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3 years ago

What is the volume of the box if it is scaled down by a factor of 1/10?

Mathematics

1 answer:

Natalka [10]3 years ago

8 0

Answer:

8.4in²

Step-by-step explanation:

We are given the dimensions of a box as :

7in = Height

6in = Length

2in = Width

The volume of a box = Length × Width × Height

Volume of a box = 7in × 6in × 2in

= 84in²

We are also told in the question to find the volume of the box if it is scaled down by a factor of 1/10

Hence,the new volume = 84in² × 1/10

= 8.4in²

Therefore, the volume of the box if it is scaled down by a factor of 1/10 is 8.4in²

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Answer:

Step-by-step explanation:

Complementary angles are two angles whose measures add to 90°.

m<CFD = 150° - 100° = 50°

m<EFD = 180° - 150° = 30°

Sum = 80°

m<AFB = 40°

m<DFE = m<EFD = 30°

Sum = 70°

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Sum > 100°

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Answer: D.

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2 years ago

Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50. Jason went into the same movi

ruslelena [56]

The price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25

Solution:

Let d" be the price of 1 drink

Let "p" be the price of 1 pretzel

Given that, Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50

Therefore, we can frame a equation as,

3 x price of 1 drink + 10 x price of 1 pretzel = 54.50

$3 \times d + 10 \times p = 54.50$

3d + 10p = 54.5 ---------- eqn 1

Jason went into the same movie theater and bought 9 drinks and 5 pretzels, costing a total of $57.25

9 x price of 1 drink + 5 x price of 1 pretzel = 57.25

$9 \times d + 5 \times p = 57.25$

9d + 5p = 57.25 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 3

9d + 30p = 163.5 ----- eqn 3

Subtract eqn 2 from eqn 3

9d + 30p = 163.5

9d + 5p = 57.25

( - ) -----------------------

25p = 106.25

p = 4.25

Substitute p = 4.25 in eqn 1

3d + 10(4.25) = 54.5

3d + 42.5 = 54.5

3d = 54.5 - 42.5

3d = 12

d = 4

Thus price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25

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3 years ago

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just olya [345]

Answer:

The Answer Is E, $6.75

Step-by-step explanation:

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2 years ago

Given the following trigonometric ratio, enumerate the meaning ratio

Likurg_2 [28]

Answer:

The trigonometric ratios are presented below:

$\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}$

$\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}$

$\cot \theta = \frac{BC}{AC}$

$\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}$

$\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}$

Step-by-step explanation:

From Trigonometry we know the following definitions for each trigonometric ratio:

Sine

$\sin \theta = \frac{y}{h}$ (1)

Cosine

$\cos \theta = \frac{x}{h}$ (2)

Tangent

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$ (3)

Cotangent

$\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}$ (4)

Secant

$\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}$ (5)

Cosecant

$\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}$ (6)

Where:

$x$ - Adjacent leg.

$y$ - Opposite leg.

$h$ - Hypotenuse.

The length of the hypotenuse is determined by the Pythagorean Theorem:

$h = \sqrt{x^{2}+y^{2}}$

If $y = AC$ and $x = BC$ , then the trigonometric ratios are presented below:

$\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}$

$\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}$

$\cot \theta = \frac{BC}{AC}$

$\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}$

$\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}$

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3 years ago

In a two-digit number the tens’ digit is 1 more than the units’ digit. The number itself is 6 times the sum of the digits. Find

Gennadij [26K]

The answer is 54, 5 is 1 more than 4, they equal 9, 54 is 6 times greater than 9

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3 years ago

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