2. [5pts.] COS X = Solve - 2 sin ZA 2 √₂ 2 for X:

I remember every thing it was so good j set ramp

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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Answer:

We have to find the product of ,

(a+3)(a-2)

We will use the identity

(x+a)(x+b)=x² + (a+b)x+ab

So, (a+3)(a-2)=a²+(3-2)a+ (3)×(-2)

       = a²+1 × a -6

       = a²+a-6

Or , you can use the following method, to find the product.

a×(a-2)+3×(a-2)

=a² -2 a + 3 a-3×2

=a²+a-6

The true statements for the given function f(x) are:

The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .

The function g(x) = f( x - 3 )

g (1) = f (1 -3 )

       = f (-2 )

       = 3

g (-1) = f (-1 -3)

       = f (-4)

       = - 1

Substituting , x = 0 to find the y intercept of g(x)

g ( 0 ) = f ( 0 - 3)

          =f (-3)

          =1

The y intercept of g(x) is at the point (0, 1)

Thus, options 1 and 4 are the true statements for the given function.

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Tax = price of car x tax rate

Tax = 3500 x 0.05 = 175

Now add everything together:

175 + 85 + 60 + 35 = 355

She needs to pay $355

Answer:

355$

Step-by-step explanation:

5% of 3,500 = 175:

3500/x=100/5

(3500/x)*x=(100/5)*x  

3500=20*x  

3500/20=x  

175=x  

x=175

175 + 85 + 60 + 35 = 355

a. The expression for the surface area of a dilated cube is 6k², where k is the scale factor.

b. The expression for the volume of a dilated cube is k³, where k is the scale factor.

c. The expressions for surface area and volume differ in terms of the power of the scale factor: surface area is proportional to k², while volume is proportional to k³.

a. When a unit cube is dilated by a scale factor k, all sides of the cube are multiplied by k. Since a cube has six faces, the surface area of the dilated cube can be calculated by multiplying the area of one face (which is k²) by 6. Therefore, the expression for the surface area of the dilated cube is 6k².

b. The volume of a cube is calculated by multiplying the length, width, and height of the cube. In this case, each side of the unit cube is scaled by a factor of k, so the expression for the volume of the dilated cube is k³.

c. Comparing the expressions for surface area and volume, we observe that the power of the scale factor differs. The surface area is proportional to k², indicating that the surface expands in two dimensions (length and width) when the scale factor increases. On the other hand, the volume is proportional to k³, demonstrating that the space inside the cube expands in three dimensions (length, width, and height) as the scale factor increases. This means that the volume of the dilated cube increases faster than its surface area as the scale factor grows, resulting in a greater change in volume compared to the change in surface area.

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Answer: the answer is 4 cups of walnuts

Option B is correct for the given system of equations.

The given system of equations 13(v-w)=52 and 12(v+w)=72.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Now, 13(v-w)=52⇒v-w=4-----(1) and 12(v+w)=72⇒v+w=6------(2).

By adding (1) and (2), we get

v-w+v+w=4+6⇒2w=10⇒w=5

By substituting w=5 in equation (1), we get v-5=4⇒v=9.

Thus, the statement "Andy flew his model aeroplane at full speed straight into the wind for 13 seconds before turning it around and flying directly with the wind for 12 seconds. The aeroplane flew 72 yards on the way out and 52 yards on the way back" is correct for the given system of equations.

Therefore, option B is correct for the given system of equations.

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Answer:

5x+8

Step-by-step explanation:

The from is the key word

That means the second term is first

6x^2 -2x +6 - (6x^2 -7x -2)

Distribute the minus sign

6x^2 -2x +6 - 6x^2 +7x +2

Combine like terms

5x+8

The retailer's average daily sales rate is approximately 142.5 bottles per day.

