Answer:
Q1: D
Q2: D
Step-by-step explanation:
Question No 1:
The given sequence is:
-2, 0, 3, 7, ...
We can easily determine that this is not an arithmetic sequence because the common difference between terms is not same.
i.e.
0-(-2) = 0+2 = 2
3-0 = 3
7-3 = 4
As the common difference is not same so the sequqnce is not an arithmetic sequence.
Question no 2:
Given sequence is:
28, 18, 8, -2, ..
We can see that the common difference is -10 i.e 18-28 = -10
And it is same for all numbers.
The standard formula for arithmetic sequence is:
[tex]a_n=a+(n-1)d\\Here\\a = 28\\d=-10\\So,\\a_n=28+(-10)(n-1)\\a_n=28-10n+10\\a_n=38-10n[/tex]
Now for the 52nd term:
[tex]a_{52} = 38-10(52)\\= 38-520\\=-482[/tex] ..
Expected future value $125,000 3% of 2 years
Answer:
$132,612.50
Step-by-step explanation:
We will use the present value - future value formula. WHich is:
[tex]FV=PV(1+r)^t[/tex]
Where
FV is the future value (amount)
PV is the present value (amount)
r is the rate of interest (per year)
t is the number of years
In the problem given, the present amount (PV) is 125,000. The rate of interest (r) is 3%, or 0.03. And the time frame is 2 years, or t = 2.
Plugging these info in the equation, we can get the future value as shown:
[tex]FV=PV(1+r)^t\\FV=125,000(1+0.03)^2\\FV=125,000(1.03)^2\\FV=132,612.5[/tex]
This is the future vallue of $125,000 3% in 2 years.
Which of the following is not a service offered by public health programs?
Answer:
The answer is B) Medical Research
Step-by-step explanation:
Medical research is something typically done by private companies.
Answer: B. Medical research.
Step-by-step explanation: Public Health Programs: the types of public health programs that address STIs are: Prevention education, testing and counseling, and diagnosis and treatment.
:)
the sum number of boys and 15 girls
Answer:
b + 15
Step-by-step explanation:
Let:
"boys" = b
"girls" = g = 15
Note that: "sum" = addition.
Combine:
b + 15 is your numerical expression of your question.
~
Answer:
1 to 15
Step-by-step explanation:
1 boy/ 15 girls
A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. Which statement is true about the box plots? The interquartile range of the trail mix data is greater than the range of the cracker data. The value 70 is an outlier in the trail mix data. The upper quartile of the trail mix data is equal to the maximum value of the cracker data. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
Answer:
its D
Step-by-step explanation:
Answer:
D, The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
You are trying to decide what to wear today. You take out 2 shirts, 2 pairs of pants, and 4 pairs of shoes that all
coordinate.
How many different outfits can be made with a shirt, a pair of pants, and a pair of shoes?
Answer:
16
Step-by-step explanation:
You can choose
1 pair of shoes in 2 different ways1 pair of pants in 2 different ways1 pair of shoes in 4 different waysIn total there are
[tex]2\cdot 2\cdot 4=16[/tex]
different outfits.
