Find the distance between the points (1, 6) and (9, 0).

Solution :

Yes, the conveyors are in a proportional relationship.

Given,

A conveyor belt moves at a constant rate of 12 feet in 3 seconds.

A second conveyor belt moves 16 feet in 4 seconds.

There is a proportional relationship if the ratios of each pair of values are the same.

- First conveyor belt

12 feet in 3 seconds.

Ratio = 12 / 3 = 4

- Second conveyor belt

16 feet in 4 seconds.

Ratio = 16 / 4 = 4

Ratios are the same.

4 = 4

Thus the conveyors are in a proportional relationship.

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Finding the value of any term in a given sequence is known as an arithmetic sequence if each term in the sequence is equidistant from the terms before and after. To find any term in a sequence, we first have to find the pattern of the sequence. Then we can multiply the distance between any two terms by one less than the number of terms we are looking for. Adding this to the first term gives you the term you want.

Here the first term a=2,

Common difference d=4-2=2

We know that,

f(n)=a+(n-1) d

f (10) =2+(10-1) (2)

=2+(18)

=20

We know that,

Sn=n2[2a+(n-1) d]

∴S10=102⋅ [2(2) +(10-1) (2)]

=5⋅ [4+(18)]

=5⋅ [22]

=110

Hence, the 10th term of the given series is 20, and the sum of the first 10th term is 110.

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b = 0.02

divide both side by 5    

Answer:

I think that B equals 0.02

Using linear function concepts, it is found that since the two lines have the same slope, they are parallel.

A linear function is modeled by:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The first road goes through points (0, 16) and (20,0), hence the slope is:

m = (0 - 16)/(20 - 0) = -0.8.

The second road goes through points (0,8) and (10,0), hence the slope is:

m = (0 - 8)/(10 - 0) = -0.8.

Since the two lines have the same slope, they are parallel.

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From the given equation y = 30(0.92)d, she should expect 193 phone calls after a week.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "="..

If the number of phone calls she should expect can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days, then we can calculate the expected amount phone calls after a week.

To determine how much phone calls she should expect after a week, substitute the value of d.

y = 30(0.92)d

where d = 1 week = 7 days

y = 30(0.92)(7)

y = 193.2

Rounding off to the nearest whole number,

y = 193

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The values of the square numbers are:

a. -16

b. 16

c. 16

From the information given, we have the following expressions;

Let's write the squares in simpler form

-4² = - (4 × 4)

This is so because the square was only assigned to 4 and not the negative sign

(-4)² = - 4 × - 4

This is so because the square was assigned to both the negative sign and 4

4² = 4 × 4

This is so because the square was assigned to 4

Now, we have

- (4 × 4) = -16

- 4 × - 4 = 16

4 × 4 = 16

Thus, the values are - 16, 16 and 16 respectively.

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Answer:

D. 2 × 3​

Step-by-step explanation:

Let's take the prime factorization of 30 and 42

30: 2*15=2*3*5

42: 2*21=2*3*7

Notice any common factors?

GCF: 2*3=6

GCF: 6

The sum of the 8 terms of the series 1-1-3-5- ... -13 is -48

The given sequence is:

1,-1,-3,  . . -13

and there are 8 terms.

The related series of this sequence is:

1-1-3-5- ... -13

Notice that the series is an arithmetic series with:

first term, a(1) = 1

common difference, d = -1 - (1) = -2

last term, a(8) = -13

To find the sum of the series, use the sum formula:

S(n) = n/2 [(a(1) + a(n)]

Substitute n = 8, a(1) = 1, a(n) = a(8) = -13 into the formula:

S(8) = 8/2 [1 + (-13)]

S(9) = 4 . (-12) = -48

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The present age of the daughter is 10 years old.

The age of a woman is four times the age of her daughter.

let

x = age of the daughter

Therefore,

age of the woman = 4x

Five years later, the age of the woman will be three times the age of her daughter.

Therefore,

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

4x - 3x = 15 - 5

x = 10

Therefore, the present age of the daughter is 10 years old.

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Answer: x=+9

Step-by-step explanation:

18=3x-9    18-(3x-9)=0    3x+9+18=0    -3x+27=0

-3x=-27

x=-27/-3

x=+9

Hope this helps! :) Have a great day!  ^-^

Answer:

x=3

Step-by-step explanation:

18-3x=9

-18    -18      Subtract 18 from both sides of the equation to leave 3x by itself.

3x=9

/     /

3    3           Divide both sides by 3 to isolate x.

x=3   Final answer.

Suppose f(x)=2 x-5 and g(x)=|-3 x-1| Find the value. g(2)-f(0)

g(2)- f(0) = 12

Given:

f(x)=2 x- 5

g(x)=|-3 x-1|

To find g(2), substitute x=2 in g(x).

g(x)=|-3 x-1|

g(2)=|-3 (2)-1|

     =|-6-1|

     =|-7|

g(2) = 7

To find f(0), substitute x=0 in f(x).

f(x)=2 x- 5

f(0)=2(0)- 5

f(0) = -5

Now,  g(2)-f(0)  =7-(-5)

                        =7+5

                        =12

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After solving the equation, y = 20x is the value of y in (3/4)y=15 x

⇒ (3/4)y=15 x

⇒ y = 15x/(3/4)

⇒ y = 20x

To solve Linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The probability that the archer will hit the center which is 122 centimeters in diameter with 10 concentric circles whose diameters decrease by 12.2 centimeters as they get closer to the center is 1/100.

