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satela [25.4K]
3 years ago
11

I need help please will give you 5 stars and good rating

Mathematics
2 answers:
Brums [2.3K]3 years ago
3 0

Answer:

Step-by-step explanation:

atroni [7]3 years ago
3 0

Answer:

x=12

Step-by-step explanation:

To solve for the variable, we must isolate the variable, which is x.

\sqrt{x+4} -3=1

3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.

\sqrt{x+4} -3+3=1+3

\sqrt{x+4} =1+3

\sqrt{x+4} =4

The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.

(\sqrt{x+4})^2 =4^2

x+4=4^2

Evaluate the exponent.

4^2= 4*4=16

x+4=16

4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.

x+4-4=16-4

x=16-4

x=12

The solution to this equation is x=12.

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F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?
Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

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Therefore;

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Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) =  (1, 4)

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We check the length of HF, from the equation for the length to of a line to get;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

l_{HF} = \sqrt{\left (4-7  \right )^{2}+\left (1-(-11)  \right )^{2}} = \sqrt{\left (-3  \right )^{2}+\left (12  \right )^{2}} = 3\cdot \sqrt{17}

Similarly, we check the length of HJ, to get;

l_{HF} = \sqrt{\left (3-7  \right )^{2}+\left (5-(-11)  \right )^{2}} = \sqrt{\left (-4  \right )^{2}+\left (16  \right )^{2}} = 4\cdot \sqrt{17}

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

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