The only triangle with the usual triangle centers coincident is an equilateral triangle.
The centroid is the meet of the medians, which are the segments from a vertex to the midpoint of its opposite side. The centroid is the balance point of the triangle. It always divides the medians into a 2:1 ratio, the long piece connected to the vertex.
The circumcenter is the center of the circumcircle, which is the circle through the vertices. That's only going to be the centroid when that 2 part of the 2:1 ratio is the same for each median. That's only going to happen when the sides are the same length so the centroid makes congruent triangles.
The incenter is the center of the inscribed circle, which is the meet of the angle bisectors of each vertex. Again it wont be the centroid unless the sides are equal.
The orthocenter is the meet of the altitudes and it's the same story.
An equilateral triangle is the only type of triangle where its circumcenter, incenter, centroid, and orthocenter coincide at the same point. This unique property emphasizes the symmetry of the equilateral triangle.
Explanation:The type of triangle where its circumcenter, incenter, centroid, and orthocenter are all at the same point is an equilateral triangle. In an equilateral triangle, all sides are equal in length, and all angles are equal to 60 degrees.
An equilateral triangle has the unique property that its circumcenter (intersection of perpendicular bisectors of sides), its incenter (intersection of angle bisectors), its centroid (intersection of medians), and its orthocenter (intersection of altitudes) all coincide at the same point, which is the geometric center and also the triangle's center of mass.
This property is exclusive to equilateral triangles and emphasizes their symmetry. This also applies in three-dimensional forms such as in an icosahedron where each face is an equilateral triangle, demonstrating further the symmetrical properties of these shapes.
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A famer had 612 tomatoes. He put them in baskets of 100. How many baskets did he fill completely. How many tomatoes where left over.
Answer:
6 baskets were filled and 12 tomatoes were left
Step-by-step explanation:
Just do 612/100= 6
Which functions are even? Select all that apply
Answer:
The even functions are options 2, 3, and 5
Step-by-step explanation:
Please, see the attached file.
Thanks.
Answer:
Options B, C and E are even functions.
Step-by-step explanation:
If f(x) = f(-x) then function is called to be even.
A). f(x) = ∛8x
f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)
Therefore f(x) ≠ f(-x)
So function is not an even function.
B). [tex]f(x)=log_{9}x^{6}[/tex]
[tex]f(-x)=log_{9}(-x)^{6}[/tex]
[tex]=log_{9}(x)^{6}[/tex]
f(x) = f(-x)
So this function is even.
C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]
[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]
= [tex]\frac{1}{x^{8}+7x^{6}}[/tex]
f(x) = f(-x)
Therefore given function is even.
D). f(x) = [tex]e^{x^{8}-x }[/tex]
[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]
Therefore f(x) ≠ f(-x)
So the given function is not even.
E). f(x) = |8x| - 3
f(-x) = |8(-x)| - 3
= |8x| - 3
f(x) = f(-x)
Therefore, function is even.
F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]
[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]
f(x) ≠ f(-x)
Therefore the given function is not an even function.
Options B, C and E are even functions.
A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is. This research is an example of a ______.
census
survey
convenience sample
simple random sample
Answer: Census.
Step-by-step explanation:
Given statement:- A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is.
This research is an example of a census because research in which information is obtained through the responses that all available members of an entire population give to questions.
In other words "Census is an official survey of population in a certain area and records various details about the individuals".
The study querying every factory worker in Ohio for their birth year to determine the average age of all U.S. factory workers is a census, as it attempts to gather data from every member of the entire population of interest. (First option)
The research study done to find the average age of all U.S. factory workers where the researchers asked every factory worker in Ohio their birth year is an example of a census. A census involves gathering information about every individual in the entire population of interest.
In this case, the population of interest would be all factory workers, and by querying every one of them (assuming it was indeed every single factory worker in Ohio), it constitutes a census, not a survey, which typically involves a representative sample.
It is not a convenience sample since that would imply a non-random selection based on ease of access, and it's not a simple random sample because not all members of the larger population (nationwide factory workers) have an equal chance of being included.
PLEASE SHOW ALL STEPS!!!!
find the center and radius of the circle.
x2 −2x + y2 − 6y = 26
Answer:
Center (1,3) and radius 6
Step-by-step explanation:
We must complete the square to find the center and radius of the circle.
First make sure the x and y squared terms have 1 as their coefficients. We also make sure x and y terms together.
[tex]x^2-2x+y^2-6y=26[/tex]
We now create space between the x and y terms with parenthesis.
