It's a arithmetic sequence
First term=a=3common difference=d=-1-3=-4Nth term rule:-
[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_n=3+(n-1)-4[/tex]
[tex]\\ \rm\Rrightarrow a_n=3-4n+4[/tex]
[tex]\\ \rm\Rrightarrow a_n=7-4n[/tex]
20th term
[tex]\\ \rm\Rrightarrow a_{20}=7-80=-73[/tex]
Can someone please please tell me what the general form for (x-6)^2+(y-3)^2=16 is. I would really appreciate the help!
Answer:
x² + y² - 12x - 6y + 29 = 0
Step-by-step explanation:
Simplifying the equation using (a + b)² = a² + 2ab + b²:
(x - 6)² + (y - 3)² = 16
⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16
⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
General form of a circle = x² + y² + Cx + Dy + E = 0
Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.
Subtract 16 both sides:
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
Reorganizing the equation in general form:
x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x - 6y + 20 + 9 = 0
⇒ x² + y² - 12x - 6y + 29 = 0
Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.
2/5 g+3h -6 when g=10 h=6
let's evaluate this expression
[tex]\pmb{\displaystyle\frac{2}{5}g+3h-6 }[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+3(6)-6}[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+18-6}[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+12}[/tex]
Multiply:
[tex]\pmb{\displaystyle\frac{2}{5} *\frac{10}{1} =\frac{20}{5} =4}[/tex]
Final Step:-
[tex]\pmb{4+12}[/tex]
[tex]\pmb{16}[/tex]
======================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
karen and mary are saving money. karen has 150 and disposits an additional $25 a week. mary has $200 and deposits an additional $10 a week. what is the minimum number of weeks it will take for karen to have more saving then mary
Answer:
4 weeks
Step-by-step explanation:
original base amount 150 200
1st week deposit 175 210
2nd week deposit 200 220
3rd week deposit 225 230
4th week deposit 250 240
ASAPPPPP!!!!!!!!!!!!!!
Answer:
297 [tex]cm^{2}[/tex]
Step-by-step explanation:
area of triangle x 4 + area of rectangle
[tex]\frac{1}{2}[/tex] x 12 x 9 x 4+ 9 x 9
|-9| + |12| = ?
Question options:
A -3
B 3
C -21
D 21
Answer:
21
Step-by-step explanation:
-9=9
9+12=21
Please help thank you
Answer:
Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.
Step-by-step explanation:
So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:
m = 28.8 g
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec
Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
B. 15 sec
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y = 14t^2[/tex]
[tex]y = 130t + 1200[/tex]
They will be side by side when:
[tex]14t^2 = 130t + 1200[/tex]
[tex]14t^2 - 130t - 1200 = 0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta = (-130)^2 - 4(14)(-1200) = 84100[/tex]
[tex]x_1 = \frac{130 + \sqrt{84100}}{28} = 15[/tex]
[tex]x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71[/tex]
Time is a non-negative measure, hence option B is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
Answer:
B: 15 sec
Step-by-step explanation:
I took the algebra exam
When Sally decided to run for class treasurer, she predicted how many votes she would get. After the election, Sally found out she had received 150 votes. She had predicted she would get 20% fewer votes than that. How many votes did Sally predict she would get?
Answer:
3000
because you need to dived it
Line of best fit has a y intercept of 6 and goes through the point(4,22) what is the slope of the line
Answer:
0.7
Step-by-step explanation:
you have a slope of 6 and it goes through 4,22 so slope = rise over run so you would divide them
!!!!!!!!!!!!!!!!!!!!!!!!!HELP!!!!!!!!!!!!!!! Find the slope of the line.
