Find the surface area of the prism.

Answer:

See below.

Step-by-step explanation:

The domain is the x values involved in the equation/graph. The lines seemingly goes from -5 to 6. The x values between those points also count since there is a line. Therefore, the domain of f is [-5, 6]. The brackets are used since the dots on -5 and 6 are shaded in meaning they also count for the domain.

Interval Notation: [-5, 6]

Inequality Notation: -5 ≤ x ≤ 6

The equation \(3x^2 + 14x - 27 = 0\) have two solutions were found.  x = -1.467, x = 6.134.

The quadratic formula, x, provides the solution to equation \(Ax^{2} +Bx+C = 0\), where A, B, and C are three numerical values that are commonly referred to as coefficients:

In our case,  A  =  3

                     B =  -14

                     C =  -27

Accordingly, \(B^{2}-4AC=196-(-324) = 520\)

Applying the quadratic formula:

 x  = 14 ± \(\sqrt{520}\)/6

The prime factorization of 520 is

\(2*2*2*5*13\)

To be able to take something from beneath the radical, there must be two instances of it (because we are taking the second root of a square).

after four decimal places have been added, \(\sqrt{130}\)  equals 11.4018.

So now we are looking at:

x = (14 ± 2*11.402 ) / 6

Two real solutions:

x \(=(14+\sqrt{520})/6=(7+\sqrt{130})/3= 6.134\)

or:

x\(=(14-\sqrt{520})/6=(7-\sqrt{130})/3= -1.467\)

Two solutions were found.

x \(=(14-\sqrt{520})/6=(7-\sqrt{130})/3= -1.467\)

x \(=(14+\sqrt{520})/6=(7+\sqrt{130})/3= 6.134\)

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The correct answer is 4. (3 cos θ - sin θ, 3 sin θ + θ cos θ)

To derive the parametric equations for P, we can use the concept of involutes, which is a curve that is generated by unwinding a taut string from a circle. Let O be the center of the circle, and let P be a point on the involute curve that is obtained by unwinding the thread from the spool.

We can use the angle 0 as the parameter for the parametric equations of P. Let OP = r, and let the tangent to the circle at P intersect the x-axis at point Q. Since PQ has length 30, we have:

PQ = rθ = 30

Differentiating both sides with respect to θ, we get:

r + r'θ = 0

where r' denotes the derivative of r with respect to θ. Solving for r', we get:

r' = -r/θ

Next, we can express the coordinates of P in terms of r and θ. Since P lies on the circle of radius 3 centered at O, we have:

x = 3cosθ
y = 3sinθ

To find the coordinates of Q, we note that the tangent to the circle at P is perpendicular to the radius OP. Therefore, the slope of the tangent at P is given by:

dy/dx = -cosθ/sinθ = -cotθ

Since the tangent passes through P, we can use the point-slope form of the equation of a line to get:

y - 3sinθ = -cotθ(x - 3cosθ)

Simplifying, we get:

y = 3sinθ - θcosθ

Finally, we can express the coordinates of P in terms of r and θ by eliminating r between the equations for r' and PQ, and substituting for x and y in terms of θ. This gives:

x = 3cosθ - rsinθ
y = 3sinθ + rcosθ

Substituting r' = -r/θ, we get:

x = 3cosθ - 3sinθ(θ/r)
y = 3sinθ + 3cosθ(θ/r)

Multiplying both sides of each equation by r, we get:

rx = 3r cosθ - 3θ sinθ
ry = 3r sinθ + 3θ cosθ

Therefore, the parametric equations for P in terms of θ are:

x = 3 cos θ - sin θ
y = 3 sin θ + θ cos θ

which matches option 4.

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The two populations are the words in book A and the words in book B.

Dakarai could choose a page from each book randomly, or he could choose a specific page number from each book, or he could choose a page that corresponds to a specific chapter or section in each book.

It should be noted that to collect the data, Dakarai will need to count the length of every word on the chosen pages of each book. He can record the data in a table or spreadsheet with two columns: one for the book and one for the word length. He can also use a histogram or box plot to display the distribution of word lengths for each book.

The best average to use would be the mean, as it provides a representative value for the central tendency of the data. The mean is calculated by adding up all the word lengths and dividing by the total number of words.

Dakarai can compare the two mean word lengths to see if his prediction is correct. If the mean word length for book A is higher than the mean word length for book B, then his prediction is correct.

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Answer:

(5r + 6)(5r² + 4)

Step-by-step explanation:

Given

25r³ + 30r² + 20r + 24 ( factor the first/second and third/fourth terms )

= 5r²(5r + 6) + 4(5r + 6) ← factor out (5r + 6) from each term

= (5r + 6)(5r² + 4)

After solving the quadratic equation, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

Let's assume that one leg of the right triangle is x units. According to the problem, the other leg is 4 more than twice the length of x, which can be represented as 2x + 4 units.