[tex](x^2-2x)+(y^2-6y)=26[/tex]
We complete the square by taking the middle terms -2x and the -6y - divide each and square them.
[tex]\frac{-2}{2} =(-1)^{2} =1[/tex]
[tex]\frac{-6}{2} =(-3)^{2} =9[/tex]
We add the squares to both sides.
[tex](x^2-2x+1)+(y^2-6y+9)=26+1+9[/tex]
Simplify.
[tex](x^2-2x+1)+(y^2-6y+9)=36[/tex]
And write the quadratics in factored form.
[tex](x-1)^{2} +(y-3)^{2} =36[/tex]
The center is (h,k) or (1,3). The radius is the square root of 36 which is 6.
Given that f(x) = 1-x x . What is the domain of f-1(x)? A) R B) R, x ≠ 0 C) R, x ≠ 1 D) R, x ≠ -1
Answer:
The required domain is [tex]x\ne -1[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1-x}{x}[/tex]
We need the inverse of this function.
We first of all have to let [tex]y=f(x)[/tex].
This implies that,
[tex]y=\frac{1-x}{x}[/tex]
Next, we interchange [tex]x[/tex] and [tex]y[/tex] to obtain,
[tex]x=\frac{1-y}{y}[/tex]
We make y the subject to get,
[tex]xy=1-y[/tex]
[tex]xy+y=1[/tex]
[tex](x+1)y=1[/tex]
[tex]y=\frac{1}{1+x}[/tex]
The inverse function is
[tex]f^{-1}(x)=\frac{1}{1+x}[/tex]
The domain of this function is
[tex]x+1\ne 0[/tex]
[tex]\Rightarrow x\ne -1[/tex]
The correct answer is D
What is the graph of this function?
Answer:
See attachment.
Step-by-step explanation:
The main part of the function is an absolute value function and so it forms a V with the center of the V at (0,0). The sides of the V go up and over 1 unit at a time. However, since 2 is added to the it outside of the absolute value, the center of the V moves from (0,0) to (0,2). The sides stay the same. The division by 2 changes the sides. The sides move from up and over 1 unit to up 1 unit and over two units. It spreads or widens the graph. Lastly, the interval selects a specific part of the graph only from 0 to 6 on the x-axis. This takes just one side of the V and looks like a line segment. See attachment.
Answer:
We are given a function,
[tex]y=\frac{|x|+2}{2}[/tex] if 0 ≤ x < 6
We need to draw the graph of the function.
We know that Parent function of the given function is Modulus function | x |.
Consider given function,
[tex]y=\frac{|x|+2}{2}[/tex]
[tex]y=\frac{|x|}{2}+\frac{2}{2}[/tex]
[tex]y=\frac{|x|}{2}+1[/tex]
So, the given function is translated 1 unit upward and compressed by factor of 1/2.
So the obtained graph is attached.
These are just like the last ones please help.
8.
Statement Reason
1. A'F is perpendicular bisector of JK 1. Given
2. JA ≅ KA 2. Dfinition of perp bisector
3. ∠JAF and ∠KAF are right angles 3. Dfinition of perp bisector
4. A'F ≅ A'F 4. Reflexive Property
5. ΔJFA ≅ ΔKFA 5. SAS Theorem
6.
(ANGLE): It is given that ∠AMD ≅ ∠EDM
(SIDE): MD ≅ MD by the Reflexive Property
Which angle would satisfy AAS? ∠MAD ≅ ∠ DEM
NOTE: If you chose the other angle, it would satisfy ASA
Xander goes to the movies with his family. Each family member buys a ticket and two boxes of popcorn. If these are five members of his family,let t represent the cost of a ticket and p represent tye cost of a box of popcorn. Write two different expressions that represents the total amount his family spent.
Final answer:
The total cost can be expressed as 5t + 10p or (5t) + (5 × 2p), representing the combined cost of five movie tickets and twice the amount of popcorn boxes for each of the five family members.
Explanation:
The total amount Xander's family spent on movie tickets and popcorn can be expressed with two different algebraic expressions. The cost for one family member is the cost of one ticket plus the cost of two boxes of popcorn. Since there are five members in the family, we multiply the cost of one person by five.
The first expression is 5t + 10p, which represents the cost of five tickets (5t) and ten boxes of popcorn (2 boxes per person), therefore, 5 times 2 boxes of popcorn (10p).
An alternative expression is (5t) + (5 × 2p), which explicitly shows the cost of five tickets (5t) plus the cost of two boxes of popcorn for each of the five members (5 × 2p).
