(a) Find the value of xif 10, x and 30 are in A.P.
(b) If 6,x,y, and 18 are in A.P., find the value of x and y.
it's a optional mathematics Questions please solve him
Part A
Answer: x = 20--------------------------------
Explanation:
AP = arithmetic progression, which is another way of saying arithmetic sequence.
Let d = common difference
first term = 10second term = first+d = 10+d = xthird term = second+d = x+d = 30Apply substitution like so
x+d = 30
10+d+d = 30 ... replaced x with 10+d
10+2d = 30
2d = 30-10
2d = 20
d = 20/2
d = 10 is the common difference
Therefore,
x = 10+d = 10+10 = 20
The AP {10,x,30} updates to {10,20,30}. We see the gap between terms is 10 units. All AP's have the same gap width between adjacent terms.
=============================================================
Part B
Answers: x = 10 and y = 14--------------------------------
Explanation:
We use the same ideas mentioned back in part A.
d = common difference = unknown for now
first term = 6second term = first+d = 6+d = xthird term = second+d = x+d = (6+d)+d = 6+2d = yfourth term = third+d = y+d = (6+2d)+d = 6+3d = 18Hopefully you can see how each term builds up to form the next one. We'll solve that last equation like so
6+3d = 18
3d = 18-6
3d = 12
d = 12/3
d = 4
So we then can say:
x = 6+d = 6+4 = 10y = 6+2d = 6+2(4) = 6+8 = 14The arithmetic sequence {6,x,y,18} updates to {6,10,14,18}. There's a gap of 4 between each adjacent term.
HELP RN PLS
simplify (4^3)^5
Answer:
(4^3)5 = 4^15
hope this helpsStep-by-step explanation:
Identify the terms, coefficients, constant terms, and like terms of the
expression.
1.-3x - 5- 7x - 9
2.-10c - 6 + c
Answer:
1) terms: -3x, -5, -7x, 9
Coefficients: 3 and 7
Constant: -5, -9
Like terms: -3x and -7x (-3x + -7x = -10x)
-5 and -9 = -14
2) terms: -10c, -6, c
Coefficients: -10 and 1
Constant: -6
Like terms: -10c and c (-10c + c = -9c)
Step-by-step explanation:
Write in exponential form
ахахахахаха
Answer:
the exponential form of this is a to the power 6
I.e a⁶
mark me as brainliest
12a+5b-3c, 6c-5a+8b, -8b+5c-7a
Answer:
11c-12a
Step-by-step explanation
Combine like terms
Show that 6 – 4x - x^2 can never be greater than 10.
( This is an Additional Math Question )
Answer:
see explanation
Step-by-step explanation:
Given
6 - 4x - x²
Since the coefficient of the x² term < 0 then parabola has a maximum vertex.
To find the x- coordinate of the vertex
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
with a = - 1 and b = - 4 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{-2}[/tex] = - 2
The corresponding y- coordinate is found by substituting x = - 2 , that is
6 - 4(- 2) - (- 2)² = 6 + 8 - 4 = 10
vertex = (- 2, 10 )
The maximum value of the function is the y- coordinate of the vertex
Then maximum value is 10
Thus 6 - 4x - x² is never greater than 10
Select all ratios equivalent to 7:5.
Answer:
77 : 55
Step-by-step explanation:
77 : 55
divide the ratio by 11.
7 : 5
Geometry
Topic: Measure Angles
Answer:
BOC = 42
Step-by-step explanation:
90 = 6z - 6 + 5z + 8
Combine common factors
90 = 11x + 2
Subtract 2 from both sides
88 = 11x
Divide both sides by 11
8 = x
Plug in 8 for x
6(8)- 6
48 - 6
42
1.
