The equation that measures the shape of your contact lens is -0.5x2 + 6x – 16 = 0. The lens maker cuts the lens material at the x-axis for fitting. Find the zero(s) where the lens material starts and ends.

Answer:

[tex]\large\boxed{\dfrac{1}{x^2}+x^2=23}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{1}{x}+x\right)^2=25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(\dfrac{1}{x}\right)^2+2(x\!\!\!\!\diagup)\left(\dfrac{1}{x\!\!\!\!\diagup}\right)+x^2=25\\\\\dfrac{1}{x^2}+2+x^2=25\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x^2}+x^2=23[/tex]

The value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex]  is [tex](a+b)^2 = a^2 +b^2 +2ab[/tex].

Given that if [tex](\frac{1}{x } +x)^2[/tex] = 25 then find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] .

To find the  value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] by using the algebraic identity and follow the steps:

Apply the algebraic identity to the given equation, that is :

 [tex](a+b)^2 = a^2 +b^2 +2ab[/tex]

Given that :

[tex](\frac{1}{x } +x)^2=25[/tex]

Expand the LHS by using mentioned algebraic identity:

[tex]\frac{1}{x^2 } +x^2+2x\times\frac{1}{x} =25[/tex]

On cancelation of the variable x in third term of the LHS gives:

[tex]\frac{1}{x^2 } +x^2+2=25[/tex]

Subtract by 2 on both sides, gives:

[tex]\frac{1}{x^2 } +x^2=23[/tex]

Therefore, the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex]  is

[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]

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Answer: First option.

Step-by-step explanation:

 To simplify the polynomial [tex]2x^2y + 8x^3 - xy^2 - 2x^3 + 3xy^2 + 6y^3[/tex] you need to add the like terms, then you get:

[tex]=2x^2y+6x^3+2xy^2+6y^3[/tex]

Now, you know that Raj put this polynomial in standard form with the last term being 6y³, this means that he ordered it in descending order of "x" power and in ascending order of "y" power:

[tex]=6x^3+2x^2y+2xy^2+6y^3[/tex]

You can observe that the first term of the polynomial  that Raj ended up with, is:

[tex]6x^3[/tex]

Answer:

The answer would b A

Answer:

C.

Step-by-step explanation:

A hexahedron has 6 equal sides. Like the cube shown.

The name of the platonic solid shown is hexahedron.

Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.

Hexahedron - Any polyhedron with six faces is called a hexahedron.

Octahedron - An octahedron is a polyhedron with eight faces in geometry.

Dodecahedron - In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces

The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.

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Answer:

Yes

Step-by-step explanation:

Yes because all three sides have the same ratio

Answer:

24

Step-by-step explanation:

4x6 = 24

-2 and 2 are 4 apart

2 and -4 are 6 apart

Answer:

24 square units

Step-by-step explanation:

Answer:

[tex]x^{15}.y^{9}[/tex]

Step-by-step explanation:

[tex]\frac{x^{19} . y^{21}}{(x^2. y^6)^2} \\\\Here\,\, exponent\,\, rules\,\, will\,\, be\,\, used.\\First\,\, multiply\,\, power\,\, of \,\,2\,\, with\,\, denominator \,\,exponents\\\\\frac{x^{19} . y^{21}}{x^4. y^{12}}\\If \,\, same\,\, bases\,\, are\,\, divided\,\, then\,\, their\,\, exponents\,\, are \,\,subtracted\,\,\\\\x^{19-4}.y^{21-12}\\\\x^{15}.y^{9}[/tex]

Answer:

[tex] log_{b}( {m}^{p} ) = p \: log_{b}(m) [/tex]

Answer:

x² - 22x + y² + 20y = 4

x² - 22x + 121 + y² + 20y + 100 = 225

(x - 11)² + (y + 10)² = 15²

Center: (11, -10)

Radius: 15

The side length of the triangle are as follows:

a = 11.71 and b = 15.56

The side of a triangle can be found using sine rule or cosine rule depending on the sides and angles given in a triangle.

Therefore, the sides a and b can be found in the triangle using sine rule as follows:

a / sin A = b / sin B = c / sin C

b / sin 110 = 7 / sin 25°

cross multiply

b sin 25 = 7 sin 110°

b = 7 sin 110° / sin 25

b = 6.5778483455 / 0.42261826174

b = 15.5625174507

b = 15.56 units

Let's find a as follows:

a / sin 45 = 7 / sin 25

a sin 25 = 7 sin 45

a = 7 sin 45 / sin 25

a = 4.94974746831 / 0.42261826174

a = 11.7108376716

a = 11.71 units

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The volume of the pencil holder with dimensions 6 cm, 4 cm, and 10 cm is 240 cubic centimeters, as calculated using the formula for the volume of a rectangular prism.

