Answers
Option D:
all real numbers
Solution:
Definition of domain:
The domain of the function is the set of all possible
x-values (independent variable).
Definition of range:
The range of a function is the set of all possible resulting values
of y-values (dependent variable).
i.e The range of a function is the resulting y-values we get after substituting all the possible x-values.
Given function: [tex]y=\log_8x[/tex]
Domain of y: (0, ∞) (or) {x | x > 0}
Range of y: (–∞, ∞) (or) {y | y > R}
i.e all real numbers
Option D is the correct answer.
Hence the range of y is all real numbers.
Related Questions
Identify the zeros of f(x) = (x + 9)(x − 4)(6x + 1).
−9, −1 over 6,4
9, 1 over 6, 4
−9, −1 over 6,−4
−9, 1 over 6, −4
Answers
Step-by-step explanation:
We have,
f(x) = (x + 9)(x − 4)(6x + 1)
To find, all zeroes of the given equation = ?
∴ f(x) = (x + 9)(x − 4)(6x + 1)
⇒ (x + 9)(x − 4)(6x + 1) = 0
⇒ x + 9 = 0 or, x − 4 = 0 or, 6x + 1 = 0
⇒ x + 9 = 0 ⇒ x = - 9
⇒ x − 4 = 0 ⇒ x = 4
⇒ 6x + 1 = 0
⇒ 6x = - 1
⇒ x = [tex]\dfrac{-1}{6}[/tex]
∴ x = - 9 , [tex]\dfrac{-1}{6}[/tex], 4
Thus, the required 'option a) - 9 , [tex]\dfrac{-1}{6}[/tex], 4' is correct.
Final answer:
To find the zeros of the function f(x) = (x + 9)(x − 4)(6x + 1), we solve for x in each factor: x = -9, x = 4, and x = -1/6, which means the zeros are -9, 4, and -1/6.
Explanation:
To identify the zeros of a function, you need to find the values of x for which the whole expression equals zero. The function given is f(x) = (x + 9)(x − 4)(6x + 1). To find the zeros, we set each factor equal to zero and solve for x.
(x + 9) = 0 → x = -9
(x − 4) = 0 → x = 4
(6x + 1) = 0 → 6x = -1 → x = -1/6
Therefore, the zeros of the function are -9, 4, and -1/6.
Alex is a house painter and uses large buckets to transport his paint from room to room. He needs to measure the volume of the bucket to determine how much paint it will hold. Which measurement would be appropriate for the bucket's volume?
A) 15.4 quarts
B) 22.05 quarts
C) 20 quarts
D) 18.25 quarts
Answers
Answer:
d
Step-by-step explanation:
How many solution does the inequality x>12 have explain
Answers
infinity numbers above 12
The inequality x > 12 has infinitely many solutions as it represents all numbers greater than 12 without any upper limit.
Explanation:The inequality x > 12 actually has infinitely many solutions, since any number greater than 12 satisfies the inequality condition.
In mathematics, inequalities that do not contain restrictions other than the comparative operator (in this case, '>') have a set of solutions that can be represented on a number line extending infinitely in one direction.
For example, if x > 12, then numbers such as 13, 14.5, 100, and 1234 are all solutions.
This can be visualized on a graph where x > 12 would be shown as an open interval starting from 12 and extending to the right toward infinity.
How many triangles can be constructed with angles measuring 10,80,and 90?
Answers
All triangles add up to 180
So, if you add all the given angles together (10+80+90=180)
3x/x^ 2 - 6x = 1 . Solve for x.
Answers
Answer:
X=-3
Step-by-step explanation:
what value of x makes the equation 3(x-6)-8x=-2+5(2x+1) true ?
