Answer as an inequality: [tex]x > 0[/tex]
Answer in interval notation: [tex](0, \infty)[/tex]
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
======================================================
Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.
------------------------
The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
[tex]\log_e(x) = \text{Ln}(x)[/tex]
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
------------------------
In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
Luis, Diego, and Cecil are going fishing.
Luis brings 4 cans of worms. Diego brings
3 cans of worms plus 2 extra worms. Cecil
brings 2 cans of worms. If they have a
total of 65 worms and each can contains
the same number of worms, how
many worms are in each can?
Answer:
7
Step-by-step explanation:
If we call the number of worms in a can x, we can write:
4x + 3x + 2 + 2x = 65
9x + 2 = 65
9x = 63
x = 7 worms
Help me please and thank you
Answer:
Below
Step-by-step explanation:
The domain tells you if there are any restrictions on the x's
The -5 in the function tells us that it has moved 5 units RIGHT from the original parent function. Because of this, any x coordinates have to be bigger or equal to 5!
So, the domain of this function is x >/ 5
Hope this helps!
Find the lateral surface area of the
following prism:
5 cm
5 cm
-apothem = 3.44 cm
5 cm
5 cm
10 cm
5 cm
Answer:
250 cm²
Step-by-step explanation:
Lateral area of the prism is,
5×10×5
= 250 cm²
Lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].
What is lateral surface area?" Lateral surface area is defined as the sum of area of the all the surfaces except top and bottom of the given geometrical shape."
Formula used
Lateral surface area of pentagonal prism [tex]=5ah[/tex]
[tex]a=[/tex] edge length of the base
[tex]h=[/tex] height of the prism
According to the question,
For the given pentagonal prism,
Edge length of the base [tex]'a' = 5cm[/tex]
Height of the prism [tex]'h' = 10cm[/tex]
Substitute the value in the formula of lateral surface area we get,
Lateral surface area of pentagonal prism [tex]= 5 \times 5\times 10[/tex]
[tex]= 250cm^{2}[/tex]
Hence, lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].
Learn more about lateral surface area here
https://brainly.com/question/14001755
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I need help I need help
Answer:
[tex]{ \boxed{ \bf{c}}} \: \: \frac{3.8}{4} = s[/tex]
Step-by-step explanation:
[tex]{ \tt{4 \: pies \: = \: 3.8 \: ounces}} \\ { \tt{1 \: pie \: = \: ( \frac{1}{4} \times 3.8) \: ounces}} \\ { \tt{ = 0.95 \: ounces}}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \: † \: alone}}}}[/tex]
2c+17.6 =6 / 4 SOLVE give your answer as a decimal get brainly
Answer:
-8.05
Step-by-step explanation:
In order to solve for C you first have to subtract 17.6 from both sides.
2c=(6/4)-17.6
6/4 is 1.5
1.5-17.6=-16.1
2c=-16.1
c=-8.05
Answer:
1.5
Step-by-step explanation:
2c+17.6=6/4
2c+176/10=6/4
2c+88/5=6/4
2c=6/4-88/5
2c=30-352/20
2c=-322/20
2c=-161/10
c=-8.05
Proof:
2c+17.6=6/4
2(-8.05)+17.6=6/4
-16.1+17.6=6/4
1.5=1.5
Hope this helps ;) ❤❤❤
In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German? 4 people speak two languages but do not speak Spanish One fifth of the group speaks more than one language.
Answer:
x + a=5
Step-by-step explanation:
Let
number of people who speak only English = E
the number of people who speak only German = G
the number of people who speak only Spanish = S
the number of people who speak only English & German but not Spanish = x
the number of people who speak only English & Spanish but not German = y
the number of people who speak only German & Spanish but not English = z;
the number of people who speak only German & Spanish & English = a
Find the the value of (x + a).
Statement 1: 4 people speak two languages but do not speak Spanish.
x = 4.
x+a
Value for a is unknown.
(x + a). Insufficient.
Statement 3: One-fifth of the group speaks more than one language.
x + y + z + a
= 25/5
= 5
value of (x + a) unknown
Insufficient.
Putting (1) and (2) together
x + y + z + a = 5
x = 4 and a=1,
we have only one possible solution from
x + y + z + a = 5
x + a
= 4 + 1
= 5.
Sufficient.
please answer the following question(math question)
don't spam
Answer:
well hlo again ( ˘ ³˘)♥ (◍•ᴗ•◍)❤
for the answer: The florist needs at least 1/3 gallons of nutrient rich water for each bushel of flowers he buys. If w is the gallons of water and f is the bushels of flowers, then:
w≥1/3f
I don't understand how you derive this equation.
