Four students participate as a team in a 1000 m wacky relay race. In a wacky
relay race, the students each run a portion of the 1000 m length, but they do not
run equal lengths. Andrea and Billie run 1
8
and 1
5
of the total length, respectively.
Carol runs the average of what Andrea and Billie run. Dana runs the remainder
of the length.
Determine the fraction of the total length that Dana runs.

Answer:

1/12, 0.2, 22%, 1/4

Step-by-step explanation:

1/12 = 0.083333

1/4 = 0.25

22% = 0.22

0.2

So: 1/12, 0.2, 22%, 1/4

A diameter of a circle is any straight line segment that passes through the center of the circle and has endpoints on the circle.

The diameter of the circle is 28 inches.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, CF is a radius and the diameter is twice the radius.

Diameter of a circle = 2r

d = 2r

Where, r = 14

Diameter of a circle, d = 2r

Diameter of a circle = 2(14)

Diameter of a circle = 28

Therefore, the diameter of the circle is 28 inches.

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Answer:

[tex]y = - \frac{1}{5} x + 4[/tex]

Step-by-step explanation:

The slope-intercept form equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope.

[tex]\boxed{\text{Slope}= \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Slope of line, m

[tex] = \frac{6 - 3}{ - 10 - 5} [/tex]

[tex] = \frac{3}{ - 15} [/tex]

[tex] = - \frac{1}{5} [/tex]

Substitute value of m into equation:

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

Substitute any point the line passes through into the above equation:

When x= 5, y= 3,

[tex]3 = - \frac{1}{5} (5) + c[/tex]

3= -1 +c

c= 3 +1

c= 4

Substitute the value of c into the equation:

[tex]y = - \frac{1}{5} x + 4[/tex]

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Answer:

inverse

In math, a reciprocal is also called an inverse.

Step-by-step explanation:

Answer:

A correlative is another name for a reciprocal.

Correlative:

A degree into which 2 or more values are associated.

Answer:

74/100

37/50 (this is the answer if 74/100 is simplified)

Hope this helps :)

Explanation right below.

Step-by-step explanation:

The 4 in 0.74 ends in the hundredths place, so 74 will be put over 100 in a fraction to get 74/100. If 74/100 needs to be simplified then divide the numerator and denominator by 2 to get 37/50.

The required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left

Here,
Given expression,

13=-2(y-4)+3y

Approach 1,
13 = -2 (y - 4) + 3y
13 = -2y + 8 + 3y
13 = y + 8
13 - 8 = y
5 = y

Approach 2
13 = -2 (y - 4) + 3y
13 - 3y = -2y + 8
Adding 3y both side
13 - y = +8
Subtracting 13 on both sides
-y = -5

Multiplying by -1 on both sides
y = 5

Approach 3
13 = -2 (y - 4) + 3y
transposition of the variable to the left and contents to the right
2(y - 4) - 3y = -13
2y - 8 -3y = -13
-y -8 = -13
-y = -13 + 8
-y = -5
y = 5

Thus, the required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left

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

Work Shown:

5a^2

5(2)^2

5(4)

20

Explanation:

I replaced 'a' with 2, since a = 2. Then use PEMDAS to simplify the expression into one single number at the end. The value b = 6 won't be used at all since b is not found anywhere in the original expression.

Answer:

5a² = 20

Step-by-step explanation:

Given expression,

→ 5a²

Now we have to,

→ Evaluate the given expression.

We have to use,

→ a = 2

→ b = 6

Let's evaluate the expression,

→ 5a²

→ 5 × (a)²

→ 5 × (2)²

→ 5 × 4

→ 20 => {solution}

Therefore, the answer is 20.

The  linear equation that is being represented by the graph is  y=-3x +2.

A linear equation  can be described as the equation that has its highest power of the variable as  1 and this is been refereed to as the  one-degree equation.

It should be noted that  slope, of the the equation is usually in the form y=mx+b where mx is slope, however the linear equation usually have   one or two variables and when a  variable in a linear equation  has a power greater than 1 then it is no more linear.

Therefore, option A is correct.

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The order number that conveys a different information between the two analytical reports presented in tabular form is Order 102

The report that accompanies a similar question consists of two tabular forms of (analytical) reports, as follows;

Report 1.

Order. Stock # Qty

101. 27–671. 1

102. 27–781. 2

103. 27–090. 3

Report 2.

