heres the table and graph

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.

Answer:

Gross Pay for 1 paycheck

Deductions for federal tax, state tax, and city tax hope it helps :)

Step-by-step explanation:

The net monthly income of Jason is $194.68 and the net annual salary is 23324.16.

Gross pay of an employee is basically sum of his basic pay, dearness allowance, any other allowance only. Public providend fund, income tax are not deducted from it.

1) Gross paycheck=2*40*25.5=$2040.

2) Federal tax=2040*21%=$428.4

3) State tax=25=$25

4) City tax=2040*12%=$244.8.

5) Deductions=2040*12.45=$252.96.

6) Net monthly income=2*(Gross pay-federal tax-state tax-city tax-deductions-deductions for F.IC.A. or social security tax)

=2*[2040-428.4-25-244.8-252.96-117]

=1943.68

7) Net annual salary=12* net monthly income.

=1943.68*12  ( 1year= 12 months)

=$23324.16

Hence the net monthly income of Jason is $194.68 and the net annual salary is 23324.16.

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There are 5 ways you could choose the group in tennis.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The total no of students is 16,

As there can be only a maximum of 10 students in a group,

If the student in Swimming is 10 then in Tennis it will be 6,

If the student in Swimming is 9 then in Tennis it will be 7,

If the student in Swimming is 8 then in Tennis it will be 8,

If the student in Swimming is 7 then in Tennis it  will be 9,

If the student in Swimming is 6 then in Tennis it will be 10,

Therefore, there are 5 ways you could choose the group in tennis.

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Answer:

25x - 4

Step-by-step explanation:

10x + 2 + 8x + 7x - 6

= 25x - 4

Answer:

-500

Step-by-step explanation:

i knew the answer

have a great day ;)

Step-by-step explanation:

option A is correct answer

Answer:

Should be C if not then A

Step-by-step explanation:

Answer: 6457/25=258.28

Step-by-step explanation:

Answer:

258.28  Hope this helps! Please mark brainliest it means a lot to me

Step-by-step explanation:

Th=0

H=2

T=5

0=8

tenth=2

hundredth=8

You could get the answer by doing long division/standard algorithm

A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:

B. Substitution Angle Angle Postulate.

A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is [tex]360^{o}[/tex].

To prove that ∠ BAD ≅ ∠ DCB, we have:

Given parallelogram ABCD;

<BAC ≅ <ACD (alternate angle theorem)

<DAC ≅ <ACB (alternate angle theorem)

<BAC + <DAC = <BAD

Also,

<BCA + <DCA = <BCD

Therefore,

<BAD ≅ <DCB (Substitution Angle Angle Postulate)

Thus, the missing reason in the partial proof is:

option B. Substitution Angle Angle Postulate

A sketch is attached to this question for more clarifications.

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Answer:

19 or 17

Step-by-step explanation:

Answer:

c = 2.

Step-by-step explanation:

When the first part of the function has the value 0,  f(x) will also be 0 if the c wasn't there.

So the value of c is 2.

From the given graph n is a positive odd number.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

From the graph,

All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.

So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).

Also, we can see that the function increases, if n was a negative number, like: n = -N

We would have: [tex]f(x)=\frac{a}{(x+k)^{\frac{1}{N} }} +c[/tex]

So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.

Then n is a positive odd number.

Therefore, n is a positive odd number.

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Answer:

The discount is $77, and the discount percent is 5%

Step-by-step explanation:

Discount: $1,540 - $1,463 = $77

Discount percent: $1,463 / $1,540 = 0.95, 1.00 - 0.95 = 0.05, 0.05 = 5%

Answer:

E

Step-by-step explanation:

We must write and solve a system of equations to see how many of each type of coin Carlos has.

The answer is:

We start by defining the variables:

We know there are 46 coins in total, thus:

x + y + z= 46

The number of pennies and dimes is the same, thus:

x = y

The total value of the coins in the box is $4.09, then:

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

So we can write the system of equations:

x + y + z= 46

x = y

x*$0.01 + y*$0.10 + z*$0.25 = $4.09

First, we can replace x by y in the first and third equations (by using the second one) to get:

2y + z =  46

y*$0.11 + z*$0.25 = $4.09

Now we can isolate z in the first equation to get:

z = 46 - 2y

And replace that in the other equation:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

Now we can solve the equation for y:

y*$0.11 + (46 - 2y)*$0.25 = $4.09

y*$0.11 + $11.50 - y*$0.50 = $4.09

y*($0.11 - $0.50) = $4.09 - $11.50

y*(-$0.39) = -$7.41

y = (-$7.41)/(-$0.39) = 19

if y = 19, then x = 19

By using the first equation:

x + y + z = 46

19 + 19 + z = 46

z = 46 - 19 - 19  = 8

We can conclude that:

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Answer:

The answer would be -7/12

Step-by-step explanation:

Use math.way itll help you tremendously :)

The number is 3947

It should be noted that 36 hundreds will be equal to:

= 36 × 100

= 3600

It should be noted that 34 tens will be:

= 34 × 10

= 340

7 ones will be:

= 7 × 1

= 7.

Therefore, the sum will be:

= 3600 + 340 + 7 = 3947

Answer:

3947

Step-by-step explanation:

2 − 3 = −5

First we need to Add 3 to both sides of the equation:

2 − 3 + 3 = −5 + 3

Then we simplify:

2 = −5 + 3

 2 = −2

Now we divide both sides of the equation by the same term:

2 / 2 = −2 / 2

Final answer: = −1

I hope this helps!

