Help! I don't understand rate of change??

Answer:

[tex]\frac{a+1}{(a-2)(a-1)(a-1)}=[/tex]

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to factor the expression. In order to subtract (or add) two fractions, both fractions have to have common denominators. When the fractions are factored one can easily see the least common denominator. Convert both fractions to the least common denominator by multiplying the numerator (number over the fraction bar) and denominator (number under the fraction bar) by the value such that both fractions have the same denominator. Finally, one can subtract the numerators of the two fractions.

2. Factoring and Least common denominator

[tex]\frac{3}{a^2-3a+2}-\frac{2}{a^2-1}=[/tex]

Factor the expression, rewrite the quadratic polynomials as the product of two linear polynomials,

[tex]\frac{3}{a^2-3a+2}-\frac{2}{a^2-1}=[/tex]

[tex]\frac{3}{(a-2)(a-1)}-\frac{2}{(a-1)(a+1)}=[/tex]

The least common denominator is: ([tex](a-2)(a-1)(a-1)[/tex])

Convert both fractions to the least common denominator, multiply both the numerator and denominator by the same value to do so,

[tex]\frac{3}{(a-2)(a-1)}-\frac{2}{(a-1)(a+1)}=[/tex]

[tex]\frac{3}{(a-2)(a-1)}*\frac{a-1}{a-1}-\frac{2}{(a-1)(a+1)}*\frac{a-2}{a-2}=[/tex]

Simplify,

[tex]\frac{3}{(a-2)(a-1)}*\frac{a-1}{a-1}-\frac{2}{(a-1)(a+1)}*\frac{a-2}{a-2}=[/tex]

[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]

3. Solving the expression

[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]

Distribute, multiply every term inside the parenthesis by the term outside of it,

[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]

[tex]\frac{3a-3}{(a-2)(a-1)(a-1)}-\frac{2a-4}{(a-1)(a+1)(a-2)}=[/tex]

Simplify further,

[tex]\frac{3a-3}{(a-2)(a-1)(a-1)}-\frac{2a-4}{(a-1)(a+1)(a-2)}=[/tex]

[tex]\frac{3a-3-(2a-4)}{(a-2)(a-1)(a-1)}=[/tex]

[tex]\frac{3a-3-2a+4}{(a-2)(a-1)(a-1)}=[/tex]

Combine like terms,

[tex]\frac{3a-3-2a+4}{(a-2)(a-1)(a-1)}=[/tex]

[tex]\frac{a+1}{(a-2)(a-1)(a-1)}=[/tex]

Answer:

https://vietjack.com/giai-toan-lop-9/images/bai-38-trang-62-sgk-toan-9-tap-1-

Step-by-step explanation:

Vẽ đồ thị y = 2x (1):

   Cho x= 0 ⇒ y= 0 ta được O (0, 0)

   Cho x= 2 ⇒ y = 4 ta được điểm (2; 4)

- Vẽ đồ thị y = 0,5x (2):

   Cho x= 0 ⇒ y = 0 ta được O (0; 0)

   Cho x = 4 ⇒ y = 2 ta được điểm (4; 2)

- Vẽ đồ thị y = -x + 6 (3):

   Cho x = 0 ⇒ y = 6 được điểm (0; 6)

   Cho y = 0 ⇒ x = 6 được điểm (6; 0)

Để học tốt Toán 9 | Giải bài tập Toán 9

The three possible sets of integers whose product is -7 are:

1. (1, 1, -7) (least to greatest)

2. (-1, 1, 7) (least to greatest)

3. (-1, -1, 7) (least to greatest)

To find the three possible sets of integers whose product is -7, we need to consider all the combinations of three integers whose product results in -7. Keep in mind that each set should use unique integers. Let's explore the options:

1. Set 1: [tex]\(1 \times 1 \times -7 = -7\)[/tex]

2. Set 2: [tex]\((-1) \times 1 \times 7 = -7\)[/tex]

3. Set 3: [tex]\((-1) \times (-1) \times 7 = -7\)[/tex]

The three possible sets of integers whose product is -7 are:

1. (1, 1, -7) (least to greatest)

2. (-1, 1, 7) (least to greatest)

3. (-1, -1, 7) (least to greatest)

Each set consists of unique integers, and the product of all three integers in each set is -7.

