Today you ran seven-eighths of a mile. Yesterday you ran three-fourths of a mile. How much farther did you run today?

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

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Answer:

[tex]21x \: - \frac{1}{3} \\ 3[/tex]

Answer:

x = 2

Step-by-step explanation:

4x + 3 = 11

(4x + 3) - 3 = 11 - 3

4x = 8

4x/4 = 8/4

x = 2

As you can see, to isolate x, we must do the opposite operations to both sides.

The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of bottles of mustard be represented as A

Now , the equation will be

The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle

Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup

Substituting the values in the equation , we get

The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle

On simplifying the equation , we get

The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )

The number of bottles of mustard used A = ( 1/6 ) of the bottle

Therefore , the value of A is 1/6

Hence , the number of bottles is 1/6

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A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.

We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.

These were something that every family owned at least one of.

A random selection of one of the families is made, and a computer is discovered there.

Check to see if there is a TV there as well.

union: # with computer, # with TV, - # with both, # with both

400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400

P(computer AND TV) = 200/400 = 1/2 ——-

P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6

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Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

4366 softballs will fit inside of a storage.

What is volume ?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Diameter of softball = 8.3 in

Radius of softball = 4.15 in

                              = 0.345 ft

Volume of sphere = 4/3 π r³

                = 4/3 π (0.345)³

                = 4/3 * 0.1289

                = 0.1718

Volume of cuboid = l * b * h

                              = 15 * 10 * 5

                              = 750

Number of softballs that can fit inside the storage = 750 / 0.1718

                                                                      = 4366

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Step-by-step explanation:

one side : 2x - 1

so, 5 sides (the perimeter is the sum of all sides) :

5 × (2x - 1) = 10x - 5

Answer:

E

Step-by-step explanation:

Let

A = # of slices Alice got

B = # of slices Bob got

C = # of slices Charles got

D = # of slices Darwin got

First, write equations based on given information:

A = 0

B = 2C

5C = D

D = C + 8

5C = D -> D = 5C

Now that we have two equations for D, we can set them equal to each other:

5C = C + 8

4C = 8

C = 2

Now just plug in the rest:

A = 0

B = 2(2) = 4

C = 2

D = 2 + 8 = 10

Add all solutions together to get (E) 16 slices

The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

Answer:

Step-by-step explanation:

The solution is the point where the 2 lines intersect.

If they intersect where x = 1 and y = 2 the solution is (1, 2).

2170 toys Jamal assemble altogether during his first 20 days.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Here, we have

Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.

We have to find how many toys did Jamal assemble altogether during his first 20 days.

We apply the arithmetic sequence formula and we get

tₙ = t₁ + (n-1)d

137 = t₁ + (20-1)(3)

t₁ = 80

To calculate the total number of toys that Jamal assemble in his first 20 days,

S₂₀ = (20/2)(2×80 + (20-1)(3))

S₂₀ = 2170

Hence, 2170 toys Jamal assemble altogether during his first 20 days.

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Answer:

Slope = -2  Y intercept is (0,4)

Step-by-step explanation:

To know whether Elena is correct or not, you need to find out the height of each stack of file folder.

Assume that all 200 files have the same height.

Let the height of each file folder be m inches.

So, by unitary method the height of each file folder would be,

m = Total height of stack / Number of file folders

here, the total height of stack = 5.125 inches

And the number of file folders = 200

So, m = 5.125 / 200

m = 0.0256 inches

But Elena guesses that each file folder is 0. 035 inches thick.

This means, Elena is wrong as the answer Elena gave is too large than the actual answer.

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Answer:

  -4/17

Step-by-step explanation:

You want the slope of the line described by the equation 20x +85y = 120.

Putting the equation in slope-intercept form by solving for y gives ...

  20x +85y = 120

  85y = -20x +120

  y = -20/85x +120/85

  y = -4/17x +24/17

The slope is the coefficient of x: -4/17.

The rate of change is -4/17.

Answer:

not sure if I understand but I believe you are talking about writing it down

In any version of Microsoft Word, type m2, then highlight the 2. Now press and hold Ctrl and Shift, then press the + key and it will be changed to superscript and will look like this: m2

The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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Answer:

a：20 km

b：384

Step-by-step explanation:

a：

[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]

[tex]x = 20[/tex]

b：

[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]

[tex]y = 384[/tex]

Answer:

37/56

Step-by-step explanation:

Answer: 3/5 = 0.6

Step-by-step explanation:

1. 2 2/5 x 1/4 = 12/20

2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5

3. 12/5 times 1/4 = 12/20

4. 12/20=3/5

The place with the highest temperature is Oslo.

The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .

The new temperature in Moscow is 11 degrees Celsius .

When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.

The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:

= - 4 . 3 - ( - 9 . 5 )

= - 4.3 + 9 .5

= 5. 2 degrees Celsius

The new temperature in Moscow is:

= - 7.9 - 3.1

= 11 degrees Celsius

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Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4

Step (i): The type of transformation change of the function

a) The translated left "c" units are x - c;

b) The translated right "c" units are x + c

Step (ii) The given function is translated "2" units right side, then the new function is

followed by the translated "4" units left sides and reflected across the y-axis.

