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3 years ago

You will drive 200 miles and need to calculate your gas expense (25km per gallon and gas costs $6.00/gallon).

1 answer:

7 0

First you do 200 miles divided by 25 km. It is 8. This means you need 8 gallons for the whole trip. 8 times 6dollars is 48 dollars. You will need to pay 48 dollars in gas prices.

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Find the slope of the line that contains (−1, −6) and (−15, 2).

mestny [16]

(8/16) would be the slope

4 0

3 years ago

The graph of function g(x) is a transformation of the graph of function f(x) = x2.g(x) =

mariarad [96]

Given:

The graph of function g(x) is a transformation of the graph of function f(x) = x²

As shown: the graph of g(x) is open down

So, we will reflect f(x) over the x-axis, the function will be ⇒ -x²

And there is horizontal compression so, the factor of compression will be > 1

So, the function will be ⇒ -2x²

Finally, there is a vertical shift down 3 units

So,

$g(x)=-2x^2-3$

6 0

1 year ago

Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

5 0

3 years ago

What are the coordinates of the midpoint of ab?

mars1129 [50]

Your answer will be A because you have to get the sum of 4 and 8 and then divide by 2. Which is 6 for the x coordinate. The you need to take the sum of -5 and -1 and then divide by 2. Which is -3 for the y coordinate. So the answer is (6,-3).

7 0

3 years ago

Read 2 more answers

Which the slope-intercept form of the equation of each line the slope and y-intercept?

Delvig [45]

SPOTLIGHT DEMYSTIFIED QUIZZES GALLERIES LISTS ON THIS DAY BIOGRAPHIESSEARCH BRITANNICAWhat are you looking for?SearchBROWSE POPULAR TOPICS:Pearl Harbor attack American Revolution Reign of Terror Photosynthesis Las PosadasYou have reached Britannica's public website.For ad-free access to your Britannica School or Library account CLICK HEREChemical compoundWRITTEN BY: Melvyn C. UsselmanRichard O.C. NormanSteven S. ZumdahlCarl R. NollerSee Article HistoryChemical compound, any substance composed of identical moleculesconsisting of atoms of two or more chemical elements.Methane, in which four hydrogen atoms are bound to a single carbon atom, is an example of a basic chemical compound. The structures of chemical compounds are influenced by complex factors, such as bond angles and bond length.Encyclopædia Britannica, Inc.All the matter in the universe is composed of the atoms of more than 100 different chemical elements, which are found both in pure form and combined in chemical compounds. A sample of any given pure element is composed only of the atoms characteristic of that element, and the atoms of each element are unique. For example, the atoms that constitute carbon are different from those that make up iron, which are in turn different from those of gold. Every element is designated by a unique symbol consisting of one, two, or three letters arising from either the current element name or its original (often Latin) name. For example, the symbols for carbon, hydrogen, and oxygen are simply C, H, and O, respectively. The symbol for iron is Fe, from its original Latin name ferrum. The fundamental principle of the science of chemistry is that the atoms of different elements can combine with one another to form chemical compounds. Methane, for example, which is formed from the elements carbon and hydrogen in the ratio four hydrogen atoms for each carbon atom, is known to contain distinct CH4 molecules. The formula of a compound—such as CH4—indicates the types of atoms present, with subscripts representing the relative numbers of atoms (although the numeral 1 is never written).

6 0

3 years ago