Azlyn can ride her horse 15.2 miles per hour. She is in an endurance race that is 76 miles
long! How long should this race take her to complete?

After applying some properties of logarithm the correct expression for the given logarithmic equation we get is 3x = log₂ 10.

Use the concept of  logarithm defined as:

The logarithmic function is the opposite of the exponentiation of that function.

It can be mathematically defined as:

For [tex]x > 0 , a > 0[/tex], and [tex]a\neq1[/tex],

[tex]y= log_a x[/tex] if and only if x = ay

Then the function is given by

[tex]f(x) = log_a x[/tex]

Where a is the base of function.

The given expression is:

[tex]2^{3x} = 10[/tex]

Take log both sides,

[tex]\text{log } 2^{3x} = \text{log } 10[/tex]

Since we know that,

[tex]\text{ log} a^n = n\text{ log} a[/tex]

Therefore,

3x log 2 = log 10

Dividing both sides by 2

3x = log10/log2

Since we know that,

[tex]\text{log} _a b = \dfrac{\text{log}_c b}{\text{log}_c a}[/tex]

Therefore,

3x = log₂ 10.

Hence,

The correct expression is 3x = log₂ 10.

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Answer:

x = -6

y = 9

Step-by-step explanation:

The sum of two numbers is 3

x + y = 3

twice the larger number is 36 more than three times the smaller number

2y = 3x + 36

Divide both sides by 2

y = 1.5x + 18

substitute for y in the first equation

x + (1.5x + 18) = 3

2.5x = -15

divide both sides by 2.5

x = -6

Substitute for x in the first equation

-6 + y = 3

y = 9

The sum of two numbers is 3, and twice the larger number is 36 more than three times the smaller number. The number are x = -6 and y = 9.

A linear equation is an equation in which each term has at max one degree.

Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on a cartesian plane

with axes of those variables, give a straight line.

It is given that the sum of two numbers is 3.

x + y = 3

Also, twice the larger number is 36 more than three times the smaller number, then

2y = 3x + 36

Divide both sides by 2

y = 1.5x + 18

By substituting for y in the first equation

x + (1.5x + 18) = 3

2.5x = -15

now, divide both sides by 2.5

x = -6

Substitute for x in the first equation

-6 + y = 3

y = 9

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The total area of the room and the sitting room is 286.93 feet squared

The figure above is a composite figure as it has both rectangle and a semi circle.

The area of the figure(sitting room) is as follows:

total area = area of rectangle + area of semi circle

area of rectangle = lw

where

Therefore,

l = 15 ft

w = 14 ft

area of rectangle = 15 × 14 = 210 ft²

Area of semi circle = πr² / 2

Area of semi circle = 3.14 × 7² / 2

Area of semi circle = 3.14 × 49 / 2

Area of semi circle = 153.86 / 2

Area of semi circle = 76.93 ft²

Area of the sitting room and room= 210 + 76.93 = 286.93 ft²

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Use solving math

Link:

WWW.SOLVINGMATH.COM

Answer:

Step-by-step explanation:

I think it's b

Answer:

$49.14 is the total amount

$3.64 is the sales tax

Step-by-step explanation:

45.5 x 0.08 = 3.64

45.5 + 3.64 = 49.14

Answer:

Step-by-step explanation:

[tex]sin ~x=sin~x \times \frac{cos~x}{cos~x} =\frac{sin~x}{cos~x} \times cos ~x=tan~x*cos ~x[/tex]

Answer:

Subtract 1/3 from 2/3 dont forget to add the variable h!

1/3h + 11 = 8

-11            -11

1/3h = -3

Now we multiply by 3 on both sides

H = -9

Answer:

6

Step-by-step explanation:

Answer:

10 pieces with 8" left over

Step-by-step explanation:

[tex]8 \div \frac{3}{4} = 8 \times \frac{4}{3} = \frac{32}{3} = 10 \frac{2}{3} [/tex]

so there's 10 pieces and 2/3 of a leftover piece.

2/3 of a foot is

[tex] \frac{2}{3} (12) = 8[/tex]

so there are 8" left

Answer:

B and D

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

280/2016 * 13000000

answer is option d 2.8 million

The ANSWER is Four Digits

When you'll square root - 36000000 you'll get 6000 there are four digits in 6000

Answer:

$324.19

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Price = $475

Price tag down = 35%

Tax = 5%

So, price after tag down = $475 - ( $475 × 35%)

= $475 - $166.25 = $308.75

Now, we calculate tax value after price tag down,

Tax value = $308.75 × 5% = $15.44

So, we can calculate the bed cost by using following formula,

Bed cost = Price after tag down + Tax value

= $308.75 + 15.44

= $324.19

Answer: D) The sum of a number and twelve

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

Explanation:

r = an unknown number

r+12 = sum of the unknown number and 12

The term "sum" refers specifically to the result of an addition problem.

As another example, saying 2+3 = 5 has a sum of 5.

Answer:

Graph A

Step-by-step explanation:

Graph A flour is half the sugar

Graph B folur is twice the sugar

Graph C flour is equal the sugar

Answer:

Weathering

Step-by-step explanation:

Weathering is when water, ice, or wind wear/break down rock into smaller pieces and into sediments.

