Algebra II | Progressions
It’d be very much appreciated if someone could a.) solve this for me, and b.) kindfully explain how to get the correct answer in simple terms. It looks easy, but the lesson isn’t making it make sense. Thank you! :)
Answer:
Option 1
Step-by-step explanation:
Substiute the value of n with 1 to 6 and find each term.
When n = 1 ,
[tex]\sf First \ term = \dfrac{1}{2*1+1}=\dfrac{1}{2+1}=\dfrac{1}{3}\\\\[/tex]
[tex]\sf When n = 2,\\\\Second \ term = \dfrac{2}{2*2+1}=\dfrac{2}{4+1}=\dfrac{2}{5}\\\\[/tex]
When n = 3 ,
[tex]\sf Third \ term = \dfrac{3}{2*3+1}=\dfrac{3}{6+1}=\dfrac{3}{7}[/tex]
When n = 4,
[tex]\sf Fourth \ term =\dfrac{4}{2*4+1}=\dfrac{4}{8+1}=\dfrac{4}{9}\\[/tex]
When n = 5 ,
[tex]\sf Fifth \ term = \dfrac{5}{2*5+1}=\dfrac{5}{10+1}=\dfrac{5}{11}\\\\When \ n = 6,\\\\ \: Sixth \ term =\dfrac{6}{6*2+1}=\dfrac{6}{12+1}=\dfrac{6}{13}[/tex]
[tex]Answer: \dfrac{1}{3}+\dfrac{2}{5}+\dfrac{3}{7}+\dfrac{4}{9}+\dfrac{5}{11}+\dfrac{6}{13}[/tex]
What is the exact circumference of a circle with a radius of 17 mm?
•
8.5T mm
O
177 mm
O 347 mm
O
687 mm
Answer:
[tex]34\pi[/tex]
Step-by-step explanation:
Given,
r = 17 mm
→ Circumference =
[tex]2\pi \: r[/tex]
→ 2x3.14x17
→ 34x3.14 =
[tex]34\pi[/tex]
↓
c = 106.76 mm
Lane loads his stuck with 3 tons of bricks. How many pounds of bricks does he have
equation of circle: mastery test HELPPPP PLS !!
PQ is the diameter so the midpoint of PQ is the center of the circle. if we suppose the center point of the circle called o then ;
[tex]o = \frac{pq}{2} \\ [/tex]
[tex]pq = \sqrt{ { (- 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]o = \frac{( -10 ,10) + (6 , - 2) }{2} \\ [/tex]
[tex]o = \frac{( - 10 +6 ,10 - 2)}{2} \\ [/tex]
[tex]o = ( \frac{ - 4}{2} , \frac{8}{2} ) \\ [/tex]
[tex]o = ( - 2,4)[/tex]
For the second step we need to find the radius of the circle which has the half the PQ distance measure, so we have to find the the PQ distance and divide it by 2 :
_____________________________________________
As u know the distance between 2 point is going to find by following formula :
[tex]pq = \sqrt{ {(x(p) - x(q)})^{2} + {(y(p) - y(q)})^{2} } \\ [/tex]
[tex]pq = \sqrt{ ({ - 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]pq = \sqrt{ ({ - 16})^{2} + ({12})^{2} } [/tex]
[tex]pq = \sqrt{256 + 144} [/tex]
[tex]pq = \sqrt{400} [/tex]
[tex]pq = 20[/tex]
Thus :
[tex]radius = \frac{pq}{2} \\ [/tex]
[tex]radius = \frac{20}{2} \\ [/tex]
[tex]radius = 10[/tex]
_____________________________________________
Ok we're almost done cuz we have what we needed:
If we suppose that the first coordinate of the center is a and the second coordinate of the center is b and the radius shown by r then :
[tex] ({x -a})^{2} + ( {y - b})^{2} = {r}^{2} [/tex]
Is the equation of the circle in the standar form thus :
[tex] ({x - ( - 2)})^{2} + ({y - 4})^{2} = {10}^{2} \\ [/tex]
[tex] ({x + 2})^{2} + ({y - 4})^{2} = 100[/tex]
As u can see option B is the correct answer.
