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3 years ago

Find the gradient of lines A and B

Mathematics

1 answer:

AleksAgata [21]3 years ago

6 0

Answer:

The gradient of lines A is 8 and B is -4

Step-by-step explanation:

As we know, the gradient of a line is its slope.

The formula to find the slope of a linear line is:

m = $\frac{y2-y1}{x2-x1}$

Line A

As we can see the line A goes through points:

C (x1, y1) = (0, -6)

D (x2, y2)= (2.5, 14)

<=> the slope of line A is:

= $\frac{14 - (-6)}{2.5-0}$

= $\frac{20}{2.5}$

= $8$

Line B

As we can see the line A goes through points:

E (x1, y1) = (2, 0)

F (x2, y2)= (0, 8)

<=> the slope of line B is:

= $\frac{8-0}{0-2}$

= -4

Hence, the gradient of lines A is 8 and B is -4

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Simplify<br> a(cube)-1000b(cube)<br> 64a(cube)-125b(cube)

Elanso [62]

The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.

<h3>Simplification</h3>

Question 1: a³ - 1000b³

a³ - b³

= (a-b) × (a² +ab +b²)

1000 is the cube of 10
a³ is the cube of a¹
b³ is the cube of b¹

So,

(a - 10b) × (a² + 10ab + 100b²)

Question 2: 64a³ - 125b³

a³ - b³

= (a-b) × (a² +ab +b²)

64 is the cube of 4
125 is the cube of 5
a³ is the cube of a¹
b³ is the cube of b¹

So,

(4a - 5b) • (16a² + 20ab + 25b²)

Learn more about simplification:

brainly.com/question/723406

#SPJ1

8 0

2 years ago

Give a combinatorial proof that the cardinality of the power set of a finite set A is 2^|A|

juin [17]

There are $\dbinom{|A|}k$ ways of building a subset of $k$ elements from $A$ , so the total number of subsets you can build is

$\displaystyle\sum_{k=0}^{|A|}\binom{|A|}k$

Recalling the binomial theorem, the above sum is equal to

$\displaystyle\sum_{k=0}^{|A|}\binom{|A|}k1^k1^{|A|-k}=(1+1)^{|A|}=2^{|A|}$

as required.

3 0

4 years ago

I don’t know I think u times both of them 40 and 36 then divide by 4 then times by 2 i don’t know

uranmaximum [27]

What is the question?

7 0

3 years ago

The area A, in square meters, of a rectangle with a perimeter of 160 meters is given by the equation A = 80w − w2, where w is th

Sonja [21]

Answer:

the width is 10 m

Step-by-step explanation:

if the relationship between area and width is

A = 80*w − w²

for an area A=700 m² , we have

700 m² = 80*w − w²

w² - 80*w + 700 m² = 0

aw² + b*w + c = 0

where a=1 , b=-80 and c=700

this quadratic equation has as solution the following formula

w = [-b ± √ ( b² - 4*a*c) ]/(2*a)

replacing values

w = [80 ± √ ( 80² - 4*1*700) ]/(2*1) = (80 ± 60)/2

then

w₁=(80 - 60)/2 = 10 m

w₂ =(80 + 60)/2 = 70 m

since the area has the form A= length * width = 80*w − w² = (80− w)*w

then the length of the rectangle is

length = 80− w

for w₁=10 m → length = 80− 10 = 70 m

for w₁=70 m → length = 80− 70 = 10 m

by definition the shorter side is the width ( and the longer one , the length) , therefore the only possible option is the first one .

Thus the width is 10 m

7 0

3 years ago

When Θ = 5 pi over 3, what are the reference angle and the sign values for sine, cosine, and tangent?

Sonbull [250]

Answer:

the reference angle is given by $\frac{\pi}{3}$

sine = negative

cosine = positive

tangent = negative

Step-by-step explanation:

We have been given the angle $\theta=\frac{5\pi}{3}$

The angle lies in Quadrant IV. Hence, in order to find the reference angle, we can subtract this angle with $2\pi$

Therefore, the reference angle is given by

$2\pi - \frac{5\pi}{3} \\\\=\frac{\pi}{3}$

In Quadrant IV, cosine and secant functions are positive and rest trigonometric functions are negative.

Thus, we have

sine = negative

cosine = positive

tangent = negative

4 0

3 years ago

Read 2 more answers