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3 years ago

9

Ricardo bought a jacket priced at $40. The total cost of the jacket, including sales tax, was $43. What was the sales tax rate t

o the nearest tenth of a percent?

1 answer:

Arte-miy333 [17]3 years ago

7 0

The closest answer I got was: 6.9%

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5 times 7/8 then converted to simplest form?

pantera1 [17]

5*7/8 = 4 3/8
5/1 * 7/8 = 35/8
convert into mixed number because numerator is bigger than the denominator so it it
4 3/8

7 0

3 years ago

A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr

seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

Required

$a + b$

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$(x_1,y_1) = A(0,1)$

$(x_2,y_2) = B(3,4)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

$CD = \sqrt{10}$

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}$

$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

$DA = \sqrt{10}$

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

$Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}$

$Perimeter = 4\sqrt{2} + 2\sqrt{10}$

Recall that

$Perimeter = a\sqrt{2} + b\sqrt{10}$

This implies that

$a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}$

By comparison

$a\sqrt{2} = 4\sqrt{2}$

Divide both sides by $\sqrt{2}$

$a = 4$

By comparison

$b\sqrt{10} = 2\sqrt{10}$

Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

3 0

3 years ago

If csc x = −5, find csc(−x) find the period and horizontal shift

ella [17]

Answer:

$\csc (-x) = - \csc x = - ( - 5) = 5$

Period is 2π

Horizontal shift = 0

Step-by-step explanation:

We know that $\sin (-x) = - \sin x$ and as $\csc x = \frac{1}{\sin x}$ , so, we can write $\csc (-x) = - \csc x$

Therefore, the if $\csc x = - 5$ then $\csc (-x) = - \csc x = - ( - 5) = 5$ (Answer)

Now, the period of $\csc x$ is 2π, hence the period of $\csc (- x)$ is also 2π. (Answer)

Again. $\csc ( - x) = \csc (-x + 0)$ , hence, the horizontal shift of $\csc (- x)$ is 0. (Answer)

6 0

3 years ago

-x-6y=10 x-2y=-2 using elimination?

Lana71 [14]

Answer: x = -4, y = 1

4 0

3 years ago

Read 2 more answers

A poker hand consisting of 7 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactl

77julia77 [94]

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

7 0

3 years ago