To calculate the volume of a rectangular pencil holder with the given dimensions of 6 cm, 4 cm, and 10 cm, the formula for the volume (V) of a rectangular prism should be used, which is:

V = length × width × height

Substitute the given measurements into the formula:

V = 6 cm × 4 cm × 10 cm = 240 cm³

Therefore, the volume of the pencil holder is 240 cubic centimeters.

Answer:

[tex]\large\boxed{_7P_2=42}[/tex]

Step-by-step explanation:

[tex]_nP_k=\dfrac{n!}{(n-k)!};\ n!=1\cdot2\cdot3\cdot...\cdot n\\\\\text{We have:}\\\\_7P_2=\dfrac{7!}{(7-2)!}=\dfrac{7!}{5!}=\dfrac{5!\cdot6\cdot7}{5!}=6\cdot7=42[/tex]

The permutation 7P2 calculates the number of ways to arrange 2 items from a set of 7. It is found using the formula nPr = n! / (n-r)!, resulting in 42 different arrangements.

The student is asking about how to calculate a permutation, specifically 7P2. Permutations are used to determine the number of ways to arrange a subset of items from a larger set, where the order does matter. To compute 7P2, we use the formula for permutations, which is nPr = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to arrange.

To evaluate 7P2, we plug in 7 for n and 2 for r, which gives us: 7P2 = 7! / (7-2)! 7P2 = 7! / 5! 7P2 = (7 x 6 x 5!) / 5! 7P2 = 7 x 6 7P2 = 42

Therefore, there are 42 different ways to arrange 2 items from a set of 7.

Answer:

The maximum of y = sin x is 1. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

The answer is:

It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.

So, writing the equations, we have:

Calculations for Ava:

We have the following information,

[tex]v_{Ava}=6mph[/tex]

Then, writing the equation,

[tex]x_{Ava}=x_{o}+v_{Ava}*t[/tex]

[tex]x_{Ava}=x_{o}+v_{6mph}*t[/tex]

Calculations for Kelly:

We have the following information,

[tex]v_{Kelly}=8mph[/tex]

We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.

Then, writing the equation,

[tex]x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t[/tex]

[tex]x_{Ava}+0.75miles=x_{o}+v_{8mph}*t[/tex]

Now, substituting Ava's speed into the second equation, we have:

[tex]x_{o}+6mph*t+0.75miles=x_{o}+8mph*t[/tex]

[tex]6mph*t+0.75miles=+8mph*t[/tex]

[tex]8mph*t-6mph*t=0.75miles[/tex]

[tex]2mph*t=0.75miles[/tex]

[tex]t=\frac{0.75miles}{2mph}=0.375hours[/tex]

Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

Have a nice day!

Answer:

So what the other guy said in minutes was 22.5 minutes

Step-by-step explanation:

Answer:

The cosine function that models this reaction is:

[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]

Step-by-step explanation:

The general cosine function has the following form

[tex]y = Acos(bx) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:

[tex]A =\frac{160-20}{2}\\\\A= 70[/tex]

The reaction completes a cycle in 8 hours

Then the period is 8 hours.

Thus:

[tex]\frac{2\pi}{b}=8\\\\ b=\frac{2\pi}{8}\\\\ b=\frac{1}{4}\pi[/tex]

The function is:

[tex]y = 70cos(\frac{1}{4}\pi x)+k[/tex]

when [tex]t=0[/tex] y is minumum therefore [tex]y=-cos(x)[/tex]

So

[tex]y = -70cos(\frac{1}{4}\pi x)+k[/tex]

Now we substitute [tex]t = 0[/tex] in the function and solve for k

[tex]20 = -70cos(0)+k\\\\k=20+70\\\\k=90[/tex]

Finally

[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]

I'm pretty sure the answer is Ronald. It might be Dennis though.

The vertices of a triangle are also called the points. Every triangle has 3 vertices. In this case, they are given.

A(-4,4)

B(-4,8)

C(0,4)

I graphed these points for you :)

Answer:

Frequency is the number of times that roll occurred.

Ex: 7 occurred 5 times...... 5 goes in the frequency column.

Answer:

A

Step-by-step explanation:

Given

- 2x(5x - 2) = 0

Equate each factor to zero and solve for x

- 2x = 0 ⇒ x = 0

5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]

Solutions are

x = 0, x = [tex]\frac{2}{5}[/tex]

When y = 6 and x = 5, the value of [tex]\( y^2 - x^2 \)[/tex] is 11.

To find the value of [tex]\( y^2 - x^2 \)[/tex] when y = 6 and x = 5, you simply substitute these values into the expression and calculate.

