What is the minimum value of F(x)= 10x^{2} -6x-3
3/10 or -39/10

Answer:6

Step-by-step explanation:

Answer: -2 1/12

Step-by-step explanation:

Answer:

Step-by-step explanation: 7/12

Answer:

a. The area of the wall is 60 ft.²

b. The minimum length of wallpaper to be purchased is 30 ft

Step-by-step explanation:

a. The given diagram is a pentagon, with the two vertical sides equal in length and the  two slant sides equal in length and one horizontal

The length of the vertical sides = 6 feet each

The length of the horizontal side = 8 feet

The height of the pentagon = 9 feet

The pentagon can be split into a rectangle with a triangular cap by an horizontal line drawn at point of intersection of the vertical sides and the horizontal sides

The area of the formed rectangle = Base  × Height of rectangle

∴ The area of the formed rectangle = 6 × 8 = 48 ft.²

The area of the triangular part of the figure = 1/2 × base × Height of triangle

a = 9 - 6 = 3 feet

∴ The area of the triangular part of the figure = 1/2 × 8 × 3 = 12 ft.²

The area of the wall = The area of the formed rectangle + The area of the triangular part of the figure

∴ The area of the wall = 48 ft.² + 12 ft.² = 60 ft.²

The area of the wall = 60 ft.²

b. The width of the sold wallpaper = 2 feet wide

The area of wallpaper = Length of wallpaper × The width of the sold wallpaper

The area of wallpaper required = The area of the wall = 60 ft.²

∴ 60 ft.² = Length of wallpaper × 2 ft.

Length of wallpaper = 60 ft.²/2 ft. = 30 ft.

The minimum length of wallpaper to be purchased = 30 ft.

The radical of the quotient is the product of the radicals of the numerator and denominator.

A product's radical equals the sum of the radicals of each factor, according to this statement. "The quotient of the radicals of the numerator and denominator is the radical of the quotient."

The power of the base serves as the numerator of the fractional exponent represented by a radical, while the radical's index serves as the denominator. A product's nth root is the sum of the nth roots of all its components. You must have the same indices.

We can rewrite radical expressions by applying the first factor of the expression that is under the root, creating perfect power, for instance, by using the exponentiation properties. Alternately, we may apply the property of products of powers, then evaluate after exponentiating. To simplify an equation, we can also use the Quotient of Powers Property.

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Answer:

\(f^{-1}(x)\) = \(-\frac{x+7}{6}\)

Step-by-step explanation:

y = -6x-7?

x = -6y - 7

Add 7 on both sides

x + 7 = -6y

Divide -6 on both sides

y = \(-\frac{x+7}{6}\)

\(\textit{arc's length}\\\\ s=\cfrac{r\theta \pi }{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{in~degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =50 \end{cases}\implies s=\cfrac{(4)(50)\pi }{180}\implies s=\cfrac{10\pi }{9}~mm\)

Unit conversion is a way of converting some common units into another. The cost of buying 0.45 pounds of Lily's tea is $144.93.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

As it is given that one gram is equivalent to 0.035273 ounces, while 1 pound is equal to 16 ounces. Therefore, if we convert 0.45 pounds to grams,

Pounds to Ounces

\(\rm 1\ pound = 16\ ounces\\\\0.45\ pounds = 0.45 \times 16 = 7.2\ ounces\)

Grams to Ounces

\(\rm 1\ gram = 0.035273\ ounces\\\\1 ounce=\dfrac{1}{0.035273} = 28.35\ grams\\\\7.2\ ounces = 7.20 \times 28.35 = 204.12\ grams\)

Since it is given that the cost of 1 gram of tea is $0.71, therefore, the cost of 204.12 grams of tea can be written as,

\(\rm Total\ cost= 204.12 \times \$0.71 = \$144.93\)

Hence, the cost of buying 0.45 pounds of Lily's tea is $144.93.

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Answer:

D. m<RST = 2(m<TSU)

Step-by-step explanation:

Given that m<RST = 76°, m<RSU = 48°, and m<TSU = 38°, this implies that:

SU is an angle bisector of angle RST. Thus,

m<RST is twice the measure of <RSU or <TSU.

Therefore, the only option that is correct is:

D. m<RST = 2(m<TSU)

The correct statement for a monopolistic competitor in long-run equilibrium is: p = ATC = MC = MR. The correct answer is B.

In long-run equilibrium, a monopolistic competitor maximizes its profit by setting its marginal cost (MC) equal to its marginal revenue (MR) and producing the quantity where MC = MR. At this quantity, the firm charges a price (p) equal to the average total cost (ATC) to cover all its costs.

