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3 years ago

Evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2

Mathematics

2 answers:

blondinia [14]3 years ago

4 0

Answer:

Step-by-step explanation:

sashaice [31]3 years ago

3 0

Answer:

Step-by-step explanation:

13 - 0.75 (12) + 8 (0.5)

13 - 0.75 (12) + 4

13 - 9 + 4

4 + 4

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Suppose z equals f (x comma y ), where x (u comma v )space equals space 2 u plus space v squared, y (u comma v )space equals spa

barxatty [35]

$z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}$

We're given that $f_x(6,1)=3$ and $f_y(6,1)=-1$ , and want to find $\frac{\partial z}{\partial v}(1,2)$ .

By the chain rule, we have

$\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}$

and

$\dfrac{\partial x}{\partial v}=2v$

$\dfrac{\partial y}{\partial v}=-1$

Then

$\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)$

(because the point $(x,y)=(6,1)$ corresponds to $(u,v)=(1,2)$ )

$\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}$

4 0

3 years ago

Explain why 7* 6 x 5 x 4*3*2*1+5 is a composite numbers

xenn [34]

Answer:

7×6×5×4×3×2×1+5 can be written as 5*[7*6*5*4*3*2*+1] or 5*(1009). So, other than the number and 1, it has 5 and 1009 as its factors too. So it is a composite number.

Step-by-step explanation:

A composite number is a positive integer that has a factor other than 1 and itself.

7 0

3 years ago

Suppose line g is the line with the equation y = x. Given A (7,-3) , B (6,3), and C (-2,-7), what are the coordinates of the ver

juin [17]

Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)

Step-by-step explanation:

Reflecting over y = x maps (x,y) onto (y,x).

4 0

2 years ago

The length of a rectangle is 59 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the

Paul [167]

So.. hmm notice the picture here

we know the length is 59 more than twice the width,
twice the width, 2 * w, or 2w
59 more than that
2w + 59

we also know that, whatever that is, the diagonal of it is,
2 more inches than that, or
(2w + 59) + 2

now.. use the pythagorean theorem
$\bf c^2=a^2+b^2\implies \qquad 
\begin{cases}
a=2w+59\\
b=w\\
c=(2w+59)+2\to 2w+61
\end{cases}
\\\\\\
(2w+61)^2=(2w+59)^2+(w)^2
\\ \qquad\qquad \uparrow\qquad \qquad\qquad \qquad \uparrow \\
\textit{expand using binomial theorem, or FOIL}$

you'd end up with a quadratic, after simplifying, solve for "w"

7 0

3 years ago

1) ACT Prep: Linear Pair angles have measures (6x -9)°and (9x-6)° 1.

iris [78.8K]

The measure of angles are 69 degree and 111 degree

Solution:

Given is linear pair angles

The measure of angles are: (6x - 9) degrees and (9x - 6) degrees

A linear pair of angles is formed when two lines intersect.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore,

$(6x - 9) + (9x - 6) = 180\\\\\text{Remove the parenthesis and solve}\\\\6x - 9 + 9x - 6 = 180\\\\\text{Combine the like terms}\\\\6x + 9x - 15 = 180\\\\15x - 15 = 180\\\\\text{Move the constants to right side}\\\\15x = 180 + 15\\\\15x = 195\\\\x = 13$

Thus the measure of angles are:

$(6x - 9) \text{ degrees } = 6(13) - 9 = 78-9 = 69 \text{ degrees }\\\\(9x - 6) \text{ degrees } = 9(13) - 6 = 117 - 6 = 111 \text{ degrees }$

Thus measure of angles are 69 degree and 111 degree

5 0

3 years ago