[tex]\dfrac{5+2\sqrt3}{7+4\sqrt3}=\dfrac{5+2\sqrt3}{7+4\sqrt3}\cdot\dfrac{7-4\sqrt3}{7-4\sqrt3}\\\\\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{(5+2\sqrt3)(7-4\sqrt3)}{7^2-(4\sqrt3)^2}\\\\\text{use distributive property}\\\\=\dfrac{(5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3)}{49-4^2(\sqrt3)^2}\\\\=\dfrac{35-20\sqrt3+14\sqrt3-8(3)}{49-16(3)}=\dfrac{35-6\sqrt3-24}{49-48}=\dfrac{11-6\sqrt3}{1}\\\\=11-6\sqrt3\\\\11-6\sqrt3=a+b\sqrt3\to\boxed{a=11\ and\ b=-6}[/tex]
Jason will use a 1/3 gallon pitcher to fill an empty 3/4 water jug. How much water is needed to completely fill the water jug?
Answer:
Pitcher 1/3 gallon = 4/12 gallon
Jug 3/4 = 9/12 gallon
So, it will take 2 pitchers plus 1/12 of a gallon to fill the jug.
Step-by-step explanation:
Find the distance between points P(7, 4) and Q(1, 2) to the nearest tenth.
What is the midpoint of
PQ?
The distance between points PQ is [tex]2\sqrt{10}[/tex].
The midpoint of PQ is [tex]( 4, 3)[/tex].
Given that,
The points are P(7, 4) and Q(1, 2).
We have to determine,
The distance between the points and,
The midpoint of PQ.
According to the question,
To calculate the distance between two points by using distance formula;
[tex]Distance \ formula = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }[/tex]
Where, [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]
Substitute the values in the formula;
[tex]PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\\\\PQ = \sqrt{(1-7)^2 + (2-4)^2 }\\\\PQ = \sqrt{(-6)^2 + (-2)^2 }\\\\PQ = \sqrt{36+ 4 }\\\\PQ = \sqrt{40}\\\\PQ = 2\sqrt{10}[/tex]
And, The midpoint of PQ calculated by using formula;
[tex]Midpoint \ of \ PQ = (\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} )[/tex]
Where, [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]
Substitute the values in the formula;
[tex]Midpoint \ of \ PQ = (\dfrac{7+1}{2} ,\dfrac{4+2}{2} )\\\\Midpoint \ of \ PQ = (\dfrac{8}{2} ,\dfrac{6}{2} )\\\\Midpoint \ of \ PQ = (4,3)[/tex]
Hence, The distance between points PQ is [tex]2\sqrt{10}[/tex].
The midpoint of PQ is [tex]( 4, 3)[/tex].
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Double Delicious Bakery sells a dozen double chocolate dounts for $7.80
A) What is the price per donut? B) What is the cost of 1 and 1/2 dozen donuts?
Answer:
A) each donut costs $0.65
B) the price for 1 and 1/2 dozen of donuts (18 donuts) is $11.70
Step-by-step explanation:
For a you have to divide $7.80 by 12 (since its a dozen) and thats how you get $0.65
For b you have to multiply the price of each donut ($0.65) by the 1 and 1/2 dozen (18 donuts) and thats how you get $11.70
A) The price per donut is approximately $0.65, and B) the cost of 1 and 1/2 dozen donuts is $11.70.
Certainly, let's break it down:
A) To find the price per donut, divide the total cost by the number of donuts in a dozen:
Price per donut = $7.80 / 12 ≈ $0.65
B) Calculate the cost of 1 dozen:
Cost of 1 dozen = $7.80
Now, for [tex]\( \frac{1}{2} \)[/tex] dozen, multiply the price per donut by 6 (half of 12):
Cost of [tex]\( \frac{1}{2} \)[/tex] dozen = $0.65 × 6 = $3.90
Add the cost of [tex]\( \frac{1}{2} \)[/tex] dozen to the cost of 1 dozen:
Total cost for 1 and [tex]\( \frac{1}{2} \)[/tex] dozen = $7.80 + $3.90 = $11.70
In summary, A) the price per donut is approximately $0.65, and B) the cost of 1 and [tex]\( \frac{1}{2} \)[/tex] dozen donuts is $11.70.
