Answer:
Proof below.
Step-by-step explanation:
Let f(n)=10+ n^2 - (n - 2)^2.
We want to prove f is even for integer n > or = 1.
Let's show f is even for the base case, n=1.
f(1)=10+1^2-(1-2)^2
f(1)=10+1-(-1)^2
f(1)=11-(1)
f(1)=10
f(1) is even.
Let's assume the for some integer k > or = 1 , we have f(k) is even. This means there is some integer m so that f(k)=2m.
Note: f(k)=10+ k^2 - (k - 2)^2.
We want to show f(k+1) is even.
f(k+1)=10+ (k+1)^2 - ([k+1] - 2)^2
f(k+1)=10+ (k+1)^2 - (k-1)^2
f(k+1)=10+ ((k+1)^2 - (k-1)^2)
That difference is a difference of squares. Let's try factoring it.
f(k+1)=10+ (k+1-[k-1])(k+1+[k-1])
f(k+1)=10+ (2)(2k)
Multiply:
f(k+1)=10+4k
Turns out we didn't even need to use our induction hypothesis since 10+4k is 2(5+2k) which makes f(k+1) even given the factor of 2 present.
This proves for all integers n>=1 that f(n) is even.
We could have this without induction then. Let's do that here below this line.
-------------------
10+ n^2 - (n - 2)^2
10+[n^2 - (n - 2)^2]
Factor difference of squares:
10+(n-(n-2))(n+(n-2))
Simplify:
10+(2)(2n-2)
Factor:
2[5+(2n-2)]
Because of the factor of 2, the given expression is always even for integer n.
What is the quotient of 36 and -3
(WILL MAKE BRAINLIEST )
plss answer it correctly...I need asap
Answer:
sorry I cannot understand that
Choose the equation that has m = 5 as the solution.
m + 4 = 20
m – 3 = 8
22 + m = 25
12 = m + 7
Combine the like terms to create an equivalent expression:
-12-6p-(-2)
Answer:-2(5+3p)
Step-by-step explanation:
Who Is Nathan Drake?
Answer:
he's the guy from uncharted
Answer: Nathan Drake is a fictional character and the protagonist of the Uncharted video game series, developed by Naughty Dog.
The sum of the squares of two numbers is 202 the difference of the numbers is -2 both numbers are positive find the numbers
Answer: a2 + b2 = 202
Step-by-step explanation: Since they are consecutive odd integers, then we can just divide 202 by 2, square root it, then round to the nearest two odd integers. In this case, 202 / 2 = 101 ⇒ 1010.5 ≈ 10.04. The two nearest odd integers are 9 and 11. We can verify that this is the pair: 92 + 112 = 81 + 121 = 202.
Answer:
[tex]\left \{ {x-y=-2\atop {x^2+y^2=202[/tex] ⇔ [tex]\left \{ {{y=11} \atop {x=9}} \right.[/tex]
Step-by-step explanation:
The range of F(x) = logo x is the set of all real numbers.
A. True
O B. False
Answer:
The range of F(x) = logo x is the set of all real numbers is True.
Step-by-step explanation:
Yes, Because range of the logarithmic function is the set of ''all real numbers.'
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ f (x) = log x
Now,
The given function is a logarithmic function.
And, The range of the logarithmic function is the set of all real numbers.
Hence, The range of function F(x) = log x is the set of all real numbers.
Thus, The range of F(x) = log x is the set of ''all real numbers''.
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the first term of an AP is 2,and the last term is 59.if the sum of the first terms is 610,Find the common difference
Answer:
d = 3
Step-by-step explanation:
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( a + l)
where a is the first term and l the last term
Here a = 2, l = 59 and sum = 610 , then
[tex]\frac{n}{2}[/tex] (2 + 59) = 610
[tex]\frac{n}{2}[/tex] × 61 = 610 ( divide both sides by 61 )
[tex]\frac{n}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )
n = 20
Then the sequence has 20 terms with a₂₀ = 59
The nth term of an AP is
[tex]a_{n}[/tex] = a + (n - 1)d
where d is the common difference , then
2 + 19d = 59 ( subtract 2 from both sides )
19d = 57 ( divide both sides by 19 )
d = 3
Find the slope from points (9,-13), (7,-11)?
That’s what my question is
Answer:
Step-by-step explanation:
The entered points belong to an increasing, linear function.
Equation: y = 1x + 4.
The currency in China is the Yuan. The
exchange rate is approximately $1 for
every 8 Yuan. At this rate, how many
Yuan would you get if you exchanged $10?
Answer:
80 Yuan for 10 Dollars
Step-by-step explanation:
1 dollar = 8 yuan
10 x 8 = 80
Answer:
80 yuan
Step-by-step explanation:
$1= 8
you have $10
10*8= 80
I’m a poll, 100 people were asked to indicate if they prefer to drive a truck or car and their gender. Based on the table, which of the following statements is NOT true?
Answer:
B) men are less likely to prefer driving trucks than women
Step-by-step explanation:
solve pls brainliest
Answer:
1/4
Step-by-step explanation:
The constant of proportionality is 1/4.
Answer:
b
Step-by-step explanation:
The form of an equation representing proportion is
y = kx ← k is the constant of proportionality
y = [tex]\frac{1}{4}[/tex] x ← is in standard form
with k = [tex]\frac{1}{4}[/tex]
(9u+w)^2
(use foil).................