Answer:
3/1
Step-by-step explanation:
Make sure you know a few concepts first:
The point where the line crosses the y-axis (or vertical axis) is called the y-intercept.Slope is commonly taught using [tex]\frac{rise}{run}[/tex] as I will teach it here.First, find the y-intercept of the line. This line crosses the y-axis as (0,0), so that is the y -intercept.Find another point on the line, preferably where it crosses a whole-number coordinate (just for simplicity… you can use any point on the line). We will use the point (1,3). Counting in your head, count vertically from (0,0) until you are horizontal to the point (1,3) we chose earlier. Put the distance it took to reach that point on the top (numerator) of the fraction. Because it takes 3 counts to be horizontal, your fraction should look like [tex]\frac{3}{run}[/tex].Count horizontally until you reach the point (1,3). Put the number of units on the bottom (denominator) of the fraction. The number was 1 unit, so your finished fraction which is the slope is [tex]\frac{3}{1}[/tex].Alternatively
Use the formula for slope from two points… [tex]\frac{x_{1} -y_1}{x_2-x_1}[/tex]Find two points on the line. We will use (0,0) and (1,3). Designate one point as 1 and the other as 2. We will choose (0,0) to be 1 and (1,3) to be 2.Plug in the points following the “key” you created: Let x₁ be the x coordinate from ordered pair 1, let y₁ be the y coordinate point from ordered pair 1, etc. Following this pattern, you should be set up like this: [tex]\frac{3-0}{1-0}[/tex]Subtract to get [tex]\frac{3}{1}[/tex] as your slope.A babysitter charges an hourly rate. The equation y = 12x represents the relationship between hours of babysitting, x, and total pay, y, in
dollars.
What is the salary per hour for the babysitter?
salary : $12 per hour
Find the value of c that makes the trinomial a perfect square. .
x² – 24x7c
Answer:
144
Step-by-step explanation:
The equation to find c is:
[tex](\frac{b}{2} )^{2}[/tex]
So put -24 into b:
[tex](\frac{-24}{2} )^{2}[/tex]
Which simplifies to:
144
So if you want to test this:
x^2 - 24x + 144
is
(x-12)^2
Walnuts are priced
according to the chart
below.
POUNDS (LBS)
COST (S)
3
$7.77
5
$ 12.95
8
$20.72
What is price per pound for the
walnuts?
A.
$2.59
B. $3.86
C. $2.17
D. $3.07
Answer:
A. $2.59
Step-by-step explanation:
If you divide the costs by the pounds:
3/7.77 = 2.59
12.95/5 = 2.59
20.72/8 = 2.59
Therefore, the answers is $2.59
Hope this helps :)
Mary has $311.75 to convert into yen. the currency exchange she is using charges a surcharge of 6% when converting currency. about how many more yen will mary receive if she makes her trade on the day with the most favorable exchange rate than if she makes her trade on the day with the least favorable exchange rate? a. ¥1,125 b. ¥1,513 c. ¥1,609 d. ¥1,706
Mary will receive 1512.4931 more Yen if she makes her trade on the day with the most favorable exchange rate than that of the least favorable exchange rate.
What is the exchange rate?It is the factor by which currency conversion of two countries is done.
The most Favorable day is Friday because the exchange rate on Friday is the highest.
So, Mary will receive on Friday= 311.75 x 92.7120 x 94/100
Mary will receive on Friday(a)=27168.788 Yen
The least Favorable day is Wednesday because the exchange rate on Wednesday is the least.
So, Mary will receive on Wednesday= 311.75 x 87.5507 x 94/100
So, Mary will receive on Wednesday(b)= 25,656.2949 Yen
Difference between (a) and (b) = 1512.4931 Yen
Hence, Mary will receive 1512.4931 more Yen if she makes her trade on the day with the most favorable exchange rate than if she makes her trade on the day with the least favorable exchange rate.
To get more about the exchange rate visit:
https://brainly.com/question/1366402
Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x 7) = 3. Log Subscript 2 Baseline left-bracket x (x 7) right-bracket = 3. X (x 7) = 2 cubed. X squared 7 x minus 8 = 0. (x 8) (x 1) = 0. X = negative 8, 1 x = negative 8 x = 1 x = 1 and x = negative 8 x = 1 and x = 8.
The value which shows the true solution to the given logarithmic equation is 1.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The given logarithmic equation is,
[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]
Use the addition property of log in the above expression.
[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]
Solve the quadratic equation we get,
[tex](x+8)(x-1)=0[/tex]
x = -8, 1
Here, the logarithmic function is defined only for positive real numbers as its input.
