Two suitcases are similar rectangular prisms. The smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long.

b. What is the volume of the larger suitcase? Round to the nearest tenth.

Answer:

Step-by-step explanation:

How many solutions does each of the following equations have?

6(x-3)+12=6x-6

6x - 18 + 12 = 6x - 6

-18 + 12 = -6

-6 = -6

0 = 0

Does the infinite series converge or diverge? The series converges.

If it converges, what is the sum?

a. 1/2 + 3/4 + 9/8 + . . . . .

The sum of the infinite series is -1

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]

Since ,[tex]\vert r\vert < 1[/tex], the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]

The sum of the infinite series is -1

What is an infinite geometric series?

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The combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Length of yellow fabric = 5 yards

Length of purple fabric = 8 yards

Let x be the cost of per yard purple fabric.

Then, cost of per yard yellow fabric = 2 + x

Now since, Total amount paid is $62.80

Therefore,

5(2 + x) + 8x = 62.8

expanding the brackets we get,

10 + 5x + 8x = 62.8

Solving we get,

10 + 12x  = 62.8

or, 12x = 52.8

⇒ x = 62.8/12

⇒ x = $5.23

Thus the cost of per yard purple fabric = $5.23

Similarly, cost of per yard yellow fabric = 2 + 5.23 = $7.23

Thus, combined cost of 2 yards of yellow and 1 yard of purple

fabric = 2*$5.23 + $7.23

= $10.46 + $7.23

= $17.69

Thus, the combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69

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The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

The measure of < LRQ is 112.5.

The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]

The sum of the measures of the central angles of a circle with no interior points in common is 360 .

Here, 360 is divided into 8 equal arcs and each arc measures

360/ 8 = 45.

Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.

[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].

Therefore, the measure of < LRQ is 112.5.

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Answer:

c

Step-by-step explanation:

its one full square and 1/4

The difference quotient of f(t) is: (6 - 2h - 4t)

And when h tends to zero is (6 - 4t)

Here we have the function:

f(t) = (2t)(3 - t)

Expanding the function we get:

f(t) = 6t - 2t^2

Now we want to get the difference quotient, which is:

(f(t+h) - f(t))/h

Replacing our function there, we will get:

( 6*(t + h) - 2*(t + h)^2 - 6*t + 2*t^2)/h

Now we can simplify the numerator to get:

(6*t + 6*h - 2t^2 - 2h^2 - 4*t*h - 6t + 2t^2)/h

(6h - 2h^2 - 4th)/h

Now divide by h so we get:

(6 - 2h - 4t)

Now, remember that in the difference quotient we need to take the limit when h tends to zero, in that limit we will get:

(6 - 4t)

That is the difference quotient of the function f(t).

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The slope of the line determined by the equation 2 x+y=5 is -2

A line's inclination or steepness can be determined using the slope formula. Finding the proportion of the change in the y-axis to the change in the x-axis allows it to be used to calculate the slope of any line.

The change in a line's "y" coordinate relative to its "x" coordinate is known as the line's slope.

The given equation =  2x + y = 5

It can be rewritten as: y = -2x + 5            (subtracted 2x from both the sides)

This is the slope-intercept form:  y = mx + c

where m is the slope

If we check our equation, here m = -2

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The system of equations that can be used to determine the cost for each pound of jellybeans and almonds is

5x + 3y = 16

2x + 6y = 22

The cost of one pound of jellybeans is $1.25.

The cost of one pound of almonds is $3.25.

Given this two equations:

5x + 3y = 16 equation 1

2x + 6y = 22  equation 2

Take the following steps to determine the required values:

Multiply equation 1 by 2

10x + 6y = 32 equation 3

Subtract equation 2 from equation 3

8x = 10

Divide both sides of the equation by 8: x = 10 / 8

x = 1.25

Substitute for x in equation 1:

5(1.25) + 3y = 16

6.25 + 3y = 16

3y = 16 - 6.25

3y = 9.75

y = 9.75 / 3

y = 3.25

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Answer:

x = 12

Step-by-step explanation:

NB. Supplementary angles / Angles of a straight line add up to 180°

180° - 124° (the given angle)

= 56°

This means that the other part of the angle must be equal to 56° ...in other words (4x + 8)° = 56°

(4x + 8)° = 56°

56° - 8°

= 48°

So 4x = 48°

-Divide both sides by 4 in order to get rid of the 4 infront of the x so that you're able to get x alone to solve.

4x ÷4 = 48° ÷4

x = 12

You can substitute 12 in the place of x to see if this is correct.

