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1 year ago

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Jason grew from 36 inches to 40 inches in 1 year. By percent did his growth increase? Round your answer off to the nearest tenth

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1 answer:

IrinaVladis [17]1 year ago

7 0

Answer:

33%

Step-by-step explanation:

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Given the general identity tan X =sin X/cos X , which equation relating the acute angles, A and C, of a right ∆ABC is true?

irakobra [83]

First, note that $m\angle A+m\angle C=90^{\circ}.$ Then

$m\angle A=90^{\circ}-m\angle C \text{ and } m\angle C=90^{\circ}-m\angle A.$

Consider all options:

A.

$\tan A=\dfrac{\sin A}{\sin C}$

By the definition,

$\tan A=\dfrac{BC}{AB},\\ \\\sin A=\dfrac{BC}{AC},\\ \\\sin C=\dfrac{AB}{AC}.$

Now

$\dfrac{\sin A}{\sin C}=\dfrac{\dfrac{BC}{AC}}{\dfrac{AB}{AC}}=\dfrac{BC}{AB}=\tan A.$

Option A is true.

B.

$\cos A=\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}.$

By the definition,

$\cos A=\dfrac{AB}{AC},\\ \\\tan (90^{\circ}-A)=\dfrac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}=\dfrac{\sin C}{\cos C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AC}}=\dfrac{AB}{BC},\\ \\\sin (90^{\circ}-C)=\sin A=\dfrac{BC}{AC}.$

Then

$\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}=\dfrac{\dfrac{AB}{BC}}{\dfrac{BC}{AC}}=\dfrac{AB\cdot AC}{BC^2}\neq \dfrac{AB}{AC}.$

Option B is false.

3.

$\sin C = \dfrac{\cos A}{\tan C}.$

By the definition,

$\sin C=\dfrac{AB}{AC},\\ \\\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.$

Now

$\dfrac{\cos A}{\tan C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{AB}{BC}}=\dfrac{BC}{AC}\neq \sin C.$

Option C is false.

D.

$\cos A=\tan C.$

By the definition,

$\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.$

As you can see $\cos A\neq \tan C$ and option D is not true.

E.

$\sin C = \dfrac{\cos(90^{\circ}-C)}{\tan A}.$

By the definition,

$\sin C=\dfrac{AB}{AC},\\ \\\cos (90^{\circ}-C)=\cos A=\dfrac{AB}{AC},\\ \\\tan A=\dfrac{BC}{AB}.$

Then

$\dfrac{\cos(90^{\circ}-C)}{\tan A}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AB}}=\dfrac{AB^2}{AC\cdot BC}\neq \sin C.$

This option is false.

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2 years ago

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Grogg typed the following $1000$ expressions into his calculator, one by one: \[\sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \dots, \

sergey [27]

Answer:

pano po yan hinde ko po alam

Step-by-step explanation:

paturo po

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1 year ago

When full, one of the pools at Sapphire Island will hold 43,000 gallons. The pool currently holds 20,000 gallons of water and is

SpyIntel [72]

Answer: Explanation and answer is attached.

Step-by-step explanation:

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2 years ago

The diameter of Circle Q terminates on the circumference of the circle at (0,3) and (0,-4). Write the equation of the circle in

Gnesinka [82]

First, determine the center of the circle by getting the midpoint of the points given for the circumference.
midpoint = ((0 + 0)/2, (3 + -4)/2)
midpoint (0, -0.5)
Then, we get the radius by determining the distance from either of the circumferential point to the center.
radius = √(0 - 0)² + (3 +4)² = 7
The equation for the circle would be,
x² + (y + 0.5)² = 7²

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1 year ago

The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the func

Hunter-Best [27]

Answer:

<em>A) (-5,7)</em>

Step-by-step explanation:

<u>Functions and Relations</u>

A set of values A can have a relation with another set B as long as at least one element of A has at least one image in B. Functions are special relations where each element of A (the domain of the function) has one and only one image on B (the range of the function).

By looking at the options, we can see that x=9, x=-8, and x=-1 already have defined values in Y, so if we define another value for any of them the relation will stop being a function. The only possible choice to preserve the function is the option

$\boxed{A)\ (-5,7)}$

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2 years ago