What are precise definitions of perpendicular and parallel lines

Answer:

ray:

Part of a line, containing one endpoint and extending to infinity in one direction.

line segment

Two points on a line, and all the points between those two points.

Step-by-step explanation:

The president draw 15 lines on map.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

here, it is given that :

there are 6 cities

No three of the cities are collinear that is are not in a straight line.

Now, to find the lines did the president draw use the formulae :

n(n-1)/2

where, n = number of cities

lines did the president draw = 6 x 5/ 2

                                                = 15

Therefore, The president draw 15 lines on map.

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The rate of the water being pumped into the tank is 289,753 cm3/min

d = 4m

∴ r = 2m

h = 6m

Therefore r = h/3

The formula for the volume of the cone is:

V=(1/3)π•r2h

substitute:

V=(1/3)π (h/3)2h

V=(1/27)π h3

Derive both sides with respect to time:

dV/dt = (1/9) π h2• dh/dt

When h= 2 meters = 200 cm when dh/dt = 20

dV/dt = (1/9) π (200)2• (20)

dV/dt = (800,000/9) π ~ 279,252.68

Meaning the volume of water is increasing at a rate of 279,252.68 cm3/min.

However, it's leaking out at a rate of 10,500 cm3/min. Therefore the rate of the water being pumped into the tank is:

279,252.68 + 10,500 = 289,752.68 ~ 289,753 cm3/min

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Answer: 5 and the power is 2

the power used is 2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

x = 19

Step-by-step explanation:

Alternate Exterior Angles Theorem

When a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Therefore:

⇒ 8x + 11 = 5x + 68

⇒ 8x + 11 - 5x = 5x + 68 - 5x

⇒ 3x + 11 = 68

⇒ 3x + 11 - 11 = 68 - 11

⇒ 3x = 57

⇒ 3x ÷ 3 = 57 ÷ 3

⇒ x = 19

The required solution in scientific notation is 2 × 10¹ .

Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).

The given expression is (6.4 × 10³) ÷ (3.2 × 10²)

Simplifying we get :

(6.4 × 10³) ÷ (3.2 × 10²) = 20

This can be written in the scientific notation as : 2 × 10¹

Therefore the required solution is 2 × 10¹

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Given in the question the matrix

A  =   [ 1    -1         B =  [ 1    5        C = [ 1     2

          -2    3 ]                8   -8 ]              3     4]

after solving AX + B = C, we get the value of x

x  =         [ 1        -21/5

              -1           8/5]  ..........(ii)

Given A =   [ 1    -1         B =  [ 1    5        C = [ 1     2

                   -2    3 ]               8   -8 ]              3     4]

find x, if AX + B = C

AX + B = C

AX = C -B =      [ 1     2                        [ 1    5  

                                           -    

                         3     4]                         8   -8 ]

AX =   [ 1-1        2-5      =      [ 0   -3

          3-8        4+8 ]           -5    12]

X = A -1        [ 0   -3

                    -5    12]   .........(i)

A =   [1     1            |A|  = {3*1 - 1 *(-2)}

       -2    3]                  = 5

A-1  = [tex]\frac{adj A}{|A|}[/tex]

Adj  A = [cofactor A]^1 =       [ [tex]a_{11}[/tex] = 3        [tex]a_{12}[/tex]  = 2

                                               [tex]a_{21}[/tex]  = -1           [tex]a_{22}[/tex]  = 1 ] ^1

adj A = [ 3  -1            A -1 =  1/5    [ 3    -1

             2    1]                               2     1]

x = 1/5   [3     -1                 [ 0     -3

              2     1]                 -5      12]

   = 1/5 [ 5    -21        =     [ 1        -21/5

             -5     8]              -1           8/5]  ..........(ii)

Hence, required solution of the given matrix is equation (ii)

Therefore, Given the matrix A  =   [ 1    -1         B =  [ 1    5        C = [ 1     2

                                                         -2    3 ]                8   -8 ]              3     4]

after solving AX + B = C, we get the value of x

x  =         [ 1        -21/5

              -1           8/5]  ..........(ii)

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The percentage of puffin eggs that hatch given in decimal form by the quadratic function, f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61, gives;

a. At 51 °F, 1.5% of the eggs will hatch

b. The temperature at which the maximum percentage of puffin eggs will hatch is approximately 49.5 °F