And we're done ...
Have a great day ♡♡♡♡♡Find the area of the figure
Step-by-step explanation:
there is one central rectangle :
from (-4, 2) to (2, -2).
that means it dimensions are 6×4 (for x from -4 to +3, for y from +2 to -2).
and then there are 3 additional triangles
(2, -4) (2, 2) (6, 2)
(-4, -2) (2, -2) (2, -4)
(-6, 2) (-4, 2) (-4, -2)
with the leg lengths
(2, -4) to (2, 2) = 6, and (2, 2) to (6, 2) = 4
(-4, -2) to (2, -2) = 6, and (2, -2) to 2, -4) = 2
(-6, 2) to (-4, 2) = 2, and (-4, 2) to (-4, -2) = 4
the area of the rectangle is
6×4 = 24 square units
the area of the first triangle is
6×4/2 = 3×4 = 12 square units
the area of the second triangle is
6×2/2 = 6 square units
the area of the third triangle is
2×4 = 8 square units.
so, the total area is
24 + 12 + 6 + 8 = 50 square units.
A right cylinder with a diameter of 8 ft and a height of 15 ft. Help!!
Given :-
Diameter = 8ft , radius = 4ft.Height = 15ftWe can find Total Surface Area , Lateral Surface Area and Volume of Cylinder by given values.
Volume of Cylinder = πr²h
putting the known values ,Volume = 3.14×4²×15 cubic feet
Volume = 753.6 cubic feet
Total Surface Area of Cylinder = 2πr(r+h)
TSA = 2×3.14×4(4+15) square feet
TSA = 477.28 square feet
Lateral Surface Area Of Cylinder = 2πrh
CSA = 2×3.14×4×15
CSA = 376.8 square feet
check if 5/11 and 7/6 are rational numbers.
Answer:
they are rational numbers
Step-by-step explanation:
Any fraction with integers in numerator and denominator is a rational number.
__
5, 6, 7, 11 are integers, so the fractions 5/11 and 7/6 are rational numbers.
On Tuesday 27% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought gas. How many of these 300 customers made additional purchases?
Answer:
81
Step-by-step explanation:
how to calculate procentage:
300(total) x 27(procentage) : 100 = 81
give brainliest
Solve it
x / 5 + (x - 1) / 3 = 1/5
Hello ~
My name is Irxdscent, and I will be answering your question today! :D
[tex]\huge\pmb{\frak{\underline{Answer:}}}[/tex]
[tex]\sf{x = 1}[/tex]
[tex]\huge\pmb{\frak{\underline{Explanation:}}}[/tex]
[tex]\sf{\frac{x}{5} \: + \: \frac{(x \: - \: 1)}{3} = \frac{1}{5}[/tex]
[tex]\sf{\frac{x}{5} \: + \: \frac{x \: - \: 1}{3} = \frac{1}{5}[/tex]
Find The Least Common Multipler of [tex]\bold{^5^,^3^: \: ^1^5}[/tex]Multiply by LCM = [tex]\bold{15}[/tex]
[tex]\sf{\frac{x}{5} \: . \: 15 \: + \frac{x \: - \: 1}{3} \: . \: 15 = \frac{1}{5} \: . \: 15}[/tex]
Simplify :[tex]\sf{3x \: + \: 5(x \: - \: 1) = 3[/tex]
Expand [tex]\sf{^5^(^x \: ^- \: ^1^)^: \: ^5^x \: ^- \: ^5}[/tex][tex]\sf{3x \: + \: 5x \: - \: 5 = 3}[/tex]
Add similar elements: [tex]\sf{^3^x \: ^+ \: ^5^x \: ^= \: ^8}[/tex][tex]\sf{8x \: - \: 5 \: + \: 5 \: = 3 \: + \: 5}[/tex]
Simplify :[tex]\sf{8x \: = \: 8[/tex]
Divide both sides by [tex]\bold{8}[/tex][tex]\sf{\frac{8x}{8} = \frac{8}{8}[/tex]
Simplify :[tex]\sf{x = 1}[/tex]
Hope It Helps! ~
~ Learn With Lrxdscent ~
[tex]\underline{Answer :}[/tex]
ɪ ʀ x ᴅ ꜱ ᴄ ᴇ ɴ ᴛ
Answer:
x = 1Step-by-step explanation:
In the question we have given an equation that is x / 5 + ( x - 1 ) / 3 = 1 / 5 . And we are asking to solve the equation that means we have to find the value of x.
