Express the side length of a square as a function of the length d of the square’s diagonal. then express the area as a function of the diagonal length.

Answer:

1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

Step-by-step explanation:

We are asked to find the relationship between the 6s in 660,472.

Upon looking at our given number, we can see that 1st see is in 10 thousands place and 2nd 6 is in hundred thousands place.

Place value of 1st 6: 60,000

Place value of 2nd 6: 600,000

Let us compare our both numbers as:

We can see that 600,000 is 10 times greater than 60,000, therefore, 1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

Answer:

109

Step-by-step explanation:

Given that there is a sequence of numbers as

4,11,25,53,...

We have to find the next number.

To find the next number, let us see the pattern from the given four numbers

We have

I number = 4

II number = 4+7

III number = II number + 2(7)

Iv number = III number +4(7)

So if we guess this pattern continues the next number namely v number would be

V number = IV number +8(7)

=53+56

109

i.e. I number is added by 7, II number by 2(7), III number by 2^2(7)

hence next number 2^3(7)

Answer is 109

The next number in the sequence is:

As can be seen, the first number is a selected number, which in this case is four, to which seven are added to obtain:

Then double 7 is added to that number, that is 14, with which you get:

And to get the next number, double 28 must be added, which is 56, therefore:

By this reason, the next number in the sequence is 109.

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A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.

Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Answer:

[tex]\( f(x) + g(x) = -4x - 10 \).[/tex]

To find the domain of [tex]\( f(x) + g(x) \)[/tex], we need to consider the values of [tex]\( x \)[/tex] for which the function is defined. Since [tex]\( f(x) \)[/tex]  and [tex]\( g(x) \)[/tex] are both linear functions, their domain is all real numbers.

So, the domain of [tex]\( f(x) + g(x) \)[/tex] is [tex]\( \mathbb{R} \)[/tex] , which means that [tex]\( x \)[/tex] can be any real number.

Explanation:

To find [tex]\( f(x) + g(x) \)[/tex] , we simply add the functions [tex]\( f(x) \) and \( g(x) \)[/tex] together:

[tex]\[ f(x) + g(x) = (2x - 7) + (-6x - 3) \][/tex]

Now, let's simplify:

[tex]\[ f(x) + g(x) = 2x - 7 - 6x - 3 \][/tex]

[tex]\[ f(x) + g(x) = (2x - 6x) + (-7 - 3) \][/tex]

[tex]\[ f(x) + g(x) = -4x - 10 \][/tex]

The solutions to the given quadratic equation are x=1 and x=1.

The given quadratic equation is x²-2x+1=0.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

Here, a=1, b=-2 and c=1

Now, x = [2 ± √(4 - 4)]/2

x=2±0/2

x=1

With factoring, we get

x²-2x+1=0

x²-x-x+1=0

x(x-1)-1(x-1)=0

(x-1)(x-1)=0

(x-1)=0

x=1

Therefore, the solutions to the given quadratic equation are x=1 and x=1.

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Answer:

[tex]\frac{60}{100}[/tex]

Step-by-step explanation:

Here, the given expression,

18 cm per sec

That is, measure in 1 sec = 18 cm

∵ 1 minute = 60 seconds,

⇒ 1 second = [tex]\frac{1}{60}[/tex] minutes,

Also, 1 meters ( m ) = 100 centimeters ( cm ),

⇒ 1 cm = [tex]\frac{1}{100}[/tex] m,

So, the measure in [tex]\frac{1}{60}[/tex] minutes = 18× [tex]\frac{1}{100}[/tex] cm,

Thus, the measure in 1 minute = [tex]18\times \frac{60}{100}[/tex] cm

Hence, the conversion factors are used to multiply to 18 cm/s to get meters per minute is [tex]\frac{60}{100}[/tex]

In this composition, we first apply the function h, which is simply the identity function, to the input 4, resulting in 4. Then, we apply the function g to this result. As g(x) = 5x - 3, g(4) equals 17. Hence, (g◦h)(4) = 17.

To find (g◦h)(4), which represents the composition of functions g and h evaluated at x = 4, we first need to find h(4), then substitute the result into g(x).

Given h(x) = x, h(4) = 4.

Now, we substitute h(4) into g(x).

So, g(h(4)) becomes g(4).

Given g(x) = 5x - 3, substituting x = 4 into g(x), we get g(4) = 5(4) - 3 = 20 - 3 = 17.

Therefore, (g◦h)(4) = 17.

divide the two

40.8 / 8 = 5.1 gallons per container

The solution of the given inequality is z ≥ 3.1

The Graph of the solution of the inequality z - 4.7 ≥ -1.6 is attached below.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Given that the inequality;

z - 4.7  ≥  -1.6

Solving;

z ≥ 1.6 + 4.7

z ≥ 3.1

Therefore, The solution of the given inequality is z ≥ 3.1

The Graph of the solution of the inequality z - 4.7 ≥ -1.6 is attached below.

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The compound inequality will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil and each pencil can have a mass of 10.5 grams.

Explanation

Suppose, the mass of a single pencil in the pack is  [tex]x[/tex] gram.

So, the total mass of 5 pencils will be:  [tex]5x[/tex] grams.

Each package has a mass of 15 grams. So, the total weight of the pack of 5 pencils [tex]=(5x+15)[/tex] grams.

To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. So, the compound inequality will be..........

[tex]60\leq 5x+15\leq 95\\ \\ 60-15\leq 5x+15-15\leq 95-15\\ \\ 45\leq 5x\leq 80\\ \\ \frac{45}{5}\leq \frac{5x}{5}\leq \frac{80}{5}\\ \\ 9\leq x\leq 16[/tex]

So, the compound inequality to represent the mass of a single pencil in a pack will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil.

Answer: The manager sold the couch at $163.85.

Step-by-step explanation:

Since we have given that

Wholesale price of the couch = $113.00

If Jessica's Furniture Store marks up all furniture by 45%.

So, Increment in whole sale price is given by

[tex]\frac{45}{100}\times 113\\\\=\frac{5085}{100}\\\\=\$50.85[/tex]

So, the manager sold the couch at the price is given by

[tex]\$113.00+\$50.85\\\\=\$163.85[/tex]

Hence, the manager sold the couch at $163.85.

Final answer:

To determine the first time Carly and Matt will have a soccer game on the same day, we find the least common multiple (LCM) of 4 and 5, which is 20. Thus, they will both have a game on the 20th day.

Explanation:

The question is asking when Carly, who has a soccer game every 4th day, and Matt, who has a soccer game every 5th day, will both have a game on the same day. This is a problem that can be solved using the concept of the least common multiple (LCM). The LCM of two numbers is the smallest number that is a multiple of both numbers. To find when Carly and Matt will have a soccer game on the same day, we need to find the LCM of 4 and 5.

List the multiples of 4 (4, 8, 12, 16, 20, ...) and 5 (5, 10, 15, 20, ...).

Identify the smallest multiple that is common to both lists, which would be 20.

Therefore, the first day Carly and Matt will have a game on the same day is the 20th day.

Lev and Jim have a total of 100 in tens, and with Dawn's 9 ones added, they make the number 109.

Lev has 9 tens which is equal to 90 (because 9 times 10 equals 90). Jim has 1 ten which is equal to 10. When they put all their tens together, we add 90 and 10 to get 100. Dawn then adds 9 ones to the tens. To find the final number, we add Dawn's 9 ones to the previously combined tens, which is adding 9 to 100, resulting in 109. Therefore, by pooling together their tens and ones, they made the number 109.

An example of one possible outcome in the sample space:

[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]

[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]