Find the first, fourth, and eighth terms of the sequence. A(n) = –2 • 2^n–1
A. –4; –32; –512
B. 1; –64; –16,384
C. –8; –64; –1,024
D. –2; –16; –256
Answer:
D
Step-by-step explanation:
given that
A(n)=-2•2^(n-1)
n->represent the terms
A(1)=-2•2^(1-1)=>-2•2^0
A(1)=-2•1=-2
For the fourth term
A(4)=-2•2^(4-1)
A(4)=-2•2^(3)
A(4)=-16
for the 8th term
A(8)=-2•2^(8-1)
A(8)=-2•2^(7)
A(8)=-256
Therefore first, fourth and eight => -2;-16;-256
Which one describes the algebraic expression for the phrase, "twice a number decreased by 5 is greater than 12"? 2n - 5 = 12
2n - 5 < 12
12 + 5n > 2
2n - 5 > 12
Answer:
2n - 5 > 12[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
8x-5y-2x-3y simplify the expression by combining like terms
How do you simplify 5 to the 3 power times 25
Answer:
5^5
Step-by-step explanation:
5^3 * 25
Note that 25 = 5^2 (which is 5 * 5)
so we can rewrite the first expression as
5^3 * 5^2
We can add the exponents because we are multiplying and there is the same base (5):
5^(3+2) = 5^5
(HELP ASAP!!)
If you deposit $5000 into an account paying a rate 15% simple interest annually, how much interest will you make in 24 months
Answer:
1500
Step-by-step explanation:
24 month means 2 years ( N )
rate 15 pcpa ( R )
amount is 5000 ( P )
so by formula
interest = P×N×R/100
so ( I ) = 5000×2×15/100
so( I ) = 50×2×15 ....... ( here 100 ( 2 zero ) and 5000.( 2 zero ) got canceled
so ( I ) = 50×2×15
so ( I ) = 100×15
so ( I ) = 1500
MARK AS BRAINLIST IF IT IS USEFUL
I need to describe and fix this error
9+(-6)=-3
Answer: 9 - 6 = 3
Step-by-step explanation:
Find the least common multiple of 3 and 8
Answer:
the right answer is 24
hope it help
To graph an exponential, you need to plot a few points, and then connect the dots and draw the graph. Where do you
come up with values to use in the graph?
T-chart using positive real numbers C. T-chart using all real numbers
b. T-chart using negative real numbers d. T-chart using random values for x and y
a.
Please select the best answer from the choices provided
OA
ОВ
D
and Guit
Submit
To graph an exponential,
d. T-chart using random values for x and y.
What is mean by graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Now,
We know an exponential function is a function in which the independent variable is the exponent.
One such function is y = eˣ
Now, To graph an exponential function you come up with values to use in the graph should be a T-chart using random values for x and y.
As it would result in graphing the complete nature of the function.
Learn more about graphs here :
brainly.com/question/2288321
#SPJ7
Suppose Clare labels the books at a constant speed of s books per minute. Write an equation that represents the relatinoship between her labeling speed and the number of minutes it would take her to finish labeling.
it will take her 34 mins coz I said so innit
Solve the problem by writing a inequality
Answer:
first option
Step-by-step explanation:
number of shirts = x
price of shirts made = 9x+20
amount u earn by selling the shirts = 15x
profit = 15x - (9x+20)
profit of at least 150,
15x - (9x+20) ≥ 150
Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and points***
Answer:
1) 4900 is square
2) The greatest common factor 30 and 126 is 6. The GCF of 126 and 39204 is 18
3) i) 44100 ii) 48024900
Which terms must be removed from 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 if the sum of the remaining terms is to equal 1?
1/4
Step-by-step explanation:
0.5+0.25+0.17+0.13+0.1+0.1=1.25
What division problem iS
being
modeled?
Answer: I THINK fraction
Step-by-step explanation:
1/4 = fraction
round off 7284 to 1sf
Answer:
7000
Step-by-step explanation:
This is because when you round to the significant figure, you basically look at any digits at the start of the number, which isn't zero. In this case, it would be in the thousands place 7284. So you round 7284 to the nearest thousands, which, would be 7000
Find the 7th term of the geometric sequence shown below
10x^3, 40x^8, 160x^13,…
Answer:
[tex]a_7=40960x^{33}[/tex]
Step-by-step explanation:
Geometric sequence has explicit form:
[tex]a_n=a \cdot r^{n-1}[/tex] where [tex]a[/tex] is first term and [tex]r[/tex] is the common ratio.
First term here is [tex]a=10x^3[/tex] and [tex]r[/tex] could be found by doing second term divided by first term, [tex]\frac{40x^8}{10x^3}=4x^5[/tex].
Therefore the [tex]n[/tex]th term is given by
[tex]a_n=10x^3 \cdot (4x^5)^{n-1}[/tex].
