Answer:
Step-by-step explanation:
n is an integer greater than 1
Prove algebraically that 10+ n^2 - (n - 2)^2 is always an even number.
Your final line must have, 'always even' as part of the line.
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.
6. Adlise Leiber started the day with a bank balance of $343.64.
She used another bank's ATM to withdraw $100 cash. The
charge for using the ATM was $2.50. Adlise then used her
card to make purchases of $85.10, $23.95, and $8.47. Find
the balance in her account after the bank processed these
transactions.
Answer:
$123.62
Step-by-step explanation:
85.10 + 23.95 + 8.47 = 117.52
117.52 + 100 + 2.50 = 220.02
$343.64 - $220.02 = $123.62
PLS HELP WILL MARK YOU BRAINLIEST!
Answer:
Option C
Step-by-step explanation:
[tex]\frac{(2x^3y^2z)^2(-3xyz^2)^2}{18x^6y^7z^3} =[/tex]
[tex]\frac{(4x^6y^4z^2)(9x^2y^2z^4)}{18x^6y^7z^3} =[/tex]
[tex]\frac{36x^8y^6z^6}{18x^6y^7z^3} =[/tex]
[tex]\frac{2x^2z^3}{y}[/tex]
Please answer! I’ll give you Brainliest
A)
The four small squares are all 3x3, so the perimeter is 3+3+3+3 = 12.
12 * 4 = 48
We can find the perimeter of the large diamond shape using the Pythagorean theorem, a^2 + b^2 = c^2
a = 4
b = 4
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
c = 5.65685425
So the perimeter of the large diamond shape is
5.65685425+5.65685425+5.65685425+5.65685425 = 22.627417
48+22.6 = 70.6
B)
The areas of the small squares are 3x3 = 9
9 * 4 = 36
The area of the large diamond shape is
5.65685425 * 5.65685425 = 32
36 + 32 = 68
I need #8 done (Show work) will mark brainliest
Answer:
see explanation
Step-by-step explanation:
Since BD bisects ∠ ABC , then
∠ ABD = ∠ DBC , substitute values
3x + 4 = 55 ( subtract 4 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
Step-by-step explanation:
Statement Reason
BD bisects ∠ABC Given
m∠ABD = (3x + 4)°, m∠DBC = 55° Given
∠ABD ≅ ∠DBC Definition of angle bisector
3x + 4 = 55 Definition of congruence
3x = 51 Subtraction property
x = 51/3 Division property
x = 17 Proved
What is the value of x?
Answer:
x = 9
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!
Answer:
1 and 3
Step-by-step explanation:
The reason 1 and 3 are similar due to the fact 3x2 is 6 (one side of 3) and 5x2 is 10 (another side of 3) therefore they are similar because one is sized up slightly.
The formula for area of a trapezoid is A =1/2 h(b1 + b2). Express h in terms of A, b1 and b2
Answer:
H is the height
Step-by-step explanation:
A= Area
B= Base
1/2= 0.5
PLZZZ HELP FOR BRAINLIST
Answer:
I D K GUESS ITS 1 2 4 I GUESS THINKING
Step-by-step explanation:
Type the expression that results from the following series of steps
Start with y subtract d, multiply by a, then add c.
Answer:
(y-d) × a + c
Step-by-step explanation:
You start with y:
y
subtract d:
y-d
multiply by a:
(y-d) × a
then add c:
(y-d) × a + c
Hope that helps! :)
plz help me fast Simplify t12/t6
Answer:
t^6
Step-by-step explanation:
when dividing exponents, you subtract (refer to exponent rule)
t^12 - t^6 = t^6
John rented a jet ski for $199.95. The rental included a rental fee of $75 and an additional charge of $24.99 per hour. How many hours did John rent the jet ski?
Answer:
John rented the jet ski for 5 hours
Step-by-step explanation:
Step 1- Subtract $75 from $199.95 and you should end up with $124.95
Step 2- Divide $124.95 by $24.99 and you should end up with 5
Step 3- John rented the jet ski for 5 hours
Answer:
John rented the jet ski for 5 hours.
