,2) and (3,3) is 1/4, which corresponds to answer choice B.
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Help me please I’ll mark brainliest
Answers
After replacement, we now have the equation shown in A.
Hope this helps!
Movements to the left and to the right in graphs change the x-values, while movements up and down in graphs change the y-values. Further, when shifting left, you'll add to x, and when shifting right, you'll subtract from x. When shifting up, you'll add to y, and when shifting down, you'll subtract from y. (Upward and downward movements are more intuitive than movements to the left or movements to the right.)
g(x) is f(x) shifted to the left 3 units, so we'll add 3 to x in the function:
f(x) = x² + 5x - 1
g(x) = (x + 3)² + 5(x + 3) - 1
The answer is A.
Rewrite the slope intercept equation of the line y=1/3x-2 in standard form
Answers
3y = x - 6
x - 3y = 6 ...this is standard form
The standard form of the given equation is x - 3y = 6.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, y = 1/3 x - 2
The given equation is in slope intercept form, i.e. y = mx+ c, where m is slope and c is constant,
Here, slope (m) = 1/3 and constant (c) = -2
Converting the equation in standard form,
y = 1/3 x - 2
3y = x - 6
x - 3y = 6
Hence, the standard form of the equation is x - 3y = 6
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How can categorical data for two categories be summarized?
Answers
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Hope this answer has helped you...
The sum of two numbers is 50 and the difference is 22 . what are the numbers?
Answers
substitute the first x into the second equation (22-y)-y=10 22-2y=10 22-10=2y 12=2y y=6
now plug in the known y into the first equation x+6=22 x=22-6 x=16
now, let's check this sum is 22=16+6 checks difference is 10=16-6 checks
16 is the larger number
6 is the smaller number.
hope this helps.
What is 65% written as a fraction in its simplest form?
Answers
(divide by 5 on both sides)
Hope this helped!
Which polynomial is in standard form
Answers
what is the image of g for a 240° counterclockwise rotation about the center of the regular hexagon
A. A
B. N
C. H
D. X
Answers
This would move G to the point H
C. H