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3 years ago

Solve the following equation for b. 10a + 2b = 12

2 answers:

5 0

When questions asks us to solve for something unknown, it usually wants us to express the unknown in terms of other numbers.
Therefore, we can solve this by imagining all the other algebra are a number.
10a + 2b = 12
Shift 10a to the other side, turning it negative.
2b = 12 - 10a
Shift 2 from 2b to the other side, dividing 12 - 10a
b = (12 - 10a) / 2
Therefore the answer should be
$b = \frac{12 - 10a}{2}$

Svetradugi [14.3K]3 years ago

4 0

10a + 2b = 12 ; Solve for b

In order to solve for b, we must isolate it. That just means that we need to get "b" onto its own side of the equal sign! :)

So, we must first subtract 10a from both sides.

10a + 2b - 10a = 12 - 10a

Simplify.

2b = -10a + 12

Then, we simply divide both sides by 2.

2b ÷ 2 = (-10a + 12) ÷ 2

Simplify.

b = -10a/2 + 12/2

Simplify.

b = -5a + 6

~Hope I helped!~

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In a box of mixed soft toys 25% are animal toys what is 25% as a fraction in its simplest form

densk [106]

25% = 0.25 = 25/100 = 1/4 in simplest form

5 0

3 years ago

In Cecilia’s CD collection, 1/5 of her Jazz CDs represents 1/10 of all her CDs. What is the ratio of her Jazz CDs to her non-Jaz

KatRina [158]

Answer: The required ratio is 1:1.

Step-by-step explanation:

Let the total number of CDs be 100

$\frac{1}{10}$ of CDs is given by

$\frac{1}{10}\times 100\\\\=10$

According to question,

$\frac{1}{5}$ of her Jazz CDs represents $\frac{1}{10}$ of all her CDs.

Let the number of Jazz CDs be x

So, it becomes

$\frac{1}{5}\times x=10\\\\x=10\times 5\\\\x=50$

So, Number of Jazz's CDs is 50

Number of Jazz non CDs is given by

$100-50=50$

Ratio of her CDs to her non- CDs is given by

$50:50\\\\1:1$

Hence, the required ratio is 1:1.

6 0

3 years ago

Andrea made a replica of the Empire State Building. The surface area of the model is 45 ft2. What is the surface area of the act

melamori03 [73]

Answer:

87,120 ft²

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Surface area of the Empire State building replica = 45 square feet

Scale factor = 44

2. What is the surface area of the actual Empire State Building in square feet?

For answering the question, we will make the following calculations:

45 square feet = 9 feet * 5 feet or,

45 square feet = 10 feet * 4.5 feet, or,

45 square feet = 20 feet * 2.25 feet.

Now, let's apply the scale factor to all of these probable lengths of the sides of the surface area of the replica, as follows:

(9 *44) * (5 * 44) = 396 * 220 = 87,120 ft²

(10 * 44) * (4.5 * 44) = 440 * 198 = 87,120 ft²

(20 * 44) * (2.25 * 44) = 880 * 99 = 87,120 ft²

As we proved, no matter what are the lengths of the sides of the surface area of the replica. after applying the scale factor, the result is the same: 87,120 ft²

6 0

3 years ago

What is the vertex of a parabola having the equation y = –2(x – 5)2 + 7? Which direction does the parabola open?

Vika [28.1K]

$y = -2(x-5)^2 + 7$

That's vertex form for a parabola $y=a(x-p)^2+q$ and we read off vertex (p,q) as

Answer: Vertex (5,7)

The negative a tells us this is a downward opening parabola (upside down from the usual $y=x^2$ . I remember CUP - Concave Up Positive; here a is negative so not a cup, instead concave down. The same rule applies to second derivatives in calculus so memorize it now and use it later.

Answer: downward

7 0

3 years ago

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% p

andrew11 [14]

Answer: There are 32 pints of first type and 128 pints of second type in mixture.

Step-by-step explanation:

Since we have given that

Percentage of pure fruit juice in first type = 60%

Percentage of pure fruit juice in second type = 85%

Percentage of pure fruit juice in mixture = 80%

We will use "Mixture and Allegation" to find the ratio of first and second type in mixture:

First type Second type

60% 85%

80%

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

85-80 : 80-60

5% : 20%

1 : 4

so, the ratio of first and second type is 1:4.

Total number of pints of mixture = 160

Number of pints of mixture of first type in mixture is given by

$\dfrac{1}{5}\times 160\\\\=32\ pints$

Number of pints of mixture of second type in mixture is given by

$\dfrac{4}{5}\times 160\\\\=4\times 32\\\\=128\ pints$

Hence, there are 32 pints of first type and 128 pints of second type in mixture.

6 0

3 years ago