When you divide a unit fraction by a whole number greater than 1, the quotient is always smaller than the unit fraction being divided. Why is this true?

There are an improper fraction of 29/20 ounces or a mixed fraction of one whole number and a fraction of 1/20 ounces in the mixture.

We shall add the two fractions 4/5 and 13/20, but firstly we find the lowest common multiple (LCM) of their denominators to enable us get a single denominator before simplifying the numerator.

LCM of 2 and 20 is equal to 20

20/5 = 4 and 20/20 = 1

4/5 + 13/20 = (4×4 + 1×13)/20

4/5 + 13/20 = (16 + 13)/20

(4/5 + 13/20) ounces = 29/20 ounces

Therefore, 29/20 is an improper fraction gotten by adding the fraction of ounces, but when expressed as mixed fraction is one whole number, and a fraction 1/20 ounces in the mixture.

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The equations that have the solution x = 5 are 25/x + 4 = 9 and 32 − 4x = 12

From the question, we have the following parameters that can be used in our computation:

x⁵ + 5 = 6

25/x + 4 = 9

32 − 4x = 12

11 + 6x = 22

3x + 1 = 9

18 − 2x = 9

Solving each equation, we have

Equation 1: x⁵ + 5 = 6

Evaluate the like terms

x⁵  = 1

Take the fifth-root

x = 1

Equation 2: 25/x + 4 = 9

Evaluate the like terms

25/x = 5

So, we have

5x = 25

Divide by 5

x = 5

Equation 3: 32 − 4x = 12

Evaluate the like terms

4x = 20

Divide by 4

x = 5

Equation 4: 11 + 6x = 22

Evaluate the like terms

6x = 11

Divide by 4

x = 11/6

Equation 5: 3x + 1 = 9

Evaluate the like terms

3x = 8

Divide by 3

x = 8/4

Equation 6: 18 − 2x = 9

Evaluate the like terms

2x = 9

Divide by 2

x = 9/2

Hence, the equations are 25/x + 4 = 9 and 32 − 4x = 12

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The length of the segment TQ is equal to 27 for the chord PQ intersecting another chord RS.

When two chords are intersecting each other inside a circle, then the product of the segments of one of the chord is equal to the product of the segments of the other chord.

The chords PQ and RS are interesting each other, so;

18(2x - 5) = 14(2x + 1)

36x - 90 = 28x + 14

36x - 28x = 14 + 90

8x = 104

x = 104/8

x = 13

the segment TQ is derived as;

2(13) + 1 = 27

Therefore, the segment TQ have a length equal to 27 for the chord PQ intersecting another chord RS.

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Answer:

The answer is $10

Step-by-step explanation:

It means she paid tax of $8.60 which is 6%

So,

(8.60 × 6) ÷ 100

51.6/100 = $0.516

Here, The tax was $0.516

Total cost of meal

= $0.516 + $8.60 = $9.116 (including tax)

(9.116 × 10) ÷ 100 = $0.9116

Total cost (including tip)

= $9.116 + $0.9116 = $10.0276 ≈ $10

Thus, Tara spend $10 altogether.

The slope of the line made by these given coordinates is 7/6.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.

Given coordinates of a graph. Since the coordinates are proportional thus, these coordinates represent the graph of the line as shown in the figure below.

From the general formula of the slope of the line (m) =  [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

The slope of the line = (14-7) / (12- 6)

The slope of the line = 7/6

Equation of the line id y = 7/6x + c

Since, the line passes through the point (18, 21)

21 = 7 /6 * 18 + c

c = 0

thus, the equation of the line is 6y = 7x

therefore, the slope of the line made by these given coordinates is 7/6 and this line passes through the origin.

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Answer:

-2

Step-by-step explanation:

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

-6+4

-2

Answer:

y=-3/2x+2

Step-by-step explanation:

3x+2y=4

Subtract 3x from both sides of the equation

2y=-3x+4

Divide both sides by 2

y=-3/2x+2

Change the original equation to slope intercept form (y=mx+b), by moving the x to the other side, and dividing by the y.

y=3/2x+4

33°

Since it's a right triangle that has an immediate 90° angle, we have 90°'s left to worry about. We have two angles to worry about it, and since one angle is bigger than the other by 24°, it means that the gap between them is 24°. After doing some mental math, you get 57° + 33°. The gap between them is 24°, and they add up to 90°. Finally, since you're looking for the smaller angle in this problem, then 33° would be your answer.

