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3 years ago

The square root of 9x plus 7 plus the square rot of 2x equall to 7

Mathematics

1 answer:

Oliga [24]3 years ago

4 0

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
x=2

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If 2(4x + 3)/(x - 3)(x + 7) = a/x - 3 + b/x + 7, find the values of a and b.

zmey [24]

Answer:

$a=3$ and $b=5$ .

Step-by-step explanation:

So I believe the problem is this:

$\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}$

where we are asked to find values for $a$ and $b$ such that the equation holds for any $x$ in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

$\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)$

$2(4x+3)=a(x+7)+b(x-3)$

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

$2(4\cdot -7+3)=a(-7+7)+b(-7-3)$

$2(-28+3)=a(0)+b(-10)$

$2(-25)=0-10b$

$-50=-10b$

Divide both sides by -10:

$\frac{-50}{-10}=b$

$5=b$

Now we have:

$2(4x+3)=a(x+7)+b(x-3)$ with $b=5$

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

$2(4\cdot 3+3)=a(3+7)+b(3-3)$

$2(12+3)=a(10)+b(0)$

$2(15)=10a+0$

$30=10a$

Divide both sides by 10:

$\frac{30}{10}=a$

$3=a$

So $a=3$ and $b=5$ .

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3 years ago

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in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?

lora16 [44]

Answer:sin =perpendicular/hypotenuse

Step-by-step explanation:

Sin angle is given use tan theta or cos theta to find the RS

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3 years ago

A large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Quinn randomly selects 1 marble

12345 [234]

40% because if their are 5 colors of equal amounts, than each one is 20% amd if you try and get 2 then you multiply %20 by 2 and you get %40

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3 years ago

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A store offers four different brands of a product. It decides to eliminate the brand that is most likely to be returned. The tab

STatiana [176]

Answer: brand C

Step-by-step explanation:

i just took the quiz

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3 years ago

Fifteen 2 inch nails weigh 35 grams. How many of these nails weigh 175 grams? Can you explain how to do this please thankyou so

polet [3.4K]

Solving:

1) Pass: Make the rule three (Directly proportional)

Two inch nails ______ grams (<span>Weight)
</span>15 ----------------------------35
n ----------------------------- 175

2) Pass: <span>Multiply cross
</span>
$35*n = 15*175$

3) Pass: Simplify
$35*n = 15*175$
$35n = 2625$
$n = \frac{2625}{35}$
$\boxed{n = 75}$

Answer:
75 nails weigh 175 grams

8 0

3 years ago