To know more about integers:

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Answer:Integer Numbers?

Step-by-step explanation:

Answer:

5 newspapers in 1 pile

Step-by-step explanation:

If there are 10 newspapers in 2 piles, to find the number of newspapers in 1 pile, we need to divide 10÷2 which equals 5.

Answer: 5 newspapers per pile

Step-by-step explanation:

= 10 newspapers in 2 piles

= newspaper per pile = 10 / 2

= 5

So , newspaper per pile is 5

This is your answer

Answer:

probably giving false information or something

Step-by-step explanation:

Answer:

No, they are not.

Step-by-step explanation:

A ratio can be written as a fraction. So 3:5 is the same as 3/5 and 2:4 is the same as 2/4.

3/5 = 2/4

0.6 = 0.5 INCORRECT

As you can see, the both don't equal the same numbers, so they aren't equivalent.

Answer:

Silurian

Triassic

Jurassic

Tertiary

Step-by-step explanation:

i hope its right

Answer:

a) -99

b) -12

c) -105

d) -46

Answer:

a) | -81 - 17 | = 98

b) | 8 - 20 | = 12

c) | -76 - 25 | = 101

d) | -91 + 45 | = 46

Remember, absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Hope this helps! :)

Answer:

4

Step-by-step explanation:

they're the same triangle, but one is bigger. the 2,5 and 5 sides are equivalent, so with that we are able to know the big triangle is exactly 2x bigger. u multiply the 2 side (because it's equivalent to the x side) by 2 (bc the triangle is 2 times bigger) and you get 4 = x

Answer:

C

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

it can be expressed as a product of two smaller numbers 9×9

Answer: (for 11b) 15/6

Step-by-step explanation:

I added image of how I solved (I’m 99% sure this is right)

Hope this helps :-))

Answer:

[tex] \frac{5}{2} [/tex]

Step-by-step explanation:

the answer done is of (b)

Hope it helps.

Answer: x+5/8 = 1 is the equation where x is the remaining coffee.

Step-by-step explanation:

he drank = 5/8

whole coffee = 1

so

let coffee remaining be x

1-5/8 = x

x+5/8 = 1

The required equation, for the remaining cup of coffee, is x = 1+(- 5/8).

To determine the addition equation of coffee remaining in the cup, for the condition Kelly bought a cup of coffee and drank 5/8 it.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

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,
Let the coffee remaining in the cup be x,
Now, according to the question,
1 = x + 5/8
x = 1 - 5/8
For the addition equation,
x = 1 +(-5/8)

Thus, the required equation, for the remaining cup of coffee, is x = 1+(- 5/8).

Learn more about arithmetic here:

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Answer:

The answer is 410 5/8

Answer:

y = 1500x + 20690

Step-by-step explanation:

    We already know the slope. The prompt tells us that in 1996 there were 29,690 movie screens. We can write this as the point (6, 29690). We can find the y-intercept by substituting information into the point-slope formula.

[tex]y-y_1=m(x-x_1)\\\\y-29690=1500(x-6)\\\\y-29690=1500x-9000\\\\y=1500x+20690[/tex]

    Now we know that number of movie screens in 1990 was 20,690 and that it increased by 1500 each year.

Answer:

3

Step-by-step explanation:

12/4=3 per car

Answer:

Irrational

Step-by-step explanation:

Because irrational numbers are defined as a subset of real numbers, all irrational numbers must be real numbers.

Answer:

6) a) 69 b) 97 c)86 d)71

7) A.

