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3 years ago

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1 answer:

mote1985 [20]3 years ago

6 0

Answer: The equation that represents the other equation is $y=\dfrac{1}{3}x+5$ .

The solution of the system is <u>(3,6).</u>

Step-by-step explanation:

Linear equation: $y=mx+c$ , where m= slope

c = y-intercept.

In the first table, the y-intercept = 5 [ y-intercept = value of y at x=0.

Slope for first table = $\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}$

The equation that represents the first table:

$y=\dfrac{1}{3}x+5$

So, the equation that represents the other equation is $y=\dfrac{1}{3}x+5$ .

Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.

Here, x=3 and y=6 is the common value in both tables.

So, the solution of the system is <u>(3,6).</u>

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2 years ago

Find the values of y = c(x) = for x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, , 0.729, and 1.

kondaur [170]

c(x) is a function, then we will solve the problem for two different functions.

1. If $c(x)=\frac{x}{0.5}+x$

Then

$y=c(x)$

$y=\frac{x}{0.5}+x$

Using each of the values for x we have.

When x=0 the result is: $y=\frac{0}{0.5}+0=0$

When x=0.008 the result is: $y=\frac{0.008}{0.5}+0.008=0.016+0.008=0.024$

When x=0.027 the result is: $y=\frac{0.027}{0.5}+0.027=0.054+0.027=0.081$

When x=0.064 the result is: $y=\frac{0.064}{0.5}+0.064=0.128+0.064=0.192$

When x=0.125 the result is: $y=\frac{0.125}{0.5}+0.125=0.25+0.125=0.375$

When x=0.216 the result is: $y=\frac{0.216}{0.5}+0.216=0.432+0.216=0.648$

When x=0.343 the result is: $y=\frac{0.343}{0.5}+0.343=0.686+0.343=1.029$

When x=0.512 the result is: $y=\frac{0.512}{0.5}+0.512=1.024+0.512=1.536$

When x=0.729 the result is: $y=\frac{0.729}{0.5}+0.729=1.458+0.729=2.187$

When x=1 the result is: $y=\frac{1}{0.5}+1=2+1=3$

2. If $c(x)=sin(x)+2x$

Then

$y=c(x)$

$y=sin(x)+2x$

Using each of the values for x we have.

When x=0 the result is: $y=sin(0)+2(0)=0$

When x=0.008 the result is: $y=sin(0.008)+2(0.008)=0.000139+0.016=0.016139$

When x=0.027 the result is: $y=sin(0.027)+2(0.027)=0.000471+0.054=0.054471$

When x=0.064 the result is: $y=sin(0.064)+2(0.064)=0.001117+0.128=0.129117$

When x=0.125 the result is: $y=sin(0.125)+2(0.125)=0.002182+0.25=0.252182$

When x=0.216 the result is: $y=sin(0.216)+2(0.216)=0.003769+0.432=0.435769$

When x=0.343 the result is: $y=sin(0.343)+2(0.343)=0.005986+0.686=0.691986$

When x=0.512 the result is: $y=sin(0.512)+2(0.512)=0.008936+1.024=1.032936$

When x=0.729 the result is: $y=sin(0.729)+2(0.729)=0.012723+1.458=1.470723$

When x=1 the result is: $y=sin(1)+2(1)=0.017452+2=2.017452$

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3 years ago

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kykrilka [37]

Answer:

B

Step-by-step explanation:

the product (2x² - 3x - 8)(3x² + 5x + 1) is required

multiply each term in the second factor by each term in the first factor.

= 2x²(3x² + 5x + 1) - 3x(3x² + 5x + 1) - 8(3x² + 5x + 1) ← distribute

= 6 $x^{4}$ + 10x³ + 2x² - 9x³ - 15x² - 3x - 24x² - 40x - 8

collecting like terms gives

6 $x^{4}$ + x³ - 37x² - 43x - 8 → B

8 0

3 years ago