Another way to solve this problem is simply count all outfits:
Shirts [tex]Sh_1, \ Sh_2[/tex]
Pants [tex]P_1,\ P_2[/tex]
Shoes [tex]S_1, \ S_2,\ S_3,\ S_4[/tex]
All outfits
[tex]Sh_1P_1S_1, \\ Sh_1P_1S_2, \\ Sh_1P_1S_3, \\ Sh_1P_1S_4, \\ Sh_1P_2S_1, \\ Sh_1P_2S_2, \\ Sh_1P_2S_3, \\ Sh_1P_2S_4, \\ Sh_2P_1S_1, \\ Sh_2P_1S_2, \\ Sh_2P_1S_3, \\ Sh_2P_1S_4, \\ Sh_2P_2S_1, \\ Sh_2P_2S_2, \\ Sh_2P_2S_3, \\ Sh_2P_2S_4[/tex]
using the quadradic formula to solve x^2=5-x, what are the values of x
Answer:
x1 = 2.79129, x2 = 1.79129
Step-by-step explanation:
x^2-5-x
x^2-5+x=0
x^2+x-5=0
-1+-square root od=f 1^2 - 4x1x(-5) / 2x1 = -1+- square root of 21 (add numbers together) / 2
then solve the formula with a plus sign instead of +- then and solve the formula with a - this time and you should get x1 = 2.79129, x2 = 1.79129, or -1 +square root of 21 (add numbers together) / 2 and -1 - square root of 21 (add numbers together) / 2
For this case we must solve the following equation:
[tex]x ^ 2 = 5-x[/tex]
By manipulating algebraically we have:
[tex]x ^ 2 + x-5 = 0[/tex]
The quadratic formula is given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 1\\b = 1\\c = -5[/tex]
Substituting we have:
[tex]x = \frac {-1 \pm \sqrt {1 ^ 2-4 (1) (- 5)}} {2 (1)}\\x = \frac {-1 \pm \sqrt {1 + 20}} {2}\\x = \frac {-1 \pm \sqrt {21}} {2}[/tex]
So, we have two roots:
[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2} = 1,7913\\x_ {2} = \frac {-1- \sqrt {21}} {2} = - 2.7913[/tex]
Answer:
[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2}\\x_ {2} = \frac {-1- \sqrt {21}} {2}[/tex]
A metal worker has several 1-kilogram bars of a metal alloy that contain 23% copper and several 1-kilogram bars that contain 79% copper. How many bars of each type of alloy should be melted and combined to create 48 kilograms of a 44% copper alloy?
Answer:
30 each of 23% bars and 18 each of 79% bars
Step-by-step explanation:
If x is the number of 1 kg 23% copper bars, and y is the number of 1 kg 79% copper bars, then:
x + y = 48
0.23x + 0.79y = 0.44(48)
Substituting and solving:
0.23x + 0.79(48-x) = 0.44(48)
0.23x + 37.92 - 0.79x = 21.12
16.8 = 0.56x
x = 30
y = 48 - x
y = 18
You need 30 each of 23% bars and 18 each of 79% bars.
Select the graph of the solution. Click until the correct graph appears.
Draw the graph please.
Answer:
The picture provided is the correct answer
Step-by-step explanation:
It needs to be greater than 4 or less than -4 in order for the absolute value to be greater than 7, so you're good.
Using the number 3,5,and 8 can you right nine proper fractions and nine improper fractions
Answer with step-by-step explanation:
We are to write nine proper fractions (where the numerator is smaller than the denominator) and nine improper fractions (where the denominator is bigger than the numerator) using the number 3, 5 and 8.
Proper fractions:
[tex] \frac { 3 } { 5 },\frac { 3 } { 8 } \frac { 5 } { 8 }, \frac { 3 }{ 5 . 8 },\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8} \imples\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}[/tex]
Improper fractions:
[tex]\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}[/tex]
Answer: Yes, you can write nine Proper Fractions and nine Improper Fractions using the numbers 3,5,and 8.
Step-by-step explanation:
You need to remember that a fraction is Proper when the numerator is less than the denominator and it is Improper fraction when the numerator is greater than the denominator.
Knowing this, you can write the following nine Proper Fractions and nine Improper Fractions, using the numbers 3,5 and 8:
Proper Fractions:
[tex]\frac{3}{5},\frac{3}{8},\frac{3}{5+8},\frac{3}{8*5},\frac{5}{8},\frac{5}{3+8},\frac{5}{8*3},\frac{5-3}{8},\frac{8}{5*3}\\\\\\\frac{3}{5},\frac{3}{8},\frac{3}{13},\frac{3}{40},\frac{5}{8},\frac{5}{11},\frac{5}{24},\frac{1}{4},\frac{8}{15}[/tex]
Improper Fractions:
[tex]\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{8+3}{8},\frac{5+8}{3},\frac{3*5}{8},\frac{8*5}{3},\frac{3+8}{5},\frac{8*3}{5}\\\\\\\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{11}{8},\frac{13}{3},\frac{15}{8},\frac{40}{3},\frac{11}{5},\frac{24}{5}[/tex]
What is the axis of symmetry for the function shown in the graph?
