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sertanlavr [38]
3 years ago
9

What number is 21% more than 5/11?

Mathematics
1 answer:
mr Goodwill [35]3 years ago
5 0

Answer:

Step-by-step explanation:

21% more then 5/11...

5/11 + 21% of 5/11 = 5/11 + 0.21(5/11) = 5/11 + (21/100 * 5/11) =

5/11 + 21/220 = 11/20 <===

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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
Assume a fair deck of playing cards. Find the probability of drawing a 10, replacing it and drawing an ace.
cupoosta [38]

Answer:

There are 52 cards in a deck. The total number of outcomes possible when picking 2 cards and replacing them is 52 * 52 = 2704.

There are 4 10s and 4 aces so the total number of successful outcomes = 4 * 4 = 16.

Probability = 16 / 2704 = 1 / 169

6 0
3 years ago
Does a heptogon have parallel lines please. help me
Tpy6a [65]
No they do not have parallel lines
4 0
3 years ago
17.
IrinaVladis [17]

Answer:

$32 + $0.25x < $50

Step-by-step explanation:

1.he buy a backpack for $32

2. he buys x amount of pencils. Each pencil cost 0.25. ($0.25x)

3. all of that is less than(<) $50

4 0
2 years ago
When will the equation xn = c, where c is a whole number, have two solutions? Explain.
Kazeer [188]
If x=n then it would have 2 solutions because it would be x^2 = c which has a positive and negative solution but idk if that is what you are asking for
3 0
3 years ago
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