(4(12) +8)° = 56°

56° + 124° = 180°

....therefore x = 12

The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.

What is Translation ?

Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.

That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,

So, the measurement of segment A'B' would be 2 unit.

Verification :

Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,

Also, the rule of translation 6 unit right is,

(x,y) → (x + 6, y)

By the distance formula,

The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²

Thus, if A'B' is the transformed segment of segment AB,

Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)

So, the measure of segment A'B' =

√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²

Hence, the measure of AB = measure of A'B'.

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Answer:

c ) it either shows diameter or radius

d) I am not sure

C. When elements are represented in a Venn diagram (using circles), the placement of elements inside or outside the circles indicates their relationship to the sets being represented.

D. Yes, the elements written at the intersection of both circles form a subset of the two sets.

C. Place an element inside a circle to indicate that it is a member of the set indicated by the circle.

An element that is positioned at the intersection of two circles denotes an element that is a part of both sets that are symbolized by those circles.

Outside the circles: In a Venn diagram, an element that is positioned outside every circle does not belong to any of the sets being represented.

D. This is so because these components are a part of the intersection of the two sets and as such, they are a part of both sets. In set theory, all of the components that are shared by two sets are contained in their intersection. Due to their simultaneous membership in both sets, the elements at the intersection are a subset of both sets.

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Answer:

I might be able to help. :))

Answer:

B. Squaring, 2

Step-by-step explanation:

When you Square a number, doing the opposite is finding the square root. When squaring a number, you multiply the number by itself, the number it raises the the power of 2.

Answer:

10 + 204 y

Step-by-step explanation:

Answer:

13.

Step-by-step explanation:

8+[(84/12)-4]^2-7+3

= 8 + (7 - 4)^2 - 7 + 3

= 8 + 3^2 - 7 + 3

= 8 + 9 - 7 + 3

= 17 - 7 + 3

= 10 + 3

= 13.

The steps 5 and 6 in the construction of a new line segment  ensures the lengths are equal.

A line segment in geometry has two different points on it that define its boundaries. Alternatively, we may define a line segment as a section of a line that joins two points.

Below are the steps for copying a line segment:

Hence steps 5 and 6 are the steps in the construction of a new line segment which ensures the lengths are equal.

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The equivalent expression is negative eleven sixths times n minus one twelfth. Option C

Equivalent expressions are simply defined as expressions that have same solution but differ in the arrangement of their variables, terms, constants and coefficients.

From the information given, we can represent the expression as;

{ - 3 1/ 3n + 1/ 6 } +  { 1 3/ 6n - 3/ 12 }

Convert mixed fraction to improper fractions and expand the bracket

{ -10/3n + 1/ 6 } + { 9/6n - 3/ 12}

-10/3n + 1/ 6 +  9/6n - 3/ 12

Now, collect like terms

-10/3n + 9/ 6n + 1/ 6 - 3/ 12

Find the lowest common multiple

-20+ 9n/6 + 2 - 3 /12

-11n/ 6 - 1/ 12

Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C

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Answer:

C

Step-by-step explanation:

i had this and got it right

Equation of the line is y = mx + b , and the equation is x + 2y = 8

The equation of the line with the slope and y-intercept in the slope-intercept form is:

          y = mx+b

Where m = slope of the line

           b = y-intercept

           x,y = variable

Now we have to find an equation of the line whose slope (m) is -1/2 and y-intercept(b) is 4.

From the equation we have:

    y = (-1/2)x + 4

    2y = -x + 8

    x+2y = 8

Therefore the equation of the line is x + 2y =8 with slope m=-1/2 and y-intercept = 4.

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hope it will help you...good luck

The magnitude of the vector RS is found to be - 6√2.

The direction of the given vector RS is - Ф = 45° in the fourth quadrant clockwise

The algebraic representation of the distances among two points based on their coordinates (in coordinate system). The Pythagorean theorem is used to calculate distances between points in 2- and 3-dimensional Euclidean space using rectangular coordinates.

Now, in response to the question;

The coordinates of points R and S are (-3,3) and (-9,9), respectively.

The distance formula is described as follows for the points R and S:

RS² = (x₂ - x₁)² + (y₂ - y₁)²

RS = √[(x₂ - x₁)² + (y₂ - y₁)²]

R and S's coordinates are-

(x₁,y₁) = (-3,3)  and (x₂,y₂) = (-9,9).

Changing the values with in formula;

RS = √[(-9 + 3)² + (9 - 3)²]

RS = √[(-6)² + (6)²]

RS = √[36 + 36]

RS  = 6√2 (magnitude of the vector RS)

Now, estimate the direction of the vector RS.

