What is the smallest natural number value
for n if the solution for √56n is also a
natural number?

The closest estimate of x when the functions satisfy the condition f(x) = g(x) is 1.65

What is a function?

Function is a mathematical law that establishes the relationship between an independent variable and a dependent variable.

Given,

[tex]f(x) =[/tex] [tex]\log\x_{3} (2x)[/tex]

[tex]g(x) = -4x^{2} + 3x +7[/tex]

Now plotting both the graphs in Desmos, we got the result as in the below figures.

Given f(x) = g(x)

So from the graphs, we can find an intersecting point. This intersecting point is common to both f(x) and g(x)

Therefore from the graph, the closest estimate of x is 1.65.

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Answer: This is a geometric sequence and the common ratio is equal to 1/3.

Step-by-step explanation:

The given sequence is a geometric sequence with the common ratio 1/3.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

The given sequence is 9, 3, 1, .......

Arithmetic sequence is a sequence where the numbers are arranged in an order such that the difference of two consecutive numbers, called common difference, is a constant.

3 - 9 = -6

1 - 3 = -2

Difference is not constant, so not an arithmetic sequence.

3/9 = 1/3

1/3 = 1/3

Ratio is constant.

So the sequence is geometric sequence.

And the common ratio in the simplest form is 1/3.

Hence the sequence is geometric with common ratio 1/3.

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The speed of the object is 9.14 cm per day.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given that, An object is moving at a speed of 3 yards per month. we are asked to express this speed in centimeters per day.

For this, we will have to convert the units,

1 yard = 91.44 cm

3 yards = 91.44 × 3 = 274.32 cm

Therefore, we can say the object is moving 274.32 cm per month

Now,

If it moves 274.32 cm in one month,

Therefore, in day, it will move = 274.32 / 30    [1 month = 30 days]

= 9.144

Hence, the speed of the object is 9.14 cm per day.

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Answer:

[tex] - 2 - ( - 7) \\ = - 2 + 7 \\ = 5[/tex]

Answer:

5

Step-by-step explanation:

-2-(-7)

-2 + 7

= 5

Answer:

36%

Step-by-step explanation:

18/50 = 0.36 --> 36%

The probability that a student preferred a class trip to the zoo given they are in 11th grade is; 0.36

Total number of eleventh graders is; 32 + 18 = 50

Number of class trip to the zoo given they are in the 11th grade = 18

Thus, probability that a student preferred a class trip to the zoo given they are in 11th grade is;

P(11th grade trip to zoo) = 18/50

P(11th grade trip to zoo) = 0.36

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The answer to this question is B

Step-by-step explanation:

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

9514 1404 393

Answer:

  Any of ...

Step-by-step explanation:

The question is asking you what combinations of rotation, reflection, translation, and dilation will make the W have the position, orientation, and size of the M.

The image (M) is the same size as the preimage (W), so no dilation is involved.

The up-down orientation of the image is opposite that of the preimage, so reflection across a horizontal line, or rotation 180° will be involved. Depending on the line of reflection or the center of rotation, translation to the final image position may be required.

The preimage is symmetrical about a vertical centerline, so translation left or right can also be accomplished by reflection about a suitable vertical line.

_____

If you have trouble visualizing this, it can help to cut the letter from a piece of paper and manipulate it to model rotation, reflection, or translation.

Answer:

f(x + 2) = - 3x - 1

Step-by-step explanation:

substitute x = x + 2 into f(x) , that is

f(x + 2)

= 5 - 3(x + 2)

= 5 - 3x - 6

= - 3x - 1

Answer:

the answer to this problem is 165.85.

Step-by-step explanation:

After 0.6412 years the average for mobile device and television usage will coincide.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here the equations as  y=-9.11x+280x and  y=12.34x + 169.9 the period for which the averages are equal will be given by

9.11x+280x=12.34x + 169.9

       x   = 0.6412 years

Again, after 7 years in 2021 the respective averages will be                  9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes

Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.

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Answer:

100 lb

Step-by-step explanation:

1 lb = 16 oz

100 lb = 1600 oz

1600 oz > 1000 oz

Answer:

1000 oz = 62.5 lb

[tex]100 > 62.5[/tex]

100 lb is heavier

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The solution to the polynomial is x = -1, x = 1/2 and x = -1

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

2x³ - x² - 2x + 1

Expand

2x³ - x² - 2x + 1 = 2x³ - x² - 2x + 1

Factorize the expression

This gives

2x³ - x² - 2x + 1 = x²(2x - 1) - 1(2x - 1)

Factor out 2x - 1

2x³ - x² - 2x + 1 = (x² - 1)(2x - 1)

Express x² - 1 as difference of two squares

2x³ - x² - 2x + 1 = (x - 1)(x + 1)(2x - 1)

So, we have

(x - 1)(x + 1)(2x - 1) = 0

Solve for x

x = 1, x = -1 and x = 1/2

Reorder the solutions

x = -1, x = 1/2 and x = -1

Hence, the solution is x = -1, x = 1/2 and x = -1

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Answer:

x=30m

Step-by-step explanation:

Smaller triangle of sizes 26m and 10m...

using Pythagoras rule...let the middle line that so the triangle be y...