Answer:
see below
Step-by-step explanation:
The phrase "at least" indicates that you use the symbol ≥, so that's where they got the ≥ from. The amount of water needed for each bushel is 1/3 * f or 1/3f because you need 1/3 gallons of water per one bushel. We know that the amount of water needed is at least 1/3 gallons per bushel. Since the amount of water is w, "at least" is ≥ and 1/3 gallons per bushel is 1/3f, the inequality is w ≥ 1/3f. I hope this makes sense.
Find the standard deviation for the set of data.
{5,4, 18, 14, 22, 20, 6, 16, 12}
[tex]\sqrt{x^{2} +5x+3} +2x^{2} +10x-15=0[/tex]
please mark this answer as brainlist
the probability of getting an ace or a King from a pack of 52 cards is :
1/4
2/13
5/13
6/13
Answer:
2/13
Step-by-step explanation:
Cdgfsggdehfetgfrhfer
Andrew rents rooms in his hotel for an average of $97 per night. The variable cost per rented room is $36. His fixed costs are $52,000 per month. How many rooms does he have to rent per month in order to break even?
Answer:
853 rooms
Step-by-step explanation:
If someone just opens the door with the intent to stay, Andrew has variable costs to pay which come off the 97 dollars. So his actual profit is 97 - 36 = 61 dollars. So how many rooms in total does he have to rent?
52000 / 61 = 853 rounded.
Is this realistic? The average month has 30 days
853 / 30 = 29 rooms rounded
Each room of 29 would have to be rented every night. I would say he better sell the hotel and go into something else.
Quadrilateral ABCD is inscribed in circle P as shown. Which statement is necessarily true?
Answer:
B. m∠A + m∠C = m∠B + m∠D
Step-by-step explanation:
To inscribe a quadrilateral in a circle, the sums of its opposite angles must be equal (each sum of its opposite angles equals 180 °)
Can someone please help me with these 3 questions?
25) First, find the amount of minutes in 2 hours. Note that there are 60 minutes in one hour:
2 x 60 = 120 minutes per 2 hours.
Next, the bacteria doubles every 20 minutes. 120/20 = 6, which means that the bacteria will double 6 times:
1 x 2 = 2
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
16 x 2 = 32
32 x 2 = 64
64 bacteria will be your answer.
~
26) The Area of a circle = πr²
Set the equation:
400π = π(r + 2)²
First, divide common factors from both sides, or π.
(400π)/π = (π(r + 2)²)/π
400 = (r + 2)²
√400 = √(r + 2)²
r + 2 = √400
r + 2 = √(20 x 20)
r + 2 = 20
r + 2 (-2) = 20 (-2)
r = 20 - 2
r = 18
18 is your final answer.
~
27)
The volume of a box can be found by multiplying length x width x height:
[tex]V (box) = l * w * h[/tex]
The volume given is 90, the height 3, and the width is 1 foot less then length:
First solve what you know:
[tex]V(box) = 90\\h = 3\\l = l\\w = l - 1[/tex]
Plug in the corresponding terms with the corresponding variable. Isolate the variable, l. Divide 3 from both sides of the equation:
[tex]90 = 3 * l (l - 1)\\\frac{90}{3} = \frac{3 * l(l -1)}{3}\\30 = l(l - 1)\\[/tex]
Distribute l to both terms in the parenthesis:
[tex]30 = l(l - 1)\\30 = l^2 - l[/tex]
Solve:
[tex]30 = (6)^{2} -6\\30 = 36 - 6\\30 = 30[/tex]
∴ [tex]l = 6[/tex]
Solve for width. Width is 1 less foot then length:
[tex]l - 1 = w\\l = 6\\[/tex]
∴ [tex]6 - 1 = w\\w = 5[/tex]
Equation: [tex]V (box) = l * w * h[/tex]
or
[tex]l = \frac{V(box)}{w * h}[/tex]
[tex]V(box) = 90\\h = 3\\l = 6\\w = 5[/tex]
The square root of the product of two positive numbers is called their geometric mean. What is the geometric mean of 16 and 64?
Answer:
Geometric mean of a and b: Square root of axb.
16x64 = 1024
Square root of 1024: 32.
So, the geometric mean is 32.
Hope this helps!
Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6
Answer:
The answer is option CStep-by-step explanation:
2√24 + 5√54
To combine the radicals first make sure the radicals have the same square root
That's
For 2√24[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]Since they have the same square root we can combine them
That's
[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]We have the final answer as
[tex]19 \sqrt{6} [/tex]Hope this helps you
What is the image of the point (4,7) after a reflection about the line y = 4.?
