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3 years ago

Find the slope of the line going through the given pair of points. (-4, 0) and (0, -3)

Mathematics

2 answers:

Lynna [10]3 years ago

8 0

Answer:

Step-by-step explanation:

alexdok [17]3 years ago

5 0

Slope = (difference of y-coordinates)/(difference of x-coordinates) = (0-(-3))/(-4-0) = 3/(-4) -3/4

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Rename 0.600 as place values

Vlad1618 [11]

0.600 = six thousandths written out

5 0

3 years ago

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

Can someone please help me <br>a<br>show your work please

sertanlavr [38]

Answer:

x= 3

Step-by-step explanation:

19x-5=7+15x

19x-15x=7+5

4x=12

x=12/4

x=3

8 0

3 years ago

Read 2 more answers

On a workday, the average decibel level of a busy street is 70 db, with 100 cars passing a given point every minute. if the numb

nignag [31]

70dB is represented by 100cars in 60sec. Therefore if the number of cats is reduced by 3/4 in the same amount of time(60s), then the decibel level will reduce by 3/4 also. So 70dB * .25= 17.5dB

4 0

3 years ago

The shown bellow question answer

Serhud [2]

Answer:

The area of the shape can be divided into the area of the rectangle, and the area of the semi-circle.

The area of the rectangle can be found by $11*4=44$

The area of a semi-circle can be found with the formula $\frac{1}{2} \pi r^2$ where r is the radius.

Since we know the diameter of the semi-circle is 4,

the radius will be 4 ÷ 2 = 2.

Therefore, the area of the semi-circle is $\frac{1}{2}\pi 2^2=\frac{1}{2}\pi*4=2\pi$

Therefore, the area of the shape is $44+2\pi$ or $50.283cm^2$ (3 decimal places)

3 0

2 years ago