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3 years ago

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Eva played her favorite video game for 14 hours last week. Today, Eva's parents restricted her to 4 additional hours each week f

or the next 7 weeks. Create the function, f(x), that models Eva's total video game time, and explain what each number in the situation represents graphically, using complete sentences.

1 answer:

34kurt3 years ago

5 0

The function would be:
f(x) = 14 + 4x; 0 ≤ x ≤ 7

The y-intercept would be 14. This is the point when the line would hit the y-axis. The slope would be 4 and the range is 0 to 7. At x =7, the value of the function would be 42.

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If it is 9:26, what time will it be in 54 minutes?

Nata [24]

Answer:

In 54 minutes, it'll be 10:30.

6 0

3 years ago

Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .

$x =1$ is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

$\dfrac{2a^2-4a+2}{3a^2-3}$

Let us simplify the numerator and denominator separately.

The numerator is given as $2a^2-4a+2$

2 is a common factor in all the three terms. So, we factor it out. This gives,

$=2(a^2-2a+1)$

Now, $a^2-2a+1=(a-1)(a-1)$

Therefore, the numerator becomes $2(a-1)(a-1)$

The denominator is given as: $3a^2-3$

Factoring out 3, we get

$3(a^2-1)$

Now, $a^2-1$ is of the form $a^2-b^2=(a-b)(a+b)$

So, $a^2-1=(a-1)(a+1)$

Therefore, the denominator becomes $3(a-1)(a+1)$

Now, the given expression is simplified to:

$\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}$

There is $(x-1)$ in the numerator and denominator. We can cancel them only if $x\ne1$ as for $x=1$ , the given expression is undefined.

Now, cancelling the like terms considering $x\ne1$ , we get:

$\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}$

Therefore, the simplified form is $\dfrac{2(x-1)}{3(x+1)}$

The simplification is true only if $x\ne1$ . So, $x =1$ is the excluded value for the given expression.

8 0

3 years ago

Every hour of driving uses

xenn [34]

Answer:

45 gallons

Step-by-step explanation:

1 hour = 3 gallons

2 hours = 6 gallons

3 hours = 9 gallons

4 hours = 12 gallons

5 hours = 15 gallons

10 hours = 30 gallons

15 hours = 45 gallons

4 0

3 years ago

Write an equation of the circle with center (3,-2) and radius 6

Lubov Fominskaja [6]

Answer:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

Step-by-step explanation:

We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.

Recall that the equation of a circle is given by:

$\displaystyle (x-h)^2 + (y-k)^2 = r^2$

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is at (3, -2), <em>h</em> = 3 and <em>k</em> = -2. <em>r</em> = 6. Substitute:

$\displaystyle (x-(3))^2 +(y-(-2))^2 = (6)^2$

Simplify:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

In conclusion, the equation of the circle will be:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

8 0

2 years ago

A student made the table to find 40% of 130. Which expression can be used find 40% of 130?

g100num [7]

$\bf \begin{array}{|c|ll}
\cline{1-1}
\textit{a\% of b}\\
\cline{1-1}
\\
\left( \cfrac{a}{100} \right)\cdot b
\\\\
\cline{1-1}
\end{array}~\hspace{5em}\stackrel{\textit{40\% of 130}}{\left( \cfrac{40}{100} \right)130}\implies \stackrel{\stackrel{26\cdot 2}{\downarrow }}{52}$

4 0

3 years ago

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