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Debora [2.8K]
3 years ago
13

Hunter is going to graph the ordered pairs that are represented by this table on a coordinate plane.

Mathematics
2 answers:
Maksim231197 [3]3 years ago
4 0

Answer:

b

Step-by-step explanation:

Vesnalui [34]3 years ago
3 0

Answer:

1

Step-by-step explanation:

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0
3 years ago
How do you solve this
AlladinOne [14]

Answer:

  • domain: all terms are defined for <em>all real numbers</em>
  • solution: x = 6

Step-by-step explanation:

Rewrite the equation as a single exponential. After taking the log, the solution becomes obvious.

5^{x-2}-7^{x-3}=7^{x-5}+11\cdot 5^{x-4}\\\\5^{x-2}-11\cdot 5^{x-4}=7^{x-3}+7^{x-5}\\\\5^{x-2}(1-11\cdot 5^{-2})=7^{x-3}(1+7^{-2})\\\\5^{x-2}\dfrac{14}{25}=7^{x-3}\dfrac{50}{49}\\\\1=\dfrac{2\cdot 7^{x-3}5^4}{2\cdot 5^{x-2}7^3}=\left(\dfrac{7}{5}\right)^{x-6}\\\\0=(x-6)\log(1.4)\\\\x=6

6 0
3 years ago
Which of the given shapes has a larger area?
Simora [160]

Answer:

Rectangle

Step-by-step explanation:

Count the units. For the triangle, A=0.5bh. 0.5(4)(6)=A. A=12

Now, for the rectangle, A=bh. A=(3)(5). A=15. The rectangle is larger

5 0
3 years ago
One angle of a triangle measures <img src="https://tex.z-dn.net/?f=10degrees" id="TexFormula1" title="10degrees" alt="10degrees"
iVinArrow [24]

Answer:

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

Step-by-step explanation:

Let

x ----> the measure of one angle of the triangle

y ---> the measure of the second angle

z ----> the measure of the third angle

we know that

The sum of the measure of the interior angles in any triangle must be equal to 180 degrees

x+y+z=180^o -----> equation A

One angle of a triangle measures  10 degrees more than the second

x=y+10 ----> equation B

The measure of the third angle is twice the sum of the first two angles

z=2(x+y) ---> equation C

substitute equation B in equation C

z=2(y+10+y)

z=4y+20 ----> equation D

substitute equation D and equation B in equation A

(y+10)+y+(4y+20)=180^o

solve for y

6y=180-30\\6y=150\\y=25^o

Find the value of x

x=25+10=35^o

Find the value of z

z=4(25)+20=120^o

therefore

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

5 0
3 years ago
Give an example from your classroom of a three collinear point
Doss [256]
Chess board? , the board if there is like a line with points that has points on the same line
6 0
3 years ago
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