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3 years ago

What is the total cost of a compact disc that costs $13.99 plus a 4% sales tax

Mathematics

2 answers:

iren [92.7K]3 years ago

7 0

If you multiply 13.99x0.04=.5596

then you added

13.99+.5596=14.5496

And this is your answer

Rasek [7]3 years ago

6 0

Answer:

19.59

Step-by-step explanation:

first multiply 13.99 and . 4 and you get 5.60

then add 6.60 to 13.99 to get the answer of 19.59

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Let L be the line parametrized by x = 2 + 2t, y = 3t, z = −1 − t. (a) Find a linear equation for the plane that is perpendicular

Elden [556K]

Answer:

Step-by-step explanation:

Given that L is a line parametrized by

$x = 2 + 2t, y = 3t, z = −1 − t$

The plane perpendicular to the line will have normal as this line and hence direction ratios of normal would be coefficient of t in x,y,z

i.e. (2,3,-1)

So equation of the plane would be of the form

$2x+3y-z =K$

Use the fact that the plane passes through (2,0,-1) and hence this point will satisfy this equation.

$2(2)+3(0)-(-1) =K\\K =5$

So equation is

$2x+3y-z =5$

b) Substitute general point of L in the plane to find the intersecting point

$2(2+2t)+3t-(-1-t) =5\\4+8t+1=5\\8t=0\\t=0\\(x,y,z) = (2,0,-1)$

i.e. same point given.

3 0

3 years ago

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

What is the equation of the line in the graph

earnstyle [38]

b = - 4

slope m = (0 + 4)/(4 - 0) = 4/4 = 1

equation

y = x - 4

7 0

3 years ago

A rectangular yard has area 96 square feet. If the width of the yard is 4 ft less than length, what is the perimeter,in feet, of

marusya05 [52]

Area of the rectangular yard = 96 square feet
Let us assume the length of the yard = x feet
Width of the yard = x - 4 feet
Then
Area of the yard = length * width
96 = x(x - 4)
96 = x^2 - 4x
x^2 - 4x - 96 = 0
x^2 - 12x + 8x - 96 = 0
x(x - 12) +8(x - 12) = 0
(x - 12)(x + 8) = 0
As the value of length cannot be negative so
x - 12 = 0
x = 12
So
Length of the yard = 12 feet
Width of the yard = x - 4 feet
   = 12 - 4 feet
   = 8 feet
Then
Perimeter of the yard = 2 (length + width)
   = 2(12 + 8)
   = 2 * 20 feet
   = 40 feet.
So the perimeter of the yard is 40 feet.

6 0

3 years ago

Write the improper fractions for these mixed numbers. 6 1/3 8 1/2 4 3/5

Juliette [100K]

6 1/3 is 19/3
8 1/2 is 17/2
4 3/5 is 23/5
Pls mark brainiest

3 0

3 years ago

Read 2 more answers