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ddd [48]
3 years ago
13

Find two numbers with a sum of 20 and a difference of 14.

Mathematics
1 answer:
vivado [14]3 years ago
4 0
A and B Definitely. 3 and 17, -3 and -17
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At a deli counter,
Arisa [49]

Answer:

Step-by-step explanation:

8 0
2 years ago
A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}

\Rightarrow x=0.1528,8.18

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, V''|_{x=0.1528}=24(0.1528)-100

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

4 0
3 years ago
Write the polynomial in standard form (-5x^3+6x^2-3x+7)+(7x^3+8x^2-10x-10)
Greeley [361]

Answer:

2x^3 +14x^2 -13x-3

Step-by-step explanation:

5 0
3 years ago
Finding the Median from a Dot Plot
MAXImum [283]

Answer:

median rainfall for highland storms = 18mm

median rainfall  for lowland storms = 18mm

or

median rainfall  for lowland storms = 17mm if the list of numbers is

2  4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Step-by-step explanation:

The median is the middle number of a sequence of ordered numbers.

The formula for the median is:

median = (n + 1 )/ 2

where n = total number of values

Note: the number that you find with this formula is the position. SO you have to go to the sequence of numbers and find the number that lies in that position.

Highland storms:

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

The numbers are already in ascending order so we can proceed.

n = 15

∴ median = (15+1)/2

                = 16/2

                = 8

The median is the umber in the 8th position

so, the median rainfall for highland storms is 18mm

Lowland storms:

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

The numbers are already in ascending order so we can proceed.

n = 15

∴ median = (15+1)/2

                = 16/2

                = 8

The median is the number in the 8th position.

∴  median rainfall for lowland storms is = 18mm

<u>Unclear: if this is the list of numbers: </u>

2  4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

then the median would be:

n = 16

median = (16+1)/2  

             = 17/2

             = 8.5

This means the median lies between the numbers in the 8th and 9th position.

∴ The median is =  (16 + 18)/2

                           = 34/2

                           = 17

5 0
3 years ago
Read 2 more answers
Let f(x) be an exponential functionWhich transformations to the graph of f(x) would describe e - f(x - 3) ?
gayaneshka [121]

Look at the graph below carefully

Observe the results of shifting ={2}^{x}f(x)=2​x

​​  vertically:

The domain, (−∞,∞) remains unchanged.

When the function is shifted up 3 units to ={2}^{x}+3g(x)=2​x +3:

The y-intercept shifts up 3 units to (0,4).

The asymptote shifts up 3 units to y=3y=3.

The range becomes (3,∞).

When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 ​x​​ −3:

The y-intercept shifts down 3 units to (0,−2).

The asymptote also shifts down 3 units to y=-3y=−3.

The range becomes (−3,∞).

3 0
2 years ago
Read 2 more answers
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