Step-by-step explanation:

6)

a) -1-[9(-8)]-2 = -1 - (-72) -2

= -3 + 72 = 69

b) 81 + 4² = 81 + 16

= 97

c)12×7 + 6÷3 =(12×7)+(6÷3)

= 84 + 2

=86

d)74 + 9 ÷ -3 = 74 + (9÷ -3)

= 74 - 3

= 71

7)

Statement: Larry has at most seven miles left in the race

This statement is represented by the inequality;

[tex]x \leqslant 7[/tex]

Answer:

Part A.

69

Part B.

97

Part C.

93

Part D.

86

Step-by-step explanation:

Part A.

-1-9x(-8)-2

-1+72-2

69

Part B.

81+4^2

81+16

97

Part C.

12x7+6+3

84+6+3

93

Part D.

74+9+3

83+3

86

Answer:

A and B are irrational

Step-by-step explanation:

A cannot be reduced to a whole number.

same with B.

C can be reduced to 9 as 9x9 = 81

D can be reduced to 8 as 8x8 = 64

Answer: Thrid choice. 4

Step-by-step explanation:

Given equation

(-3/4)m - (1/2) = 2 + (1/4)m

The least common multiple of the denominator

First three multiples of 2: 2, 4, 6

First three multiples of 4: 4, 8, 12

Since 4 is the first common multiple, 4 is the least common multiple of 2 and 4.

By multiplying [tex]\boxed{4}[/tex] on both sides, the fraction can be eliminated.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The savings were changed by $88

Step-by-step explanation:

1 backpack costs 8 dollars and they bought 8 of them, you have to multiply 8 dollars by 8 cause there is 8 backpacks which is 64 , pen and pencils for 1 backpack costs 3 dollars , so you have to multiply 3 by 8  cause there are 8 backpacks which is 24. then you add 64 and 24 which is 88

Answer: 4 : 20

Step-by-step explanation:

1 : 5 = 4 : __

= 1 * 4 = 4

= 5 * 4 = 20

= 4 : 20

So, this is your answer

b, a, d, c, b, a + b, c, d, d

Answer:

Surface Area = 264π

Volume = 576π

Step-by-step explanation:

in the picture

Answer:

SA= 829.38 Inches² which is 829.38/3.14159 = 264π inch³

V = 110.43 inches³.   which is 110.43/ 3.14159 = 35.15π inch³

Step-by-step explanation:

To find the surface area of cylinder, we calculate two area of circle 2πr² and one area of rectangle 2πrh first, and then add them 2πr²+2πrh.

SA of a cylinder =2πrh+2πr², where π≈3.14159

Radius given is 12/2 = 6 inches

=  2 x π x 6 x 16 + 16  x π6 x 6 ≈ 829.3804 = 829.38 Inches²

Volume = h*π *r^2

V = 16 x π

= 110.43 inches³.

Answer

1/2

Step-by-step explanation:

A regular number cube would be half odd half even so 1/2 of the time it wouldnt be odd

Step-by-step explanation:

a) is really easy, right ?

the surface area consists of 6 rectangles (as you know, every die has 6 sides). they are 3 pairs of equally sized rectangles.

there are 2 rectangles 7×1, 2 rectangles 7×2, and 2 rectangles 2×1

SA = 2×7×1 + 2×7×2 + 2×2×1 = 14 + 28 + 4 = 46 in²

the volume is just length×width×height

V = 7×2×1 = 14 in³

b)

a little bit more difficult, but with a little trick just as easy.

the surface area consists of the 2 circle areas and the mantle "coating".

the area of a circle is pi×r².

we have to be careful as the given 10 ft is the diameter of these circles. the radius is half of it : 5 ft.

the area of the "mantle" we can calculate by imagining we simply slice it open with one straight line from top to bottom. and then we cut it off the two circles and put it flat on the table.

now we see it is just a rectangle. one side is 12ft. the other is the circumference of the previously attached circles.

circumference of a circle is 2×pi×r

so the surface area is 2×circle + (circumference circle)×12

SA = 2×pi×5² + (2×pi×5)×12 = 50pi + 120pi = 170pi =

≈ 534.07 ft²

the volume is one base area (circle) times height

V = pi×5²×12 = 300pi ≈ 942.48 ft³