The side lengths of a 45-45-90 triangle are in the ratio 1:1:√2. What is sin 45°?

Answer:

Step-by-step explanation:

Begin by combining like terms and then factoring. Combining like terms will give you

[tex]10p^2-17p-20=0[/tex] Using the "old-fashioned" way of factoring, the a times c method, our a = 10, b = -17 and c = -20.

a * c = 10(-20) = -200 and now we need the factors of 200 (don't worry about the negative) that combine to give us that middle term, -17p (here is where the negative matters). The factors of 200 are:

1. 200;  2, 100;  4. 50;  5, 40;  8, 25;  10, 20

The combination of those numbers that can be manipulated to give us a -17p is the 8, 25 as long as we say that the 25 is negative and the 8 is positive. Rewrite the original polynomial to reflect those factors:

[tex]10p^2-25p+8p-20=0[/tex] and then factor by grouping:

[tex](10p^2-25p)+(8p-20)=0[/tex] and factor out from each set of parenthesis what is common:

[tex]5p(2p-5)+4(2p-5)=0[/tex] again factor out what is common:

(2p - 5)(5p+ 4) = 0. These are the factors; therefore the solutions are

2p - 5 = 0 so

2p = 5 and

p = 5/2  and

5p + 4 = 0 and

5p = -4 so

p = -4/5

Answer:

i believe it's -6? option a.

Step-by-step explanation:

okay.

60 degrees + a right angle, 90 degrees = 150 degrees

a triangle is normally 180 degrees.

180-150=30

so we need to get 30 from that equation, x + 36

x + 36 = 30

you solve.

x = -6

if im wrong, feel free to correct me + sub to gauthmath sub reddit if ya can !

Answer:

16 post cards

Step-by-step explanation:

bcos (6postcards÷3days)=2. so 2postcards in a day. So the 2 postcards per day u multiply it by 8. (2postcards ×8 days)= 16 post cards

Answer:

y= [tex]\frac{c-2x}{3}[/tex]

Step-by-step explanation:

2x+3y=C

isolate y

3y=C-2x

y= [tex]\frac{c-2x}{3}[/tex]

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  1

-6+3x+4=2-4x+3

-8+7x+1=0

7x=7

x=1

Answer:

x=1

Step-by-step explanation:

SEE IMAGE for Solution

Answer:

c = 9.7

Step-by-step explanation:

Using the law of sines

sin 55       sin 82

---------- = ---------------

8                    c

Using cross products

c sin 55 = 8 sin 82

c = 8 sin 82 / sin 55

c=9.67115

To the nearest tenth

c = 9.7

Answer:

missing angle= 44°

Step-by-step explanation

sin=opposite/hypotenuse

cos=adjacent/hypotenuse

tan=opposite/adjacent

x is opposite of 19 and  41 is the biggest side so that is the hypotenuse. with that being said you will put in your calculator sin(19/41) and make sure that it is in radian mode. This gives you the answer of 44°

Answer:

B) 14%

Step-by-step explanation:

principal = 220000

First two years 10% paid.

.10 x 220000 = 22000

220000-22000 = 198000

x = percent

x = [tex]\frac{New -Old}{Old}[/tex]

x = [tex]\frac{170000-198000}{198000}[/tex]

x = -.1414

Round to .14

14% is the difference in amounts.

The principal (198000) will need to be reduced 14% to equal 170000

Answer:

The alphabets Z, H, S, N and O have rotational symmetry.

Answer:

Step-by-step explanation:

[tex] \frac{1}{15} \times \frac{1}{3} [/tex]

[tex] = \frac{1}{15 \times 3} [/tex]

[tex] = \frac{1}{45} (ans)[/tex]

Answer:

y=3/x

Step-by-step explanation:

Answer:

2y+3x-2=0

Step-by-step explanation:

The slope of the line is 3/2 and the equation of line is y=-1.5x+1

Answer:

864

Step-by-step explanation:

A=6a^2=6·12^2=864

Answer:

864 in^2

Step-by-step explanation:

2(144+144+144) = 2(432) = 864 in^2.

Hope this helped!

Answer:

2 19/56 is the answer.