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plz help me thank u math question
Which of the following expressions is equal to g(x)?
Answer:
D. log (x-2)
Step-by-step explanation:
We can see that in the graph of the function g(x), the graph is shifted toward the right.
We know that, to shift a graph to the right, we subtract that number of units inside the function.
For example if we are plotting a graph of F(x) and if we have to shift the function to the right by 2 units, we can write it as, [tex]F(x-2)[/tex].
Similarly, here the graph of log (x) is shifted 2 units to the right so we can write the function as,
[tex]log (x-2)[/tex] (we subtract inside the function).
Answer:
D. [tex]log(x-2)[/tex]
Step-by-step explanation:
We have been given function's [tex]f(x)=log(x)[/tex] graph and graph of function g(x). We are asked to choose the correct function formula for g(x).
We can see that our parent function f(x) is translated to right to get function g(x).
The rule for translating a function to right by k units is:
[tex]f(x)\rightarrow f(x-k)[/tex]
We can see that our parent function is shifted 2 units to right as our parent function crosses x-axis at x equals 1, while our new function crosses x-axis at x equals 3. So our new function g(x) will be:
[tex]g(x)=log(x-2)[/tex]
Therefore, the expression [tex]log(x-2)[/tex] is equal to g(x) and option D is the correct choice.
Last year, Mr. Jones made $30,000. His boss just informed him that he will be receiving at least an 11.2% raise for this year. How much will he make this year?
Answer:
$33 336
Step-by-step explanation:
Increase = 30 000 × 0.112
Increase = $3336
New salary = 30 000 + 3336
New salary = $33 336
The cost of toner cartridges is 19.50 more than the cost of an ink cartridge. Colleen ordered 11 ink and 4 toner cartridges and thw total cost 460.50. Write and solve a system of equations to fons the cost of each cartridge.
Answer:
Toner = $45.00; ink = $25.50
Step-by-step explanation:
Let T = the cost of a toner cartridge and I = the cost of an ink cartridge
We have two conditions:
(1) T = I + 19.50
(2) 4T + 11I = 460.50 Substitute (1) into (2)
4(I + 19.50) + 11I = 460.50 Remove parentheses
4I + 78.00 + 11I = 460.50 Combine like terms
15 I + 78.00 = 460.50 Subtract 78.00 from each side
15I = 382.50 Divide each side by 15
(3) I = 25.50
=====
Substitute (3) into (1)
T = 25.50 + 19.50
T = 45.00
=====
Check:
(1) 45.00 = 25.50 + 19.50
45.00 = 45.00
(2) 4×45.00 + 11×25.50 = 460.50
180.00 + 280.50 = 460.50
460.50 = 460.50
What is 36 divided by 1/4
Answer:
144
Step-by-step explanation:
36 ÷ 1/4
We will use copy dot flip
36 * 4
144
On monday,Cathy tead 1/6 if her book, and on tuesday, she read 2/6 of the book. How much has she read?
Answer:
Cathy has read 3/6 or 1/2 of her book.
Step-by-step explanation:
1/6+2/6=3/6 or 1/2
N/8 - 3 = -11 What does n equal?
Hey there!
Firstly, [tex]simplify[/tex] both sides of your equation[tex]\frac{1}{8}n+ (-3)[/tex] [tex]=-11[/tex][tex]\frac{1}{8}n -3[/tex][tex]=-11[/tex]Second, [tex]add[/tex] by the number [tex]3[/tex] on each of your sides[tex]\frac{1}{8}n - 3[/tex][tex]+3[/tex]Cancel: [tex]-3 +3[/tex] because it gives you the result of [tex]0[/tex]Keep: [tex]-11+3[/tex] because it has the number we need to solve for the answer[tex]-11 + 3 =[/tex] [tex]-8[/tex][tex]\frac{1}{8}n = -8[/tex]Third, [tex]multiply[/tex] by the number [tex]8[/tex] on each of your sides [tex]8(\frac{1}{8}n)[/tex] [tex]= 8(-8)[/tex]Cancel: [tex]8(\frac{1}{8})[/tex] because it doesn't give you what you're looking forKeep: [tex]8(-8) [/tex] because it gives you your answer[tex]8(-8)= -64[/tex]Answer↓[tex]\boxed{n = -64}[/tex]Good luck on your assignment and enjoy your day! ~[tex]LoveYourselfFirst:)[/tex]Which expression represents 3 less than four times a
Answer:
4a - 3
Step-by-step explanation:
"four times a" = 4 * a = 4a
"3 less than" = -3
Combine the terms: 4a - 3
~
HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
A) X = -5, Y = 1
B) X = -2, Y = 4
C) X = -5 , Y = 4
Step-by-step explanation:
The reflection over an x-axis means the values associated with the x remains same while y-axis variable change their sign.
