Answer:
See belowStep-by-step explanation:
Find the sum:
1/2n(n+1) + 1/2(n+1)(n+2) =1/2(n² + n) + 1/2(n² + 3n + 2) =1/2(n² + n + n² + 3n + 2) = 1/2(2n² + 4n + 2) = n² + 2n + 1 = (n + 1)²Proved
Solution:
Work:
[1/2(n)(n + 1)] + [1/2(n + 1)(n + 2)]Simplifying in Brackets
=> [1/2(n² + n)] + [1/2(n² + 2n + n + 2)]=> [n²/2 + n/2] + [n²/2 + n + n/2 + 1]Removing Brackets.
=> n²/2 + n/2 + n²/2 + n + n/2 + 1Solving.
=> n² + n + 1=> (n + 1)²Since the result has a "square" sign, the statement is proved has true.
Hoped this helped.
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Help me!!!
Find the equation of the locus of a point which moves so that (i) its abscissa is always 3 units.
Answer:
Can you show a screenshot of the problem
If there are 5 routes for traveling between two places A and B, how many option are there for a person travel from A to B and return back?
If you can repeat routes, then there are 5*5 = 25 different options
If you cannot reuse a road, then there are 5*4 = 20 different options
x > 7
On a number line
Answer:
Step-by-step explanation:
Look at attachment.
When drawing an equality on a number line, you must remember these two things:
The direction of the "alligator" matters. The alligator always favors the bigger number!
"...or equal to" matters. If it has an underline underneath the alligator, the dot should be closed - in other words, it should be filled in. You will lose points if you do not catch this.
If there is no underline, the dot should be open - in other words, a circle.
This problem is an open dot that goes towards infinity.
Question: What is the equation of this trend line?
Enter your answers by filling in the boxes
K=_ J+_
Answer:
A trend line is a straight line that illustrates the points on a scatter plot.
The equation of the trend line is: k = -2j + 24
Step-by-step explanation:
From the graph, we have the following points
(j, k) = (6, 12)(4, 16)
Start by calculating the slope
m = k2 - k1 / j2 - j1
So, we have:
m= 16 - 12 / 4 - 6
m = 4 / -2
m= -2
The equation is then calculated as:
k=m(j – j1) + k1
This gives:
k= -2(j - 6) +12
Expand
k= -2j + 12 +12
k= -2j + 24
Take 2 points (J,K)
(2,24)(4,20)[tex]\\ \tt\longmapsto m=\dfrac{20-24}{4-2}=\dfrac{4}{2}=2[/tex]
Equation
[tex]\\ \tt\longmapsto K-24=2(J-2)[/tex]
[tex]\\ \tt\longmapsto K-24=2J-4[/tex]
[tex]\\ \tt\longmapsto K=2J+20[/tex]
Find the greatest common factor of these two expressions.
20u®w and 28uºwy?
6 4 2
Answer:
brainlest answer please thanks and follow me
In the diagram, all measurements are in centimetres.
ABC is an isosceles triangle.
AB - 2x
AC - 2x
BC - 10
(a) Find an expression, in terms of x, for the perimeter of the triangle
Simplify your expression.
(2)
The perimeter of the triangle is 34 cm.
(b) Find the value of x.
Answer:
y = 4x + 10 x = 6
Step-by-step explanation:
a) perimeter = 2x + 2x + 10 = 4x + 10
b) perimeter = 34
⇒ 4x + 10 = 34
⇒ 4x = 34 - 10 = 24
⇒ x = 24 ÷ 4 = 6
GUYS PLEASE HELP ME ON THIS ONE!, i will give brainliest to the right answers
Aisha has $40 to spend for her ornithology club. She spends some of it buying birdseed and saves the rest. Her savings is given by f(x)=40−1.25x, where x is the number of pounds of birdseed she buys at $1.25 per pound.
Answer:
c. If x = 3. Substitute. f(3) = 40 - 3.75, which means if Aisha buys 3 pounds of birdseed, she saves $36.25.
c. If x = 18. Substitute. f(18) = 40 - 22.5, which means if Aisha buys 18 pounds of birdseed, she saves $17.50.
c. If x = 36. Substitute. f(36) = 40 - 45, which means if Aisha buys 36 pounds of birdseed, she needs $5.00 extra.
d. 8
Step-by-step explanation:
f(x) = 40 - 1.25x
c.
