The given descriptions "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
First, let us understand the logarithmic function:
The inverses of exponential functions are logarithmic functions, and any exponential function could be represented in logarithmic form.
The given description fully stated about the logarithmic function.
Thus, the given description "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
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19. Factor to find the zeros: f(x) = x² + 6x.
(-6,0)
no solution
(0,0) and (-6,0)
(6,0)
Zeros of f(x) = [tex]x^{2} +6x[/tex] is (0,0) and (-6,0).
Given, f(x) = [tex]x^{2} +6x[/tex]
= x(x+6)
For zeros, function f(x) = 0
x(x+6) = 0
x = 0 x+6 = 0
x = -6
Putting values of x in equation,
For x = 0
f(x) = [tex]0^{2}+6(0)[/tex]
= 0
Therefore, (0,0)
For x = -6
f(x) = [tex](-6)^{2}+6(-6)[/tex]
= 36 - 36
= 0
Therefore, (-6,0)
Hence, zeroes for f(x) is (0,0) and (-6,0).
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3. Alex rode his bike at a constant speed. He rode 1 mile in 6 minutes. Write two equations to model this situation using t as time in minutes, and d as distance in miles. T=D=
will give brainliest
Answer: t = 5d t = 1/5d
Step-by-step explanation:
8 < x (7 − x)
Please help, no one has answered this question
I Think thatthe answer is 2
use the communitive property to simplify the expression. 1/3 + 3/5 + 2/3
The simplified expression using the commutative property is in the first option : 1/3 + 2/3 + 3/5 = 1 + 3/5 = 1 3/5 .
now the given expression is 1/3 + 2/3 + 3/5 .
Therefore this expression can be simplified using the commutative property where we put the like terms together.
1/3 + 3/5 + 2/3
= 1/3 + 2/3 + 3/5 (here we use commutative property on the second and third terms of the expression)
= 1 + 3/5 (we know that 1/3 +2/3 = 1)
=1 3/5
Hence by using the commutative property we calculate the sum easily.
The commutative property applies to the arithmetic operations of addition and multiplication. This suggests that no matter how the numbers are arranged or placed, the result of adding or multiplying them remains the same.
As an illustration, 1 + 5 = 6 and 5 + 1 = 6. No matter how two numbers are added, the sum is unaffected. Multiplication uses the same principle. The commutative property does not hold for division and subtraction because the results are completely different when the numbers are rearranged.
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!*EMERGENCY, WILL GIVE BRAINLIEST QUICK*!
This table represents the cups of coffee, c, a coffee shop has left after being open for h hours. When graphed, all of the points in the table lie on the same line. What is the slope and y-intercept of the line? Drag and drop the slope and y-intercept into the corresponding boxes.
Slope -48, 9 ,48 ?
y-intercept 432, C, 6, 9?
(LEFT SIDE IS HOURS, RIGHT SIDE CUPS)
TABLE-------
HOURS, H / CUPS, C
0 / 432
3 / 288
6 / 144
9 / 0
Answer:
Slope is -48, y-intercept is 432
[tex]y = - 48x + 432[/tex]
Step-by-step explanation:
[tex]m = \frac{432 - 288}{0 - 3} = \frac{144}{ - 3} = - 48[/tex]
[tex]432 = - 48(0) + b[/tex]
[tex]432 = 0 + b[/tex]
[tex]b = 432[/tex]
[tex]y = - 48x + 432[/tex]
Justify 3(2x + 5) - 7 = 2x + 32
f/4 + 6 ≤ 7 what is the answer
Answer:
f ≤ 4
Step-by-step explanation:
f/4 + 6 ≤ 7
f/4 ≤ 7 - 6
f/4 ≤ 1
f ≤ 4
Answer:
F<4
________
________
Please help!!!
How many complex roots does the equation 0= 3x^5-x^4-5x^2 +1 have?
The polynomial equation 0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.
Describe a polynomial.
A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.
Below is a polynomial equation that is given:
0 = 3x⁵ − x⁴ − 5x² + 1
Which can also be written as
3x⁵ − x⁴ − 5x² + 1 = 0
A polynomial of degree 5 is used in the accompanying polynomial equation.
Using a graphing application to solve it graphically is the simplest approach.
The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.
Now that we have the graph, we can use it to find the equation's roots.
There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.
The polynomial equation 0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.
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two cars start moving from the same point. one travels south at 60 miles per hour. the other car travels west at 25 miles per hour. at what rate is the distance between the cars increasing 2 hours later?
The distance between the cars increasing 2 hours later is 65mph
Let’s say, the velocity in the west is x, the velocity in the south is y, and the distance between them is s at any time t. Since the west and south directions are perpendicular to each other, this will be for a right-angled triangle.
So, we have [tex]x^2 + y^2 = s^2[/tex] --------------(1)
(please note all of them are changing as t increases.)
