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3 years ago

Graph equation y-5=-5(x-1)

Mathematics

1 answer:

Yakvenalex [24]3 years ago

3 0

Answer:

your slope intercept form is y=-5x+6

Step-by-step explanation:

you distribute the -5 and then you add 5 to your now positive 5 to isolate your y variable

then once you have the equation you start at your y-intercept (0,6) and then you go up and or down 5 then you move to the left one because you have a negative slope

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Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through th

Bond [772]

The three vectors $\langle0,0,1\rangle$ , $\langle1,0,8\rangle$ , and $\langle0,1,9\rangle$ each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

$\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle$

$\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle$

Then the cross product of these two results is normal to the plane:

$\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle$

Let $(x,y,z)$ be a point on the plane. Then the vector connecting $(x,y,z)$ to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

$\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0$

which reduces to the equation of the plane,

$-7x-8y+z-1=0\implies z=7x+8y+1$

Let $z=f(x,y)$ . Then the volume of the region above $R$ and below the plane is

$\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}$

6 0

3 years ago

Solve the radical equation x – 7 = square root of -4x+28. Which statement is true about the solutions to the radical equation? T

Julli [10]

Answer:

x = 3 and 7

There are two true solutions.

Step-by-step explanation:

To solve $x-7 = \sqrt{-4x+28}$ , use inverse operations by squaring both sides of the equal sign.

$(x-7)^2 = (\sqrt{-4x+28})^2\\x^2-14x+49 = -4x+28\\x^2-14x+4x+49-28 = 0\\x^2-10x+21=0$

The quadratic expression can be factored into binomials and set equal to 0 by the zero product property to find x.

(x - 3) ( x - 7) = 0

x-3 = 0 so x=3

x-7 = 0 so x=7

Now check each solution into the original equation to be sure it solve the solution and is not extraneous.

$7-7 = \sqrt{-4(7)+28}\\ 0=0$

and

$3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4$ [/tex]

3 0

3 years ago

Which graphs below have a domain of all real numbers? Which have a range of all real numbers? Which are functions?

slava [35]

Answer:

Step-by-step explanation:

From the picture attached,

Graph (A)

Domain of the function : (-∞, ∞) or a set of real numbers

Range of the function : (-∞, ∞) or a set of real numbers

Graph (B),

Domain : (-∞, ∞) Or a set of real numbers

Range : (-∞, 6] Or x ≤ 6

Graph (C),

Domain : [-2, ∞) or x ≥ -2

Range : (-∞, ∞) Or a set of real numbers

Therefore, Graphs (A), (B) have the domain of all real numbers and Graph (C) has the range of all real numbers.

Since all the parabolas are not the functions,

Therefore, Graph (C) is not a function. Graphs (A) and (B) are the functions.

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3 years ago

What is the principal, if the interest earned is $22, the simple annual interest rate is 2%, and the time is one year?

seropon [69]

Answer:

$1,100

Step-by-step explanation:

first find the principal first Multiply the rate 0.02 by the time 1 year this gives us 0.02 then divide the interest ($22) by 0.02 then you get $1,100.

Hope that helped!

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3 years ago

Write the prime factorization of 48. use exponents when appropriate and order the factors from least to greatest

horrorfan [7]

What can be divided? For example, for 48 you can divide 1, and 48 and you can also divide it by two which equals to 24 so keep writing that from least to greatest. You don't have repeat answers.
1,2,3,4,6,8,12,16,24,48

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3 years ago