February 2, the temperature at 11 AM was 5°F. At

Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope for

Bess [88]

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

<h3>What is the slope of an equation?</h3>

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$ .

The standard form of an equation is Ax + By = C.

The given the point-slope form is $y+1=\frac{2}{3} (x-8)$ .

Multiply each term by 3 of the equation.

$(y+1) \times3=\frac{2}{3} (x-8) \times3$

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

To learn more about the slope visit:

brainly.com/question/3605446.

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4 0

2 years ago

Samantha had 8 balloons. Jacob has 1/2 as many. How many does Jacob have?

stealth61 [152]

Jacob has 4 balloons.

6 0

3 years ago

Read 2 more answers

What’s the answer? I don’t understand

pashok25 [27]

The system of equations does not have one solution because the lines will never intersect (last one)

8 0

3 years ago

Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

Phantasy [73]

Answer:

Part A

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the given values we get;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

$a = R \cdot cos \left(\dfrac{\pi}{n} \right)$

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the values gives;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore, we get;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

5 0

2 years ago

A object 6.3 feet tall casts a shadow of 18.9 feet long, so a oject that is 13.8 feet tall casts a shadow of?