Answer:

Y= - 1

Step-by-step explanation:

2y-3= - 5

  +3    +3

   2y= -2

   /2    /2

Y= -1

Step 1: Add 3 to both sides because you want to cancel out the 3 so you do the opposite of what is say's. For example, if it says 2y-3 add 3 or 2y+3 subtract 3 from both sides.

Step 2: Add 3 to -5 which would be -2

Step 3: Since you're "multiplying" Y to 2 you're going to divide 2 to get Y by itself. So 2/2 cancels out and now you're left with y

Step 4: Divide 2 form -2 and you get -1

Let me know if you have any questions and I hope this helps

Answer:

108$.

Step-by-step explanation:

Answer:

subtract the actual measurement from the initial measurement

ie. 92-90.3 =1.7 %

You can calculate the error and then measure how much percent of the real value, the error came.

The percent error in the considered measurement is of approx 1.88%

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To calculate percent error, we will measure how much percent of actual value, the error is, in the estimated value.

[tex]\text{Percent error} = |\dfrac{Error}{\text{Actual value}}| \times 100 = |\dfrac{\text{(Actual value - Estimated value)} }{\text{Actual value}}| \times 100[/tex]

Sine in the given condition, we have:

Thus, we have

Error = 90.3 - 92 = -1.7 miles per hour

Thus, the percent error is calculated as:

[tex]\text{Percent error} = |\dfrac{-1.7 }{90.3}|\times 100 = \dfrac{1.7 \times 100}{90.3} = \dfrac{170}{90.3} \approx 1.88\%[/tex]

Thus,

The percent error in the considered measurement is of approx 1.88%

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Answer:

lower left

Step-by-step explanation:

v+3<=6.5

v<=3.5

-18 is less than 3.5

Step-by-step explanation:

It can't be the first one because [tex]v=-18[/tex] and were saying [tex]-v[/tex] and to negatives make a positive so our equation is

[tex]18+3[/tex] ≤[tex]-6.5[/tex] which is incorrect

The one below the first one is incorrect

It's correct since our equation is

[tex]-18+3\leq 6.5[/tex] which is correct

The top right one is correct because our equation is

[tex]18+3\leq 6.5[/tex] which is incorrect

The one below that is correct because our equation is

[tex]-18+3\geq 6.5[/tex] which is incorrect

Answer:

x = 6

Step-by-step explanation:

To get rid of the fraction at the left side of the equation, multiply both sides by 4

20x + 60 = 180 now subtract 60 from both sides

20x = 120 divide both sides by 20

x = 6

Btw also found a spelling mistake in the question:instead of newtons you put netwons-      lol-

btw  

Rounded to the nearest thousandth would be 4.444 Newtons (same units you solved for k with)

But anyway here you go:

Answer:

x-2y=12

Solve for y

x-2y=12

Subtract x on both sides

-2y=-x + 12

Divide both sides by -2

y=\frac{1}{2}x - 6y=21x−6

the domain is {-3,-1,0,2,5}

Domain are the set of x values

Range are the set of y values

We are given with domain x, we need to find out y values using the equation y=\frac{1}{2}x - 6y=21x−6

when x=-3 , y=\frac{1}{2}(-3)-6=\frac{-15}{2}=-7.5y=21(−3)−6=2−15=−7.5

when x=-1 , y=\frac{1}{2}(-1)-6=\frac{-13}{2}=-6.5y=21(−1)−6=2−13=−6.5

when x=0 , y=\frac{1}{2}(0)-6=-6y=21(0)−6=−6

when x=2 , y=\frac{1}{2}(2)-6=-5y=21(2)−6=−5

when x=5 , y=\frac{1}{2}(5)-6=\frac{-7}{2}=-3.5y=21(5)−6=2−7=−3.5

Range is {-7.5, -6.5, -6 , -5, -3.5}

Step-by-step explanation:

solve the equation ? 1 equation with 2 variables ? that is not possible.

what you mean is probably find the range.

x - 2y = 12

-2y = -x + 12

2y = x - 12

y = (x - 12)/2 = (1/2)x - 6

x = -3

y = 1/2 × -3 - 6 = -1.5 - 6 = -7.5

x = -1

y = 1/2 × -1 - 6 = -0.5 - 6 = -6.5

x = 0

y = 1/2 × 0 - 6 = -6

x = 2

y = 1/2 × 2 - 6 = 1 - 6 = -5

x = 5

y = 1/2 × 5 - 6 = 2.5 - 6 = -3.5

so, the corresponding range of the function is

{-7.5, -6.5, -6, -5, -3.5}

Answer:

54°

Step-by-step explanation:

All the angle measures of a triangle must add up to equal 180°. So,

59°+67°+x°=180°

x=54°

Using proportions, it is found that the height of the lighthouse is of 84 ft.

The rule of three is:

5.25 feet - 8 feet

x feet - 128 feet

Applying cross multiplication:

[tex]8x = 5.25(128)[/tex]

[tex]x = \frac{5.25(128)}{8}[/tex]

[tex]x = 84[/tex]

The height of the lighthouse is of 84 ft.

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Answer:

parallel, perpendicular are opposite

Answer:

PARALLEL PERPENDICULAR

Step-by-step explanation:

Answer:

top to bottom,

Yes

No

Yes

Yes

Answer: x=-2

Step-by-step explanation:

Add three to both sides of the equation

4x-3=2x+7

4−3+3=2−7+3

simplify

4=2−4

4−2=2x-4−2

simplify

2=−4

Divide both sides of the equation by the same term

2=−4

2/2=−4/2

=−2

Answer: x = 5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.x=5