A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross sectional area to allow the greatest amount of water to flow

The value of x is 12 and Shakeel got 18 points.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Adam scored x points. Imran scored 3 points fewer than Adam. Shakeel scored twice as many points as Imran. together they scored 39 points

Establishing the equation, we get

Adam scored x points.

Imran scored x-3 points.

Shakeel scored 2(x-3) points.

Together they scored 39 points:

x + (x-3) + 2(x-3) = 39

x + x -3 + 2x - 6 = 39

4x = 48

x = 12

∵ Shakeel scored = 2(x-3) points.

Putting x = 12, to get the marks scored by him,

Shakeel's score = 2(12-3) = 18

Hence, The value of x is 12 and Shakeel got 18 points.

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Answer:

yoo hoo

Step-by-step explanation: This was in 2016 but its 1/5

Answer: x + 7/ 3

Assuming the said quantity is divided by 3x+15 as a denominator in fraction form.

After dividing, the simplest form, x + 7/ 3, can be found after dividing both the numerators and the denominators by the smallest common factor.

Proof of validity is shown below.

Aaron should pay $80 in the first month to satisfy the conditions of repaying $150 in 4 monthly installments, with each subsequent payment being half of the previous one.

Aaron needs to pay back a total of $150 in 4 monthly installments, with each payment being half the amount of the previous month. Let's denote the first payment amount as X. Then, the second payment would be X/2, the third would be X/4, and the fourth would be X/8. These four payments need to sum up to $150, which is the total amount Aaron borrowed.

To find the value of X, we can set up the following equation based on the aforementioned information:

X + X/2 + X/4 + X/8 = 150

To solve this equation, we should find a common denominator, which is 8 in this case, and rewrite the equation as:

8X/8 + 4X/8 + 2X/8 + X/8 = 150

Adding the numerators together gives us:

(8X + 4X + 2X + X) / 8 = 150

15X / 8 = 150

Multiplying both sides by 8 and then dividing by 15 gives us:

X = (150 × 8) / 15

X = 1200 / 15

X = 80

Thus, Aaron should pay $80 in the first month to repay the money on schedule as he promised.

because it is arithmetic not geometric 14,x,56 An = An-1 + d x = 14 +d --> d = x-14 56 = x +d --> d = 56-x By substitution x-14 = 56-x 2x = 70 x = 35 the sequence is 14,35,56

Answer:

Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]    

Step-by-step explanation:

Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins. Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.

We have to find the total number of dozen muffins did they both bake.

To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and  number of dozen of muffins Nina bake

That is

Mathematically written as ,

Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake

Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins

and Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.

Total number of dozen muffins = [tex]1\frac{7}{12}+1\frac{1}{12}[/tex]  

Simplify, we get,

Total number of dozen muffins = [tex]1\frac{19}{12}+\frac{13}{12}[/tex]  

Adding, we get,

Total number of dozen muffins = [tex]1\frac{19+13}{12}=\frac{32}{12}[/tex]  

Thus, Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]    

Final answer:

The actual distance between two cities on a map with a scale of 1 cm:12 km, where the map distance is 6.8 cm, can be calculated as 6.8 cm × 12 km/cm, resulting in an actual distance of 81.6 kilometers.

Explanation:

Understanding Map Scale Problems

To calculate the actual distance between two cities on a map using the scale given, you would use the following steps:

First, identify the scale of the map provided; in this case, it is 1 cm : 12 km.

Next, measure the distance on the map between the two cities; the distance is 6.8 cm.

Finally, multiply the distance on the map by the scale factor to find the actual distance. That is, 6.8 cm (distance on the map) × 12 km/cm (scale factor) = 81.6 km (actual distance).

Therefore, the estimated actual distance between the two cities is 81.6 kilometers.

Answer:

D

Step-by-step explanation:

its reflected off the L-axis

a

Square root of 5 units

Step-by-step explanation:

i just had this problem

To find the marginal cost at the given production level x, differentiate the cost function C(x) and substitute the value of x. The units of measurement for the marginal cost are dollars per unit (x).

To find the marginal cost at the given production level x, we need to find the derivative of the cost function C(x) with respect to x. Let's differentiate the function:

C'(x) = 70 - 1,000/x^2

Now, substitute x = 100 into the derivative:

C'(100) = 70 - 1,000/100^2 = 70 - 1 = 69

The units of measurement for the marginal cost are dollars per unit (x).

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tan(θ) = -1/6.

Given that sec(θ) = √37/6 and sin(θ) < 0, we can find tan(θ) using the trigonometric identity:

sec²(θ) - tan²(θ) = 1

First, we need to find the value of tan(θ) using the given information:

Since sec(θ) = √37/6, we know that sec(θ) = 1/cos(θ), so cos(θ) = 6/√37.

Since sin²(θ) + cos²(θ) = 1, we can find sin(θ):

sin²(θ) + (6/√37)² = 1

sin²(θ) + 36/37 = 1

sin²(θ) = 1 - 36/37

sin²(θ) = (37-36)/37

sin²(θ) = 1/37

Given that sin(θ) < 0, sin(θ) is negative. Therefore, sin(θ) = -1/√37.

Now that we have sin(θ) and cos(θ), we can find tan(θ):

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-1/√37) / (6/√37)

tan(θ) = -1/6

Therefore, tan(θ) = -1/6.

The answer to this is: TRUE

The 40th term of the given arithmetic sequence is -374. Hence the correct option is B.

The 40th term of the arithmetic sequence is found using the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Given the sequence: 16, 6, -4, -14, the common difference d = 6 - 16 = -10. Plugging into the formula: a40 = 16 + (40-1)(-10) = -374.

The strength of a cable is directly proportional to the square of its diameter. This relationship allows us to compute the strength of a cable of given diameter. Using given data, a cable with 3cm diameter can support 1800kg.

The strength of a cable is said to be proportional to the square of its diameter. This is a mathematical concept of direct proportionality. In this specific case, the proportionality can be written as S=k(D^2), where S is the strength (or weight it can support), D is the diameter and k is a constant.

For a 2-cm cable, we can plug the values into the equation to find the constant: 800= k(2^2), therefore k=800/4=200.

Now, knowing that k=200, we can calculate the strength of a 3-cm cable by plugging in the values: S=200*(3^2) =1800. Therefore, a cable with a 3-cm diameter can support 1800kg.

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Answer: The sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Step-by-step explanation:

Since we have given that

Number of runners = 4

Four runners are as follows:

Fran, Gloria, Haley, and Imani.

Since Haley is the first runner in the relay,

So, Sample space showing the possible order of the other three runners.

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Hence, the sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Answer:

10 + 10 = 20 ; 456 + 543 = 999

Step-by-step explanation: