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.
The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?
A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.
B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
if you still need the answer, its C.
Step-by-step explanation:
Last month, dory biked 11 times as many miles as karly. Togetherthey biked a total of 156 miles . How many miles did dory bike last month
Answer:
143 miles
Step-by-step explanation:
Let the distance Karly biked be x
Then Dory biked 11x
So x+11x=156
x=156/12=13
So Dory biked 11 ⋅ 13= 143 miles
Is this correct?
What percentage is the fraction `2/(10)` equal to?
Answer:
20%
Step-by-step explanation:
Percentage means out of 100
We need to get 2/10 to be out of 100
Multiply by 10/10
2/10*10/10
= 20/100
This is 20%
Our Einstein has baked a cake and cut it into 8 slices. If he hands out 3 slices to his guests, what fraction of the cake is left?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].
He hands out 3 slices to his guests. Let us find out part of the cake given to guests.
[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]
To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.
[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]
Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.
Answer:
As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.
⇒ Total slice of cake Einstein has baked = 8
Also, it is given that if he hands out 3 slices to his guests.
⇒ Number of slice he hands out to his guests = 3
Remaining slice of a cake Einstein left with = 8 -3 = 5.
We have to find the fraction of the cake is left.
Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.
Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]
Substitute the given values we get;
[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]
therefore, the fraction of the cake is left is, [tex]\frac{5}{8}[/tex]
There are 120 students surveyed (30 from each grade). Use the table below to determine that probability that a student selected at random is in 11th grade or selected Math as their favorite subject?
Find P (11th or math)
a. 7/120
b. 1/2
c. 67/120
d. 59/120
Answer: 59/120 (choice D)
Add up the values in the "math" column and the "11th" row to find the total number of people who are either in 11th grade, in math, or in both.
So,
(12+10+8+7) + (14+5+3) = 59
represents the number of people who are in either category. This is out of 120 (given). This is where 59/120 comes from.
can someone help me with this question?
Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]
Step-by-step explanation:
Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.
d = r · t
÷ t ÷ t
[tex]\dfrac{d}{t}=r[/tex]
Now plug in the given d and t values from the table to solve for r:
[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex] simplified the fraction
You can check this by plugging in the other 3 values from the table:
[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
pease help, thank you
Answer: -2
=====================================================
Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.
Repeat the same steps as before to find that (8,4) is also on the parabola
We need to find the slope of the line through (4,12) and (8,4)
m = (y2 - y1)/(x2 - x1)
m = (4-12)/(8 - 4)
m = -8/4
m = -2
The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.
The line goes down 2 units each time you move to the right 1 unit.
Midsegment of Triangles
Find x
Answer: x = 3
Step-by-step explanation:
If 3x is the midsegment of the triangle, then it is half the length of the base, which implies that the length of the base equals twice the length of the midsegment:
base = 2 * midsegment
18 = 2 (3x)
18 = 6x
÷6 ÷6
3 = x
There were 50 students in the chess club. The membership went up by 10%. How many more students joined the club?
The membership went up by 10%.
There are now 55 total students in the club.
The formula for calculating the percentage change is
[tex]p=\frac{N-O}{O}.100[/tex]
where p is the percent change, N is the New Value and O is the Old Value.
In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for N:
[tex]10=\frac{N-50}{50} .100\\10=2(N-50)\\5=N-50\\N=55[/tex]
There are now 55 total students in the club.
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George bought 30 packs of football cards.There were 14 cards in each pack.How many cards did George buy
Answer:
there would be 420 cards in total
Step-by-step explanation:
How can you tell by looking at the coordinates of the two triangles that δ a'b'c' is a 180° rotation of δ abc?
a.the coordinates cannot prove a 180° rotation.
b.the y-coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc.
c.the x-coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc. eliminate
d.both the x and y coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc?
Answer:
Option d is correct.
Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.
