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2 years ago

Is the following irrational or rational?

Mathematics

1 answer:

prisoha [69]2 years ago

4 0

6.4 is Rational. It ends in a decimal
if the nine is the last number and it does not go on (indicated by ...) then the number is rational
-2 is rational. It's an integer. All integers are rational.

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If a complementary angle measures 24 more than the other what is that angle

Lelu [443]

The definition of a complementary angle is one angle who can be added to another complementary angle to sum to 90 degrees. More simply, just an angle is complementary to another angle if they add up to 90 degrees. In this case, to find the other angle, you subtract 24 from 90 which equals 66 degrees.

5 0

3 years ago

Consider the function: f(x) = 2x^2 - 1.5x - 5 and its graph.

Dominik [7]

Answer:

f(x) = -4x² + 19x - 18

Step-by-step explanation:

$f(x) = 2x^2 - 1.5x - 5$

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

$y=f(x-2) = 2(x-2)^2 - 1.5(x-2) - 5\\y = 2(x^2-4x+4) - 1.5x+3 - 5\\y=2x^2-8x+8-1.5x+3-5\\y=2x^2-9.5x+6$

f(x) = 2x² - 9.5x + 6

If it is then translated 3 units in the positive y, we add 3 to the input function to get:

$y=f(x)+3=2x^2-9.5x+6+3\\y = 2x^2-9.5x+9$

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

$y =2( 2x^2-9.5x+9) = 4x^2-19x+18\\y= 4x^2-19x+18$

iii) reflected across the x-axis

we multiply the parent function by –1, to get a reflection about the x-axis.

$y= -1(4x^2-19x+18)=-4x^2+19x-18\\y=f(x)=-4x^2+19x-18$

5 0

3 years ago

You plant a spruce tree that grows 4 inches per year and a hemlock tree that grows _____ inches per year. The initial heights ar

UNO [17]

Complete Question:

You plant an 8-inch spruce tree that grows 4 inches per year and a 14-inch hemlock tree that grows 6 inches per year.

The initial heights are shown.

Write a system of linear equations that represents this situation.

Answer:

$s(x) = 8 + 4x$

$h(x) = 14 + 6x$

Step-by-step explanation:

Given

Spruce Tree (s):

$Initial\ Height = 8$

$Growth = 4$ (yearly)

Hemlock Tree (h):

$Initial\ Height = 14$

$Growth = 6$ (yearly)

Required

Represent as system of linear equations

Let the number of years be x.

In both cases, the equation can be formed using:

$Equation = Initial\ Height + Growth * x$

For Spruce Tree (s):

$s(x) = 8 + 4 * x$

$s(x) = 8 + 4x$

For Hemlock Tree (h):

$h(x) = 14 + 6 * x$

$h(x) = 14 + 6x$

Hence, the equations are $s(x) = 8 + 4x$ and $h(x) = 14 + 6x$

3 0

2 years ago

A chef has 10 spice jars, but his new spice rack only holds 8 spice jars.

miskamm [114]

This is a statistics problem on permutation and combination. To differentiate this, permutation involves on the arrangement in which order doesn't matter. For combination, order matters.

For example, if you arrange A, B and C, for permutation it could be AB, BA, CA, AC, BC and CB. But for combination, it would just be AB, AC and BC.

So, in this problem where he is asked to arrange 8 jars in which order doesn't matter. It is permutation. You can solve this just by calculator. The formula would be nPr, where n is the total number of items while r is the number of items to be sorted. Thus,

nPr = 10P8 = 1, 814,400

Thus, the answer is B.

5 0

3 years ago

Which of the following number(s) are rational? Select all that apply.

Lana71 [14]

Answer:

2.323232...

2.32222...

2.323148

4 0

3 years ago

Read 2 more answers