WHICH OF THE FOLLOWING VARIABLES ( WRITTEN IN BOLD) HAVE A PROPORTIONAL RELATIONSHIP????

Answer:

The optimal volume is 63.1142 in3, with a cut of 1.5767 inches

Step-by-step explanation:

If we make a cut of x inches to create the box, the dimensions of the box will be:

Length = 10 - 2x

Width = 9 - 2x

Height = x

So the volume of the box would be:

Volume = (10 - 2x) * (9 - 2x) * x

Volume = 4x3 - 38x2 + 90x

To find the maximum volume, we need to take the derivative of the volume and find the values of x where it is equal to zero:

dV/dx = 12x2 - 76x + 90 = 0

6x2 - 38x + 45 = 0

Using Bhaskara's formula, we have:

Delta = 38^2 - 4*6*45 = 364

sqrt(Delta) = 19.08

x1 = (38 + 19.08) / 12 = 4.7567

x2 = (38 - 19.08) / 12 = 1.5767

Testing these values in the volume equation, we have:

Volume1 = 4*(4.7567)^3 - 38*(4.7567)^2 + 90*(4.7567) = -1.1883

(Negative value for the volume is not valid)

Volume1 = 4*(1.5767)^3 - 38*(1.5767)^2 + 90*(1.5767) = 63.1142

So the optimal volume is 63.1142 in3, with a cut of 1.5767 inches

Answer:

B

Step-by-step explanation:

The 115° angle is adjacent to both unknown angles in the triangles, thus

unknown angles = 180° - 115° = 65°

The sum of the 3 angles in a triangle = 180°, thus

∠ 1 = 180° - (65 + 80)° = 180° - 145° = 35°

∠ 2 = 180° - (65 + 85)° = 180° - 150° = 30°

Answer:

if B is centre and BCD lie on diameter then

length of diameter = 47

47

Step-by-step explanation:

Answer:

10 degrees on Tuesday.

But only if the whole question states Monday was -5 degrees and it increases by 15 degrees.

Step-by-step explanation:

Answer:

In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.

Step-by-step explanation:

hope that helps love!

Answer:

In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.

That's what google says :)

Step-by-step explanation:

I tried answering this question but got it wrong. Please ignore this message D:

Answer:

see below

Step-by-step explanation:

1. 2m = 24

Divide each side by 2

2m/2 = 24/2

m = 12

2. y – 9 = 30

Add 9 to each side

y-9+9 = 30+9

y = 39

3. X/4 = 12

Multiply each side by 4

x/4*4 = 12*4

x = 48

4. k + 12.5 = 30

Subtract 12.5 from each side

k+12.5-12.5 = 30-12.5

k =17.5

5. 3r = 15.3

Divide by 3

3r/3 = 15.3/3

r =5.1

Hey!!!!

Here's your answer:

1. 2m=24

or,m=24/2

m=12

2. y-9=30

or,y=30+9

y=39

3. 3x=12

or,X=12/3

x=4

4. k+12.5=30

or,k=30-12.5

k=17.5

5. 3r=15.3

or,r=15.3/3

r=5.1

Good luck on your assignment

The fraction 33/8 to a mixed number is 4 1/8

From the question, we have the following parameters that can be used in our computation:

Number = 33/8

Divide 33 by 8

So, we have

Quotient = 4

Next, we have

Remainder = 33 - 4 * 8

Evaluate the products

Remainder = 1

Hence, the fraction to a mixed number is 4 1/8

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Answer:

Just write whatever it says so quotient means divide, more means add, and product means multiply

x/4+1

Make your the equation is in order by checking the words after, than, next to see if the equation is in order

Hope this helps

If you have any questions you can ask

Step-by-step explanation:

Answer:

[tex]y = - 3[/tex]

Step-by-step explanation:

[tex]5(y + \frac{2}{5} ) = - 13 \\ 5y + \frac{10}{5} = - 13 \\ 5y + 2 = - 13 \\ 5y = - 13 - 2 \\ 5y = - 15 \\ \frac{5y}{5} = \frac{ - 15}{5} \\ y = - 3[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

a

c

c

d

d

Step-by-step explanation:

Answer:

10 oz

Step-by-step explanation:

edge

The total ounces of perfume in trials 1, 2, and 3 are 7.8 oz, 7.3 oz, and 7.65 oz.

Given to us,

For Trial 1,

A = 2 oz

B = 4 oz

C = 4 oz

Percentage of rose oil = 22%

weight of trail 1 = A+ B+ C = 2+ 4+ 4 = 10 oz.

Weight of rose oil in trial 1 = weight of trail 1 x Percentage of rose oil in 1

                                           =  10 oz x 22% = 2.2 oz

total ounces of perfume in trial 1

                                               = weight of trail - Weight of rose oil in trial 1

                                               = 10 - 2.2 = 7.8 oz

For Trial 2,

A = 4 oz

B = 2 oz

C = 4 oz

Percentage of rose oil = 27%

Total weight of trail 2 = A+ B+ C = 2+ 4+ 4 = 10 oz.

Weight of rose oil in trial2 = weight of trail 2 x Percentage of rose oil in 2

                                           =  10 oz x 27% = 2.7 oz

total ounces of perfume in trial 2

                                               = weight of trial 2 - Weight of rose oil in trial 2

                                               = 10 - 2.7 = 7.3 oz

For Trial 3,

A = 1 oz

B = 7 oz

C = 2 oz

Percentage of rose oil = 23.50%

Total weight of trail 3 = A+ B+ C = 2+ 4+ 4 = 10 oz.

Weight of rose oil in trial 3= weight of trail 3 x Percentage of rose oil in 3

                                           =  10 oz x 23.50% = 2.350 oz

total ounces of perfume in trial 3

                                             = weight of trail - Weight of rose oil in trial 3

                                             = 10 - 2.2 = 7.8 oz

Hence, The total ounces of perfume in trials 1, 2, and 3 are 7.8 oz, 7.3 oz, and 7.65 oz.

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Answer:

[tex]y = 2 (x-7)^{2} +6[/tex] is the equation of parabola.

Step-by-step explanation:

Vertex form of a parabola is given as :

[tex]y = a (x-h)^{2} +k ...... (1)[/tex]

(h,k) is the co-ordinate of vertex of parabola.

(x,y) are the points on parabola.

We are given that vertex is at (7,6) and a point on parabola is (6,8).

h = 7

k = 6

x = 6 and

y =8

Putting all the values in equation (1):

[tex]8 = a (6-7)^{2} +6\\\Rightarrow 8 = a + 6\\\Rightarrow a = 2[/tex]

Putting values of (h,k) and a in equation (1) to obtain the equation of parabola:

[tex]y = 2 (x-7)^{2} +6[/tex] is the equation of parabola with vertex at (7,6) and contains the point (6,8).

Answer:

Step-by-step explanation:

y = 2x2 – 28x + 52

wrong its not that

Answer:

it could either be n15

15n

because a number multiplied by 5 is

n15

but in mathematics a number comes before a letter when writing a mathematical expression

Answer:

The answer is n15

Hope this helps!!!

Please mark as brainliest

Step-by-step explanation:

Answer:

p=10

Step-by-step explanation:

I don't know what you're asking with the situation, but p is equal to 10

Answer:

p = 10

Step-by-step explanation:

i hope this helps, can you please make me brainliest.

Answer:

9. x = 16

10. x = 18

Step-by-step explanation:

9. 2x + 9 + 3x + 1 = 90

5x + 10 = 90

5x + 80

x = 16

10. 90 - 53 = 47

2x + 11 = 47

2x = 36

x = 18

Answer:

Yes i think it is misleading because five employees get 10.50 wich is 2.50 less than the avrege and the sixth employee is getting 24 dollars. Wich is a lot more than the averege.

Step-by-step explanation:

Answer:

c i think have a great day

Step-by-step explanation:

Answer:

[tex]5^{15}[/tex]

Step-by-step explanation:

You need to use PEMDAS for this.

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

[tex]( 5^{3})^{9}[/tex]÷[tex]5^{12} =\\[/tex]

[tex]125^{9}[/tex]÷[tex]5^{12} =[/tex]

7,450,580,596,923,828,125‬÷244140625=

30,517,578,125

[tex]5^{24} = 59,604,644,775,390,625[/tex]

[tex]5^{15} =30,517,578,125[/tex]

The correct answer is [tex]5^{15}[/tex]

(You don't actually have to multiply it all out, I just did it to make sure you understand)

[tex]\sqrt{5\\[/tex] is the correct answer.  you use the Pythagorean Theorem with 2 as a and 1 as b.  So the equation is [tex]c^{2}[/tex] = [tex]2^{2}[/tex] + [tex]1^{2}[/tex].  

Answer:

-2,3

Step-by-step explanation:

because you are going to the left you would end up getting -2 for the x and since you are going one down you would have 3 for the y.

Answer:

MISSING LENGTH IS 12 M

Step-by-step explanation:

9+9+ ? + ? = 42m

18+ X + X = 42m

2X=42-18

2X=24

X=12

Answer:

The missing length is 12 meters.

Step-by-step explanation:

9+9+x+x=42

Subtract 9 from both sides

9+x+x=33

Subtract 9 from both sides

x+x=24

2x=24

Divide both sides by 2

x=12

The missing length is 12 meters.