The maximum percentage of eggs that hatch is approximately 91.8 %

A quadratic function is a polynomial of the second degree (degree 2) such that the highest power of the variables in a quadratic function is 2

The quadratic function is presented as follows;

f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61

Where;

f(x) = The percentage of the eggs that hatch

x = The mean sea surface temperature of the area in degrees Fahrenheit

a. The percentage of the eggs that will hatch at 51° is therefore;

f(51) = -0.379•(51 - 46)² + 2.62•(51 - 46) - 3.61 = 0.015

The percentage of the eggs that hatch at 51° d is f(51) = 0.015 × 100% = 1.5%

b. The temperature for which the percentage of hatched puffin eggs is a maximum, is given by the maximum value of the quadratic function as follows;

At the maximum value of the quadratic function, f(x) = a•x² + b•x + c, we have;

x = -b/(2•a)

Therefore, where we have;

f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61

At the maximum value;

x - 46 = -2.62/(2×(-0.379)) = 1310/379

Which gives;

Second part;

The percentage of eggs that hatch at the temperature that gives the maximum percentage of eggs is the maximum percentage of eggs, which is found as follows;

f(46 + 1310/379) = -0.379•(1310/379)² + 2.62•(1310/379) - 3.61 ≈ 0.9179683

The maximum percentage of puffin eggs is therefore;

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Answer:

[tex]\frac{2y^5}{x^6}[/tex]

you have chosen the correct answer

___________________
900
___________________

Answer:

y = [tex]\frac{2}{5}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{5}[/tex] and line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{2}{5}[/tex] x - 3 ← equation of line

Answer: Yes it does.

Step-by-step explanation:

The discriminant of the quadratic equation is 11.1.

The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.

The discriminant is given as;

√b^2 - 4ac

Given;

3x^2 - 10x + 2 = 0

a = 3

b = -10

c = 2

We have;

√(-10)^2 - 4(-3) (2)

√100 + 24

11.1

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We are asked to find the values needed for the length CB

The coordinates of points C and B are given as

C(-a, -5b)

Recall that the distance formula is given by

For the given case,

Let us substitute these coordinates into the above distance formula

Therefore, the required values are

In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].

In mathematics, a line's slope, also known as its gradient, is numerical representation of  line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.

The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.

Let, x= -3, x1= -2, y= 5, y1= 2

Then,

slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]

now,

y= mx+c

y= [tex]\frac{-1}{3}[/tex]x+ 5

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If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep.  The rate that the water level changes when the water is 8 inches deep is: 3 /32π.

dv/dt = rate of cup  loss water per minutes=0.5

r = radius when the water is 8 inches deep

Hence,

20/10  = 8/r

r = 4

Volume of conical cup

v= 1/3πr²h

dv/dt=1/3πr² dh/dt

0.5 = 1/3π × (4)² dh/dt

dh/dt =3 /32π

Therefore the rate is 3 /32π.

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Answer - The constant proportionality constant of proportionality between the actual dimensions of the pavers and the model is 9. The proportionality constant for the area is 81.

Step-by-step explanation: To solve this problem, let's transform all quantities to the same units (inches)

The actual dimensions of the pavers are:

Then we divide the real dimensions between those of the model:

Width:

Long =

Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.

Actual length = model length * (9)

The "A" area of a paver is the product of its width multiplied by its length.

So:

(real width) * (real length) = ((9) Model width) * ((9) model length)

(real width) * (real length) =  * (Model width) * (model length)

(real area) = 81 * (Model area)

The proportionality constant for the area is 81.

Answer:

a) 225 meters

b) -162°C

Step-by-step explanation:

a) 5 meters per second for 45 seconds. 5*45 = 225 meters

b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C

Answer:

a) 225 meters.

B) -2 °

Step-by-step explanation:

a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.

So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225

B)  In 9 hours it cooled 18 degrees 18/9 = 2.  This means that is cooled 2 degrees per hour.

Distance from point (0, -3) to the line y = x - 1 = [tex]\sqrt{2}[/tex]

Given:

Point =(0,-3) => x = 0; y = -3

Line = y = x - 1 => a= 1, b= -1, c=-1

How is the distance from the point to the line calculated?

Let us consider the distance to be d,

[tex]d= \frac{ax+by+c}{\sqrt {a^{2}+b^{2}} } \\\\=\frac{1(0)-1(-3)-1}{\sqrt{2} } \\\\=\frac{2}{\sqrt{2} } = \sqrt{2}[/tex]

What is the distance from a point to a line?

