solve log(x+1)= -x^2 +10
Answers
[tex]\boxed{x \approx 3.064}[/tex]
Step-by-step explanation:There is no general property that we can use to rewrite:
[tex]log_{a}(u\pm v)[/tex]
Then, we'll solve this problem graphically. Let's say that we have two functions:
[tex]f(x)=log(x+1) \\ \\ g(x)=-x^2 +10[/tex]
[tex]f(x)[/tex] is a logarithmic function translated one unit to the left of the pattern logarithmic function [tex]log(x)[/tex]. On the other hand, [tex]g(x)[/tex] is a parabola that opens downward and whose vertex is [tex](0,10)[/tex]. So:
[tex]f(x)=g(x)[/tex]
implies that we'll find the value (or values) where these two functions intersect. When graphing them, we get that this x-value is:
[tex]\boxed{x=3.064}[/tex]
Then, for [tex]x=3.064[/tex]:
[tex]f(x)=log(x+1) \\ \\ f(3.064)=log(3.064+1) \\ \\ f(3.064)=log(4.064) \\ \\ Using \ calculator: \\ \\ f(3.064) \approx 0.6 \\ \\ \\ g(x)= -x^2 +10 \\ \\ g(3.064)= -(3.064)^2 +10 \\ \\ g(3.064)=-9.388+10 \\ \\ g(3.064) \approx -0.6[/tex]
Related Questions
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answers
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
I will assume which we determining which set of points is a solution
(2,2) is in all the sets, so we ignore it
Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0)
Again looking at the graph (2,0) is not a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0) x
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Given the coordinates of the vertices of a pre-image figure, describe how to find the coordinates of the image vertices if the figure is translated vertically.
Answers
Step-by-step answer:
Step 1:
find out the amount and direction of the vertical translation.
+3 means translating 3 units up, and -6 means translating 6 units down.
Step 2:
to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).
For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).
Repeat for the rest of the vertices.
Step 3:
Check by graphing both image and preimage to see if the shapes are identical. If not, look for a mistake in the translation process.
To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.
To find the coordinates of the image vertices when a figure is translated vertically,
you need to follow these simple steps:
Identify the translation value: Determine the distance by which the figure is to be translated vertically. Let's say the translation value is 'k' units.Add the translation value to the y-coordinates: For each vertex of the pre-image figure, a translation involves modifying only the y-coordinate.If the original vertices of the pre-image are (x, y), then the new vertices (image) will be (x, y + k).Suppose you have a triangle with vertices A(2,3), B(5,4), and C(1,7). If the figure is translated vertically by 3 units up, the coordinates of the image vertices will be:A'(2, 6), B'(5, 7), and C'(1, 10).
This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.
True or False
1/5^-2=25
Answers
That is true for sure!!!
The statement 1/5⁻² =25 is true.
Explanation:The statement 1/5⁻² = 25 is true.
To simplify the expression, we can rewrite 1/5⁻² as 5²/1. When we have a negative exponent in the denominator, it moves to the numerator and becomes positive.
Therefore, 1/5⁻² is equivalent to 5²/1.
Since 5² equals 25, we can conclude that 1/5⁻² is indeed equal to 25.
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The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?
Answers
Answer:
=13.73 ft²
Step-by-step explanation:
The diameter of the largest possible circle that can be cut out of a square is equal to the length of the side of the square.
Therefore the diameter of the circle cut from a square of side 8ft =8ft
r=4ft
Area of the remaining board= Area of square- area of circle
=side²-πr²
=8²-π×4²
=64-16π
=13.73 ft²
y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b
Find the value of a and the value of b
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = (x - h)² + k (h, k) are the coordinates of the vertex
Given y = x² + 7x - 5
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
y = x² + 2( [tex]\frac{7}{2}[/tex] )x +[tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] - 5
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] - [tex]\frac{20}{4}[/tex]
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{69}{4}[/tex]
Hence
a = [tex]\frac{7}{2}[/tex] and b = - [tex]\frac{69}{4}[/tex]
A scientist cools some water at a constant rate. the graph and table show how the temperature of the water changes with time.
CAN SOMEONE ANSWER THIS. ?
Answers
Answer:
C
Step-by-step explanation:
The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).
From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).
A little thinking would get us to plug the numbers in C first.
[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]
Works!!
Now, second number:
[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]
Works!!
Hence, C is the correct answer.
Answer:
[tex]a(n)=46-(n-1) \times 4[/tex]
Step-by-step explanation:
It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.
To find the correct equation, we could find the slope first with the following formula and the two given points
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]
Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.
