Answers
x = 4
Explanation:
For the right hand side:
log base 9 of 8 + log base 9 of (x-2) = log base 9 (8*(x-2))
= log base 9 of (8x-16)
For the left hand side:
2*log base 9 of x = log base 9 of x^2
Now, equating the two sides and solving for x:
log base 9 of (8x-16) = log base 9 of x^2
This means that:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x-4)^2 = 0
Therefore:
x = 4
Hope this helps :)
Related Questions
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Line segment CT contains the point C(−2, 5) and a midpoint at A(1, −3). What is the location of endpoint T? T(4, −11) T(3, −8) T(5, −1) T(−0.5, 1)
Answers
To find CT, you need to find the distance of CA then applies 2 times of the distance to the point C
Xca= Xa-Xc= 1- (-2)= 3
Yca= Ya- Yc= -3 -5= -8
Xt= Xc + 2* Xca= -2 + 2*3= 4
Yt= Yc + 2* Yca= 5 + 2*-8= -11
T(Xt, Yt)= T(4, -11)
The coordinate for point T would be (4, -11)
$394.63781 Round to the nearest dollar
Answers
Here is your answer:
The proper answer to your question is "$390.00
Here is how:
394.63781=$390
Your answer is $390!
If you need anymore help feel free to ask me!
Hope this helps!
.6 is higher than .4 so the dollar amount would go up one.
hope this helps
You are reducing a map of dimensions 2 ft by 3 ft to fit on a piece of paper 8 in. by 10 in. what are the dimensions of the largest possible map that can fit on the page?
Answers
Answer:
The dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
Step-by-step explanation:
You are reducing a map of dimensions 2 ft by 3 ft
Lets change them to inches.
1 foot = 12 inches
So, 2 feet = [tex]2\times12=24[/tex] inches
3 feet = [tex]3\times12=36[/tex] inches
So, dimensions are : 24 inches x 36 inches
[tex]\frac{24}{36}=\frac{2}{3}[/tex]
Since 10 inch will be the longer side, we can find the shorter side by :
[tex]\frac{x}{10}=\frac{2}{3}[/tex]
[tex]3x=20[/tex]
[tex]x=\frac{20}{3}[/tex]
or [tex]x=6\frac{2}{3}[/tex] inches
So, the dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
The dimension of the largest possible map which can fit on the paper can be used is [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
Map dimension = 2 feets by 3 feets Area of paper = 8in by 10inConverting the map dimension to inches :
1 feet = 12 inches2 feets = 2 × 12 = 24 inches
3 feets = 3 × 12 = 36 inches
Scale factor = 24 / 36 = 2/3
Longer side of the paper = 10 inches
Using the scale to obtain the length of the shorter side :
2/3 = x/10
Cross multiply
3x = 2 × 10
3x = 20
x = (20 ÷ 3)
x = 6 2/3 inches
The dimension of the largest possible map would be [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
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Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy. What is Daniel’s annual premium? Use the table.
$611.20
$728.00
$1268.80
$1652.80
Answers
Male, 35-39, 10-year
The figure in this category shows $4.55, telling us that the annual premium per $1000 of coverage is $4.55.
Daniel bought $160,000 worth of life insurance, so that is 160 one-thousands.
So, we multiply the annual premium per $1000 ($4.55 as identified) by 160 to give us our answer:
4.55×160= $728
Therefore, the answer is $728
Answer:
the answer is b 728
Step-by-step explanation:
Evaluate the expression Arcsec(sqrt 2). Do not use your calculator to answer this question. Do not express answer in decimals.
Answers
You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.
sqrt(2) = 1/x
x*sqrt(2) = 1
x = 1/sqrt(2)
Let's multiply both numerator and denominator by sqrt(2), so
x = sqrt(2)/2
And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:
45 * (2*pi)/360 = 90*pi/360 = pi/4
So your answer is pi/4 radians.
Energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called_____energy resources
Answers
Answer: Non- renewable
The energy is derived from various sources on the basis of origin the energy can be derived from the renewable and non-renewable sources of energy. Renewable sources are those, which are abundantly available in nature and they can be replenished after a single use. For example, sunlight energy, wind energy, tidal energy, geothermal energy. But non- renewable sources are those which are available in limited amount hence, are expensive and cannot be replenished once they are used. For example fossil fuels such as coal, petroleum and natural gas. These are the resources which takes millions of years for their formation. Their genesis takes place inside the earth's geosphere under high heat and pressure conditions and by the action of the soil microbes acting upon the dead remains of plants and animals.