Step-by-step explanation:

10 5/8 - 8 2/7

or, 85/8 - 58/7

or, (595-464)/56

or, 131/56

= 2 19/56

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1  (-1)^2 = 1

Add 1  (But remember the 3 out front so we are really adding 3  so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

The vertex is (1,-21)  

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

Answer:

We can convert the 2/3 bag of candy that we got to 16/24, by multiplying both the top and bottom by 8. Similarly, we multipy the 1/8 bag of candy that our friend got by 3 on the top and bottom to get 3/24.

We find the difference between these two:

(16/24) - (3/24) = (16-3)/24 = 13/24

So we get 13/24 more of the bag of candy than our friend did.

Answer:

1/6

Step-by-step explanation:

you’re being asked the difference between the amounts of your candy and your friend’s candy.

So you must subtract 1/3 from 1/2.

=> 1/2 - 1/3

=> 3*1 - 2*1/3*2. ( You criss-cross and you multiply the denominators)

=>. 3 - 2 /6

=> 1/6

So you got 1/6 more candies in your bag than your friend.

9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

A) 5 sides = 72.00

interior =108.00

B) 9 sides = 40.00

interior = 140.00

C) 15 sides = 24.00

interior = 156.00

D) 19 sides = 18.95

interior = 161.05

These are exterior angles right? y'know what I'll just put both

Step-by-step explanation:

(f*g) (x)=f(x) * g(x)

=(x+3)(2x^2-4)

=2x^3-4x+6x^2-12

Answer:

25 used games

Step-by-step explanation:

Divide his money by the price for one used game

300/12

25

Answer:

y=0

12x=300

X=300/12

X=25

he can buy 25 used games .

Step-by-step explanation:

Answer:

I believe the answer would be 48.6 milliliters

Step-by-step explanation:

54 * 0.9 = 48.6

Answer:

[tex]{ \tt{ {3x}^{2}(5 {x}^{3} ) = 15 {x}^{5} }}[/tex]

Step-by-step explanation:

[tex]{ \sf{3 {x}^{2}(5 {x}^{3} )}} \\ = { \sf{ {x}^{5} (3 \times 5)}} \\ = { \sf{15 {x}^{5} }}[/tex]

Answer: 12 Basil leaves

Step-by-step explanation:

Given

Monica uses 3 basil leaves for every 8 tomatoes

For 32 tomatoes she needs

[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]

Thus, she needs 12 basil leaves.

Answer:

11 mm

Step-by-step explanation:

121=area of a rectangle and area of triangle

121=x*8+(0.5)*x*(14-8), 11x=121, x=11

Answer:

[tex]11mm[/tex]

Step-by-step explanation:

Let the unknown side be x

[tex]Area \: \: \: of \: \: the \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: \: the \: \: parallel \: sides) \times height \\ 121= \frac{1}{2} \times (8 + 14) \times x \\ 121 \times 2 = 22x \\ 242 = 22x \\ \frac{242}{22} = \frac{22x}{22} \\ 11 = x[/tex]

Answer:

y=3x+9......(i)

y=-4x-12...(ii)

these are the equation

Answer:

6.82

Step-by-step explanation:

Cos( 30 ) = 19√3 / x

√3 / 2 = 19√3 / x

Simplify √3 from both sides

1 / 2 = 19 / x

Multiply both sides by x

1 /2 × x = 19 / x × x

x / 2 = 19

Multiply both sides by 2

x / 2 × 2 = 19 × 2

x = 38

_____________________________

Sin( 30 ) = y / x

1 / 2 = y / 38

Multiply both sides by 38

38 × 1 / 2 = 38 × y / 38

38 / 2 = y

19 = y

y = 19

Answer:

I think the correct answer is F. y = 6x

We will see that the line equation is y = 6*x

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, the line passes through the points: (0, 0) and (-1/2, -3)

Then the slope is:

[tex]a = \frac{0 - (-3)}{0 - (-1/2)} = 6[/tex]

Then the line is of the form y = 6*x + b

To find the value of b, we use the fact that the line passes through the point (0, 0), then we have:

0 = 6*0 + b

0 = b

We can conclude that the line is y = 6*x

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386