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3 years ago

The equation that corresponds to this diagram is 6 (x+ 1)=24.

Mathematics

1 answer:

Annette [7]3 years ago

7 0

Answer:

x is 3

Step-by-step explanation:

6 (x + 1) = 24

6 (x) + 6(1) = 24

6x + 6 = 24

Subtract 6 on both sides

6x + 6 - 6 = 24 - 6

6x + 0 = 18

6x = 18

x = 18/6

x = 3

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A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.

Kobotan [32]

Answer:

The numbers are

$-2+3\sqrt{5}$ and $3\sqrt{5}$

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

$x=y-2$

$y=x+2$ ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

$4y+x^2=49$ ----> equation B

substitute equation A in equation B

$4(x+2)+x^2=49$

solve for x

$x^2+4x-41=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^2+4x-41=0$

$a=1\\b=4\\c=-41$

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}$

$x=\frac{-4\pm\sqrt{180}} {2}$

$x=\frac{-4\pm6\sqrt{5}} {2}$

$x=-2\pm3\sqrt{5}$

The positive real number is

$x=-2+3\sqrt{5}$

Find the value of y

$y=x+2$

$y=-2+3\sqrt{5}+2$

$y=3\sqrt{5}$

6 0

4 years ago

The perimeter of a triangle garden is 54 feet. Find the length of the three sides if the middle length side is 4 feet greater th

jeka94

9514 1404 393

Answer:

9 ft, 22 ft, 23 ft

Step-by-step explanation:

Let s represent the length of the shortest side. Then the middle length side is (2s+4) and the longest side is (3s-4). The perimeter is the sum of the side lengths:

54 = s +(2s +4) +(3s -4)

54 = 6s . . . . . . . . . . . . . . collect terms

9 = s . . . . . . . . . . divide by 6

2s+4 = 2·9 +4 = 22

3s -4 = 3·9 -4 = 23

The lengths of the three sides are 9 feet, 22 feet, and 23 feet.

6 0

3 years ago

For a two way frequency tables the variables can be found

34kurt

Answer: C. Along the rows and columns .

Step-by-step explanation:

3 0

3 years ago

Find the area of the polygon

Evgesh-ka [11]

Answer:

784m^2

Step-by-step explanation:

is a rectangle with sides of 40m and 20m, in the upper right corner a right triangle has been removed with the legs of: 40 - 32 = 8m and 20 - 16 = 4m, we find the area of the rectangle (b * h).

40 * 20 = 800m ^ 2, then we find the area of the right triangle

1/2 b * h: 1/2 8 * 4 = 16 m ^ 2.

we remove the area of the triangle from the rectangle and we have the area of the figure: 800 - 16 = 784m^2

3 0

2 years ago

The least common multiple of two numbers is 60. the prime factorization of one number is 3 times 5. what is the prime factorizat

gulaghasi [49]

The first number would be 3×5=15.
Another number could have different values. it could be
4=2×2
12=2×2×3
20=2×2×5
60=2×2×3×5

7 0

3 years ago