Step-by-step explanation:
Take the total cost: $199.95, and subtract $75 because that was included in the cost. You get 124.95. Next you divide $24.99 by 124.95, because $24.99 was the amount he paid per hour, and $124.95 is the amount that he paid in total for all the hours that he jet skied, and you get 5 hours.
Find the value of question mark
0.0346 written in standard form
Answer:
3.46x10-2
×
10
−
2
3.46
×
10
−
2
Explanation:
a number expressed in
standard form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
a
×
10
n
2
2
∣
∣
∣
−−−−−−−−−−−−
where
1
≤
a
<
10
and n is an integer
express
0.0346
as a number between 1 and 10
3
∙
46
we now have to move the decimal point 2 places to
the left to retain equality
move to the right
→
then n is positive
move to the left ←
then n is negative
⇒
0.0346
=
3.46
×
10
−
2
A group of 8 people are sharing jellybeans each person wants 4 jellybeans and each bag has 7 jellybeans how many bags should they order
Answer:
5 bags
Step-by-step explanation:
if eight people each want four jellybeans you can multiply eight by four and get 32 jelly beans
this is the amount they need: 32
so we divide 32 by 7 to find out how many bags we need
32/7 is 4.57... so we need 5 bags because you cannot order half a bag
which ordered pair represents the coordinate of point h?
(0.6, - 1.4) (-1.4, 0.6) (-1.2 , 0.3) (0.3, - 1.2)
Answer:
-1.2 is the answer i think
Order from least to greatest.
595.05, 595.50, 595.005
Answer
595.005, 595.05,595.50 that's from least to greatest. please let me have brainliest
Step-by-step explanation:
595.005 , 595.50 595.05
Of the 250 sheep in a flock, 42% are spotted. What is the total number of spotted sheep in the flock?
Answer:
should be 105 right
Step-by-step explanation:
Answer:
105 sheep are spotted.
Step-by-step explanation:
42% of the 250 sheep are spotted. We would need to find 42% of 250.
250 * 0.42 = 105
105 sheep are spotted.
Hope this helps.
Eduardo spent 35% of his time at the theme park on a roller coaster if he was there for eight hours how much time did you spend on roller coasters
Answer:
2.8
Step-by-step explanation:
How many solutions does 7( X -5 ) = X +13
Answer:
x=8 (one solution)
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
7(x−5)=x+13
(7)(x)+(7)(−5)=x+13(Distribute)
7x+−35=x+13
7x−35=x+13
Step 2: Subtract x from both sides.
7x−35−x=x+13−x
6x−35=13
Step 3: Add 35 to both sides.
6x−35+35=13+35
6x=48
Step 4: Divide both sides by 6.
x=8
Answer:
x = 8 (one solution)
Step-by-step explanation:
7x - 35 = x + 13
-x -x
6x - 35 = 13
+35 + 35
6x = 48
divided by six on both sides
x = 8
Elimination Method: 6x - 4y = -24 and 4x + 5y = -2
Answer:
[tex](-2;-6)[/tex]
Step-by-step explanation:
First of all, let's rewrite the first one after dividing both sides by 2.
[tex]\left \{ {{3x-2y=-12\atop {4x+5y=-2}} \right.[/tex]
Now, let's pick one you want to eliminate.
Eliminating x: Let's multiply the first one by 4, the second by 3, and subtract one from the other. Rest is simply solving an equation in one variable
[tex]4I-3II : 12x-8y-12x+15y = -48 - (-6)\\7y = -42 \rightarrow y= -6[/tex]
Eliminating y: Let's multiply the first by 5, the second by 2, and add them together. Rest is simply solving an equation in one variable
[tex]5I+2II: 15x -10y +8x +10y = -60 +4\\23x = -56 \rightarrow x=-2[/tex]
Solve -4=2/7p. solve for p
Answer:
forma exata
p=-1/14
Step-by-step explanation:
p=-0.0714285
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
Answer:
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
Step-by-step explanation:
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
The constant of proportionality for the relationship of letters to minutes is 180.
What is Proportionality?Two set of quantities are said to be directly proportional or just simply proportional if the corresponding elements of these two sets has a constant ratio. This constant is called the proportionality constant or coefficient of proportionality.
We have the proportional relationship between letters typing and the time in minutes taken to type the letters.
