Anyone know the answer to this ?

Determine the standard form of the equation of the line that passes through (-6,6) and (3, -2)

viva [34]

Answer:

(8/9)x +y = (2/3)

Step-by-step explanation:

General standard form of an equation of a line is y = mx+b, where m is the slope of the line and b is the y-intercept ( where the line intersects the y-axis.)

For points (-6, 6) and (3, -2)

m= (y2-y1)/(x2-x1) = (-2-6) / (3-(-6)) = -8 / 9

y = (-8/9)x +b

Substitute any of the 2 points to find b. If we choose (x=3, y= -2) then

-2 = (-8/9)*3 +b, simplify (-8*3)/9

-2 = (-8/3)+b, add (8/3) to both sides

-2+(8/3) = b, find the common denominator and add the fractions

(-6+8)/3 =b

2/3 =b

The standard form of the equation of the line that passes through (-6,6) and (3, -2) is (8/9)x + y = (2/3)

7 0

3 years ago

I need help on this math problem

abruzzese [7]

Answer:

for the first one, simply add g(x) and h(x) :

x+3 + 4x+1 = 5x + 4

the second one, you would multiply them :

(x+3)(4x+1) = 4x^2 + 13x + 3

the last one, you would subtract :

(x+3)-(4x+1) = -3x + 2

and then substitute 2 for 'x' :

-3*2 + 2 = -6 + 2 = -4

8 0

3 years ago

Read 2 more answers

Leon bought 50 backpacks at a sporting store. 20% of the backpacks were pink and 1/2 of the backpacks were blue. How many of the

My name is Ann [436]

20% of 50 is 10

Half of 50 is 25

25 + 10 = 35

50 -35 = 15

15 of the backpacks were neither pink or blue

Hope this helps :)

5 0

4 years ago

NEED HELP ASAP, WILL GIVE BRAINLIEST

Stella [2.4K]

Given:

The equation of circle is

$(x+3)^2+y^2=9$

To find:

The polar form of given circle.

Solution:

We have,

$(x+3)^2+y^2=9$

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

$(x^2+y^2)+6x+9=9$

Subtracting 9 from both sides, we get

$(x^2+y^2)+6x=0$

We know that, $x^2+y^2=r^2$ and $x=r\cos \theta$ .

$r^2+6(r\cos \theta)=0$

$r(r+6\cos \theta)=0$

$r=0$ and $r+6\cos \theta=0$

We know that, r is radius it cannot be 0. So,

$r+6\cos \theta=0$

$r=-6\cos \theta$

Therefore, the correct option is A.

4 0

3 years ago

A man 2 m high observes the angle of elevation to the top of a building to be 71° and the angle of depression to the bottom of t

Yuki888 [10]

Answer:

The building is 13.91 m tall

Step-by-step explanation:

The parameters given are;

Angle of elevation to the top of the building = 71°

Angle of depression to the bottom of the building = 26°

Height of the man = 2 m

Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:

The hypotenuse side = The sight of the man to the bottom of the building

Hence;

In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building

∴ ∠A + Angle of depression to the bottom of the building = 90°

∠A = 90° - 26° = 64°

∠B = 90° and ∠C = 26° (Sum of angles in a triangle)

$Tan(C) = \frac{AB}{BC}$

Distance of the man from the building = BC

$Tan(26) = \frac{2}{BC}$

$BC= \frac{2}{ Tan(26) } = 4.1 \, m$

Given that the angle of elevation to the top of the building = 71°, we have;

ΔAET

Where:

A is at the head level of the man,

E is the point on the building directing facing the man and

T is the top of the building

Hence AE = BC and ∡TAE = 71°

TE + AB= The height of the building

$Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}$

∴ TE = tan(71°) × 4.1 = 11.91 m

Hence the height of the building = 11.91 + 2 = 13.91 m.

4 0

3 years ago