Which expression is equivalent to 17 s minus 10 + 3 (2 s + 1)?
23 s minus 9
23 s minus 7
11 s minus 7
11 s minus 9

The length of side b is 56m, angle A is 45°, and angle C is 67°.

In the given triangle with side lengths a = 74m, b ≈ 56m, and c = 36m, the length of side b is approximately 56m.

To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees. Given angle B = 67°51', we have:

Using the Law of Cosines, we have:

b² = a² + c² - 2ac * cos(B)

Substituting the known values:

b² = 74² + 36² - 2 * 74 * 36 * cos(67°51')

Calculating the value of b:

b ≈ √(74² + 36² - 2 * 74 * 36 * cos(67°51'))

b ≈ 55.92m (rounded to the nearest whole number, b ≈ 56m)

Using the Law of Cosines again, we have:

cos(A) = (b² + c² - a²) / (2 * b * c)

Substituting the known values:

cos(A) = (56² + 36² - 74²) / (2 * 56 * 36)

Calculating the value of A:

A = cos⁻¹((56² + 36² - 74²) / (2 * 56 * 36))

A ≈ 45° (rounded to the nearest whole number)

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

Substituting the known values:

C ≈ 180° - 45° - 67°51'

Calculating the value of C:

C ≈ 67°9' (rounded to the nearest whole number, C ≈ 67°)

Therefore, in the given triangle, the length of side b is approximately 56m, angle A is approximately 45°, and angle C is approximately 67°.

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Answer:

Step-by-step explanation:

f(x) = √(5 + 4)

f(x) = √(9) = √(3 · 3) = 3

Steps to solve:

f(x) = √(x + 4) when x = 5

~Substitute

f(5) = √(5 + 4)

~Add

f(5) = √9

~Simplify

f(5) = 3

Best of Luck!

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Using AP, we can determine that the three integers are = 22 46 15

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How to convert litres into grams?

The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

A. Line of Best Fit

A regression line is a statistical tool used to predict the value of a response variable based on the value of one or more predictor variables. It is also known as a line of best fit because it is used to show the best fit of a given data set. The line of best fit is a straight line that best represents the data by minimizing the sum of the squared distances between the observed data points and the line. The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

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Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

Answer:y= - 2x + 16

Step-by-step explanation:

Answer:

A) d = \(\frac{C}{\pi}\)

B) d = \(\frac{8}{\pi}\) or 2.55 inches

C) r = 3 inches

Step-by-step explanation:

Given the formula for the circumference of a circle, C = πd, where d represents the diameter of a circle.

In order to solve for d, divide both sides of the equation by π:

\(\frac{C}{\pi} = \frac{\pi d }{\pi}\)

d = \(\frac{C}{\pi}\).

Given the circumference of the circle, C = 8 inches:

Use the formula for the diameter of the circle from part A of this post.

d = \(\frac{C}{\pi}\)

d = \(\frac{8}{\pi}\) or 2.55 inches.

Since the diameter of a circle is the same as twice the measure of the radius, r:  d = 2 × r

Then, we can rewrite the formula for the circumference of a circle as:

C = 2πr

Divide both sides by 2π to isolate r :

\(\frac{C}{2\pi } = \frac{2\pi r}{2\pi }\)

r = \(\frac{C}{2\pi }\)

Given the circumference of a circle, C = 6π:

\(r = \frac{6\pi }{2\pi } = 3\)

Therefore, the radius of the circle is 3 inches.

Answer:

\(\frac{33}{7}\)

Step-by-step explanation:

\(7\)×\(4=28\)

\(28+5=33\)

Thus, it becomes \(\frac{33}{7}\)

Answer:

33/7

multiply whole number with denominator and add numerator

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

\(f(x)=3^x+9\)

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

The tangent line is vertical (−3, −8) and (1, 14).

To find where the tangent line is vertical or horizontal, we need to find where dy/dx is equal to 0 or undefined.