Let's prove it for [tex]n=6[/tex]
[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]
As the table shows.
Therefore, choice C is correct.
What is the value of this limit?
Answers
Answer:
a
Step-by-step explanation:
At a competition with 6 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answers
Answer: 120 different ways. It is a permutation.
Step-by-step explanation:
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
The number of ways to award the medals in 120 different ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
Given
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
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28lbs is what % of 58
Answers
Answer:
48.28
Step-by-step explanation:
2800:58 = 48.28
In the problem to the left, if Tim mows 9 lawns this week, by how much will he have exceeded his goal?
Answers
Answer:
Step-by-step explanation:
a - number of lawn that Tim needs to mow
310 < 120 + 30a
190 < 30a
6.333 < a
a > 6.333
Tim needs to mow at least 7 lawns to earn more than $310
Solve for y. Py + qy = -4y + 8
Answers
[tex]\bf Py+qy=-4y+8\implies Py+qy+4y=8\implies \stackrel{\textit{common factor}}{y(P+q+4)}=8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{8}{P+q+4}~\hfill[/tex]
Answer:
y = 8 / (P + q + 4)
Step-by-step explanation:
Group ALL y terms on the left side: Py + qy + 4y = 8.
Factor y out of the left side: y(P + q + 4) = 8
Divide both sides by (P + q + 4): y = 8 / (P + q + 4)
I WILL GIVE BRAINLIEST What is the value of x?
Answers
Answer:
A 30
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70-70 +x
30 =x
An angle measuring pi/8 radians is equal to which of the angle measures given
below? Round your answer to 2 decimal places after each conversion step.
Check all that apply.
A. 22.50
B. 39.25
c. 22°5
D. 22°30
Answers
Answer:
A. 22.5° AND D. 22°30’
Step-by-step explanation:
First of all, it's the correct answer on ap*x
To convert π/8 to degrees, replace π with 180°.
π/8 = 180°/8 = 22.5° (A)
Convert 22.5° to degrees minutes seconds
22.5° = 22°30’ (D)
To convert an angle from radians to degrees, multiply by 180/π. The angle measuring π/8 radians is equal to 22.5°.
Explanation:To convert an angle from radians to degrees, we use the conversion factor 180/π. So, an angle of π/8 radians is equal to:
π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°Therefore, the angle measuring π/8 radians is equal to 22.5°.
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jillian calculates that see will take 95 minutes to run 7 miles. she runs the distance in 80 minutes. what is jillians percent error.
Answers
Answer:
15.79%
Step-by-step explanation:
do 95-80 which is 15
then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%
Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.
Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:
Calculate the absolute difference between estimated time and actual time: |95 minutes - 80 minutes| = 15 minutes.Divide the difference by the estimated time: 15 minutes / 95 minutes = 0.1579.Multiply by 100 to convert to a percentage: 0.1579 times 100 = 15.79%.Therefore, Jillian's percent error in her estimation is 15.79%.
What is the quotient of 3,968 ÷ 32?
Answers
Answer:
124
Step-by-step explanation:
Answer:
124
Step-by-step explanation:
32 goes into 39 one time, 39-32= 7
bring down the 6
32 goes into 76 two times, 76 - 64= 12
bring down the 8
32 goes into 128 four times, 128 - 128 = 0
So 3968/32 = 124
What is the surface of a sphere with a radius of 9 units
Answers
Answer: 324π units²
Step-by-step explanation:
The formula for the surface area of a sphere is: A=4πr²
Now we just plug in 9 for r:
A = 4π(9)²
A = 4π*81
A = 324π
Answer:
1018 units^2
Step-by-step explanation:
The surface area of a sphere is given by A = 4pi(r)^2, where r is the radius.
Here, A = 4(3.14159)(9 units)^2 = 1018 units^2, to the nearest integer.
What is the value of x?
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.
Answers
Answer:
54 is x
Step-by-step explanation:
Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52
2=1x-52. Subtracted 2x on both sides
54=1x. Added 52 on both sides
54=x. Since 1 times x is x
Which is the simplified form of the expression?
Answers
Answer:
Step-by-step explanation:
a
Answer:
4/x14y8 - Last Option
6. A quadrilateral has three acute angles, each measuring 75°. Find the fourth angle
Answers
Answer:
Heya mate here's the answer
let the 4th angle be x
so 75°+ 75°+75° +x= 360°
=> x= 360 - 225
=> x = 135°
therefore the 4th angle= 135°
hope this helps
Step-by-step explanation:
a number multiplied by 1/3 is 1/18
Answers
Answer:
1/6
Step-by-step explanation:
[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]
[tex]x=3/18\\x=1/6[/tex]
if it takes one hour to paint 85ft then how long will it take to paint 410.2ft?
