Given right triangle ABC what is the value of tanA AB=26 BC=24 AC= 10

Answers

Answer 1

Answer:

Answer:

tanA = 12/5

Step-by-step explanation:

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1+4=5 2+5=12 3+6=21 8+11=

Explain the distance formula. Then use it to calculate the distance between A(1,1) and B(7,-7).

Answers

the distance formula:
$d= \sqrt{ (x_(2) - x_(1)) ^(2)+ (y_(2) -y_(1)) ^(2) }$

A(1,1) B(7,-7)

$d= \sqrt{ (7 - 1) ^(2)+ (-7 -1) ^(2) }$

$d= \sqrt{ (6) ^(2)+ (-8) ^(2) }$

$d= √( 36 + 64 )$

$d= √( 100 )$

$d=10$

The answer is 10

Answer:

d=10

Step-by-step explanation:

The equation S = p( 1+r )^2 can be used to model a person’s future income. S = future salary, p = current salary, r = rate of increase(% in decimal form), and t = time in years. Bob’s salary increases by 5% each year. If he starts at $35,000 per year, what will his salary be in 5 years?

Answers

S = p(1 + r)^t
S = 35,000(1 + .05)^5
S = 35,000(1.05^5)
S = 44669.85 rounds to 44,670

The coordinates of the vertices of △DEF are D(2, −1) , E(7, −1) , and F(2, −3) . The coordinates of the vertices of △D′E′F′ are D′(0, −1) , E′(−5, −1) , and F′(0, −3) . What is the sequence of transformations that maps △DEF to △D′E′F′

Answers

Answer:

reflection across the y-axis and translation 2 units right. :)

Step-by-step explanation:

It seems to be a reflection across line x = 1.

A bird catches a fish and flies 100 yards in a straight line at an angle of elevation x degrees from the ground. After flying for 100 yards the bird drops the fish. The fish lands at a spot y yards horizontally from where the bird caught it. What is x?A.)cos -1 y/100

B.)sin -1 y/100

c.)tan -1 y/100

D.)cos -1 100/y

E.)sin -1 100/y

Answers

Answer: Hello there! The correct answer is A.

If the bird flies 100 yards with an angle of elevation of x from the ground, then you could think this as a tringle rectangle, where the hypotenuse is 100 yards, the opposite cathetus is sin(x)*100 and this represents the height at which the bird dropped the fish, not really useful here.

The adjacent cathetus us 100*cos(x), in this case, you are calculating the displacement adjacent to them (because the angle is with respect to the ground) and knowing that the fish lands in a translated y yards horizontally we could write: y = cos(x)*100

now we want to isolate x:

y/100 = cos(x)

arcos(y/100) = arcos(cos(x)) = x

x = arcos(y/100) (or cos-1(y/100) like in the option A)

then, knowing the value of y, we could obtain the angle x with that equation.

The angle of elevation can be solved using B.)sin -1 y/100, which makes use of trigonometric functions.

Which expression is equivalent to (12x−5y−1)+(17y−4−13x−3y)?which one is it?

1. −4x+12y−5
2. −x+9y−5
3. −x−25y+5
4. 25x−19y+3

Answers

The expression that is equivalent to the given expression is -x+9y−5. The correct option is 2. −x+9y−5

From the question,

We are to determine the expression which is equivalent to the given expression.

First, we will simplify the given expression

The given expression is (12x−5y−1)+(17y−4−13x−3y)

The expression can be simplified as shown below

(12x−5y−1)+(17y−4−13x−3y)

12x−5y−1+17y−4−13x−3y

Collect like terms

12x−13x+17y−5y−3y−4−1

This becomes

-x+9y−5

The simplified expression is -x+9y−5

Hence, the expression that is equivalent to the given expression is -x+9y−5. The correct option is 2. −x+9y−5

Learn more on simplifying expressions here: brainly.com/question/10618632

Answer:

The correct answer is 2. -x+9y-5

Explanation:

All you have to do is to remove the parentheses, collect the like term and then simply.

Let f be the function defined by f(x) =x^4 -3x^2 +2A)find the zeros of f
B)write an equation of the line tangent to the graph of f at the point where x=1
C) find the x coordinate of each point at which the line tangent to the graph of f is parallel to the line y=-2x+4

Answers

A convenient way to find the zeros of $f(x)=x^4-3x^2 +2$ is by factoring.

a) The equation,

$x^4-3x^2 +2=0$

can be rewritten as,

$(x^2)^2-3(x^2) +2=0$

We can think of this equation as a quadratic equation in $x^2$ , with $a=1,b=-3\:\: and \:\: c=2$ .

Observe that $ac=1 * 2=2$ .

We find two factors of 2 that adds up to $-3$ . These are, $-2,-1$ .

Now let us split the middle term. to obtain;

$(x^2)^2-(x^2) -2(x^2)+2=0$

We can factor to get,

$(x^2)(x^2-1)-2((x^2-1)=0$

We factor further to obtain;

$(x^2-1)((x^2-2)=0$

$\Rightarrow (x-1)(x+1((x- √(2))(x+ √(2))=0$

Hence the zeroes of $f(x)$ are;

$x=1,x=-1,x= √(2),x=- √(2)$

b) To find the line tangent, we must first, find the slope using differentiation. That is,

$Slope\:\: function=f'(x)=4x^3-6x$

At $x=1$ ,

$Slope=f'(1)=4(1)^3-6(1)=-2$

Also, we need to determine the $y$ value at $x=1$ . That is;

$f(1)=(1)^4-3(1)^2+2=0$

Now we can use the slope $m=-2$ and the point $(1,0)$ to write ythe equation of the line tangent.

$y-y_1 =m(x-x_1)$

$\Rightarrow y-0 =-2(x-1)$

$\Rightarrow y=-2x+2$

If the line tangent is parallel to the line $y=-2x+4$ , then

$f'(x)=-2$

Since parallel lines have the same slope.

$\Righarrow 4x^3-6x=-2$

$\Righarrow 4x^3-6x+2=0$

$\Righarrow (x-1)(2x- ( √(3)-1)(2x+ ( √(3)-1)=0$

Hence the x-coordinates are,

$x=1,x= ( √(3)-1)/(2),x= -(√(3)-1)/(2)$

The zeros of the function can be determined by equating the equation to zero and determining the values of x.
0 = x4 - 3x2 + 2 the roots are x1 = sqrt 2 x2 = -sqrt 2x3 = 1x4 = -1
The tangent line is determined by differentiating the polynomial and substituting x by 1 to get the slope. That is, m = 4x^3 - 6 x = 4*1 - 6 = -2y-y1 = m(x-x1)when x =1 , y = 1-3+2 = 0
y - 0 = -2*(x-1)y = -2x + 2
c. y = -2x + 4 m = -2 -2 = 4x3 - 6x x= -1.3666 ; y =-0.1160 x= 1.3666 ; y =--0.1160
x =1 ; y = 0

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