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3 years ago

THE SUM OF 36 AND TWICE THE FIRST NUMBER IS EQUAL TO THREE TIME THE SECOND NUMBER.

1 answer:

3 0

So 36+2x=3y
-x+y=z
z/2=8
(y-x)/2=8
first you want to find what x or y is by isolating one of them
so (y-x)/2=8
multiply both sides by 2
y-x=16
subtract 16 from both sides
y-x-16=0
add x to both sides
y-16=x
subtitute into first equation
36+2(y-16)=3y
distrubute
36+2y-32=3y
add like terms
4+2y=3y
subtract 2y from both sides
4=y
subutue into second equation
(4-x)/2=8
multiply both sides by 2
4-x=16
add x to both sides
4=16+x
subtract 16 from both sides
-12=x
y=4

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Select the system of linear inequalities whose solution is graphed.

elixir [45]

Answer:

$y\geq 3x-1$ ; $x+3y\leq 6$

Step-by-step explanation:

we know that

step 1

Find the inequality of the solid line x+3y=6

The solution is the shaded area below the solid line

therefore

The equation of the inequality is

$x+3y\leq 6$

step 2

Find the inequality of the solid line y=3x-1

The solution is the shaded area above the solid line

therefore

The equation of the inequality is

$y\geq 3x-1$

therefore

The system of linear inequalities is

$y\geq 3x-1$ ; $x+3y\leq 6$

5 0

3 years ago

What is the solution to the system of equations? y = A system of equations. Y equals StartFraction 2 over 3 EndFraction x plus 3

Sauron [17]

Answer:

The solution to the given system of equations is (-2, $\frac{5}{3}$ )

Therefore the values of x and y are x=-2 and $y=\frac{5}{3}$

Step-by-step explanation:

Given equations can be written as

$y=\frac{2}{3}x+3\hfill (1)$

$x=-2x+3x=-2\hfill (2)$

Solving equation(2) we get

x=-2

Substitute x=-2 in equation (1) we get

$y=\frac{2}{3}(-2)+3$

$=-\frac{4}{3}+3$

$=\frac{-4+9}{3}$

$=\frac{5}{3}$

Therefore the values of x and y are x=-2 and $y=\frac{5}{3}$

The solution to the given system of equations is (-2, $\frac{5}{3}$ )

5 0

2 years ago

Read 2 more answers

The graphs below have the same shape. what is the equation of the red graph?

Naily [24]

Answer:

Option D. $G(x)=x^{3}-1$

Step-by-step explanation:

we have

$F(x)=x^{3}$ -----> the parent function

The vertex of the function F(x) is the origin (0,0)

The vertex of the function G(x) is the point (0,-1)

The rule of the translation is equal to

(x,y)------> (x,y-1)

That means ------> The translation is 1 unit down

Applying the rule of the translation to F(x)

F(x)-------> G(x)

$G(x)=x^{3}-1$

7 0

3 years ago

What is the simplified value of the exponential expression 64 1/4

katrin [286]

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
64^{\frac{1}{4}}\qquad \boxed{64=2^6}\qquad (2^6)^{\frac{1}{4}}\implies 2^{6\cdot \frac{1}{4}}\implies 2^{\frac{6}{4}}\implies 2^{\frac{3}{2}}
\\\\\\
\sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2^1}\implies 2\sqrt{2}$

3 0

3 years ago

Nola was selling tickets at the high school dance. At the end of the evening she picked up the cash box and noticed a dollar lyi

Blizzard [7]

Answer:

The $1 belongs to the cash box

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine if the $1 belongs to the cash box or not

Represent singles with s and couples with c.

From the attachment, we have:

$s + c = 47$ --- total attendance

$5s + 4c =200$ --- ticket sold

Solve for s and c.

Make s the subject in (1)

$s = 47-c$

Substitute 47 - c for s in (2)

$5(47 - c) + 4c = 200$

Open bracket

$235 - 5c + 4c = 200$

$235 - c = 200$

$c = 235 - 200$

$c = 35$

This means that the total individual which makes up the couples are 35. This is not possible because couples are in 2's and the total should be an even number.

<em>So, we can conclude that the $1 belongs to the cash box</em>

4 0

2 years ago