Order. Stock # Qty

101. 27–671. 1

102. 27–783. 2

103. 27–090. 3

From the above reports, by examination, we have at order 102

Stock number (Stock #) for Order 102 in Report 1 = 27–781

Stock number (Stock #) for Order 102 in Report 2 = 27–783

Therefore;

The order(s) that have (has) a different information between the reports is; Order 102

The correct option is therefore;

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first look at the equation you’re given. It’s in y-intercept form. The slope is 5.

A line perpendicular to it has a slope that is the opposite reciprocal, -1/5. You are told that the y-intercept of the line is 4, so the equation for the Since the slope of the line is -1/5, and the y-intercept is 4, the equation of the line is,

y = (-1/5)x + 4

Multiply both sides by 5 and put into standard form,

x + 5y = 20line in y-intercept form is y= -1/5x+4

When we have a linear equation in standard form, we can find the x- and y-intercepts of the corresponding line. This also allows us to graph it.

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Answer: 66 degrees for 1st angle

52 degrees for 2nd angle

62 degrees for 3rd angle

Step-by-step explanation:

3x+(x + 30)+(x + 40)=180

3x+x+30+x+40=180

3x+x+x+30+40=180

5x+70=180

5x=110

x=22

3x=

3(22)=66 degrees for 1st angle

x+30=

22+30=52 degrees for 2nd angle

x+40=

22+40=62 degrees for 3rd angle

Answer:

3x=66

x+30=52

x+40=62

66,42,62

Step-by-step explanation:

(3x)+(x+30)+(x+40)=180

5x+70=180

5x=110

x=22

3x=66

x+30=52

x+40=62

The car comes to a complete stop when t = 14secs.

What is velocity  ?

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. Put another way, speed is a scalar value, while velocity is a vector.

Given:

velocity v(t) = 0.5t^2 – 14t + 80

Differentiating the equation with respect to t to get the velocity,

we get ,

dv/dt = 2 x .05t - 14

when the car stops the velocity becomes 0.

Therefore,

2 x .05t - 14= 0

=> t = 14 secs

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Question:

A car's velocity is modeled by v(t) = 0.5t2 – 14t + 80 for 0 ≤ t ≤ 14, where the velocity is in feet per second and time is in seconds. When does the car come to a complete stop?

20 seconds

14 seconds

8 seconds

4 seconds

The answer should be $2.16.

Explanation:

1.5 pounds is 24 ounces

24 divided by 4 = 6

So, 0.36 x 6 = $2.16

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

Hope this helps!

Have a great day and God bless! :)

The cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the cost of 5 pens and 3 rulers is 90p the cost of 2 pens and 1 ruler is 33p. the cost of 3 pens and 2 rulers will be calculated as below:-

From the equations and solve:-

5p + 3r = 90p

2p + r = 33p

5p + 3r = 90p

-6p - 3r = -99p

Cost of one pen P = 9

The cost of the 1 ruler:-

2p + r = 33p

2 x 9 + r = 33

18 + r = 33

r = 33 - 18

r = 15

Cost of 3 pens = 3 x 9 = 27

Cost of 2 rulers = 2 x 15 = 30

Therefore, the cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

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Answer:

x= 36 y= 67 and z=77

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180

can be written as x+y+z=180

The sum of the measures of the second and third angles is four times the measure of the first angle.  

It can be written by:  x+y=4z

The third angle is 10 more than the second

It can be written as z=y+10

By solving the equations systems the above values can be determined.

x+y+z=180

x+y=4z

z=y+10

72/6=12

that means every tutor would have 12 students. if the academy has 120 students then we divide 120 by 12 to get 10. That means the academy needs 10 tutors.

For each line,  an equation in slope-intercept form :

y = (-1/4)x - 2 .

Summary of the lesson. The slope-intercept form is just a means of stating a line's equation so that the slope (steepness), as well as y-intercept (where the line crosses the vertical y-axis), as well as y-intercept (where the line crosses the vertical y-axis), are obvious. This form is also known as the y = MX + b form.

The slope, m, of a line represents its steepness. The slope of something like the line is however termed a gradient, sometimes. A line's y-intercept, b, represents the y-coordinate of something like the point where the line's graph intersects the y-axis.

To begin, use the slope formula to determine the average slope here between two points.

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

= (-1 - (-4))/ (-4-8)

= 3/(-12)

= -1/4

So the slope is -1/4.

We must now determine the y-intercept. This will be accomplished by converting a single of the points and indeed the slope through into point-slope form of something like a linear equation, which is y2-y1 = m(x2-x1).