The three co-ordinates of this figure are
A) X = -5, Y = -1
B) X = -2, Y = -4
C) X = -5 , Y = -4
Now going by the above rule to determine the co-ordinates when the image is reflected over x-axis, the new co-ordinates are:
A) X = -5, Y = 1
B) X = -2, Y = 4
C) X = -5 , Y = 4
Step-by-step explanation:
Please find the attachment.
We have been given an image on coordinate plane and we are asked to reflect our given image over the x-axis.
The rule for reflection for an image over x axis is: [tex](x,y)\rightarrow(x,-y)[/tex]. This means that after reflection about x axis, x coordinates remain same but y-coordinates are transformed into their opposite sign.
Let us give names to vertices of our pre-image. A(-5,-1), B(-5,-4) and C(-2,-4).
When we will reflect our pre-image (ABC) about x-axis, x coordinates will remain same, so x coordinates will remain negative.
Since y-coordinates will change into their opposite sign, so coordinates of y will be positive for our image as y-coordinates of pre-image are negative.
A A'
(-5,-1) (-5,1)
B B'
(-5,-4) (-5,4)
C C'
(-2,-4) (-2,4)
Therefore, coordinates of our image A'B'C' will be: A'(-5,1), B'(-5,4) and C'(-2,4).
Which of the following must be true?
A. BC
B. BC>ED
C. BC=ED
D. BC_<(more than or equal to) ED
Answer:
BC < ED ⇒ answer A
Step-by-step explanation:
* Lets revise some facts in the triangle
- If one side of a triangle is longer than another side, then the angle
opposite the longer side will be larger than the angle opposite the
shorter side
- If one angle in a triangle is larger than another angle in a triangle,
then the side opposite the larger angle will be longer than the side
opposite the smaller angle
* Lets solve the problem
- In the two triangles BCD and DEB
∵ CD = 8 and BE = 8
∴ CD = BE
∵ Side BD is a common side in the two triangles
- The third side in Δ BCD is BC and the third side in DEB is DE
∵ BC is the opposite side to the angle of measure 24°
∵ ED is the opposite side to the angle of measure 30°
∵ The measure 24° < the measure 30°
∴ The side opposite to the angle of measure 24° < the side opposite
to the angle of measure 30°
∵ The other two sides of the 2 triangles BCD and DEB are equal
∴ We can compare between the 3rd sides in the Δ BCD and Δ DEB
∴ BC < ED
write an expression for the product of 6 and Q
Answer: 6*Q= 6Q or 6*Q= y
Step-by-step explanation:
The product is the answer to a multiplication problem, therefore 6*Q will be the first part.
The second part will be the answer. Normally, this would be represented just by 6Q, but you can use another letter to represent it. We'll use y for an example.
6*Q= 6Q
or
6*Q= y
Step-by-step explanation:
ANSWER: 6*q
help guys............
Answer:
slope = 0
Step-by-step explanation:
To find the slope when you have 2 points, we use the formula
m = (y2-y1)/(x2-x1)
m = (-5--5)/(18--2)
= (-5+5)/(18+2)
= 0/20
The slope is zero
This a horizontal line, because the y values do not change
Which expression can represent 70% of x?
A. 3(x/4) -1/2 (x/10)
B. 3(x/4)- (x/10)
C. (X/2) + (x/10)
D. (X/2) + 1/2 (x/4
Pleas help
Answer:
Option A is correct
[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]
Step-by-step explanation:
Given that:
70% of x.