Solution : -
[tex] \longmapsto \qquad \dfrac{x}{5} + \dfrac{(x - 1)}{3} = \dfrac{1}{5} [/tex]
Step 1 : Bye taking L.C.M solving left side :
[tex] \longmapsto \qquad \dfrac{3x + 5(x - 1)}{15} = \dfrac{1}{5} [/tex]
On further calculations, We get :
[tex] \longmapsto \qquad \dfrac{3x + 5x - 5}{15} = \dfrac{1}{5} [/tex]
[tex] \longmapsto \qquad \dfrac{8x - 5}{15} = \dfrac{1}{5} [/tex]
Step 2 : Multiplying 15 on both sides :
[tex] \longmapsto \qquad \dfrac{8x - 5}{ \cancel{15}} \times \cancel{15 } = \dfrac{1}{ \cancel{5}} \times \cancel{15}[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad 8x - 5 = 3[/tex]
Step 3 : Adding 5 on both sides :
[tex] \longmapsto \qquad8x - \cancel{5} + \cancel{ 5} = 3 + 5[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad8x = 8[/tex]
Step 4 : Dividing with 8 on both sides :
[tex] \longmapsto \qquad \dfrac{ \cancel{8}x}{ \cancel{8}} = \cancel{\dfrac{8}{8} }[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad \blue{\underline{\blue{\boxed{ \frak{x = 1}}}}}[/tex]
Henceforth, value of x is 1 .Verifying : -
We are verifying our answer by substituting value of x in the given equation . So ,
x / 5 + ( x - 1 ) / 3 = 1 / 51 / 5 + (1 - 1 ) / 3 = 1 / 51 / 5 + 0 / 3 = 1 / 5 (0 / 3 is equal to 0) 1 / 5 + 0 = 1 / 51 / 5 = 1 / 5 L.H.S = R.H.SHence , Verified .Therefore, our solution is correct .
#Keep Learninghelp i need help and this is due soon
Answer:
8π or 35.133 (3 d.p.)
Step-by-step explanation:
Volume of cone is [tex]V=\pi r^{2}\frac{h}{3}[/tex], where V is the volume, r is the radius, and h is the vertical heightSubstitute in the values[tex]V=\pi\times 2^{2}\times\frac{3}{3}[/tex][tex]V=4\pi\times 1[/tex][tex]V=4\pi[/tex]There are 2 cones, so times by 2This gives 8πWhat is the value of χ2 for the two-way table?
A B C D
X 5 10 15 20
Y 7 13 17 21
(2 points)
0.5320
0.0801
1.08
0.2830
0.9632
Answer:
0.2830
Step-by-step explanation:
Observed Values
Add totals for the rows and columns to the two-way table (see attachment 1).
Expected Values
Create an "Expected Values" table by multiplying each row total by each column total and dividing by the overall total (see attachment 2).
Chi-square test statistic
[tex]\sf \dfrac{(observed-expected)^2}{expected}[/tex]
Create a third table by using the formula to calculate the chi-square test statistic for each cell of the table (see attachments 3 and 4)
Chi-square
Add the values from the table in attachment 4.
[tex]\sf X^2=0.05556+0.03945+0.002315+0.05465+0.04789+0.03401+0.001996+0.04711[/tex] [tex]\implies \sf X^2=0.2830 \:(4 \:sf)[/tex]
Can someone pleas help???????
