In right triangle ABC with the right angle at C, sin A= 2x + .1 and cos B = 4x - .7. Determine and state the vaule of x.

Answers

Answer 1
Answer: Imagine \angle A at the top of the triangle and \angle B at the bottom. (or used the attached picture for reference)

\sin A= (opposite)/(hypotenuse)

\cos B = (adjacent)/(hypotenuse)

One thing to note, however, is that the side opposite \angle A is the same side as the one adjacent to \angle B! Thus \sin A=\cos B.

Substitute these values for 2x+0.1 and 4x-0.7 and solve.

 4x-0.7=2x+0.1 \n 4x=2x+0.8 \n 2x=0.8\n \boxed{x=0.4}

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HELP ME FIND X AND Y: 2x = 4y + 6 and 3x - y = -1
Decrease 40 by 12.5%

How do you find the derivative of h(t)=sqrt(t)(1-t^2)

Answers

Answer:

Step-by-step explanation:

h(t)=√((t)(1-t^2))\nh^(2)(t)=t(1-t^2)=t-t^3\n diff. w.r.t.,\n2 h(t)h'(t)=1-3t^2\nh'(t)=(1-3t^2)/(2 h(t)) \nh'(t)=(1-3t^2)/(2√((t)(1-t^2)) )

What is the point of origin on a number line

Answers

0 is the point of origin because it's not really a number, it's more of a starting point for positive and negative numbers. 

What is the solution of the system? Use elimination.3x - 4y = 9
-3x + 2y = 9

A. (3,9)
B. (-27,9)
C. (-3,-6)
D. (-9,9)

Answers

(one way is to subsitute since both equal 9 you do 3x-4y=-3x+2y then add 3x to both sides 6x-4y=2y add 4y to both sides 6x=6y divide by 6 x=y now subsitute 3x-4x=9 -x=9 multiply -1  x=9  x=y y=-9)


use elimination
add them together to cancel x terms
3x-4y=9
-3x+2y=9  +
0x-2y=18
-2y=18
divide by 2
-y=9
multiply -1
y=-9
subsituete

3x-4y=9
3x-(4 times -9)=9
3x-(-36)=9
3x+36=9
subtract 36 from both sides
3x=-27
divide both sides by 3
x=-9

x=-9
y=-9

the answer is  in (x,y) form
(-9,-9)
the answer is none of them (D is closest)

Answer:

(-9,-9)


Explanation:

The two given equations are:

3x - 4y = 9

-3x + 2y = 9


First step is to add the two equations in order to eliminate the x.

This will give us:

-4y + 2y = 9 + 9

-2y = 18

y = -9


Now, we substitute with the value of y in any of the equations to get x as follows:

3x - 4y = 9

3x - 4(-9) = 9

3x + 36 = 9

3x = -27

x = -9


Hope this helps :)



Jan Quint earns $11.00 an hour at her job and is entitled to time-and-a-half for overtime, and double time on holidays. Last week she worked 40 hours of regular time, 9 hours of overtime, and 12 hours of holiday time. How much did she earn last week?A. $720.50
B. $612.00
C. $852.50
D. $803.00
Please explain the answer..

Answers

time and a half mean
example, if he work for 1 hour normal, then he get 1 hour pay
but time and a half, is if he works 1 hour overitme, he gets paid for 1.5 time
double time is work 1 hour, get paid 2 hours

basically, multiply all normal hours by 1, multpliy al overtime hours by 1.5 and multiply al holiday hours by 2

40 hours normal
9 hours overtime
12 hours holidy
40*1=40
9*1.5=13.5
12*3=24
add up
40+13.5+24=77.5 hours counted

now 11 per our
11 times 77.5=852.50

C is answer

Beryl calculated the total text messages sent by sophomores, juniors and seniors for a week using the matrix equation: Z = X + Y What are the values for the elements of this matrix? Z11 = z12 = z13 =

Answers

Answer:

z11= 523

z12= 714

z13= 468

Step-by-step explanation:

just did the assigment these are right

Answer:

first part is 1x3 and second part is

523

714

468

Step-by-step explanation:

just did it on edge

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.X + 3y = 9
 

3x –y =  7

Answers


Let's write both equations in the standard form of  [ y = mx + b ],
and then see what we can tell about their graphs.

First equation:             x + 3y = 9
Subtract 'x' from each side:  3y = -x + 9
Divide each side by  3:            y = -1/3 x + 3
This line crosses the  y-axis  at  y=3,  and it has a slope of  -1/3 .

Second equation:            3x - y = 7 
Subtract  3x  from each side:  -y = -3x + 7
Multiply each side by  -1 :        y = 3x - 7
This line crosses the y-axis at  y=-7, and it has a slope of  3 .

-- The two lines have different slopes, so they're not parallel. 
They must intersect somewhere.
-- They're not the same line, so they can't 'intersect' everywhere.
-- They have slopes of  -1/3  and  3 .    Their slopes are negative reciprocals,
so the lines are perpendicular.

All of this says that the two equations can't have no solution, and they can't have
infinitely many solutions.  They must have one and only one solution.
I guess that  means that it's our job to find it now.

============================================

For each equation, the "mx + b" form is equal to 'y' .  Since these two things are
equal to the same thing, they must be equal to each other, and we can write:

                                   -1/3 x + 3  =  3x - 7

Multiply each side by  3 :  -x + 9  =  9x - 21

Add 'x' to each side:                9  =  10x - 21

Add  21  to each side:           30  =  10x

Divide each side by  10 :       3  =  x

The intersection/solution is some place where  x=3 .
Let's put that back into the first equation:

                                         x + 3y = 9

                                         3 + 3y = 9

Subtract  3  from each side:   3y = 6

Divide each side by  3 :            y = 2

And there's your solution:      x = 3
                                               y = 2
On the graph, the two lines intersect at the point  (3, 2) .

We used the first equation to get part of the solution, so we can't use
the same equation to check the solution.  We'll put our solution into the
second equation, and see whether it checks there:

                                       3x - y  =  7

                                    3(3) - (2) = 7

                                       9  -  2  =  7

                                           7     =  7             yay !

The two equations have one and only one solution,
and it is definitely    x = 3,   y = 2 .

Substitution or Elimination

im using substitution

1. solve for variable for one of the equation

x + 3y = 9

x = 9 - 3y

2. Substitute the variable into one of the equation

3 (9-3y) - y = 7

27 - 9y - y = 7

27 - 10y = 7

-10y = 7 - 27

-10y = -20

y = 2

3. sub y = 2 into any equation to find x

3x - 2 = 7

3x = 7 -2

3x = 5

x = 5/3

X+3(2) = 9

x + 6 = 9

x = 9-6

x= 3

therefore there are two solutions x = 3 and x= 5/3