⇒[tex]\frac{70}{100} \times x[/tex]
⇒[tex]\frac{7x}{10}[/tex]
Option A:
[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]
⇒[tex]\frac{3x}{4}-\frac{x}{20}[/tex]
⇒[tex]\frac{60x-4x}{80}[/tex]
⇒[tex]\frac{56x}{80}[/tex]
Simplify:
⇒[tex]\frac{7x}{10}[/tex]
Option B:
[tex]3(\frac{x}{4})-(\frac{x}{10})[/tex]
⇒[tex]\frac{3x}{4}-\frac{x}{10}[/tex]
⇒[tex]\frac{30x-4x}{40}[/tex]
⇒[tex]\frac{26x}{40}[/tex]
Simplify:
⇒[tex]\frac{13x}{20}[/tex]
Option C:
[tex](\frac{x}{2})+(\frac{x}{10})[/tex]
⇒[tex]\frac{6x}{10}[/tex]
Simplify:
⇒[tex]\frac{3x}{5}[/tex]
Option D:
[tex](\frac{x}{2})+\frac{1}{2}(\frac{x}{4})[/tex]
⇒[tex]\frac{x}{2}+\frac{x}{8}[/tex]
⇒[tex]\frac{5x}{8}[/tex]
Therefore, only option which is equivalent to 70% of x is, Option A i.e [tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]
Answer:
a
Step-by-step explanation:
‼️ 30 POINTS ‼️
Which table best classifies the following numbers as rational and irrational?
Answer:
D
Step-by-step explanation:
Lets look at the numbers
sqrt(4) = 2 which is a rational number
sqrt(5) cannot be simplified, it is an irrational number
-6/5 a ratio of integers, which is the definition of a rational number, so it is a rational number
3.5 = 35/10 a ratio of integers, which is the definition of a rational number, so it is a rational number
.555555 = 5/9 a ratio of integers, which is the definition of a rational number, so it is a rational number
Rational numbers: sqrt(4), -6/5, 3.5 , .5555(repeating)
Irrational numbers: sqrt(5)
Answer: D
Step-by-step explanation:
A construction worker is building a wall. The wall is 17.5 yds long. He needs to place a stud every 15 inches. The first stud has already been placed at one end of the wall. How many additional studs are needed, if the last stud will be placed at the other end of the wall? First fill in the blanks on the left side using the ratios shown. Then write your answer.
The correct answers are:
Box-1: [tex]\frac{3\thinspace ft}{1\thinspace yd}[/tex]
Box-2: [tex]\frac{12\thinspace \thinspace in}{1\thinspace ft}[/tex]
Box-3: [tex]\frac{1\thinspace stud}{15\thinspace in}[/tex]
Box-4: 42 studs
Explanation:
Given:
Wall is 17.5 yds long.
In 1 yard, there are 3 feet.
Therefore,
[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}[/tex]
In Box-1, you should put [tex]\frac{3\thinspace ft}{1\thinspace yd}[/tex].
In 1 foot, there are 12 inches.
Therefore,
[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}[/tex]
In Box-2, you should put [tex]\frac{12\thinspace \thinspace in}{1\thinspace ft}[/tex].
He needs to place 1 stud every 15 inches.
Therefore,
[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in}[/tex]
In Box-3, you should put [tex]\frac{1\thinspace stud}{15\thinspace in}[/tex].
Now multiple all the numbers, you will get the number of studs.
[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in} = 42\thinspace studs[/tex]
In Box-4, write 42 studs.
-i
To calculate the number of additional studs needed, convert the length of the wall to inches and divide by the interval between each stud. Subtract 1 from the total number of intervals to find the number of additional studs needed.
To determine the number of additional studs needed, we need to calculate the number of intervals between studs. First, we need to convert the length of the wall to inches, which is 17.5 yds * 3 ft/yd * 12 in/ft = 630 inches. Next, we divide the length of the wall by the interval between each stud, 630 inches / 15 inches = 42 intervals. Since the first stud has already been placed, we subtract 1 from the total number of intervals to find the number of additional studs needed: 42 - 1 = 41 additional studs.
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how do you factor 24a + 12b - 30?