On the basis of the above description, energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called non- renewable resources energy resources
Given: line segment AB is 10 inches long. Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 1 2 . A) 1 2 inches B) 5 inches C) 10 inches D) 20 inches
Answers
[tex]|A'B'| = 5 \: units[/tex]
EXPLANATION
The formula for calculating the scale factor is
[tex]k = \frac{image \: length}{object \: length} [/tex]
Or
[tex]k = \frac{ |A'B'| }{ |AB|} [/tex]
Where k is the scale factor.
We were given
[tex] |A'B'|=10[/tex]
This is the image length.
We substitute the scale factor and the image length in to the formula to get,
[tex] \frac{1}{2} = \frac{ |A'B'| }{ 10} [/tex]
Multiply both sides by 10 to get,
[tex] \frac{1}{2}\times 10= |A'B'|[/tex]
[tex]|A'B'| = 5 \: units[/tex]
Answer:
Option (b) is correct.
The length of A'B' is 5 inches.
Step-by-step explanation:
Given : line segment AB is 10 inches long. AB is dilated to form A'B' with a scale factor of [tex]\frac{1}{2}[/tex]
we have to find the length of A'B'
Dilation of a figure is the increase or decrease in the length of the figure by a fixed scaling factor. if scaling factor is greater than 1 , then figure size increases, and if scaling factor is less than 1 , then figure size decreases.
Here, scaling factor is [tex]\frac{1}{2}[/tex] which less than 1 , so line segment A'B' decreases.
New image = scaling factor × original image
that is A'B' = [tex]\frac{1}{2}\times 10=5[/tex]
Thus, the length of A'B' is 5 inches.
Option (b) is correct.
The tables below show two functions. For each set of data:
a) Determine whether the data represents a linear function, exponential function or neither and explain why.
x f(x)
-2 18
-1 22
0 26
1 30
2 34
x g(x)
-2 2
-1 4
0 8
1 16
2 32
Rubric:
Points Concept Addressed
/2 Correctly determines whether each table represents linear, exponential or neither
/2 Correctly explains their answer.
Answers
(between the first two points): m = (y₂ - y₁)/(x₂ - x₁) = (22-18)/(-1--2) = 4/(-1+2) = 4/1 = 4. The rate of change between any two points is the same:
(between the last two points): m = (34-30)/(2-1) = 4/1 = 4.
The second table, representing g(x), is exponential. The data points are multiplied by the same constant between successive points. 2*2 = 4; 4*2= 8; 8*2 = 16, etc.
Use the clues to find the mystery number.
It is greater than 37,493.
It is less than 37,503.
It is an even number.
The value of the mystery number rounded to the nearest ten is less than the mystery number.
The value of the mystery number rounded to the nearest thousand is greater than the mystery number.
The mystery number is
Answers
FAST HELP!! 30 POINTS!!!
what type of solutions do the methods for solving systems of equations find and how does this relate to setting the equations equal to each other
Answers
Final answer:
Explanation of solutions for systems of equations and how setting equations equal to each other helps find solutions.
Explanation:
Solutions for systems of equations can be classified as unique, no solution, or infinitely many solutions. The method of setting equations equal to each other typically helps find the intersection points where the equations are simultaneously true, representing the solution to the system.
True or false All equilateral triangles are isosceles
Answers
Answer:
TRUE
Step-by-step explanation:
When all sides are the same length, at least one pair of sides is the same length.
Answer:
the answer is true
Step-by-step explanation:
Consuela and her three friends order 2 pizzas. Consuela cuts each pizza into 8 equal slices. She saves 2 slices of pizza for her older brother, Then she and her friends share the rest of the pizza, each eating the same number of slices. What fraction of the 2 pizzas is left over?
Answers
x--------------> the number of slices eating by Consuela and her three friends
we know that
[total slices]=8*2=16 slices
[slices of pizza for her older brother]=2
x=16-2=14 slides
Consuela and her friends share the rest of the pizza, each eating the same number of slices---------> 14/4= 3.5 slides of pizza each (this part is not necessary, but it is shown in a didactic way)
the question is
What fraction of the 2 pizzas is left over?
[slices of pizza for her older brother]/[total slices]=2/16=1/8
the answer is (1/8)
Final answer:
To find the fraction of the 2 pizzas left over, calculate the total slices consumed and subtract from the total. Consuela and her friends ate 14 slices out of 16, leaving 2/16 or 1/8 of the 2 pizzas left over.
Explanation:
Consuela and her friends ordered 2 pizzas, each cut into 8 slices. Consuela saved 2 slices, then shared the rest equally. Each person ate 2 slices.
To find out what fraction of the 2 pizzas is left over, calculate the total slices consumed and subtract from the total.
Each pizza had 8 slices, so 2 pizzas have 16 slices in total.Consuela saved 2 slices, so she and her friends ate 14 slices in total.Thus, the fraction of the 2 pizzas left over is 2/16 or 1/8.Why are epidemics and pandemics a relatively recent phenomenon in human history?