Let’s plug in the point (8,-4).

So we get y-(-4) = (-1/4)(x-8) ⇒  y+4

= (-1/4)x + 2  ⇒  y

= (-1/4)x - 2.  

So y = (-1/4)x - 2  

For each line, write an equation in slope-intercept form y = (-1/4)x - 2.

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Answer:

Hello,

1/37

Step-by-step explanation:

Explanation on the picture

There will be total 6 pathways to directly connect to every other building

It is given that,

There are four buildings on the Mansfield High School Campus with a condition that none of the three can stand in straight line.

We need to find,

The total number of ways through which all the four buildings can be directly connected with each other in such a way that none can stand in straight line

Firstly, Let us consider that the buildings are arranged on the corner points of an imaginary square.

Then the number of ways through which all four buildings can be directly connected is by going straight from one building to other by following the imaginary square boundary lines = 4

the number of ways through which all four buildings can be directly connected is by going diagonally from one building to other by following the diagonal of the imaginary square = 2

Hence, The total number of pathways to directly connect to every other building = 4 +2 = 6

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Answer: 2 1/2 as a decimal is 2.5

2 as a decimal is 0.02

Step-by-step explanation:

The figure have AE = FD

given,

AB =CD

AB = AE + EB

CD = CF + FD

AE + EB = CF + FD

CF = EB given,

AE = FD

 if the triangle ABC and triangle DEF are identical. More specifically their side lengths and their angle measures are all the same, therefore we can consider them congruent figures. And that's exactly how you prove two figures are congruent by matching their corresponding parts.

SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side).

Triangles that have exactly the same size and shape are called congruent triangles.

Identifying Congruent Figures in the Real World

    2.If the corresponding sides of two figures with the same shape have the same length, then the two figures are congruent.

They are the same shape but not the same size. Non-congruent rectangles. These two polygons have matching sides equal but their matching angles are not equal and so they are not congruent. They are different shapes even though the sides are the same size.

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In fraction, June is 9/8 as old as David.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

The required fraction is (3/4) x (3/2) = 9/8

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Answer: 10 tutors

Step-by-step explanation:

Make the proportion:

72 students - 6 tutors

120 students - x tutors

Hence,

[tex]\displaystyle\\x=\frac{(120)(6)}{72} \\\\x=\frac{720}{72} \\\\x=\frac{(72)(10)}{72}\\\\ x=10\ tutors[/tex]

Answer:

26.5

Step-by-step explanation:

Planteamiento:

a - 1 = 3b

a + b = 35

Desarrollo:

de la primer ecuación del planteamiento:

a = 3b + 1

sustituyendo este último valor en la segunda ecuación del planteamiento:

(3b+1) + b = 35

4b = 35 - 1

4b = 34

b = 34/4

b = 8.5

de la segunda ecuación del planteamiento:

a + 8.5 = 35

a = 35 - 8.5

a = 26.5

Comprobación:

de la primer ecuación del planteamiento:

a - 1 = 3b

26.5 - 1 = 3*8.5

25.5 = 25.5

Respuesta:

ya que:

26.5>8.5

El número mayor es:

26.5

1:4 is the ratio of the pigeon's aorta radius to that of the goose.

So,

Canceling it to the simplest form:

So, the ratio is 1:4.

Therefore, 1:4 is the ratio of the pigeon's aorta radius to that of the goose.

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The description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation

The rule is given as

(x,y) --> (x-4, y+8)

The above rule represents a translation transformation

This is evident because it has the format

(x,y) --> (x + h, y + k)

By comparison, we have

h = -4

k = 8

This represents a 4 unit left translation and 8 units up translation

Hence, the description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation

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After solving the equation the value of x is -23, 25 in the equation 19+|x-1|=33

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.

⇒ 9+|x-1| = 33

For positive case

⇒ 9+|x-1| = 33

⇒ (x-1) = 33 - 9

⇒ x - 1 = 24

⇒ x = 25

For negative case

⇒9+|x-1| = 33

⇒ -(x-1) = 33 - 9

⇒ -x + 1 = 24

⇒ - x = 23

⇒ x = -23

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   A parabola having vertex at the origin and focus at (0, -1.5) is expressed by the following equation:

y = -x²/6

 A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

(x - 0)² = 4p(y - 0)

Focus

f = (0, 0 + p)

0 + p = -1.5

p = 0 -1.5

p = -1.5

(x - 0)² = 4*(-1.5)(y - 0)

(x)² = -6(y)

y = -x²/6

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