A vector's direction is described by the angle it makes with such a horizontal line.

To determine the direction of a vector, use one of the following equations:

tan Ф = Δy/Δx

Where, x = horizontal change

and, y = vertical change

tan Ф = (y₂ - y₁)/(x₂ - x₁)

         = (-9 + 3)/(9 - 3)

tan Ф = -1

Ф = 45° angle of direction in the fourth quadrant clockwise.

As a result, the distance between coordinates R and s is observed to be 6√2, which is same as the magnitude of the given vector RS,

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The unknown variable's result of the equation 24² + x² = 26² is 10

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

24² + x² = 26²

576 + x² = 676

x² = 676 - 576

x² = 100

x = [tex]\sqrt{}[/tex]100

x = 10

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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The amount of springs the machine will make by 6 pm is; 96 strings

We are given that;

Amount of paper clips machine can make in an hour = 300 paper clips

Amount of strings the machine can make in an hour = 360 strings

Now, the machine starts working at 1pm and makes 450 paper clips.

Thus, time taken = 450/360 = 1.25 hours

This is at 2:15 pm

By 6pm, time taken would be 6:00 - 2:15 = 3:45 or 3.75 hours

Thus, number of springs made = 360/3.75 = 96 springs

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Answer:

1260 springs

SBS answer:

(pc = paper clips)

(s = springs)

300 pc = 1 hour

therfore

450 pc = 1.5 hours

1 pm + 1.5 hours will take us to 2:30 pm

2:30pm to 6:00pm will take 3.5 hours

360 c = 1 hour

so

1080 c = 3 hours

so

1260 = 3.5 hours

taking us to 6pm

Answer: a=√3    b=√6

Step-by-step explanation:

We have a right-angled isosceles triangle

Hence, a=√3

According to the sine theorem :

[tex]\displaystyle\\\frac{b}{sin90^0} =\frac{a}{sin45^0} \\\\\frac{b}{1} =\frac{\sqrt{3} }{\frac{\sqrt{2} }{2} } \\\\b=\frac{2\sqrt{3} }{\sqrt{2} } \\\\b=\frac{2\sqrt{3}(\sqrt{2)} }{\sqrt{2} (\sqrt{2}) } \\\\b=\frac{2\sqrt{6} }{2} \\\\b=\sqrt{6}[/tex]

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

Work Shown:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

C = area of the front rectangular face

C = length*width = 10*7 = 70

D = area of the face in back on the left

D = length*width = 6*7 = 42

E = area of the face in back on the right

E = length*width = 8*7 = 56

Total surface area = A+B+C+D+E = 24+24+70+42+56 = 216 square meters

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

Alternative Method:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

LA = lateral area = wall area

LA = (perimeter of the base)*(height)

LA = (6+8+10)*(7)

LA = 24*7

LA = 168

Total surface area = A+B+LA = 24+24+168 = 216 square meters

Answer:

Step-by-step explanation:

2500+150x=3000+125x

150x-125x=3000-2500

25x=500

x=500/25

x=20 mo

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

2500+150*20=3000+125*20

5500=5500 total paid after twenty months

Hope this helps! ;0

Answer:

Step-by-step explanation:

It is given that we need to find the correct measurement indicated by the arrows on the lines to the left​.

Now, let us have a look at the figure;

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

Work Shown:

M = number of miles

L = cost to rent a luxury car = 1.15M + 16.40

E = cost to rent an economy car = 0.80M+10.95

C = difference in price

C = L - E

C = (1.15M + 16.40) - (0.80M+10.95)

C = 1.15M + 16.40 - 0.80M-10.95

C = 0.35M + 5.45

Don't forget to distribute the negative to each term in the second parenthesis.

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

Optional Section:

Let's say you drove M = 100 miles as an example.

The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.

The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.

The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.

Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45

This means you pay $40.45 more if you go for a luxury car instead of an economy car.

The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers

Given data

size of rectangular plate = 5 cm by 3cm.

the length should be within   = 0.25 of 5 cm  

This means the length, L of the rectangular plate can be mathematically represented as

5 - 0.25 ≤ L ≤ 5 + 0.25

4.75 ≤ L ≤ 5.25

Area of rectangle =  Length × Width.

Width = 3

minimum length = 4.75

maximum length = 5.25

minimum length

= 4.75 * 3

= 14.25 cm^2

maximum length

= 5.25 * 3

= 15.75 cm^2

Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

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Answer:

(-15, -15)

Hope this helps!

Answer: 30,000 rounded to 1 significant figure

I hope this helped!