So the [tex]7[/tex]th term is given by
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex].
Let's simplify:
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex]
[tex]a_7=10x^3 \cdot (4x^5)^{6}[/tex]
[tex]a_7=10x^3 \cdot (4^6(x^5)^6)[/tex]
[tex]a_7=10x^3 \cdot (4096x^30)[/tex]
[tex]a_7=40960x^{33}[/tex]
the capacity of cylinder tank is 539 litres . if its height is 1.4m then find the area of base
Step-by-step explanation:
Solution:
Here,
Volume of the tank=539 litres
=539×1000cm^3=539000cm^3
Height=1.4×100cm=140cm
Let the radius of the base be r cm
Then,
22/7×r^2×140=539000
or,r^2=539000×7/22×140
or,r^2=1225
or,r=35 cm
So,
Area of base=pie r^2
=22/7×35^2
=3850 cm^2
Keep smiling and hope u r satisfied with my answer.Have a good day :)
Given Data:
Capacity of the Cylinder tank, V = 539 litres =
Height, h = 1.4 m
Area of the Cylinder, A = ?
Convert litres to m³: I litre = 0.001 m3
: . Capacity of the Cylinder tank = 539 litres = 0.539 m³
Let the radius of the base be r cm.
Find the radius of Cylinder:
Volume = πr²h
0.539 = πr²(1.4)
0.539 ÷ 1.4π = r²
r² = 0.12255
r = √0.12255
r = 0.35m
Find Area of Base:
Area, A = πr²
Area = π(0.35)² = 0.385 m²
Answer: The Area of base is 0.385 m²
What load can be lifted by an effort of 800N if the effort arm is 80cm and the load arm is 20cm?
Step-by-step explanation:
Solution,
Effort=800N
Effort arm=80 cm
Load arm=20 cm
Load=?
Now,
by the principle of lever, we have
Load×Load arm=Effot×Effort armLoad×20=800×80Load=800×80/20Load=3200 NSo, the load of 3200N can be lifted .
Answer:
load (l) =?
LOAD ARM = 20 CM
EFFORT ( E)= 800N
EFFORT ARM = 80cm
load *load arm = effort *effort arm
l*20 cm = 800 *80
L = 64000/20
answer = 3200
Find the cube root of 1.331
Answer:
answer is 1.1
Step-by-step explanation:
11(1331)
11(121)
11(11)
(1)
10(1000)
10(100)
10(10)
(1)
(11/10*11/10*11/10)^(1/3)
=11/10
=1.1.
Answer:
1.1
Step-by-step explanation:
Money is
divisible, and each unit is
equivalent. In other words,
money is a blank
Answer:
is this a question or something else ?
Pliz help solve this what's 3+4×2.00×29
Here the other question 5n+1 find the sequence
Answer:
Step-by-step explanation:
1) 3 + 4*2*29 = 3 + 232 = 235
First we have to do multiplication and then we have to add
2) 5n + 1
Term 1 ; n = 1 ; 5n + 1 = 5*1 + 1 = 5 + 1 = 6
Term 2 ; n = 2 ; 5n + 1 = 5*2 + 1 = 10 + 1 = 11
Term 3 ; n = 3 ; 5n+ 1 = 5*3 + 1 = 15 + 1 = 16
Term 4; n = 4 ; 5n + 1 = 5*4 + 1 = 20 + 1 = 21
The sequence : 6 , 11, 16 , 21 ..........
………………………………….. x z z z
Answer:
a: 7:3
b:by reading 10 hours
Answer:
a: 4 : 1
b: 12 (water) : 3 (sugar)
Step-by-step explanation:
ratio is similar to a fraction
water to sugar
the "to" is for what of every what it needs
to = can be used as ":"
For example:
For every 1 cup of sugar you need 4 cups of water to make the humming bird nectar. (it needs to be IN ORDER which is why for letter 'a' I did it water to sugar)
This chart shows the temperature recorded at noon for some world cities . Which two cities had different of 25°c
Answer: London and Moscow.
Step-by-step explanation: This problem is simple. First, we use process-of-elimination. None of the positive values have a difference of 25 degrees, so one of the two values must be -12 degrees aka Moscow. From there, we add 25 to -12 to get 13. This means that the other city is London since it is 13 degrees.