(*1,4)
(1,-4)
(1,4)
(-1,3)
Answer:
x = 1
Step-by-step explanation:
The axis of symmetry for a vertically opening parabola is a vertical line with equation
x = h
where h is the value of the x- coordinate the line passes through.
The axis of symmetry passes through the vertex 1, 4 ) with x- coordinate 1
Hence equation of axis of symmetry is x = 1
what is a line segment
Answer:
A line that does not have an end to it.
Step-by-step explanation:
For example a line is forever, but if you put dots on the end, it will not be forever.
Answer:
A line segment is like a straight line, but has two dots on the edge of each end. A line segment has a starting and stopping point, which can help people tell the difference between other lines.
A line segment usually looks like this:
\/ \/
•----------•
Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola? y = one fourthx2 + 3 y = −one fourthx2 + 3 y = −one fourthx2 − 3 y = one fourthx2 − 3
Answer:
y = - [tex]\frac{1}{4}[/tex] x² + 3
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and directrix.
Using the distance formula
[tex]\sqrt{(x-0)^2+(y-2)^2}[/tex] = | y - 4 |, that is
[tex]\sqrt{x^2+(y-2)^2}[/tex] = | y - 4 |
Squaring both sides
x² + (y - 2)² = (y - 4)² ← distribute parenthesis
x² + y² - 4y + 4 = y² - 8y + 16 ( subtract y² - 8y from both sides )
x² + 4y + 4 = 16 ( subtract x² + 4 from both sides )
4y = - x² + 12 ( divide both sides by 4 )
y = - [tex]\frac{1}{4}[/tex] x² + 3
Answer:
same as him took test right
Step-by-step explanation:
HELP ME PLEASE!!! Steps would be helpful :)
Answer:
i believe the answer is 9.5
Step-by-step explanation:
cos60 = c / 19 = 9.5
Simplify:
a. (-18x2y)/(3x)
Answer:
Step-by-step explanation: Sorry no time gtg : / (if you really need it I'LL ANSWER TOMMOROW
Answer: The required simplified expression is -6xy.
Step-by-step explanation: We are given to simplify the following rational expression :
[tex]E=-\dfrac{18x^2y}{3x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property of exponents :
[tex]\dfrac{z^a}{z^b}=z^{a-b}.[/tex]
From expression (i), we get
[tex]E\\\\\\=-\dfrac{18x^2y}{3x}\\\\\\=-\dfrac{18}{3}x^{2-1}y\\\\=-6xy.[/tex]
Thus, the required simplified expression is -6xy.
Identify the radius and the center of a circle whose equation is (x - 5)2 + y2 = 81.
The radius of the circle is
The center of the circle is at (1
units.
Answer:
The center is (5,0) and r=9.
Step-by-step explanation:
The standard form of a circle is [tex](x-h)^2+(y-k)^2[/tex] where (h,k) is the center and r is the radius.
On comparing your equation of
[tex](x - 5)^2 + (y-0)^2 = 9^2[/tex], we should see that h=5,k=0, and r=9.
The center is (5,0) and r=9.
Answer:
The center is at (5,0) and the radius is 9
Step-by-step explanation:
(x - 5)^2 + y^2 = 81.
An equation for a circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r is the radius
Rewriting the equation
(x - 5)^2 + y^2 = 81.
(x - 5)^2 + (y-0)^2 = 9^2
The center is at (5,0) and the radius is 9
the graphs of 2x+3Y=5 and 3x+y=18 contain two sides of a triangle. a vertex of the triangle is at the intersection of the graphs. what are the coordinates of the intersection?
Answer:
(7, - 3 )
Step-by-step explanation:
Solve the 2 equations simultaneously to find intersection.
