Answer:
A
Step-by-step explanation:
The explicit formula for a geometric sequence is
f(n) = f(1) [tex](r)^{n-1}[/tex]
where f(1) is the first term and r the common ratio
Here f(1) = 64 and r = [tex]\frac{f(2)}{f(1)}[/tex] = [tex]\frac{16}{64}[/tex] = [tex]\frac{1}{4}[/tex] , then
f(n) = 64 [tex](\frac{1}{4}) ^{n-1}[/tex] → A
What would be the denominator after rationalizing 7/(5√3 - 5√2)?
Answer:
The denominator will be [tex]5\sqrt{3} +5\sqrt{2}[/tex]
Step-by-step explanation:
Find the values of p and q for which the following system of equations has infinitely many
solutions:
2x + 3y = 7
(p + q + 1)x + (p + 2q + 2)y = 4(p + q) + 1
Answer:
p = 3
q = 2
Step-by-step explanation:
they have infinitely many solutions, if they are basically the same equations. in other words, when they can be combined/reduced into a statement of tautology, a statement that is always true, no matter what.
like 15 = 15 or 8x = 8x
now we need to aim for creating the same (or multiples of the same) factors in the original equation 2 as in the original equation 1.
in other words we find the p and q, where we get the same ratios between the factors of squadron 1 and equation 2.
2/(p+q+1) = 3/(p+2q+2) = 7/(4p +4q +1)
p+q+1 = 2/3 × (p+2q+2) = 2/7 × (4p + 4q + 1)
3p + 3q + 3 = 2p + 4q + 4 = 6/7 × (4p+4q+1)
21p + 21q + 21 = 14p + 28q + 28 = 24p + 24q + 6
7p - 7q = 7
p - q = 1
p = 1 + q
14(1+q) + 28q + 28 = 24(1+q) + 24q + 6
14 + 14q + 28q + 28 = 24 + 24q + 24q + 6
42 + 42q = 30 + 48q
12 = 6q
q = 2
p = 1 + 2 = 3
Your business of household products manufacturing is about to start a venture to producing self-squeezing mops with an initial budget of Php 8,500,000.00. To be competitive in the market, the board plans to sell one unit for only Php 600.00 with a computed variable cost for each of Php 237.00. How many units of the mops shall represent the breakeven point?
Answer:
break-even point in units = 23,416 units (Approx.)
Step-by-step explanation:
Given:
Initial budget of Php = 8,500,000
Sales price of Php = 600
Variable price of Php = 237
Find:
break-even point in units
Computation:
break-even point in units = Initial budget of Php / [Sales price of Php - Variable price of Php]
break-even point in units = 8,500,000 / [600 - 237]
break-even point in units = 8,500,000 / 363
break-even point in units = 23,415.978
break-even point in units = 23,416 units (Approx.)
A woman's salary is increased by 20%. A week later her company loses one of its best customers and her salary is reduced by 35%. If her salary is now $4446, what was her original salary?
Answer:
$5472
Step-by-step explanation:
Set up a reverse ratio for each change:
4446/x = 65/100
65x = (4446) x (100)
65x = 444,600
x = 6840
Before her salary was reduced by 35%, she was earning $6840.
x/6840 = 20/100
100x = (6840)(20)
100x = 136,800
x = 1368 = 20%
$6840 - $1368 = $5472
help me plsss thankyouuuu
Answer:
a) 231
b) 52.8
Step-by-step explanation:
210*.10 = 21. 21+210 = 231
48*.10=4.8 4.8+48 =52.8
Answer:
a) 231
b) 52.8
Step-by-step explanation:
a)210x.1=21
210+21=231
b)48x.1=4.8
48+4.8= 52.8
Mark invests $8,008 in a retirement account with a fixed annual interest rate of 2% compounded 6 times per year. What will the account balance be after 16 years?
Please help i need the answer by tomorrow!
Given:
Principal value = $8,008
Rate of interest = 2% compounded 6 times per year.
Time = 16 years
To find:
The account balance after 16 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest, n is the number of times interest compounded in an year and t is the number of years.
Putting [tex]P=8,008, r=0.02,n=6,t=16[/tex] in the above formula, we get
[tex]A=8008\left(1+\dfrac{0.02}{6}\right)^{6(16)}[/tex]
[tex]A=8008\left(\dfrac{6.02}{6}\right)^{96}[/tex]
[tex]A=11022.1721148[/tex]
[tex]A\approx 11022.17[/tex]
Therefore, the account balance after 16 years is $11022.17.
1045.521984 to the nearest pound
Answer:
Step-by-step explanation:
1046 pound
Answer:
1,046
Step-by-step explanation:
because 5 rounds up we raise it to the next whole number
What is the class width for the class (65-72)kg?
