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podryga [215]
3 years ago
10

Three consecutive even integers are such that the sum of the smallest and three times the second is 38 more than twice the third

. Find the integers.
Mathematics
2 answers:
trasher [3.6K]3 years ago
7 0

x,\ x+2,\ x+4-\text{the three consecutive even integers}\\\\\text{The equation}\\\\x+3(x+1)=2(x+4)+38\ \ \ \ |\text{use distributive property}\\\\x+3x+3=2x+8+38\\\\3x+3=2x+46\ \ \ \ |-3\\\\3x=2x+43\ \ \ \ |-2x\\\\x=43\\x+2=45\\x+4=47

algol133 years ago
6 0

Answer:

20, 22, 24

Step-by-step explanation:

since the integers are even: x, x+2, x+4

x+3(x+2)=38+2(x+4)

x+3x+6=38+2x+8

4x+6=46+2x

2x=40

x=20

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Please find the value of x in the figure
notka56 [123]

Answer:

Step-by-step explanation:

E is the midpoint of Ac & D is the midpoint of AB

DE = (1/2)BC        {Midpoint theorem}

x +1 = \dfrac{1}{2}(4x - 6)\\\\\\
Multiply \ the \ whole \ equation \  by 2\\\\
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8 0
2 years ago
PLEASE ANSWER
oksano4ka [1.4K]

Answer:

x² + 9x + 8 = (x + 1)(x + 8)

x² + 9x + 8 = (x + 8)(x + 1)

Step-by-step explanation:

* Lets explain how to factorize the polynomial using the pattern

- The form of the quadratic polynomial is x² + px + q, where p is the

  coefficient of x and q is the numerical term

∵ x² + (a + b)x + (ab) = (x + a)(x + b)

- From the formula above the coefficient of x is the sum of the two

 factors a and b

∴ p = a + b and q = ab

- That means p is the sum of two numbers and q is the product of

  the same numbers

* Lets solve the problem

∵ x² + 9x + 8 is a quadratic polynomial

∵ x² + px + q is the form of quadratic polynomial

∴ p = 9 and q = 8

∵ p = a + b and q = ab

∴ a + b = 9 ⇒ (1)

∴ ab = 8 ⇒ (2)

- We must to find two numbers their product is 8 and their sum is 9

∵ The possibility of 8 as a product of two numbers is:

   2 × 4 OR 1 × 8

∵ The sum of 1 + 8 = 9

∴ The value of a and b are 1 and 8

- It does't matter which of them = 1 or which of them = 8

∴ x² + (a + b)x + ab = x² + (1 + 8)x + (1)(9)

∵ x² + (a + b)x + (ab) = (x + a)(x + b)

∴ x² + (1 + 8)x + (1)(9) = (x + 1)(x + 8)

∴ x² + 9x + 8 = (x + 1)(x + 8)

- OR

∴ x² + 9x + 8 = (x + 8)(x + 1)

3 0
3 years ago
PLEASE HELP WITH THIS
Anuta_ua [19.1K]

Answer:

528\ cm^2

Step-by-step explanation:

1. Approach

The surface area is the two-dimensional space around a three-dimensional object. In other words, if one was going to wrap an object with paper, the surface area is the amount of paper one would need. To find the surface area, one could find the area of each face of the prism and then add up all of the values.

2. Finding the surface area,

To find the area of each face of the prism, one must multiply the length of the face by the width of the face. After doing so, add up all of the resulting values.

10 * 20 = 200

8 * 20 = 160

6 * 20 = 120

\frac{1}{2} * 6 * 8 = 24

\frac{1}{2} * 6 * 8 = 24

Add up all of the values,

200 + 160 + 120 + 24 + 24

= 528

4 0
3 years ago
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