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Liula [17]
3 years ago
7

Please help ASAP!!!!!!

Mathematics
1 answer:
ahrayia [7]3 years ago
6 0

Answer:

Equation in point slope form is: y+3=4(x+6)

Solving for y we get: \mathbf{y=4x+21}

Step-by-step explanation:

We are given:

Slope = 4

Point (-6,-3)

Point Slope form:

We need to write equation for point-slope form

The general equation of point slope form is: y-y_1=m(x-x_1)

Where m is slope and y_1\: and\: x_1\\ are points on the line

Now putting values of slope m= 4, x_1=-6, y_1=-3 and finding equation

y-y_1=m(x-x_1)\\y-(-3)=4(x-(-6)\\y+3=4(x+6)

So, equation in point slope form is: y+3=4(x+6)

Solve for y

y+3=4(x+6)\\y+3=4x+24\\y=4x+24-3\\y=4x+21

So, solving for y we get: \mathbf{y=4x+21}

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1 + tanx / 1 + cotx =2
Lera25 [3.4K]

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer:  x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

4 0
3 years ago
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region? 2x2 4x2 6x2 8x2
Savatey [412]
The picture in the attached figure

we know that
area of the <span>the shaded region=area of rectangle -area of a kite

area of rectangle=(3x+x)*(x+x)----> 4x*2x---> 8x</span>²

area of a kite=(1/2)*[d1*d2]
where d1 and d2 are the diagonals
d1=4x
d2=2x
so
area of a kite=(1/2)*[4x*2x]----> 4x²

area of the the shaded region=8x²-4x²-----> 4x²

the answer is 
4x²

4 0
3 years ago
Read 2 more answers
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equa
Setler [38]

Answer:

b=0.5 in

b=2 in

Step-by-step explanation:

we know that

The perimeter of triangle is equal to

2a+b=15

Solve for a

a=\frac{15-b}{2} -----> equation A

Applying the Triangle Inequality Theorem

a+a > b

2a > b -----> inequality B

<u>Verify each case</u>

case 1) b=-2 in

This value not make sense, the length side cannot be a negative number

case 2) b=0 in

This value not make sense

case 3) b=0.5 in

substitute the value of b in the equation A and solve for a

a=\frac{15-0.5}{2}=7.25\ in

substitute the values of b and  a in the inequality B

2a > b

2(7.25) > 0.5

14.50 > 0.5 -----> is  true

therefore

b=0.5 in  make sense for possible values of b

case 4) b=2 in

substitute the value of b in the equation A and solve for a

a=\frac{15-2}{2}=6.5\ in

substitute the values of b and  a in the inequality B

2a > b

2(6.5) > 2

13 > 2 -----> is true

therefore

b=2 in  make sense for possible values of b

case 5) b=7.9 in

substitute the value of b in the equation A and solve for a

a=\frac{15-7.9}{2}=3.55\ in

substitute the values of b and  a in the inequality B

2a > b

2(3.55) >7.9

7.1 > 7.9 -----> is not true

therefore

b=7.9 in  not make sense for possible values of b

5 0
3 years ago
Read 2 more answers
Find the surface area of the cylinder in terms of pi. 9cm and 19cm
Natali [406]

Answer:

Surface area of cylinder= 211.5π

Step-by-step explanation:

Given,

Height of cylinder = 19cm

Diameter of cylinder = 9cm

i.e Radius of cylinder = diameter/2 = 9/2 = 4.5cm

Surface area of cylinder = 2πrh + 2πr²

Plug corresponding values of r and h in surface are formula.

Surface area of cylinder = 2πrh + 2πr² = 2π*4.5*19 + 2π*4.5²

Surface area of cylinder = 171π+40.5π = 211.5π

Hence we get surface area of cylinder= 211.5π


3 0
3 years ago
-4(4x + 4) + 7(1 + 9x)
SVEN [57.7K]

Answer:

47x - 9

Step-by-step explanation:

-4(4x + 4) + 7(1 + 9x)

-16x -16 + 7 + 63x

47x -9

You can find what x = because there is no = sign. This is in simplest form.

4 0
3 years ago
Read 2 more answers
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