Now the new function is h(x).

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Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

Answer:

240

Step-by-step explanation:

The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday

Answer:

278

Step-by-step explanation:

average = sum/count

count = 7 (7 days)

monday = 150

tuesday = 250

wednesday = 200

thursday = 250

friday = 350

saturday = 450

sunday = 300

sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950

mean = 1950/7 = 278.571428571 ≈ 278

A slope field for the given differential equation dy/dx = xy/2 at the 9 points indicated is shown below.

We know that a slope field represents the slope of a differential equation at certain vertical and horizontal intervals on the coordinate plane.

First we construct a table which contains the values of slope.

Consider given differential equation dy/dx = xy/2

where -1 ≤ x ≤ 1,

1 ≤ y ≤ 3

Let the slope be m

so, dy/dx = m

For x = -1, y = 1

m = (-1 × 1)/2

   = -1/2

For x = -1, y = 2

m = (-1 × 2)/2

   = -1

For x = -1, y = 3

m = (-1 × 3)/2

   = -3/2

For x = 0, y = 1

m = (0 × 1)/2

   = 0

For x = 0, y =2

m = (0 × 2)/2

   = 0

For x = 0, y = 3

m = (0 × 1)/2

   = 0

For x = 1, y = 1

m = (1 × 1)/2

   = 1/2

For x = 1, y = 2

m = (1 × 2)/2

   = 1

For x = 1, y = 3

m = (1 × 3)/2

   = 3/2

So, the table is:

x/y     1  2    3

-1     -1/2   -1      -3/2

0     0   0   0

1       1/2     1      3/2

Therefore, the slope field is as shown below.

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Answer:

1.Given points are:-

(1,2)=(x1/,y1)

(3,4)=(x2,y2)

Now,from two point formula,

y-y1=(y2-y1)/(X2-X1)×(X-X1)

or,y-2=(4-2)/(3-1)×(X-1)

or,y-2=2/2×(X-1)

or,y-2=1(X-1)

or,y-2=X-1

or, X -1-y+2=0

or,X-y+1=0 is the req. eqn in standard form

2.Given points are:-

(2,5)=(x1, y1)

(3,7)=(x2,y2)

Now, from two point formula,

y-5=(7-5)/(3-2)×(X-2)

or,y-5=2/1×(X-2)

or,y-5=2(X-2)

or,y-5=2X-4

or,2X-y-4+5=0

or,2x-y+1=0 is the req. eqn in standard form.

c.do similarly

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equations in slope- intercept form

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

(1)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) , then

4 = 3 + c ⇒ c = 4 - 3 = 1

y = x + 1 ( subtract y from both sides )

0 = x - y + 1 ( subtract 1 from both sides

- 1 = x - y , that is

x - y = - 1 ← in standard form

Use the same procedure for the next 2 questions

(2)

(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )

m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

y = 2x + c ← is the partial equation

using the point (2, 5 ) to find c

5 = 2(2) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = 2x + 1 ( subtract y from both sides )

0 = 2x - y + 1 ( subtract 1 from both sides )

- 1 = 2x - y , that is

2x - y = - 1 ← in standard form

(3)

(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )

m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then

y = - 5x + c

using the point (5, 2 ) to find c

2 = - 5(5) + c = - 25 + c ( add 25 to both sides )

27 = c

y = - 5x + 27 ( add 5x to both sides )

5x + y = 27 ← in standard form

A) The model that expresses the revenue R as a function of x is R(X) = -1/7x + 200

B) The domain of R is (-∞, +∞)

C) If 200 units are sold, then the revenue is $228.57

D) The quantity that maximizes revenue is 200 and the maximum revenue is $228.57

E) The price should the company charge to maximize revenue $228.57

Here we have given the function that can be model  that expresses the revenue R as a function of x is written as,

=> R(X) = -1/7x + 200

Here the domain value of R has take the value from negative infinity to positive infinity.

When we take the value of x as 200, then the revenues of the sold goods is calculated as,

=> R(200) = -1/7 (200) + 200

When we simplify this one then we get the value of R as

=> R = 28.57 + 200

=> R = 228.57

As per the given function the maximum number of units sold is written as 200, and the maximum revenue is written as 228.57

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The needed two values of x are: 59 and -12.

The difference between a sequence's maximum value and minimum value is referred to as the sequence's range.

A sequence's range is just a set that identifies the sequence. The set x1, x2, x3, and so forth is typically used to describe the range; it is also written as xn; n = 1, 2, 3,...

Given sequence of 8 numbers as: 28, 39, 21, x , 33, 38, 2, 45

Given range of above sequence: 57

Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that  the range remains at 57.

Case 1: x as minimum value of given sequence:

If so, then the maximum value is 45. Then-

range = maximum value - minimum value

57 = 45 - x

x = -12

Case 2: x as maximum value of the given sequence:

If so, then the minimum value of the sequence is 2. Then-

range = maximum value - minimum value

57 = x - 2

x = 59

Thus, the needed two values of x are: 59 and -12.

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Answer:

The Hypotenuse

Step-by-step explanation:

The Hypotenuse is the longest side of a Triangle.