Question

1. 8x(x-7)=1080 2.(k+11):23=273.900:(210+x)=364.40+x:70=545.142-(123-x)+14=1116.67-36:x=55

Answer 1

Ответ:

1) 8*(х-7)=1080

х-7=1080:8

х-7=135

х=135+7

х=142

2) (k+11):23=27

k+11=23*27

k+11=621

k=621-11

k=610

3)900:(210-x)=36

210-x=900:36

210-x=25

x=210-25

x=185

Пошаговое объяснение:

Answer 2

Let's solve each equation step by step:

1. 8x(x-7) = 1080

First, expand the left side of the equation: 8x(x-7) = 8x^2 - 56x

Now, set the equation equal to 1080: 8x^2 - 56x = 1080

Subtract 1080 from both sides: 8x^2 - 56x - 1080 = 0

Now, we have a quadratic equation. To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 8, b = -56, and c = -1080.

x = (56 ± √((-56)² - 4 * 8 * (-1080))) / (2 * 8)

x = (56 ± √(3136 + 34560)) / 16

x = (56 ± √37796) / 16

Now, calculate the two possible values of x:

x₁ = (56 + √37796) / 16 ≈ 16.34 x₂ = (56 - √37796) / 16 ≈ -5.84

So, the solutions to the equation are approximately x ≈ 16.34 and x ≈ -5.84.

2. (k+11)/23 = 273.900 / (210+x) = 364.40 + x/70 = 545.142 - (123-x) + 14 = 1116.67 - 36/x = 55

This equation is quite complex with multiple fractions and variables. Let's solve it step by step:

Step 1: Simplify each part of the equation.

• (k+11)/23 = 273.900 / (210+x)
• 364.40 + x/70
• 545.142 - (123-x) + 14
• 1116.67 - 36/x
• 55

Step 2: Solve each part of the equation separately.

For the first part, (k+11)/23 = 273.900 / (210+x), cross-multiply to eliminate fractions:

23 * (k+11) = 273.900 * 23 / (210+x)

k + 11 = 6307.7 / (210+x)

Now, solve for k:

k = 6307.7 / (210+x) - 11

For the second part, 364.40 + x/70, no further simplification is needed.

For the third part, 545.142 - (123-x) + 14, simplify it:

545.142 - 123 + x + 14 = 436.142 + x

For the fourth part, 1116.67 - 36/x, no further simplification is needed.

Now, we have:

364.40 + x/70 = 436.142 + x

To solve for x, first, subtract x from both sides:

364.40 - 436.142 + x/70 - x = 0

-71.742 + (x/70 - x) = 0

Now, solve for x:

x/70 - x = 71.742

To eliminate the fraction, multiply both sides by 70:

x - 70x = 71.742 * 70

-69x = 5021.4

x = -5021.4 / 69

x ≈ -72.74

So, the value of x is approximately x ≈ -72.74.

Now that we have x, you can substitute this value into the expression for k:

k = 6307.7 / (210+x) - 11

k = 6307.7 / (210 - 72.74) - 11

k ≈ 33.57

So, the value of k is approximately k ≈ 33.57.