Divide 54 into the ratio 11:7

The minimum surface area for the rectangular container is [tex]588cm^{2}[/tex].

A solid object's surface area is a measurement of the overall space that the object's surface takes up.  Compared to the definition of the arc length of a one-dimensional curve or the definition of the surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is much more complex.

Let s be the side of the square base and h be the height.

Surface Area=[tex]s^{2}+4sh[/tex]

Volume=[tex]s^{2}h[/tex]

According to the question,

[tex]s^{2}h=1372\\ h=\frac{1372}{s^{2} }[/tex]

So, surface area=[tex]s^{2} +4s(\frac{1372}{s^{2} })[/tex]

                          =[tex]s^{2}+\frac{5488}{s}[/tex]

Differentiate with respect to s,

Surface area=[tex]2s-\frac{5488}{s^{2} }[/tex]

Now, [tex]2s-\frac{5488}{s^{2} }=0[/tex]

[tex]2s=\frac{5488}{s^{2} } \\2s^{3}=5488\\ s^{3}=2744\\ s=14[/tex]

Find the value of h from the volume.

[tex]14*14*h=1372\\h=\frac{1372}{14*14}\\ h=7[/tex]

Thus, the minimum surface area=[tex]14^{2}+4*14*7[/tex]

                                                      =[tex]588cm^{2}[/tex]

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Answer:

4 legs from the bed and 4 from the chair im guessing since not all have 4

Hope This Help

Answer:

4 legs from the bed and 4 from the chair

Step-by-step explanation:

im a math wizard fr

The width is 1 meter.

Given,

Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond.The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters

Let the border be width  = x

then the area of the border will be

2(6x) + 2(15x) +4x2 = 46

= 12x +30x+ 4x2 = 46

= 4x2 + 42x - 46 = 0

=> x =( -42 +- √42² +4*4*46)/8

x =1 , x = -11.5

since the width is 1 meter.

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1. Lines a and b are parallel by the converse of alternate interior angles theorem

2. l║m by the converse of consecutive interior angles theorem.

Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.

1. Lines a and b are parallel.

Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.

2. Lines l and m are parallel.

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Answer:

D

Step-by-step explanation:

This result is true by De Moivre's theorem.

The graph that corresponds to the proportional relationship M = 3n is graph vs.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.

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The equation with infinitely many solutions is:

9x + 80 - 1x = 8*(x + 10)

An equation has infinitely many solutions when the dependence on x vanishes.

If you look at the third equation, we get:

9x + 80 - 1x = 8*(x + 10)

If we simplify the left side and expand the right side, we get:

8x + 80 = 8x + 80

So we have the exact same thing in both sides, this means that the equation is true for any value of x, so the equation has infinite solutions.

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Answer:

https://brainly.com/question/14172055?referrer=searchResults

Step-by-step explanation:

Your question has already been answered.

Here is the link to the answer:

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Hope this helps!

If not, I am sorry.

To solve the expression, the steps are add 19 and multiply by 5

Given the equation;

-3 = -19 + d/5

First,

Collect like terms

-3+ 19 = d/5

Add the values on the left side

We have

16 = d/5

Cross multiply

16 × 5 = d

We then have

d = 80

Thus, to solve the expression, the steps are add 19 and multiply by 5

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Answer:

(2x - 5)(3x + 1)

Step-by-step explanation:

6x² - 13x - 5

ax² + bx + c

ac = 6 × (-5) = -30

-30 = -15 × 2

-13 = -15 + 2

6x² - 13x - 5 =

= 6x² - 15x + 2x - 5

= 3x(2x - 5) + 1(2x - 5)

= (2x - 5)(3x + 1)

Answer: its a.) (2x-5)(3x+1)

Step-by-step explanation:

6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)

and got it right on the test review.

The t-test is a type of inference statistic used to determine if there is a significant difference between the means of two groups that may be related to a particular characteristic. The t-test is one of many tests used to test statistical hypotheses.

Inference statistics have two main purposes. Estimates for population groups (for example, the average SAT score for all 11th graders in the United States). Hypothesis testing to draw inferences about the population

One-way ANOVA is a common method for comparing three or more group means. The usual goal is to determine if the mean (or median) of at least one group is different from the other. Subsequent multiple comparison tests are often used to determine where differences occur.

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The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

An equation is an expression that shows the relationship between two or more variables and numbers.

Let w represent the width, hence:

length = w + 33, height = w - 13

Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w

V(w) = w³ + 20w² - 429w

Rate of change = dV/dw = 3w² + 40w - 429

When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423

When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118

Rate = 10118 - 5423 = 4695 in³/in

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

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The expected value of x is 10.

It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.

Thus E(X) = 5*2 = 10.

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A function assigns the values. The cost of advertising for 10 minutes will be equal to £100.

A function assigns the value of each element of one set to the other specific element of another set.

Let the number of minutes of advertising be represented by x, and the cost of advertising be represented by y.

Given the function through which the cost of advertising can be determined. Therefore, the cost of advertising for the 10 min program will be when the value of x is 10. Therefore, the cost of advertising for 10 mins will be £100.

Hence, the cost of advertising for 10 minutes will be equal to £100.

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If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.

Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6

We have to find the income in dollars received if f(x) shows the income.

