Answer:
(a+b)³=a³+3a²b+3ab²+b³
Answer:
Step-by-step explanation:
Hello!
(a+b)(a+b)(a+b)
(a+b)(a+b) = a²+2ab + b²
(a²+2ab + b²) (a+b)=
a³ + a²b + 2a²b + 2ab² + ab² + b³ =
a³ + b³ + 2a²b + 2ab² + ab² + a²b
The sum of 30 terms of series in A.P, whose last term is 98, is 1635. Find the first term and the common difference.
Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are
a(2) = a(1) + d = a + d
a(3) = a(2) + d = a + 2d
a(4) = a(3) + d = a + 3d
and so on, up to
a(n) = a + (n - 1) d
We're given that the 30th term is 98, so
a(30) = a + 29d = 98
The sum of the first 30 terms is 1635, so that
[tex]\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2[/tex]
so that
30a + 435d = 1635
Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.
-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635
-30a - 870d + 30a + 435d = -2940 + 1635
-435d = -1305
d = 3
Then
a + 29 (3) = 98
a + 87 = 98
a = 11
if a = 6 b=5, then find the value (a+b)
Step-by-step explanation:
Put the numbers as the value is given
So,
(6+5)= 11 Answer
Factor the following expression completely. 16x^5-x^3
Answer:
x³ (4x + 1)(4x - 1)
Step-by-step explanation:
Answer:
x^3 (4x-1)(4x+1)
Step-by-step explanation:
16x^5-x^3
Factor out x^3
16* x^2*x^3 - x^3
x^3(16x^2 -1)
The term inside the parentheses is the difference of squares
a^2 - b^2 = (a-b)(a+b)
x^3 ( (4x)^2 -1^2)
x^3 (4x-1)(4x+1)
solve using identities
Answer:
Solution given
Cos[tex]\displaystyle \theta_{1}=\frac{13}{15}[/tex]
consider Pythagorean theorem
[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]
Subtracting [tex]Cos²\theta[/tex]both side
[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]
doing square root on both side we get
[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]
Similarly
[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]
Substituting value of [tex]Cos\theta_{1}[/tex]
we get
[tex]Sin\theta_{1}=\sqrt{1-(\frac{-13}{15})²}[/tex]
Solving numerical
[tex]Sin\theta_{1}=\sqrt{1-(\frac{169}{225})}[/tex]
[tex]Sin\theta_{1}=\sqrt{\frac{56}{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{56}}{\sqrt{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{2*2*14}}{\sqrt{15*15}}[/tex]
[tex]Sin\theta_{1}=\frac{2\sqrt{14}}{15}[/tex]
Since
In III quadrant sin angle is negative
[tex]\bold{Sin\theta_{1}=-\frac{2\sqrt{14}}{15}}[/tex]Answer:
- 2√14/15Step-by-step explanation:
In the quadrant III both the sine and cosine get negative value.
Use the identity:
sin²θ + cos²θ = 1And consider negative value as mentioned above:
sinθ = - √(1 - cos²θ) sinθ = - √(1 - (-13/15)²) sinθ = - √(1 - 169/225)sinθ = - √(56/225)sinθ = - 2√14/15PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
An alphabetical list is generated of each member of the student body at a local middle school. The first name on the list is in the sample, along with every 5th name on the list after that. This is an example of a __________________.
A. systematic sample
B. stratified random sample
C. convenience sample
D. random sample
Answer:
Option A, systematic sample
Simplify and find the perimeter of the triangle
Answer:
2x - 19
Step-by-step explanation:
Perimeter = sum of sides
First let's simplify each side
We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.
2(x + 5)
Distribute by multiplying x and 5 by 2
2 * x = 2x and 2 * 5 = 10
2x + 10
1/2(4x + 8)
Distribute by multiplying 4x and 8 by 1/2
1/2 * 4x = 2x and 1/2 * 8 = 4
2x + 4
-3(2x + 11)
Distribute by multiplying 2x and 11 by -3
-3 * 2x = -6x
-3 * -33
-6x - 33
Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )
2x + 10 + 2x + 4 - 6x - 33
Combine like terms
2x + 2x - 6x = -2x
10 + 4 - 33 = -19
Perimeter: -2x - 19
Answer:
Perimeter = - 2x - 19
Step-by-step explanation:
[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]
So, the perimeter is - 2x - 19.
What is the translation from the preimage to the image in the graph?
Answer:
(x, y ) → (x + 7, y + 5 )
Step-by-step explanation:
Consider the coordinates of R and R'
R (- 5, 0 ) and R' (2, 5 )
x- direction : - 5 → 2 is + 7 units
y- direction : 0 → 5 is + 5 units
Translation rule is (x, y ) → (x + 7, y + 5 )
GEOMETRY QUESTION- Find m < h
9514 1404 393
Answer:
m∠H = 38°
Step-by-step explanation:
External angle GFD is the sum of internal angles G and H.