If x = 3. Substitute. f(3) = 40 - 3.75, which means if Aisha buys 3 pounds of birdseed, she saves $36.25.
If x = 18. Substitute. f(18) = 40 - 22.5, which means if Aisha buys 18 pounds of birdseed, she saves $17.50.
If x = 36. Substitute. f(36) = 40 - 45, which means if Aisha buys 36 pounds of birdseed, she needs $5.00 extra.
d.
x = x. f(x) = 40 - 1.25x = 30
1.25x = 10
Divide by 1.25 on both sides to isolate x.
x = 8
8 pounds is the answer.
Hope this helps :)
Have a nice day!
Please help I will give brainliest
Answer:
15
Step-by-step explanation:
1/2(5)(6) =
1/2(30) =
15
Answer:
Step-by-step explanation:
A = bh/2
= 6in(5in)/2
= 30in squared/2
= 15in squared
Yoko is going for a walk. She walks 6.4 miles in 4 hours. What is her speed?
4) It is known that 3 is the remainder when 99 is divided by a, and 70 is 2 short from being divisible by a. How many positive integers can a be
Answer:
5 integers: {4, 6, 8, 12, 24}Step-by-step explanation:
From the given info we have:
99 - 3 = 96 is divisible by the number, the number is greater than 3 since the remainder was 3.70 + 2 = 72 is divisible by same number.Using the above info, find all factors of the two numbers, greater than 3:
96 = 4*24 = 6*16 = 8*12 = 12*8 = 16*6 = 24*4 = 32*3 = 48*272 = 4*18 = 6*12 = 8*9 = 12*6 = 18*4 = 24*3 = 36*2The common divisors are:
4, 6, 8, 12, 24Which ones are right angles
PLS I NEED HELP RN!!!
Answer:
tbh idek that is
Step-by-step explanation:
6x-3x-7=x+2x-12
what type of solution is this?
Answer:
No Solutions
Step-by-step explanation:
First, let's simplify the equation:
Solve:
6x - 3x - 7 = x + 2x - 123x - 7 = 3x - 12-7 = -12See what happened! -7 does not equal -12, so this equation has no solutions
Another way:
6x - 3x - 7 = x + 3x - 123x - 7 = 3x - 123x + 5 = 3x5 = 0-Chetan K
Find the solutions to the system below
y=x2+6x
y=x−4
both and then combine them or just find them 1 by 1
balance on a 20,000 deposit earning 3.5% compounded quarterly after 10 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=20000\left(1+\frac{0.035}{4}\right)^{4\cdot 10}\implies A=20000(1.00875)^{40}\implies A\approx 28338.18[/tex]
Capacity planning answers the question "__________"
Answer:
How to be more efficient and how to pay for a project.
Hope it helps!
Step-by-step explanation:
DO U USE BRAINLY ALL THE TIME
yes yes yes yes yes yes yes yes yes yes yes yes yes yes
plsss answer the questions
Answer:
1) (7x - 8) - (2x + 4)
= 7x - 8 - 2x - 4
= 5x - 12
2) (8x - 6y) - (2x - y)
= 8x - 2x -6y + y
= 6x - 5y
3) (12xy + 5y) - (23xy - 3y)
= 12xy - 23xy + 5y + 8y
= -11xy + 13y
= 13y - 11xy
Fraction with a denominator of 6 that is greater than 2/4
Answer:
5/6
Step-by-step explanation:
If we simplify 2/4 to 1/2, now we can easily see that any fraction (with a denominator of 6) above 3/6 (also 1/2) is a correct answer.
In this case we only have two simplified fractions above 3/6 which are 4/6 (2/3), and 5/6.
We can choose 5/6 because it's the only fraction that is simplified and still has a denominator of 6. (Plus, it's greater than 2/4).
Hope this helps!!
Simplify the expression. Your answer must contain only positive exponents.