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Answer:

D = 1.9

You can find for d by using the associative property of division (divide instead of multiply):

5.7 divided -3 = 1.9

Step-by-step explanation:

Hope it helps! =D

The perimeter and area of each of the composite figure is:

a. Area: 138.6 mm²; Perimeter = 50.27 mm.

b. Area: 120.5 cm²; Perimeter = 42.7 cm

c. Area: 521.1 mm²; Perimeter: 95.8 mm

Area of a circle = πr²

Area of a triangle = 1/2(base)(height).

Area of a rectangle = (length)(width).

The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.

a. The area of the composite figure = area of rectangle + area of two semicircles

Two semicircles = 1 circle

Area of the rectangle = (15)(5) = 75 mm²

Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²

The area of the composite figure = 75 + 63.6 = 138.6 mm².

Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)

Perimeter = 5(2) + 4(3) + (2πr)

Perimeter = 5(2) + 4(3) + (2π(4.5))

Perimeter = 50.27 mm.

b. Area = area of triangle + area of square + area of half circle

Area = 1/2(base)(height) + s² + 1/2(πr²)

Base = 5 cm

Height = 7 cm

s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]

r = 8.6/2 = 4.3 cm

Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))

Area = 120.5 cm²

Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)

Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)

Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))

Perimeter = 42.7 cm

c. Area = area of triangle + area of rectangle + area of half circle

Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)

Base = 32 - 20 = 12 mm

Height = 14 mm

Length = 20 mm

Width = 14 mm

r = 1/2(20) = 10 mm

Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))

Area = 521.1 mm²

Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)

Hypotenuse = √(12² + 14²) = 18.4 mm

Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4

Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4

Perimeter of the composite figure = 95.8 mm

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Answer:

40

Step-by-step explanation:

140 + x  = 3*(100-x)

140 + x = 300 - 3x

x + 3x = 300 - 140

4x = 160.

x = 40.

In linear equations, x = 9.5 Paula use the division property of equality.

What is a formula for linear equations?

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/b = c/d

The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

    -6x = 57      ( Divide both sides by -6)

-6x/6  = 57/-6

x = 9.5

Hence, we can conclude that the division property of equality.

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The complete question is -

Paula used these steps to solve an equation:

Step 1: -4(7 + 8) - 21 = 25

Step 2: -4r – 32 - 2x = 25

Step 3: -61 – 32 = 25

Step 4: -6x = 57

Step 5: x = -95

Between which two steps did Paula use the division property of equality?

The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.

So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.

Now on dividing 5.5 by 1.5,

Divisor = 1.5

Dividend = 4.5

(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3

Quotient = 3

On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.

So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

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Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.

This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.

Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.

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The number of binder on the bookshelf is one

The given parameters are:

Width of the bookshelf = 31 3/4 inches

Width of the binders = 28 inches

From the question, we understand that the binders are stacked side by side

This means that the quotient of the width of the bookshelf and the width of the binder will give the number of binders

So, we have

Number of binders = Width of the bookshelf/Width of the binders

This gives

Number of binders = (31 3/4)/28

Evaluate the quotient

Number of binders = 1.13

Approximate

Number of binders = 1

Hence, there is only one binder on the bookshelf

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The distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}[/tex]

It is given that:

The distance between each pair of points (-1,4) and (1,-1)

Two points are (-1,4) and (1,-1)

To estimate the distance between the above two points utilize the distance formula:

[tex]$\mathrm{d}=\sqrt{(1-(-1))^2+(-1-4)^2}$$[/tex]

[tex]$\mathrm{d}=\sqrt{(1+1)^2+(-1-4)^2}$$[/tex]

The arithmetic operation can be described as the operation in which we do the addition of numbers, subtraction, multiplication, and division

d = √[(2)² + (-5)²]

simplifying the above equation, we get

d = √(4 + 25)

d = √29 units

Therefore, the distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

The complete question is:

Find the distance between each pair of points (-1,4) and (1,-1)

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Answer:

b

Step-by-step explanation:

The graph was reflected over the y-axis.

Integers are 3, 4 and 5.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

Given Data

Let the three consecutive integers are :

x, x+1 and x+2

According to question
3(x+1) = 4 - 2(x+x+2)

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

3x + 3 = 4 - 4x - 4

3 = 4x-3x

x= 3

Integers are 3, 4 and 5.

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