Find a negative integer M so that the equation (x-12)(x+m) = m-51

Solve equations show all steps 1. 2x-10=44+8x 2. 7x-4=20=3x 3. 2(x-3)=-20 4. 15-4x+5=32

Inga [223]

Answer:

2x - 10 = 44 + 8x

7x - 4 = 20 =3x

2(x-3) = -20

15 - 4x + 5 = 32

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x-10-(44+8*x)=0

Pull out like factors :

-6x - 54 = -6 • (x + 9)

-6 = 0

Solve : x+9 = 0

Subtract 9 from both sides of the equation :

x = -9

Move all terms containing

x

to the left side of the equation.

4

x

−

4

=

20

Move all terms not containing

x

to the right side of the equation.

4

x

=

24

divide each term by 4

x = 6

2(x−3)=−20

Step 1: Simplify both sides of the equation.

2(x−3)=−20

2x−6=−20

Step 2: Add 6 to both sides.

2x−6+6=−20+6

2x=−14

Step 3: Divide both sides by 2.

2x

2

=

−14

2

x=−7

−4x+20=32

Step 2: Subtract 20 from both sides.

−4x+20−20=32−20

−4x=12

Step 3: Divide both sides by -4.

−4x

−4

=

12

−4

x=−3

4 0

3 years ago

An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir

finlep [7]

Answer:

The area of the copper circle is 31.4 inches.

Step-by-step explanation:

Given:

An artist used silver wire to make a square that has a perimeter of 40 inches.

She then used copper wire to make the largest circle that could fit in the square, with perimeter of 40 inches.

Use 3.14 to represent π.

Now, to find the area of the copper circle.

Perimeter of square = 40 inches.

So, we get the side of square by putting formula:

$Perimeter=4\times side$

$40=4\times side$

Dividing both sides by 4 we get:

$10=side.$

$Side=10\ inches.$

Now, as the side of square is 10 inches it is the diameter of the circle as the square is fit inside the circle:

For getting the area of circle we find the radius:

Radius (r) = $\frac{Diameter}{2} \\=\frac{10}{2}= 5\ inches.$

Now, putting the formula to get the area of the circle:

$Area=2\times \pi \times r$

$Area=2\times 3.14\times 5$

$Area=31.4\ inches.$

Therefore, the area of the copper circle is 31.4 inches.

6 0

3 years ago

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co

lisov135 [29]

Answer:

The complete solution and step by step explanation is written below.

Note:

Here is the complete question you were probability asking as you may have unintentionally missed to mention the parts (a) and (b). So, after a little research, I figured out that this was probably the complete question you had meant to ask. So, I am answering based on the reference of this complete question that may indeed clear your concepts.

Complete Question:

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs $2.40 per gallon, and milk from dairy II costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9% butterfat, and dairy II can supply at most 80 gallons averaging 2.9% butterfat. Answer parts a and b.

A. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? (Also, what IS the maximum amount of butterfat?)

B. The solution from part A leaves both dairy 1 and dairy 2 with excess capacity. Calculate the amount of additional milk each dairy could produce.

Step-by-step explanation:

Let A be number of gallons of the amount of milk the company bought from Dairy 1.

(100 - X) be the number of gallons of the amount of milk the company bought from Dairy 2.

Milk from dairy I costs $2.40 per gallon and milk from dairy II costs $0.80 per gallon.

So, the equation of total cost available for purchasing the milk be:

Cost = 2.40A + ( 100 - A)0.80

As $144 is the total cost available for purchasing the milk.

Hence, Cost equation would be as follows:

Cost = 2.40A + ( 100 - A)0.80

144 = 2.40A + ( 100 - A)0.80

144 = 2.40A + 80 - 0.80A

1.6A = 64

So, A = 64 ÷ 1.6

= 40 gallons

Calculation of gallons of Dairy 1 and Dairy 2:

gallons of Dairy 1 ⇒ A = 40 gallons

gallons of Dairy 1 ⇒ 100 - A = 100 - 40 = 60 gallons

The equation for Fat will be:

Fat for dairy 1 = 40 × 3.9% = 1.56

Fat for dairy 2 = 60 × 2.9% = 1.74

ADD = 1.56 + 1.74 = 3.3 %

Calculation Part B:

Dairy 1 will have = 50 - 40 = 10 gallons ( excess)

Dairy 2 will have = 80 - 60 = 20 gallons (excess)

Keywords: word problem, equation solving

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5 0

3 years ago

6

SVETLANKA909090 [29]

Answer:

56.52 units²

explanation:

We should know circle's area: πr²
Then the semi circle shall have half area, so formula: (1/2)πr²

Steps:

Using the formula:

→ (1/2)πr²

→ (1/2)(3.14)(6)²

→ 56.52 units²

6 0

2 years ago

Read 2 more answers

Use the ALEKS calculator to write 47/21 as a decimal rounded to the nearest tenth.

quester [9]

Answer:

2.2

Step-by-step explanation:

47/21 = 2.238095

round to tenth = 2.2

3 0

3 years ago

Read 2 more answers

Find a negative integer M so that the equation (x-12)(x+m) = m-51​

Find a negative integer M so that the equation (x-12)(x+m) = m-51