Using the Pythagorean theorem, we can set up the equation:

\(x^2 + (2x + 4)^2 = 26^2\)

Expanding and simplifying the equation:

\(x^2 + 4x^2 + 16x + 16 = 676\)

\(5x^2 + 16x - 660 = 0\)

We can now solve this quadratic equation to find the value of x. By summing the lengths of the legs (x + 2x + 4), we can determine the final answer.

After solving the quadratic equation, we find two possible solutions: x = 11 and x = -12. Since the lengths of the sides cannot be negative, we consider x = 11 as the valid solution.

Therefore, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

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To calculate the ratio strength of a medication, we compare the amount of active ingredient (lorazepam in this case) to the total volume of the medication.

In this case, the lorazepam injection contains 4 mg of lorazepam per milliliter.

Therefore, the ratio strength can be calculated as:

Ratio Strength = Amount of Active Ingredient / Total Volume

In this case, the amount of active ingredient is 4 mg, and the total volume is 1 mL.

Ratio Strength = 4 mg / 1 mL

Thus, the ratio strength of the lorazepam injection is 4:1 (4 to 1) or 4.

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"The speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph" correctly describes the consistency of the speeds of the cars in the two races.

Based on the given information, the box plot for race A has a larger range of speeds (from 120 to 170 mph) compared to the range of speeds in race B (from 125 to 165 mph). The box plot for race A also has a larger interquartile range (from 143 to 165 mph) compared to the interquartile range in race B (from 140 to 150 mph). However, the median speed in race A (153 mph) is lower than the median speed in race B (145 mph).

Therefore, it is not accurate to say that the speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near 165 mph. Likewise, it is not accurate to say that the speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near 125 mph.

The correct answer is that the speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near 153 mph. This is because the medians of the two box plots are relatively close to each other, and the box plot for race B has a smaller range and interquartile range, indicating greater consistency in the speeds of the cars in that race compared to race A.

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Check the picture below.

we can simply get the volume of the larger sphere, then the volume of the smaller sphere and subtract it from that of the larger sphere and what's leftover is the region between both.

\(\stackrel{\textit{\large volumes}}{\stackrel{\textit{sphere with r=6}}{\cfrac{4\pi (6)^3}{3}}~~ -~~\stackrel{\textit{sphere with r = 3}}{\cfrac{4\pi (3)^3}{3}}}\implies 288\pi -36\pi \implies 252\pi \approx \stackrel{cubic~units}{791.68}\)

The region within the larger sphere and not within the smaller sphere is 789.02 cubic units.

The volume of sphere is the measure of space that can be occupied by a sphere.  If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³

Given that, there are two concentric spheres of radii 3 units and 6 units.

Now,

Volume of sphere with radius 3 units is

V₁ = 4/3×3.14×3³

= 4/3×3.14×27

= 4×3.14×9

= 113.04 cubic units

Volume of sphere with radius 6 units is

V₂ = 4/3×3.14×6³

= 4/3×3.14×216

= 902.06 cubic units

Now, difference is 902.06-113.04

= 789.02 cubic units

Therefore, the region within the larger sphere and not within the smaller sphere is 789.02 cubic units.

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Answer:

b) octogon

c) irregular pentagon

d) irregular hexagon

Step-by-step explanation:

Answer:

a = 4

b = 4

Step-by-step explanation:

NOTE: THIS EXPLANATION ASSUMES YOU HAVE A BASIC UNDERSTANDING OF COMMON TRIANGLES, PYTHAGOREAN THEOREM, ISOCELES TRIANGLE THEOREM, AND BASIC ALGEBRA

Since the triangle is a right triangle, and you know one of the angles is a 45 degree angle, you know the other angle is a 45 degree angle. This is a classic  45-45-90 right triangle.

If two angles are equal two each other the opposite sides of the corresponding angles are also equal each other, courtesy of the isosceles triangle theorem.

So if a = b, we can just substitute one for the other. For this explanation, I'll be using 'a' for both 'a' and 'b'.

The Pythagorean Theorem is

a^2 + b^2 = c^2

Since a = b we can say

a^2 + a^2 = c^2

Then simplify

2a^2 = c^2

Now let's just substitute the numbers

2a^2 = (4\(\sqrt{2}\))^2

2a^2 = 32

a^2 = 16

a = 4

Since 'a' and 'b' are equal, 'b' also equals 4.

Hope this helped! :)

Answer:

19. sqrt{305}

20. 3*sqrt{7}

Step-by-step explanation:

You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.

Step-by-step explanation:

hope this will gel help u

The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

The quadratic inequality defined on the graph is given as follows:

y ≥ 2/3(x + 3)² - 24.

The coordinates of the vertex of the quadratic function are given as follows:

(-3, -24).

Hence the quadratic function is given as follows:

y = a(x + 3)² - 24.

In which a is the leading coefficient.

When x = 3, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(3 + 3)² - 24

36a = 24

a = 24/36

a = 2/3.

Hence:

y = 2/3(x + 3)² - 24.

The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:

y ≥ 2/3(x + 3)² - 24.