14x +1 = 89° +(5x -7)
9x = 81°
x = 9°
Then the measure of angle H is ...
angle H = 5(9°) -7° = 38°
Pls I need help!!!Question 6 (Essay Worn 6 points) (06.03) 9(5x + 1) = 37 From the expression above, pronde an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write 'not present."
Answer:
5x+1=6.136
5x=6.136-1
5x=5.136
x=5.135/5
x=1.03
x=1
What number line shows Point A at -4, Point B at 2.5, Point C at -2 1/2, and Point D, which is the opposite of Point A.
Answer: Choice A
Explanation:
Since -3/5 > -0.8, this means -3/5 is to the right of -0.8
Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.
Any negative value is always to the left of 0, so -3/5 is to the left of 0.
That's why the answer is choice A.
Shaded areas ( What is the area of the shaded region? )
Answer:
119.43 cm²
Step-by-step explanation:
The shaded area (A) is calculated as
A = area of rectangle - area of circle
= (11 × 12) - π × 2²
= 132 - 4π
≈ 119.43 cm² ( to the nearest hundredth )
solve this questions
Answer:
3 a) solution:-
Discount=Rs 1,200
S .P =RS 4,000
M P=?
we know that,
Discount= M.P - S.P
or, Rs 1,200= M.P - Rs 4,000
or, M.P = RS (4,000-1,200 )
M.P = RS 2,800
In no. 3 all we have to make like this .........
Hope it helps
Answer:
Step-by-step explanation:
2)a) M.P =₹ 5000
S.P = ₹4000
Discount amount = M.P - S.P
= 5000 - 4000
= ₹1000
Discount percent = [tex]\frac{discount \ amount}{M.P}*100[/tex]
[tex]= \frac{1000}{5000}*100\\[/tex]
= 20%
3)a) Discount = ₹ 1200
S.P = ₹ 4000
M.P = S.P + discount
= 4000 + 1200
= ₹ 5200
4)a ) Discount rate = 15%
S.P= ₹ 4000
[tex]M.P = \frac{100+Discount rate}{100}*S.P\\\\=\frac{115}{100}*4000[/tex]
= ₹ 4600
Inverse trigonometry functions I need help finding the answers everything I’ve tried says it’s wrong
Answer:
see below
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 13/20
Taking the inverse cos of each side
arccos ( cos x ) = arccos( 13/20)
x = arccos ( 13/20)
x =49.45839
x = 49 to the nearest whole number
sin theta = opp/ hyp
sin y = 13/20
Taking the inverse sin of each side
arcsin ( sin y ) = arcsin( 13/20)
y = arcsin ( 13/20)
y=40.5416
y = 41 to the nearest whole number
Setting y = 0 allows you to determine the what
of a graph
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
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10,4,7
The above set 4 numbers have a mean of 8
what could the mystery number
11 is the mystery number
Answer:
The mystery number is 11
Step-by-step explanation:
→ Set up an equation
( 10 + 4 + 7 + x ) ÷ 4 = 8
→ Multiply both sides by 4
21 + x = 32
→ Minus 21 from both sides
x = 11
An object that weighs exactly 1
pound is placed on a digital scale that measures weight in ounces.
If the scale is accurate and precise, what weight might be shown on the scale?
pls help !! answer both 1a and 1b pls
Answer:
KM = 50 mm , ∠ K = 104°
Step-by-step explanation:
Note that KM = KL = 50mm ( congruent legs )
This indicates the triangle is isosceles with base angles congruent, both 38°
∠ K = 180° - (38 + 38)° = 180° - 76° = 104°
Answer:
So the answer is 398°
Step-by-step explanation:
hope it helps
Please help explanation if possible
Answer:
y=-3x+5
Step-by-step explanation:
concepts: y=mx+b is slope intercept equation formula
m=slope
b= y intercept
Therefore we need to find the slope and y intercept
first find slope
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
let y2 be 2
let y1 be -4
let x2 be 1
let x1 be 3
[tex]\frac{2-(--4)}{1-3}[/tex]
6/-2 = -3
m=-3
slope is -3
y= -3x+ b
we need find y intercept now
just plug in (1,2) into that equation
2=-3(1)+b
b=5
y=-3x+5
Which regular polygon can be used to form a tessellation?
I need help
Answer: Option 4 (Hexagon)
Step-by-step explanation:
A equilateral triangle, square and hexagon can be used to form a tessellation.
Please click thanks and mark brainliest if you like
An expression is shown below: \sqrt(50)+\sqrt(2) is it irrational or rational
Answer:
Irrational
Step-by-step explanation:
It's an irrational number since both of them are irrational
5. For an acute angle 0, cos(0) = sin(33) is true. What is the value of 0?
Answer:
Value is 57
Step-by-step explanation:
sin 33
= sin (90-57)
= cos 57
Answered by GAUTHMATH
3/4plus 1/9
In the simplest form
Answer:
0.861
Step-by-step explanation:
Answer:
31/36
Step-by-step explanation:
3/4 + 1/9
= 31/36 --> this is the simplest form, you can't simplify any further.
when graphing y=-2x+10, is it a line that shows only one solution to the equation, all solutions, or shows the y-intercept?
