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2 years ago

X+x+y+y+z+z=24

Mathematics

1 answer:

JulijaS [17]2 years ago

3 0

Answer:

b = 7/2

x = 11/2

y = 21/2

z = -4

Step-by-step explanation:

2x + 2y + 2z = 24

x + y + z = 12

b + 2x + y + z = 21

2b + 2y = 28

b + y = 14

3x + y + z = 23

we can start anywhere by transforming these equations in a way that always one variable is excised by others.

so, e.g.

b = 14 - y

14 - y + 2x + y + z = 21

2x + z = 7

z = 7 - 2x

3x + y + 7 - 2x = 23

x + y = 16

16 + z = 12

z = -4

-4 = 7 - 2x

-11 = -2x

11 = 2x

x = 11/2

11/2 + y = 16

y = 16 - 11/2 = 32/2 - 11/2 = 21/2

b = 14 - 21/2 = 28/2 - 21/2 = 7/2

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3 years ago

In a company, 80% of the workers are women. If 480 men work for the company, how many workers are there in all? Use pencil

nekit [7.7K]

Answer:

The total workers are 2400.

Step-by-step explanation:

Given:

In company 80% of the workers are women.

480 workers are men.

Now, to find the total workers in all.

In first way:

If women are 80%, then men would be 100-80 = 20%.

Let the total workers be $x$ .

According to question:

$20\%\ of \ x=480$

⇒ $\frac{20}{100} \times x=480$

⇒ $0.20\times x=480$

⇒ $0.20x=480$

Dividing both sides by 0.20 we get:

⇒ $x=2400$ .

Total workers = 2400.

Now, in second way.

Again, let the total workers be $x$ .

According to question:

$x-80\%\ of\ x=480$

⇒ $x-\frac{80}{100}\times x=480$

On solving:

⇒ $x-0.80x=480$

⇒ $0.20x=480$

Dividing both sides by 0.20 we get:

⇒ $x=2400$ .

Total workers = 2400.

Therefore, the total workers are 2400.

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3 years ago

A bank loaned out $8200, part of it at a rate of 7.9% per year and the rest of it at a rate of 7.4% per year. The total amount o

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The amount that the bank loaned out at 7.9% is $1,574.00

How do represent the amounts lent at different rates?

On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate

interest on 7.9% loan=7.9%*x=0.079x

interest on 7.4% loan=7.4%*(8200-x)

interest on 7.4% loan=606.80-0.074x

total interest=0.079x+606.80-0.074x

total interest=0.005x+606.80

total interest on loans=614.67

614.67=0.005x+606.80

614.67-606.80=0.005x

7.87=0.005x

x=7.87/0.005

x=amount loaned at 7.9%=$1,574.00

y=$8200-$1574

y=$6,626.00

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1 year ago

An object is launched at an initial velocity of 19.6

Karolina [17]

Answer:

Step-by-step explanation:

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2 years ago

2. The acute angle below has a degree measurement that is one fifth of the degree measure of the obtuse

Ksenya-84 [330]

Answer:

Acute angle = 30°

Obtuse angle = 150°

Step-by-step explanation:

Method 1:

Let x represent the measurement of the obtuse angle

Obtuse angle = x

Acute angle = ⅕ of x = x/5

Thus:

x + x/5 = 180° (angels on a straight line)

Solve for x

(5x + x)/5 = 180

Multiply both sides by 5

5x + x = 180 × 5

6x = 900

x = 900/6

x = 150

Obtuse angle = 150°

Acute angle = x/5 = 150/5 = 30°

Method 2:

Since acute angle = ⅕ of the obtuse angle, therefore,

Obtuse angle = 5*acute angle

Let acute angle = x

Obtuse angle = 5x

Equation:

5x + x = 180° (angles on a straight line)

Solve for x

6x = 180

x = 180/6

x = 30

Acute angle = x = 30°

Obtuse angle = 5x = 5*30 = 150°

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3 years ago