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3 years ago

Match the definition to the mathematical terms they describe

Mathematics

1 answer:

lbvjy [14]3 years ago

4 0

Answer:

1. All coplanar points equidistant from a given point:

CIRCLE

2. piece of a line with one endpoint:

RAY

3. two rays with a common endpoint:

ANGLE

4. Piece of a line with two endpoints:

LINE SEGMENT

Step-by-step explanation:

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What is the inverse of y= 10^x +8?

shepuryov [24]

Answer:

$x = \log_{10}(y - 8)$ , where $y > 8$ .

Step-by-step explanation:

The question is asking for an expression for $x$ in terms of $y$ .

The first step is to move as many constants away from the side with $x$ as possible. In this question, that could be done by subtracting $8$ from both sides of the equation.

$y - 8 = 10^{x} + 8 - 8$ .

$y - 8 = 10^{x}$ .

Notice how $x$ is in the position of an exponent. Logarithms could help move $x$ out of that position.

For any base $b > 0$ :

$\log_{b} b^{x} = x\, \log_{b}\, b = x$ .

In this question, $10$ would be the base. That is: $b = 10$ .

Take the logarithm (with $10$ as the base) of both sides of the equation $y - 8 = 10^{x}$ :

Left-hand side: $\log_{10} (y - 8)$ .
Right-hand side: $\log_{10} \left(10^{x}\right) = x\, \log_{10}\left(10\right) = x$ .

Equate both sides to find an expression for $x$ :

$x = \log_{10}(y - 8)$ .

6 0

2 years ago

Which octant contains the image of point A( 1, -3, 4) after a reflection about the xz - plane?

ANTONII [103]

Hi,

Concept: The given problem is based on 3 Dimensional Geometry.

Consider three axes in defined space be x, y & z in their positive directions then - x , -y & -z be their negative axes.

The coordinate of given point A(x1, y1, z1) = (1, -3, 4)

If we take the reflection of point A about xz - plane x and z coordinates will remain same and y-coordinate will give its reflection. It means the value of y-coordinate will be changed which will be +ve 3.

Hence, the reflection of A(1, -3, 4) will be A'(x2, y2,z2= (1, 3, 4).

7 0

3 years ago

a lemon pie was cut into 6 equal pieces. being on a diet, Matilda ate only half a piece. what fraction of the whole pie did she

WINSTONCH [101]

Matilda only ate 1/12 of the pie as 1/2 of 1/6 = 1/12

5 0

3 years ago

A bag of corn tortilla chips costs 2.89 after a 15% discount. What is the original price?

Montano1993 [528]

Answer:

3.4