Answer:
(4, 1)
Step-by-step explanation:
See attachment courtesy of Desmos.
Please help me with this trigonometry math question ASAP! Thanks so much!
Answer:
[tex]cos\alpha =\frac{7}{25}; \ tan\alpha =-\frac{7}{24}.[/tex]
Step-by-step explanation:
if π<α<2π and cotα<0, then 1.5π<α<2π. It means, that cosα>0 and tanα<0.
1) tanα=1/cotα; ⇒tanα= -7/24;
2) [tex]cos\alpha =\frac{1}{\sqrt{1+cot^2\alpha }}}; \ cos\alpha =\frac{7}{25}.[/tex]
Moly completes 3/10 of her science project in 4/5 hour
Answer:
1.5 per hour
Step-by-step explanation:
If PR = 4X - 2 AND RS = 3X - 5 which expression represents PS?
Answer:
7x - 7
Step-by-step explanation:
If PR, RS, and PS are line segments then the equation below will work.
PR + RS = PS
(4x-2) + (3x-5) = 7x - 7
6 less than twice a number
Answer:
6-2x
Step-by-step explanation:
six less than (subtraction) twice a number. 2 times a number x
why is gravitational force between two object usually unnoticeable
Answer:
gravitational attraction is based upon mass.More the mass more the force.When the object is as big as a moon it has a very less gravity.When we are talking about small objects like 2 pencils the force exists but is so weak that no noticabke movement takes place
Answer:
To notice that force, the objects have to have a big mass and be close to each others.
Generally in eveydays life, you don't notice this force since it is weak but that doesn't mean it does't exist.
If you go the space, you can notice this force since planets have big mass. If you get close to the gravitational field of a planet, you will feel a force that is pulling you toward the planet.
50 points and brainliest, please show your work :D (trying to learn so an explanation would be appreciated)
( a ) Well we know that the limit for the range is 400 dollars, as ( 1 ) her greatest balance was 400 dollars, and ( 2 ) the balance is dependent on the days, and hence represents the range. Respectively the limit for the domain would be 3 weeks.
( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.
( c ) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be :
B(12) = 0
( d ) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.
Jorge walked 25 steps north. then he walked 75 steps south what is Jorges final position
Answer:
If Jorge goes up 25 (positive) and then goes 75 steps south (negative). Then you have to calculate 25-75. This equals -50. We know negative distance is south so he's final position will be 50 steps south.
Step-by-step explanation:
23^3 (-12)^3 +(-11)^3 without actually calculating cubes
Answer:
9108
Step-by-step explanation:
23^3+(-12)^3+(-11)^3 remove parentheses
= 23^3-12^3-11^3 group difference of two cubes
= (23-12)(23^2+23*12+12^2) + 11^3 factor difference of two cubes
= 11 (23^2+23*12+12^2-11^2) factor ou 11
= 11(23(23+12) + (12+11)(12-11)) apply difference of two squares
= 11 (23*35+23*1) factor out 23
= 11(23*(35+1)) simplify
= 11*23*36 convert 11*23 into difference of 2 squares
= (17^2-6^2)*6^2 expand parentheses
= 102^2-36^2 evaluate squares
= 10404 - 1296 subtraction
= 9108
(no calculator required)
Would someone plz help me out with this
Answer:
$25,500
Step-by-step explanation:
Its an increase of $1,500 each year
Can someone help me with this
Answer:
Does the answer help you?
evaluate the following expressions if a = 2, b = 3, x = 4, y = 5
Answer:
18
Step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Triangle A' B' C' is a dilation of a triangle ABC. The scale factor is [tex]\frac{3}{4}[/tex]. Point B is 11 inches away from the center of dilation is point B'?
Answer:
None of the options are correct
Step-by-step explanation:
Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:
[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]
If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:
[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]
Therefore the distance cannot be gotten until the center of dilation is given
elizas backpack weights 18 7/8 pounds with her math book in it. without her math book, her backpack weighs 14 7/9 pounds
I'm assuming your trying to find the weight of the math book so here it is:
Answer:
4 5/36
Step-by-step explanation:
You'd have to do 18 7/8 - 14 7/9 but you can't subtract them yet because they don't have common denominators. So, you have to multiply the 7/8 by 9 and the 7/9 by 8. Then you would get 63/72 and 56/72. Then you put that into the equation and get, 18 63/72 - 14 53/72. If you subtract those, you get the answer, 4 10/72. Which can be simplified as 4 5/36.