Solve for x in log3 81 = x.

The sum of all the edges in the solid shape is 24 unit.

Length is a measurement οf distance οr size. It can refer tο the physical extent οf an οbject, the size οf an area, οr the amοunt οf time sοmething takes. Length is measured in units such as centimeters, meters, feet, inches, yards, miles, and sο οn. Length is an impοrtant cοncept in mathematics and physics, used tο measure distances and calculate speed and οther quantities.

The sum οf all the edges in the sοlid shape is 24. This is calculated by adding the 4 edges οf the square (4 x 1 = 4) plus the 12 edges οf the 4 equilateral triangles (12 x 1 = 12).

Therefοre, 4 + 12 = 24.

Since all the sides οf the triangles and the square are equal in length, it can be said that all the edges in the sοlid shape are equal. This means that the length οf each edge is equal tο 24/24, οr 1. This means that the length οf each edge οf the sοlid shape is 1 unit.

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Complete question:

The solid shape below is made up four equilateral triangles and a square. What is the sum of all the edges in the solid shape?​

[Given each side is 1 unit]

Answer:

Step-by-step explanation:

2

Answer: $41.62

Step-by-step explanation:

let the price of the jacket be X

then the price of belt will be X-8.61

according to question

X + X-8.61 = 91.85

2X - 8.61 = 91.85

2X = 91.85 + 8.61

2X = 100.46

X = $50.23

cost of jacket = $ 50.23

cost of belt = $ 41.62

Hope this helps!!!

Answer: $41.62

Step-by-step explanation:

*j = jacket*  *b = belt*
belt + jacket = 91.85 (the total cost of the belt and jacket)
belt = jacket - 8.61 (the price of the belt is $8.61 less than the jacket)

We can use substitution to solve for the value of b.
Substitute the second equation into the first equation:
(j - 8.61) + j = 91.85

Simplify by combining like terms:
2j - 8.61 = 91.85
Add 8.61 to both sides:
2j = 100.46
Divide both sides by 2:
jacket = 50.23

b = j - 8.61

b = 50.23 - 8.61

b = 41.62

The ordered pair that would make the function true is option 4 (-1, -4).

As the name implies, an ordered pair is a set of items where the order in which they are placed is of particular significance. In coordinate geometry, ordered pairs are typically used to represent a point on a coordinate plane. They may also be used to depict aspects of a relationship.

The given equation of the graph is y = -0.25x - 2.

Substituting the coordinates in the options we have:

For (0, - 3):

y = -0.25x - 2

- 3 = -0.25(0) - 2

- 3 = -2 False.

For (4, 3)

y = -0.25x - 2

3 = -0.25(4) - 2

3 = -3 False

For (8, 4):

y = -0.25x - 2

4 = -0.25(8) - 2

4 = - 4

False.

For (-4, -1)

-1 = -0.25(-4) - 2

- 1 = -1

True.

Hence, the ordered pair that would make the function true is option 4 (-1, -4)

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Answer:

Let's suppose that Mr. Lee puts "x" apples into each box.

According to the first statement, when he puts an equal number of apples into 8 boxes, he has one apple left. This can be represented by the equation:

8x + 1 = n, where n is the total number of apples Mr. Lee has.

Similarly, the second statement says that when he puts the same number of apples into 5 boxes, he has 7 apples left. This can be represented by the equation:

5x + 7 = n

Now we have two equations with two unknowns (x and n). We can solve for x by setting the two equations equal to each other:

8x + 1 = 5x + 7

Subtracting 5x from both sides, we get:

3x + 1 = 7

Subtracting 1 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So Mr. Lee puts 2 apples into each box. To find the total number of apples he has, we can substitute x = 2 into either of the two equations we started with:

8x + 1 = 8(2) + 1 = 17

So Mr. Lee has 17 apples

Answer: 32 presents can be wrapped with 8 yards of ribbon

Step-by-step explanation:

Convert yards to inches

1 yard = 36 inches

8 yards = 288 inches

Divide 288 inches by 9 inches

288/9 = 32

Answer: You can wrap 32 presents with 8 yards.

Step-by-step explanation:

So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.

Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.

Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).

You can wrap 32 presents with 8 yards.

I hope this helped!

Step-by-step explanation:

$60÷8=$7.50

divide by 8 because 5+3=8

each book should of cost $7.50

Answer:

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12

Step-by-step explanation:

Let's use P, D, and R to represent the number of plain burgers, double cheeseburgers, and regular cheeseburgers, respectively.