Answers
If you were offered a job would you choose the one with the pay increase according to an arithmetic sequence formula or a geometric sequence formula? Justify your response.
Answers
Final answer:
For maximizing earning potential over time, a geometric sequence salary increase is typically more beneficial due to exponential growth, while an arithmetic sequence offers steady, predictable increases that may appeal to those who value consistency.
Explanation:
If offered a job with a salary increase tied to either an arithmetic sequence or a geometric sequence, the preferable option typically depends on the long-term financial goals and growth potential you are looking for. An arithmetic sequence will give you steady, predictable increases. However, a geometric sequence formula will often result in larger increases over time, especially if the ratio is 2 or more. Due to the exponential nature of a geometric sequence, your salary could grow significantly faster than with an arithmetic sequence. For example, if you start with a salary of $50,000, and the arithmetic sequence increase is $1,000 each year, after five years you would be earning $55,000. On the other hand, for a geometric sequence with a modest ratio of 1.05 (5% increase each year), you would start at the same $50,000 but after five years be earning approximately $63,814.
Considering this, if your primary goal is to maximize earning potential over time, the geometric sequence would be the more appealing option. However, if you value consistency and predictability in pay increases, or if the progression starts very low, an arithmetic sequence might be more in line with your personal financial planning.
helppppppppppppppppppppppppppppppp
Answers
((2 ^ (1/2)) * (2 ^ (3/4))) ^ 2
We use for this case the properties of lso exponents:
((2 ^ (1/2)) * (2 ^ (3/4))) ^ 2
((2 ^ (2/2)) * (2 ^ (6/4)))
((2 ^ (1)) * (2 ^ (3/2)))
((2 ^ (1 + 3/2))
((2 ^ (5/2))
answer:
((2 ^ (5/2))
option 2
can you please help me thank you you will be given brainley
Answers
ΔZVY ≅ ΔWVY . . . . . . corresponds to the 2nd selection
.help thanks please :)
Answers
Simplify the ratio 30 ml: 45 ml
Answers
In the ratio 30 ml :45 ml the GCF is 15
making the simplified ratio to be 2 ml:3 ml
How to tell if a scatter plot is positive or negative or no ttend?
Answers
The speed of an object in space is shown in the graph.
What is the slope of the line?
10
15
20
25
Answers
= 15
the slope of the line = 15
the answer is B.
Answer:
Option B is correct
15
Step-by-step explanation:
Formula for slope is given by:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]
As per the statement:
Form the graph:
Consider two points:
(0.2, 3) and (0.4, 6)
then;
[tex]\text{Slope} = \frac{6-3}{0.4-0.2}[/tex]
⇒[tex]\text{Slope} = \frac{3}{0.2}[/tex]
⇒[tex]\text{Slope}= 15[/tex]
Therefore, the slope of the line is, 15
Rowan raised $640 In a charity walk last year.this year he raised 15% more than he raised last year. How much money did Rowan raise this year?
Answers
1.15 × $640 = $736
the area of a trapezoid is 72.8 square feet. the length of one of its bases is 7.4 feet and the length of its other base is 10.8 feet. what is the height of the trapezoid?
Answers
What is the length of the base of a right triangle with an area of 20 m² and a height of 4 m? A.5 m B.10 m C.80 m D.160 m
Answers
l or b = length or base
w or h = width or height
a = area
b x h = a
b x (4) = 20
4b = 20
4b/.4 = 20/4
b = 20/4
b = 5
A. 5m is your answer
hope this helps
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
y------> the length of the rectangle
x-----> the width of the rectangle
we know that
perimeter of the rectangle=2*[x+y]
Since the barn is used as one of the sides (let's say y) we can subtract y
we don't need fencing for this side
That makes the perimeter 2x + y
Since we have 300 feet of fencing
we set these equal:
2x + y = 300-------> y=(300-2x)------> equation 1
area of the rectangle=x*y
substitute the equation 1 in the area formula
Area=[(300-2x)]*x-----> Area=(-2x²)+300x
This is a quadratic equation
Since the leading coefficient is negative (-2) we know it opens downward
We are looking for the x-coordinate of the highest point called the vertex
using a graph tool
see the attached figure
the vertex is the point (75,11250)
that means for x=75 (width of the rectangle)
the area is 11250 ft²
the answer is
the maximum area that can be enclosed by the fencing is 11250 ft²
Answer:
The Answer is 11250 ft~
Step-by-step explanation:
I did the test and got it correct
PLZZ HELP ME I WILL GIVE YOU THE BRAINLESS PERSON I GIVE YOU 12PTS
Please describe in detail using your vocabulary terms, directions, and the number of steps to explain how the pre-image became the image in this picture. Type your answer in a word document and upload it to this dropbox for me to grade. (5 pts)
Answers
A reflection across an axis is when the image is flipped over that axis that is mentioned. This is happening two times starting with the original. First it crosses the Y axis which will be flipping it to the left. The X values in the original ordered pair would all be the opposite of the original.
