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3 years ago

Which of the following is a linear function?

Mathematics

1 answer:

Tamiku [17]3 years ago

3 0

Answer:

Step-by-step explanation:

$\text{The equation of a linear function:}\\\\f(x)=mx+b\\\\m-slope\\b-y-intercept\\----------------------------\\\\A.\ f(x)=\dfrac{2}{x}+7\qquad\bold{NOT}\ /\text{x is in denominator}/\\\\B.\ f(x)=\sqrt{2+7x}\qquad\bold{NOT}\ /\text{x is under square roots}/\\\\C.\ f(x)=2-7x\qquad\bold{YES}\ /m=-7,\ b=2/\\\\D.\ f(x)=2+x+x^2\qquad\bold{NOT}\ /\text{x is in the second power}/$

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A shirt retails for $22.40. A 10% tax is then applied to the original. What’s the final price after tax?

IrinaK [193]

<em>Answer:</em>

24.64

<em>Method:</em>

You get 10% of the shirt cost, and it on to the 22.40

6 0

3 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

maxonik [38]

Answer:

Total weight of the wheat placed on 45th square will be = $1.26\times 10^{6}tons$

Step-by-step explanation:

King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.

In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.

We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)

In a geometric progression we know the nth term = $a(r^{n-1})$

where a = first term of the series, r = common ratio, n = number of terms

Now we have to calculate the weight of all wheat placed on 45th square.

So we will put the values in the given formula 45th term =

$1\times (2^{45-1})$ = $2^{44}$ = $1.76\times 10^{13}$

Then the weight of wheat will be = $2.51\times 10^{9}pounds$ = $1.26\times 10^{6}tons$

7 0

3 years ago

Solve the inequality IxI < 5

Elodia [21]

Answer:

the correct answer is the second one

3 0

3 years ago

A perfectly straight 24 ft tall tree grows on the edge of the bank of a 45 foot wide river. A bird sitting at the top of the tre

True [87]

Answer:

Distance covered by the bird before meeting the water is: 51.264 ft

Step-by-step explanation:

Notice that if the bird catches the fish in 2 seconds, then the fish was able to dive down a total of 6 feet before being caught:

$distance=Vel\,* time=3\,\frac{ft}{s} *\,2\,\,s=6 \,\,ft$

So the bird needs to fly in the direction of the hypotenuse of a right angle triangle (see attached image) that has one leg of length (24 ft + 6 ft) = 30 ft, and another one 22.5 ft (half the width of the river.

Such hypotenuse is (using Pythagoras theorem):

$hyp =\sqrt{(60\,ft)^2+(22.5\.ft)^2} =\sqrt{4106.25} \,ft=64.08\,ft$

Now, in order to find the distance D the bird covers from the top of the tree to the water (marked in red in our image), we use similar triangles. The bigger triangle is that of legs 60 ft and 22.5 ft and hypotenuse 64.08 ft.

The smallest triangle we use in the proportion is the one shaded yellow in the image, which has one leg equal to 24 ft, and unknown hypotenuse:

So we make the proportion between known legs, and hypotenuses:

$\frac{24\,ft}{30\,ft} =\frac{D}{64.08\,ft} \\D=\frac{64.08\,ft\,*\,24\,ft}{30\,ft} \\D=51.264\,ft$