Write the equation of the line in fully simplified slope-intercept form.

Tyler is overdrawn at the bank by $180 He gets $70 for his birthday and deposits it what is his account balance now

polet [3.4K]

Answer:

-$110

Step-by-step explanation:

An overdrawn bank account would be -$180. you would have to add $70 .

given 70 is not large enough to fully bring the balance to 0. long story short, subtract 70 from 180. since 70 is < 180 the number is therefore negative since 180 is negative in this problem

I hope this helps!!^^

3 0

3 years ago

Read 2 more answers

3/4 x 8 = ? I need help for this question.

ahrayia [7]

Answer:

6 hope this was fast

7 0

2 years ago

Read 2 more answers

49/6 into a mixed number

mote1985 [20]

49/6 into a mixed number would be 8 1/6. This is because you would see how many times 6 can go into 49. Since 6 times 8= 48, you subtract that from 49. You are left with one. You put the number you multiplied 6 by as the whole number and the leftover one over six. I hope this helps!

4 0

3 years ago

Read 2 more answers

Can someone help me with this math homework please!

Daniel [21]

Answer:

1st, 2nd and 6th options

Step-by-step explanation:

Given

$\frac{2}{3}$ - x + $\frac{1}{6}$ = 6x ( multiply through by 6 to clear the fractions )

4 - 6x + 1 = 36x ← option 1 will have the same solution set

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Adding the 2 fractions on the left side gives

$\frac{4}{6}$ + $\frac{1}{6}$ - x = 6x , that is

$\frac{5}{6}$ - x = 6x ← option 2 will have the same solution set

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From

4 - 6x + 1 = 36x ( add 6x to both sides )

5 = 42x ← option 6 will have the same solution set

8 0

2 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.

5 0

3 years ago