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2 years ago

2/3 b + 5 =20 - b solve for b

Mathematics

2 answers:

Alborosie2 years ago

8 0

Answer:

b = 9

Step-by-step explanation:

$\frac{2}{3} b + 5 = 20-b\\\frac{2}{3} b+5+b=20-b+b\\\frac{5}{3} b+5=20\\\frac{5}{3} b+5-5=20-5\\\frac{5}{3}b=15\\b= 15*\frac{3}{5} \\b= 9$

Wittaler [7]2 years ago

4 0

Answer:

$b = 9$

Step-by-step explanation:

$\frac{2}{3} b + 5 = 20 - b$

In order to solve for b, we must isolate the variable. We can start by subtracting 5 from both sides.

$\frac{2}{3} b + 5 - 5 = 20 - b - 5$

Simplify.

$\frac{2}{3} b = 15 - b$

Add b to both sides.

$\frac{2}{3} b + b = 15 - b + b$

Simplify.

$\frac{2}{3} b + b = 15$

Multiply everything by 3 to remove the fractions.

$3(\frac{2}{3}b+b) = 3(15)$

Simplify.

2b + 3b = 45

Simplify.

5b = 45

Divide 5 from both sides.

5b ÷ 5 = 45 ÷ 5

Simplify.

b = 9

For more information on solving variables, check out the following answers!

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Answer:

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write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind o

BlackZzzverrR [31]

Answer:

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Step-by-step explanation:

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3 years ago

Solve 3x²-x-2=0. Please show all work.

lorasvet [3.4K]

3x²-x-2=0

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x₁,₂= $\frac{1(+/-)\sqrt{25} }{6}$

x₁,₂= $\frac{1(+/-)5}{6}$

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4 years ago

1. Find the vertex of the following: y = (x - 4)(x - 10) *

horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

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3 years ago