9514 1404 393
Answer:
7.056 × 10^31
Step-by-step explanation:
The applicable rule of exponents is ...
(10^a)(10^b) = 10^(a+b)
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![(1.2\times10^{19})\times(5.88\times10^{12})=(1.2\cdot5.88)\times10^{19+12}\\\\=\boxed{7.056\times10^{31}}](https://tex.z-dn.net/?f=%281.2%5Ctimes10%5E%7B19%7D%29%5Ctimes%285.88%5Ctimes10%5E%7B12%7D%29%3D%281.2%5Ccdot5.88%29%5Ctimes10%5E%7B19%2B12%7D%5C%5C%5C%5C%3D%5Cboxed%7B7.056%5Ctimes10%5E%7B31%7D%7D)
As you know, the commutative and associative properties of multiplication let you rearrange the order of the product to any convenient form. Here it is convenient to group the mantissas together and the powers of 10 together.
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<em>Additional comments</em>
This is a product your scientific or graphing calculator can produce for you. Likely it will display the result in scientific notation because it won't have enough display digits to show you the product any other way. For smaller numbers, you can set the display mode to give you scientific notation.
If you choose to use a spreadsheet to perform this calculation, the numbers would be entered as 1.2e19 and 5.88e12. The result will be something like 7.056e31. You may have to format the display to show 3 decimal places.
Answer:
![y=2x^2-\frac{4}{3}x-\frac{10}{3}](https://tex.z-dn.net/?f=y%3D2x%5E2-%5Cfrac%7B4%7D%7B3%7Dx-%5Cfrac%7B10%7D%7B3%7D)
Step-by-step explanation:
we know that
The roots of the quadratic function (x-intercepts) are
x=-1 and x=5/3
so
we can write the equation of the parabola as
![y=a(x+1)(x-\frac{5}{3})](https://tex.z-dn.net/?f=y%3Da%28x%2B1%29%28x-%5Cfrac%7B5%7D%7B3%7D%29)
where
a is a coefficient
Remember that
The parabola pass through the point (5,40)
substitute the value of x and the value of y of the ordered pair in the quadratic equation and solve for a
x=5, y=40
![40=a(5+1)(5-\frac{5}{3})](https://tex.z-dn.net/?f=40%3Da%285%2B1%29%285-%5Cfrac%7B5%7D%7B3%7D%29)
![40=a(6)(\frac{10}{3})](https://tex.z-dn.net/?f=40%3Da%286%29%28%5Cfrac%7B10%7D%7B3%7D%29)
![40=20a\\a=2](https://tex.z-dn.net/?f=40%3D20a%5C%5Ca%3D2)
substitute
![y=2(x+1)(x-\frac{5}{3})](https://tex.z-dn.net/?f=y%3D2%28x%2B1%29%28x-%5Cfrac%7B5%7D%7B3%7D%29)
apply distributive property
![y=2(x^2-\frac{5}{3}x+x-\frac{5}{3})\\\\y=2(x^2-\frac{2}{3}x-\frac{5}{3})\\\\y=2x^2-\frac{4}{3}x-\frac{10}{3}](https://tex.z-dn.net/?f=y%3D2%28x%5E2-%5Cfrac%7B5%7D%7B3%7Dx%2Bx-%5Cfrac%7B5%7D%7B3%7D%29%5C%5C%5C%5Cy%3D2%28x%5E2-%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B5%7D%7B3%7D%29%5C%5C%5C%5Cy%3D2x%5E2-%5Cfrac%7B4%7D%7B3%7Dx-%5Cfrac%7B10%7D%7B3%7D)
see the attached figure to better understand the problem
A dilation is a transformation that changes the size but not the shape of a figure. Therefore, the image created by the dilation is not congruent to the pre-image, the original figure; it is similar. Each point of the image is distinguished from those of the pre-image by using a prime symbol.
Answer:
CE and GD
Step-by-step explanation:
A secant of a circle is a line which passes through only 2 points of the circle. So it bisects the circle at exactly 2 points. BF is not a secant because even though the points are labelled there is no line passing through. The reason why GD is a secant is because there are the points G and F and a straight line runs through them so that's why it's a secant