Answers
Answer:
x = (-7)/5
Step-by-step explanation:
Solve for x:
3 (x - 6) - 8 x = 5 (2 x + 1) - 2
3 (x - 6) = 3 x - 18:
3 x - 18 - 8 x = 5 (2 x + 1) - 2
Grouping like terms, 3 x - 8 x - 18 = (3 x - 8 x) - 18:
(3 x - 8 x) - 18 = 5 (2 x + 1) - 2
3 x - 8 x = -5 x:
-5 x - 18 = 5 (2 x + 1) - 2
5 (2 x + 1) = 10 x + 5:
-5 x - 18 = 10 x + 5 - 2
Add like terms. 5 - 2 = 3:
-5 x - 18 = 10 x + 3
Subtract 10 x from both sides:
(-5 x - 10 x) - 18 = (10 x - 10 x) + 3
-5 x - 10 x = -15 x:
-15 x - 18 = (10 x - 10 x) + 3
10 x - 10 x = 0:
-15 x - 18 = 3
Add 18 to both sides:
(18 - 18) - 15 x = 18 + 3
18 - 18 = 0:
-15 x = 3 + 18
3 + 18 = 21:
-15 x = 21
Divide both sides of -15 x = 21 by -15:
(-15 x)/(-15) = 21/(-15)
(-15)/(-15) = 1:
x = 21/(-15)
The gcd of 21 and -15 is 3, so 21/(-15) = (3×7)/(3 (-5)) = 3/3×7/(-5) = 7/(-5):
x = 7/(-5)
Multiply numerator and denominator of 7/(-5) by -1:
Answer: x = (-7)/5
12. Describe the shape that would result from a vertical slice of the figure below
13. Explain how a cross section of the figure below can result in a trapezoid
Answers
Answer:
12. Pentagon
13. The cross-section will have one pair of parallel sides and one pair of sides that are not parallel along with two opposite triangular faces.
How can you write the expression with a rationalized denominator?
Answers
Yo sup??
This question can be solved by multiplying the numerator and denominator by 3^1/2
and the answer u will get will be
5*3^1/2-6^1/2)/3
Hope this helps
Which ordered pair in the form(x,y) is a solution of this equation?
7x-5y=1
A] (-3,-2)
B] (-2,-3)
C] (0,4)
D] (4,0)
Answers
The ordered pair is (-2, -3)
Step-by-step explanation:
Step 1: To find whether an ordered pair is a solution, substitute values of x and y and see whether it satisfies the equation.(-3, -2) ⇒ 7 × -3 - 5 × -2 = -21 + 10 = -11 ≠ 1
(-2, -3) ⇒ 7 × -2 - 5 × -3 = -14 + 15 = 1
(0, 4) ⇒ 0 - 5 × 4 = 20 ≠ 1
(4, 0) ⇒ 7 × 4 - 0 = 28 ≠ 1
So the ordered pair is (-2, -3)
The ordered pair that is a solution to the equation 7x-5y=1 is option B, (-2,-3), as it is the only pair that satisfies the equation when the values are substituted.
Explanation:The question asks which ordered pair is a solution to the equation 7x-5y=1. To find the solution, we simply substitute the x and y values from each ordered pair into the equation and see which pair satisfies the equation.
For option A (-3,-2), let's plug it in: 7(-3) - 5(-2) = -21 + 10 = -11, which does not equal 1.For option B (-2,-3), we get: 7(-2) - 5(-3) = -14 + 15 = 1, which does equal 1. Therefore, this is the correct solution.For option C (0,4), we get: 7(0) - 5(4) = -20, which does not equal 1.Lastly, for option D (4,0), plugging it in gives us: 7(4) - 5(0) = 28, which does not equal 1.So, the ordered pair that is a solution to the equation is option B, (-2,-3).
11. The completion of a chemical reaction is expressed by the equation y = 300 - 4x - XP, where y is
the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius
at which the reaction occurs. If the reaction is complete in 160 sec, what is the temperature at which
the reaction occurs?
Answers
Answer:
The reaction ca occur at 10 degree Celsius or -14 degree Celsius.
Step-by-step explanation:
We are given the following in the question:
The completion of a chemical reaction is expressed by the equation
[tex]y = 300 - 4x -x^2[/tex]
where y is the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius at which the reaction occurs.
We have to find the temperature at which the reaction occurs, if the completion time of reaction is 160 seconds.