Thus, the value which shows the true solution to the logarithmic equation solved above is 1.
Learn more about the domain and range of the function:
brainly.com/question/2264373
Answer:X=1
Step-by-step explanation:b on edge
How many milliliters could a container with a volume of 154 cm cubed hold?
A. 0.154 ml
B. 1.54 ml
C. 154 ml
D. 15,540 ml
154 cm3 = 0,154 dm3 = 0,154 l = 154 ml
3x+1=38 solve and check please
Hello!
The first step is to subtract 1 from both sides.
[tex]\bf{3x+1=38}[/tex]
[tex]\bf{3x=37}[/tex]
Now, divide both sides by 3:
[tex]\bf{\displaystyle\frac{37}{3} }[/tex]
Can this fraction be simplified? Nope.
Why? Because 37 and 3 do not have any common factors, except 1 (and what's the point of dividing by 1?)
Hence, the answer is
[tex]\huge\boxed{\text{Answer:{\boxed{\circ\star{\frac{37}{3} }}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepOnLearning
[tex]\boxed{An~Emotional~Helper!}[/tex]
Will give brainiest!!!!
Jocelyn participates in three track events: the 200-meter sprint, the 400-meter hurdles, and the 800-meter run. She calculated the mean absolute deviation of her race times throughout the season in each event.
200-meter sprint: mean absolute deviation of 2.05
400-meter hurdles: mean absolute deviation of 2.82
800-meter run: mean absolute deviation of 1.9
In which event were her times the most spread out?
200 meter sprint
800 meter run
400 meter hurdles
Answer:
The awnser is 400 meter run
Step-by-step explanation:
i took the quiz
The mean absolute deviation shows that the event were her times the most spread out is C. 400 meter hurdles.
What is a mean absolute deviation?It should be noted that the mean absolute deviation means the average distance that's between each data point and the mean.
In this case, the mean absolute deviation shows that the event were her times the most spread out is 400 meter hurdles. This was illustrated as it has has the highest mean absolute deviation when compared to others.
Learn more about mean absolute deviation on:
https://brainly.com/question/17381861
Three friends share 2 bags of trail mix equally.
What fraction of a bag of trail mix does each friend get?
Answer:I think that each friend would get 1.5/ 1 1/2.
Step-by-step explanation:
3 divided by 2 equals 1.5
UNIQUE
SIZE
What Does Cate Often
Call Her Twin Sister?
Answer:
a dupli-CATE
Step-by-step explanation:
HAHAHAHA OMG THIS IS ACTUALLY FUNNY
The cost of 3 scarves is $26.25. What is the unit price?
Answer : $8.75
Answer:
$8.75
8.75x3=26.25
Step-by-step explanation:
Answer:
$8.75
Step-by-step explanation:
To find out the unit price, take the whole and divide it by the number of units. In this case the whole cost is $26.25. There are 3 scarves in a whole. Divide $26.25 by 3 to find out the cost of the unit price. It is $8.75. Knowing how to figure out a unit price for something is very useful. For example, if you wanted to buy some Pepsi but didn't know if the 24-pack, 12-pack or 36-pack was a better deal, you can find out the unit price to see which is cheaper. For example, if the 24-pack of Pepsi cost $5, the unit price per can would be .21. A 12-pack at$ 2.75 would be .22 per can. A 36-pack at $6.50 is .18 per can. This tells you that you'd save more money per can if you bought the 36-pack of Pepsi.
If I have 1 and 10 dollar bill and 4 quarters, that makes 15$.
Hey there!
$10.00 + 0.25¢ + 0.25¢ + 0.25¢ + 0.25¢
= $10.25 + 0.25¢ + 0.25¢ + 0.25¢
= $10.50 + 0.25¢ + 0.25¢
= $10.75 + 0.25¢
= $11.00
OR YOU COULD READ THE EQUATION LIKE:
$10.00 + $1.00
= $11.00
Thus, your answer is: FALSE because $10 + 4 quarters gives you $11 NOT $15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
False
Step-by-step explanation:
$10+$1=$11 and .25+.25+.25+.25=$1
which would equal $12 so your answer would be falses if thats what your asking
if i was asked to think of a number and multiply it by 2, I could write this algebraically as 2x Write the following using x as your unknown. "I think of a number, take away 1 and multiply the result by 3.