Step-by-step explanation:
The rule of 180 degree rotation about the origin is:
[tex](x, y) \rightarrow (-x , -y)[/tex]
Since a Rotation of a point through 180°, about the origin when a point a(h, k) is rotated about the origin through 180° in anticlockwise or clockwise direction.
then, By the rule of 180 degree rotation;
[tex]a(h, k) \rightarrow a'(-h , -k)[/tex]
so, it takes the new position i.e, [tex]a'(-h , -k)[/tex]
Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.
A recursive rule for a geometric sequence is a1=3;an=1/2an−1.
What is the explicit rule for this sequence?
Enter your answer in the box.
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]
--------------------------------------------------
Exciplit rule:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]
Answer:
The answer is: a_n = 6*(1/2)^n
A football signs a contract that pays him $16 million over 4 years. What is his average pay per year?
Answer:
the footballer's average pay would be $4 million/annum.
Stephanie bought 3 pizzas for a total of $9.00. Which expression shows p, the cost of each pizza?
Answer:
the answer is 3
Step-by-step explanation:
3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:
9 divided by 3
9/3
3
Hey y'all please help me with this geometry problem,would really appreciate it :)
180-(x+50)+180-4x+180-(2x+40)+180-3x=360
720-x-50-4x-2x-40-3x=360
630 - 10x=360
-10x=360-630
-10x=-270 /:(-10)
x=27
Saul in third in line. Enid is last in line. There are 3 children between them. What position is Enid in line?
Final answer:
Starting with Saul in the 3rd position and counting the 3 children between him and Enid, Enid is determined to be in the 7th position in the line.
Explanation:
To find the position of Enid in line, we start with Saul who is third in line. If there are 3 children between Saul and Enid, and Enid is last, we need to count the positions:
Saul is 3rd in line.
1st child after Saul is in the 4th position.
2nd child after Saul is in the 5th position.
3rd child after Saul is in the 6th position.
Enid is after the 3rd child, placing her in the 7th position.
Therefore, Enid is in the 7th position in line.
Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Answer:
Step-by-step explanation:
A builder uses 32 wooden slats to make 4 fence panels. Fatima wants to know how many slats are needed for 1 panel. Gerard wants to know how many slats he will need to make 8 panels. Drag an expression to answer each question.
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Wooden slates required to make 4 fence panels = 32
To find wooden required to make 1 panel, use ratio property,
4 fence panels = 32 wooden slates
1 fence panel = 8 wooden slates
Also, to find wooden required to make 8 panels, use ratio property,
4 fence panels = 32 wooden slates
8 fence panels = 64 wooden slates
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
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Final answer:
Gerard needs 64 slats to make 8 panels, as it is a proportional relationship.
Explanation:
To find out how many slats are needed for one panel, we simply divide the total number of slats by the number of panels. Since a builder uses 32 slats to make 4 panels, for one panel, Fatima would need:
Number of slats for one panel = Total number of slats \/ Number of panels
Number of slats for one panel = 32 / 4 = 8 slats
For Gerard's question, if 1 panel requires 8 slats, then to make 8 panels he would need:
Number of slats for 8 panels = Slats per panel x Number of panels
Number of slats for 8 panels = 8 x 8 = 64 slats
It's a straightforward example of a proportional relationship in mathematics, where the number of slats scales directly with the number of fence panels.
Which is a root of [tex]f(x)=0[/tex] with a multiplicity of 2?
Answer:
3
Step-by-step explanation:
The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.
x 1 2 3 4
y 5 10 15 20
What's the constant?
Answer:
x ---> 1
y ---> 5
Step-by-step explanation:
We are given paired values for two variables x and y and we are to determine the constant number by which each term is increased such that they are in a proportional relationship.
For x, we have the following paired values:
[tex]x: 1, 2, 3, 4[/tex]
So here the difference between each consecutive term is 1 so the constant is 1.
And for y, we have:
[tex]y: 5, 10, 15, 20[/tex]
In this case, the difference between each consecutive term is 5 so the constant is 5.
One number is five more than another and their sum Is there less than three times the smaller find the numbers
Answer:
The numbers are 8 and 13
Step-by-step explanation:
In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.
Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
5 = x - 3
8 = x
Now to find the larger number, put into the larger number equation.
x + 5
(8) + 5
13
The numbers are 8 and 13.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''One number is five more than another and their sum Is there less than three times the smaller''.
Now,
Let the smaller number = x
Then, The another number = x + 5
Write the expression as;
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
2x - 3x = - 3 - 5
- x = - 8
x = 8
And, The another number = x + 5
= 8 + 5
= 13
Thus, The numbers are 8 and 13.
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Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4).
A) y = 3x - 26
B) y = -3x + 16
C) y = 1/3 x-2
D) y = -1/3 x+6
Answer:
D) y = -1/3 x+6
Step-by-step explanation:
If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope. Knowing y= mx+b we need to find the slope of the old line.
3x+9y=7
Subtract 3x from each side
3x-3x +9y = -3x+7
9y = -3x+7
Divide each side by 9
9y/9 = -3x/9 + 7/9
y = -1/3 x + 7/9
We know the slope of the old line is -1/3, so the slope of the parallel line is -1/3.
If we know the slope of the line and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y-4 = -1/3(x-6)
Distribute the -1/3
y-4 = -1/3 x -1/3*-6
y-4 = -1/3x +2
Add 4 to each side
y-4+4 = -1/3x +2+4
y = -1/3x+6
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The quotient of a number and 18 is 109.8.
which statements are correct?
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be x/18=109.8
The equation should be 18x=109.8
The answer is 6.1.
The answer is 1,976.4.
Answer:
2. It can be solved by using the multiplication property of equality.
3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]
6. The answer is 1,976.4.
Step-by-step explanation:
Let x be the number.
We have been given that the quotient of a number and 18 is 109.8.
Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.
[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]
We can represent our given information as:
[tex]\frac{x}{18}=109.8[/tex]
By using multiplication property of equality we will get,
[tex]18*\frac{x}{18}=18*109.8[/tex]
[tex]x=18*109.8[/tex]
[tex]x=1976.4[/tex]
Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.
A bag contains 7 good apples and 3 bad apples. Nick takes two apples at random from the box, WITHOUT replacement.
This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.
Explanation:The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.
The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.
Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.
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If a matrix does NOT have an inverse, what do know about the determinant?
A) The determinant does not exist.
B) The determinant is O.
C) The determinant is 1.
D) The determinant is -1.
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A dartboard is divide into sections numbered 1-20. Leon throws a dart at the board 30 times. 8 times the dart lands on the number 2. What is the experimental probability that the dart lands on number 2?
Answer:
4/15
Step-by-step explanation:
Experimental probability is the actual times the event occurs divided by the number of trials
Actual times : 8
Number of trials: 30
Experimental probability of a 2: 8/30 = 4/15
Find f(x) if it is known that f(x−2)=2x−4
Answer:
f(x) = 2x
Step-by-step explanation:
Remark
What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.
Solution
f(x - 2) = 2x - 4 Take out a common factor on the right of f(x -2)f(x - 2) = 2(x - 2) Now what that means is that in the original equation, wherever you saw an x, you put in x - 2. So the original equation must have beenCheck
f(x) = 2x To check this put x - 2 back inf(x - 2) = 2(x -2) Remove the brackets. f(x - 2) = 2x - 4 which is what it should be.Final answer:
To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.
Explanation:
To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.
Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.
Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.
A school replaced 20% of its computers with new ones what is the total number of computers in the school if 55 computers were replaced
Answer:
There were 275 computers
Step-by-step explanation:
Computers replaced = total computers * percent replaced
What do we know?
The percent replaced is 20 = .2
55 computers were replaced.
Substitute this in
55 = total computers * .2
Divide each side by .2
55/.2 = total computers *.2 /.2
275 = total computers
There were 275 computers
helps please i need it
Anita does the same number of jumping jacks each day over a period of several days. On the fifth day, she has completed a total of 325 jumping jacks. By the eighth day, she has completed a total of 520. What value equals the slope of the line of the total number of jumping jacks when graphed against the day?