To arrive at this answer, we can use the inventory turnover formula:

Inventory turnover = Cost of goods sold / Average inventory

Since we don't have the cost of goods sold, we can use the number of units sold instead:

Inventory turnover = Units sold / Average inventory

We know that the inventory turnover is 48 times per year, so we can set up the equation:

48 = Units sold / 414

Solving for units sold, we get:

Units sold = 48 * 414 = 19,872

To find the average daily sales rate, we divide the total units sold by the number of days in a year:

Average daily sales rate = 19,872 / 365 = 54.4

Therefore, the retailer's average daily sales rate is approximately 142.5 bottles per day (rounded to 1 decimal place). This means that the retailer sells, on average, 142.5 bottles of soda every day throughout the year. This information can be useful for the retailer in managing its inventory levels and ensuring that it has enough stock on hand to meet customer demand. It can also be used to calculate revenue and profit margins based on the cost of goods sold.

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Answer:

Below

Step-by-step explanation:

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Answer:

x = 8

Step-by-step explanation:

AB/AC = BD/DC

2x/12 = x+4/x+1

12x + 4 = 2x² + 2x

2x² - 10x - 48 = 0

x² - 5x - 24 = 0

(x-8) (x+3) = 0

x = 8 (or) x= -3 (impossible)

x = 8

Answer:2.18$

Step-by-step explanation: 26 + 7% tax is 27.82 so 30 - 27.82 = 2.18$

Answer:

45

Step-by-step explanation:

The angle of intersection between the equation f(x) = 3x and g(x) = 4-x² is 45⁰

Here, f(x) = 3x

then slope of f(x), \(m_{1}\) = 3

g(x) = 4 - x²

then slope of g(x) , \(m_{2}\) = -2  at x = 1

Now, Angle of intersection, tan θ = \(\frac{m_{2}-m_{1} }{1+ m_{1}m_{2} }\)

tan θ = (-2 - 3) / (1 + 3.(-2))

tan θ = -5 / -5

tan θ = 1

θ = 45⁰

Thus, The angle of intersection between the equation f(x) = 3x and g(x) = 4-x² is 45⁰.

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Answer:

20cubic yard

Step-by-step explanation:

Volume of cone formula:1/3hπr^2=1/3h(base)

1/3(6)(10)=20cubic yard

Answer:

72°

Step-by-step explanation:

3x = 4x - 24 (alternate exterior angles theorem)

x = 24

So, angle RST measures 72°.

Answer:

I think it may be 52.2 miles

Step-by-step explanation:

The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Given stress function is 50x² - 60xy - 70y²

To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.

Strain components are given as,

εx = ∂υ/∂x + (du/dx)

εy = ∂υ/∂y + (du/dy)

γxy = ∂υ/∂y + (du/dx)

Here,

υ = 50x² - 60xy - 70y²

du/dx = 100x - 60

ydu/dy = -60x - 140y

∂υ/∂x = 100x - 60y

∂υ/∂y = -60x - 140y

∂²υ/∂y² = -140

∂²υ/∂x² = 100

Now,εx = 100x - 60

yεy = -140y - 60

xγxy = -60y - 60x

Taking derivative of εy w.r.t x,

∂(εy)/∂x = -60

Similarly, taking derivative of εx w.r.t y,

∂(εx)/∂y = -60

∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Stress components are given as,

σx = (C11εx + C12εy)

σy = (C21εx + C22εy)

τxy = (C44γxy)

Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0

Therefore,

σx = 100(100x - 60y) - 60(-140y - 60x)

= 19600x - 8800

yσy = -60(100x - 60y) + 100(-140y - 60x)

= -19600y + 8800x

τxy = 0

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Answer:

25.7 miles apart

Step-by-step explanation:

this may not be right, if its not im sory

Answer:

Point M

1 divided by 3 is 0.3 (repeated)

jump 3 times from 5 and go in the middle of the 0.3 and 0.2 and it should be around the middle which is point M.

La suma de las cifras del precio del rollo de alambre es aproximadamente 27.

Para resolver este problema, vamos a llamar "x" al precio del rollo de alambre en soles (S/).