Step-by-step explanation:
(x - 1)×3
a random number minus 1, and the result is multiplied by 3.
bingo !
Answer:
3(x - 1).
Step-by-step explanation:
Taken away 1 is x - 1
Multiply this by 3 is 3(x - 1).
Solve for X. Leave your answer in the simplest radical form.
Image down below!
Someone please help me with this, I’ll give you brainlist and points!
Apply Pythagorean theorem
P²=10²-4²P²=100-16P²=84p=2√21Again
x²=84-8²x²=84-64x²=20x≈√20=√4×5=2√5Answer:
2√5
Step-by-step explanation:
The given pyramid is composed of two right angle triangles. Notice the triangles of the pyramid share a common side. With the help of it, we can figure out x
recall Pythagoras theorem
[tex] {a}^{2} + { b }^{2} = {c}^{2} [/tex]
Case-1: Finding the opposite sidehere,
a=4c=10To find:
bnow plug in the value of a and c in the formula respectively:
[tex] {4}^{2} + { b }^{2} = {10}^{2} \\ \implies {b}^{2} = {10}^{2} - {4}^{2} \\ \implies {b}^{2} = 84 \\ \implies \boxed{ b_{1} = 2\sqrt{21}}[/tex]
Case-2: Finding xhere,
[tex]b_1 \implies c=2\sqrt{21}[/tex]b=8a[tex]\implies[/tex] xUtilizing Pythagoras theorem yields:
[tex] {x}^{2} + { 8}^{2} = {(2\sqrt{21})}^{2} \\ \implies {x}^{2} = {(2\sqrt{21})}^{2} - {8}^{2} \\ \implies {x}^{2} = 20\\ \implies \boxed{ x= 2\sqrt{5}}[/tex]
and we're done!
A pet store has 5 tanks of fish. Each tank has 30 fish. How many fish does the store have?
Answer:
30 fish
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
5 tanks with 30 fish each so 5x30
5x30=150
Patrick is a comdeion who makes $120 for short performance and $260 for long performance. how much will he earn if he completes 11 short and 12 long performences?
Answer:
$4440 for all performances
Step-by-step explanation:
11 × ¢120 for short performances
12 × $260 for long performances
$1320 for short performances
$3120 for long performances
To get the totel you add them up
( $1320 + $3120)
The total is $4440
please check picture and answer correctly please.
Answer:
27
Step-by-step explanation:
multiply 9 x 6 and you get 54. Since it's a triangle divide by 2 and you get 27
Is (3, 1) a solution to this system of equations?
3x + 3y = 12
12x + y = 13
Yes or no
Answer: No
Step-by-step explanation:
(3,1) is not a solution because when plugging in x=3 and y=1 to the second equation, you get: 12(3) + 1 = 13 → 36 + 1 = 13 → 37 = 13, which is false.
A bakery made 100 donuts. In the display case, 40/100 were chocolate,
3/10 were glazed, and the rest were cinnamon. Which fraction of the donuts were cinnamon?
A.30/100
B.43/100
C.57/100
D.70/100
Answer:
Step-by-step explanation:
57 of them were cinnamon.
Explanation:
100-40 = 60 and 3 of those were glazed so that leaves us with 57
6. Didi took out a loan of S12,600 to buy a car. After one month, an interest fee of 0.5% on this
loan is added to what she owes. After the fee is added, she then makes a payment of $200 to
start paying off her loan.
Given that the interest fee will increase what she owes while the payment will decrease what
she owes, how much money does Didi owe after one month
Answer:
$12,463
Step-by-step explanation:
The amount owed after one month is the sum of the original amount and the interest fee, less the amount paid.
__
The interest fee is 0.5% of $12,600, so is ...
0.005 × $12,600 = $63
After her $200 payment, the amount Didi owes is ...
$12,600 +63 -200 = $12,463 . . . owed after 1 month