The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).
What is the rewritten form of the expression?The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;
2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)
= log {(x+3)²(x-2)^5}/(x-7)³(x²)
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The graph is of a function in the form p(t) = a*b^t. What is the function?
Answer:
p(t) = 5*2^t
Step-by-step explanation:
We can solve for 'a' and 'b' using the point coordinates shown on the graph.
SetupSubstituting for (t, p(t)), the two equations we can make from the given points are ...
p(t) = a*b^t
5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)
10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)
SolutionThe first equation tells you ...
5 = a
The second equation tells you ...
10 = 5*b
2 = b
EquationThe function is ...
p(t) = a*b^t
p(t) = 5*2^t
Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check
all that apply.
p(x) = 14(x + 7)² + 1
g(x) = -5(x + 10)² - 1
s(x) = –(x − 1)? +0.5
g(x) = 2x² + 10x-35
t(x) = -2x² - 4x - 3
Using translation concepts, the functions that have a maximum and are transformed to the left and down of the parent function are given by:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For the translations, we have that:
Shift left, hence x -> x + a, a > 0.Shift down, hence y -> y - a, a > 0.Having a maximum means that the leading coefficient is negative.The functions that respect these conditions are:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3 = -2(x² + 2x) - 3 = -2(x + 1)² - 1More can be learned about translation concepts at https://brainly.com/question/4521517
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BRAINLIEST!!!!!!!!!!!!!!!!!!!!!
Answer:
Move all the points on the graph two points to the right
Step-by-step explanation:
f(x-2) is just a translation to the right by 2. The whole formula is typically y = a f(b(x + c)) + d. In this case, the C value is the one being changed and that indicates a translation left or right. -2 indicates 2 to the right.
Answer:
The Slope: 0
The y-intercept: (0,0_
x y
0 0
1 0 (there is supposed to be a line between the x and y that goes down all the way down the numbers but i cannot type that)
Step-by-step explanation:
Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5 .)
The frequency which is to filled in the table is 3,1,2,4.
Given shopping time of ten shopkeeper: 36,20,32,18,20,33,28,34,37,23.
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Shopping time is given as 36,20,32,18,20,33,28,34,37,23.
Intervals for which frequency is given is 18 to 22, 23 to 27, 28 to 32, 33 to 37.
Numbers in the range 18 to 22=18,20,23 therefore 3
Numbers in the range 23 to 27=23 therefore 1
Numbers in the range 28 to 32=32 , 28 therefore 2
Numbers in the range 33 to 37=36, 33, 37, 34 therefore 4.
Hence the frequency which is to filled are 3,1,2,4.
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What is the slope of a line parallel to the line with equation 2x−5y=9?
25
−25
−95
−52
Answer:
For this one the parallel slope is going to be 2/5
Step-by-step explanation:
Choose the lowest common denominator.
03 04 05 06 08 010 012
Find the sum:
Alw
The sum is
and
colch
The expression written in equivalent form with a
common denominator is
Done
1) 8
2) [tex]-\frac{3}{4}=-\frac{6}{8}[/tex], so it is equal to [tex]-\frac{6}{8}+\frac{5}{8}[/tex]
3) 1/8
The coordinates of the points P, Q and R are given by (-2, 1), (1, 4) and (4, k) respectively. Find the value(s) of k if
(b) PQ=QR(clue:distance).
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
How to find the missing value of a coordinate
Herein we can find the value of the missing coordinate of point by the Pythagorean theorem, which is described below:
PQ = QR (1)
[tex](Q_{x}-P_{x})^{2} + (Q_{y}-P_{y})^{2} = (R_{x}-Q_{x})^{2} + (R_{y}-Q_{y})^{2}[/tex]
If we know that P(x, y) = (- 2, 1), Q(x, y) = (1, 4) and R(x, y) = (4, k), then the missing value of the point R is:
[1 - (- 2)]² + (4 - 1)² = (4 - 1)² + (k - 4)²
(k - 4)² = 9
k - 4 = ± 3
k = 4 ± 3
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
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Giving brainliest to first accurate answer
Answer:
x<3
Step-by-step explanation:
There isn't a question that I can see for the first image, and I cannot see the yellow part, so I am not 100% sure if this is an accurate answer to the question you were asking.
Given that a bag of m&ms has 21 brown candies, 15 orange candies, 10 yellow candies, 14 red candies, and 5 green candies, find the probabilities
The probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that a bag of candies that have
21 brown candies
15 orange candies,
10 yellow candies,
14 red candies,
5 green candies,
probabilities of drawing each candy =?