Answers
Find the equation of the line that passes through the pair of points.
(1,5), (1, - 3)
Answers
Answer:
x = 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 5) and (1, -3).
Substitute:
[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]
Dividing by zero is not possible.
The slope does not exist.
Conclusion: this is a vertical line with the equation x = a
From the points
(1, 5) → x = 1, y = 5
(1, -3) → x = 1, y = -3
we have the equation x = 1.
How do you find the same y intercept
Answers
Answer:
D
Step-by-step explanation:
The y-intercept is the number or constant at the end of the equation.
D sets both of their y-intercepts to -6, so it's correct.
=============================================
Explanation:
Plug x = 0 into f(x)
f(x) = 4x + 1
f(0) = 4(0) + 1
f(0) = 1
The y intercept of f(x) is 1
----------
Now plug x = 0 into g(x)
g(x) = 3^x - 2
g(0) = 3^0 - 2
g(0) = -1
The y intercept of g(x) is -1
----------
Note how the y intercepts are 2 units apart.
Each of the answer choices are in the form of f(x) + M and g(x) + N. The goal is to see which M and N values will be 2 units apart. In this case, that would be choice C where M = -1 and N = 1
We see that f(x) - 1 = f(0) - 1 = 1 - 1 = 0 and g(x) + 1 = g(0) + 1 = -1 + 1 = 0
Therefore, f(x) - 1 and g(x) + 1 have the same y intercept of 0.
A flute is on sale for 20% off. Including the discount and 8% tax, the sales price is $216.
Answers
Answer:
Before Tax: $240
After Tax: $259.20
Step-by-step explanation:
If we are trying to find the original price then here:
216/1.08 = 200
This took away the tax now we need to take away the discount:
200 x 1.2 = 240
Before Tax: $240
After Tax: $259.20
The original after tax price of the flute is $259.20.
Determining the original after tax price of the flute.
The first step is to remove tax from the sales price. In order to remove tax, divide the sales price by (1 + tax): $216 / 1.08 = $200
The second step is to remove the effect of discount. In order to do this multiply 200 by (1 + discount): 200 x 1.2 = $240.
The after tax original price = $240 x 1.08 = $259.20
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A family membership at a tennis club cost a flat fee of $150, plus $25 per person. If n stands for the number of people, then the membership cost is modeled by ?
Answers
Answer:
total cost = 150 + 25n
Step-by-step explanation:
total cost = flat fee + cost per person* number of people
total cost = 150 + 25n
Colette took a speed reading class, and afterward she was able to read a 368-page book in 46 minutes. At what rate did Colette read?
Answers
Answer:
8 pages/ minute
Step-by-step explanation:
To find the rate, we take the pages and divide by the minutes
368 pages / 46 minutes
8 pages/ minute
(-5+1)(((3+6)*2-2)(5)-1) evaluate.
Answers
Answer:
-316
Step-by-step explanation:
Each operation shown in bold is done on the next line.
(-5+1)(((3+6)*2-2)(5)-1) =
= (-4)((9*2-2)(5)-1)
= (-4)((18-2)(5)-1)
= (-4)(16(5)-1)
= (-4)(80-1)
= (-4)(79)
= -316
pls can someone help me with this, and please explain why?
Answers
Hope this helps!
Answer:
C
Step-by-step explanation:
recall the property [tex]a^{1/b}= \sqrt[b]{a}[/tex]
if we apply this to this case,
[tex]x^{1/4} = \sqrt[4]{x}[/tex]
- [tex]x^{1/4} = - \sqrt[4]{x}[/tex]
Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
8,000 + 24x
8,000 − 24x
8,000 + 2x
8,000 − 2x
Answers
Answer:
8,000-24x
Step-by-step explanation:
there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x
Answer:
B. [tex]8,000-24x[/tex].
Step-by-step explanation:
We have been given that Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period.
Since the value of car depreciates at a constant rate each month, so the value of car depreciated in 2 years would be [tex]2\times 12=24[/tex].
There are 24 months in two years, so value of car depreciated in 2 years would be 24x.
The initial value of car is $8,000, so value of car after 2 years would be [tex]8,000-24x[/tex].
Therefore, option B is the correct choice.
Which expression is equivalent to -2 1/4÷ (-2/3)
Answers
Answer:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]
Step-by-step explanation:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]