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Answer:

Step-by-step explanation:

3y+6x-2y=2

then group like terms 3y-2y+6x=2

then{Add similar elements)

y+6x=2

then sub from both sides

y+6x-y=2-y

{Simplify}

6x=2-y

divided both sides by 6

\frac{6x}{6}=\frac{2}{6}-\frac{y}{6}

x=\frac{2-y}{6}

Answer:

0.4375

Step-by-step explanation:

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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We will use the dedepriciation formula;

where A = value of the car after 5 years

P = current value of the car

r = depretiation rate

t = time in years

From the question,

P = $14 000

r = 9

Count the years from 2007 to 2011 starting from 2008 to get the number of years

t =4

Substitute the values into the formula

Therefore the car will worth $9600 to the nearest hundred dollars

Answer:

A.  9.4 mi

Step-by-step explanation:

Sketch a right triangle with legs of 8 and 5.  Shortest distance back to the starting point is the hypotenuse (h) of the triangle:

h² = 8² + 5² = 89

h = √89 = 9.43 mi

Answer:

45 - 43.7 = $1.3

Step-by-step explanation:

a) Kohl’s is selling the speaker for $60.00. Mrs. House has a Friends and Family discount coupon for 25% off.

This means that the amount that he would have to pay would be the cost of the speaker - 25% of this cost and multiplied by 100. It becomes

60 - (25/100 × 60) = 60 - 15 = $45

So she would be paying $45 at Kohl

b) Target purchased the speaker for $38.00 and marked it up by 15% to sell in the store. The price that she will pay at Target would be the sum of the price at which Target purchased it + 15% of this price. It becomes

38 + (15/100 × 38) = 38 + 5.7 = 43.7

So she would be paying $43.7 at Target.

c) she would get the best deal at Target because it is cheaper there. She would be saving

45 - 43.7 = $1.3

Answer:

it is c

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

Took the lesson on edge 2021

Answer:

-x-15

Step-by-step explanation:

The square matrix is A.  Transpose is A^T = ⎣

⎡

​

2

3

−5

7

​−11

−5

2

8

​

8

2

0

7

​

3

1

1

−6

​⎦

⎤

A square matrix is a matrix that has an equal number of rows and columns. In this case, matrix A has dimensions 4x4, meaning it has 4 rows and 4 columns. Therefore, matrix A is a square matrix.

The transpose of a matrix is obtained by interchanging its rows and columns. To find the transpose of matrix A, we simply need to swap its rows with columns. The transpose of matrix A is denoted by A^T.

The transpose of matrix A is:

A^T = ⎣

⎡

​

2

3

−5

7

​−11

−5

2

8

​

8

2

0

7

​

3

1

1

−6

​⎦

⎤

​This means that each element in matrix A is swapped with its corresponding element in the transposed matrix. The rows become columns and the columns become rows.

Therefore, the transpose of matrix A is shown above.

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The system of linear equations to find the cost of an apple and the cost of an apricot is as follows:

9x + 6y = 8.50

3x + 2y = 7.40

Jeremiah bought 9 apples and 6 apricots for $8.50 yesterday. He bought 3 apples and 2 apricots for $7.40 today.

The system of linear equation to find the cost of an apple and the cost of an apricot can be represented as follows:

Therefore, system of equation can be solved using different method such as elimination method, substitution method and graphical method.

The linear equation is as follows:

9x + 6y = 8.50

3x + 2y = 7.40

where

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Answer: there are no answer choices but f > 2

Step-by-step explanation:

By responding to the query, we can therefore deduce that the answer to u is: \(u\geq -2\)

In mathematics, an equation is a claim that two expressions are equivalent. Two parts that are separated by the algebraic symbol (=) make up an equation. As an illustration, the claim "\(2x+3 = 9\)" makes the statement

Finding the value or values of the variable(s) necessary for the equation to be correct is the goal of equation solving. Equations can have one or more components and be straightforward or complex, regular or nonlinear.

The formula "\(x^{2} +2x-3=0\)" raises the variable x to the second degree. In many various branches of mathematics, including algebra, calculus, and geometry, lines are used.

\(-15\leq u-13\\-15+13\leq 13+13\\-2\leq u\)

Therefore the solution of \(u\geq -2\)

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The percentage increase in the price of petrol is approximately 5.56%.

Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:

A discount or a markup in prices

The increase or decrease in a quantity or value

The proportion of a quantity compared to a whole

The probability of an event occurring.

In the given question,

To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.

The difference between the old price and the new price is:

R 13.28 - R 12.58 = R 0.70

Dividing the difference by the old price:

R 0.70 ÷ R 12.58 ≈ 0.0556

Multiplying by 100 to convert to a percentage:

0.0556 × 100 ≈ 5.56%

Therefore, the percentage increase in the price of petrol is approximately 5.56%.

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Answer:

A

Step-by-step explanation:

the given equation can be simplified to 12m+17

so if we simply the other options we see that A = 13m+17

Please look at the scanned picture.