(10^2+8^2+6^2+4^2+2^2)- (9^2+7^2+5^2+3^2+1^2)

4x - 5y = -12

-x + 5y = 18

Add the equations together:

4x + -x = 3x

-5y + 5y = 0

-12 + 18 = 6

So now you have:

3x = 6

Divide both sides by 3:

X = 2

Now you have the value of x, replace x with 2 in one of the equations and solve for y:

4(2) -5y = -12

8 -5y = -12

Subtract 8 from both sides:

-5y = -20

Divide both sides by -5:

Y = 4

The solution is x = 2 and y = 4 which is written as (2,4)

Answer:

LN=4

Step-by-step explanation:

Since BA is the mid-segment of ΔLMN the end-segment will be twice the length. [tex]2*2=4[/tex]

Answer:

1. (you could have used your calculator too ...)

625

46225

11.56

1.5625

0.3364

2. a, b, c, d are not prefect squares

3. a and c squares will end with a "1" in the units place.

4. b and c squares will end with a "6" in the units place.

5. a. 17

b. 161

6. 25

7. a. 144 + 145

b. 264 + 265

c. 480 + 481

d. 1012 + 1013

8. a, d, e

9. a. d

Step-by-step explanation:

1. is just plain calculator work

2. a. no perfect square

Property 1: A number having 2, 3, 7 or 8 at unit’s place is never a perfect square. In other words, no square number ends in 2, 3, 7 or 8.

2. b. no perfect square

Property 2: The number of zeros at the end of a perfect square is always even. In other words, a number ending in an odd number of zeros is never a perfect square.

2. c. no perfect square

the same as 2.b.

2. d. no perfect square

the same as 2.a.

2. e. is a perfect square (of 250)

3.

Property 6: The unit’s digit of the square of a natural number is the unit’s digit of the square of the digit at unit’s place of the given natural number.

for 81² : as 1²=1, therefore 81² will also end with a 1.

for 119² : as 9²=81 ends with 1, 119² will also end with a 1.

all others do not meet that criteria.

4.

again Property 6.

44² : 4²=16, therefore 44² will also end with a 6.

126² : 6² = 36, therefore 126² will also end with a 6.

5.

given a number n and its following number n+1, the difference between their squares is

(n+1)² - n² = n² + 2n + 1 - n² = 2n + 1

there cannot be any perfect square number in between n² and (n+1)², as the base number would have to be between n and n+1 (which is impossible).

a. 2×8 + 1 = 17

b. 2×80 + 1 = 161

6. as 5.

2×12 + 1 = 25

7.a.

n + n + 1 = 17²

2n + 1 = 17²

n = (17² - 1)/2 = 144

n+1 = 145

b.

2n + 1 = 23²

n = (23² - 1)/2 = 264

n+1 = 265

c.

n = (31² - 1)/2 = 480

n+1 = 481

d.

n = (45² - 1)/2 = 1012

n+1 = 1013

8.

Property 3: Squares of even numbers are always even numbers and square of odd numbers are always odd.

therefore, only 256, 1296 and 144 can be squares of even numbers.

9.

again Property 3.

therefore, only 529 and 361 can be squares of odd numbers.

f(2)= f(1+1) ,where n= 1

=-6

= -2×3

= -2f(1)

f(n+1 )= -2f(n)

OPTION C is the correct answer

Answer:

option 3 is the answer.

Step-by-step explanation:

3, - 6, 12, - 24, 48, .....

Here,

f ( 1 ) = 3

f ( 2 ) = - 6

f ( n + 1 ) = - 3 f ( n )

f ( 1 + 1 ) = - 3 f ( 1 )

f ( 2 ) = - 3 x 3

f ( 2 ) = - 9

This recursive formula is not correct.

f ( n + 1 ) = - 2 f ( n )

f ( 1 + 1 ) = - 2 f ( 1 )

f ( 2 ) = - 2 ( 3 )

f ( 2 ) = - 6

This recursive formula is correct.

Answer:

24 6

Step-by-step explanation:

""6_6_6&6&6&6__5ddyfouoyfkykyky

9514 1404 393

Answer:

  ₹1442

Step-by-step explanation:

The new price will be 1+3% = 1.03 times the old price.

  ₹1400 × 1.03 = ₹1442

Answer:

45 độ

Step-by-step explanation:

SA vuông góc (ABC) => góc SAB = 90 độ; góc giữa SB và mặt phẳng đáy = góc SBA

SA=AB=a => SAB là tam giác cân

KL: góc giữa SB và mặt phẳng đáy SBA = 45 độ

-1 + 2 - 3 + 4 - 5 + 6 - … - 999 + 1000

= -(1 + 3 + 5 + … + 999) + (2 + 4 + 6 + … + 1000)

= -((2 - 1) + (4 - 1) + (6 - 1) + … + (1000 - 1)) + 2 (1 + 2 + 3 + … + 500)

= -((2 + 4 + 6 + … + 1000) - 500) + 2 (1 + 2 + 3 + … + 500)

= -(2 (1 + 2 + 3 + … + 500) - 500) + 2 (1 + 2 + 3 + … + 500)

Let S = 1 + 2 + 3 + … + 500. Then this sum is equal to

= -(2S - 500) + 2S

= -2S + 500 + 2S

= 500

and multiplying by 4 gives 2000.

