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IrinaK [193]
4 years ago
5

Please Help! Which of the following properties was used in the expression shown here?

Mathematics
1 answer:
Elena L [17]4 years ago
3 0

Answer:

Distributive Property

Step-by-step explanation:

Multiply 5 with each number in the parentheses

Then add the variables after

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Using the given information, give the vertex form equation of each parabola.
Amanda [17]

Answer:

The equation of parabola is given by : (x-4) = \frac{-1}{3}(y+3)^{2}

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:(\frac{47}{12},-3)

The general equation of parabola is given by.

(x-h)^{2} = 4p(y-k), When x-componet of focus and Vertex is same  

(x-h) = 4p(y-k)^{2}, When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

For value of p:

p=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

p=\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}

p=\sqrt{(\frac{1}{12})^{2}}

p=\frac{1}{12} and p=\frac{-1}{12}

Since, Focus is left side of the vertex,

p=\frac{-1}{12} is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p=\frac{-1}{12}

(x-h) = 4p(y-k)^{2}

(x-4) = 4(\frac{-1}{12})(y+3)^{2}

(x-4) = \frac{-1}{3}(y+3)^{2}

8 0
3 years ago
Which of the following shows the correct value of 50
Orlov [11]

Answer:

None of the options is correct

Step-by-step explanation:

It is important to know that he expression a < x < b means that x is greater than a and less than b. So, for finding the correct value let's analyse each option.

A. 4 < 50 < 5

50 is greater than 4 but it is not less than 5, so, option A is incorrect.

B. 7 < 50 < 8

50 is greater than 7 but it is not less than 8, so, option B is incorrect.

C. 8 < 50 < 9

50 is greater than 8 but it is not less than 9, so, option C is incorrect.

D. 10 < 50 < 11

50 is greater than 10 but it is not less than 11, so, option D is incorrect.

Thus, none of the options is correct.

8 0
3 years ago
Which of these points lies on the circle with center (2 3) and radius 2
Grace [21]

Answer:

(x-2)^2 + (y-3)^2 = 4

Step-by-step explanation:

Use the equation (x-h)^2 + (y-k)^2 = r^2 where the center of the circle is (h,k) and the radius is r.

4 0
3 years ago
Let a be a non-zero rational number and be an irrational number. Is a/b rational or irrational?
vodka [1.7K]

Answer: Irrational, assuming b is irrational

Step-by-step explanation:

You didnt state what "b" is, but:

Youre dividing "a" by an irrational number. you could do something simple like 4 divided by pi. Youre going to get an irrational number

7 0
3 years ago
What is 2logx−logy+2logz written as a single logarithm? log(xz)^2/y log2x/2yz logx^2y/z^2 logx^2/yz^2
Klio2033 [76]

Answer: \log\dfrac{x^2z^2}{y}

Step-by-step explanation:

Properties of logarithm:

(i)\ \ n\log a = a^n\\\\ (ii)\ \ \log m +\log n =\log (mn)\\\\ (iii)\ \ \log m-\log n =\log\dfrac{m}{n}

Consider,

2\log x-\log y+2 \log z\\\\ =\log x^2-\log y+\log z^2\ \ \ \ \text{[By (i)]}\\\\= \log x^2+\log z^2-\log y\\\\=\log(x^2z^2)-\log y\ \ \ \ [\text{By } (ii) ]\\\\=\log(\dfrac{x^2z^2}{y})    \ \ \ \ [\text{By (iii)}]

3 0
3 years ago
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