(7^-8)(7^3)
Answer:
[tex]\frac{1}{7^5}[/tex]
Step-by-step explanation:
When multiplying bases that are the same with different exponents, you add the exponents:
[tex]7^{-8}*7^3=7^{-8+3}=7^{-5}=\frac{1}{7^5}[/tex]
Which two expressions are prime polynomials? x2 - 5x + 3 oxx - xy² – x2 - 7x + 6 2xy - 4x2y3 + 5x8y2 X4y3 - 3x3 + 4x2y2 - x wa
Answer:
A polynomial is prime if it can not be factored into polynomials of lower degree also with integer coefficients.
For example, the first option:
x^3 + b*x^2 can be rewritten as:
(x - 0)*(x^2 + b*x)
So it is not prime.
The second option:
x^2 -4x - 12
Because here we can factor this into:
(x + 2)*(x - 6) = x^2 - 6x + 2*x - 12 = x^2 - 4x - 12
Now, the third option is a two variable polynomial, here the degree is equal to the sum of the degrees of both variables.
x^4 + 8*x*y^3
(x - 0)*(x^3 + 8*y^3)
So each side has a lower degree than the original polynomial, then it is not prime.
4th option:
x^2 - b^3
This can be written as:
(x + b^(3/2))*(x - b^(3/2))
Now, here we have a problem.
If for example, b = 1, this would not be a prime.
because 1^(3/2) = 1.
But if b^(3/2) is not an integer, then we can not factorize the initial polynomial into lower degree polynomials with only integer coefficients, then we can not be 100% sure that this is not a prime polynomial, then this is the correct option.
Select the equation that represents the question. 0.5% of what number is 12?
Write 33% as a fraction.
Use / to write your answer in fraction form. For example 1/2
Answer:
1/3, 2/6, 3/9
Step-by-step explanation:
33% is a third of 1, so 1/3
The product of 5p2q and -4p3q4 is
Answer:
-20p^5q^5
Step-by-step explanation:
20p^5q^5 that's your answer
Samantha surveyed 30 students at Texas Middle School.
Of those students, 21 said they would vote for Jenny for
cheerleader. There are 575 students who will vote in the
election. If the results of Samantha's survey are used to
predict the outcome of the cheerleader elections, about how
many votes would Jenny receive?
Answer:
C - 403
Step-by-step explanation:
One number is four less than a second number. Five times the first is 14 more than 3 times the second. Find the numbers.
Answer:
x=17 and y=13
Step-by-step explanation:
let y the first number and x the second number.
y+4=x
5y=14+(3x)
two equations with two unknowns
x=17 and y=13
Find the distance between the two numbers on a number line. Write your answer as a mixed number.
−7, −3 2/3
The distance between the two numbers is ???? Whoever can help me solve this thank you so much, you've made my day. Worth 20 points?????
Answer:
−7, −3 2/3
Step-by-step explanation: basically you take -3/7 and -2/3 subtract them. (-3/7) - (-2/3) find a common denominator and alter fractions based on it. -9/21 + (14/21)
Mr. Akika has 36 18 cent and 30 cent stamps all told. The stamps are worth $9.48. How many each kind of stamps does he have?
Answer:
30-cent: 2518-cent: 11Step-by-step explanation:
Using the generic solution we found in this problem ...
https://brainly.com/question/26243664
we find the number of 30-cent stamps to be ...
x = (948 -36(18))/(30 -18) = 300/12 = 25
Mr. Akira had 25 30-cent stamps and 11 18-cent stamps.
Suppose that BCD is isosceles with base BC. Suppose also that m B=(2x+47) and m D= (3x+51). Find the degree measure of each angle in the triangle
Answer:
57, 57, 66
Step-by-step explanation:
This is isosceles, so angle B is the same measure as angle C, and all 3 angles add to 180.
2x+47 + 2x+47 + 3x+51 = 180
7x + 145 = 180
7x = 35
x = 5
Angles B and C are 2x + 47, so 2(5) + 47 = 57
Angle D is 3x+51, so 3(5) + 51 = 66
A plant is already 11.00 meters tall, and it will grow 25 centimeters every month. The plant's helght, H (in meters), after x months is given by the following.
H= 11.00 +0.25x
What is the plant's height after 15 months?
Answer:
14.75
Step-by-step explanation:
Since x represents the months and we're solving for 15 months, you substitute x for 15. Then you solve it like any other equation.
H=11.00 + 0.25(15)
H= 11.00 + 3.75
H= 14.75