So, 3t² - 12 = 0

t² = 4

t= 2

or, 3t² - 3t = 0

t= ±1

Put t= 1

x= 1 - 3 -1 = -3 or y= -8

Put t= -1

x= 1 or y= 14

Thus, the tangent line is vertical (−3, −8) and (1, 14).

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Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

A function is even if the graphic is symmetric with respect to the y-axis.

You can symbolize an even function as -f(x)=f(x) for all values of x on the domain of the function f.

A)

The expression |y| indicates that its the absolute value of y. This means that y can be positive or negative.

This function is even.

B)

In this example x is expressed as an absolute value and can be either positive or negative:

This function is symetrical with respect to the y-axis, so it an even function.

C)

This function is not symetrical with respect to the y-axis

D)

This function is not symmetrial with respect to the y-axis

Answer:

Triangle JKE and Triangle KEJ

Step-by-step explanation:

You have to look at each answer choice for this. For example, for A, it starts at K and then goes to E then to j. That forms a triangle. Whatever answer choice makes a complete triangle is your answer.

The sequence with the given recursive formula a(1) = 5 and a(n) = a(n-1) - 4 for n >= 2 is an arithmetic sequence. The first five terms of the sequence are 5, 1, -3, -7, -11.

In summary, the first five terms of the sequence are 5, 1, -3, -7, -11, and the sequence is arithmetic.

To explain the answer, let's examine the given recursive formula. The initial term of the sequence is given as a(1) = 5. Then, for each subsequent term, we subtract 4 from the previous term to obtain the next term. This implies that each term is obtained by subtracting 4 from the previous term.

Starting with the initial term a(1) = 5, we can calculate the subsequent terms as follows:

a(2) = a(1) - 4 = 5 - 4 = 1

a(3) = a(2) - 4 = 1 - 4 = -3

a(4) = a(3) - 4 = -3 - 4 = -7

a(5) = a(4) - 4 = -7 - 4 = -11

We can observe that each term is obtained by subtracting 4 from the previous term, indicating a constant difference between consecutive terms. This characteristic of the sequence makes it an arithmetic sequence.

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The formula to convert mL into L is mL=L×\(1000\).

To convert milliliters to liters, divide the volume by the conversion ratio.

Since 1 liter is equal to 1,000 milliliters, it can be converted using this simple formula:

Liters = Milliliters ÷ 1,000

Both milliliters and liters are units of volume measurement.

The milliliter is the SI unit of volume in the metric system. In the metric system, "milli" is the prefix for 10-3. Milliliters are sometimes called milliliters. Milliliter can be abbreviated as ml, and can also be abbreviated as ml or ml. For example, 1 milliliter can be written as 1 mL, 1 mL, or 1 mL.

The liter is an SI-recognized unit of volume for use in the metric system. A liter is sometimes called a liter. Liters can be abbreviated as l and sometimes as L or ℓ. For example, 1 liter can be written as 1 l, 1 L, or 1 ℓ.

Therefore, Liters = Milliliters ÷ 1,000.

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The three consecutive entries in Pascal's Triangle that are in the ratio 3:4:5 occur in the 14th row.

The ratio 3:4:5 can be expressed as 3x, 4x, and 5x, where x is a constant. Using this ratio, we can find the values of the entries in the 14th row of Pascal's Triangle.

Starting from the left, the entries in the 14th row are 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, and 1.

We can see that the ratio of the 5th, 6th, and 7th entries (715, 1287, and 1716) is 3:4:5. Therefore, the answer is the 14th row.

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There are 6.7 parts in each of the new car

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

There were 9 toy cars each with 10 parts

So, the ratio is

Ratio = 10 parts/9 cars

The boy created 6 cars

This means that the the number of parts in each car is

Parts = 6 cars * 10 parts/9 cars

Evaluate

Parts = 6.7

Hence, there are 6.7 parts in each of the new car

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Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer:

2.720 : 16 : 2 = 85

Step-by-step explanation:

Dado que, en caso de no funcionar la tecla del 3 en la calculadora para tipear el número 32, no se podrá realizar el calculo de 2.720 : 32, que tiene como resultado 85, se puede realizar otro cálculo sin tipear dicho número para llegar al mismo resultado.