Time taken by Shama to type 12 letters = 4 seconds
= 4 / 60 minutes
= 1/15 minutes
Proportionality constant can be found by taking the ratio of these quantities.
That is, proportionality constant = 12 / (1/15)
The fraction in the denominator will be taken to the numerator as the reciprocal and the operation changes into multiplication.
Proportionality constant = 12 × (15/1) = 180
Hence the proportionality constant for the relationship of the quantities letters and minutes is 180.
To learn more about Proportionality, click :
https://brainly.com/question/29126727
#SPJ5
[tex]\sqrt{17} \times \sqrt{17}[/tex]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The equivalent value is ~
[tex] \boxed{17}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
[tex] \sqrt{17} \times \sqrt{17} [/tex][tex]( \sqrt{17}) {}^{2} [/tex][tex]{(17 {}^{ \frac{1}{2}}) }^{2} [/tex][tex]17[/tex]Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers
Step-by-step explanation:
two consecutive numbers means that one is larger by 1 than the other number.
so, we have to choices depending on whether the first number (multiplied by 3) is the larger one, or the second number.
to show what I mean, let's start with the second number being the larger one.
we are dealing therefore with x and (x+1).
3x + (x+1) - 2 = 144
4x - 1 = 144
4x = 145
x = 145/4
this is not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution.
therefore we are checking the other approach :
we are dealing therefore still with x and (x+1). but now we multiply the other number by 3.
3(x+1) + x - 2 = 144
4x + 1 = 144
4x = 143
x = 143/4
this is still not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution either.
and now I am beginning to think you left out some important information in the question.
could it be these 2 numbers are consecutive even or consecutive uneven numbers ?
because then the difference between the both of them is 2 and not 1.
we are dealing therefore with x and (x+2). first attempt to make the smaller number the "first" number :
3x + (x+2) - 2 = 144
4x = 144
x = 144/4 = 36
ah ! now that looks different !
36 and 38 are valid solutions under the changed assumptions. and we are dealing with consecutive even numbers.
let's check :
36×3 + 38 - 2 = 36×3 + 36 = 36×4 = 144
correct.
and fun fact, if we turn this around and make the larger number the "first" number, we are still dealing with x and (x+2), but now we multiply the larger number by 3 :
3(x+2) + x - 2 = 144
4x + 6 - 2 = 144
4x + 4 = 144
4x = 140
x = 140/4 = 35
35 and 37 are also valid solutions under the new assumptions and two consecutive uneven numbers ...
so, please check what your original question (and maybe the headlines and description around it) says. and then pick the right solution.
plus $5 per day. The fee for the game booth is $50 plus $7 per day.
Write an expression for how much both booths will cost for the same number of days.
Question:
A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game both is $50 plus $7 per day. Write an expression for how much both will cost for the same number of days.
Answer:
105 times 15= 1575
57 times 20= 1140
1140+1575= 2715
(2715)(d)= x
The standard diameter of a golf ball is 42. 67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0. 002 mm. Which function could represent this situation?.
The absolute value function that could represent this situation is:
[tex]|D - 42.67| = 0.002[/tex]
The absolute value function is defined by:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance of a point x to the origin.The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:
[tex]|D - 42.67| = 0.002[/tex]
A similar problem is given at https://brainly.com/question/24514895
10. El siguiente circulo está dividido en 8 rebanadas iguales. ¿Qué fracción del circulo está sombreada?
Answer:
2/8
Step-by-step explanation:
2/8 porque ahy 8 y 2 estan coloridas.Si gustarias simplifar seria .25
Laura has $96 to divide between her 3 friends. How much money does each friend get?
Answer: EACH FRIEND GETS 32 DOLLARS
Step-by-step explanation:
DIVIDE 96 BY 3
Answer:
$32
Step-by-step explanation:
Divide 96 to 3
96 ÷ 3
= $32
Can someone plz help me out i rlly need to pass this
In the diagram, z∘ and y∘ are the measures of two complementary angles.
Also, the measure of one of the angles is 29.6∘
What is the correct value for x?
Enter your answer as a decimal, if necessary, like this: 42.5
Answer:
x= 60.4
Step-by-step explanation:
y = 60.4
z= 29.6
x= 60.4
By complementary angle rule