There are 65 students who walk to West Middle School each day. This is 12.5% 0f the total student at the school. How many students attend West Middle School
someone help i cant do math bc im pretty
Answer:
52
Step-by-step explanation:
One way is to simply count the number of yellow squares.
I count 52, so the area is 52 square units.
Another way is to find the area of the larger rectangle and subtract from it the area of the smaller rectangle.
The larger rectangle is 11 by 6. Area = 11 * 6 = 66.
The smaller rectangle is 7 by 2. Area 7 * 2 = 14.
Area shaded in yellow = 66 = 14 = 52
Answer: area = 52 square units
Answer:
"i cant do math cuz im pretty" such pick me vibes LOL
Step-by-step explanation:
Ava is saving for A new computer that cost 1218 she has already saved half of the money Ava earns $14 per hour how many hours must a work in order to save the rest of the money
Ava must work 43.5 more hours in order to save the rest of the money
Further explanationMoney is any item that generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. In math, it can be defined as the medium of exchange such as notes, coins, and demand deposits, to pay for commodities and services.
If you're self-employed, it's unwise to work more than 40 hours a week on a regular basis because, you'll get a burst of productivity, the extra hours have diminished returns over time and within any time period.
Ava is saving for A new computer that cost 1218 she has already saved half of the money
[tex]\frac{1218 }{2} = 609[/tex] $, hence she has already saved half of the money ($609), so she needs $609
Ava earns $14 per hour
Hence [tex]\frac{609}{14} = 43.5[/tex] hours
Ava must work 43.5 more hours in order to save the rest of the money
Hope it helps!
Learn moreLearn more about hours https://brainly.com/question/2645145Learn more about work https://brainly.com/question/10711591Learn more about computer https://brainly.com/question/2901657Answer details
Grade: 5
Subject: math
Chapter: hours
Keywords: hours, money, saved, order, Ava
Camilla borrows a book from the library for d days. The library charges a late fee 0.10 dollars per day that the book is late. If Camilla returns the book more than 21 days after she borrowed it, the expression 0.10(d?21) represents the total late fee Camilla owes. What does (d?21) represent in this context?
Answer: (d-21) represent in this context
The number of days the book is late
Step-by-step explanation:
The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Camilla borrows a book from the library for d days.
The library charges a late fee 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it.
Then the expression will be 0.10d.
The total amount is given as
Total amount = 0.10 d
Total amount = 0.10 x 21
Total amount = $2.1
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A card is chosen at random from a deck of 52 cards. It is replaced, and a second card is chosen. What is the probability that both cards chosen are jacks?
A.) 1/26
B.) 1/13
C.) 1/169
D.) 2/13
Answer:
C.) 1/169
Step-by-step explanation:
There are 4 jacks in a deck of 52 cards
The probability the first card is a jack
4/52 = 1/ 13
Since we replace the card
The probability the second card is a jack
4/52 = 1/ 13
To get the probability that we get a jack then a jack, we multiply the probabilities
1/13 * 1/13 = 1/169
What is 6,3.6,2.16,1.296,...
a common ratio of r
Answer:
r=0.6
Step-by-step explanation:
Consider geometric sequence
[tex]b_1=6,\\ \\b_2=3.6,\\ \\b_3=2.16,\\ \\b_4=1.296,...[/tex]
In geometric sequence
[tex]b_i=b_{i-1}\cdot r,[/tex]
then
[tex]b_2=b_1\cdot r[/tex]
and
[tex]3.6=6r,\ r=\dfrac{3.6}{6}=0.6.[/tex]
Note that
[tex]2.16=3.6\cdot 0.6,\\ \\1.296=2.16\cdot 0.6.[/tex]
This means that ratio r=0.6.
Carlos can type 228 words in 4 minutes. Which equation represents the number of words Carlos types per minute?
Answer:
see explanation
Step-by-step explanation:
For words per minute divide 228 by 4
words per minute = [tex]\frac{228}{4}[/tex] ( = 57 )
Final answer:
To find the number of words Carlos types per minute, set up an equation and solve for 'x'.
Explanation:
To find the number of words Carlos types per minute, we can set up an equation using the given information. Let's assume that the number of words Carlos types in 1 minute is 'x.' We know that Carlos can type 228 words in 4 minutes. So, the equation would be:
228 words in 4 minutes = x words in 1 minute
To solve this equation, we can cross-multiply and divide:
(228 words) x (1 minute) = (4 minutes) x (x words)
Simplifying further:
x = (228 words) / (4 minutes)
Therefore, the equation that represents the number of words Carlos types per minute is:
x = 228 / 4
Please answer this question! 20 points and brainliest!