Answer: Super Lightweight to Middleweight
Step-by-step explanation: I'm assuming you're talking about boxing weight class. If not, please let me know.
if the price of an article is without tax is ₹ 800, and the price with tax is ₹ 860 the sales tax rate is_____________
9514 1404 393
Answer:
7.5%
Step-by-step explanation:
The tax as a proportion of the selling price is ...
₹(860 -800)/₹800 = 60/800 = 0.075 = 7.5%
Which rule is a recursive rule for the sequence 1, -6, 36, -216,...?
( I'll put the answers a screenshot )
PLZZ Help I've been stuck for so long
Answer:
The last answer
Step-by-step explanation:
We can check
For example,
a5=-6×a4
a5=-6×(-216)
a5=1296
The perimeter of a rectangle is 25 2/5 ft. The length is
width. Find the length and width of the rectangle.
A. = 9.375 ft and w = 3.125 ft
B. = 9.525 ft and w = 3.175 ft
C. = 19.05 ft and w = 6.35 ft
D. = 7.85 ft and w = 4.85 ft
Answer:
Width = 4.85 feet
Length = 7.85 feet
Step-by-step explanation:
Given:
Perimeter of a rectangle = 25 2/5 ft = 25.4 feet
Length = 3 + Width
Computation:
Assume;
Width = a
So,
Length = 3 + a
Perimeter of a rectangle = 2(l + b)
25.4 = 2[(3 + a) + a]
25.4 = 2[3 + 2a]
25.4 = 6 + 4a
4a = 19.4
a = 4.85
Width = 4.85 feet
Length = 3 + 4.85
Length = 7.85 feet
SOMEONE PLEASE HELP ME ASAP !!!
Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four students in order to do labs. She has a total of 120 students and 32 total groups are formed.
If t represents the number of three person groups and frepresents the number of four person groups, then write a system of equations that models this situation.
How many four person groups are there? Only an algebraic solution will receive full credit.
PLEASE HELP !!!!
x + y = 32 (1)
3x + 4y = 120 (2)
x = 8; y = 24
Step-by-step explanation:
Total students = 120
Number of groups = 32
If the number of three person groups = x
Number of four person groups = y
write a system of equations that models this situation
x + y = 32 (1)
3x + 4y = 120 (2)
From (1)
x = 32 - y
Substitute x = 32 - y into (2)
3(32 - y) + 4y = 120
96 - 3y + 4y = 120
- 3y + 4y = 120 - 96
y = 24
Substitute y = 24 into (1)
x + y = 32
x + 24 = 32
x = 32 - 24
x = 8
x = 8; y = 24
Determine which quadratic equations have
2 real solutions. Select two that apply.
Answer:
A & D
First and last
Step-by-step explanation:
Maxine is taking 5 gallons of drinking water on a camping trip. How many quarts of drinking water is Maxine taking on the camping trip?
Answer:
20 quarts
Step-by-step explanation:
There are 4 quarts in a gallon
5 gallons * 4 quarts / 1 gallon = 20 quarts
Answer:
20 US quarts
Step-by-step explanation:
there are 4 quarts in a gallon so you have to multiply 5 x 4 to get the total amount of quarts in a gallon.
Hope it helps c:
find two consecutive odd number such that six times the smaller plus four times the greater comes to 138 hint let the number be x and x + 2
Step-by-step explanation:
here's the answer to your question
pls help and pls provide workings
(x-h)²+(y-k)²=r²
(3-h)²+(3-0)²=5²
h²-6h+9+9=25
h²-6h-7=0 —> (h-7)(h+1)=0
h=7 , h=-1
h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>
x²-14x+49+y²=25 —> x²+y²-14x+24=0
h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>
x²+2x+1+y²=25 —> x²+y²+2x–24=0
I hope it helped you ^_^
зх:
90
Х
2х:
What is the value of x?
Answer:
60
Step-by-step explanation:
To get the value of x;
3x:90
(90/3) = 30
x = 30
To get the value of 2x;
(2×X);
2 × 30
=60
which set of ordered pairs represent a function
Answer:
A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.
Step-by-step explanation:
Can you answer this math homework? Please!
Answers:
airspeed = 42 mphwind speed = 12 mph============================================================
Explanation:
Let's solve the first equation for y
[tex]18 = (x+y)\frac{1}{3}\\\\18*3 = x+y\\\\54 = x+y\\\\x+y = 54\\\\y = 54-x\\\\[/tex]
Then we'll plug this into the second equation and solve for x
[tex]18 = (x-y)*\frac{3}{5}\\\\18 = (x-(y))*\frac{3}{5}\\\\18 = (x-(54-x))*\frac{3}{5}\\\\18 = (x-54+x)*\frac{3}{5}\\\\18 = (2x-54)*\frac{3}{5}\\\\18*5 = 3(2x-54)\\\\90 = 6x-162\\\\6x-162 = 90\\\\6x = 90+162\\\\6x = 252\\\\x = 252/6\\\\x = 42\\\\[/tex]
This is the average airspeed of the plane, in miles per hour (mph). It's the speed without accounting for the wind. If there's no wind at all, then this would be the ground speed of the plane.