Putting y = 160
[tex]160 = 300 - 4x -x^2\\x^2 + 4x - 140 = 0\\x^2 + 14x -10x -140 = 0\\x(x+14)-10(x+14)=0\\(x-10)(x+14) = 0\\(x-10) =0, (x+14) =0\\x = 10, x = -14[/tex]
Thus, the reaction ca occur at 10 degree Celsius or -14 degree Celsius.
A post it note has an area of A square inches.the width of the post it note is 4 inches.which equation represents x,the length of the post it nots in inches. A x= 4/A. B X=A+2(4) C X=A/4. D X=A-2(4)
Answers
The right answer is Option C.
Step-by-step explanation:
Given,
Area of post it note = A square inches
Width of post it note = 4 inches
Length of post it note = X
We know that;
Area = Length * Width
[tex]A=X*4\\A=4X[/tex]
As we have to find length, we will divide both sides by 4
[tex]\frac{A}{4}=\frac{4X}{4}\\\\\frac{A}{4}=X\\\\X=\frac{A}{4}[/tex]
The equation [tex]X=\frac{A}{4}[/tex] represents the length of post it notes in inches.
The right answer is Option C.
Keywords: area, multiplication
Learn more about areas at:
brainly.com/question/11280112brainly.com/question/11286417#LearnwithBrainly
I need the answer key of riddle time called why did the school cook become a history teacher?
Answers
The response to the riddle " why did the school cook become a history teacher" is she was a expert in Acient grease
What is the riddle?
The riddle is based on history, and it should be noted that in term of history, ancient grease can not be underestimated because they have been existing since time past.
The city-states of ancient Greece were autonomous, however occasionally some would join alliances and hegemonies and serve a more powerful city. Greece was merely a small component of Alexander the Great's empire when it was founded—albeit for a very short time.
Julianne is planting a ground cover in one area of her yard. The area she wants to cover is rectangular shaped and measures 7.25 ft by 4.25 ft. The manager of the garden shop tells her that she will need to purchase four plants for every square foot of area she wishes to cover. How many plants will she need to buy to complete this project?
Answers
Answer:
124 plants
Step-by-step explanation:
7.25*4.25=30.8125
30.8125*4=123.25
Since you can't buy 1/4 of a plant, you must round up to 124.
Where is the vertex of the equation?y = x2 – 18x + 80
Answers
Answer:
vertex = (9, - 1 )
Step-by-step explanation:
Given a quadratic in standard form, y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 18x + 80 ← is in standard form
with a = 1 and b = - 18, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-18}{2}[/tex] = 9
Substitute x = 9 into the function for corresponding value of y
y = 9² - 18(9) + 80 = 81 - 162 + 80 = - 1
Vertex = (9, - 1 )
Which pair shows equivalent expressions?
2 (two-fifths x + 2) = 2 and two-fifths x + 1
2 (two-fifths x + 2) = four-fifths x + 4
2 (two-fifths x + 4) = Four-fifths x + 2
2 (two-fifths x + 4) = 2 and two-fifths x + 8
Answers
2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 4 which is the second option is the equivalent expression.
Explanation:
First, we need to calculate the value of two-fifths of x. It means 2 portions out of the five portions of x which equates to [tex]\frac{2}{5}[/tex]x.
Now we calculate the values of the two expresssions on the LHS.
1) 2 (two-fifths x + 2) = 2 ([tex]\frac{2}{5}[/tex]x + 2) = [tex]\frac{4}{5}[/tex]x + 4.
2) (two-fifths x + 4) = 2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 8.
Now we determine values of the four expressions on the RHS.
1) Two and two-fifths x + 1 = 2[tex]\frac{2}{5}[/tex]x + 1
2) Four-fifths x + 4 = [tex]\frac{4}{5}[/tex]x + 4
3) Four-fifths x + 2 = [tex]\frac{4}{5}[/tex]x + 2
4) Two and two-fifths x + 8 = 2[tex]\frac{2}{5}[/tex]x + 8.
Out of the various LHS and RHS values, the [tex]1^{st}[/tex] LHS value and [tex]2^{nd}[/tex] RHS value is the same. So option 2 is the answer.
Answer:
second option
Step-by-step explanation:
If a customer bought an item from a retailer and eventually received a $12.50
rebate check in the mail after sending in a rebate form, which of these
transactions occurred?