La mitad de 32 es 16, osea que, dividiendo 2.720 por 16, estaremos obteniendo un resultado que será el doble de lo pretendido, es decir, 170. Por lo tanto, dividiendo dicho resultado por 2, obtendremos el número 85, realizando así el mismo cálculo que el deseado inicialmente.

Notice that the area of the shaded region is the area of the semicircle minus the area of the triangle.

To compute the area of the semicircle, we use the following formula:

Substituting r=3yd and π=3.14 we get:

Now, notice that the base of the triangle is the diameter of the semicircle, and its height is the radius, using the formula for the area of a triangle we get that:

Finally, the area of the shaded region is:

Answer:

(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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Answer:

there's 104 days of summer vacation

Answer:

(2xye^x²  -  2xy³) / (5y^4  + 3y²x² - e^x²)

Step-by-step explanation:

differentiate each term:

d/dx (y^5) + d/dx (x² y³) = d/dx (1) + d/dx (ye^x²)

any time y is differentiated, make sure to include dy/dx:

5y^4 dy/dx  +  2xy³ + 3y²x² dy/dx  = 0 + e^x² dy/dx + 2xye^x²

collect terms with dy/dx:

dy/dx (5y^4 + 3y²x² - e^x²)  =  2xye^x² - 2xy³

divide both sides  by  (5y^4 + 3y²x² - e^x²):

dy/dx = (2xye^x²  -  2xy³) / (5y^4  + 3y²x² - e^x²)

The domain of the function f(x) = x² - 2x + 1 is all real numbers, which is denoted as (-∞, +∞).

To find the domain of the function f(x) = x² - 2x + 1, we determine the set of all possible values for x that make the function well-defined.

The given function is a polynomial-function, and polynomial functions are defined for all real numbers. So, the domain of f(x) = x² - 2x + 1 is the set of all real numbers, which can be represented as (-∞, +∞).

It means that any real-number can be substituted into the function, and it will give a valid output. There are no limitations on the possible values of x in this case.

Therefore, the domain is all real numbers.

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The given question is incomplete, the complete question is

Find the domain of the function f(x) = x² - 2x + 1.

Answer:

Step-by-step explanation:

A is certainly true. If you put 30 into your calculator, you get factions for the cube root and square root. True

B is true. 5^2 = 25 Twenty five is made up of 2 fives.

C is a perfect cube. 10 * 10  * 10 = 1000. But it is not a perfect square. False.

D 64 is a perfect cube. (It is also a perfect square).

E false 16 is a perfect square. It is not a perfect cube

True Statements

A B D

The dimensions of the tank with minimum  weight  is height= 7 and width and length= 14.

The minimum surface area implies that the tank has minimum weight.

Given that the base is square, its width is equal to its length.

Let x= the base width and length of the tank.

Let h = the height .

We are given the volume of the tank that is 1372 ft^3. The formula is given by

V = hx^2

We're given that V = 1,372 ft^3, so

hx^2 = 1,372

h = 1,372 / x^2  ----------(equation 1)

Surface area can be calculated using the below given formula.

A = x^2 + 4xh

Substituting the value of euation 1, h in A, we get,

A = x^2 + 4x(1,372 / x^2)

= x^2 + 5,488 / x

To get the minimum surface area to get the minimum weight, we need to differentiate  A with respect to x and equate it to zero.

dA/dx = 2x - 5,488 / x^2 = 0

2x^3 - 5,488 = 0

x =\(\sqrt[3]{\frac{5,488}{2} }\)

x= 14

We got the value of x, we substitute the value in equation 1, we get the value of h.

h = 1,372 / 14^2

h= 7

So, the dimensions of the tank with minimum weight are width and length is 14 and height is 7.

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