Function is a relationship between variables and it have each value of y for each value of x.

To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.

f(53)=35.5*53+6=1887.5

f(42)=35.5*42+6=1497

f(55)=35.5*55+6=1958.5

f(63)=35.5*63+6=2242.5

f(58)=35.5*58+6=2065

f(47)=35.5847+6=1674.5

Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.

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Using supplementary angles, it is found that the measure of angle x is of 65º.

Angles are called supplementary if the sum of their measures is of 180º.

In this problem, angles x, 25, and 90º are supplementary, hence:

x + 25 + 90 = 180

x = 180 - (25 + 90)

x = 65º.

The measure of angle x is of 65º.

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The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

An equation is an expression that shows the relationship between two or more variables and numbers.

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is:

= 4x⁴ - 8x³ + 4x³ - 8x² - 8x² + 16x

= 4x⁴ - 4x³ - 16x² + 16x

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

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Answer:

1/256

Step-by-step explanation:

4^-4 is the same thing as 1/4*1/4*1/4*1/4 which is 1/256

Answer:

1/256

Step-by-step explanation:

4⁻⁴ = 1/(4⁴) = 1/256

Hello !

[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow AX = B [/tex]

With

[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]

[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

The solution is given by [tex]X=A^{-1}B[/tex].

[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]

The point of intersection between the lines is (4;5).

Have a nice day

Answer:

Point of intersection (4,5)

Step-by-step explanation:

5x + 3y - 35 = 0

3x - 4y = -8

 ⇒ 5x + 3y = 35

     3x - 4y = -8

  Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.

[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]

[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]

AX = B

 [tex]\sf X =A^{-1}B[/tex]

[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],

Find the workout in the document attached.

Answer:

x<3

Step-by-step explanation:

3x - 4 < 17 - 4x

So, the -4 shall cross to the other side and replace the -4x which will now take the place of where the -4 used to be and the signs of both digits will change to a positive (+)

Remember the inequality sign (<) shall not change

so now the equation shall appear like this;

3x + 4x < 17 + 4

add both sides and it will appear like this;

7x < 21

simplify both sides by 7 and you'll get

x < 3

Answer:

○ The distance between a and b on the number line is 0.47 units.

Explanation:

The first statement is not true because the distance between a and b on the number line is not 0.47.

Distance between a and b = 5.25 - (-5.72)

                                             = 10.97

• The second statement is true because the sum of a and b is negative:

Sum = a + b

        = -5.72 + 5.25

        = -0.47

• The third statement is true because the quotient of a and -b is:

a ÷ -b

⇒ -5.72 ÷ -5.25

⇒ 1

And the quotient of -a and b is:

-a ÷ b

⇒ -(-5.72) ÷ 5.25

⇒ 1

This shows that the quotients are the same.

• The fourth statement is true because the product of a and -b:

a × -b

⇒ -5.72 × -(5.25)

⇒ 30.03 ,

is positive.

Answer: 2/13

Step-by-step explanation:

To solve this word problem expression, we can first convert the mixed number to an improper fraction so it's easier to work with.

1 1/3 = 4/3

Adding 4/3 to 0.4, we get 5.2/3.

4/15 divided by 5.2/3 is 4/26, or 2/13

Answer:

B E F

Step-by-step explanation:

as the graphic shows, f(x) = 0 means that the y value is 0. and that means these are the points, where the curve intersects the x-axis.

they are already marked in the graphic :

for x = -1, 2, 4

Answer: D

Step-by-step explanation:

See attached image.

Answer:

4th option

Step-by-step explanation:

L = larger softball and S = smaller softball ,then

L + S = 80 → (1) ← equation based on number of softballs ordered

2.75L + 3.25S = 245 → (2) ← equation based on cost

subtract S from both sides in (1)

L = 80 - S → (3)

substitute L = 80 - S into (2)

2.75(80 - S) + 3.25S = 245 ← distribute parenthesis and simplify left side

220 - 2.75S + 3.25S = 245

220 + 0.5S = 245 ( subtract 220 from both sides )

0.5S = 25 ( divide both sides by 0.5 )

S = 50

substitute S = 50 into (3)

L = 80 - 50 = 30

50 small softballs and 30 large softballs were ordered

Answer:

the 4th answer option

Step-by-step explanation:

L, S are the number of balls of that size.

so, L + S = 80. as we order a total of 80 balls.

then each large ball costs $2.75. and each small ball costs $3.25.

so, the total price is

2.75L + 3.25S = 245

as we order balls in total for $245.

so, this set of 2 equations with 2 variables allows us to find the solution.

one defines the total number of balls, and one defines the total amount of money spent by using the individual prices for each type of ball.

the advantage of variables is that we can define the rising and dependencies before we have to calculate any of them specifically.

and once we have all of them defined, then we can start solving the numbers.

The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

The function is given as:

f(x) = 6x + 4

Rewrite as:

y = 6x + 4

Swap x and y

x = 6y + 4

Subtract 4 from both sides

6y = x - 4

Divide through by 6

y = (x - 4)/6

Rewrite as:

f^-1(x) = (x - 4)/6

Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

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The parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x – 5)^2 + 7

From the resulting image after translation, we can see that the parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units

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