A. The manufacturer of the item sent the retailer a check for $12.50
who then passed it along to the customer.
B. The retailer sent the manufacturer of the item a check for $12.50,
who then passed it along to the customer.
C. The manufacturer of the item sent the customer a check for
$12.50 directly
D. The retailer sent the customer a check for $12.50 directly
Answers
Answer:
The correct option would be option D.) The retailer sent the customer a check for $12.50 directly.
Step-by-step explanation:
A customer bought an item from a retailer and eventually received a $12.50
rebate check in the mail after sending in a rebate form.
The transaction that occurred would be
D.)The retailer sent the customer a check for $12.50 directly
Answer:
the manufacturer of the item sent the customer a check for 12.50 directly.
Step-by-step explanation:
Square A B C D is shown. Each side is 30 yards long. A diagonal is drawn from point D to point B to form 2 triangles.
Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?
15 yd
30 yd
30 StartRoot 3 EndRoot yd
30 StartRoot 3 EndRoot yd
Answers
Answer:
Length = 30√2 yards.
Step-by-step explanation:
There is a plot of land of square shape that has 30 yards on each side. Jules owns this plot. He plans to divide the land in half by building a fence along the diagonal of the plot.
We have to calculate the length of the fence.
Now, the length of the diagonal will be the length of the fence.
So, the length = [tex]\sqrt{30^{2} + 30^{2}} = 30\sqrt{2}[/tex] yards. (Answer)
Answer:
C. 30√2 yd
Step-by-step explanation:
List all 6 whole numbers between -3.5 and 5.5
Answers
Answer012345
Step-by-step explanation:
Find the slope of the line passing through the points (-4, 7) and (2, -8)
Answers
What is the equation in standard form for (0,3) and (7,0)
Answers
Answer:
3x + 7y = 21
Step-by-step explanation:
We have value of two points (0,3) and (7,0)
First, let's find the slope of this line. The formula for slope is:
Change in y/Change in x or (y₂ - y₁)/(x₂-x₁)
Where x₁ = 0 x₂= 7 y₁ = 3 y₂ = 0
(y₂ - y₁)/(x₂-x₁)
= (0-3)/(7-0)
=-3/7
Now we can write the equation in point-slope form:
y-y₁ = m(x-x₁)
y - 3 = -3/7(x-0)
y-3=-3x/7
y=-3x/7 + 3
Now let's convert this to standard form, by making the y-intercept by itself:
Ax + By = C
y=-3x/7 + 3
Multiply through by 7
7(y) = 7(-3x/7) + 7(3)
7y = -3x + 21
3x + 7y = 21
Which choice is NOT equal to the others? A) − 2/ 5 B) −2/ 5 C) 2/ 5 D) 2/ −5
Answers
Answer:
c) 2/5
Step-by-step explanation:
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Final answer:
The choice that is NOT equal to the others is C) 2/5, because it is the only positive fraction, while the others represent the negative fraction − 2/5.
Explanation:
The student's question asks which of the given choices is NOT equal to the others. The choices provided include A) − 2/5, B) − 2/5, C) 2/5, and D) 2/ −5. To find the answer, we must compare the values.
Options A and B are the same, which is − 2/5 or negative two-fifths. Option D, which is 2/−5, simplifies to − 2/5 because division by a negative number yields a negative result, making it equivalent to options A and B. However, option C is the only one that is different because it is 2/5, which is positive two-fifths, not negative. Therefore, the answer is C) 2/5 as it is not equal to the other options, which are all negative two-fifths.
17x + 36y = 479
Y= 2x - 4
Answers
Answer:
X=7
Y=10
Step-by-step explanation:
Replace expression Y=2x-4 in 17x + 36y = 479
17x+36(2x-4)=47917x+72x-144=47989x-144=47989x=479+14489x=623x=[tex]\frac{623}{89}[/tex]x=7Now, replace X=7 in expression Y=2x-4
Y=2(7)-4Y=1017x+72-144=479
17x+72x=335
89x=335
x=3.76
Find the area of the shape shown below.
