Which equation shows how the properties of numbers extend to negative whole numbers by the Commutative Property of Addition?
A) −2 + 4 = 4 + (−2)
B) −2(4) = 4(−2)
C) (−2 + 4) + 3 = −2 + (4 + 3)
D) −2(4 + 3) = (−2 x 4) + (−2 x 3)

Answer:

Step-by-step explanation:

Givens

The second given statement expresses that this year there are 34 LESS floats. So, to know how many floats were there last year, we just need to sum

[tex]127+34=161[/tex]

Therefore, last year were 161 floats, that is, 34 more than this year.

y'' by implicit differentiation is y'' = -16x/5y^3.

To find y'' by implicit differentiation, we need to differentiate both sides of the equation .4x3 + 5y3 = 9 twice with respect to x.

First, we differentiate both sides once with respect to x to find dy/dx. This gives us:

12x^2 + 15y^2 (dy/dx) = 0

Next, we differentiate both sides once again with respect to x to find d^2y/dx^2 (y''). This gives us:

24x + 30y^2 (dy/dx) + 15y^2 (d^2y/dx^2) = 0

We can now solve for d^2y/dx^2 (y'') by substituting dy/dx from the first equation into the second equation. This gives us:

24x + 30y^2 (-12x^2/15y^2) + 15y^2 (d^2y/dx^2) = 0

Simplifying this equation, we get:

d^2y/dx^2 = -16x/5y^3

Therefore, y'' = -16x/5y^3.

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Answer:

The answer to your question is:   x = 7; y = 6

Step-by-step explanation:

                                             2x+y=20             ( 1 )  Multiply by 5

                                             6x−5y=12            ( 2 )

                               5 (2x+y=20)    = 10x + 5y = 100

                                          10x + 5y = 100

                                            6x − 5y =   12             Eliminate y

                                          16 x        = 112

                                           x = 112 / 16

                                           x = 7

                                 2(7) + y = 20                 Substitution

                                 14 + y = 20

                                 y = 20 - 14

                                 y = 6

The possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -

(8, 10)

(- 10, - 8)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given product of two consecutive even integers is 80.

Assume that the first integer is [n]. Then the second integer will be [n + 2]. According to the question, we can write -

n x (n + 2) = 80

n² + 2n = 80

n² + 2n - 80 = 0

n² + 10n - 8n - 80 = 0

n(n + 10) - 8(n + 10)

(n - 8)(n + 10) = 0

n = 8  and n = - 10

If → n = 8 then (n + 2) = 10.

If → n = - 10 then (n + 2) = -8.

Therefore, the possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -

(8, 10)

(- 10, - 8)

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Final answer:

The consecutive even integers whose product is 80 are 8 and 10. This is found by setting up an equation for consecutive even integers and factoring the number 80.

Explanation:

The question is asking to find two consecutive even integers whose product is 80. When two numbers are consecutive even integers, they can be represented as n and n + 2, where n is an even integer. To find these numbers, we set up the equation n(n + 2) = 80.

First, we need to find two numbers that multiply to give 80. We can start by listing the factors of 80: 1 x 80, 2 x 40, 4 x 20, 5 x 16, 8 x 10. Since we are looking for even integers, we pick the pairs where both numbers are even: 4 x 20, 8 x 10. However, the numbers must also be consecutive even integers, which is the case for the pair 8 and 10, but not for 4 and 20.

Therefore, the pair of consecutive even integers that multiply to give 80 are 8 and 10.

Answer: 6

Step-by-step explanation:

Answer:

a,b,c

Step-by-step explanation:

i guessed and then they told me the right answer .

Answer:

Measure of arc AC = 100°

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : AB and CD are the diameters of the circle K and m∠BKD = 100°

To find : measure of arc AC

Solution :

The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC

Now, m∠BKD = 100°

and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)

⇒ m∠AKC = 100°

Hence, Measure of the arc AC = 100°

The playing surface where the college basketball semi-finals are played is called the court. It is rectangular in shape and has various markings such as the three-point line and free-throw line.