Answer:
[tex]x>-3[/tex]
Step-by-step explanation:
To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.
We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.
[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]
To graph, we draw a number line, draw an open circle at -3.
Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3
David and Jillian are playing a board game together. Jillian wants to trade her wool cards for David's ore cards. The double number line shows that David will trade 33 ore cards to Jillian for 66 wool cards. Based on the ratio shown in the double number line, how many wool cards does Jillian need to trade for 44 ore cards?
Answer:8
Step-by-step explanation:6%3=2
4x2=8
I swear its 8 check if i'm wrong I dare you
A car travels 6 kilometers in 3.75 miles. How many miles will it travel in 40 kilometers?
Answer:
25 miles
Step-by-step explanation:
[tex]\frac{6}{40} :\frac{3.75}{y} \\y=25[/tex]
Answer: In the question, 3.75 miles is equal to 6 kilometers (that's rounding in a real life situation. It would actually be about 3.72... but who cares?! :)). So, if you divide 3.75/6... you get 0.625. Now, you multiply 40 by 0.625. After so, you get 25. 40 kilometers is equal to 25 miles!
Last year my family decided to put on a play It was A Great success . 200 people attended and we earned a total of 800 . If adults tickets cost 4 and children coat 2 dollar , how many adults were there
Answer:
200 adults
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know children and adults attended. We will let c be the number of children and a be the number of adults. Since 200 people attended, then c+a=200.
We also know they made $800 and adult tickets cost $4 and child tickets cost $2. We can write 2c+4a=800.
We will solve by substituting one equation into the other. We start by solving the first equation for c. c+a=200 becomes c=200-a.
Now we substitute c=200-a into 2c+4a=800. Simplify and isolate the variable a.
2(200-a)+4a=800400-2a+4a=800400+2a=800400-400+2a=800-4002a=400a=200This means that 200 adults attended and 0 children attended.
Banu is 20 years older than binu. In 5 years, Banu will be twice as old as binu. Find their present age.
Answer:
15?
Step-by-step explanation:
If Binu is 15, in 5 years they will be 20. And if Banu is 20 years older, in 5 years they will be 40 (becuase 15 + 20 = 35 and then + the 5 years) Thats twice Binu's age. So Binu is 15 I would assume?
How wide is a rectangular strip of land with a length of 3/4 miles and an area of 1/2 square mile?
The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.
To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:
Area = Length × Width
Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):
Area = 1/2 square mile
Length = 3/4 miles
1/2 = (3/4) × Width
To solve for the width (W), divide both sides by 3/4:
Width = (1/2) ÷ (3/4)
When dividing by a fraction, you can multiply by its reciprocal:
Width = (1/2) × (4/3)
Now, multiply the numerators and denominators:
Width = 4/6
The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Width = 2/3
So, the width of the rectangular strip of land is 2/3 miles.
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Write the equation in standard form. Identify the important features of the graph:
x^2+y^2-9x+10y+15=0
Answer:
Standard form: [tex]\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
Step-by-step explanation:
Consider expression [tex]x^2+y^2-9x+10y+15=0.[/tex]
First, form perfect squares:
[tex](x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
Help me with these math questions.......
Answer: 118.40, 300, $18,000
Step-by-step explanation:
a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]
p(8) = [tex]-\frac{8}{5} + 120[/tex]
= -1.60 + 120
= 118.40
b) R(x) = x * p(x)
= [tex]x(-\frac{1}{5}x + 120)[/tex]
= [tex]-\frac{1}{5}x^{2} + 120x[/tex]
a=[tex]-\frac{1}{5}[/tex], b=120
x = [tex]\frac{-b}{2a}[/tex]
= [tex]\frac{-120}{-\frac{2}{5}}[/tex]
= [tex]\frac{-120(5)}{-2}[/tex]
= 300
c) R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]
R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]
= -18,000 + 36,000
= 18,000
***********************************************************************
sec θ = [tex]\sqrt{6}[/tex]
[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]
adjacent² + opposite² = hypotenuse²
1² + opposite² = (√6)²
1 + opposite² = 6
opposite² = 5
opposite = √5
csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]
cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]
sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]
cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]
tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]
**********************************************************************
Answer: 144°
Step-by-step explanation:
[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]
π(5x) = 180(4π)
x = [tex]\frac{180(4\pi)}{5\pi}[/tex]
= 36(4)
= 144
Find an equation of variation where y varies directly as x and y = 15 when x = 5, find y when x is 19.
