Add the equations 2x-3y=-1 + 3x+3y=26 A. 5x-6y=-27 B. 5x=27 C. 6y=25 D. 5x=25

Mathematics

2 answers:

jenyasd209 [6]3 years ago

6 0

Answer:

D) 5x = 25

Step-by-step explanation:

-1+26 = 25

2x + 3x = 5x

-3y + 3y = 0

viktelen [127]3 years ago

3 0

Answer:

pretty sure it is b

Step-by-step explanation:

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Damon makes 20 cups of lemonade by mixing lemon juice and water. The ratio of lemon juice to water is shown in the tape diagram.

Effectus [21]

Answer: 4 cup

Step-by-step explanation:

Here, the total number of cups in lemonade = 20 cups

In which some are cup of lemon juice and some are cups of water.

And, the ratio of cups of lemon juice and water in one lemonade = 1 : 4

Let the cups of lemon juice in one lemonade = 1 x

And, The cups of water in one lemonade = 4 x

Where x is any number.

Thus, 1 x + 4 x = 20

⇒ 5 x = 20

⇒ x = 20/5 = 4

Thus, Damon uses 4 cup of lemon juice in one lemonade.

6 0

3 years ago

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Daniel is completing a home project. He needs 13 pieces of wood, each 112 feet long, to complete the project. How much wood does

snow_lady [41]

13 x 112 = 1456 ft

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3 years ago

Find sin(a+b) if tan(a)=7/24 where a is in the third quadrant

ludmilkaskok [199]

The complete question in the attached figure

we have that
tan a=7/24 a----> III quadrant
cos b=-12/13 b----> II quadrant
sin (a+b)=?

we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant

step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325