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4 years ago

Write an equation for the line perpendicular to y = 5x – 12 that contains (–3, –1).

2 answers:

6 0

The answer is B

Write an equation for the line perpendicular to y = 5x – 12
that contains (–3, –1).
----------------
The given equation has slope = 5
----
The desired equation must have slope = -1/5
-------
Form: y = mx + b
Solve for "b" when m = -1/5 and y = -1 when x = -3

==================
-1 = (-1/5)(-3) + b
-1 = (3/5) + b
b = -8/5
------------------
Answer=y + 1 = 5(x + 3)

Fed [463]4 years ago

5 0

Y = 5x - 12
Here, slope = 5
Perpendicular line slope = -1/5 [ opposite and reciprocal ]

Now, y - y1 = m(x - x1)
y + 1 = -1/5 (x + 3)

In short, Your Answer would be Option B

Hope this helps!

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1) PART A : determine the domain and range of the function in the graph.

anzhelika [568]

1) Domain: x is greater than -2 and greater than or equal to 5
Range: y is greater than -1 and less than or equal to 3

2) No the function is not one to one because one to one functions can’t have multiple points on a function with the same y value.

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3 years ago

Using the simple interest formula I = PRT, calculate the interest that would be earned.

Korolek [52]

SI = P × R × T

SI = 1000 × 6/100 × 2 = $120

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3 years ago

Solve for equation √-5p=√24-p

blsea [12.9K]

Answer:

Step-by-step explanation:

25,219,829 solved | 850 online

p2-5p-24=0

Two solutions were found :

p = 8

p = -3

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2".

Step by step solution :

Step 1 :

Trying to factor by splitting the middle term

1.1 Factoring p2-5p-24

The first term is, p2 its coefficient is 1 .

The middle term is, -5p its coefficient is -5 .

The last term, "the constant", is -24

Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24

Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .

-24 + 1 = -23

-12 + 2 = -10

-8 + 3 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3

p2 - 8p + 3p - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

p • (p-8)

Add up the last 2 terms, pulling out common factors :

3 • (p-8)

Step-5 : Add up the four terms of step 4 :

(p+3) • (p-8)

Which is the desired factorization

Equation at the end of step 1 :

(p + 3) • (p - 8) = 0

Step 2 :

Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : p+3 = 0

Subtract 3 from both sides of the equation :

p = -3

Solving a Single Variable Equation :

2.3 Solve : p-8 = 0

Add 8 to both sides of the equation :

p = 8

8 0

4 years ago

How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?

RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

$y = f(x)$

To find the area under the curve $y = f(x)$ between $x = a$ and $x = b$ , all we need is to integrate $y = f(x)$ between the limits of $a$ and $b$ .

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

$A=\int _a^b|f\left(x\right)|dx$

= $\int _{-2}^2\left|x^2-4\right|dx$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=\int _{-2}^2x^2dx-\int _{-2}^24dx$

solving

$\int _{-2}^2x^2dx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}$

$=\left[\frac{x^3}{3}\right]^2_{-2}$

computing the boundaries

$=\frac{16}{3}$

Thus,

$\int _{-2}^2x^2dx=\frac{16}{3}$

similarly solving

$\int _{-2}^24dx$

$\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax$

$=\left[4x\right]^2_{-2}$

computing the boundaries

$=16$

Thus,

$\int _{-2}^24dx=16$

Therefore, the expression becomes

$A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx$

$=\frac{16}{3}-16$

$=-\frac{32}{3}$

$=-10.67$ square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

6 0

3 years ago

What is the perimeter of a square with a side length 6x - 5

jolli1 [7]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{24x - 20}}}}}$

Step-by-step explanation:

Given,

Length ( L ) = 6x - 5

Perimeter of a square ( P ) = ?

Finding the perimeter of a square having length of 6x- 5

$\boxed{ \bold{ \boxed{ \sf perimeter \: of \: a \: square \: = 4l}}}$ ( where l is the side of the square )

plug the value of length

⇒ $\sf{4(6x - 5)}$

Distribute 4 through the parentheses

⇒ $\sf{4 \times 6x - 4 \times 5}$

⇒ $\sf{24x - 20}$

Hope I helped!

Best regards!!

4 0

3 years ago