Answer:
[tex]y=3x[/tex]
y=57, when x is 19.
Step-by-step explanation:
We are asked to write an equation of variation where y varies directly as x.
Since we know that a directly proportional equation is in form: [tex]y=kx[/tex], where k is the constant of proportionality.
Upon substituting x=5 and y= 15 in our equation of variation we will get,
[tex]15=k*5[/tex]
[tex]k=\frac{15}{5}[/tex]
[tex]k=3[/tex]
Upon substituting k=3 in the standard equation of variation we will get our desired equation of variation as: [tex]y=3x[/tex].
Now let us find y, when x is 19.
[tex]y=3*19[/tex]
[tex]y=57[/tex]
Therefore, y equals 57, when x is 19.
Find the 20th term of the arithmetic sequence
Answer:
-99
Step-by-step explanation:
Given :
Arithmetic sequence : 15 , 9 ,3 , -3 , ........
To Find : 20th term .
Solution :
Formula of nth term in Arithmetic mean : [tex]a_{n} = a+(n-1)*d[/tex] ---(A)
where
a = first term of sequence
n = term position
d = common difference
[tex]a_{n}[/tex] = the term you want to find
Thus in the given sequence:
a = 15 ( first term )
n = 20 th term ( given )
d = 9-15 = 3-9 = -6(common difference)
Putting values in (A)
⇒[tex]a_{20} = 15+(20-1)*(-6)[/tex]
[tex]a_{20} = 15-114[/tex]
[tex]a_{20} = -99[/tex]
Hence the 20th term is -99 i.e. option 1
Janine has 93 beads. She uses 7 beads for each bracelet. She makes as many bracelets as possible. How many beads will Janine have left over?
The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate of 1.8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2000?
Answer:
3746148
Step-by-step explanation:
i know you probably just want the answer but hear me out it is just simple math and can be resolved with a quick search. Find or search 1.8% of 3,381,000 and multiply it times the years progressed.
60858 x 6 = 3746148
Final answer:
Using the exponential growth formula, the approximate population of Henderson City in the year 2000 is calculated to be around 3,769,706 if the annual growth rate remains constant at 1.8%.
Explanation:
To calculate the approximate population of Henderson City in the year 2000, we can use the formula for exponential growth. The formula is
[tex]A = P(1 + r)^t[/tex]
where A is the amount of the final population, P is the initial population, r is the growth rate expressed as a decimal, and t is the time in years. In this case:
P (initial population) = 3,381,000r (annual growth rate) = 1.8% or 0.018t (time from 1994 to 2000) = 6 yearsSo the equation becomes:
A =[tex]3,381,000(1 + 0.018)^6[/tex]
Calculating this gives us the approximate population, A:
A ≈[tex]3,381,000(1.018)^6[/tex]
A ≈ 3,381,000(1.1155)
A ≈ 3,769,706
Therefore, the approximate population of Henderson City in the year 2000 would be 3,769,706 residents if the growth rate remains constant at 1.8%.
Can someone give 2 examples of a logarithmic equation with infinite solutions?
Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.
[tex]\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0[/tex]
and
[tex]\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x[/tex]
Logarithmic equations with infinite solutions have graphs that look like dying-out exponentials. They can have infinite solutions because there are infinitely many values of y that satisfy the equation.
Examples of Logarithmic Equations with Infinite Solutions:
1. Logarithms to the base 10 (common logarithms):
In the equations below, y is the exponent to which 10 must be raised to equal x, so y is the common logarithm (log) of x.
x = 10^y
x = 10^y+1
2. Logarithms to the base e (natural logarithms):
In the equations below, y is the power to which e must be raised to equal x, so y is the natural logarithm (ln) of x.
x = e^y
x = e^y+1
Both of these equations have graphs that look like dying-out exponentials. They have infinite solutions because there are infinitely many values of y that satisfy the equation. Whenever the base is positive and not equal to 1, logarithmic equations can have infinite solutions.
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Lines y and z are parallel.
What is the measure of angle 2?
Answer:
28 degrees
Step-by-step explanation:
180 = 10x + 5 + 65 because they are supplementary. x = 11.
Angle 2 = 180 - (Angle 1 + (4x - 7))
Angle 2 = 180 - ((180 - 65) + 4x - 7)
Angle 2 = 180 - (115 + 4x - 7)
Angle 2 = 180 - 152
Angle 2 = 28 degrees
20 POINTS!!!Which ray is a bisector of angle ABC? BC BD BA BF
Answer:
The answer is BD is the bisector angle