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2 years ago

I needed help on this

Mathematics

1 answer:

Strike441 [17]2 years ago

5 0

Answer:

Step-by-step explanation:

Let Freda's sum = x

Donnie has 3/4 x

He spends 63 dollars. His sum is now

3/4x - 63

Now the equation looks like this

6(3/4x - 63) = x Remove the brackets

6*3/4 x - 378 =x

6 * 3/4 = 4 1/2

4 1/2 x - 378 = x Add 378 to both sides

4 1/2 x = x + 378 Subtract x from both sides

3.5 x = 378 Divide by 3.5

x = 378 /3.5

x = 108

Since x = 108, that's how much Freda had. (She spent nothing).

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Simplify 2x^2+6x-7x+8-3x^2+1

Doss [256]

$(((((2*(x^2))+6x)-7x)+8)-3x^2)+1 \\ \\ ((((2x^2 + 6x) - 7x) + 8) - 3x^2) + 1 \\ \\ we \ would \ then \ (pull \ out) \ like \ terms. \\ \\ -x^2 - x + 9 = -1 * (x^2 + x - 9) \\ \\ \left[\begin{array}{ccc} -9 + 1 = -8 \\
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\end{array}\right] \\ \\ Your \ answer: \boxed{\boxed{\bf{ -x^2 - x + 9
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I hope this helps you!

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3 years ago

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Nana76 [90]

Answer:

P(Multiple of 3) = 33/100

Step-by-step explanation:

We have 3 + 6 + 8 + 11 + 14 + 16 + 15 + 12 + 9 + 5 + 1 = 100 total rolls

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Step-by-step explanation:

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2 years ago

Find the difference:7 7/8-3 1/4=?

Arlecino [84]

Answer:

4 5/8

Step-by-step explanation:

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3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

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3 years ago