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CaHeK987 [17]
3 years ago
12

What is the minimum number of binary bits needed to represent each of the following unsigned decimal integers? a. 65

Mathematics
2 answers:
professor190 [17]3 years ago
7 0

Answer: N >/= 7 bits

Minimum of 7 bits

Step-by-step explanation:

The minimum binary bits needed to represent 65 can be derived by converting 65 to binary numbers and counting the number of binary digits.

See conversation in the attachment.

65 = 1000001₂

65 = 7 bits :( 0 to 2^7 -1)

The number of binary digits is 7

N >/= 7 bits

satela [25.4K]3 years ago
3 0

Answer:7

Step-by-step explanation:n8

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32546455 rounded to the nearest hundred
Ivan
The answer is 32,546,500.
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3 years ago
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Find the exact solutions of x2 − 3x − 5 = 0 using the quadratic formula. Show all work! 75 points please help!!!!!
noname [10]

Answer:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Step-by-step explanation:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0

<u>Given quadratic equation</u>:

x^2-3x-5=0

<u>Define the variables</u>:

\implies a=1, \quad b=-3, \quad c=-5

<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:

\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}

\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}

\implies x=\dfrac{3 \pm \sqrt{29}}{2}

Therefore, the exact solutions to the given <u>quadratic equation</u> are:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Learn more about the quadratic formula here:

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8 0
2 years ago
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HELP ASAP (Geometry)
Andrei [34K]

1) Parallel line: y=-2x-3

2) Rectangle

3) Perpendicular line: y = 0.5x + 2.5

4) x-coordinate: 2.7

5) Distance: d=\sqrt{(4-3)^2+(7-1)^2}

6) 3/8

7) Perimeter: 12.4 units

8) Area: 8 square units

9) Two slopes of triangle ABC are opposite reciprocals

10) Perpendicular line: y-5=-4(x-(-1))

Step-by-step explanation:

1)

The equation of a line is in the form

y=mx+q

where m is the slope and q is the y-intercept.

Two lines are parallel to each other if they have same slope m.

The line given in this problem is

y=-2x+7

So its slope is m=-2. Therefore, the only line parallel to this one is the line which have the same slope, which is:

y=-2x-3

Since it also has m=-2

2)

We can verify that this is a rectangle by checking that the two diagonals are congruent. We have:

- First diagonal: d_1 = \sqrt{(-3-(-1))^2+(4-(-2))^2}=\sqrt{(-2)^2+(6)^2}=6.32

- Second diagonal: d_2 = \sqrt{(1-(-5))^2+(0-2)^2}=\sqrt{6^2+(-2)^2}=6.32

The diagonals are congruent, so this is a rectangle.

3)

Given points A (0,1) and B (-2,5), the slope of the line is:

m=\frac{5-1}{-2-0}=-2

The slope of a line perpendicular to AB is equal to the inverse reciprocal of the slope of AB, so:

m'=\frac{1}{2}

And using the slope-intercept for,

y-y_0 = m(x-x_0)

Using the point (x_0,y_0)=(7,1) we find:

y-1=\frac{1}{2}(x-7)

And re-arranging,

y-1 = \frac{1}{2}x-\frac{7}{2}\\y=\frac{1}{2}x-\frac{5}{2}\\y=0.5x-2.5

4)

The endpoints of the segment are X(1,2) and Y(6,7).

We have to divide the sgment into 1/3 and 2/3 parts from X to Y, so for the x-coordinate we get:

x' = x_0 + \frac{1}{3}(x_1 - x_0) = 1+\frac{1}{3}(6-1)=2.7

5)

The distance between two points A(x_A,y_A) and B(x_B,y_B) is given by

d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}

In this problem, the two points are

E(3,1)

F(4,7)

So the distance is given by

d=\sqrt{(4-3)^2+(7-1)^2}

6)

We have:

A(3,4)

B(11,3)

Point C divides the segment into two parts with 3:5 ratio.

The distance between the x-coordinates of A and B is 8 units: this means that the x-coordinate of C falls 3 units to the right of the x-coordinate of A and 5 units to the left of the x-coordinate of B, so overall, the x-coordinate of C falls at

\frac{3}{3+5}=\frac{3}{8}

of the  distance between A and B.

7)

To find the perimeter, we have to calculate the length of each side:

d_{EF}=\sqrt{(x_E-x_F)^2+(y_E-y_F)^2}=\sqrt{(-1-2)^2+(6-4)^2}=3.6

d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}=\sqrt{(-1-2)^2+(3-4)^2}=3.2

d_{GH}=\sqrt{(x_G-x_H)^2+(y_G-y_H)^2}=\sqrt{(-1-(-3))^2+(3-3)^2}=2

d_{EH}=\sqrt{(x_E-x_H)^2+(y_E-y_H)^2}=\sqrt{(-1-(-3))^2+(6-3)^2}=3.6

So the perimeter is

p = 3.6 + 3.2 + 2 + 3.6 = 12.4

8)

The area of a triangle is

A=\frac{1}{2}(base)(height)

For this triangle,

Base = XW

Height = YZ

We calculate the length of the base and of the height:

Base =XW=\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}=\sqrt{(6-2)^2+(3-(-1))^2}=5.7

Height =YZ=\sqrt{(x_Y-x_Z)^2+(y_Y-y_Z)^2}=\sqrt{(7-5)^2+(0-2)^2}=2.8

So the area is

A=\frac{1}{2}(XW)(YZ)=\frac{1}{2}(5.7)(2.8)=8

9)

A triangle is a right triangle when there is one right angle. This means that two sides of the triangle are perpendicular to each other: however, two lines are perpendicular when their slopes are opposite reciprocals. Therefore, this means that the true statement is

"Two slopes of triangle ABC are opposite reciprocals"

10)

The initial line is

y=\frac{1}{4}x-6

A line perpendicular to this one must have a slope which is the opposite reciprocal, so

m'=-4

Using the slope-intercept form,

y-y_0 = m'(x-x_0)

And using the point

(x_0,y_0)=(-1,5)

we find:

y-5=-4(x-(-1))

Learn more about parallel and perpendicular lines:

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#LearnwithBrainly

8 0
3 years ago
An egg carton holds 12 eggs. A breakfast buffet uses 96 eggs by
Blizzard [7]

Answer:

13 Cartoons

Step-by-step explanation:

As, in 1 cartoon = 12 eggs

x cartoon = 156

X = 156 / 12

X = 13

Therefore, 13 Cartoons were used after 10:30 am

4 0
3 years ago
could someone out there perhaps help me? i’m so lost even though it’s probably so simple. i’ll give you brainleist :)
Temka [501]

Answer:

y= -x+7, b= sqrt(2P/a), c=3P^2-b

Step-by-step explanation:

First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will      get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.

Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).

Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.

8 0
3 years ago
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