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3 years ago

The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions

Mathematics

1 answer:

stiks02 [169]3 years ago

5 0

Answer:

width = 15 inches

length = 36 inches

Step-by-step explanation:

To solve you need to find the width...

width = w

length = 2w + 6

the perimeter is all the way around the area, so..

2w + 2(2w + 6) = 102

because there are 2 widths and 2 lengths in a perimeter.

Solve for w:

2w + 4w + 12 = 102

subtract 12 from both sides and combine like terms...

6w = 90

divide both sides by 6...

w = 15

the width = 15, and the length = 2(15) + 6 = 36

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zhenek [66]

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

∵ CB = 12 units ⇒ opposite

∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ $sin(x)=\frac{BC}{AB}$

∴ $sin(x)=\frac{12}{13}$

∴ $x=sin^{-1}(\frac{12}{13})$

∵ $cos(x)=\frac{AC}{AB}$

∴ $cos(x)=\frac{5}{13}$

∴ $x=cos^{-1}(\frac{5}{13})$

∵ $tan(x)=\frac{BC}{AC}$

∴ $tan(x)=\frac{12}{5}$

∴ $x=tan^{-1}(\frac{12}{5})$

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

All of the functions shown below are either exponential growth or decay functions.

AlekseyPX

Answer:

Step-by-step explanation:

If an exponential function is in the form of y = a(b)ˣ,

a = Initial quantity

b = Growth factor

x = Duration

Condition for exponential growth → b > 1

Condition for exponential decay → 0 < b < 1

Now we ca apply this condition in the given functions,

1). $y=3.2(1+0.45)^{2x}$

Here, (1 + 0.45) = 1.45 > 1

Therefore, It's an exponential growth.

2). $y=(0.85)^{3x}$

Here, (0.85) is between 0 and 1,

Therefore, it's an exponential decay.

3). y = (1 - 0.03)ˣ + 4

Here, (1 - 0.03) = 0.97

And 0 < 0.97 < 1

Therefore, It's an exponential decay.

4). y = 0.5(1.2)ˣ + 2

Here, 1.2 > 1

Therefore, it's an exponential growth.

5 0

3 years ago

a gardener has 322 tulip bulbs she wants to plant rows of 15 bulbs how many bulbs can be planted how many bulbs will she have le

Elden [556K]

Answer:315 bulbs planted and 7 left over

Step-by-step explanation:322/15 = 21.44

Roughly around 21 rows.

21 x 15 = 315 bulbs planted

322 - 315 = 7 bulbs left over

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3 years ago

Ends of a diameter: (-9, -16) and (3,0)

lbvjy [14]

Answer:

One example is the equation:

2x + 6 = 4x/2 + 12/2

To solve this, we need to transpose like terms to the same side.

2x - 4x/2 = 12/2 - 6

2x - 2x = 6 - 6

0 = 0

Since both sides are zero, it means that the equation has infinite number of solutions.

Step-by-step explanation:

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2 years ago

To those who are struggling with geometry or any maths class download “Gauthmath”. it has actual tutors who will give answers an

Alekssandra [29.7K]

Answer:

Thanks this can come in handy for me

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3 years ago

The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions￼

The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions