Find the missing side
length of the right
triangle. Remember
a² + b² = c²
12 ft
5 ft
?

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A · cos B = sin (A + B) + sin (A - B)

2 cos A · cos B = sin (A + B) + sin (A - B)

Given:  cos A + cos B = 1/2      and      sin A + sin B = 1/4  

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \tan\dfrac{A+B}{2}[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}[/tex]

[tex]\text{Multiplication:}\qquad \quad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}\bigg(\dfrac{2\cos\frac{A-B}{2}}{2\cos \frac{A-B}{2}}\bigg)[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{2\sin \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}{2\cos \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}[/tex]

[tex]\text{Product to Sum:}\qquad \dfrac{\sin A+\sin B}{\cos A+\cos B}[/tex]

[tex]\text{Given:}\qquad \qquad \qquad \quad \dfrac{\frac{1}{4}}{\frac{1}{2}}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1}{2}[/tex]

LHS = RHS:    1/2 = 1/2  [tex]\checkmark[/tex]

Answer:

10

Step-by-step explanation:

42-2=40(since 2 extra)

=>For each bag=40/10=4

Answer:

Step-by-step explanation:

Using the equation of motion S = ut + 1/2at² where;

S is the distance travelled = 20m

u is the initial velocity = 0m/s (car starts from rest)

a is the acceleration = ?

t is the time taken = 4s

To get the acceleration of the car, we will substitute the given parameters into the given equation.

S = ut + 1/2at²

20 = 0(4)+1/2a(4)²

20 = 0+ a/2*16

20 = 8a

divide both sides by 8

20/8 = 8a/8

20/8 = a

a = 20/8

a = 2.5m/s²

Hence the acceleration of the car is 2.5m/s²

To determine which ratio would result in a valid proportion when set equal to StartFraction 7 over 3 EndFraction, we need to find the ratio that is equivalent to StartFraction 7 over 3 EndFraction.

To do this, we can cross-multiply. When we cross-multiply StartFraction 7 over 3 EndFraction and another ratio, the product of the numerator of StartFraction 7 over 3 EndFraction and the denominator of the other ratio should be equal to the product of the denominator of StartFraction 7 over 3 EndFraction and the numerator of the other ratio.

Let's check each option:

1. StartFraction 9 over 49 EndFraction:

7 x 49 = 343

3 x 9 = 27

These values are not equal, so it is not a valid proportion.

2. StartFraction 18 over 42 EndFraction:

7 x 42 = 294

3 x 18 = 54

These values are not equal, so it is not a valid proportion.

3. StartFraction 42 over 18 EndFraction:

7 x 18 = 126

3 x 42 = 126

These values are equal, so it is a valid proportion.

4. StartFraction 49 over 9 EndFraction:

7 x 9 = 63

3 x 49 = 147

These values are not equal, so it is not a valid proportion.

Therefore, the ratio that results in a valid proportion when set equal to StartFraction 7 over 3 EndFraction is StartFraction 42 over 18 EndFraction.
Hope It Helps :)

Answer:

number 3. is wrong you can reduce once more and it will equal 3/5. and number 4 would be 5/7.

Step-by-step explanation:

divide 12/20 by 2 on the top and bottom. you should get 6/10. you can divide that once more by 2 on the top and bottom and you should get 3/5. thats simplest form.

divide 25/35 by 5 on the top and bottom youll get 5/7. thats the simplest form.

hope this helped :)

Answer:

yo no se pero ahorita yo te ayudo

Answer: (a) ([tex]x_{2},y_{2}[/tex]) = (3,2)

              (b)  ([tex]x_{2},y_{2}[/tex]) = (19,-7)

Step-by-step explanation: Midpoint of a segment is halfway between 2 endpoints. It is calculated using the formulas:

[tex]x_{m}=\frac{x_{1}+x_{2}}{2}[/tex]

[tex]y_{m}=\frac{y_{1}+y_{2}}{2}[/tex]

Isolating [tex]x_{2}[/tex]:

[tex]2x_{m}=x_{1}+x_{2}[/tex]

[tex]x_{2}=2x_{m}-x_{1}[/tex]

And [tex]y_{2}[/tex]:

[tex]2y_{m}=y_{1}+y_{2}[/tex]

[tex]y_{2}=2y_{m}-y_{1}[/tex]

(a) Replacing values and calculating [tex]x_{2}[/tex]:

[tex]x_{2}=(2*2)-1[/tex]

[tex]x_{2}=3[/tex]

Calculating [tex]y_{2}[/tex]:

[tex]y_{2}=[2*(-1)]-(-4)[/tex]

[tex]y_{2}=2[/tex]

[tex](x_{2},y_{2})=(3,2)[/tex]

(b) [tex]x_{2}=(2*5)-(-9)[/tex]

[tex]x_{2}=19[/tex]

[tex]y_{2}=(2*6)-19[/tex]

[tex]y_{2}[/tex] = -7

[tex](x_{2},y_{2})=(19,-7)[/tex]

Answer:

D is the Right answer got it right on test and teacher said it was right

Step-by-step explanation:

Ym

Answer:

add 13 to both sides

Step-by-step explanation:

4x-13=43

4x=56

x=14

Answer:

107 cm

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Answer:

107 cm

Step-by-step explanation:

To find this you just first add the 26cm three times because thats the length of 3 sides and you get 78 then you multiply 14.5 times 2 for the other two sides that length and you get 29. Next you add 78+29 and you get 107cm

Answer:

367.87

Step-by-step explanation:

the 100th place is the 2nd digit in the decimal. After the "7" is "27" so it rounds down to just ".8700." We don't include the "infinite zeros" or whatever so therefore your answer is 367.87.

Hope this helps and have a nice day!

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

K (5, 6) P (1, 1)

The distance from K to P is

[tex] |KP| = \sqrt{ ({5 - 1})^{2} + ({6 - 1})^{2} } \\ = \sqrt{ {4}^{2} + {5}^{2} } \\ = \sqrt{16 + 25} \\ = \sqrt{41} \\ = 6.403124[/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

From the problem statement, from the score which is given as  15._66.

it is only one digit that is missing and not a combination of two digits.

This makes our guess easier as we have a range of 0-9 to guess from

therefore the list of possible digits to select from can be given as

from between 0-9 which is

{0,1,2,3,4,5,6,7,8,9}

Answer:

Step-by-step explanation:

D

Answer:

Here are the answers:

Step-by-step explanation:

C. 4.6x10^7 = 4.6x 10x10x10x10x10x10x10 = 46,000,000

D. 4.6x10x10x10x10x10x10x10

E. You Simplify your expression by mutiplying 10x10x10x10x10x10x10 to get rid of the exponent. You find the sum by multiplying 10x10x10x10x10x10x10 first. You get 10,000,000. Then Multiply 4.6 by 10,000,000. You should get 46,000,000. The sum is 46,000,000.

Answer:

x=4/9

Step-by-step explanation:

We first let 0.4 (4 being repeated) be x.

10x=4.4

10x-x=4.4-0.4

9x=4

x=4/9

Answer:

50.01

Step-by-step explanation:

7y-2=15

7y=15+2

7y=17

y=2.4285714286

21y-1

21(2.4285714286)-1

51.01-1

50.01

Hope this helps ;) ❤❤❤

Answer:

0

Step-by-step explanation:

First of all, simplify the equation on both sides. You will get 5x - 2 = 2x - 2. Add two to both sides, and you get 5x=2x. Subtract 2x from both sides to get 3x=0, so x will equal 0.

Answer:

5x = 2x

Step-by-step explanation:

5x- 2 = 2 + 2x

5x - 2+ 2 = -2 + 2x +2

Answer:

A. (x+12)(x-12)

Step-by-step explanation:

Use foil method

x * x = x^2

x * - 12 = - 12x

12 * x = 12 x

12 * - 12 = - 144

x^2 [- 12x + 12x= 0x = 0] - 144

x^2 + 0 - 144 =

x^2 - 144 #

Answer:

What are the factors of x2 – 144?

✔ (x – 12)

 and

✔ (x + 12)

Step-by-step explanation:

Answer:

31/100

Step-by-step explanation:

Answer:

0.10

Step-by-step explanation:

between 1980 and 2010 : 30 years

the change of price:3.99-0.99= 3 dollars

the average rate : 3/30=0.10 or 10 %

Answer:

Step-by-step explanation:

20x+5y=15

Subtract 20x from both sides.

5y=15−20x

Divide both sides by 5.

__5y_  = _15-20x_____

    5                5

y=  __15-20______

            5

Divide 15−20x by 5.

y=3−4x

Answer:

2 is the answer

Step-by-step explanation:

2x/3+x/3-2=0

Now take lCM of all the three term,

3x/3-2=0

Now you have solve it

x=2

Answer:

No solution

Step-by-step explanation:

[tex] \frac{2}{3} x + \frac{1}{3} x - 2 = 0[/tex]

Collect like terms and simplify

[tex] \frac{2}{3} x + \frac{1}{3} x = 2 [/tex]

[tex] \frac{2}{3} + \frac{1}{3} = \frac{2 + 1}{ 3} = \frac{3}{3} = 1[/tex]

[tex]1 = 2[/tex]

Answer: 64

Step-by-step explanation:

When you come across question of evaluation, substitute all the variables.

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

Given

 4m+23+np-3

Substitute value m, n, and p

=4(7)+23+(2)(8)-3

Use PEMDAS to simplify

=28+23+16-3

=51+16-3

=67-3

=64

Answer:

x=-5

Step-by-step explanation:

Answer:

The probability of drawing a red card from a deck is 50%

The probability of drawing clubs from a deck is 25%

Step-by-step explanation:

Answer:

992

Step-by-step explanation:

1 pound equals 16 ounce

So, 27x16=432

432+400+160=992

[tex]:\implies\sf\:x-\dfrac{3}{4}=2x-\dfrac{9}{7}[/tex]

[tex]:\implies\sf\:\dfrac{9}{7}-\dfrac{3}{4}=2x-x[/tex]

[tex]:\implies\sf\:\dfrac{36-21}{28}=x[/tex]

[tex]:\implies\boxed{\bf{\red{x=\dfrac{15}{28}}}}[/tex]