Answer:
there is always a y-intercept in all graphs.
Step-by-step explanation:
be it a line graph, quadratic graph or cubic graph. all graphs will definitely have a y-intercept. and in this case, since y=mx + c where c is the y-intercept. the y intercept of this graph is 10
simplify 4x^2-3xy+2xy+9x^2
Answer:
13x^2 - xy
Step-by-step explanation:
4x^2-3xy+2xy+9x^2
=13x^2-xy
what is 7/8 divided by 1/8
Answer:
7
Step-by-step explanation:
Concepts:
Division: a system of distributing a collection of things into equal partsFractions: #s that represent a part of a wholeDividing Fractions: dividing a fraction by another fraction = multiplying the fraction by the inverse (reciprocal) of the other oneInverse Operations: operations that are opposite of each other (e.g. inverse of addition is subtraction)Solving:
1. First, let's set up the equation:
7/8 ÷ 1/8
2. We can get the reciprocal of 1/8 by doing the opposite of division; multiplication. 1/8 becomes 1 · 8, and that's equal to 8.
3. Now, since we know dividing a fraction by another one is exactly the same as multiplying the fraction by the reciprocal of the other, let's multiply 7/8 by the inverse of 1/8, which is 8.
7/8 · 8 = 56/8 = 7
Therefore, 7/8 divided by 1/8 is equal to 7.
On Saturday, the fruit and juice bar was selling 22 glasses of fruit punch an hour. By 4 p.m., they had sold 132 glasses. If their goal was to sell more than 264 glasses of fruit punch, which inequality can be used to find h, the number of hours they must stay open to make their goal?
A. 132 + 22h > 264
B. 22h < 264 + 132
C. 132 + 22h < 264
D. 132 + 264 > 22h
Answer:
A. 132 + 22h > 264
Step-by-step explanation:
Hourly sales = 22 glasses of fruit punch
Sales by 4 p.m = 132 glasses
Goal = more than 264 glasses
h = number of hours they must stay open to make their goal
The inequality:
132 + 22h > 264
22h > 264 - 132
22h > 132
h > 132/22
h > 6 hours
This means, the number of hours they must stay open to make their goal of more than 264 glasses is more than 6 hours
The height and radius of a cone are each multiplied by 11. What effect does this have on the volume of the cone?
The volume of the cone is multiplied by (Blank 1).
The volume of the new cone would be 1331 times more than the volume of the original cone. Thus, The volume of the original cone is multiplied by 1331
The volume of the cone can be calculated by the given formula:
The volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
where r = radius of the cone
h = height of the cone
Solution:
The volume of the original cone= .......1
It is given that the height and radius of a cone are multiplied by 11.
then volume
= [tex]\frac{1}{3} \pi (11r)^{2} (11h)[/tex]
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex] .........2
The change in volume of the cone after multiplying 11 to r and h would be
dividing equation 2 by equation 1
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex]/[tex]\frac{1}{3} \pi r^{2} h[/tex]
= 121*11
= 1331
Thus, The volume of the original cone is multiplied by 1331
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The receipt shows the prices of goods that Mr. Baker bought at the store.
The state Mr. Baker lives in has a sales tax rate of 7% on all purchases.
How much money does Mr. Baker pay in sales tax and what is the total amount he must pay for his purchases?
Answer:
The answer is $82.46 sales tax
$1,260.46 Total
Step-by-step explanation:
Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46
Simplify [2(5 – 4) + 6(7 – 3)] ÷ 2
I'LL MARK BRAINLY PLEASE HELP ME I'M STRUGGLING
Answer:
13
Step-by-step explanation:
[2×1+6×4]÷2
[2+24]÷2
26÷2
13
Hey can someone help me figure out what 3/4(x-8)=12
Answer:
x=24
Step-by-step explanation:
3/4(x-8)=12
Multiply each side by 4/3
4/3*3/4(x-8)=12*4/3
x-8 = 16
Add 8 to each side
x-8+8 = 16+8
x=24
Answer:
x = 24
Step-by-step explanation:
Essentially, you need to break this apart.
You need to isolate the x to figure it out with division or something.
To isolate, you need to get rid of the numbers around it.
To get rid of the 3/4, you can convert it to a decimal to make it easier, and then divide both sides by 0.75 to get rid of it on the x's side.
You now have
x-8 = 12/0.75
You can quickly punch the right side into a calculator to make it easier.
x - 8 = 16
You then add 8 to both sides to finish off the x, to get
x = 24
