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2 years ago

The slope of the line below is 2. Use the coordinates of the labeled point to find a point-slope equation of the line.

Mathematics

1 answer:

stich3 [128]2 years ago

3 0

Answer:

Option: D is the correct answer.

The equation of line in point-slope form is given by:

y-9=2(x-1)

Step-by-step explanation:

We know that the point-slope equation of a line is given by:

y-b=m(x-a)

where (a,b) is the point from which the line passes and m is the slope of the line.

Here we are given that:

The line passes through (1,9) and slope of the line is given to be 2.

Hence,

(a,b)=(1,9) and m=2

Hence, the equation of line is given by:

y-9=2(x-1)

Therefore, the point slope intercept equation of the line is: D

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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

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3 years ago

How do you write 100, in an exponential form

Allushta [10]

1. 10^2

2. 10^5

3. 10^4

Hope this helped!

Nate

8 0

2 years ago

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schepotkina [342]

Answer:

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Step-by-step explanation:

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2 years ago

Stephen's lunch bill is currently at $8.33. Stephen orders a fruit salad for take-out, and wants to leave $2.25 as a tip for his

Salsk061 [2.6K]

Answer:

$1.53

Step-by-step explanation:

The computation of the change in the bill is shown below:

Total money he has to pay is

= $8.33 + $2.25

= $13.47

And, he have

= $10 + $5

= $15

So, the change would be

= $15 - $13.47

= $1.53

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2 years ago

Last month, a dwarf lemon tree grew half as much as a semi dwarf lemon tree. A full size lemon tree grew three times as much as

Nadusha1986 [10]

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2 years ago