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3 years ago

Is the relation a function (-5,7),(-2,-1),(03),(4,7)

Mathematics

1 answer:

vova2212 [387]3 years ago

6 0

The correct choice is
D Yes; only one range value exists for each domain value.

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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 $b=5$ .

4 0

2 years ago

Read 2 more answers

2 r squared + 3s cubed minus r squared + 40 squared minus r squared if R equals -2 s equals -3 and T equals 5

Flura [38]

$2r^2+3s^2-r^2+4t^2-r^2\\\\\text{simplify}\\\\(2r^2-r^2-r^2)+3s^2+4t^2=3s^2+4t^2\\\\s=-3;\ t=5\\\\3(-3)^2+4(5)^2=3(9)+4(25)=27+100=127$

6 0

3 years ago

A shipment of 8 tons of sugar is separated into containers of equal size. If the shipment fills 3 1/3 containers, how much sugar

liubo4ka [24]

Take 8 and divide it by 3 1/3. to make it easer 1/3 could be .3 as a decimal.
so 8 divided by 3.3.
8/3.3= 2.42
so it would be 2.42 tons of sugar per container.

3 0

2 years ago

If y varies directly as x and y = 12 when x = 8, find y when x = 14.

Alex17521 [72]

The direct variation between x and y may be written as,
y = kx
where k is the constant of variation. From the first set of values of the variables,
12 = k(8)
the value of k is 1.5. Substituting the next set to the same equation,
y = 1.5(14)
The value of y is 21.

8 0

2 years ago

Green paint is made by mixing blue, yellow and white paints in the ratio 2 : 7 : 1. How much blue paint is needed to make 64 lit

Lyrx [107]

Answer:

12.5 litres of Blue paint

Step-by-step explanation:

2+7+1=10

therefore;

10=64

2=??

cross-multiply

(2×64)÷10

answer= 12.4 liters or 12.5

6 0

2 years ago