Determine the value of x?

Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?

Use the Pythagorean theorem:
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\
6^2+6^2=x^2 \\
6^2 \times 2=x^2 \\
\sqrt{6^2 \times 2}=x \\ \sqrt{6^2} \times \sqrt{2}=x \\ 6\sqrt{2}=x
$

The length of the hypotenuse is 6√2 units.

5 0

3 years ago

Is 81 A Prime Or Composite Number?

sukhopar [10]

81 is a composite number. It is a positive number that is divisible by some other number other than 1 and itself. 81 can be divided by 9 (9 x 9 = 81).

3 0

3 years ago

Read 2 more answers

Modeling real life last week you finish level to of a video game and 32 minutes today you finish level 2 in 28 minutes what is t

rusak2 [61]

Answer:

-12.5%

Step-by-step explanation:

The percentage change in your time can be computed using ...

pct change = ((new value)/(old value) -1) × 100%

= (28/32 -1) × 100%

= (0.875 -1) × 100% = -12.5%

The time to finish level 2 decreased by 12.5%.

6 0

3 years ago

What is the solution set?<br><br> −9x+202>94

olya-2409 [2.1K]

5 0

3 years ago

the company also discovered that it costs 30 to 2 widgets, 118 to produce 4 and 766 to produce 10 widgets. Find the total cost o

miv72 [106K]

We will first write cost function. As we are given three points here so we will use them to write quadratic function

$y = ax^{2} +bx+c$ ----------------------------------------(1)

So we will plug point (2,30) in it first ( for 2 widgets cost is 30)

So simply plug 30 in y place and 2 in x place in equation (1) as shown

$30 = a(2)^{2} +b(2)+c$

$30 = 4a +2b +c$ ----------------------------------------------(2)

Similarly plug next point (4,118) now in equation (1)

$118 = a(4)^{2} +b(4)+c$

$118 = 16a +4b +c$ ----------------------------------------------(3)

Similarly plug third point (10,766) now in equation (1)

$766 = a(10)^{2} +b(10)+c$

$766 = 100a +10b +c$ ----------------------------------------------(4)

Now we have to solve system of linear equations (2),(3) and (4) for a,b,c

We can use method of elimination

Subtract equation (3) - equation (2)

118 = 16a +4b +c

-(30 = 4a +2b +c)

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

88 = 12a +2b -----------------------------------(5)

Similarly subtract equation (4)-equation (3)

766 =100a +10b +c

-( 118 = 16a +4b +c)

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

648 = 84a + 6b ------------------------(6)

Now to eliminate b in equations (5) and (6) multiply equation (5) by -3 and then add to equation (6)

-3×(88 = 12a +2b)

-264 = -36a - 6b

648 = 84a + 6b

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

384 = 48a

Now solve for a

$\frac{384}{48} = \frac{48a}{48}$

8 = a

Plug 8 in a place in equation (5) or (6) and solve for b as shown

88 = 12(8) +2b

88 = 96 + 2b

88 -96 = 96 +2b -96

-8 = 2b

$\frac{-8}{2} = \frac{2b}{2}$

-4 = b

now plug 8 in a place, -4 in b place in either of equations (2),(3) or (4) and solve for c

30 = 4(8) +2(-4) +c

30 = 32 -8 + c

30 = 24 + c

30 - 24 = 24 + c - 24

6 = c

So plugging values of a as 8, b as -4 and c as 6 in equation (1) we get

$y = 8x^{2} -4x+ 6$

So thats the cost function. So now for 6 widgets, plug 6 in x place in this equation and find y value

$y = 8(6)^{2} -4(6)+ 6$

y = 8(36) - 24 +6

y = 288 -24 +6

y = 270

So $270 is the cost for producing 6 widgets and thats the final answer

4 0

3 years ago