Evaluate 4s^2 for s = 1/4. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.

From the line theorems explained below and when we apply it to the given image, we have; X║Y, A║B, Z ⊥ A

The perpendicular transversal theorem states that in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Now, since we are told that Line X is perpendicular to Line A, then it means that Line X is also perpendicular to line B.

The inverse of perpendicular transversal theorem states that if there are two perpendicular lines to a straight line, they're parallel to each other. Thus, it means that Line X is parallel to Line Y and similarly, line A is parallel to Line B.

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The average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%

The average work weeks are given as:

Year 2009 = 43 hours

Year 2010 = 42 hours 30 minutes

Rewrite as:

Year 2010 = 42.5 hours

The percentage change is then calculated as:

Percentage change= (Final - Initial)/Initial * 100%

So, we have:

Percentage change= (42.5 - 43)/43* 100%

Evaluate

Percentage change= -1.16%

Hence, the average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%

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The number of solutions there are for the functions, -f(x) and f(-x) are; 2 and 2 respectively.

According to the task content, the function given initially is; f(x).

Hence, the function -f(x) represents a reflection of the function f(x) over the x axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

Also, the function f(-x) represents a reflection of the function f(x) over the y-axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

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This graph has its maximum at 4. There is no minimum while the inflection is at 2, 10/3.

We have ( x-2²) (x-4)

x-2²) = 0, or x - 4

x - 2 = 0, x = 2

Hence we can see that the graph has its minimum at x = 4

b. The graph here does not have a local maximum

To do this you have to differentiate the equation

Use the product rule of differentiation in order to solve for the solution.

(x-2)²[ (x-4) 2 (x-2)]

This would then give us

x -2, 3x -10

In both equations we have to make x the subject of the equation

X = 2, x = 10/3

Hence the point of inflection is 2 and 10/3

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Answer:

  (a)  Theorem 9

Step-by-step explanation:

Any of the given theorems can be used to prove lines are parallel. We need to find the one that is applicable to the given geometry.

The marked angles are between the parallel lines (interior) and on opposite sides of the transversal (alternate).

Theorem 9 applies to congruent alternate interior angles.

The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

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The simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

The expression is given as:

[tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex]

Factor the numerator

[tex]\frac{x^{2}(x-8)}{x^2-64}[/tex]

Express the denominator as a difference of two squares

[tex]\frac{x^{2}(x-8)}{(x-8)(x + 8)}[/tex]

Cancel out the common factor

[tex]\frac{x^2}{x + 8}[/tex]

Hence, the simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

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Answer: B

Step-by-step explanation:

The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].

This allows us to eliminate all the options except for B.

[tex]\cos \left(\frac{3\pi}{2}-x \right)=\sin x \\ \\ =\cos \left(\frac{3\pi}{2} \right)\cos x -\sin \left(\frac{3\pi}{2} \right) \sin x \\ \\ =0\cos x -(-1)(\sin x) \\ \\ =\sin x[/tex]

Levada borrows $30,900 from her bank to open a florist shop at rate of 0.98% per month.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

It is given that Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.

P = $30,900

T = 18 months

Interest  = 5.5%

Interest rate =  P×R×T

5.5 = 30,900 × R × 18

R = 0.000988

Or, R = 0.98% per month.

The complete question is

"a) How much must she pay the bank in 18 months?"

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The measure of angle E in the secant intersection is 21 degrees.

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other

Therefore,

m∠E = 1 / 2 (∠AB - ∠CD)

m∠E = 1 / 2 (80 - 38)

m∠E = 1 / 2 (42)

m∠E = 42 / 2

m∠E = 21 degrees.

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Hello,

If we want to factor the expression, we have to solve

3x² + 10x + 8 = 0

a = 3 ; b = 10 ; c = 8

∆ = b² - 4ac = 10² - 4 × 3 × 8 = 4 > 0

x1 = (-b - √∆)/2a = (-10 - 2)/6 = -12/6 = -2

x2 = (-b + √∆)/2a = (-10 + 2)/6 = -8/6 = -4/3

Factor :

a (x - x1)(x - x2)

= 3(x + 2)(x + 4/3)

= (x + 2)(3x + 4)

Answer:

2

Step-by-step explanation:

8/3 = 2 with a Remainder of 2

Answer:

x^4-3x+2

Step-by-step explanation:

There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.

see image.

Factor an x from the top. Cancel that x with the bottom x. See image.

(***Also, note: never "cancel" anything connected by a + or a - )

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{x^{5}+(3\times x^{2}) +(2\times x) }{x}} \end{gathered}$}[/tex]

Takes into account expressions that have not yet been taken into account.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\not{x}}(x-1)(x^{3}+x^{2} +x-2) }{\red{\not{x}} } } \end{gathered}$}[/tex]

Cancel x in both the  numerator and the denominator.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^{3}+x^{2} +x-2) } \end{gathered}$}[/tex]

The expression expands

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^{4}-3x+2 } \end{gathered}$} }[/tex]

Answer:

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Answer:

There are four lines of symmetry in this figure.

Step-by-step explanation:

First look at the mainframe, it has 2 lines of symmetry. And if you look at it diagonally, it has another 2 more lines.

So therefore there is 4 lines of symmetry in this H figure.

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The resulting coordinates for each row are (-2, 2), (0, 4),()2, 6), (6, 10) and (8,12) respectively

Given the linear function expressed as;

y = x + 4

where

x are the input values and y are the output values

If x = -2

y = -2+4

y = 2

The coordinate (x, y) will be (-2, 2)

If x = 0

y = 0+4

y = 4

The coordinate (x, y) will be (0,4)

If x = 2

y = 2+4

y = 6

The coordinate (x, y) will be (2, 6)

If x = 6

y = 6+4

y = 10

The coordinate (x, y) will be (6,10)

If x = 8

y = 8+4

y = 12

The coordinate (x, y) will be (8, 12)

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The amount of money Craig paid more than Tim if the shop has an offer of reduction if a particular amount is spent is £88.

The shop discount:

£5 reduction if you spend more than £100

or

£10 reduction if you spend more than £140

or

£20 reduction if you spend more than £180

Cost of a shirt = £49

Tim buys 3 shirts

Total cost of Tim's shirt = £49 × 3

= £147

Amount Tim paid = £147 - £10

= £137

Craig buys 5 shirts

Total cost of Craig's shirt = £49 × 5

= £245

Amount Craig paid = £245 - £20

= £225

Difference between Tim and Craig's pay = £225 - £137

= £88

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If one of the roots is [tex]w=B+2i[/tex], then the other root is its conjugate [tex]\bar w=B-2i[/tex]. So we can factorize the quadratic to

[tex]z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))[/tex]

Expand the right side and collect all the coefficients.

[tex]z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4[/tex]

From the [tex]z[/tex] and constant terms, we have

[tex]\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}[/tex]

From the second equation we get

[tex]B^2 = 16 \implies B = \pm4[/tex]

Then

[tex]4+(A+1)i = \pm8[/tex]

[tex](A+1)i = 4 \text{ or } (A+1)i = -12[/tex]

Since [tex]\frac1i=-i[/tex], we have

[tex]-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12[/tex]

[tex]A+1 = -4i \text{ or } A+1 = 12i[/tex]

[tex]\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}[/tex]

The second option saves time and cleaning elements, so that one is better.

We know that every day you sell a total of 50 bowls, and each one needs 8 oz of onion, this means that you need:

50*8 oz = 400 oz

So you need 400 ounces of onion per day.

If you buy at $1.99 per pound (1 lb = 16 oz)

Then the cost per ounce is:

c = $1.99/16

And the cost of 400 ounces is:

C = ($1.99/16)*400 = $49.75

In the case of the pre-sliced onions, the total cost would be:

C' = ($2.99/16)*400 = $74.75

So in the first case, each portion costs:

$49.75/50 = $0.995

And in the second case:

$74.75/50 =$1.495

So the extra cost is returned by the extra time and savings in cleaning elements, thus, the second option is better.

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The function is increasing on the interval (3, ∞)

Given the rational function shown below

g(x) = -2√x-3

For the function to be a positive function, the value in the square root  must be positive such that;

x - 3 = 0

Add 3 to both sides

x = 0 + 3

x = 3

Hence the interval where the function is increasing is (3, ∞)

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The value of x in the similar triangles is 18

Similar triangles have the same shapes but may have different sizes.

Corresponding side of similar triangles are a ratio of each other.

Therefore,

UV / BC = AU / AB

Hence,

UV = 444 units

BC = 703

AU = 20x + 108

AB = 20x + 108 + 273 = 20x + 381

Therefore,

444 / 703 = 20x + 108 /  20x + 381

cross multiply

444( 20x + 381) = 703(20x + 108)

8880x + 169164 = 14060x + 75924

8880x  - 14060x  = 75924 -  169164

-5180x = -93240

x = -93240 / -5180

x = 18

Therefore, the value of x in the similar triangles is 18

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The probability of drawing a red marble and then a green marble is:

P = 1/6.

In the jar we have a total of 16 marbles, such that:

First, the probability of getting a red marble is give by the quotient between the number of red marbles and the total number of marbles:

p = 4/16 = 1/4

Now we need to draw a green one, the probability is computed in the same way, but this time there are 15 marbles, because we already took one.

q = 10/15

The joint probability (first drawing red, then green) is given by the product between the individual probabilities:

P = p*q = (1/4)*(10/15) = 10/60 = 1/6

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Answer:

0.2

Step-by-step explanation:

y = mx + b  The slope is the number before the x.

Use the slope-intercept form to estimate the slope and y-intercept.

Slope: 0.2

y-intercept: (0,−6.9)

The slope intercept form in math exists as one of the forms utilized to estimate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.

The slope-intercept form exists y = mx + b, where m exists the slope and b exists the y-intercept.

y = mx + b

Use the slope-intercept form to estimate the slope and y-intercept.

Slope: 0.2

y-intercept: (0,−6.9)

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Answer:

[tex]\fbox {Required equation : 4(x + 3) = 20}[/tex]

[tex]\fbox {Result : x = 2}[/tex]

Step-by-step explanation:

Let our number be x.

1) 3 is added to this number.

2) It is multiplied by 4.

3) It is equated to 20.

∴ This is our framed equation.

Steps to solve :

1) Divide by 4 on both sides.

2) Subtract 3 on both sides.

∴ The number is 2.

The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400

The ratio based on the information given will be:

= 1200/600

= 2

Therefore, the constant ratio is 2.

In 6 years, the population will be:

= 600 × 2^6

= 600 × 64

= 38400

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The place value in thousands for the 0 in 10000 is 0 thousands

From the question, we are to the determine the place value in thousands for the 0 in the given number

The given number is

10000

The place value in thousands for the 0 in 10000 is 0 thousands

Hence, the place value in thousands for the 0 in 10000 is 0 thousands

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The drivers will travel 200x miles during the race.

A definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that A race track is miles long

The car race is 200 laps then we have to find the number of miles the driver travel.

If the race track is x miles long, then one lap around the track is x miles.

If the race is 200 laps, the total distance covered by the drivers is:

200 laps ×  x miles/lap = 200x miles.

Therefore, the drivers will travel 200x miles during the race.

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From the line bisected with the given midpoints, we have been able to prove that; BC = CE by substitution property of Equality

We are given that;

C is the midpoint of BD

D is the midpoint of CE

1) Thus, BC = CD because of definition of Midpoint.

2) Similarly, by definition of midpoint we know that CD = DE.

3)  We can say that BC = DE because of substitution property of equality.

4) We can say that BC + CD = BD because of segment addition postulate.

5) Similarly, by segment addition postulate, we can say that CD + DE = CE.

6) Finally we can say that BC = CE by substitution property of Equality

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Answer:

[tex]2xy^2(xy-1)(xy-3)[/tex]

====================

Given expression

[tex]2x^3y^4-8x^2y^3+6xy^2[/tex]

The greatest common factor of all three terms is [tex]2xy^2[/tex].

Factor this out:

[tex]2xy^2(x^2y^2-4xy+3)[/tex]

Complete the square:

[tex]2xy^2(x^2y^2-4xy+4-1)=[/tex]

[tex]2xy^2((xy-2)^2-1)[/tex]

Factorize further using the identity for the difference of squares:

[tex]2xy^2(xy-2+1)(xy-2-1)=[/tex]

[tex]2xy^2(xy-1)(xy-3)[/tex]