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2 years ago

Write out the steps to find the solutions for the following quadratic: (x-2)^2 = 25

Mathematics

1 answer:

natta225 [31]2 years ago

5 0

Answer:

x=7

Step-by-step explanation:

Starting with (x-2)² = 25

First, square root both sides to get rid of the square on the left. You'll get:

x-2 = 5

Add 2 to both sides to get x alone. You'll get:

x=7

Check your answer by filling in 7 for x:

(7-2)² = 25

(5)² = 25

25 = 25

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3 years ago

If (5x− 4)(3x+ 7) = 15x²-ax-b,then find the value of a and b

Mkey [24]

Answer:

$a=-23\\\\b=28$

Step-by-step explanation:

Let's start by using distributive multiplication:

$(a\pm b)(c\pm d)=ac\pm ad \pm bc \pm bd$

So:

$(5x-4)(3x+7)=15x^2+35x-12x-28\\\\$

Grouping like terms:

$15x^2 +(35x-12x)-28\\\\15x^2+23x-28$

Now, $15x^2+23x-28$ is equal to:

$15x^2-ax-b$

In this sense:

$15x^2+23x-28=15x^2-ax-b$

In order to satisfied the equality:

$23x=-ax\hspace{10}(1)\\\\and\\\\-28=-b\hspace{10}(2)$

Hence, from (1), let's solve for a:

$23x=-ax\\\\-a=\frac{23x}{x} \\\\-a=23\\\\a=-23$

And from (2), let's solve for b:

$-28=-b\\\\b=28$

Let's verify the result evaluating the values of a and b into the original equation:

$(5x-4)(3x+7)=15x^2+23x-28=15x^2 -ax -b\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 -(-23)x -(28)\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 +23x -28$

As you can see, the values satisfy the equation, therefore, we can conclude they are correct.

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3 years ago

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masya89 [10]

Step 1: Multiply 15 by 3, which equals 45.
Step 2: Multiply 45 by 2, which gives you 90.
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Step 4: Find the percent of 15 people in a group of 150 people by diving 150 by 15.

150 / 15 = 10.

FINAL ANSWER: 10%

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