Write 3 + 2 log z - log(x² + 2x + 1) +1/2 log y as a single logarithm with coefficient 1.
Answer:
[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Choose the more appropriate answer
Step-by-step explanation:
I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:
[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Using the graph of the function g(x) = log5 (x – 3), what are the x-intercept and asymptote of g(x)? The x-intercept is 4, and the asymptote is located at x = 3. The x-intercept is 3, and the asymptote is located at x = 4. The x-intercept is 4, and the asymptote is located at y = 3. The x-intercept is 3, and the asymptote is located at y = 4.
The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
What is an Asymptote ?An asymptote is a line that a curve approaches but it never reach.
The given equation
y = log₅(x-3)
To find the asymptote
Set the argument of the logarithm equal to zero.
x - 3 = 0
The vertical asymptote occurs at
x = 3
The equation can also be written as
[tex]\rm 5^y = x-3[/tex]
To find the x intercept we will put the value of y = 0 ;
therefore
5⁰ = x -3
1=x-3
x = 4
Therefore ,The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.
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Answer:
The x-intercept is 4, and the asymptote is located at x = 3.
Step-by-step explanation:
I got it right on the test.
PLEASE HELP!!!
Which point is tangent to the circle?
A
D
M
Q
Answer:
M is target to the circle
Which of the following statements are true?
f(x)
g(x)
. A. Both graphs have exactly one asymptote.
B. Both graphs have been shifted and flipped.
. C. Both graphs are exponential functions.
0 D. Both graphs are logarithmic functions
The true statements are; A. Both graphs have exactly one asymptote. C. Both graphs are exponential functions. B. Both graphs have been shifted and flipped.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
There usual form is specified below. They are written in several such equivalent forms.
For example, y^x
, where a is a constant is an exponential function.
The graphs are exponential functions because as x increases, the y approaches infinity.
Here, the graphs have exactly one asymptote.
we can see that both graphs appear to have been shifted and flipped especially when at their respective coordinates.
The true statements are;
A. Both graphs have exactly one asymptote.
C. Both graphs are exponential functions.
B. Both graphs have been shifted and flipped.
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PLEASE HELP!!!!!! WHATS THE ANSWER
Answer:
3
Step-by-step explanation:
pls mark brainliest
What is the range of this exponential function?
f(x) = 2.7x
The range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The exponential function is given below.
f(x) = 2.7ˣ
We know the value of the exponential function is always positive.
Then the range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).
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Krista got paid $43.75 for working 3.5 hours. How much did she earn per hour?
Answer:
12.5
Step-by-step explanation:
divide 43.75 by 3.5 to get your answer
Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used
The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
[tex]9x\² - 36x + 36 = 0[/tex]
The above equation is a quadratic equation which can be represented as:
[tex]ax\² + bx + c = 0[/tex]
The discriminant (d) is calculated as:
[tex]d = b\² - 4ac[/tex]
So, we have:
[tex]d = (-36)\² - 4 * 9 * 36[/tex]
[tex]d = 0[/tex]
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solutionThe equation is given as:
[tex]x\² - x + 4 = 0[/tex]
The above equation can be represented as:
[tex]ax\² + bx + c = 0[/tex]
The discriminant (d) is calculated as:
[tex]d = b\² - 4ac[/tex]
So, we have:
[tex]d = (-1)\² - 4 * 1 * 4[/tex]
[tex]d = -15[/tex]
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expressionWe have:
[tex]4x\² + 23 - 35[/tex]
Evaluate the difference
[tex]4x\² -12[/tex]
Factor out 4
[tex]4(x\² -3)[/tex]
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
The pie chart for the expenditure of a housewife for a particular day is shown below.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
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There are 9 students performing in the talent show, 7 of whom will perform a dance.
If 6 students are randomly chosen to perform during the first section of the show, what is the
probability that all of them will perform a dance?
Write your answer as a decimal rounded to four decimal places.
Which algebraic rule describes the translation of quadrilateral ABCD to quadrilateral A’B’C’D?
The algebraic rule that best describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is P'(x, y) = (x + 8, y + 7). (Correct answer: A)
How to determine the translation of a quadrilateral on a Cartesian plane
According to the image attached we understand that the quadrilateral ABCD is transformed into quadrilateral A'B'C'D' by applying pure translation. Translations are a kind of rigid transformation, defined as a transformation applied on a geometric locus such that Euclidean distance is conserved at every point of the construction.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vector.By direct comparison, we conclude that the quadrilateral ABCD is translated 8 units in the +x direction and 7 units in the +y direction. Hence, the algebraic rule that describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is:
P'(x, y) = (x, y) + (8, 7)
P'(x, y) = (x + 8, y + 7)
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What is an equation of a circle whose center is at (2,-4) and is
tangent to the line x = -2?
