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2 years ago

Solve for a.

Mathematics

2 answers:

FinnZ [79.3K]2 years ago

8 0

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

pychu [463]2 years ago

8 0

Answer:

$\large\boxed{a=\dfrac{3b}{2}=\dfrac{3}{2}b=1.5b}$

Step-by-step explanation:

$7a-2b=5a+b\qquad\text{add}\ 2b\ \text{to both sides}\\\\7a-2b+2b=5a+b+2b\\\\7a=5a+3b\qquad\text{subtract}\ 5a\ \text{from both sides}\\\\7a-5a=5a-5a+3b\\\\2a=3b\qquad\text{divide both sides by 2}\\\\\dfrac{2a}{2}=\dfrac{3b}{2}\\\\a=\dfrac{3b}{2}$

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Suppose you are building an aquariam of volume 2880 in^3 . The aquarium will be 12 in high and the base of the rectangle with th

Sholpan [36]

Answer:

Step-by-step explanation:

The volume of the aquarium is 2880 in^3.

Height of the aquarium is 4 inches

The base of the aquarium is rectangular in shape.

Let the length be L

Let the width be W

The length of the rectangle is 4 inches more than twice the width. It means that

L = 2W + 4

The volume of the aquarium is expressed as L × W × H

Therefore

L × W × H = 2880

Since H = 4,

4LW = 2880

LW = 2880/4 = 720

LW = 720 - - - - - - - -1

Substituting L = 2W + 4 into equation 1, it becomes

W(2W + 4) = 720

2W^2 + 4W - 720 = 0

W^2 + 2W - 360 = 0

W^2 + 20W - 18W- 360 = 0

W(W +20) - 18(W + 20) = 0

W-18 = 0 or W + 20 = 0

W = 18 or W = -20

Since the width cannot be negative, it is 18 inches

L = 720/W = 720/18

L = 40 inches

Length is 40 inches

Width is 18 inches

4 0

2 years ago

Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, as shown colon

Nadusha1986 [10]

Answer:

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ where $a\geqslant 0$ "

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Step-by-step explanation:

Given that " Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, "

It can be written as $\sqrt{54a^7b^3}$ where $a\geqslant 0$

The given expression is $\sqrt{54a^7b^3}$ where $a\geqslant 0$

To find Sadie's error and explain the correct answer :

Sadie's steps are

$\sqrt{54a^7b^3}$ where $a\geqslant 0$

$=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$

$=3ab\sqrt{6a^5b}$

<h3> $\sqrt{54a^7b^3}=3ab\sqrt{6a^5b}$ where $a\geqslant 0$ </h3><h3><u>Now corrected steps are</u></h3>

$\sqrt{54a^7b^3}$ where $a≥0$

$=\sqrt{(9\times 6)(a^{6+1})(b^{2+1})$

$=\sqrt{(3^2\times 6)(a^6.a^1)(b^2.b^1)$ (by using the identity $a^{m+n}=a^m.a^n$

$=\sqrt{3^2\times 6\times ((a^3)^2.a)(b^2.b)$ (by using the identity $a^{mn}=(a^m)^n$ )

$=3ab\sqrt{6ab}$

Therefore $\sqrt{54a^7b^3}=3ab\sqrt{6ab}$ where $a\geqslant 0$

<h3>The correct answer is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ " where $a\geqslant 0$

Because she made error in splitting the powers to simplify the square root

<h3>Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$ </h3>

5 0

2 years ago

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A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches.

stealth61 [152]

Answer:

<u>The volume of the container is 37.7 cubic inches and the equation is π * r² * h/3, where r is the radius and h is the height of the cone.</u>

Step-by-step explanation:

Let's recall that the formula for finding out the volume of a cone is:

Volume of a cone = π * r² * h/3

Replacing with the real values, we have:

diameter = 4 inches ⇒ radius = 2 inches

Volume of a cone = 3.1416 * 2² * 9/3

Volume of a cone = 3.1416 * 4 * 3

Volume of a cone = 37.7 cubic inches

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2 years ago

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tamaranim1 [39]

Answer:

B) 54

Step-by-step explanation:

A mode of a number set is the number the appears the most.

In the list given, 54 was the number that appeared the most.

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2 years ago

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On Tuesday morning, the temperature is -5º F. The temperature rises 3 4 degree each hour for 6 hours before dropping 1 4 degree

Mice21 [21]

Answer:

The temperature in degrees after 9 hours is -1.25 degrees Fahrenheit

Step-by-step explanation:

Here, we want to know the temperature after 9 hours

Per hour rise each hour is 3/4 degree = 0.75 degree

In 6 hours that will be 0.75 * 6 = 4.5 degrees

Or hour drop is 1/4 = 0.25 degree

In 3 hours, that will be 0.25 * 3 = 0.75 degree

Since it is a drop, we have -0.75 degree

Temperature after 9 hours will be;

-5 + 4.5 -0.75

= -5.75 + 4.5 = -1.25 degrees fahrenheit

8 0

2 years ago