why is the sum of two negative numbers not a positive number
please dont make the whole answer a example:)

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

Answer:

answer for your question is B 2(-22+20)

Answer:

1 2x-4,x-42,2-4x I hope it will help you please follow me

Answer:

[tex] \sqrt{ - 147} = \sqrt{147} \times \sqrt{ - 1} = 7i \sqrt{3} [/tex]

I hope I helped you ^_^

The answer ; √ –108 = √108 × √–1 = 6i √3

HOPE ITS HELPFUL ^_^

Answer:50+(3x22)=116

Step-by-step explanation:

Answer: D i hope this helps

Step-by-step explanation:

In this question, we given a piece-wise function, that has different definitions depending on the domain.

Evaluate the function at x = 0.

The exercise asks for us to evaluate the function at [tex]x = 0[/tex]

We have to look at the definition, and see which definition includes [tex]x = 0[/tex]. The equal sign at [tex]x = 0[/tex] is on the second definition, that is:

[tex]f(x) = 1, 0 \leq x < 2[/tex]

Thus, at [tex]x = 0[/tex], the value of the function is 1, and the correct answer is given by option A.

For another example of evaluation of a piece-wise function, you can check https://brainly.com/question/17966003

Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

The concept of greatest common factor is used to solve this question. Then, we use it to find the number of crackers and slices of cheese, and the answer is:

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

To find the greatest number of plates, you need to find the greatest common factor between 12 and 18.

Thus, factoring them, always by the same number:

12 - 18|2

6 - 9|3

2 - 3

The greatest common factor is 2x3 = 6, which means that the greatest number of plates you can prepare is 6.

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

18 crackers, so each plate has 18/6 = 3 crackers.

12 slices of cheese, so each plate has 12/6 = 2 slices of cheese.

A similar question is given at https://brainly.com/question/18454593

Answer:

Looking at the question and goin step by step

we get to know that equation formed wud be ->

product of nine and a number - 9*x = 9x

added to 6 => 9x+6

gives us 24

so

9x + 6 = 24

now 9x = 18 and x = 18/9 = 2

and now keeping x value = 9 *(2)+6 we get 18+6 = 24

so lhs = rhs = 24

9x+6=24 option a

f(x) = 5x^2 + 25x + 30

============================================================

Explanation:

The roots, aka x intercepts, of this curve are x = -3 and x =  -2. This is where the graph crosses the x axis.

Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.

So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get

y = (x+3)(x+2)

y = (-1+3)(-1+2)

y = (2)(1)

y = 2

But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)

Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)

Now let's expand everything out and simplify

y = 5(x+3)(x+2)

y = 5(x^2+2x+3x+6)

y = 5(x^2+5x+6)

y = 5x^2+5*5x+5*6

y = 5x^2 + 25x + 30

Choice C is the final answer

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

To check this, we can plug in x = -3 and we should get 0

y = 5x^2 + 25x + 30

y = 5(-3)^2 + 25(-3) + 30

y = 5(9) + 25(-3) + 30

y = 45 - 75 + 30

y = -30 + 30

y = 0

This proves that x = -3 is a root of y = 5x^2 + 25x + 30

I'll let you check x = -2. You should also get y = 0 when plugging this x value in.

Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.

Answer:

2

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

Answer:

Step-by-step explanation:

t = [tex]cos^{-1} (\frac{3}{5})[/tex]

t ≈ 53°

cos t = cos (- t) = [tex]\frac{3}{5}[/tex]  

sec ( [tex]\pi[/tex] + t ) = -  [tex]\frac{5}{3}[/tex]

Answer:

Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.

Step-by-step explanation:

Answer:

500*2%=10

500+10=510

Step-by-step explanation:

Answer:

Se faltan por vender 201,419 rollos.

Step-by-step explanation:

Total de rollos:

238 942 rollos de papel higiénico

763 924 rollos de papel toalla

73 947 rollos de servilletas

Entonces:

[tex]T = 238942+763924+73947 = 1076813[/tex]

Se vendieron 875 394 rollos la cantidad de rollos que faltan por vender son?

Total subtraído por la cuantidad vendida. Entonces:

[tex]V = 1076813 - 875394 = 201419[/tex]

Se faltan por vender 201,419 rollos.

Answer:

y = -3x + 2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - 8 / 1 - (-2)

-9/3

= -3

y = -3x + b

-1 = -3(1) + b

-1 = -3 + b

2 = b

Answer:

x= -2   and x = 6

Step-by-step explanation:

The solutions are where the two graphs intersect

x=6, y= 10  is one point

x=-2 and y = -6 is the other point

The intersection points of both the equations are the solutions

From the graph the points are

Hence

x=-2 and x=6 are the solutions

Option D

Answer:

you have to put them in order

Answer:

No adda doesnt get free delivery

Step-by-step explanation:

Answer: A) No, the distance from the restaurant to Ada’s house is Square Root of 41 miles, which is greater than the 6-mile maximum radius.

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

3х - 6 = 6x - 9

Subtract 3x from each side

3х-3x - 6 = 6x-3x - 9

-6 = 3x-9

Add 9 to each side

-6+9 = 3x-9+9

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

3x-6=6x-9

3x-6x=-9+6

-3x=-3

-3x÷-3=-3÷-3

x=1

Answer:

A. {x| –4 < x ≤ 4}

Step-by-step explanation:

Answer:

{x| –4 < x ≤ 4}

Step-by-step explanation:

Edge Quiz 2023

Answer:  (4y-9z)( 16y^2 + 36yz + 81z^2 )

=======================================================

Explanation:

We'll use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

In this case,

So,

a^3 - b^3 = (a-b)(a^2+ab+b^2)

64y^3 - 729z^3 = (4y-9z)( (4y)^2 + (4y)(9z) + (9z)^2 )

64y^3 - 729z^3 = (4y-9z)( 16y^2 + 36yz + 81z^2 )

Answer:

16 degrees

Step-by-step explanation:

Tan(?) = perpendicular/base

Tan(?) = 13/46

?=arctan(13/46)=16

Answer:

Step-by-step explanation:

the answer is irrational hope this helps

Answer:

Rational.

Step-by-step explanation:

64 is a rational number because it's a whole number. Irrational numbers are real numbers including: [tex]\pi, \sqrt{2}[/tex], and etc. Basically, rational numbers are anything that can be expressed as the quotient of two integers: 64/1

Answer:

A is the answer to your question

Step-by-step explanation:

To do this, just distribute the 3 to each of the coefficient and see if it would result in the same coefficients in the original expression.