MATHEMATICS HIGH SCHOOL

Algebraically determine each of the following for the function y=16 - 4x(squared). A) the x and y intercepts if any. B) the symmetry type (x axis, y axis, origin, or neither.)

Answers

Answer 1

Answer:

Answer:

A) x intercept: (2, 0) , (-2, 0)

y intercept: (0, 16)

B) symmetric about y axis

Step-by-step explanation:

Given the function:

$y=16-4x^(2)$

To find:

Algebraically, A) find the x and y intercepts and B) the symmetry type.

Solution:

A) x intercept, let us put y = 0

$y=16-4x^(2)$

$0=16-4x^(2)\n\Rightarrow 4x^2=16\n\Rightarrow x^2=4\n\Rightarrow x =+2, -2$

x intercept: (2, 0) , (-2, 0)

For y intercept, put x = 0

$y=16-4x^(2)$

y = 16 - 0 =16

y intercept: (0, 16)

B) If the quadratic equation is given as: $y=ax^2+bx+c$ ,

the axis of symmetry is a vertical line $x=-(b)/(2a )$

Here, c = 16

b = 0 and

a = -4

So, Axis of symmetry is:

$x=-(0)/(2* (-4)) = 0$

which is the equation of y axis.

So, given equation is symmetric about y axis.

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A toy store marks down every toy by 15% in June .how much does a toy cost during June

Answers

Answer:

15% less than its regular price

Step-by-step explanation:

If the toy is marked down 15% in June, its cost during June is 15% less than its regular cost. (It will be 85% of its regular cost.)

What is 7 copies of the sum of 8 fifths and 4?

Answers

39¹/₅ or 39.2

Further explanation

The Problem:

7 copies of the sum of 8 fifths and 4.
Write an expression to match, and then evaluate.

The Process:

Here are some early expressions that need attention.

8 fifths is $\boxed{(8)/(5)}$
the sum of 8 fifths and 4 is $\boxed{(8)/(5) + 4}$

7 copies of the sum of 8 fifths and 4 mean that we have to multiply 7 with the sum of 8 fifths and 4. The term of "the product" is synonymous with multiplication.

Let us write an expression to match for '7 copies of the sum of 8 fifths and 4'.

$\boxed{\boxed{ \ 7 * \bigg((8)/(5) + 4 \bigg) \ }}$

Let us calculate the operation in parentheses at first.

$\boxed{ \ (8)/(5) + 4 \ }$

$\boxed{ \ (8)/(5) + (20)/(5) \ }$

$\boxed{ \ (28)/(5) \ }$

And now we solve the full expression.

$\boxed{ \ = 7 * \bigg((8)/(5) + 4 \bigg) \ }$

$\boxed{ \ = 7 * (28)/(5) \ }$

$\boxed{\boxed{ \ (196)/(5) \ }}$

In mixed fraction:

$\boxed{ \ (196)/(5) = \ ? \ }$

$\boxed{ \ = (195)/(5) + (1)/(5) \ }$

$\boxed{ \ = 39 + (1)/(5) \ }$

$\boxed{\boxed{ \ 39(1)/(5) \ }}$

In decimal:

$\boxed{ \ 39(1)/(5) = \ ? \ }$

$\boxed{ \ = 39(1 * 2)/(5 * 2) \ }$

$\boxed{ \ = 39(2)/(10) \ }$

$\boxed{\boxed{ \ 39.2 \ }}$

Thus, the result is $\boxed{\boxed{ \ 39(1)/(5) \ or \ 39.2 \ }}$ .

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Keywords: what, 7 copies, the sum of, 8 fifths and 4, write an expression to match, and then evaluate, 39¹/₅ or 39.2, multiply, parentheses, in mixed fraction, decimal

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