26² = 10²+y²

26²-10²=y²

y²=676-100

y²=576

y=√576

y=24m

the middle line is now 24m

now the larger triangle of sizes 18m, 24m and x...

using Pythagoras rule...

x²=24²+18²

x²=576+324

x²=900

x=√900

x=30m

Answer: 12 units

Step-by-step explanation:

∴ Area of Square = side length × side length

⇒144 = lengt²

⇒length = √144

⇒length = 12 units ANSWER

hope that helps...

Answer:

D

Step-by-step explanation:

i think you know this already but it's D!

The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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Answer:

I believe the answer is C. -10 < x <2

Step-by-step explanation:

In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. In light of this, the 2000 census indicates that 3,360 out of 12,000 houses use electricity for heating.

Because we've already done it 7 out of every 25 residences are heated by electricity, according to the 2000 U.S. census.At this rate, we must determine how many residences in a 12000-person neighbourhood would be heated by electricity.Let x be the number of homes in a neighbourhood that would be heated by electricity.There being a direct variation

The result is that , A neighbourhood of 12000 people with 3360 dwellings that use electricity for heating. In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. According to the 2000 Census, 3,360 dwellings out of 12,000 are heated by electricity.

[tex]$\frac{7}{25}=\frac{x}{12000}$[/tex]

[tex]$x={7 \times 12000}/{25}$$x=3360$[/tex]

As a result, 3360 households out of the 12000 in the community use electricity for heating.

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Let S be the amount of money the salesperson needs to sell in a week to earn the same amount with the two options. The salesperson earns 40 * $18 = $<<40*18=720>>720 with Option A.

We can set up the following equation to represent the amount of money the salesperson earns with Option B:

0.04S = $720

Solving for S, we find that the salesperson needs to sell $720 / 0.04 = $<<720/0.04=18000>>18,000 to earn the same amount with Option B.

Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.

If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.

If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.

If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.

Therefore, the smallest number of students for the teacher's claim to be true is three students.

It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.

Step-by-step explanation:

Answer:

Discounted price= $16.1

Step-by-step explanation:

Giving the following information:

Discount rate (d)= 30%

Regular price= $23

To calculate the discounted price, we need to use the following formula:

Discounted price= regular price*(1 - discount rate)

Discounted price= 23*0.7

Discounted price= $16.1

Answer:

Answer: Tomatoes If you multiply 10 x 0.69 (for onions) it would be 6.9If you multiply 100 x 0.99 (for tomatoes) it would be 99Lastly, if you multiply 100 x 0.69 (for lettuce) if would be 69Which are the most? Tomatoes.~ Hope this helps

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Check the picture below.

[tex]\sin(30^o)=\cfrac{\stackrel{opposite}{PQ}}{\underset{hypotenuse}{4}}\implies 4\sin(30^o)=PQ\implies 4\left( \cfrac{1}{2} \right)=PQ\implies 2=PQ[/tex]

Answer:

32

Step-by-step explanation:

I'm good at math hehe ggggggrhdgcdg

Answer:

24 ft

Step-by-step explanation:

10^2 = 100

6^2 = 36

100 - 36 = 64

[tex]\sqrt{64}[/tex] = 8

b = 8 ft

10+6+8 = 24

Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.

What is a function ?

Function can be defined as a relation , which relates an input to output is called as function.

In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,

however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.

Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.

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Answer:

20.5 and 21.5

Step-by-step explanation:

It says 2 significant figures so the least it can possibly be is 0.5 less and the most it can be is 0.5 more as if it was, lets say 20.4 it would round down to 20 not 21.

Answer:

315

Step-by-step explanation:

88.2 × 3.5742 = 315.24444

Answer: 315

For adults, there were 40 tickets sold, and for kids, there were 60 tickets sold.

There are several laws that regulate the sequence in which you should do the operations in math and algebra. The Commutative, Associative, and Distributive Laws are the three that are most frequently discussed.

Let x be the total number of adult tickets sold.

6.50 × x + 2.50 × (100 - x) = 410

6.50 × x + 250 - 2.50x = 410

4x = 410 - 250

x = 40

Hence,

a) 40 tickets were sold by adults, according to item

and

b) 100-40=60 tickets were sold to children.

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