Help please

The formula y - y1 = m(x - x1) is the point-slope form of the equation of a line where m is the slope of the line and (x, y) and

a_sh-v [17]

Answer:

The slope of a line that includes the points (4, -2) and (5, 0) is 2

Step-by-step explanation:

You know that the formula y - y1 = m(x - x1) is the point-slope form of the equation of a line where m is the slope of a line.

The line must include the points (4, -2) and (5, 0). So, being:

(x,y)= (4,-2)
(x1,y1)= (5, 0)

and replacing in the point-slope form of the equation of a line:

-2-0=m(4-5)

You solve the equation for m and get:

-2=m*(-1)

$m=\frac{-2}{-1}$

m=2

<u><em>The slope of a line that includes the points (4, -2) and (5, 0) is 2</em></u>

5 0

3 years ago

What is the number of times a base is multiplied by its self indicated by an exponent

lozanna [386]

The question is worded a bit strangely (in my opinion anyway), but I think your teacher wants you to describe how exponents work.

Let's say we had the expression $5^3$

The base is 5 as its the bottom most value (think of something like the base of a tree or building). The exponent is 3.

The exponent of 3 tells the reader to multiply the base 5 by itself 3 times like so

$5^3 = 5*5*5 = 125$

With larger exponents, it becomes more tedious to write out all the repeated multiplications, which is why many calculators have an exponent button to save time.

5 0

3 years ago

a regular rectangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface ar

Margarita [4]

A pyramid is regular if its base is a regular polygon, that is a polygon with equal sides and angle measures.
(and the lateral edges of the pyramid are also equal to each other)

Thus a regular rectangular pyramid is a regular pyramid with a square base, of side length say x.

The lateral faces are equilateral triangles of side length x.

The lateral surface area is 72 cm^2, thus the area of one face is 72/4=36/2=18 cm^2.

now we need to find x. Consider the picture attached, showing one lateral face of the pyramid.

by the Pythagorean theorem:

$h= \sqrt{ x^{2} - (x/2)^{2}}= \sqrt{ x^{2}- x^{2}/4}= \sqrt{3x^2/4}= \frac{ \sqrt{3} }{2}x$

thus,

$Area_{triangle}= \frac{1}{2}\cdot base \cdot height\\\\18= \frac{1}{2}\cdot x \cdot \frac{ \sqrt{3} }{2}x\\\\ \frac{18 \cdot 4}{ \sqrt{3}}=x^2$

thus:

$x^2 =\frac{18 \cdot 4}{ \sqrt{3}}= \frac{18 \cdot 4 \cdot\ \sqrt{3} }{3}=24 \sqrt{3}$ (cm^2)

but $x^{2}$ is exactly the base area, since the base is a square of sidelength = x cm.

So, the total surface area = base area + lateral area = $24 \sqrt{3}+72$ cm^2

Answer: $24 \sqrt{3}+72$ cm^2

4 0

3 years ago

At the beginning of spring, Caroline planted a small sunflower in her

elixir [45]

Answer:

After 10 weeks: 40 inches

Step-by-step explanation:

Equation

15 + 2.5w = h

15 = beginning height

2.5 = rate per week

w = weeks passed

h = total height

8 0

2 years ago

A line passes through the points (0, -2) and (0, 5). Is it possible to write an equation of the line in slope-intercept form? ju

Feliz [49]

Consider what the slope of this line would be. Slope is rise/run; this line rises 7 (5 - (-2)) and runs 0 (0 - 0). This means that the slope would be 7/0. Dividing by zero is not possible, therefore, it cannot be written in slope-intercept form.

7 0

3 years ago