Answer:

0.25

Step-by-step explanation:

Answer: The extract form is 1/4 And the decimal form is 0.25

Step-by-step explanation:

Answer:

t= ((ln*2)/(0.02)

Step-by-step explanation:

plug 40000 in for P and solve for t

40000=20000e^0.02t

-divide both sides by 20000: 2=e^0.02t

-in order to cancel out e, multiply both sides by the natural log (ln)

ln(2)=0.02t

-divide 0.02 on both sides to get t by its self

Answer: t = ((ln(2)/(0.02))

Answer:

1466 2/3 mg of sodium

Step-by-step explanation:

We can use a ratio to solve

550 mg         x mg

------------- = --------------

6 ounces       16 ounces

Using cross products

550* 16 = 6x

Divide each side by 6

550*16 /6 = 6x/6

8800/6 =x

4400/3 =x

Change to a mixed number

1466 2/3 mg of sodium

Answer:

1466⅔ mg

Step-by-step explanation:

oz : mg

6 : 550

16 : X

X/16 = 550/6

X = 550/6 × 16

X = 4400/3

X = 1466⅔ mg

Answer:

145

Step-by-step explanation:

The the that connects the outside line to the inside line will equal to 180 so you take 180 minus 137 to get 43 and you have two angles for the inside which is 43 and 102. You minus these two number to 180 to get the last missing angle in a triangle because the inside of a triangle is 180 and then minus 180 to 35(Last angle measure) to get the outside of the triangle and you get 145.

Answer:

?=145°

Step-by-step explanation:

The angle 137° is a supplementary angle. So subtract 137 from 180 to find the adjacent angle:

[tex]180-137=43[/tex]

The angle adjacent the angle 137° is 43°. Add this value to the angle measure in the triangle:

[tex]102+43=145[/tex]

Two angle measures within the triangle add up to 145°. The angle measures of a triangle should add up to 180°. Subtract:

[tex]180-145=35[/tex]

The third angle in the triangle is 35°. This angle is also a supplementary angle. Subtract this from 180 to find the measure of angle ?:

[tex]180-35=145[/tex]

The angle ? is 145°.

or

The outer angle of a triangle (angle ?) can be found by finding the sum of the two angles within a triangle, not including the adjacent angle (or ?'s supplementary angle). So find the measure adjacent 137°:

[tex]180-137=43[/tex]

Add the two inner angle measure together:

[tex]43+102=145[/tex]

So angle ? is 145°.

:Done

Answer:

8y = - 6

Step-by-step explanation:

Given the 2 equations

x + 6y = 9 → (1)

- x + 2y = - 15 → (2)

Adding the 2 equations term by term gives

(x - x) + (6y + 2y) = (9 - 15), that is

8y = - 6

Answer:

8y = -6

Step-by-step explanation:

I got it right on Edge 2020

Also: Plug in the slope 8 and the y-intercept -6 to check the answer. It is correct.

Answer:

shown below

explanation:

first off, you get the like terms which is 10 and 134

12x=134+10

12x=144

then you simplify which will look like this:

12x. 144

___ = ___

12. 12

144÷12=12

so the answer is option c.12

Answer:

50 ft

Step-by-step explanation:

This is the pythagorean theorem, so you should use the formula...

a squared + b squared = c squared

Then substitute in the numbers... (remember, a and b are the legs, and c is the hypotenuse)

14 squared + 48 squared = c squared

14 squared = 14 x 14 = 196

Now we have 196 + 48 squared = c squared

48 squared = 48 x 48 = 2,304

Now we have 196 + 2,304 = c squared

Add them together - 2,304 + 196 = 2,500

Now we have 2,500 = c squared

We find the square root of 2,500 which is 50

You should now have 50 = c

That is your answer. Don't forget to add units.

50 ft is your hypotenuse (c)

I hoped this helped

Answer: the missing length is 50

Step-by-step explanation:

in order to figure out the missing number, you have to do the pythagorean theorem, which is a²+b²=c². A is 14 ft, B is 48 ft, and C is the missing length. You have to square each number. 14 will be 196 and 48 would be 2304.

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Answer:

1. B) 5.7

2. A) 12

3. A) 11.4

4. A) 5.7

5. A) 16.2

6. A) 11.2

7. No, they do not form a right triangle

8. Yes, they do form a right triangle

Step-by-step explanation:

Extra tip: The hypotenuse has to be less than both sides added together, but cannot be more than either of the sides alone.

1.

16² + b² = 17²

256 + b² = 289

256 - 256 + b² = 289 - 256

b² = 33

√b² = √33

b = 5.74 or 5.7

2.

16² + b² = 20²

256 + b² = 400

256 - 256 + b² = 400 - 256

b² = 144

√b² = √144

b = 12

3.

7² + 9² = c²

49 + 81 = c²

130 = c²

√130 = √c²

11.40 or 11.4 = c

4.

7² + b² = 9²

49 + b² = 81

49 - 49 + b² = 81 - 49

b² = 32

√b² = √32

b = 5.65 or 5.7

5.

a² + 5² = 17²

a² + 25 = 289

a² + 25 - 25 = 289 - 25

a² = 264

√a² = √264

a = 16.24 or 16.2

6.

10² + b² = 15²

100 + b² = 225

100 - 100 + b² = 225 - 100

b² = 125

√b² = √125

b = 11.18 or 11.2

7.

15² + 8² = 16²

225 + 64 = 256

289 ≠ 256

8.

5² + 12² = 13²

25 + 144 = 169

169 = 169