Answer:
6(4a+3b-5)
Step-by-step explanation:
They all share a common factor of 6 so we can factor out the six, 6(4a+3b-5)
Answer:
2a+b=5/2
Step-by-step explanation:
given the expression
24a + 12b - 30
Step one :
To solve this we need to look for a common factor
Here 6 is a common factor
So divide all through by 6
24a/6+12b/6-30/6
4a+2b-5
4a+2b=5
Step two :
We can still factor 2 out for the terms with variables
2(2a+b)=5
2a+b=5/2
PLEASE I NEED HELP FAST Ben used vector DE to translate triangle ABC. Ben made an error in his work. What is Ben’s error? If Ben had completed the translation properly, what would be the correct coordinates for each vertex (A’, B’, and C’) for the image?
Answer:
He translated them the wrong way.
It should of gone up 2 and right 2 not down 2 and left 2.
The correct coordinates would be (A' = 3,0) (B' = 3, -3) (C' = 2, -2)
Please mark brainliest would rly help.
Step-by-step explanation:
(0,-1)(5-2)what is the slope
The formula of a slope m:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (0, -1) and (5, -2). Substitute:
[tex]m=\dfrac{-2-(-1)}{5-0}=\dfrac{-2+1}{5}=-\dfrac{1}{5}[/tex]
Answer: The slope = -1/5Lucio is buying candy he buys 1.7 pounds of gummy bears which cost $1.88 per pound and 0.8 pounds of caramels which cost $2.72 per pound what was the total cost of candy
Lucio spent a total of $5.37 on candy by purchasing 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound, and then summing both costs.
Explanation:To calculate the total cost of candy that Lucio is buying, we compute the cost of each candy type separately and then add those costs together. He buys 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound.
For the gummy bears: 1.7 pounds × $1.88 per pound = $3.196
For the caramels: 0.8 pounds × $2.72 per pound = $2.176
To find the total cost, we add the cost of gummy bears and caramels. Therefore, the total cost is $3.196 + $2.176 = $5.372. After rounding to two decimal places, we conclude that Lucio spent a total of $5.37 on candy.
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Your food at a restaurant costs $35.00 and tax is 6% how much would be it together
I feel like this doesnt have the right information .....
Answer:
60 child tickets were sold
Step-by-step explanation:
Let no of children tickets sold that day be c and adult tickets be a
Then since total number of tickets sold is 148, we have
c+a = 148 ... i
Also given that admission fee is 6.00 for children and 9.70 for adults
So for c children tickets sold value= 6c and for adults it is 9.7a
total revenue = 6c+9.7a=1213.60 ... ii
We got two equations in two variables c and a
Let us solve this
a =148-c. substitute this in ii
6c+9.7(148-c) = 1213.60
Simplify the above to have
222 = 3.7c
Or c = 60
No of child tickets sold = 60
the wholesale price of a couch is $235. A store marks up the price by 169%. When the couch does not sell, the store offers a 20% discount. what was the retail price of the couch? what is the sale price of the couch?
Answer: 585.15
Step-by-step explanation:
Subtract 20 from 169
Once you do so you should get 149%
figure out what $235 + 149% is then you should get five hundred eighty five dollars and fifteen cents ($585.15)
you invest 2000 in a simple interest account. The balance after 8 years is 2720. What is the interest rate?
Answer:
4.5%
Step-by-step explanation:
Find interest rate by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
I = $720, P = $2000 and t = 8 years, so
I = P*i*t
i = I/P*t
i = 720 / 2000 * 8
i = 0.045 = 4.5% per year
The interest rate, calculated with the simple interest formula, for an investment of $2000 that grows to $2720 over 8 years is 4.5%.
Explanation:The subject is about determining the interest rate for an investment in a simple interest account. The formula for calculating simple interest is: Interest = Principal x Rate x Time (I = PRT). In this case, the principal (P) is $2000, the time (T) is 8 years, and the interest (I) earned is the difference between the final balance and the initial deposit, which is $2720 - $2000 = $720.
To find the rate (R), we rearrange the formula to: R = I / (P x T). Plugging in the numbers, we get: R = $720 / ($2000 x 8) = 0.045, or 4.5% when expressed as a percentage.
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Which of the following would be appropriate to measure in centimeters
Question:
what are your choices?
You are paid $13.70/hr. You work 40 hr/wk and your deductions are FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%). Your housing and fixed expenses are 30% of your realized income per month and you want to save 6 months’ worth in an emergency fund. How much do you need to save?
a) $3,277.17
b) $3,401.55
c) $3,013.95
d) $2,858.59
Answer:
To save 6 months' worth in a fund would be $2858.59.