Answers
Answer: The Area of this shape is 32.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Area = 1/2 ×(a+b)h
a = 4, b = 12, h = 4
Area = 1/2 × (4+12)4
Area = 2(16)
Area = 32square unit
Please help my little sis!
The product of two whole numbers is 14391 and their difference is 6. What are the two numbers?
Answers
First whole number is x
Second whole number is x + 6
So try and solve x(x+6)=14391
My next step, after I put this down would be to rearrange it into a solvable quadratic
X^2 + 6X - 14391 = 0
Using the quadratic formula (below)
Answer:
117 and 123.
Step-by-step explanation:
If the 2 numbers are x and y we have the system of equations:
x - y = 6
xy = 14391
From the first equation y = X - 6 so substituting:
x(x - 6) = 14391
x^2 - 6x= 14391
x^2 - 6x - 14391 = 0
The prime factors of -13491 are -3*3*3*13*41
Now 3*3*13 = 117 and -3 * 41 = -123,
so the factors are:
(x - 123)(x + 117) = 0.
x = 123, -117.
As x is a whole number we take the positive value 123.
So x = 123 and y = 123 - 6 = 117.
Tom makes $148.65 in 3 days how much would he make in 2 days.
Answers
Answer:
$99.10
Step-by-step explanation:
Answer:
$99.10
Step-by-step explanation:
you would divide the $148.65 by the 3 days and get $49.55. then you would multiply that by the 2 and get your awnser.
A piece of string is hung from the points (-6,3) and (6,3) in the plane so that it hangs “down” (in the -y direction) to just touch the origin as it’s vertex. How high above the x axis is the string over x=2
Answers
Answer:
Step-by-step explanation:
eq. of line through (0,0) and (6,3)
[tex]slope=\frac{3-0}{6-0} =\frac{1}{2} \\y-0=\frac{1}{2} (x-0)\\y=\frac{1}{2}x\\when~x=2\\y=\frac{1}{2}*2=1[/tex]
If a^2 + b^2=c^2 then the triangle is a right triangle.
A triangle with side lengths of 12 in, 24 in and 16 inches is a right triangle.
True or False
Answers
Answer:
12² + 16² = 144 + 256 = 400 = 20²
So a triangle with side lengths of 12 in., 16 in., and 24 in. is not a right triangle.
The correct answer is False.
The sales tax in Ontario is 13%. If you paid $450 on a food bill at the restaurant, how much if it were taxes?
Solve step-by-step
Answers
Answer:
58.5%
Step-by-step explanation:
Sales tax in Ontario = 13%
If you paid $450 on food
Tax = 13%/100% x 450
= 0.13 x 450
=58.5%
The fraction as a percent for 19/29
Answers
In a year group of 60 pupils, 3/4 like Coke, 1/5 like Sprite and 3/10 like Tango. How many children like each drink? PLZ HELP ME ASAP 15 points to correct answer
Answers
Final answer:
To find out how many children like each drink in a year group of 60 pupils, calculate each fraction of the total. 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.
Explanation:
In a year group of 60 pupils, to find out how many children like each drink, you need to calculate the fractions of the total number of pupils.
To find out how many like Coke, multiply 3/4 by the total number of pupils: 3/4 × 60 pupils = 45 pupils.For Sprite, multiply 1/5 by the total number of pupils: 1/5 × 60 pupils = 12 pupils.For Tango, multiply 3/10 by the total number of pupils: 3/10 × 60 pupils = 18 pupils.Therefore, 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.
Final answer:
45 children like Coke, 12 children like Sprite, and 18 children like Tango.
Explanation:
To find out how many children like each drink, we can use the given fractions and the total number of children in the year group.
Let's calculate the number of children who like Coke:
Total children in the year group = 60
Fraction who like Coke = 3/4
Number of children who like Coke = (3/4) x 60 = 45
Similarly, we can calculate the number of children who like Sprite and Tango:
Fraction who like Sprite = 1/5
Number of children who like Sprite = (1/5) x 60 = 12
Fraction who like Tango = 3/10
Number of children who like Tango = (3/10) x 60 = 18
Therefore, 45 children like Coke, 12 children like Sprite, and 18 children like Tango.