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2 years ago

Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).

Mathematics

2 answers:

kozerog [31]2 years ago

5 0

Answer:

Point-slope form: y-4=2(x+1)

Slope intercept form: y=2x+6

I hope this helps!

xz_007 [3.2K]2 years ago

4 0

Answer:

$y-4=2(x+1)$

Step-by-step explanation:

Point-slope form is equal to

$y-y_1=m(x-x_1)$

where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:

$4-2=m(-1-(-2))$

We can simplify negative one minus negative two as positive 1.

$4-2=m(1)$

4 minus 2 is 2, so m times 1 is 2. That means m is 2.

Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:

$y-4=2(x+1)$

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A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude

I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

( a ) = 35 cm

( b ) = 54 cm

( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

<u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

$\sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}$

where ( s ) :

$\sf \longrightarrow s = \dfrac{a + b + c}{2}$

Therefore, for the given triangle first we will calculate ( s )

$\begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}$

Now, Area of triangle will be:

$\begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}$

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

$\begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}$

3 0

1 year ago

Read 2 more answers

15. find the values of x and y

zloy xaker [14]

Answer:

y = 8

x = 21

Step-by-step explanation:

Find x first. Since there is a straight line, we can conclude it's equal to 180 degrees.

11x + 10 -61 = 180

Add 10 to negative 61.

11x - 51 = 180

Add 51 to both sides.

11x = 231

Divide 11 both sides

x = 21.

Now put x in the equations to solve.

This is for the small angle on the right side.

(21+10) = 31

This is for the big angle on the right side.

(10(21) - 61)

210 - 61 = 149.

Now for the other side, we know the degree for the smaller side on the left side since it's a vertical angle.

31 degrees for top left angle. Since we know this side is 180 just subtract 31 from 180 and you'll get 149.

18y + 5 = 149

Subtract 5 both sides.

18y = 144

y = 8.

3 0

2 years ago

A plane descends to sea level from 36 comma 400 feet after being airborne for 1 and one half hours. The entire flight time is 3

andrew-mc [135]

Answer:

350 feet per minute

Step-by-step explanation:

The amount of time it took the plane to descend is 3 hours 14 minutes minus 1 hour 30 minutes.

This means it took 104 minutes for the plane to descend 36,400 feet.

Dividing 36400 by 104, you get 350 which is the average rate of descent in feet per minute.

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3 years ago

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Nila uses the equation c=8h to figure out the total amount c she should charge a customer if she babysits for h hours.

nydimaria [60]

Answer:

c = 10h

Step-by-step explanation:

c = 8h

Where,

c = Total amount she should charge a customer

h = Number of hours

8 = amount charged per hour of babysitting

A. 8 is the constant of proportionality and it means Nila charges $8 per hour of babysitting

B. If she decides to increase the rate she charges customers by $2 per hour, then the new equation she should use to determine how much to charge her customers is:

c = (8 + 2)h

c = 10h

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2 years ago

Sarah ran 1/3 of a mile 5 days in a row. How many miles did she run in total?

Vladimir79 [104]

Answer:5/3

Step-by-step explanation:

you can do 1/3 x5 and that will give you 5/3

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2 years ago