Answer:
written all the angles below:
m<1 = 35°
m<2 = 77°
m<3 = 49°
m<4 = 77°
m <5 = 62°
m<6 = 28°
hope that helps...
PLEASE HELP I WILL GIVE YOU 5 STARS
Answer:
3/4 lbs.
Step-by-step explanation:
In order to find how much more the heavier boxes weigh than the lighter boxes, we have to subtract the lighter box weight from the largest box weight.
Lighter box weight = 4 1/2
Heavier box weight = 5 1/4
Now we can find their difference:
The heavier box weight - lighter box weight = 5 1/4 - 4 1/2 = 21/4 - 9/2 = 21/4 - 18/4 = 3/4.
The heavier boxes weigh 3/4 lbs. more than the lighter boxes.
Answer:
3/4 lbs
Step-by-step explanation:
The heavier box weight - lighter box weight = 5 1/4 - 4 1/2 = 21/4 - 9/2 = 21/4 - 18/4 = 3/4.
The difference is:
The heavier boxes weigh 3/4 lbs. more than the lighter boxes.
Please may I have brainliest
can anyone solve this?
Answer:
The answer is 14/50
Step-by-step explanation:
sin=opp/hyp
sin=14/50
please teach me how to do this
Answer:
16.4
Step-by-step explanation:
x = radius
x = 8.7 + 7.7
x = 16.4
Dividing by 1/2 means you are finding how many halves are in the dividend
to multiply it by 2 because two is the dividend and that is closest to 1
The function H(n) describes the total amount of money a movie theater receives for n ticket sold.
which domain is appropriate for this function.
all integers
all real numbers
all positive integers and zero
or
all positive real numbers and zero
The domain which is appropriate for the function, H(n) is; all positive integers and zero.
Domain of functionsFrom the task content;
We are required to identify the domain which is most appropriate for the function.On this note, we are required to determine the possible values for the number of tickets bought, n.
Ultimately, since tickets are whole, it follows that the appropriate domain for this function is; all positive integers and zero.
Read more on domain of functions;
https://brainly.com/question/1369616
What are three ratios that are equivalent to 16:12.
Answer:
4:3 = 8:6 = 12:9 = 16:12 = 20:15 = 24:18 = 28:21 = 32:24 = 36:27 = 40:30
Step-by-step explanation:
Answer:
8:4, 32:24, 48:36
Step-by-step explanation:
16 ÷3=8
12÷3=4
↓
8:4
----------------------
16 ×2=32
12×2=24
↓
32:24
-----------------------
16×3=48
12×3=36
↓
48:36
Hope this helps! Have a good day! : )
100 Points!!! WILL MARK BRAINLIEST!!!
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 35 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 15w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 36 weeks. (4 points)
Answer:
A) [tex]f(w)=45w+35[/tex]
B) f(w) is the total number of flowers that bloomed
w is the number of weeks
C) 1655 flowers
Step-by-step explanation:
Part A
[tex]f(s) = 3s + 35[/tex]
[tex]s(w) = 15w[/tex]
To create the composite function, replace the variable [tex]s[/tex] in the function f(s) with function s(w):
[tex]\implies f(w)=3(15w)+35[/tex]
[tex]\implies f(w)=45w+35[/tex]
Part B
f(w) is the total number of flowers that bloomedw is the number of weeksPart C
Substitute w = 36 into the compositie function and solve:
[tex]\implies f(36)=45(36)+35=1655[/tex]
Omar thinks you should sell sundae cups and raspberry ripple cones. He recommends that the costs to you for frozen treats be no more than $450. Based on Omar's recommendation, enter an inequality that represents the
number of sundae cups, x, and the number of raspberry ripple cones, y, that will cost you no more than $450.