[tex]y^2-x^2=(6)^2-(5)^2\\=36-25\\=11[/tex]

Answer:

1. Cost of 80 sheets of paper = $ 4.8

2. Cost of 80 sheets of paper = $ 6.4

3. Cost of 880 sheets of paper = $ 93.8

Step-by-step explanation:

1) if 40 sheets of paper cost $2.40 how much would 80 sheets cost

Solution:

Price of 40 sheets of paper = $2.40

Price of 1 sheet of paper = 2.40/40

Price of 80 sheets of paper = (2.40/40)*80

                                             = $ 4.8

2)if 25 sheets cost $2.00 how much would 80 sheets cost

Price of 25 sheets of paper = $2.00

Price of 1 sheet of paper = 2.00/25

Price of 80 sheets of paper = (2.00/25)*80

                                             = $ 6.4

3)if 15 sheets cost $1.60 how much would 880 sheets cost

Price of 15 sheets of paper = $1.60

Price of 1 sheet of paper = 1.60/15

Price of 880 sheets of paper = (1.60/15)*880

                                             = $ 93.8

This may be what you're looking for:

Answer: B.

Length x width x height

Whenever you're finding the volume of a quadrilateral, you multiply the base x width x height of the shape. In this case, you have all three of those elements.

First I substituted those numbers into their spots in the expression (it doesn't matter which you multiply first, since multiplying is commutative).

8 x 12 x 5 = 480

Your answer is 480 square inches.

Answer:

The answer would be B $6.99.  With this problem you would need to divide the total cost by 8 to get the price for a single steak.  

Step-by-step explanation:

‘an’ could represent any number

Simplify the expression to get an = an + 0, or an = an.

This means that a number is equal to itself, which is true for all numbers.

STEP 1: Convert interest rate of 2% per 6 months into rate per year.

rate per year = rate per 6 month⋅2=2%⋅2=4%

STEP 2: Convert 9 months into years.

 9 months =

9

12

 years=0.75 years

STEP 3: Find principal by using the formula

I=P⋅i⋅t

, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this example I = $15, i = 4% and t = 0.75 years, so

I

P

P

P

=P⋅i⋅t

=

I

i⋅t

=

15

0.04⋅0.75

=500

Final answer:

To calculate the amount at 6% simple interest on Rs 1200 for 9 months, apply the simple interest formula. Convert time to years, calculate the interest, then add it to the principal to find the total amount due, which is Rs 1254.

Explanation:

To find the amount at 6% simple interest on Rs 1200 due in 9 months, you can use the simple interest formula:

Simple Interest =  Principal × Rate × Time

We have the Principal (P) as Rs 1200, the Rate (R) as 6% per annum (or 0.06 when expressed as a decimal), and the Time (T) as 9 months. The rate is given per annum but we have in months so, we need to convert the time to years. There are 12 months in a year, so 9 months is ⅓ or 0.75 years.

Now, let's calculate the simple interest (SI):

SI = 1200 × 0.06 × 0.75 = Rs 54

Total Amount = Principal + Simple Interest

Total Amount = 1200 + 54 = Rs 1254

Therefore, the total amount due at the end of 9 months would be Rs 1254.

Final answer:

The correct answer is D. Distance formula to prove AC and BD are congruent, as this explains why the diagonals of a rectangle, AC and BD, are always the same length.

Explanation:

The question asks which reason validates the statement: "The diagonals of a rectangle are congruent." The correct answer is D. Distance formula to prove AC and BD are congruent. In a rectangle, the diagonals are always congruent because they connect opposite corners and because a rectangle is a parallelogram, where opposing sides are equal and parallel, making the trip from one corner to the opposite across the shape the same distance, regardless of the starting and ending points. This is proven using the distance formula, which calculates the distance between two points in a coordinate plane. The diagonal AC and diagonal BD represent these distances in a rectangle.

Answer:

C

Step-by-step explanation:

First of all their is an easier way solving this 2l/ + l^2

but how you need it is c because the base is 100 and each face is 40 how 10x8=80 80/2=40

Answer:

blank = 50,000

Step-by-step explanation:

Answer:

The height of the cone is 97 in

Step-by-step explanation:

Equate the formulas for the volume of a cylinder and that of a cone:

Vol-Cyl              Vol-Cone

πr²h         =        (1/3)πr²h

Now cancel out items that are the same on both sides (π):

r²h             =         (1/3)r²h

Now substitute the given values for both solids:

(12 in)²(8 in)  =  (1/3)(6 in)²(h-cone)

                                 1152 in³

Then (h-cone) = --------------------  =  97 in

                                   12 in²

The height of the cone is 97 in

Answer:

96 in

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

1/3 (12) +8

4+8= 12

Answer:

12

Step-by-step explanation:

we can use PEMDAS to find the solution to the expression, PEMDAS stands for:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

we look at the expression and we see parentheses, so we solve whats inside of the parentheses

(4 x 3) = 12

1/3 (12) + 2³

now, we solve for the exponents in the expression

2³ = 2 x 2 x 2 = 8

1/3 (12) + 8

now we multiply the terms in the expression that need to be multiplied.

1/3 x 12 = 4

4 + 8

we have no division in the expression, so we skip that step and move onto addition, which will be our last step as there is no subtraction in the expression either

4 + 8 = 12

our answer to the expression is 12