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SSSSS [86.1K]
2 years ago
11

In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second

Mathematics
1 answer:
Molodets [167]2 years ago
6 0

Given:

In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.

To find:

The equation for the given situation if the sum of the numbers is 77.

Solution:

a. Let the first number in the set is x.

The second is 3 more than the first. So, the second number is (x+3).

The 3rd number is a square of the second. So, the third number is (x+3)^2.

Therefore, the first, second and third numbers are x,(x+3),(x+3)^2 respectively.

b. The sum of the numbers is 77.

First number + Second number + Third number = 77

c. So, the equation in terms of x is:

x+(x+3)+(x+3)^2=77

Therefore, the required equation is x+(x+3)+(x+3)^2=77.

d. On simplification, we get

x+x+3+x^2+6x+9=77                   [\because (a+b)^2=a^2+2ab+b^2]

x^2+(6x+x+x)+(3+9)=77

x^2+8x+12=77

Subtract 77 from both sides.

x^2+8x+12-77=77-77

x^2+8x-65=0

Therefore, the simplified form of the required equation is x^2+8x-65=0.

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lions [1.4K]

Answer:

86

Step-by-step explanation:

<u>Perimeter of WXY = WSY+WRX+XY</u>

<em>--> WSY = SY x 2</em>

--> WSY = 16 x 2 = 32

<em>Since it is an isosceles triangle, WRX = WSY</em>

--> WRX = 32

<em>--> Draw a straight line from W to XY to divide it into two halves assuming it to be point A. This would form a right angle triangle of WAX.</em>

<em>--> Solve it using the cos theta rule</em>

--> Angle = Angle X = 70°

    Hypotenuse = WRX = 32

    Adjacent = WA = ?

<em>--> Cos (Angle) = Adjacent/Hypotenuse</em>

    Cos (70) = WA/32

    WA = 10.9 rounded off to 11

--> WA=AY= 11

--> XY = WA + AY = 11+11 = 22

<em>--> Perimeter = WSY+WRX+XY</em>

    Perimeter = 32+32+22

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Therefore, the perimeter of WXY is 86.

4 0
2 years ago
The length of a rectangle is 2 cm longer than its width if the perimetier of the rectangle is 44cm, find its area
Natasha2012 [34]
L=w+2 and 2w+2l=44

substitute equation for length in perimeter equation

2w+2(w+2)=44
2w+2w+4=44
4w+4=44
4w=40
w=10

substitute width into length equation to get length

l=10+2
l=12

a=lw
a=12*10
a=120 cm^2
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3 years ago
PLEASE OPEN THIS, I NEED HELP!!!! WHAT BELONGS IN THE ? AND WHY?
ruslelena [56]

Answer:  see below

<u>Step-by-step explanation:</u>

Write each equation in y = mx + b format where m is the slope and b is the y-intercept.

Left side: -4 ≤ x < -1

If you continue the line through the y-axis it will pass through (0, 4) --> b = 4

The rise over run is -1 over 1 --> m = -1

y = (-1)x + (4)   -->    y = -x + 4

Right side: -1 < x < 4

The line passes through (0,0) --> b = 0.

The rise over run is -1 over 1 --> m = -1

y = (-1)x + (0)    -->    y = -x

\large\boxed{f(x)=\bigg\{\begin{array}{ll} -x+4&;-4\leq x

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3 years ago
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