So, x=u×t and y=v×t,
so using (1), we can write
[tex][(u\times t)^2 + (v\times t)^2] = s^2[/tex]
[tex]s= \sqrt{(u^2 + v^2)}* t[/tex]
Using the value of u and v,
get [tex]\sqrt{(u^2 + v^2)}[/tex]= 65
So, s= 65 t
ds/dt = 65 mph
There fore the distance between the cars increasing 2 hours later is 65mph
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A cup of coffee is poured at 190° Fahrenheit, and is allowed to cool in a 70° room. If the temperature of
the coffee is 170° after half an hour,
a. What will the temperature be after 70 minutes?
b. How long will it take the coffee to cool to 120°2
Answer:
a) 190 - 70(2/3) = 430/3 = 143 1/3 degrees
b) 190 - (2/3)x = 120
70 = 2x/3
210 = 2x
Step-by-step explanation:
x = 105 minutes
how do i do these?
i'm having trouble figuring out which is x and which is y.
Answer:
X is horizontal axis, Y is vertical axis
Step-by-step explanation:
(x,y) in the notation
3. Here is a balanced hanger diagram.
What is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning.
Answer:bgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvddddddddddddddddddddddddddd
Step-by-step explanation:
Answer:
Step-by-step explanation:
well it will be 16 because a square has 4 sides so you multiply by the grams that would be 4. 4*4= 16
a blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd which equation models the amount of time that is left on the cd
The equation that models the amount of time that is left on the cd is 80 - m.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:
= Total minutes - Time used
= 80 - m
This illustrates the equation.
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10 PIONTS ANSWER PLEZ IT IS NOW DUE!!!!!!
15. A triangle pattern is shown below.
Figure Perimeter
1 triangle 24
2 triangles 30
3 triangles 36
Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?
(1 point)
P = 6n + 18
P = 9n + 6
P = 6n + 9
P = 9n + 12
The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
We are given:
The perimeter of the 1 triangle = 24
The perimeter of the 2 triangle = 30
The perimeter of the 3 triangle = 36
As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.
So, we can write this as,
P = 6n + 18, where n = number of triangles.
Now, check the equation formed by substituting the values;
Substitute n = 1, and we get;
P = 6(1) + 18
P = 6 +18
P = 24 True.
Substitute n = 2, and we get;
P = 6(2) + 18
P = 12 +18
P = 30 True.
Substitute n = 3, and we get;
P = 6(3) + 18
P = 18 + 18
P = 36, true.
So, it is true for all the figures.
Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
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(x-24)
296
29°
Show work
Answer:
x=59
Step-by-step explanation:
this is a full circle which is 360 degrees
We subtract 296 from 360 first
360-296=64
Then subtract 29 from 64
64-29=35
now we can set x-24 equal to 35
X-24=35
+24 +24
x=59
Hopes this helps please mark brainliest
If Bruce can eat 2 1/2 bananas per day, how many bananas can Bruce can eat in 4 weeks?
The number of bananas Bruce can eat in 4 weeks is 70 bananas
Calculating numberFrom the question, we are to calculate the number of bananas Bruce can eat in 4 weeks.
From the given information,
Bruce can eat 2 1/2 bananas per day
First, we will determine the number of days there are in 4 weeks
NOTE: There are 7 days in 1 week
If there are 7 days in 1 week
Then,
There are 4 × 7 days in 4 weeks
4 × 7 = 28 days
That is, 4 weeks = 28 days
Now, we will determine the number of bananas Bruce can eat in 28 days
If Bruce can eat 2 1/2 bananas per day
Then,
Bruce can eat 28 × 2 1/2 bananas in 28 days
28 × 2 1/2 = 28 × 5/2
= 14 × 5
= 70
Hence, Bruce can eat 70 bananas in 4 weeks
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Answer:
70
Step-by-step explanation:
Bruse can eat 2 1/2 bananas in one day so:
1day=2 1/2bananas.
if 1wk=7days
4wks=x =28days
1day=2 1/2 bananas
28da
28×2 1/2
=28×5/2=70
answer=70bananas
Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
suppose 1,872 of 2,600 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?
PLEASE HELP!!
Ian buys a two-gallon bottle of juice for $28.16. What is the unit rate of the cost of the juice per fluid ounce?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
Before you try that problem, answer the question below.
How many fluid ounces of juice did Ian buy?
Answer: 11 Cents per ounce of Juice
Step-by-step explanation:
The first step here is going to be to find how many ounces are in a gallon. This can be determined as shown using the given information you stated above:
1 gallon * 4 quarts * 2 pints * 2 cups * 8 ounces = 128 ounces in 1 gallon
Step 2 is multiplying 128 ounces by 2 because we have two gallons of juice in the bottle:
128 ounces per gallon* 2 gallons = 256 ounces
Step 3 is dividing the total cost of the juice, which is $28.16, by the number of total number ounces (256)
$28.16 / 256 ounces = .11 dollars per ounce (aka 11 cents per ounce)
Select the correct answer.
What is the domain of y= cos (x)
a.2pie
b. [-1,1]
c. (-infinity, infinity)
d. [0,infinity)
The answer should be C.
The range of definition of the cosine function is all real numbers. [tex]R[/tex]
It is also periodic in [tex]2\pi[/tex].