The playing surface where the college basketball semi-finals are played is called the court or the basketball court. The court is rectangular in shape with a length of 94 feet and a width of 50 feet. It is divided into two halves with a midcourt line and has markings such as the three-point line, free-throw line, and key.

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Explanation:

Cost of 1 loaf of bread = $5

Cost of 1 roll = $1

The baker needs to sell both items and it should be worth $35.

To find the linear equation, Suppose, the baker sells “b” loaves of bread and “r” rolls.

Then the total cost of the sales has to be $35.

So, the linear equation will be:

5b + 1r = 35

I would say that this person has lost out on 2 years salary while in school plus 5 year repayment period. Total amount divided over 5 years is:

( (2+5)(45,000) + 30,000 ) / 5 =

(7(45,000)+30,00)/5 = 69,000 salary

Answer:

69,000

Step-by-step explanation:

Given,

There is loss of 45,000 per year for two years,

So, the total lost = 2 × 45000 = 90,000

Also, the cost of school going = 30,000

∴ the total recovering amount = 90,000 + 30,000 = 120,000

If this amount must recover in 5 years or less than 5,

Then, the minimum recovering amount per year = [tex]\frac{120000}{5}[/tex] = 24,000

Now, the original salary per year  = 45,000

Hence, the new salary per year = original salary + recovering amount

= 45,000 + 24,000

= 69,000

Answer:

C

Step-by-step explanation:

Last month, more rain fell compared to two months ago, and there was less variation in the daily rainfall.

To determine whether more rain fell two months ago or last month, we need to compare the mean daily rainfall and the mean absolute deviation for both months. Two months ago, the mean daily rainfall was 9.4 cm with a mean absolute deviation of 3.5 cm. Last month, the mean daily rainfall was 11.5 cm with a mean absolute deviation of 1.6 cm.

Thus, based on this information, we can conclude that more rain fell last month. The mean daily rainfall was higher and the mean absolute deviation was lower. This indicates that there was less variation in the amount of rain that fell each day last month compared to two months ago.

The equation of the line which is parallel to the line 3x+4y=8 and passes through the point (2,-5) is y = -3/4x - 1/2.

The given equation is 3x+4y=8, which is a linear equation. To make this simpler, we can isolate 'y' to make it in the form 'y = mx + b', where 'm' is the slope. When we do this, we get y = -3/4x + 2, so the slope of this line is -3/4.

Next, we know that parallel lines have the same slope. Therefore, the equation of the line parallel to the given line and passing through (2, -5) will also have a slope of -3/4. Using the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line, and 'm' is the slope, we can substitute the given values.

Therefore, y - (-5) = -3/4(x - 2), simplifying this gives us the equation of our line: y = -3/4x - 1/2.

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Answer:

∠2; vertical angle theorem; ∠3; transitive property of congruence

Step-by-step explanation:

∠2 and ∠1 are opposite angles that share only a vertex.  This is the definition of vertical angles, and by the vertical angle theorem they are congruent.

Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.

∠4 and ∠3 are opposite angles that share a vertex.  This makes them vertical angles, and the vertical angle theorem states that they are congruent.

The transitive property, algebraically, states "if a=b and b=c, then a=c."  Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."

The required solution for the blacks,
Blank 1 = ∠2;
Blank 2 =  vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.

It is given that
∠1≅ ∠4 ​. By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank].
To determine the missing statement at the place of blanks in the statement.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Since
Black 1
∠2≅∠4
and  ∠1≅ ∠4

So ∠2 ≅ ∠1

Blank 2
∠2≅∠4 are equal by the vertical angle theorem.

Blank 3
∠4≅∠3
∠3 ≅∠1
So,
∠2 ≅ ∠1 ; ∠2≅∠3 and ∠4≅∠3  it is transitive property of congruence.

Thus, the required solution for the blacks,
Blank 1 = ∠2;
Blank 2 =  vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.

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