Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?

5 x times the square root of 104 x

20 times the square root of 290 x to the sixth

20 x times the square root of 290 x

104 x times the square root of 5 x

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.

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

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.

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.

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]

The growth rate of the hedge maple tree is 0.75 feet per year, and the tree's original height when it was planted was 6 feet.

We are tasked with finding the growth rate of a hedge maple tree and its original height when it was planted based on the given data. The tree's height was recorded at two different times: Four years after it was planted, its height was 9 feet, and eight years after planting, its height reached 12 feet.

To calculate the growth rate per year, we take the difference in height over the difference in time:
Growth rate = (Height at 8 years - Height at 4 years) / (Time at 8 years - Time at 4 years)
Thus, Growth rate = (12 feet - 9 feet) / (8 years - 4 years) = 3 feet / 4 years = 0.75 feet per year.

To determine the original height when the tree was planted, we can subtract the total growth over the four years from the height at four years after planting:
Original height = Height at 4 years - (Growth rate * 4 years)
Original height = 9 feet - (0.75 feet/year * 4 years) = 6 feet.

Answer:

D

Step-by-step explanation:

its reflected off the L-axis

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]    

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:

The coefficient of the term 13a is, 13

Step-by-step explanation:

Coefficient term are the numbers that multiply the variables or letters

In the given expression: [tex]13a+6b[/tex]

13a means 13 times a , and a is the variable,

so 13 is the coefficient .

6b means 6 times b , and b is the variable ,

so 6 is the coefficient .

therefore, the coefficient of the term 13a in the given expression is, 13.

Answer:

yoo hoo

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

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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a

Square root of 5 units

Step-by-step explanation:

i just had this problem

1. Infinite many solution.

2. No solution

3. One solution

4. No solution

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Depending upon the situation we have three case

[tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

and, [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

and, [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

1. 3x = -12y + 15 and x+4y=5

3x + 12y - 15= 0 and x+ 4y- 5 = 0

So, [tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

2. 4x - y +3 = 0 and -8x + 2y -3 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

3. x+ 4y - 12= 0 and 5x - 20y -60 = 0

So,  [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

4. -5x + y +6 = 0 and -15x + 3y +12 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

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The answer to this is: TRUE

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.