3 (x-5)+2 (3x+1)=45

Write an equation of the line that passes through the point (-6, -9) with slope-5.

Art [367]

Answer:

$y+9=-5(x+6)$

Step-by-step explanation:

We are being asked to write the equation in point-slope form:

$y-y_1=m(x-x_1)$ where m = slope and the first point = $(x_1,y_1)$

In this case, the slope is -5 and the point is $(-6,-9)$ so the equation will be:

$y+9=-5(x+6)$

Want to learn more about point-slope form? Check the link out:

https://www.albert.io/blog/point-slope-form/#What_is_point_slope_form

3 0

2 years ago

How would you solve the following problem?

seraphim [82]

The answer should be 1/9y^4

5 0

3 years ago

Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d

Stella [2.4K]

The answer is most likely A.

The integration interval [a, b] is split up into n subintervals of equal length (so each subinterval has width (b - a)/n, same as the coefficient of the sum of y terms) and approximated by the area of n rectangles with base (b - a)/n and height y.

n subintervals require n + 1 points, with

x₀ = a

x₁ = a + (b - a)/n

x₂ = a + 2(b - a)/n

and so on up to the last point x = b. The right endpoints are x₁, x₂, … etc. and the height of each rectangle are the corresponding y 's at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function G(x) continuous* over an interval [a, b] is equal to the slope of the secant line through x = a and x = b, i.e. the value of the difference quotient

(G(b) - G(a) ) / (b - a)

If G(x) happens to be the antiderivative of a function g(x), then this is the same as the average value of g(x) on the same interval,

$g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx$

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [a, b] into n subintervals of equal width (b - a)/n. Over the first subinterval, the area of a trapezoid with "bases" y₀ and y₁ and "height" (b - a)/n is

(y₀ + y₁) (b - a)/n

but y₀ is clearly missing in the sum, and also the next term in the sum would be

(y₁ + y₂) (b - a)/n

the sum of these two areas would reduce to

(b - a)/n = (y₀ + 2 y₁ + y₂)

which would mean all the terms in-between would need to be doubled as well to get

$\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)$

7 0

3 years ago

What is the product of 710 and 323? 135 11315 21730 3715

Firlakuza [10]

Answer:

I think I answer is 21730 I'm not sure tho

3 0

2 years ago

Item 20 A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the sc

siniylev [52]

Answer:

The ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

Step-by-step explanation:

Given:

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches.

Now, to find the ratio of the area of the school banner to the area of the sign.

Dimensions of school banner :

Length = 54 inches.

Width = 36 inches.

Dimension of school sign:

Length = 17 inches.

So, to we find the width of sign by using cross multiplication method:

Let the width be $x.$