Each plain burger requires 1 patty and 1 bun, so we can make a maximum of 12 plain burgers (since we have 12 buns).

Each double cheeseburger requires 2 patties, 1 bun, and 2 slices of cheese, so we can make a maximum of 9 double cheeseburgers with the available patties, buns, and cheese. (We have enough patties and buns for 18 burgers, but each double cheeseburger uses twice as many patties, so we divide the total number of patties by 2 to get the maximum number of double cheeseburgers we can make.)

Each regular cheeseburger requires 1 patty, 1 bun, and 1 slice of cheese, so we can make a maximum of 16 regular cheeseburgers with the available patties, buns, and cheese (since we have 16 slices of cheese).

To maximize our sales, we want to make as many of each type of burger as we can. Since we can only make 12 plain burgers, we should make all 12 of those. We can then make 9 double cheeseburgers (using 18 patties, 9 buns, and 18 slices of cheese), and 12 regular cheeseburgers (using 12 patties, 12 buns, and 12 slices of cheese).

So the final answer is:

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12

Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.

What are fractions?

Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.

Given,

Number of metres run Julia runs each week = 400

Time taken to run 400m dash in the beginning = 59 7/10 seconds

                                                                                = 597/10 seconds

Since the time is given in fractions, we have to do fraction subtraction for the following weeks.

Time taken in week 1 = 597/10 - 0.6 seconds = 597/10 - 6/10 = 591/10 seconds

Time taken in week 2 = 591/10 - 1/4 = 2364 - 10 / 40 = 2354/40 seconds

Time taken in week 3 = 2354/40 + 0.1 = 2354/40 + 1/10 = 2358/40

Time taken in week 4 = 2358/40 - 17/20 = 2358-34 / 40 = 2324/40

                                                                             = 581/10= 58 1/10 seconds.

Therefore Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.

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The figure is a composite figure compromising of a rectangle OHKN, two triangles ∆LMN and ∆HJK, and a semicircle of arc HP, hence the total area will be derived by the sum of area for each basic shapes.

We can observe from the figure that the lines OL and HK are parallel, likewise the lines OH and NK, so OHKN is a rectangle and its area can be simply derived by multiplying its length by the width.

LMN and HJK are two different triangles and their area can be derived by half of the multiple of their base and height.

we will be left with a semicircle of arc HP and the area is derived using the formula πr²/2, where r is the radius.

In conclusion, the area of the figure will derived by the sum of area for each basic shapes(rectangle OHKN, triangles ∆LMN and ∆HJK, and semicircle of arc HP).

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When given the area of a rectangle, and one of the sides, the unknown measure of the rectangle would be 40 meters

To find the area of a rectangle, you can use the formula:

A = l x w

where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle.

Seeing as you were given the area to be 2, 800 square meters and one of the sides measures 70 meters, the unknown measure of the rectangle would be:

70x Unknown = 2, 800

Unknown = 2, 800 / 70

Unknown measure = 40 meters

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Full question is:

Area = 2,800 square meters

Side A = 70 meters

Find the unknown measure of the rectangle

Handheld consoles are the most at risk of being discontinued compared to other types of consoles.

option A.

Handheld consoles have faced tough competition from the rise of mobile gaming on smartphones and tablets, which has impacted their market share and sales.

For example, Nintendo has faced challenges with their handheld consoles, such as the Nintendo DS and 3DS, which experienced a decline in sales due to the emergence of mobile gaming. As a result, Nintendo shifted its focus to the hybrid console, the Nintendo Switch, which can be used as both a handheld and home console.

That being said, it's important to note that the market for handheld consoles is still significant, and there are still popular handheld devices on the market such as the Nintendo Switch Lite and Sony's PlayStation Vita. The entertainment, interactive, and computer console markets also have their own unique challenges and opportunities, and each type of console has its own risks and benefits.

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Given:-

To find:-

Answer:-

The given figure is made up of a cone and a hemisphere , so to find the total volume , we would find the volume of cone and hemisphere individually and add them up to find the net volume.