The approximate surface area of the cone is equal to: B. 103.6 in².

Mathematically, the surface area (SA) of a cone can be calculated by using this mathematical expression:

Surface area (SA) of a cone = πr(l + r)

Where:

Note: Radius = diameter/2 = 6/2 = 3 inches.

Substituting the given parameters into the surface area (SA) of a cone formula, we have the following;

Surface area (SA) of a cone = πr(l + r)

Surface area (SA) of a cone = 3.14 × 3(8 + 3)

Surface area (SA) of a cone = 3.14 × 3(11)

Surface area (SA) of a cone = 103.6 in²

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Answer:

(no solutions exist)

Step-by-step explanation:

15. Triangle FLW is not congruent with triangle YLW

16. triangle TNS is congruent with triangle UHS by AAS

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Angle - Angle - Side = AAS and Side - Angle - Side = SAS to ensure that the the triangles are congruent

The AAS have it that the two triangles being compared should have their two angles and the not included side being are equal hence 16 is correct

The SAS require that the two sides and the included angel are equal while in 15, the two sides and the not included angle is what was used making it wrong.

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In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

ABC is a right-angle triangle. And BD is perpendicular to AC.

To show the equations which are true,

Use the Pythagorean theorem,

(Hypotenuse)² = (base)² + (height)²

In triangle ABC,

AC² = AB² + BC²

In triangle ABD,

(AB)² = AD² + BD²

And in triangle BCD,

BC² = CD² + BD²

Therefore, options (2), (3), and (6) are correct. Those are the only equation satisfying the Pythagorean theorem.

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The original fraction is 10/19

Let the fraction be [tex]\frac{x}{y}[/tex]

Now , according to question

[tex]\frac{x+2}{y+5}[/tex] =[tex]\frac{1}{2}[/tex]

⇒ 2(x+2)=y+5

⇒2x-y-1=0-------(1)

and [tex]\frac{x-4}{y-1}[/tex]=[tex]\frac{1}{3}[/tex]

⇒3(x-4)=y-1

⇒3x-y-11=0------(2)

subtracting 1 from 2 we get

2x-y-1

3x-y-11

-  +  +

⇒ x=10

putting in (1)

20-y-1=0

y=19

∴ The actual fraction was 10/19

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The coordinates of point S of the line segment TS will be (8, - 19).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The coordinates of point T are ​(0​,5​). The midpoint is ​(4​,​-7).

Then the coordinates of point S will be given as,

(4, -7) = [(0 + x₂) / 2, (5 + y₂) / 2]

(8, - 14) = (x₂, y₂ + 5)

(8, - 19) = (x₂, y₂)

The coordinates of point S of the line segment TS will be (8, - 19).

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The number of cups for small pitchers = 2

The number of cups for large pitchers = 4.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two small pitchers and three large pitchers can hold a total of 16 cups of water.

And, The large pitcher holds 2 more cups of water than the small pitcher.

Now,

Let number of cups for small pitchers = x

And, The number of cups for large pitchers = y

Here, Two small pitchers and three large pitchers can hold a total of 16 cups of water.

So, We can formulate;

⇒ 2x + 3y = 16  .. (i)

And, The large pitcher holds 2 more cups of water than the small pitcher.

So, We get;

⇒ y = 2 + x  .. (ii)

Substitute the value of y from (ii) in (i), we get;

⇒ 2x + 3 (2 + x) = 16

Solve for x as;

⇒ 2x + 6 + 3x = 16

⇒ 5x = 16 - 6

⇒ 5x = 10

⇒ x = 2

And, From (ii);

⇒ y = 2 + x

⇒ y = 2 + 2

⇒ y = 4

Thus, The number of cups for small pitchers is 2

The number of cups for large pitchers is 4.

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The value of x is 4 inches.

It is a polygon having six faces.

The volume of a cube is side³.

We have,

The volume of the small cube is 64 cubic inches.

This means,

Side³ = 64 inches³

x³ = 64 inches³

x = 4 inches

Thus,

x is 4 inches.

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-3x +12 -6x +21 = 12 - 9x + 21

Here the Additive property of the Equality was demonastrated.

Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality. Algebraic equations involving real numbers can be resolved with the aid of the addition, subtraction, multiplication, and division characteristics of equality.