Given the equations of the sides
2x + 3y = 5 → (1)
3x + y = 18 → (2)
Multiplying (2) by - 3 and adding to (1) will eliminate the y- term
- 9x - 3y = - 54 → (3)
Add (1) and (3) term by term
(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives
- 7x = - 49 ( divide both sides by - 7 )
x = 7
Substitute x = 7 into (1) or (2) for corresponding value of y
Substituting in (2)
21 + y = 18 ( subtract 21 from both sides )
y = - 3
Point of intersection = (7, - 3 )
Final Answer:
The coordinates of the intersection of the two lines are (x, y) = (7, -3).
Explanation:
To find the coordinates of the intersection of the two lines represented by the equations 2x + 3y = 5 and 3x + y = 18, we can solve this system of linear equations. Here's how to proceed step-by-step:
Step 1: Label the equations.
Let's call the first equation (1) and the second equation (2) for easy reference.
(1) 2x + 3y = 5
(2) 3x + y = 18
Step 2: Solve one of the equations for one of the variables.
Let's solve equation (2) for y:
y = 18 - 3x
Step 3: Substitute the expression for y in equation (1).
Now we substitute y in equation (1) with the expression we got from equation (2):
2x + 3(18 - 3x) = 5
Simplify the equation:
2x + 54 - 9x = 5
Combine like terms:
-7x + 54 = 5
Step 4: Simplify the equation for x.
Now we isolate x:
-7x = 5 - 54
-7x = -49
Divide both sides by -7 to find x:
x = -49 / -7
x = 7
Step 5: Substitute the value of x back into the equation for y.
We already have the expression for y from step 2 which was y = 18 - 3x. Now we substitute x = 7 into this expression to get y:
y = 18 - 3(7)
y = 18 - 21
y = -3
Step 6: State the coordinates of the intersection.
The coordinates of the intersection of the two lines are (x, y) = (7, -3).
Therefore, the vertex of the triangle at the intersection of the two graphs is at the point (7, -3).
What is 12x - 4y = -8 written in slope-intercept form?
y = 3x+2
y= 3x-2
y = 12x-8
y=-12X-8
Hey there!
Isolate the y variable by subtracting 12x in both sides:
-4y = -12x - 8
To solve for y divide -4 in both sides
y = 3x + 2
Our answer would be y = 3x + 2
Answer:
y = 3x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 12x - 4y = - 8 into this form
Subtract 12x from both sides
- 4y = - 12x - 8 ( divide all terms by - 4 )
y = 3x + 2 ← in slope- intercept form
Find the circumference given the area = 50.3 m². Use 3.14 for π as necessary.
The circumference of a circle with an area of 50.3 m² is 25.12 m.
Further Explanation Area Area is a measure of how much space is occupied by a given shape.Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by widthArea of a triangle = 1/2 x base x heightArea of a circle = πr². where r is the radius of a circle,Area of a square = S², Where s is the side of the square.etc.Perimeter Perimeter is defined as the distance along a two dimension shape. Perimeter of different shapes is given by different formulasFor example;
The perimeter of a rectangle = 2(length+width)The perimeter of a triangle = a+b+c; where a, b and c are the sides of the triangle. etc.The Circumference of a circle = 2πr , where r is the radius of the circleIn this case;
The Area of a circle = 50.3 m²
π = 3.14
But; Area of a circle = πr²
Therefore;
3.14r²= 50.3 m²
r² = 50.3/3.14
=16.019
r = √16.019
= 4.0023
≈ 4.00
But;
Circumference of a circle is given by 2πr
Thus;
Circumference = 2 × 3.14 × 4.00
= 25.12 m
Keywords; Perimeter, Area, Area of a circle, Circumference of a circle
Learn more about:Perimeter:https://brainly.com/question/1322653Area: https://brainly.com/question/1322653Area of a circle: https://brainly.com/question/9404782Circumference of a circle: https://brainly.com/question/9461882Level: Middle school
Subject; Mathematics
Topic: Area and Perimeter
Sub-topic: Area and circumference of a circle
Find the distance between the points (9,6) and (-4,7)
Answer:
[tex]\large\boxed{\sqrt{170}}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (9, 6) and (-4, 7). Substitute:
[tex]d=\sqrt{(-4-9)^2+(7-6)^2}=\sqrt{(-13)^2+1^2}=\sqrt{169+1}=\sqrt{170}[/tex]
The distance between the points (9,6) and (-4,7) can be found using the distance formula. By inputting the given coordinates into the formula, we find that the distance is √170 units.
