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2 years ago

1. Solve the equation using the zero-product property. -x(5x – 4) = 0

Mathematics

1 answer:

Oxana [17]2 years ago

6 0

Answer:

x = 0, 4/5

Step-by-step explanation:

The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero

Here our a term is -x and our b term is (5x - 4)
Setting each term equal to zero and solving for x we get
-x = 0 → x = 0
5x - 4 = 0 → 5x = 4 → x = 4/5

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zepelin [54]

Answer:

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$

Step-by-step explanation:

We need to find equation from the table given

x f(x)

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We can write equation in the form of $y=mx+b$

where m is slope and b is y-intercept.

Finding Slope

We can used the slope formula to find slope: $Slope=\frac{y_2-y_1}{x_2-x_1}$

From the table we have: $x_1=3, y_1=-5, x_2=7, y_2=-2$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}$

So, we get slope $m=\frac{3}{4}$

Now, finding y-intercept

Using the slope $m=\frac{3}{4}$ and point (3,-5) we can find y-intercept

$y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}$

The y-intercept is $b=\frac{-29}{4}$

So, the equation having slope $m=\frac{3}{4}$ and y-intercept $b=\frac{-29}{4}$ will be:

$y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}$

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$

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3 years ago

Given the system of equations presented here:

Bumek [7]

ANSWER

The correct answer is option B

EXPLANATION

The equations are

$3x+5y=29---(1)$

and

$x+4y=16---(2)$

When we multiply the second equation by $-3$ , we obtain;

$-3x-12y=-48---(3)$

When we combine this new equation with equation (1).

$-7y=-19$

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We can then, solve for $y$ and then substitute the result in to any of the equations to find $x$ .

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Step-by-step explanation:

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