Answer:

Number of wooden carving = a

Total amount Sam spend = 1,200 + 4a

Total revenue of Sam = 15a

Number of wooden carving make to earn profit $4,300 = 500 carvings

Step-by-step explanation:

Given:

Sales price of each wooden carving = $15

Fixed cost = $1,200

Variable cost = $4 for each

Find:

Number of wooden carving make to earn profit $4,300

Computation:

Part 1

Assume

Number of wooden carving = a

Part 2

Total amount Sam spend = 1,200 + 4a

Part 3

Total revenue of Sam = 15a

Part 4

Total profit of Sam = Total revenue of Sam - Total cost of Sam

4,300 = 15a - [1,200 + 4a]

4,300 = 15a - 1,200 - 4a

11a = 5,500

a = 5,500 / 11

Number of wooden carving make to earn profit $4,300 = 500 carvings

Question:

5/6 x 3/4 as an array is?

Answer:

0.625 or 5/8

Step-by-step explanation:

Using Arrays to Explore Numbers

Arrays are useful models for multiplication which can be used in a variety of ways, ranging from highly structured lessons to games and open investigations.

An array is formed by arranging a set of objects into rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number as the other rows.

The following array, consisting of four columns and three rows, could be used to represent the number sentence 3 x 4 = 12, 4 x 3 =12, 3 + 3 + 3 + 3 = 12 and 4 + 4 + 4 =12.

Building Multiplication Facts and Tables

Arrays can be used for building multiplication facts in a meaningful way. Before drilling and memorising tables, children must understand how these facts are derived. For example, by progressively adding another column of three objects, children can build the three-times tables for themselves. This representation not only assists in understanding the process, but provides a visual image for children to draw upon as they begin to use and memorise the basic number facts.

Using arrays to explore larger numbers

Arrays can be helpfully used to explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3. This means that children can use their known number facts to work out calculations.

Here 13 x 5 = (10 x 5) + (3 x 5).

After a while drawing all the dots can get very tedious! The blank array then becomes a very useful tool for helping children model their thinking and work out how to do more complex multiplications in an informal way.

Here's a child using the blank array, as a thinking tool, to help them work out 15 x 14.

The blank array helps children to use other strategies, such as compensating, when carrying out multiplication. Here, to work out 34 x 9, the child has decided to do 34 x 10 and then take off the 34 x 1.

Beyond the blank array this 'dividing the multiplication into easy parts' strategy can be formalised into the grid method. The children can see how the 'abstract' grid method overlays the array and formalises the blank array into a standard form.

Division as the Inverse Operation of Multiplication

Of the four operations, division is the most troublesome for young students. Full understanding of division tends to lag well behind the other operations. For many children opportunities to explore the concept with concrete materials are curtailed well before they perceive the relationships between division and the other three operations. One such relationship, the inverse relationship between division and multiplication, can be effectively illustrated using arrays.

For example; 3×5=15  or 3 rows of 5 make 15, can be represented by the following array.

Looking at the array differently reveals the inverse, that is

15÷3=5  or 15 put into 3 rows makes 5 columns - or 5 in each row.

Language clearly plays an important role in being able to express the mathematical relationships and the physical array supports this aspect of understanding by giving the children a concrete image to talk about.

Placing the mathematics into a real-life context through word problems can facilitate both understanding of the relationship and its expression through words.

For example, "The gardener planted 3 rows of 5 seeds. How many seeds did she plant?" poses quite a different problem to "The gardener planted 15 seeds in 3 equal rows. How many seeds in each row?" yet both these word problems can be modelled using the same array.

Further exploration of the array reveals two more ways of expressing inverse relationships: 5×3=15 and 15÷3=5 .

The word problems can be adapted to describe these operations and highlight the similarities and differences between the four expressions modelled by the one array.

Using the blank array

Suppose you want to figure out 176 ÷ 8. We can set this up as an array with the value of one side missing.

Using known multiplication facts the value of the missing side can be built up.

So the child can see that 22 lots of 8 is the same as 176.

The array is a very powerful tool for supporting the development of children's thinking around both multiplication and division.

Answer:

area of a triangle

1/2 base ×height

1/2×15×8.5

=63.75cm ^2

Answer:

63.75cm^2 / square centimeters

Step-by-step explanation:

The area of a triangle is calculated by multiplying 1/2 times the base, times the height.

A = (1/2)(base)(height)

A = (0.5)(15)(8.5)

A =63.75

Answer:

solution set for x = { 4,5,6}

Answer:

2<x<12

Step-by-step explanation:

Firstly, look at this formula-

a-b<x<a+b

If we make 7, A, and 5, B, then the formula would be 7-5<x<7+5

So after you do the math it would be 2<x<12

Hence, the answer is 2<x<12

BTW if the answer is correct then can you please mark me brainlyest?

I'm only 9 years old

Thanks!

Answer:

236+590=

Step-by-step explanation:

236

+590

700+120+6=820 ɨ tɦɨռҡ

Answer:

4000$

Step-by-step explanation:

its the correct answer ...because its saving account

Answer:

Step-by-step explanation:

rational integer and real

it is rational because it is a perfect root of 2

it is a integer because every positive and negative numbers are integers.

Happy Pride Month!

Part 1:

You can solve the pair of equation graphically by writing the y-intercepts which are (0,-1) and (0,-5) Then follow the slopes of each line till the intercept. The slopes are up 2 over 1 and up 4 over 1 respectivily

Part 2:

When you graph these you get the answer of (2,3)

x is 2 and y is 3

Have a good day!

Answer:

Step-by-step explanation: