Consider the set S of bit strings defined recursively by:

Answer:

D

Step-by-step explanation:

In functions like this, its best to pay attention to the end points of the rays.

On the lower line:

it ends at x -1

because it is a closed circle, that means x can also equal -1.

x≤-1

On the upper line:

it starts at -1

it is an open circle, meaning x cannot be -1

x>-1

Answer:

first 1*3+1-3*4+1

then it is in fraction

the answer is -5

Answer:2

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Answer:

Blank 1 = SAS

Blank 2 = HL

Black 3 = ASA

Blank 4 = SSS

Answer: 2

Step-by-step explanation:

When x = 3, y = -2.

When x = 6, y = 4.

The average rate of change over the interval is:

[tex]\frac{-2-4}{3-6}=\frac{-6}{-3}=\boxed{2}[/tex]

Answer:

(-2, 0)

Step-by-step explanation:

The solution to the system is the point where the graphs intersect.

Adding 2x to both sides, we get [tex]\boxed{2x+y=5}[/tex]

Answer:

127 degrees = x

Step-by-step explanation:

A six sided polygon has interior angles that sum to

(n-2)(180) =  (6-2)(180 = 720

so all of the angles in the question add to 720

 98 + 133 + x + x + 155 + 80 = 720

  solve for x = 127 degrees

Answer:

x = 127

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 , then

sum = 180° × 4 = 720°

sum the interior angles and equate to 720

x + x + 155 + 80 + 98 + 133 = 720 , that is

2x + 466 = 720 ( subtract 466 from both sides )

2x = 254 ( divide both sides by 2 )

x = 127

Answer:

x = 5 and 6

Step-by-step explanation:

1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6

Answer:

x = 5 , x = 6

Step-by-step explanation:

[tex]\sqrt{x-5}[/tex] = x - 5 ( square both sides )

x - 5 = (x - 5)² ← expand using FOIL

x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides

0 = x² - 11x + 30 ← in standard form

0 = (x - 5)(x - 6) ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 6 = 0 ⇒ x = 6

As a check

substitute these values into the equation and if both sides are equal then these values are the solutions.

x = 5

left side = [tex]\sqrt{5-5}[/tex] = [tex]\sqrt{0}[/tex] = 0

right side = 5 - 5 = 0

then x = 5 is a solution

----------------------------------

x = 6

left side = [tex]\sqrt{6-5}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 6 - 5 = 1

then x = 6 is a solution

Answer: (23, 46)

Step-by-step explanation:

The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)

Substituting into the distance formula,

[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]

Thus, the coordinates of P are (23, 46)

Answer: C

Step-by-step explanation:

An equation is formed of two equal expressions. The correct option is C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved for x as shown below, Therefore,

[tex]\dfrac{rx+t}{s} = w\\\\[/tex]

Using the multiplication property of equality, multiply s on both the sides of the equation,

rx + t = ws

using the subtraction property of equality, subtract t on both the sides of the equation,

rx = ws - t

[tex]x = \dfrac{sw-t+t}{r}[/tex]

Hence, the correct option is C.

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Answer: -120

Step-by-step explanation:

[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]

Answer:

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)

Step-by-step explanation:

Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

apply row operations:

R₂= R₂ - 2 R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

R₃= R₃ -  R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]

R₄ = R₄ +R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]

R₄ = R₄ +R₃

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]

we can clearly see that after performing row operations there are 3 non zero rows,

therefore the Rank of the given matrix is 3

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Answer:

144, 196, 256

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Answer: Each child gets 1/3

Step-by-step explanation: x/3

Answer:

x = 2

y = 4

Step-by-step explanation:

Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.

Add the 3 on its lower left to get 10.

so, 3 - x = 1. x = 2

17 - y = 13. y = 4

Answer:

Step-by-step explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

__

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

  0.15x +0.07(70000-x) = 9000

__

Simplifying the equation gives a 2-step linear equation.

  0.08x +4900 = 9000 . . . . simplified

  0.08x = 4100 . . . . . . . . . . subtract 4900

  x = 51,250 . . . . . . . . . . . .divide by 0.08

  70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.

The total distance travelled is 1075.91 km.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.

Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

The percentage change in G is 21 %

Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.

It is given that

G = ab

when a is increased by 10% the new a will be = 1.1 a

When b is increased by 10% the new b will be 1.1 b

So,

G' = 1.1a *1.1 b

G' = 1.21 ab

G' = 1.21

(G' - G)*100/G = (1.21-1)*100/1

The percentage change is 21 %

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Answer: (10, ∞)

Step-by-step explanation:

See the graph in the attached image.

Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]

Step-by-step explanation:

The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.

Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.

For the first triangle applying the moving principle gives,

Area  [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]

For the second triangle applying the additivity principle,

Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])

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Answer:

[tex]\mathsf {A. x = -5}[/tex]

Step-by-step explanation:

[tex]\implies \mathsf {-3 + x = -8}[/tex]

[tex]\implies \mathsf {x = -8 + 3}[/tex]

[tex]\implies \mathsf {x = -5}[/tex]

The numeral preceding and succeeding each of the following numerals.

Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.

Adding adds 1 to the unit digit.

Subtracting 1 gives 99 because 9 is the largest digit in base 10.

So A. 100 base 8

The largest digit in base 8 is 7, so

..., 77, 100, 101,...

B. 10000 base 7

The largest digit in base 7 is 6, so

..., 6666, 10000, 10001, ...

Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:

509 + 1 = 510.

C. 305 base 6

5 is the largest digit in base 6, so

..., 304, 305, 310, ...

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Answer:

  see attached

Step-by-step explanation:

You recognize the equation of the line as being given in point-slope form:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +3 = 2(x +3) . . . . . . given equation

This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.

__

You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.

Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.

We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).

Total miles driven is 10+50=60.

As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons

A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.

As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use

50/40=1.25 gallons;

So average miles per gallon equals to

[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]

Therefore option D is correct.

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Answer:

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

Let the initial price be x.

After the first sales quarter the price is reduced by 10% and became:

After the second sales quarter the price is reduced by 20% and became:

The decrease over the two quarters is:

This is equivalent of 28%, hence the correct answer choice is B.

If the number of multiple-choice questions is x and the number of short answer questions is y, then:

[tex]x+y=28\\\\3x+5y=100[/tex]

Answer:

44.70 US dollars

Step-by-step explanation:

euro left=(250/1.3687)-150=32.66(rounded to nearest cents

US dollars=32.66x1.3687

                =44.70US dollars