Step-by-step explanation:
At a wage of $13.70 per hour for a 40 hour work week, your gross pay (not including any taxes or deductions) is $548 per week, or $2192 per month. Deductions and taxes are 7.65% + 11.55% + 8.35%, for a total of 27.55% that comes out of your gross pay. $2192 multiplied by 27.55%, or .2755, is $603.90, therefore, in order to find your realized income per month, you must subtract your gross pay by the amount of deductions and tax withholdings: $2192 - $603.90 = 1588.10. Another 30% of your realized income is for housing and fixed expenses, or $1588.10 multiplied by 30%, or 0.30, which comes to $476.43. If you want to save 6 months' of expenses in an emergency fund, simply take your monthly expenses, $476.43, and multiply by 6 = $2,858.59.
The correct answer is option d. $2,858.59
1. Monthly gross income should be calculated using the exact number of days in the month, which can vary. However, since we are given 4 weeks per month, we will continue with that assumption.
2. The tax rates are percentages, so we need to convert them to decimals for calculation:
Total tax rate = 0.0765 + 0.1155 + 0.0835 = 0.2755.
3. The realized income after taxes should be calculated as follows:
Realized income after taxes = [tex]\$2,192 \times (1 - 0.2755) = \$2,192 \times 0.7245 = \$1,588.53.[/tex]
4. The monthly housing and fixed expenses are correct at $476.56.
5. The emergency fund calculation is also correct:
Emergency fund = [tex]6 \times \$476.56 = \$2,859.36.[/tex]
Upon re-evaluation, the correct calculation for the emergency fund is $2,859.36, which should be rounded down to $2,858. However, the options provided suggest that the correct answer is $3,277.17. This indicates that there may be an error in the provided options or in the interpretation of the question.
Given the calculations above, none of the provided options match the calculated emergency fund. The closest option is d) $2,858.59.
In the geometric progression 1, 2, 4… what term is 512?
The next term is double the previous term, so that the [tex]n[/tex]-th term is given recursively by
[tex]\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}[/tex]
This rule tells us that
[tex]a_2=2a_1[/tex]
[tex]a_3=2a_2=2^2a_1[/tex]
[tex]a_4=2a_3=2^3a_1[/tex]
and so on, with the explicit rule
[tex]a_n=2^{n-1}a_1=2^{n-1}[/tex]
for [tex]n\ge1[/tex].
If 512 is the [tex]k[/tex]-th term in the sequence, then
[tex]512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10[/tex]
Final answer:
In the geometric progression 1, 2, 4, ..., the 9th term is 512, determined by the formula for the nth term of a geometric progression.
Explanation:
The question asks us to find the term in a geometric progression where the value is 512. A geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ratio. In the given geometric progression 1, 2, 4, ..., each term is obtained by multiplying the previous term by 2. To find which term is 512, we can use the formula for the nth term of a GP, which is a_n = a_1 × r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
Since a_1 is 1 and r is 2, we have: 512 = 1 × 2^(n-1). Simplifying this gives us 2^9 = 512, which means the 9th term of the sequence is 512. Therefore, 512 is the 9th term in the given geometrical progression.
Help please ASAP I got this wrong I wanna know why and what is the right answer give explanation please
Answer:
B. The total price depends on the number of crates
Step-by-step explanation:
We can immediately rule out C & A because the two factors in the graph are crates and total price. So both the number of crates and total price will be part of our answer, but pumpkins aren't shown on the graph at all.
This leaves us with B & D. Using common sense we know that the number of crates isn't going to change if the total cost changes but rather the total cost will change depending on how many crates you buy.
I hope that helps u understand & answers ur question! (If u have a question about anything I just said lmk and I'll be glad to tell u what I mean)
Good luck! :)
I don’t understand this I don’t need an explanation can someone just please help me please
Answer:
1
Step-by-step explanation:
You can only make one because once an angle is given, the only possibility is to connect the two sides. You can't change it to an obtuse triangle with that.
Everyone else will be a congruent to the first one triangle.
SAS stands for "side, angle, side" and means that we have two congruent triangles where we know two sides and the included angle are equal.