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3 years ago

Jennifer, Luis, Robert, Anna, and Tonya are figuring out how to split the check for lunch.

Mathematics

2 answers:

kramer3 years ago

6 0

8 + 15 = 23

23 - 65.45 = 42.46.

The rest of the people in the group split $42 and 46 cents.

Hope this helped!!

shepuryov [24]3 years ago

6 0

Answer:

$12.23

explanation:

24.45 / 2 = 12.225

Round the decimal to $12.23

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What is the area cause I am having a hard trouble

fomenos

The figure consists of a triangle and two rectangles.

-----------------------------
Top Triangle:
-----------------------------
Height = 22 - 10 - 7 = 5cm
Base = 20 - 5 - 5 - 10cm
Area of triangle = 1/2 x 5 x 10 = 25 cm²

-----------------------------
Middle Rectangle:
-----------------------------
Length = 10cm
Width = 7cm
Area = 10 x 7 = 70 cm²

-----------------------------
Bottom Rectangle:
-----------------------------
Length = 20 cm
Width = 10 cm
Area = 20 x 10 = 200 cm²

-----------------------------
Total Area:
-----------------------------
Area = 25 + 70 + 200 = 295 cm²

-----------------------------
Answer: Area = 295 cm²
-----------------------------

6 0

3 years ago

Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided

scoray [572]

Let me express the equation clearly:

lim x→-9 (x²-81)/(x+9)

Initially, we solve this by substituting x=-9 to the equation.

((-9)²-81)/(-9+9) = 0/0

The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.

(2x-0)/(1+0) = 2x = 2(-9) = -18

The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999

((-8.999)²-81)/(-8.999+9) = -18

7 0

2 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

Louise measured the perimeter of her rectangular scrapbook to be 156 cm. If the scrapbook is 43 cm wide, how long is the scrapbo

Montano1993 [528]

Answer:

L=35cm

Step-by-step explanation:

Perimeter is 2(L+w)

156cm=2*(43+L)

L=35cm

8 0

2 years ago

How do you use the product rule to find the derivative of y=x√⋅cos(x)y=sqrt(x)*cos(x) ?

Ipatiy [6.2K]

$y=\sqrt x\cos x\\
y'=(\sqrt x)'\cos x+\sqrt x (\cos x)'\\
y'=\frac{1}{2\sqrt x}\cos x+\sqrt x\cdot(-\sin x)\\
y'=\frac{1}{2\sqrt x}\cos x-\sqrt x\sin x\\
$

7 0

2 years ago