The discriminante :
b^2-4ac
1^2 - 4 * -2 * -28 = 1 - 224 = -223
When the discriminant (b^2-4ac) is less than 0, the equation had no real solutions.
-223<0, so, 2x^2+x-28 = 0 has no real solutions.
Hope that helps :)
Explanation:
a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.
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b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid <em>is isosceles</em>.
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c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.
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For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.
<h3>Answer: Net Increase of 26%</h3>
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Explanation:
If it increases by 5%, then we use the multiplier 1.05
Think of it like saying 100% + 5% = 1 + 0.05 = 1.05
Similarly, an increase of 20% means we involve 1.20
Combine those multipliers to get: 1.05*1.20 = 1.26
This is a net increase of 26%
Interestingly, we get fairly close to 25% which is what many students might go for (since 5 + 20 = 25). This is a beginner's trap.
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An example:
Let's say the temperature is 20 degrees Celsius (68 degrees Fahrenheit)
An increase of 5% means it moves to 1.05*20 = 21 degrees C
A 20% increase means we go to 1.20*21 = 25.2 degrees C
The shortcut would be to do a 26% increase to get 1.26*20 = 25.2 to help confirm we have the correct combined increase.
Answer:
95
Step-by-step explanation:
The smallest number that divided by 6, 15, and 18 leavses 5 in each case is 95
the first simple interest will be $1.73 more than the second one.
<h3>
Which is the difference between the two interests?</h3>
The loan is of $575, and there are two options:
7 years at 4.5% or 8 years at 3.9%
Remember that the simple interest formula is:
SI = (P*R*T)/100
Where:
P = principal value.
R = rate (this is the percentage per year)
T = time, in years.
Then for the first option. the interest will be:
SI = ($575*4.5*7)/100 = $181.13
For the second option we will have the interest:
SI' =( $575*3.9*8)/100 = $179.4
The difference is:
$181.13 - $179.4 = $1.73
This means that the first simple interest will be $1.73 more than the second one.
If you want to learn more about simple interests:
brainly.com/question/20690803
#SPJ1
