All categories

3 years ago

1. What is the solution to the system below? x+y=5 1x- y=3

Mathematics

1 answer:

Alika [10]3 years ago

5 0

Answer:

(4,1)

Step-by-step explanation:

x+y=5

x- y=3

Add the equations together to eliminate y

x+y=5

x- y=3

--------------------

2x = 8

Divide each side by 2

2x/2 = 8/2

x = 4

Now we can find y

x+y = 5

4+y = 5

Subtract 4 from each side

4+y-4 = 5-4

y =1

You might be interested in

What is the missing angle?

Zina [86]

Answer:

I believe its 57.

Step-by-step explanation:

180-66=57.

57+57+66=180

7 0

3 years ago

What is the area of the figure? 40 ft2 84 ft2 96 ft2 can't be determined

mina [271]

Answer:

$A=80\ ft^2$

Step-by-step explanation:

we know that

The area of the figure is equal to the area of an isosceles triangle (has two equal sides) plus the area of a rectangle

step 1

Find the area of the triangle

The area of the triangle is equal to

$A=\frac{1}{2}bh$

we have

$b=16\ ft$

To find out the height of the triangle Apply the Pythagorean Theorem

$10^2=(16/2)^2+h^2$

solve for h

$100=64+h^2$

$h^2=100-64$

$h^2=36$

$h=6\ ft$

Find the area of triangle

$A=\frac{1}{2}(16)(6)$

$A=48\ ft^2$

step 2

Find the area of rectangle

The area of rectangle is equal to

$A=LW$

we have

$L=16\ ft\\W=2\ ft$

substitute

$A=(16)(2)=32\ ft^2$

step 3

Find the area of the figure

Adds the areas

$A=48+32=80\ ft^2$

5 0

3 years ago

Find the exact value of the trigonometric expression given that sin u = − 8 17 and cos v = − 24 25 . (Both u and v are in Quadra

Rashid [163]

Answer: sin u = -5/13 and cos v = -15/17

Step-by-step explanation:

The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.

So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),

==> adj of u = -12 therefore cos u = -12/13

Same argument for v: adj = -15,

opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17

The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)

I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.

3 0

2 years ago

2. What is gross income? What types of income are included in gross income?

gogolik [260]

Gross income is all a persons receipts and gains from all sources before any deductions.

8 0

3 years ago

Determine value of a

S_A_V [24]

For this case we have that by definition of trigonometric relations that the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. That is to say:

$Sin (43) = \frac {a} {26}$

Clearing the value of "a":

$a = 26 * sin (43)\\a = 26 * 0.68199836\\a = 17.73195736$

Rounding off we have:

17.7

Answer:

Option B

6 0

3 years ago