Según la información proporcionada, podemos establecer la siguiente ecuación:

\((\frac{x}{2} )+(\frac{2x}{3} )+(\frac{5x}{8} )= 3870\)

Para simplificar la ecuación, vamos a deshacernos de los denominadores multiplicando toda la ecuación por el mínimo común múltiplo (MCM) de 2, 3 y 8, que es 24.

La ecuación simplificada será:

\(12x + 16x + 15x = 24 \times 3870\)

\(43x = 92880\)

\(x = \frac{92880}{43}\)

\(x \approx 2158.605\)

El precio del rollo de alambre es aproximadamente S/2158.605.

Para obtener la suma de las cifras, redondearemos el precio a dos decimales y luego sumaremos cada dígito:

Suma de las cifras \(= 2 + 1 + 5 + 8 + 6 + 0 + 5 \approx 27\)

La suma de las cifras del precio del rollo de alambre es aproximadamente 27.

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Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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The exact length of the curve defined by the parametric equations as per given condition is equal x = \(e^t\) - t and y = 4\(e^{(t/2)\) for 0 ≤ t ≤ 4.

To find the exact length of the curve defined by the parametric equations x = \(e^{t}\)- t and y = 4\(e^{(t/2)}\), where 0 ≤ t ≤ 4,

we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t) over an interval [a, b] is ,

L = \(\int_{a}^{b}\)√[(dx/dt)² + (dy/dt)²] dt

Let us calculate the length of the curve using this formula.

First, we need to find dx/dt and dy/dt,

dx/dt = d/dt (\(e^t\) - t) = \(e^t\)- 1

dy/dt = d/dt (4\(e^{(t/2)\)) = 2\(e^{(t/2)\)

Next, we substitute these derivatives into the arc length formula,

L = \(\int_{0}^{4}\)√[(\(e^t\) - 1)² + (2\(e^{(t/2)\))²] dt

Simplifying the expression inside the square root,

L = \(\int_{0}^{4}\) √[\(e^{(2t)\)- 2\(e^t\)+ 1 + 4\(e^t\)] dt

L = \(\int_{0}^{4}\) √[\(e^{(2t)\)+ 2\(e^t\)+ 1 ] dt

Now, let us make a substitution to simplify the integral. Let u = \(e^t\)+ 1, then du = \(e^t\)dt,

L = \(\int_{0}^{4}\) √[(u²)] du

L = \(\int_{0}^{4}\) u du

L = [ (1/2)u² ] [0,4]

L = (1/2)(\(e^t\) + 1)² [0,4]

Substituting the upper and lower limits of integration,

L = (1/2)(e⁴ + 1)² - (1/2)(e⁰ + 1)²

L = (1/2)(e⁴ + 1)² - (1/2)(1 + 1)²

L = (1/2)(e⁴ + 1)² - 1

Therefore,  the exact length of the curve defined by the parametric equations x = \(e^t\) - t and y = 4\(e^{(t/2)\) for 0 ≤ t ≤ 4.

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slope = m = (4 - 0) / (1 - 0) = 4

y = mx + b

y = 4x + b

substitute (0, 0) to find b

b = 0

y = 4x

Answer:

Brainlist me!

Step-by-step explanation:

To solve the system of equations using the substitution method, you can solve one of the equations for one of the variables in terms of the other. Then, you can substitute this expression into the other equation to eliminate one of the variables.

In this case, we can solve the first equation for y in terms of x:

5x = y + 6

y = 5x - 6

Now, we can substitute this expression for y in the second equation to get a equation in terms of x:

2x - 3(5x - 6) = 4

2x - 15x + 18 = 4

-13x + 18 = 4

-13x = -14

x = 14/13

Now that we have found the value of x, we can substitute this back into the first equation to find the value of y:

y = 5x - 6

y = (5)(14/13) - 6

y = 70/13 - 6

y = (70 - 78)/13

y = -8/13

Therefore, the value of the y-coordinate is -8/13.