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OLEGan [10]
2 years ago
8

14.4 A Book and a Cake A book costs $45. Sales tax on the book is 7%. Write two different expressions that represent the final c

ost of the book in dollars. Pne of the expressions should use only a single multiplication and no other operations.
A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression (0.85).32 represents the final price of the cake in dollars
(0.85). 32 represents the final price of the cake in dollars because...​
Mathematics
1 answer:
snow_tiger [21]2 years ago
3 0

Answer: 1. $45*1.07 | $45(1.07) 2. (0.85)*32 represent the final price of the cake in dollars because (0.85) is the 15% off in decimals.

Step-by-step explanation:

1 if you multiply 45 by 1.07 it will be 48.15 and that's the final cost of the book, same with $45(1.07) is just another way to represent the multiplication.

2 As I said the 0.85 represent the 15% off, and when you multiply it will be less.

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Tristan is building a triangular roof for his treehouse. He already has two pieces of lumber that measure 6 feet long. Select al
Zarrin [17]

Answer:

6 and 12.

Step-by-step explanation:

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4 0
2 years ago
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What is the area of rhombus ABCD? Enter your answer in the box. Do not round at any steps. put the answer in units²
AlladinOne [14]

Answer:

Therefore the Area of Rhombus ABCD is 36 unit².

Step-by-step explanation:

Given:

ABCD is a Rhombus

A = (-1,0)

B = (5,-3)

C = (-1,-6)

D = (-7 ,-3)

To Find:

Area of Rhombus ABCD = ?

Solution:

We know that Area of Rhombus is given as

\textrm{Area of Rhombus}=\dfrac{1}{2}\times d_{1}\times d_{2}

Where ,

d₁ and d₂ are the Diagonals.

We have,

Diagonals as AC and BD,

Using Distance Formula we get

l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}

Substituting coordinates A and C we get

l(AC) = \sqrt{((-1-(-1))^{2}+(-6-0)^{2} )}=\sqrt{36}\\l(AC)=6\ unit

Similarly for BD we have,

l(BD) = \sqrt{((5-(-7))^{2}+(-3-(-3))^{2} )}=\sqrt{144}\\l(BD)=12\ unit

Now Substituting AC and BD in Formula we get

\textrm{Area of Rhombus}=\dfrac{1}{2}\times AC\times BD

\textrm{Area of Rhombus}=\dfrac{1}{2}\times 6\times 12=36\ unit^{2}

Therefore the Area of Rhombus ABCD is 36 unit².

6 0
2 years ago
Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by
Whitepunk [10]

\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA

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\begin{cases}x(r,\theta)=\frac r8\cos\theta\\y(r,\theta)=\frac r9\sin\theta\end{cases}

The Jacobian for this transformation is

J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\\\frac19\sin\theta&\frac r9\cos t\end{bmatrix}

with determinant \det J=\frac r{72}

Then the integral in polar coordinates is

\displaystyle\frac1{72}\int_0^{\pi/2}\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^{\pi/2}\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{\pi\sin^23}{864}}

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5 0
3 years ago
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Karolina [17]
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3 years ago
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Answer:

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Let A represent isotope ⁷⁹Br

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From the question given above, the following data were obtained:

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For isotope B (⁸¹Br):

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Relative atomic mass of Br =?

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= 40.0451 + 39.9411

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5 0
3 years ago
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