(1) (x - 2)2 + (y + 4)² = 4
(2) (x - 2)² + (y + 4)² = 16
(3) (x + 2)² + (y - 4)² = 4
(4) (x + 2)² + (y - 4)² = 16
The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:
(2) (x - 2)² + (y + 4)² = 16
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The circle has center at (2,-4), hence [tex]x_0 = 2, y_0 = -4[/tex].
The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.
Hence the equation of the circle is given by:
(2) (x - 2)² + (y + 4)² = 16
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Find the total selling price.
Alonzo and Catalyn Diaz paid a total of $23,289.26 for their new automobile. If the sales tax rate in their community is 6.5%, what was the total selling price of the Diaz's new automobile?
the assumption being that the tax is added to the amount advertised for the vehicle, namely 23289.26 + 6.5% of that.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 23289.26}}{\left( \cfrac{6.5}{100} \right)23289.26}\implies 1513.8~\hfill \underset{\textit{total selling price}}{\stackrel{23289.26~~ + ~~1513.8}{24803.06}}[/tex]
This means that 0.3 is a (n)
number. Rational or irrational
0.3 is a Rational Number written in Decimal Form
0.3 is neither an Integer nor a Whole number.
Jace gave $100 to her daughter Kailey and asked her to spend three parts and save two parts of the total amount. How much did Kailey spend and how much did she save?
Step-by-step explanation:
spending 3 parts and saving 2 parts means that there are 3+2 = 5 parts in the whole.
the whole being $100.
one of the 5 parts is then 100/5 = $20.
so, she spent 3×20 = $60 and saved 2×20 = $40.
9. Marianna is making a piñata that has a ball-like shape. The piñata has a surface area of 60 square feet. Use
the formula for the surface area of a sphere (S = 4m2) to find the radius of the piñata.
a
About 22.80 ft
C.
About 3.87 ft
D
la
b. About 4.78 ft
d.
About 2.19 ft
-2 6-2
1
Answer:
D. 2.19
Step-by-step explanation:
ok so the formula for the surface area of a sphere is 4[tex]\pi[/tex][tex]r^2[/tex]
We see that 4[tex]\pi[/tex][tex]r^2[/tex]=60.
To find the radius we must isolate r on one side of the equations.
[tex]r^2[/tex]=60/4[tex]\pi[/tex]
[tex]r^2[/tex] = 4.77464829276
r = [tex]\sqrt{4.77464829276}[/tex]
That is approximately equal to 2.19
What are the domain and range of g(x)= √x-3?
A. D: [3, ∞) and R: [0, ∞)
B. D: [–3, ∞) and R: [0, ∞)
C. D: (–3, ∞) and R: (–∞, 0)
D. D: (3, ∞) and R: (–∞, 0)
Answer:
I guess, A is the wanted answer, but
A and D together are the really correct answer.
Step-by-step explanation:
if I understand this correctly, then
g(x) = sqrt(x - 3)
the domain of a function is the definition of all valid x (input) values.
the range of a function is the definition of all valid y (result) values.
well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).
so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.
I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.
BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.
because (-x)² = (x)² = x².
so, I would have to say that the really correct answer is
A + D, because the range contains both, the positive and the negative numbers.
The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms. About 21,000 cubic feet of road salt is used during a typical snow storm.
a. What is the total volume of the storage shed?
b. How many snow storms can the town expect to handle before the storage shed needs to be refilled with additional road salt?
Answer:
a. 40000pi ft^3
b. 5 times
Step-by-step explanation:
a. the volume of a cylinder is pi * h * r^2
r = 20ft, h = 100ft
so V = pi * 100 * 20^2 = 40,000pi or around 125663.7 ft^3
b. to find the number of times, divide the volume by the amount of salt needed per storm then round down:
40000pi/21000 = 5.98 so 5 times. notes: depending on the teacher you might just round to the nearest integer
Help me answer this question, please
PLS HELP ASAP!… WILL MARK BRAINLIEST
Which of the following are exterior angles? Check all that apply.
The exterior angles in the given triangle are angles 4 and 5.
What are the exterior angles?
The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.
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Translate the sentence into an inequality.
Four times the sum of a number and 17 is at least −26.
The sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26
Translating sentences into inequalityFrom the question, we are to translate the given sentence into an equality.
The given sentence is
Four times the sum of a number and 17 is at least −26
Let the unknown number be x
Then,
The sum of a number and 17 will be
x + 17
Then,
Four times the sum of a number and 17 can be written as
4(x+17)
Now,
"At least -26" means it is greater than or equal to -26
Thus,
Four times the sum of a number and 17 is at least −26 becomes
4(x+17) ≥ -26
Hence, the sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26.
