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3 years ago

13

in winter, the price of apples suddenly went up by $0.75 per pound. Sam bought 3 pounds of apples at the new price for a total o

f $5.88

2 answers:

timurjin [86]3 years ago

7 0

0.75 × 3 = $2.25 I hope that I helped

Aleks [24]3 years ago

6 0

Answer:

$1.21

Step-by-step explanation:

khan

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For what values of the variables are the following expressions defined? 1. 5y+2 2. 18/y 3. 1/x+7 4. 2b/10−b Example: X>7

Serga [27]

Answer:

1. All real numbers

2. All real numbers except y = 0

3. All real numbers except x = -7

4. All real numbers except b = 10

Step-by-step explanation:

For any function to be defined at a particular value, it should not be <em>approaching to a value </em> $\infty$ <em> or it should not give us the </em> $\frac{0}{0}$ <em> (zero by zero) form </em> when the input is given to the function.

The value of function will depend on the denominator.

Now, let us consider the given functions one by one:

1. 5y+2

Here denominator is 1. So, it can not attain a value $\infty$ or $\frac{0}{0}$ <em> (zero by zero) form </em>

So, for all real numbers, the function is defined.

$2.\ \dfrac{18}{y}$

At y = 0, the value

$At\ y =0, \dfrac{18}{y} \rightarrow \infty$

So, the given function is <em>defined for all real numbers except y = 0</em>

<em></em>

<em></em> $3.\ \dfrac{1}{x+7}$ <em></em>

Let us consider denominator:

x + 7 can be zero at a value x = -7

$At\ x =-7, \dfrac{1}{x+7} \rightarrow \infty$

So, the given function is <em>defined for all real numbers except x = -7</em>

<em></em>

$4.\ \dfrac{2b}{10-b}$

Let us consider denominator:

10-b can be zero at a value b = 10

$At\ b =10, \dfrac{2b}{10-b} \rightarrow \infty$

So, the given function is <em>defined for all real numbers except b = 10</em>

<em></em>

7 0

3 years ago

Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis

Tasya [4]

Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5

A.
$\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx$

B.
sepearte the integrals
$\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}$

next one
$\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}$

the last one you can do yourself, it is $\frac{50}{3}$
the sum is $\frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}$

so the area under the curve is $\frac{233}{3}$

6 0

2 years ago

# of yeast cells double every 4 hours how long will it take for 6billion cells

VLD [36.1K]

Answer:

60

Step-by-step explanation:

0.25

2×5

10

0.25×10

=2.5

;4×6

=24

:2.5×24

=60

6 0

2 years ago

three bags of sweets weigh 27/4 kg. two of them have the same weight and the third bag is heavier than each of the bags of equal

Nana76 [90]

I'm here buddy,

so, let's take the value of the two bags with equal weight as x.

= x + x + (x + $\frac{6}{5}$ ) = $\frac{27}{4}$

= 3x + $\frac{6}{5}$ = $\frac{27}{4}$

= 3x = $\frac{27}{4}$ - $\frac{6}{5}$

( let's take the LCM of 4 and 5 = 20

= 3x = $\frac{135}{20}$ - $\frac{24}{20}$

= 3x = $\frac{111}{20}$

= x = $\frac{111}{20}$ ÷ $\frac{3}{1}$ = $\frac{111}{20}$ × $\frac{1}{3}$ = $\frac{37}{20}$

So, the weight of the equal bags are $\frac{37}{20}$ and the weight of the third bag ( heavy one ) is $\frac{37}{20}$ + $\frac{6}{5}$ = $\frac{37}{20}$ + $\frac{24}{20}$ = $\frac{61}{20}$

1st bag = $\frac{37}{20}$ kg

2nd bag = $\frac{37}{20}$ kg

3rd bag = $\frac{61}{20}$ kg

Hope it helps...

7 0

2 years ago

How many ways can you arrange seven different books on a shelf?

Vikki [24]

Step-by-step explanation:

There are 7 books that can go in the first spot.

After a book has been placed in the first spot, there are 6 books left that can go in the second spot.

After that, there are 5 books that can go in the third spot.

So on and so forth.

So the number of ways is:

7×6×5×4×3×2×1 = 7! = 5040

4 0

2 years ago