By setting the price equal to the average total cost and producing where marginal cost equals marginal revenue, the monopolistic competitor achieves a balance between maximizing profits and covering costs. This equilibrium condition ensures that the firm does not have the incentive to enter or exit the market in the long run, as it is earning normal profits.

Therefore, The correct answer is B. p = ATC = MC = MR.

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Answer:

y=−1/2x−1

Step-by-step explanation:

I put it in slope intercept form as I assume that is what the question is asking.

2 gallons will he have to buy

In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the UK, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L; and the US dry gallon (usdrygal), which is defined as 18 US bushel.

A gallon contains four quarts and two pints respectively. The differences between imperial and US gallons are explained by variations in pint sizes.

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Answer:

I think the answer is b

Step-by-step explanation:

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. Therefore, the value of x is -10.

Step-by-step explanation:

I hope you can please mark me as

The length of the curves are 27.893 units,  11.633 units and approximately 982.841 units, respectively.

To find the length of the curve r(t)=(2t)i+(4/3)t^(3/2)j+(t^(2)/2)k from t=0 to t=5, we use the formula for arc length

L = \(\int\limits^a_b\)√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

where a = 0 and b = 5. Evaluating the integrand for r(t), we get

√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = √[2^2 + (8/3)t + t^2]^2

Integrating this expression from 0 to 5, we get the length of the curve

L = \(\int\limits^0_5\)√[2^2 + (8/3)t + t^2] dt ≈ 27.893

Therefore, the length of the curve is approximately 27.893.

To find the length of the curve r(t)=2ti+1j+((1/3)t^(3)+1/t)k from t=1 to t=3, we use the same formula for arc length

L =\(\int\limits^a_b\)√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

where a = 1 and b = 3. Evaluating the integrand for r(t), we get

√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = √[2^2 + (1/3)^2(3t^2 + 1/t^2)^2]

Integrating this expression from 1 to 3, we get the length of the curve

L =\(\int\limits^1_3\)√[2^2 + (1/3)^2(3t^2 + 1/t^2)^2] dt ≈ 11.633

Therefore, the length of the curve is approximately 11.633.

To find the length of the curve r(t)=(ln(t))i+(2t)j+(t^2)k from t=1 to t=e^4, we use the same formula for arc length

L =\(\int\limits^a_b\) √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

where a = 1 and b = e^4. Evaluating the integrand for r(t), we get

√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = √[(1/t)^2 + 2^2 + (2t)^2]

Integrating this expression from 1 to e^4, we get the length of the curve

L = \(\int\limits^1_{e^4}\) √[(1/t)^2 + 2^2 + (2t)^2] dt ≈ 982.841

Therefore, the length of the curve is approximately 982.841.

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Answer:

Right triangle

Step-by-step explanation:

If the triangle has one angle that measures 50 degrees and another angle that measures 40 degrees, then the last angle must measure 90 degrees because the 3 angles of any triangle add up to 180, so we can set up the following:

180 - (50 + 40) = 90 degrees.

Any triangle that has a 90 degree angle is automatically a right triangle.

Hope this helps!

________________________________________________________

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

Let the 3rd angle be known as "x".

For the triangle to be classified as an isoceles triangle, two angles must be of same measure. Thus, there are two possibilities.

⇒ 50 + 40 + 40 = 180                                                   [Angle 2 = Angle 3]

-------------- Or -------------

⇒ 50 + 40 + 50 = 180                                                   [Angle 1 = Angle 3]

Possibility-1:

Possibility-2:

Therefore, the triangle cannot be an isoceles triangle.

________________________________________________________

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

Let the 3rd angle be known as "x".

For the triangle to be classified as an obtuse triangle, the third angle must be a measure greater than 90°. Therefore,

This is false because 90 is not greater than 90. Therefore, the triangle is not an obtuse triangle.

________________________________________________________

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

Let the 3rd angle be known as "x".

For the triangle to be classified as a right triangle, the third angle must be a measure equivalent to 90°. Therefore,

Therefore, this triangle is a right triangle.

________________________________________________________

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

Let the 3rd angle be known as "x".

For the triangle to be classified as an equiangular triangle, all the angles must be equivalent (60°). Therefore,

Therefore, this triangle is not an equiangular triangle.

________________________________________________________

In conclusion, we can conclude that Option C (Right triangle) is correct.

Answer:

x = 10

Step-by-step explanation:

Because the triangles are similar, the following equations must be solved in order to find out how much bigger or smaller the triangle is.