Total Candies = 21 +15+10+14+5 = 65
Probability = No. of chances / Total outcomes
Probability of drawing Brown candies = P(B) = 21 /65 = 0.323
Probability of drawing Yellow candies = P(Y)= 10/65= 0.154
Probability of drawing Orange candies = P(O) = 15/65= 0.231
Probability of drawing Red candies =P( R) = 14/65= 0.215
Probability of drawing Green candies = P(G) = 5/65= 0.077
Therefore the probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077.
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Dante has scored 30, 18, and 28 points in his three basketball games so far. How many points does he need to score in his next game so that his average (mean) is 26 points per game
Answer:
He needs to score 28 points.
Step-by-step explanation:
[tex]1^{st}\,\,score: 30\,\,points;\\\\2^{nd}\,\,score: 18\,\,points;\\\\3^{rd}\,\,score: 28\,\,points;\\\\4^{th}\,\,score: \,\,?[/tex]
Let's calculate Dante's 4th score, given that the average is 26 points:
[tex]\frac{S1 + S2 + S3 + S4}{4} = 26\\\\\frac{30 + 18 + 28 + S4}{4} = 26\\\\76 + S4 = 104\\\\S4 = 28\,\,points.[/tex]
find the values of m&n if x
2
−2
[tex]f(x) = mx ^{4} + 2x ^{3} - 3x ^{2} + nx - 4[/tex]
The values of m and n from the given equation are 1/4 and -2
Polynomial functionsGiven the polynomial function below
f(x) = mx^4+2x^3-3x^2+nx-4
If the zeros are 2 and -2, hence;
0 = 16m+16-12+2n-4
0 = 16m-16+12-2n-4
_______________
16m+2n = 0
16m - 2n = 8
Subtract
2n+2n = -8
4n = -8
n = -2
Substitute for "m'
16m + 2(-2) = 0
16m = 4
m = 1/4
Hence the values of m and n from the given equation are 1/4 and -2
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What are the solutions of the equation x4 + 3x² + 2 = 0? Use u substitution to solve.
O x=+√√√2 and x = +1
Ox=ti√√2 and x = ti
Ox=± √√2 and x = ti
Ox=+√√2 and x = +1
Answer:
[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]
Step-by-step explanation:
[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].
This gives you the equation: [tex]u^2+3u+2=0[/tex].
Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:
[tex]u+2=0\\u=-2[/tex]
Now substitute x^2 back in as u
[tex]x^2=-2[/tex]
Take the square root of both sides
[tex]x=\pm \sqrt{-2}[/tex]
Separate the radical into sqrt(-1) * sqrt(2)
[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]
Rewrite using i
[tex]x=\pm i\sqrt{2}[/tex]
Now set the other factor equal to 0
[tex]u+1=0\\u=-1[/tex]
substitute x^2 back in as u
[tex]x^2=-1[/tex]
Take the square root of both sides
[tex]x=\pm\sqrt{-1}[/tex]
rewrite using i
[tex]x=\pm i[/tex]
Use the spinner to identify the probability to the nearest hundredth of the pointer landing on a non-shaded area
Parentheses three times to parentheses divided by parentheses 5×4 parentheses
They work-infested $18,000 into accounts, one yielding 4% interest and the other yielding 12%. If he received a total of $1,280 and interest at the end of the year, how much did he invest at 4%?
Answer:
$11,000
Step-by-step explanation:
Let amount invested for 12% yield be p . Amount for 4% yield is therefore (18000-p)
Interest for 12%: 12% of p=0.12p
Interest for 4%: 4% of (18000-p)=0.04(18000-p)=720-0.04p
Total interest:
=0.12p + (720-0.04p)
=0.12p-0.04p+720
=0.08p+720
But we already know the total interest is 1280
Therefore: 0.08p+720=1280
0.08p=1280-720
0.08p=560
p=560÷0.08
p=7000
Therefore at 4% the person invested:
(18000-p)
18000-7000
$11,000
............help ?????????????
Step-by-step explanation:
Solution.x+40°+35°=180°(straight line)x+75°=180°x=180°-75°x=105hope it helps!!
Answer:
x = 75°
Step-by-step explanation:
∠ p = 40° [alternate interior angles]
∠ q = 35° [alternate interior angles]
x = ∠ p + ∠ q
x = 40° + 35°
x = 75°
Which of the following are geometric sequences?
Check all that apply.
