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3 years ago

AABC has vertices A(-4, 4), B(-1,2), and C(-4,1). What are the coordinates of

Mathematics

1 answer:

steposvetlana [31]3 years ago

6 0

Answer:

(1, - 3 )

Step-by-step explanation:

Using the translation rule (x, y ) → (x + 2, y + 1 ), then

B(- 1, 2 ) → (- 1 + 2, 2 + 1) → (1, 3 )

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(1, 3 ) → (1, - 3 )

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State whether the given measurements determine zero, one, or two triangles.. . C = 30°, a = 32, c = 16

Nat2105 [25]

Sin(A) / a = Sin(C)/c
Sin(A) = a * Sin(C)/c
Sin(A) = 32 * Sin(30)/16
Sin(A) = 32 * 0.03125
Sin(A) = 1

A = 90°

By the law of sines, angle A must be 90 degrees. That makes side a the hypotenuse of a 30-60-90 triangle. There is only one triangle. The third side is 16√3, and the third angle 60°.

6 0

3 years ago

Find the distance between points (2, 9) and (5, 4) to the nearest tenth

Troyanec [42]

Answer:

$Distance = 5.8$

Step-by-step explanation:

$d=\sqrt{(4-9)^{2} } { (5-2)} ^{2} \\$

$d = -5^{2} + 3^{2}$

$d= 25 + 9$

$d= \sqrt{34}$

$distance = 5.8$

3 0

3 years ago

Complete the identity. 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

How to find the area of a equilateral triangle that has a perimeter of 21?

Romashka-Z-Leto [24]

First, we have to find the length of each side of triangle. Equilateral triangle means 3 sides r in same length, so each side will be 21 ÷ 3 = 7
Now we need to calculate the height of the triangle. We can do this by Pythagoras theorem
Let the height be h
(7/2)^2 + x^2 = 7^2
The area should be 6.0621778265
Or u can say 6.06 corrected to 3 sig fig

8 0

4 years ago

I really need help! :'( Domain= ? Range= ?

hodyreva [135]

Domain = {x|x = 2, 9, 6}
Range = {y|y = c, 0}

I think this is the answer? I tried, it's better to fill it in than to leave it blank :/

7 0

3 years ago