Considering that a sundae cone costs $5 and a raspberry ripple cone $7, the inequality is:
[tex]5x + 7y \leq 450[/tex]
What is the inequality that models this situation?The total price can be no more than $450, hence:
[tex]T \leq 450[/tex]
To find the total price, we need the price of each a sundae cone and a raspberry ripple cone, which are not given. Hence, considering that a sundae cone costs $5 and a raspberry ripple cone $7, the total price is given by:
T = 5x + 7y
Hence, the inequality is:
[tex]5x + 7y \leq 450[/tex]
More can be learned about inequalities at https://brainly.com/question/25235995
Solve the following equation using distribution. 1 2 (4x − 12) = 5 ( 1 2 ) (4x) − ( 1 2 ) (12) = 5 2x − 6 = 5 +6 +6 2x = 11 What is the value of x? 5.5 9 11.5 13
Answer:
5.5
Step-by-step explanation:
Answer: IT IS 5.5I DID THE TEST
Step-by-step explanation:
find the absolute value of -5/8
Answer:
5/8
Step-by-step explanation:
To find the absolute value you simply remove the negative symbol
everday at 9:15 am jessie takes his for a walk for 30 min he takes the next 2 hours to work on his computer before he eats lunch what time does he eat lunch
Answer:
11:45 AM
Step-by-step explanation:
9:15 +30 mins is 9:45
9:45 +2 hours is 11:45
Hope this helps!
The table of ordered pairs gives an exponential function.
Write an equation for the function. NEED ASAP!!!
Answer:
12+34+67+12
Step-by-step explanation:
im in 12th grade with straight as trust me
100 Points!! 0_0
Solve and check for extraneous solutions.
5(3x+1)^1/2=10
Please SHow Steps!!! WIll give the brainiest!!
[tex]5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{5(3x+1)^1}{2} =10[/tex]
If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".
[tex]:\implies\dfrac{5(3x+1)}{2} =10[/tex]
Simplify the distributive property:
[tex]:\implies\dfrac{15x+5}{2} =10[/tex]
Using cross multiplication:
[tex]:\implies15x+5} =10 \times 2[/tex]
Simplify the R.H.S:
[tex]:\implies15x+5} =20[/tex]
Subtract 5 both sides:
[tex]:\implies15x+5 - 5} =20 - 5[/tex]
Simplify both sides:
[tex]:\implies15x} =15[/tex]
Divide 15 both sides:
[tex]:\implies\dfrac{15x}{15} } =\dfrac{15}{15}[/tex]
Simplify both sides:
[tex]:\implies x= 1[/tex]
For the function y = x -2, make a table of ordered pairs and graph the function on a coordinate plane.
Answer:
Step-by-step explanation:
Start by plugging in the x values -2, -1, 0, 1, and 2 into the equation to receive the y values.
For example, the first point on the table would be y=(-2)-2, or (-2, -4). Continue plugging in the points for all the points on the table
4-5 practice proving right triangles congruent worksheet 1-7
Step-by-step explanation:
1. mzoGE = M2GOE
1. Given
2. GE = OE
2.
3. E is the midpoint of AT
3. Given
4. AE ET
4. Definition of the midpoint of a line segment.
5. AE = ET
5. Congruent segments have equal length.
6. MLAEG > MZTEO
6. Given
7. AG > TO
What is the value of the expression 16 + 56/n when n = 8?
Answer:
23
Step-by-step explanation:
[tex]16 + \frac{56}{n} [/tex]
[tex]where \: n = 8[/tex]
[tex]16 + \frac{56}{8} [/tex]
[tex]23[/tex]
[tex]56 / 8 = 7[/tex]
Add second[tex]7 + 16 = 23[/tex]
With that information, your answer is twenty-three.
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By what factor were the dimensions of the pentagon multiplied?
12. 5
625
5
50
Answer:
625
Step-by-step explanation:
I just did this question
amount if you decrese 35 by 20%
Answer:
26.25
Step-by-step explanation:
So if you want to remove 25% from 35 you have to multiply the two you get 8.75 then minus that from 35 you get 26.25