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3 years ago

Calculate the slope of the points (-2, -1) and (3, 4)

2 answers:

3 0

Slope = (y₂ - y₁)/(x₂ - x₁)

(-2, -1)
x₁ y₁

(3, 4)
x₂ y₂

m = (4 + 1)/(3 + 2)
m = (5)/(5)
m = 1

The slope of the points is 1.

Burka [1]3 years ago

3 0

Slope = (4 +1)/(3 +2) = 5/5 = 1

answer
slope = 1

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What is the slope of the line shown below?

zhannawk [14.2K]

Answer:

The slope of the line is -3.

Step-by-step explanation:

The slope equation is:

m= y2-y1/x2-x1

In this case:

m= -3-6/2+1 (remember that a negative minus a negative gives you a positive)

Which equals:

m=-9/3

Divide and you get -3.

5 0

3 years ago

What is the area of this triangle ?

oee [108]

Answer:

Area of triangle is 9.88 units^2

Step-by-step explanation:

We need to find the area of triangle

Given E(5,1), F(0,4), D(0,8)

We will use formula:

$Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}$

We need to find the lengths of side DE, EF and FD

Length of side DE = a = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side DE = a = $=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60$

Length of side EF = b = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side EF = b = $=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8$

Length of side FD = c = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side FD = c = $=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4$

so, a= 8.60, b= 5.8 and c = 4

s = a+b+c/2

s= 8.6+5.8+4/2

s= 9.2

Area of triangle= $=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88$

So, area of triangle is 9.88 units^2

4 0

3 years ago

What would you expect the nominal rate of interest to be if the real rate is 4.4 percent and the expected inflation rate is 7.5

ANTONII [103]

Answer:

Nominal Interest rate=11.9%

Step-by-step explanations:

The Fisher effect is a theory propounded by an economist named Irving Fisher.

Fisher's equation shows the relationship between real Interest rate, expected inflation rate and nominal Interest rate.

It can be calculated by subtracting the expected inflation rate from the nominal Interest rate to give the real Interest rate.

Real Interest rate= nominal Interest rate - expected inflation rate

Given,

Real Interest rate= 4.4%=0.044

Expected inflation rate=7.5%=0.075

Nominal Interest rate=?

Therefore,

Real Interest rate=nominal Interest rate - expected inflation rate

Nominal Interest rate=Real Interest rate+expected inflation rate

Nominal Interest rate=0.044+0.075

Nominal Interest rate=0.119

Nominal Interest rate=11.9%

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3 years ago

Expressions cannot _____.

Arlecino [84]

Expressions cannot .....be solved.

6 0

3 years ago

Read 2 more answers

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 8exyz, (0, 0, 8

Dima020 [189]

Let $f(x,y,z)=x+y+z-8e^{xyz}$ . The tangent plane to the surface at (0, 0, 8) is

$\nabla f(0,0,8)\cdot(x,y,z-8)=0$

The gradient is

$\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)$

so the tangent plane's equation is

$(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8$

The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by $t$ , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

$(1,1,1)t+(0,0,8)=(t,t,t+8)$

or $x(t)=t$ , $y(t)=t$ , and $z(t)=t+8$ .

(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)

4 0

2 years ago