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At their last practice, the basketball team shot free throws for 17 minutes, ran for 12 minutes, and then passed the ball for 16 minutes.
For how many minutes was the team practicing? Explain how you got your answer.
Answer:
45 minutes
Step-by-step explanation:
If you're trying to find the total number of minutes, they practiced you'd have to add.
So, if they did free throws for 17 minutes
Ran for 12 minutes
And passed the ball for 16
You'd add those up
17+16+12 = 45
In conclusion they practiced for a total of 45 minutes.
Kylee is playing a game she has to receive more than 20 points average of five games to move onto the next level which inequality represents the situation is T represents the total number of points Kylee earned for five games choices are
T/5 < 20
T/5 <_ 20
T/5 >_ 20
T/5 > 20
The inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Kylee is playing a game she has to receive more than 20 points on average of five games to move onto the next level.
T is representing the total number of points Kylee earned for five games
The average is 20.
T/5 is also representing the average points of five games.
She has to receive more than 20 points on average in five games:
T/5 > 20
Thus, the inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.
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Susan, Enrique and Martin are going for a meal.
Susan pays £26, Enrique pays £20 and Martin pays £18.
What fraction of the meal did each friend pay for?
Answer:
13/32 Susan
5/16 Enrique
9/32 Martin
Step-by-step explanation:
26+20+18=64
26/64=13/32
20/64=5/16
18/64=9/32
SOMEONE PLS HELP ME. ASAP PLSSS
The formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²
From the question, we are to determine the formula that could be used to find area of the figure shaded green
From the formula for calculating area of a square
A = s²
Where A is area
and s is the side length
Then, the area of the bigger square will be
A = 9²
NOTE: Side length of the bigger square is 9m
Then,
For the smaller square, which is not shaded green
A = 4²
NOTE: Side length of the smaller square is 4m
∴ Area of the figure shaded green = 9² - 4²
Hence, the formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²
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Question 2 Write the following paragraph proof as a two-column proof. Given: AB = CD and BC = DE Prove: AC = CE A B C D E We're given that AB = CD. By the addition property of equality, we add BC to both sides of the equation to get AB + BC = CD + BC. Since we're also given that BC = DE, we use the substitution property of equality to replace BC with DE on the right side of the equation. So, AB+ BC = CD + DE. Next, by segment addition, we get that AB + BC is equal to AC and that CD + DE is equal to CE. Finally, we use the substitution property of equality on the equation AB + BC = CD + DE to replace AB + BC with AC and CD + DE with CE to get that AC = CE. Type the correct answer in the box. BIUX² X₂ 14pt === Statements Reasons B.
Answer: See below
Step-by-step explanation:
Given:
AB = CD and BC = DE
To prove:
AC = CE
Statements Reasons
AB = CD GivenAB + CB = CD + BC Addition property of equalityAB + BC = CD + DE Given: BC = DEAC = CE By segment addition: AB + BC = AC and CD + DE = CETherefore, AC = CE has been proved
x²-3x+1=0
O A. 3±√15
OB. 3+√5
3± √5
o c. 2121224
OD. 5±10
3
Answer:
X=3+-√5/3
Step-by-step explanation:
x=-b+-√b^2-4ac/2
=3+-√(-3)^2-4(1)(1)/2
ABC DEF. The area of ABC is given. Find the area of DEF
Answer: B
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the scale factor.
Scale factor = image/preimage = 48/12 = 4.So, the ratio of the areas is 16, and thus the area of DEF is (16)(90)=1440
The right pengtagonal prism has a height of of 14 units.
A pentagonal prism has a perpendicular distance of 14 units between the bases. An apothem has a length of 4 units.
The volume of the prism is 840 cubic units. What is the perimeter of the base?
12 units
15 units
21 units
30 units
2 units
3 units
4 units
The perimeter of the base of the right pentagonal prism is 30 units
How to determine the perimeter of the base?The given parameters are:
Volume = 840 cubic unitsHeight, h = 14 unitsApothem, a = 4 unitsThe volume of a right pentagonal prism is:
V = 0.5Pah
Where P represents the perimeter of the base.
So, we have:
0.5 * P * 14 * 4 = 840
Divide both sides by 0.5 * 14 * 4
P = 30
Hence, the perimeter of the base is 30 units
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please help asap
6
9
18
Answer:
18
Step-by-step explanation:
The value of n = 1 , 2 , 3. Find the first 3 term and add them.
3*1 + 3*2 + 3*3 = 3 + 6 + 9
= 18