Finding volume of cone:

The data we have is ,

As we know that the volume of cone is given by,

[tex]\implies V =\dfrac{1}{3}\pi r^2 h \\[/tex]

on substituting the respective values,we have;

[tex]\implies V =\dfrac{1}{3}\times 3.14 \times (9in.)^2 \times 14in .\\[/tex]

[tex]\implies V = \dfrac{1}{3}\times 3.14 \times 81in.^2\times 14in. \\[/tex]

[tex]\implies V = 1186.92 \ in.^3 \\[/tex]

Finding the volume of hemisphere:

As we know that the volume of hemisphere is given by;

[tex]\implies V =\dfrac{2}{3}\pi r^3 \\[/tex]

And here ,

So that;

[tex]\implies V =\dfrac{2}{3}\times 3.14\times (9\ in.)^3 \\[/tex]

[tex]\implies V =\dfrac{2}{3}\times 3.14\times 729\ in.^3 \\[/tex]

[tex]\implies V = 1526.04 \ in.^3 \\[/tex]

Hence the total volume will be ,

[tex]\implies V_{prop} = (1526.04 + 1186.92 )in.^3\\[/tex]

[tex]\implies V = 2712.96 \ in.^3 \\[/tex]

[tex]\implies \underline{\underline{ V_{prop}= 2713\ in.^3 }} \\[/tex]

Hence the volume of prop is 2713 in.³

and we are done!

Answer:

2713.0 in³  (nearest tenth)

Step-by-step explanation:

To calculate the volume of the prop, sum the volume of the cone and the volume of the half-sphere.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Therefore, the equation for the volume of the prop is:

[tex]V_{\sf prop}=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]

From inspection of the given diagram:

Substitute the values of r, h and π into the equation and solve for V:

[tex]\begin{aligned}\implies V_{\sf prop}&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (9)^2 (14)+\dfrac{2}{3} \pi (9)^3\\\\ &=\dfrac{1}{3} \pi (81) (14)+\dfrac{2}{3} \pi (729)\\\\ &=378 \pi+486 \pi\\\\ &=864 \pi\\\\&=864 \cdot 3.14\\\\&=2712.96\\\\&=2713.0\;\sf in^3\;\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the prop is 2,713.0 in³ to the nearest tenth.

Answer: 15 Liters (15L)

Step-by-step explanation:

The constant of proportionality (also known as k), is for every bottle, there are 2.5 liters. (k = y/x)

5 / 2 = 2.5 , 12.5 / 5 = 2.5, 20 / 8 = 2.5, etc.

So, we need to multiply 6 by 2.5, 6 * 2.5 = 15

For 6 bottles, there are 15 liters

these two events are dependant because the probability of the second event depends on the probability of the first event

the values of a, m, and x will be √5, 3√5, and 2 respectively.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A big right triangle has three other right triangles in it.

Since, In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem

For the smallest right triangle,

Hypotenuse = 3

thus,

3² = 2² + a²

a² = 9 - 4

a² = 5

a = √5

For the medium size triangle,

Hypotenuse = 3 + 6 = 9

Other side = 2 + 4 = 6

Base = m

Thus,

9² = 6² + m²

m² = 81 - 36

m² = 45

m = 3√5

For the biggest triangle,

hypotenuse = 3 + 6 + 3 = 12

Height = 2 + 4 + x = 6 + x

base = 5

Since the given triangle is congruent to the smallest triangle,

(6 + x)/ 12 = 2/3

6 +x = 8

x = 2

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Answer:

pemdas

Step-by-step explanation:

pemdas means Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction

you always want to go left to right

when using pemdas.

example 4^5 • (9-8)

you start from left to right

we would work in parentheses because that is what pemdas said to do.

The model of the exponential function is y = 3.40(1.86)^x

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

(6, 140) and (7, 260)

The exponential function for the model can be expressed as:

y = ab^x

Where

b = 260/140

b = 1.86

So, we have

y = a(1.86)^x

Substitute the known values in the above equation, so, we have the following representation

140 = a(1.86)^6

This gives

a = 140/(1.86)^6

Evaluate

a = 3.40

This means that

y = 3.40(1.86)^x

Hence, the function is y = 3.40(1.86)^x

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Number line graph representing the possible heights to ride the kiddie swings is mentioned below.

A number line is a visual representation of the real numbers, arranged in a linear sequence from negative infinity to positive infinity. It is a straight line that is divided into segments or intervals, with each interval representing a specific range of numbers.

The number line is typically drawn with zero in the center, and positive numbers to the right of zero and negative numbers to the left. Each point on the number line corresponds to a specific real number, with the distance between adjacent points representing a unit of one.

Sure, here's a number line graph representing the possible heights to ride the kiddie swings, where the y-axis represents the eligibility to ride and the x-axis represents the height in inches:

   |__________________|__________________|

                      0                                   48

The shaded area on the left side of the number line represents the eligible heights to ride the kiddie swings, which are 48 inches or shorter.

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follow the order

[tex]\pi /2[/tex] should be in between 0 and [tex]\pi[/tex], therefore it should be right in the middle. every 90 degrees, the circle increases by [tex]\pi /2[/tex] as well.