Answer:

[tex]4\times \left(\left(-1+2-3+4-5+6-7+1000\right)\right)[/tex]

[tex]calculate\: within \: the \:parentheses[/tex]

[tex]-1+2=1[/tex]

[tex]=1-3+4-5+6-7+1000[/tex]

[tex]1-3=-2[/tex]

[tex]=-2+4-5+6-7+1000[/tex]

[tex]-2+4=2[/tex]

[tex]=-3+6-7+1000[/tex]

[tex]3-7+1000[/tex]

[tex]=-4+1000[/tex]

[tex]=996[/tex]

[tex]Multiply:-[/tex]

[tex]4\times996[/tex]

[tex]=3984[/tex]

--------------------------

Hope it helps..

Have a great day!!

Answer:

105

Step-by-step explanation:

angle 6 and 2 are equal

angle 2 lies on a 180 line with angle 3

180-angle 2 =angle 3

180-75=105

Answer:

45

Step-by-step explanation:

corresponding angles

Answer:

Step-by-step explanation:

Can't see all the graphs, but the graph of [tex]y=-x^2[/tex] is an upside down parabola with the vertex at the origin.

Answer:

A. 9π/2km

Step-by-step explanation:

the length of the arc is

s= angle in radians* radius

the angle in radians

135 = 3π/4

therefore length of arc

s= (3π/4)*6 = 9π/2km

(10c² +49cd+49d²) ÷ (5c+7d)

(5c+7d)(2c+7d) ÷ (5c+7d)

Delete (5c+7d)

= (2c+7d)

Answer:

6.

2

1

3

10.9 to 1 place

7

a.) 36

b.)3

c.)65

d.)13

Step-by-step explanation:

Answer: India is incorrect because you multiply the exponents are supposed to be multiplied not added

Step-by-step explanation:

Answer:

16×-3

-48

I hope it's helps you

Answer:

-48

Step-by-step explanation:

16(-3) = -48

Answer:

16.67 km

Step-by-step explanation:

:)

Answer:

∠ 3 = 60°

Step-by-step explanation:

∠ 1 and ∠ 2 are same- side interior angles and sum to 180° , then

4x + 36 + 3x - 3 = 180

7x + 33 = 180 ( subtract 33 from both sides )

7x = 147 ( divide both sides by 7 )

x = 21

Then

∠ 2 = 3x - 3 = 3(21) - 3 = 63 - 3 = 60°

∠ 2 and ∠ 3 are alternate angles and are congruent, so

∠ 3 = 60°

Answer:

60°

3(21)- 3 = 60

Step-by-step explanation:

4x+36 + 3x-3 = 180

x = 21

Answer:

D. 48 sq. units​

Step-by-step explanation:

Area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 16) *6

A = 48

Answer:

A

Step-by-step explanation:

The zero of the function is where the y-value is zero.

then it's -5

Answer:

Height = 12in

Surface area = 320in²

Step-by-step explanation:

Given

Length of the square base = 8in

Volume of the prism = 768 cubic inches

Using the formula;

Volume of the prism = Base area * Height of prism

768 = 8² * H

768 = 64H

H = 768/64

H = 12in

Hence the height of the prism is 12in

Get the surface area

Surface area = 2l² + 2lh

Surface area = 2(8)² + 2 (8)(12)

Surface area = 128  + 192

Surface area = 320in²

Hence the Surface area of the prism is 320in²

Answer:

B

Step-by-step explanation:

8^2=64. -8^2 also =64.

Answer:

8.4

Step-by-step explanation:

Since we want to minimize the average, the integers should be made as small as possible. So, we have 4 integers:

1, 2, 3, 4

However, the median must be 10. The next two integers must have an average of 10 - and since the integers are distinct, we should use:

9, 11

From there, we use the smallest integers (that are still above 11) possible:

12, 13, 14, 15

The average of these 10 integers is 84/10, or 8.4.

The median is still 10, because (9+11)/2 is 10.

Answer:

8 (or 8.4)

Step-by-step explanation:

First, the problem states the words: Distinct and positive.

That means that the smallest number we can use is 0.

We can make 10 blanks for 10 numbers for us to fill in.

_ _ _ _ _ _ _ _ _ _

Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.

In this case, our two numbers are the 5th and 6th blank.

Any two numbers can be used, as long as they are the same actual value from 10.

Let us first put in the numbers we can, which are the numbers before the two middle blanks.

0,1,2,3, _ _ _ _ _ _

To find the median between two numbers, we can do:

(a+b) divided by 2 = median

We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.

Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.

4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.

Now let's place the other numbers in for these two equations.

0,1,2,3,4,16,17,18,19,20

0,1,2,3,9,11,12,13,14,15

If we add the numbers of each together, we get:

0,1,2,3,4,16,17,18,19,20=100

0,1,2,3,9,11,12,13,14,15= 80

If we now divide each sum by 10 (to find the average) we get:

10

8

Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.

Since the smaller answer we got was 8, the answer must be 8.

(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process

Answer:

A.

C.

Step-by-step explanation:

range of a function is the number interval of the y (function) values.

the domain is the number interval of the x (input) values.

A.

this function has only one constant functional value : -5

so the range is the set with only that one value.

B. no, the line goes across all possible values of x.

it is therefore not limited to a single value.

C. see B. therefore, true.

D. see A. no, only one value.

E. is simply a wrong statement. it would not be a function, if there is an x that has more than one y value. but that is not the case here. every x value has exactly one y value. they are all the same, but that does not matter.