As given in the question,

Total number of concentric circle=10

Outer circle diameter=122centimeters

Diameter decrease by 12.2 centimeters as they get closer to the center

Diameter of inner most circle= 122-9(12.2)

                                             = 12.2centimeter

Probability that archer hit the center

= (Area of inner most circle)/ (Area of target)

= π(6.1)²/π(61)²

= {π(61)²/π(61)²}× 1/100

= 1/100

Therefore, probability that the archer will hit the center is 1/100.

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Answer:

5

Step-by-step explanation:

You add 5.49 until it almost goes past 30

Then count how many times you added

I hope this helps!

Answer: 76

Step-by-step explanation:

4 * 22 = 88

88-12 = 76

The ordering of the rational and irrational numbers from greatest to least is given by:

4 and 2/3, cube root of 51, -π, -17/5.

To order numbers on the number line, we have that:

If the integer parts are equal, we look at the decimal part, following the same logic as above.

For this problem, the numbers are given as follows:

Hence the ordering of the rational and irrational numbers from greatest to least is given by:

4 and 2/3, cube root of 51, -π, -17/5.

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The slope of a line can be positive, negative, zero, or undefined. The horizontal line does not rise vertically (y1 − y2 = 0), so the slope is zero, but the vertical line does not extend horizontally (that is, x1 − x2 = 0), so the slope is undefined. As mentioned above, the horizontal line has zero slopes. This does not mean that the horizon has no slope. Since the horizontal line is m=0, it is represented symbolically by the expression y=b. Functions defined by horizontal lines are often called constant functions. The slope of the vertical line is undefined. Any two points on the vertical line have the same x-coordinate, so the gradient cannot be computed as a finite number according to the equation

M=(y2-y1)/(x2-x1)

This is because division by zero is an undefined operation.

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Answer:

$953.70

Step-by-step explanation:

sum the parts of the ratio, 12 + 16 + 17 = 45 parts

divide the total number of toys by 45 to find the value of one part of the ratio.

1530 ÷ 45 = 34 , then

Priya makes 17 × 34 = 578 toys

she is paid $1.65 per toy, so is paid

578 × $1.65 = $953.70

The square root of 63.34 IS 7.95

The square root of decimal places can be found using long division method

The solution of this question in written form is attached so do check it out

first step is to find out the number whose square root is close but less than the given number as 7 in this case

second step add the divisor and the answer that is 7+ 7and make it our new divisor

Third step after carrying down the next pair of number write the number on once place that is 14_ which is 9 in our case  and keep following the same steps unit the desired answer

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Answer:

4

Step-by-step explanation:

let the number be n then four times the number is 4n and

4n + 3 = 19 ( subtract 3 from both sides )

4n = 16 ( divide both sides by 4 )

n = 4

then the number n is 4

The slope of the line containing (3,1) and (-2,1) is  Zero(0).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = 1 , [tex]y_{1}[/tex] = 1 , [tex]x_{2}[/tex] = -2 , and [tex]x_{1}[/tex] = 3 .

On substituting the values of variables in equation1, we will get

m = ( (1)-(1) ) / ( (-2)-(3) ) = (0/(-5)) = 0.

As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (7,-3) and (-8,-3) is  Zero(0).

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Answer:

268.571429

Step-by-step explanation:

Answer:

D (he got 85% right which is more than 75%)

Step-by-step explanation:

because if you half 6/40 you get 3/20, now if you x by 5 you get 100 so do the same to the top (3x5 = 15)

Now you know that he got 15/100 = 15% wrong

so if you do 100 - 15 you get 85, so he got 85% right

85% is greater than 75% so therefore it is option D

hope this helps :)

Using algebra, The product of two consecutive numbers is 18 more then 8 times a number

Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics

The two consecutive numbers are :

x and x+1

x(x+1) = 8(x+1) + 18

x^2 + x = 8x + 8 + 18

x^2 + x = 8x + 26

x^2 + x - 8x - 26 = 0

x^2 - 7x - 26 = 0

Substitute a=1,b=−7 and c=−26 into the quadratic formula

       - B  ±  √ B2-4AC

 x =   ————————

                     2A

Accordingly,  B^2  -  4AC   = 49 - (-104) =    153

Applying the quadratic formula :

             7 ± √ 153

  x  =    —————

                  2

x  =  ( 7 ± 3 ×  4.123 ) / 2

​

Two real solutions:

x =(7+√153)/2=(7+3√ 17 )/2= 9.685

or:

x =(7-√153)/2=(7-3√ 17 )/2= -2.685

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Answer:

365/83

Step-by-step explanation:

Distribute where we can

106x - 318 + 18 =23x + 69 - 4

Get variables on one side and constants on the other

106x - 23x = 65 + 300

Do the math

83x = 365

Divide both sides by 83

365/83

Answer:

x = 365/83

Step-by-step explanation:

53(2x−6)+18=23(x+3)−4

106x-318+18=23x+69-4

106x-23x=69-4+318-18

83x = 365

x = 365/83

A circle is a curve sketched out by a point moving in a plane. The radius, diameter, and circumference of the circle are 11.4 ft, 22.8 ft, and 71.6283 ft, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that radius of the circle is 11 2/5 ft. Therefore, the radius of the circle in a simplified way can be written as,

The radius of the circle = 11 2/5 ft

                                       = (11×5 + 2)/5 ft

                                       = (55 + 2)/5 ft

                                       = 57/5 ft

Now, the diameter and the circumference of the circle can be written as,

Diameter of circle = 2 × (Radius of the circle)

                              = 2 × 57/5 ft

                              = 114/5 ft

Circumference of circle = 2 × π × (Radius of the circle)

                                        = 2 × π × 57/5 ft

                                        = (114/5)π ft

Hence, the radius, diameter, and circumference of the circle are 57/5 ft, 114/5 ft, and (114/5)π ft, respectively.

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