Answer:360

Step-by-step explanation:

Answer:

8, 39, 250, 1031

Step-by-step explanation:

(Needing a bit more context but if its sequences then:)

Answer:

↓ ↓ ↓

Step-by-step explanation:

Given: f(x)= x² -4x + 3

Find :-

a) f(1)

f(x)= x² -4x + 3

→ Substitute x with with 1:-

[tex]\tt f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt f(1)=1-4+3[/tex]

[tex]\boxed{\tt f(1)=0}[/tex]

_______________________

b) f(3)

f(x)= x² -4x + 3

→ Substitute x with with 3:-

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=3^2-4\cdot \:3+3[/tex]

[tex]\tt f(3)=3^2-12+3[/tex]

[tex]\tt f(3)=3^2-9[/tex]

[tex]\tt f(3)=9-9[/tex]

[tex]\boxed{\tt f(3)=0}[/tex]

_______________________

c) f(-1)

f(x)= x² -4x + 3

→ Substitute x with with -1:-

[tex]\tt f(-1)=\left(-1\right)^2-4\left(-1\right)+3[/tex]

[tex]\tt f(-1)=\left(-1\right)^2+4\cdot \:1+3[/tex]

[tex]\tt f(-1)=1+4+3[/tex]

[tex]\boxed{\tt f(-1)=8}[/tex]

_______________________

d) -f(1)

f(x)= x² -4x + 3

→ -f(1)

[tex]\tt -f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt -f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt -f(1)=1-4+3[/tex]

[tex]\boxed{\tt -f(1)=0}[/tex]

_____________________

Hope this helps! :)

The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

The linear equation is a mathematical statement that is used to find an unknown quantity or number in a given situation. In this, we used different types of variables to represent the unknown value.

To solve the following situations use different variables and solve them for the value of variables.

Here we have

Situation 1:

A freight company charges $ 1.45 per pound plus a handling fee of $ 3.25. A customer was charged $ 9.05 to ship a package  

Let 'x' be the weight of the package

=> 1.45x + 3.25 = 9.05

=> 1.45x = 5.8

=> x = 4

∴ weight of the package is 4 pounds

Situation 2

A tenant is charged $ 850 for rent on the 5th of the month. For every day they are early, they can deduct $ 15 from the rent. The tenant pays $ 805

Let the tenant pay the rent 'a' number of days early

=> 850 - 15a = 805

=> 15a = 45

=>  a = 3

∴ The tenant paid 3 days early.

Situation 3

Jordan pays $ 12.50 for a city bus pass lowering his bus fare to $ 1.50 per ride. In March, Jordan spent $ 39.50 to ride the city How many times did he ride the bus

Let Jordan ride for 'r' time

=> 12.50 + 1.50r = 39.50

=> 1.5r = 27

=> r = 18

∴  Jordan ride the bus 18 times

Situation 4

Jung purchased several video games priced at $ 29.95 and the shipping cost is $ 5.95. His total purchase is $ 185.65

Let Jung buy 'y' number of games

=> 29.95x + 5.95 = 185.65

=> 29.95x = 179.7

=> x = 6

∴ Jung purchased 6 video games.

Situation 5:

Milo is five inches shorter than his brother, Jayce. Milo is 42 inches tall

Let Jayce is 'x' inches and Milo is 'y' inches

=> y = x - 5

=> 42 = x - 5   [ From the data ]

=> x = 37 inches

Therefore,

The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

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The domain and range of h(n) are the set of whole numbers

The domain and the range of h(n)

Given that

The function h(n), represents the count of houses.

Both n and h(n) can take only whole values.

So, we have the domain and range to be the set of whole numbers

Evaluating h(5) and h(11)

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

The explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Given that

The function s(n), represents the count of segments.

Where the segment is twice the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

By the statement above, we have the growth pattern to be a proportional equation with a constant rate of change

The explicit function of s(n)

Based on the statements above, we have

s(n) = 2n

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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The number of days that he was in Europe will be 42 days.

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 Jordan went to Europe for vacation. He spent 1/3 of his time in Spain.

If he was in Spain for 14 days, the number of days that he was in Europe will be:

1/3 × x = 14

x = (14 × 3)

x = 42 days

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Jordan went to Europe for vacation. He spent 1/3 of his time in Spain. If he was in Spain for 14 days, how long was he in Europe?

Answer:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

Answer:

Hannah drinks 64 fluid ounces of water per day, which is equivalent to 0.5 gallons.

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]