Answer:
Step-by-step explanation:
(9u + w)(9u + w)
f: 9u * 9u = 81 u^2
o: 9u * w
i: 9u* w
l: w * w = w^2
Result
81u^2 + 9uw + 9uw + w^2
81u^2 + 18uw + w^2
Can someone help ?????
Accordingly the answer is Nineteen Fourths.
If the simple interest on 4,000 for 10 years is 2,400 then what is the interest rate
Answer:
6%
Step-by-step explanation:
I =Prt I being interest paid, P is Principal, r is rate, t is term
2400=4000x r x 10
2400=40000r
2400/40000=.06 convert to percentage by multiplying by 100 x. 06=6
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 mL water
Answer:
7.5 g salt
10g yeast
50 ML oil
450 ML water
Step-by-step explanation:
You would do 1/4 of the amount of (insert ingredient amout) added to the total (insert ingredient amount)
Write an equation representing the area Felicia covered, y, in terms of the number of tiles she used, x. I'LL GIVE 40 POINTS
The proportional equation representing the area Felicia covered, y, in terms of the number of tiles she used, x is:
[tex]y = \frac{x}{6}[/tex].
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching this problem on the internet, we have that 6 tiles cover 1 square feet, 12 tiles cover 2 square feet, and so on, hence the constant is given as follows:
[tex]k = \frac{1}{6} = \frac{2}{12}[/tex]
Hence the function is given as follows:
[tex]y = \frac{x}{6}[/tex].
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Answer: Felicia's equation is:
y=1/9x
Step-by-step explanation:
You’re loading bags of cement into a truck. You load bags weighting 175lbs, 154lbs, and 118lbs. What is the total weight you have loaded onto the truck?
Answer:
447 lbs
Step-by-step explanation:
175+154+118=447
Find the unit rate to 30 1/2 and 1 1/4
Answer:
24.4
Step-by-step explanation:
yw
Can someone solve this for me please? I would be very thankful <3
Answer:
running speed is horse power
so up with horse
it will tell its power
go and denge it
so you will get your answer by this process
A student earned $175 last week. She worked 35 hours. How much did she earn per hour?
DO NOT GIVE A LINK AS AN ANSWER
Answer:
should be 5
Step-by-step explanation:
which of the following lines has a negative slope?
Red or Black,Blue
Answer:
black <3
Step-by-step explanation:
Which choice models this situation? Marcus needs to sell 25 tickets to a fundraiser by Friday. So far, he has sold 9 tickets. How many tickets does he still need to sell?
Answer:
16
Step-by-step explanation:
Because 25 - 9 = 16
y=-2/5x-3
plzz help help meeeeeeeee
Plot the vertex at (0,-3), then go down 2 units and right units to plot a point at (5,-5). Then you can draw your line through the 2 points.
Find the quotient of
4
5
and
9
10
Give your answer as a fraction in its simplest form.
Answer:
8/9
Step-by-step explanation:
4/5 ÷ 9/10
4/5 x 10/9
40/45 or 8/9
A division is a process of splitting a specific amount into equal parts.8/9 is the quotient for 4/5 ÷ 9/10.
What is Division?a division is a process of splitting a specific amount into equal parts.
While doing division process we have some important parts of division which are dividend, divisor, remainder and Quotient.
In the given problem 4/5 is he divisor and 9/10 is the divisor.
Four by five divided by nine by ten
4/5 ÷ 9/10
When two fractions are divided, the division turn to multiplication when the denominator fraction shifts to up.
4/5 x 10/9
Cross over the fraction with 5.
40/45
8/9
Hence 8/9 is the quotient for 4/5 ÷ 9/10.
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A man Buy television set at a price exclusive of sales tax for $2124 if sales tax of 12% is changed how much money does the man pay
Answer:
2378.88
Step-by-step explanation:
12/100 x 2124
=254.88
2124+254.88=answer
HELP
One chocolate bar and two coconut bars contain 780 calories. Two chocolate bars
and one coconut bar contains 786 calories. Find the number of calories in each kind
of bar.
Answer:
Choc Bar: 258 cals
Coco Bar: 264 cals
Step-by-step explanation:
What we can do here is something called making a system of equations.
Let us name the choc. bars x and the coco. bars y.
Then, we can get:
x+2y=780
2x+y=786
Next, we solve for x in the first equation
x=780-2y
Now, we can substitute:
2(780-2y)+y=786
1560-3y=786
-3y=-774
y=258
x=780-516
x=264
The points (5, -5) and (7,r) lie on a line with slope - 1. Find the missing coordinate r.
Answer:
r = -7
Step-by-step explanation:
Slope = Change in y/Change in x
-1 = r - (-5) / 7 - 5
-1 = r + 5/ 2
-2 = r + 5
r = -7
-Chetan K
An item is regularly priced at $27. It is on sale for 35% off the regular price. What would be the sale price?
Answer:
$17.55
Step-by-step explanation:
Answer:
17.55
Step-by-step explanation:
You will pay $17.55 for a item with original price of $27 when discounted 35%. In this example, if you buy an item at $27 with 35% discount, you will pay 27 - 9.45 = 17.55 dollars
For the function , what is the maximum value?
Answer:
The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph.
I hope it helps.