When the same quantity is added to both sides of an equation, the equation still holds true, according to the definition of the addition property of equality. This condition may be formally expressed as follows: for real numbers a, b, and c, if a = b, then a + c = b + c. Equations involving algebra and arithmetic can both leverage this characteristic.

-3x +12 -6x +21 = 12 - 9x + 21

Here the Additive property of the Equality was demonastrated.

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Answer

They would both be (0,-7)

Step-by-step explanation:

The reflection Is pretty much the opposite of the line on the graph. Think of it as looking in a mirror. 0 has no opposite, and -7 is the opposite of 7.

Option A is correct.

The given line has a slope of 5 which can be calculated by counting the change in the y-direction with respect to the change in the x-direction from the graph. And the y-intercept is -1

The equation of the line is,

y=5x-1 or

5x-y=1

Checking the point (0,0) into the equation we can see that 0<1, hence, the correct inequality is,

[tex]5x-y\leq 1[/tex]

Hence, the correct inequality is not listed.

Answer:

-1

Step-by-step explanation:

:)

1) write slope formula:

       rise        y2-y1

m= -------   =-----------

       run         x2-x1

put your problem in the y and x your problem

     1 - 2            -1

m=---------=  -----------=-1

      2 - 1            1

Also you don't even need need to do this entire you can just see what it is decreasing  or increasing by it it is a whole number

Answer:

The three properties of congruence are reflexivity, symmetry, and transitivity. These properties can be applied to segments, angles, triangles, or any other shape.

Answer:

True

Step-by-step explanation:

Answer: 3/4  =   18/24   4/6=16/24  \ Chandler swam more.

Step-by-step explanation:

Answer: The question states that Carla read 11/22 of the pocketbook yesterday and today. The phrase "of the pocketbook" is referring to the entire book, so 11/22 of the entire book has been read by Carla. This fraction represents the proportion or part of the book that has been read, and can be visualized as 11 out of 22 equal parts of the book have been read.

Final Answer = 11/22 of the pocketbook has been read by Carla.

Step-by-step explanation:

Madison and her brother drove around the perimeter of their neighborhood looking for their cat. The diagram above shows the path they drove. In total, 56 kilometers did they drive. This can be solved using the concept of rectangular perimeter.

The circumference of a form is known as its perimeter. One must sum the lengths of the all four edges of a rectangular or squares to determine its perimeter. In this instance, the rectangle's length is represented by x and its width by y. P = 2 (x+y), which is the perimeter.

The diagram is actually looks like a rectangle.

Here the length becomes = 10 km

and breadth = 18 km

The question mark here is: 18 -10 = 8km

so, perimeter = 2 (length + breadth)

perimeter = 2 (18 + 10)

perimeter = 56 km.

correct option: b

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The value of the W is 1.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

8 + 4w = 12

If add or subtract or multiply or divide the same number into both sides of an equation, then the equation remains the same.

Subtract 8 from both sides of the equation:

8 + 4w - 8 =12 - 8

4w = 4

Divide both sides by 4:

4w/4 = 4/4

w = 1

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The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In triangles ΔIHD and ΔFGE, we have

∠IHD ≅ ∠FGE        (Given)

The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.

Congruent means equal. Then The measure of the angle ∠IHD is equal to the measure of the angle ∠FGE.

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An inequality to show the number of tickets that need to be sold is;

x + y ≥ $400

Inequality is simply defined as the comparison and boundary for two non equal values. Thus, we can easily say that inequality compares the values that are non equal.

We are told that the owner wants to make $400 and sets boundary that;

The least amount to make = $400

The highest amount to make = infinite

This introduces relation in inequality as $400 or greater than $400.

Therefore the money made is counted as a combination from child tickets and adult tickets. If x is the amount that is made made through child tickets and y is the amount made from the adults, then we have;

x + y ≥ $400

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The  the area and perimeter of the shapes in terms of pi are 36pi - 72.

You should understand that the perimeter of the object is the distance round the object.

A circle's area is calculated as pi*r², so a semicircle is pi*r² / 2, and a quarter circle is pi*r² / 4.

A triangle's area is 0.5*base*height.

We have a quarter circle of radius 12, of which the area is pi*(12² / 4) = 36pi.

The area of the triangle ABC is 0.5*12*12 = 72,

This means that the shaded area is 36pi - 72.

Rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of AD is actually identical in area to the blank semicircle-shaped space to the left of BC.

So if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. The area of a square is s² = 24² = 676 cm².

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Correct question:

For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).