Then it is reflected across the X axis which would be flipping it down. This time the y values end of the ordered pair would all be the opposite from the previous figure.
The pre-image becomes the image in a picture through transformations such as translation, rotation, reflection, or dilation.
Explanation:The pre-image is the original figure before any transformations. The image is the new figure after a transformation has been applied to the pre-image. In this picture, the pre-image became the image through translation, rotation, reflection, or dilation.
Translation: The pre-image is moved in a specific direction without changing its shape or size.Rotation: The pre-image is turned around a fixed point by a certain angle.Reflection: The pre-image is flipped across a line to create the image.Dilation: The pre-image is either enlarged or reduced in size.By applying one or more of these transformations to the pre-image, it can become the image in the picture.
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What’s the answer to this problem???
Answers
8y = -5x+16
divide everything by 8 to get just y
y = -5/8x+2
the slope = -5/8
The temperature, T , of a given mass of gas varies inversely with its volume, V . The temperature of a certain gas with volume of 105 cm 3 is 30º C. What will be the temperature of the gas when it is compressed to a volume of 84 cm 3? 18.8º C 48º C 24º C 37.5º C
Answers
if the temperature T of a given mass of gas varies inversely with its volume V
then
T=k/V
Step 1
Find the value of k
for T=30º C and V=105 cm³
we have
T=k/V--------> k=T*V--------> k=30*105=3150 °C*cm³
therefore
for V=84 cm³
T=3150/84=37.5 °C
the answer is 37.5 °C
Final answer:
The temperature of a gas can be calculated using the formula for inverse variation, which is T1*V1 = T2*V2. By substituting the given values into the formula, we can find that the temperature of the gas when it is compressed to a volume of 84 cm^3 is 37.5ºC.
Explanation:
To solve this problem, we can use the formula for inverse variation:
T1*V1 = T2*V2
Given that T1 = 30ºC, V1 = 105 cm^3, and V2 = 84 cm^3, we can solve for T2:
T2 = (T1*V1)/V2 = (30*105)/84 = 37.5ºC
Therefore, the temperature of the gas when it is compressed to a volume of 84 cm^3 will be 37.5ºC.
El Generico public high school got a new flagpole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janitor set up a 5-foot stick next to the flagpole and compared shadows. The 5-foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.
Use rules of similar polygons to figure out how tall the flagpole is!
Answers
Length of Stick = 5 feet
Shadow of Stick = 8 feet
Shadow of flagpole = 32 feet
Length of flagpole = x = ?
Using rule of similar polygon we can write,
[tex] \frac{5}{8}= \frac{x}{32} \\ \\ \frac{5}{8}*32=x \\ \\ x=20 [/tex]
Therefore, the length of flagpole will be 20 feet.
Factor this expression completely and then place the factors in the proper location on the grid. Note:
Place factors alphabetically in the grid! mn - 4 m - 5 n + 20
Answers
[tex]mn-4m-5n+20[/tex]
[tex](mn-4m)-(5n+20)[/tex]
Notice that our the terms in our first parenthesis have a common factor [tex]m[/tex], and the terms in our second one have the common factor [tex]5[/tex]. Lets factor those out:
[tex]m(n-4)-5(n-4)[/tex]
Now we have a common factor [tex](n-4)[/tex] in both terms, so we can factor those out as well:
[tex](n-4)(m-5)[/tex]
We can conclude that the completely factored expression ordered alphabetically is [tex](m-5)(n-4)[/tex].
Monica wants to measure the dimensions of her rectangular lawn. If the longer side of the lawn is (x + 3) feet and the diagonal length is (x + 4) feet, which function can be used to find the shorter side of her lawn?
a.] [tex]s(x)= \sqrt{2x+7} [/tex]
b.] [tex]s(x)= \sqrt{2 x^{2} +14x+25} [/tex]
c.] [tex]s(x)= \sqrt{x^{2} +7x+12} [/tex]
d.] [tex]s(x)= {x^{2} +7x+12} [/tex]
Answers
let
y--------------- > short side
applying the Pythagorean theorem
(x+4)²=y²+(x+3)²
y²=(x+4)²-(x+3)²-------> x²+8x+16-x²-6x-9=2x+7
y=√(2x+7)
which yields s^2=2x+7, hence a) is the correct answer.