Explanation:The question is asking us to find the distance between two given points, (9,6) and (-4,7). In mathematics, this is commonly done using the distance formula: √[(x₂-x₁)² + (y₂-y₁)²]. Here, coordinates (x₁,y₁) are (9,6) and (x₂,y₂) are (-4,7).
Substituting these values into our formula, we have: Distance = √[(-4-9)² + (7-6)²] = √[(-13)² + 1²] = √[169 + 1] = √170.
Therefore, the distance between the points (9,6) and (-4,7) is √170 units.
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Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = -3x+4
Step-by-step explanation:
Slope intercept form of a line is given by y = mx + b
Where
m is the slope
b is the y intercept.
To find m, we need to take any arbitrary 2 points and see how many units up/down and how many units right/left we need to go from one to another. Basically change in y by change in x.
Let's take 2 arbitrary points: (0,4) & (2,-2)
So we need to go -6 units from y = 4 to y = -2. We need to go 2 units from x = 0 to x = 2.
Hence slope is change in y by change in x, which is -6/2 = -3
b is the y-interceept, the place where it cuts the y axis. Looking at the graph, it is at y = 4
Now we can write the equation as :
y = -3x+4
Which sequence of transformation carries ABCD onto EFGH
Answer:
C. Reflection across the x-axis followed by the reflection across the y-axis.
Answer:
C
Step-by-step explanation:
Which is the most appropriate answer for this problem? Jeremy bought a sandwich for $5.98, a drink for $2.99, and an apple for $1.49. How much change will Jeremy get if he gives the cashier $20? A. exactly $9.54 B. exactly $10.46 C. about $9 D. about $10
W I L L
M A R K
B R A I N L I E S T
Answer:
A. exactly $9.54
Step-by-step explanation:
First add up how much he bought
Sandwich 5.98
drink 2.99
apple 1.49
---------
10.46
Then subtract this from 20
20.00
-10.46
--------------
9. 54
When you get money back, you get exact change.
If “u” varies directly with “v,” and u = 6 when v = -7, what’s is “u” when v = 4?
U=__
In a scenario where 'u' varies directly with 'v', the constant of variation, k is found by: k=u/v. Here, k becomes 6/-7. If we want to know the value for 'u' when v=4, we use the calculated k in our formula, resulting in u=4*(6/-7) which equals -24/7.
Explanation:The question is about the direct variation between two quantities 'u' and 'v'. If 'u' varies directly with 'v', it means that multiplying or dividing one quantity will have the same effect on the other. We use the mathematical formula for direct variation to find the values: 'u' = kv, where k is the constant of variation.
So, we first find 'k' when u = 6 and v = -7. From our formula, k = u/v = 6/-7.
When we know the k, we can find u' when v = 4. Using the formula, 'u' = kv = 4 * (6/-7) = -24/7.
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The ratio of the lengths of corresponding parts in two similar solids is 21.
What is the ratio of their surface areas?
А. 2:1
В. 8:1
D. 4:1
D. 6:1
Answer:
Option D. 4:1
Step-by-step explanation:
we know that
If two solids are similar, then the ratio of the lengths of corresponding parts is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared
In this problem
The scale factor is equal to [tex]\frac{2}{1}[/tex] (ratio of corresponding lengths)
therefore
The ratio of their surface areas is equal to
[tex](\frac{2}{1})^{2}=\frac{4}{1}[/tex]
Pleassssssse help me with number 3
Answer:
could it be letter H? please lmk
Please someone help me
a salesman who makes a comission of 18.14% on each sale, makes a comission of $152.39 on a particular sale. What is the amount of the sale?
Answer:
$840.08
Step-by-step explanation:
18.14% is the same as 0.1814. If we put the value of the sale as x that means that 0.1814x=152.39. Dividing both sides by 0.1814 you get x is approx. $840.08.