Use this value of x to find y
y = 54-x
y = 54-42
y = 12
The average speed of the wind is 12 mph.
HELPPPPPPPPPPP PLSSSSSSSSSSSSS
Answer:
6a+17
Step-by-step explanation:
This is an algebra 'expression' where you have to rearrange the question to the correct 'expression'
4a+2a= 6a
8+9= 17
Answer:
= 4a+2a+8+9
=6a+17
Find the 57th term of the following arithmetic sequence. 13, 20, 27, 34
Answer:
[tex]{ \tt{n _{th} = a + (n - 1)d}} \\ { \tt{n _{57} = 13 + (57 - 1) \times 7}} \\ { \tt{n _{57} = 405}}[/tex]
which graph represents a function
Answer:
the first one is an ellipse.is ellipse a function Gods plan I think the second one is a function.
Simplify the expression.
40 -2.32
A. 4
B. 342
C.
22
D. 28
Answer:
37.68
Step-by-step explanation:
40 -2.32
= 37.68
Answer: is C. 22
Step-by-step explanation:
Solve the system of equations.
6x – Зу = 3
-2x + y = 14
1.What number would you multiply the second equation
by in order to eliminate the x-terms when adding to the
first equation?
2.What number would you multiply the first equation by in
order to eliminate the y-terms when adding to the
second equation?
Answer:
1. Multiply by 3
2. Multiply by 1/3
Step-by-step explanation:
6x - 3y = 3
-2x + y = -14
1. In order to eliminate the x-terms, they would both have to equal the same number with opposite signs (positive and negative). Since we are only touching the second equation, how can we get from 2 to 6? We can multiply 2 by 3 to get to 6 (negative 6 in the end.) This would result as follows:
6x - 3y = 3
-6x + 3y = 42
2. In order to eliminate the y-terns through multiplying with the first equation, we have to figure out how to make 3y into 1y. We can do this by adding its reciprocal, 1/3. 1/3 × 3 = 1. This would result as follows:
2x - y = 1
Explain how you can find the constant of proportionality from a graph representing a proportional relationship when it shows a point with an x - value of 1 and if it doesn't show an x - value of 1 .
tienees que fijartelos extrreemos
Write the equation that describes the line in slope-intercept form.
slope = 2, point (–1, 2) is on the line
Answer:
y = 2x+4
Step-by-step explanation:
slope (m) = 2
point (-1,2)
so,
b = 2-2×(-1) = 4
y = mx+b
or, y = 2x+4
Please help me asap! I don’t understand
Answer:
18
Step-by-step explanation:
4*3 = 12
1/2 * 3 * 4 = 6
Please help me find this angle
Answer:
x = 78
Step-by-step explanation:
We can find angle y
D + B + y = 180 since the sum of the angles of a triangle are 180
31+47+ y =180
78+y = 180
y = 180 - 78
y = 102
x+y = 180 since they form a straight line
x + 102 = 180
x = 180-102
x = 78
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
we have to find the value of the x°=<GHC
In the triangle BDH,
<D=31°<B=47°we know that,
Sum of three angle of a triangle is 180°
According to the question,
<D+<B+<BHD=180°31°+47°+<BHD=180°78°+<BHD=180°<BHD=180°-78°<BHD=102°But,
<GHC and <BHD forms a straight line
so,
<GHC+<BHD=180°102°+x=180°x=180°-102°x=78°Therefore,
The value of x is 78°
find the equation of the lines: with a y-intercept of 4 and passes through the point (-1,3)
Answer:
equation is 4x-4y= -16
Step-by-step explanation:
b = 4
x = -1
y = 3
so
x/a + y/b = 1
or, -1/a + 3/4 = 1
or, (-4 + 3a) = 4a
or, -4 = 4a - 3a
so, a = -4
now
x/a + y/b = 1
or, x/-4 + y/4 = 1
or, 4x-4y = -16
so
equation : 4x-4y = -16
Answer:
Answer is y=x+4
Step-by-step explanation:
Find the length of the arc round your answer to the nearest tenth
Answer:
arc ≈ 4.2 cm
Step-by-step explanation:
The length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{60}{360}[/tex]
= 2π × 4 × [tex]\frac{1}{6}[/tex]
= 8π × [tex]\frac{1}{6}[/tex]
= [tex]\frac{8\pi }{6}[/tex]
≈ 4.2 cm ( to the nearest tenth )