A. 5, 10, 15, 20, 25
B. 10, 5, 2.5, 1.25, 0.625, 0.3125
C. 1, 1, 2, 3, 5, 8, 13
D. -9, -3, -1, -1/3, -1/9, -1/27
Answer: B and D
Step-by-step explanation:
A is not, it's an arithmetic sequence where each term is +5 greater than the previous
B is because each term is 1/2 the previous term (common ratio of 1/2) thus making it a geometric sequence
C is not, it's the Fibonnaci sequence which is neither an arithmetic or geometric sequence
D is because each term is 1/3 the previous term (common ratio of 1/3) thus making it a geometric sequence
9029
2066
10
4
-6-54-3-2-12- 2 3 4 5 6 x
-f(x)
-6
-8
-10
-12+
Whats the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
how long would it take to drive 18 miles while going 18 mph
Answer:
1 hour
Step-by-step explanation:
18 miles because if u go 18 miles per hour it takes a hour
324 divided into 6.846
324 divided into 6.846 is 47.33
How to evaluate the division?The statement is given as:
324 divided into 6.846
This is represented as:
324/6.846
Using a calculator, we have:
47.3269062226
Approximate
47.33
Hence, 324 divided into 6.846 is 47.33
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Maria spends $19 on lottery tickets every week and spends $122 per month on food.On an annual basis, the money spent on lottery tickets is ______% of the money spent to buy food.
The money spent on lottery tickets is 15.6% of the money spent to buy food.
How to determine the proportion?The given parameters are:
Food = $122
Lottery = $19
The proportion of the lottery tickets is:
Proportion = Lottery/Food * 100%
This gives
Proportion = 19/122* 100%
Evaluate
Proportion = 15.6%
Hence, the money spent on lottery tickets is 15.6% of the money spent to buy food.
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Given the function defined by g(x)=x²+4x-3, find g (s).
Answer:
[tex]g(s)=s^{2} +4s-3[/tex]
Step-by-step explanation:
If we have a function f(x) and want to find f(a) , just substitute by x=a in the Equation of f(x) , the Result will be f(a)So for our Question , we have [tex]g(x)=x^{2} +4x-3[/tex]
and we want to find g(s) , so just substitute by x = s in the Equation of g(x)
[tex]g(s)=s^{2} +4s-3[/tex]
To raise funds for a new fire truck, a fire department is conducting a raffle. Residents can purchase a raffle ticket for $10.00 each. After writing his/her name on the ticket, the resident will place it in a container. Later on, a fire department official will randomly select one ticket from the container. The resident who purchased the selected ticket will win a prize of $2,000.00.
a. Suppose at the time of the drawing there are a total of 1000 purchased raffle tickets in the container. If a particular resident has purchased 10 tickets, what is his/her probability of winning the prize?
b. Compute the expected profit (winnings − cost) for a particular resident who purchased 10 raffle tickets.
c. After paying out the $2,000.00 prize, how much money has the fire department raised for its new fire truck? Other than the prize, ignore any other raffle costs incurred by the fire department.
a. The probability of winning the prize by the resident who purchased 10 tickets is 1% (10/1,000).
b. The expected profit (winnings - cost) for the resident who purchased 10 raffle tickets is $1,900 ($2,000 - $100).
c. The amount raised by the fire department after paying out the $2,000 prize (ignoring other raffle costs) is $8,000 ($10,000 - $2,000).
What is a raffle?A raffle is a gambling competition or lottery organized to raise money for a purpose.
A raffle involves the sale of tickets which are drawn randomly to select some winners.
Data and Calculations:Price of a raffle ticket = $10
Prize = $2,000
Cost of purchasing 10 tickets = $100 ($10 x 10)
Number of raffle tickets sold = 1,000
Total revenue realized = $10,000 ($10 x 1,000)
Thus, if a resident purchases 10 tickets, the chance of winning the raffle is 1%.
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Evaluate the following expression.
(5x)^0
Hello,
Answer:
1
Step-by-step explanation:
(5x)⁰ = 1
Rule : a⁰ = 1
Answer:
1
Step-by-step explanation:
(5x)^0
Any base raised to the zero power is 1
a^0 = 1
5^0 =1
(5x)^0 =1
I need help with this question please!!
Answer:
31465
Step-by-step explanation:
n!/((n-r)! r!)
= 31!/(31-4)! 4!
= 31!/ 27! 4!
= 31465
3) Which letter has a perpendicular line segment?
A. Y
B. L
C. R
D. U
Answer: L
Step-by-step explanation:
The two segments that form L meet at a 90 degree angle.
Define coefficiend, base and index of an algebraic term with an example
Step-by-step explanation:
a number used multiplier variable
example 6z menas 6 times z and z is a variable so sixes coefficient variable with no number have a question of one example X is a really 1x
What is the radius of a sphere that has a surface area of 2903.33 in²?
Answer:
15.2 in
Step-by-step explanation:
The surface area of a sphere is given by the formula below:
Surface area of sphere= 4πr², where r is the radius
Given that the surface area is 2903.33 in²,
2903.33= 4πr²
Divide both sides by 4π:
[tex] {r}^{2} = \frac{2903.33}{4\pi} [/tex]
Square root both sides:
[tex]r = \sqrt{ \frac{2903.33}{4\pi} } [/tex]
r= 15.2 in (3 s.f.)
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the simplified value of the exponential expression is 1/9