10 * y = 15

16 * y = 24

You'll find that

y = 1.5

Then, you are able to insert y into the following equation and solve for x

(x - 4) * y = 9

(x - 4) * 1.5 = 9

1.5x - 6 = 9

1.5x = 15

x = 10

We can plug x back into the previous equation in order to check if it is correct

(x - 4) * 1.5 = 9

(10 - 4) * 1.5 = 9

6 * 1.5 = 9

9 = 9

ANSWER :

x = 48

EXPLANATION :

From the problem, we have :

add 12 to both sides :

\(\huge\underline\mathtt\colorbox{cyan}{1. f(-1)}\)

For this to be a solution of f(x), the answer must be 0

x^2+1=0 when x=-1

The equation of a line in slope-intercept form is  \(y = \frac{1}{8} x - \frac{41}{8}\) .

The equation of the line is given below using the slope-intercept method:

y = mx + c

where,

m = the slope of the line

c = y-intercept of the line

(x, y) represent any point on the line

To find the Slope of a line that passes through the points (2, 4) and (3, -4).

m₁ = change in y/change in x

    = y₂ - y₁ / x₂ - x₁

    = Δy/Δx

   = \(\frac{-4-4}{3-2}\)

   = \(\frac{-8}{1}\)

   = -8

Now, we find the slope of the line perpendicular to the line with the slope -8.

m₂ = -1 / m₁

    = -1 / -8

    = 1/8

So, the slope of the line is 1/8.

Next, we find the equation of a line that passes through the point (1, -5) and has a slope of 1/8.

⇒ y - y₁ = m( x- x₁)

⇒ y + 5 = \(\frac{1}{8}\) (x - 1)

Multiplying by 8 on both sides of the equation we get and then solving

⇒ 8y + 40 = x - 1

⇒ 8y = x - 41

 ⇒ \(y = \frac{1}{8} x - \frac{41}{8}\)

Therefore, the equation in slope intercept form is  \(y = \frac{1}{8} x - \frac{41}{8}\) .

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Answer:

I know that the Perimeter is 4000. So, 4000=L+2w because we are not using on of the lengths.

What I did is inputed 4000-2x in for L, but I got 0. What do I do?

Step-by-step explanation:

it just is I think it should be

Answer: 8336

Step-by-step explanation:

Answer:

2.8 is correct

Step-by-step explanation:

  4.0

-   1.2

The 0 becomes 10

10 - 2 = 8

The 4 becomes 3

3 - 1 =2

2.8

Therefore, the statement is false in general, and the equality Dkf(x, y, z) = fz(x, y, z) holds only when k = z.

The symbol Dk denotes the k-th partial derivative with respect to the variable k, so Dkf(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable k.

On the other hand, fz(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable z.

These two partial derivatives are generally not equal. For example, consider the function f(x, y, z) = x² + y² + z². Then:

Dxf(x, y, z) = 2x

Dyf(x, y, z) = 2y

Dzf(x, y, z) = 2z

In this case, we have Dzf(x, y, z) = fz(x, y, z) = 2z, so the statement is true when k = z.

However, if we consider k = x or k = y, then the statement is false in general. For example, when k = x, we have:

Dkf(x, y, z) = Dxf(x, y, z) = 2x

fz(x, y, z) = partial derivative of f with respect to z = 2z

Since 2x is generally not equal to 2z, the statement is false when k = x.

Similarly, the statement is false when k = y, because Dyf(x, y, z) is generally not equal to fz(x, y, z).

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To find a vector in the subspace spanned by the u's, we can use the process of orthogonal projection. y can be expressed as the sum of a vector in W and a vector orthogonal to W.

The projection of y onto W is given by:

projW(y) = ((y⋅u)/||u||^2)u

where ⋅ represents the dot product and ||u|| is the norm of u.

Using the given values, we can calculate:

y⋅u = (4)(1) + (3)(0) + (3)(1) + (-1)(-1) = 11

||u||^2 = (1)^2 + (0)^2 + (1)^2 = 2

So,

projW(y) = ((11)/2)*[1 0 1] = [11/2 0 11/2]

To find a vector orthogonal to W, we can subtract projW(y) from y:

y - projW(y) = [4 3 3 -1] - [11/2 0 11/2 0] = [5/2 3 1/2 -1]

Now, we can write y as the sum of a vector in W and a vector orthogonal to W:

y = [11/2 0 11/2 0] + [5/2 3 1/2 -1]

Therefore,

y = [11/2 0 11/2 0] + 5/2[1 0 1 0] + [3 0 3 0] + 1/2[0 1 0 -2] - [1 0 1 0]

Thus, y can be expressed as the sum of a vector in W and a vector orthogonal to W.

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Answer:

8^28   miles

Step-by-step explanation:

m/hr  *   hr   = miles

8^9   *   8^19   = 8^(9+19)  =  8^28 miles