Answer: [tex]\$840.08[/tex]
Step-by-step explanation:
You need to analize the information provided:
- The comission on each sale made by the salesman is 18.14%.
- On a particular sale the salesman makes a comission of $152.39.
Then, the amount of the sale represents the 100%
Let be "x" the amount of that particular sale. You can use this procedure to calculate it:
[tex]x=\frac{(\$152.39)(100\%)}{18.14\%}\\\\x=\$840.08[/tex]
if twice a number is less than the number, the number must be a) negative b) even c) 0.5 d) a square
Answer:
a) negative
Step-by-step explanation:
When you multiply a given negative number by a positive number, the result becomes smaller than the original.
For instance let [tex]-100[/tex] be the original number.
Multiply by 2.
The result is -200
We know [tex]-200\:<\:-100[/tex]
The correct answer is A.
Answer: a) negative
Step-by-step explanation:
-100x2=-200
-200 is negative.
Simplify
(4x² – 2x + 8) - (x² + 3x - 2)
Answer:
3x² – 5x + 10
Step-by-step explanation:
(4x² – 2x + 8) - (x² + 3x - 2) =
Drop the first set of parentheses because it is unnecessary.
= 4x² – 2x + 8 - (x² + 3x - 2)
To get rid of the second set of parentheses, change every sign inside.
= 4x² – 2x + 8 - x² - 3x + 2
Now, combine like terms.
= 3x² – 5x + 10
Answer:
3x^2 -5x +10
Step-by-step explanation:
(4x² – 2x + 8) - (x² + 3x - 2)
Distribute the negative sign
(4x² – 2x + 8) - x² - 3x + 2
I like to line them up vertically
4x² – 2x + 8
-x² - 3x + 2
---------------------
3x^2 -5x +10
What is the solution to the equation g^(x-2)=27
Answer:
First problem: Solving for g.
[tex]g=27^{\frac{1}{x-2}}[/tex]
Second problem: Solving for x.
[tex]x=\log_g(27)+2[/tex]
Third problem: Assuming g is 9 while solving for x.
[tex]x=3.5[/tex]
Step-by-step explanation:
First problem: Solving for g.
[tex]g^{x-2}=27[/tex]
Raise both sides by 1/(x-2).
[tex](g^{x-2})^{\frac{1}{x-2}}=27^{\frac{1}{x-2}}[/tex]
[tex]g^{1}=27^{\frac{1}{x-2}}[/tex]
[tex]g=27^{\frac{1}{x-2}}[/tex]
Second problem: Solving for x.
[tex]g^{x-2}=27[/tex]
x is in the exponent so we have to convert to logarithm form since we desire to solve for it:
[tex]\log_g(27)=x-2[/tex]
Add 2 on both sides:
[tex]\log_g(27)+2=x[/tex]
[tex]x=\log_g(27)+2[/tex]
Third problem: Assuming g is 9 while solving for x.
[tex]9^{x-2}=27[/tex]
I'm going to solve this in a different way than I did above but you could solve it exactly the way I did for x when 9 was g.
I'm going to write both 9 and 27 as 3 to some power.
9=3^2 while 27=3^3.
[tex](3^2)^{x-2}=3^3[/tex]
[tex]3^{2x-4}=3^3[/tex]
Since both bases are the same on both sides, we need the exponents to be the same:
[tex]2x-4=3[/tex]
Add 4 on both sides:
[tex]2x=7[/tex]
Divide both sides by 2:
[tex]x=\frac{7}{2}[/tex]
[tex]x=3.5[/tex]
Now earlier for x in terms of g we got:
[tex]x=\log_g(27)+2[/tex]
I we input 9 in place of g and put it into our calculator or use some tricks without the calculator to compute we should get 3.5 as the answer like we did above when g was 9.
[tex]x=\log_9(27)+2[/tex]
[tex]x=\frac{3}{2}+2[/tex]
[tex]x=1.5+2[/tex]
[tex]x=3.5[/tex]