MATHEMATICS HIGH SCHOOL

Solve using substitution


x = y +3
-3x + 3y = 6

Answers

Answer 1
Answer:

\large\bf{\underline{\underline{\mathfrak{Question}:}}}

Solve using substitution

x = y +3,

-3x + 3y = 6

\large\bf{\underline{\underline{\mathfrak{Solution}:}}}

Giventhat,

{\small{\rm{x=y+3}}}

Equation:

{\small{\rm{-3x + 3y = 6}}}

So,

By substituting the value of xthat is y+3 in the given equation we get,

:{\Longrightarrow{\small{\rm{-3(y+3) + 3y = 6}}}}

:{\Longrightarrow{\small{\rm{-3y-9+ 3y = 6}}}}

:{\Longrightarrow{\small{\rm{\cancel{-3y}-9\cancel{+3y} = 6}}}}

:{\Longrightarrow{\small{\rm{x = 6+9}}}}

:{\Longrightarrow{\small{\rm{x = 15}}}}

{\therefore{\small{\rm{Value\:of\:x = 15}}}}

Now to find the value of Y use the value of x in the givenequation.

:{\Longrightarrow{\small{\rm{-3(15) + 3y = 6}}}}

:{\Longrightarrow{\small{\rm{-45+ 3y = 6}}}}

:{\Longrightarrow{\small{\rm{3y = 6+45}}}}

:{\Longrightarrow{\small{\rm{3y = 51}}}}

:{\Longrightarrow{\small{\rm{y =(51)/(3)}}}}

:{\Longrightarrow{\small{\rm{y =17}}}}

{\therefore{\small{\rm{Value\:of\:y = 17}}}}

Forverification:

:{\Longrightarrow{\small{\rm{-3(15) + 3(17) = 6}}}}

:{\Longrightarrow{\small{\rm{6= 6}}}}

Henceverified!

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Find the unknown length. Round to the nearest tenth if necessary.

Answers

Answer:

a = 7.4

Step-by-step explanation:

Since this is a right triangle, we will use the Pythagorean theorem:

c^2 = a^2 + b^2

28^2 = a^2 + 27^2

784 = a^2 + 729

55 = a^2

a = 7.4

Answer:

55 i believe

28 + 27 = 55

Coach Shaw is buying baseball equipment for his team. he gets a reduced rate if he buys 8 baseballs for every 3 batting helmets. The reduced rate is $2.25 per baseball and $22.50 per helmet. The sales tax on each item is 6%. Coach Shaw has $400 in his budget to buy baseballs and helmets. What is the greatest number of baseballs and helmets he can buy at the reduced rate if the ratio of baseballs to helmets is 8:3?

Answers

Answer:

He can by for sets, that is, 24 baseballs and 12 batting helmets.

Step-by-step explanation:

We know that

Each baseball costs $2.25.

Each helmet costs $22.50.

This mean that 8 baseballs costs: 8(\$2.25)=\$18\n

And all 3 batting helmets costs: 3(\$22.50)=\$67.50

Now, one set of 8 baseballs and 5 helmets costs \$18 + \$67.50=\$ 85.50

If coach Shaw has $400, the total number of set he can buy is (\$400)/(\$85.50)\approx 4

This means he can by for sets, that is, 24 baseballs and 12 batting helmets.
$2.25x8=$18
$22.50x3=$67.50
Tax: 18x$0.06=$1.08~~~~$18+$1.08=$19.08. 
67.50x0.06=4.05~~~~$67.50+$4.05=$71.55
$71.55+$19.08=$90.63
$400.00/$90.63= about 4 sets of 3 helmets and 8 baseballs. 

What is an equation of the line that passes through the point (-2, -3) and isparallel to the line 4x - y = 12

Answers

Answer: y = 4x + 5

Step-by-step explanation:

Find the slope of the second line.

4x - y = 12

-y = -4x + 12

y = 4x - 12

slope = 4

Therefore, the slope of the second line must also be 4.

Use point-slope form to write the equation.

y + 3 = 4(x + 2)

y = 4x + 5

Starting from a 130 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is traveling at a constant rate of 25 feet per second. The distance between the bicycle and the checkpoint is given by the equation: d = |130 - 25t|. At what times is the bike 15 feet away from the checkpoint? a. 4.6 sec and 9.2 sec

b. 2.9 sec and 5.8 sec

c. 4.6 sec and 5.8 sec

d. 2.9 sec and 3.3 sec

Answers

for this question you can say d = 15 feet so we need the t then you can say : 
15 = l 130 - 25t l ⇒ because of the absolute value you should say : 
1) 130 - 25t = 15  ⇒ -25t = 15 - 130 ⇒ - 25t = -115 ⇒ t = 115/25 = 4.6 sec 

2) 130 - 25t = - 15 ⇒ -25t = -15 - 130 ⇒ -25t = - 145 ⇒ t = 145/25 = 5.8 sec 
so the answer is c :))
i hope this is helpful 
have a nice day 

Answer:

The answer is C - 4.6 sec and 5.8 sec

Step-by-step explanation:

Hope this helps ✿

Write an expression that can be used to check the quotient of 646 divided 3

Answers

An expression used to check the quotient would be this:
3x=646
Then, do as you normally would and divide 646 by 3:
646/3 = x
x≈215.33

(-2)to the 8th power = (-2) (-2) (-2) (-2)(-2)(-2)(-2)(-2) =258

Answers

Answer:

the answer to this would be 256.

Step-by-step explanation:

before explaining this,

- negative x negative = positive

- positive x positive = positive

- negative x positive = negative

- positive x negative = negative

this would be because -2 x -2 it equals 4. then, we multiply 4 x -2 and we get -8, then we multiply -8 x -2 and we get 16, then we keep doing the same thing until we get the answer/ used all the -2's.

1. -2 x -2 = 4

2. 4 x -2 = -8

3. -8 x -2 = 16

4. 16 x -2 = -32

5. -32 x -2 = 64

6. 64 x -2 = -128

7. -128 x -2 = 256

2+2+2x6795-90+6000x5678910+5-1x67^8
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