It is an even function. [tex]f(x)=f(-x)[/tex]
It can also be written in this form.
[tex]cos(x)=\frac{e^{-ix}+e^{ix}}{2}[/tex]PLEASE HELP
thank you !!
Answer:
34562
Step-by-step explanation:
you add them together
Write a number with one decimal place, that is bigger than 6 wholes and 4 fifths but smaller than 7
–2.5x – 7.5 = x + 6.5
Answer:
Step-by-step explanation:
x=-4 that should be the answer i don't really know how too explain but i did this 2 years ago
Answer:
Step-by-step explanation:
The slope of the line below is -1/7. write a point slope equation of the line using the coordinates of the labeled point.
The equation of a straight line can be written if its slope and any one point lying on it is given. The equation of the line for given slope and point is (y - 3) = -1 / 7 × (x - 3). The correct answer is option B.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The slope of the line = -1 / 7
The coordinate of the point on the line = (3,3)
The equation of a line having slope m and passing through a point (x₁, y₁) is given as,
(y - y₁) / (x - x₁) = m
Thus, the equation of the line for given slope and point is given as,
(y - 3) / (x - 3) = -1 / 7
=> (y - 3) = -1 / 7 × (x - 3)
Hence, the equation of the line for given slope and point is (y - 3) = -1 / 7 × (x - 3).
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Write an equation of
the line that passes
through (7, 10) and
is perpendicular to the
line y =
x-9.
Equation:
2
Equation of the line that passes through (7, 10) and is perpendicular to the line y =x-9 is y = -x+17.
Given equation, y = x-9
Slope = m = 1
Slope of line perpendicular to given line = -1/m
= -1/1
= -1
Let the equation of line be y = mx + c
Passes through A(7,10)
10 = -1(7) + c
10 = -7 + c
c = 10 + 7
= 17
Hence, equation is y = -x+17
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A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The apple mean weight's 95% confidence interval is;
CI = (119.14, 125.86) (119.14, 125.86)
The confidence interval above should be understood as;
We have a 95% confidence that each apple's average weight, across all of the apples they send, falls between 119.14 and 125.86 grams.
Ours is given;
12 for the standard deviation.
Sample size: 49; n
x = 122.5 is the indicated mean weight.
The current confidence interval formula is;
CI = x⁻ ± z(σ/√n)
Tables indicate that z = 1.96 at a 95% confidence level.
Thus;
CI = 122.5 ± 1.96(12/√49)
CI = 122.5 ± 3.36
CI = (122.5 - 3.36), (122.5 + 3.36)
CI = (119.14, 125.86)
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IIIIIIIIIII NEEEEEDDDDD HELPPPPP FASTTTTT!!!!!!!!!!!!! If a circle has a circumference of 60π, which equation shows the correct value for the radius, r?
we know that [tex]r[/tex]
area of the circle is equal to
A= [tex]\pi[/tex] × [tex]r^{2}[/tex]
solve for [tex]r[/tex]
[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]
for A=60cm2
[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]
we know that
[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5
=2[tex]\sqrt{15}[/tex]
so,
[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]
2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex] × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]
= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm
this means the answer is-
2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]
Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles. Which inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal?.
As per the concept of inequality, the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is 15 + 4m ≥ 35
Inequality
Inequality shows a non equal relationship between two numbers or two expressions.
Given,
Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles.
Here we need to determine the inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.
Here we know that, his goal for this week is to run a minimum of 35 miles.
For this week, he has already run 15 miles.
In the given inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.
=> 15 + 4m ≥ 35
Here we know that, 4m = number of m miles run in 4 days.
Therefore, inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is written as,
=> 15 + 4m ≥ 35
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BRAINLIEST FOR THE BEST ANSWER!
Question:
WRITING-Your friend is having trouble understanding the Midpoint Formula.
a. Explain how to find the midpoint when given the two endpoints in your own words.
b. Explain how to find the other endpoint when given one endpoint and the midpoint in your own words.
PLEASE DO NOTE THAT THIS IS WRITING NOT OPTIONS. Thank you in advance! :)
The formula that is used to calculate the midpoint for the given two point is written as ( (x₁ + x₂)/2 , (y₁ + y₂)/2).
Mid point:
Midpoint refers the point on a line that is at an equal distance from either end.
Given,
Here we have to explain the concept of midpoint in a simple manner.
According to the definition, midpoint refers the central point between the two points.
So, in a simple manner we have said that the mid point is calculated by finding the average of the two given point.
For example, (x₁, y₁) and (x₂, y₂) are the points, then the midpoint (xₙ, yₙ) is calculated by using the formula,
(xₙ, yₙ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)
Similarly, if one point and the midpoint is given, then the another point is calculated by apply the remaining point as (x, y) and solve it accordingly, then we can get the value of it.
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BRAINLIST! Please answer!!Parallelogram Properties
1. In Parallelogram JKLM if m
Answer:
60
Step-by-step explanation:
I believe two angles should add up to 180 in a parallelogram