-2y - 10 = x -10x
- y = −14​

Answer:

1)95

2)180

3)77

4)120

5)244

6)74

I think

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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The value of next two terms are,

⇒ 0 and - 60

A relation between a set of inputs having one output each is called a function.

Given that;

The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The function is,

⇒ f (n) = f (n - 1) + ___

For n ≥ 2

Now,

Since, The values are,

⇒ f (1) = 120,

⇒ f (2) = 60

And, The recursive formula is,

⇒ f (n) = f (n - 1) + b

For n ≥ 2

Substitute n = 2;

⇒ f (2) = f (2 - 1) + b

⇒ 60 = f (1) + b

⇒ 60 = 120 + b

⇒ b = 60 - 120

⇒ b = - 60

So, The recursive formula is,

⇒ f (n) = f (n - 1) - 60

Substitute n = 3;

⇒ f (3) = f (3 - 1) - 60

⇒ f (3) = f (2) - 60

⇒ f (3) = 60 - 60

⇒ f (3) = 0

Substitute n = 4;

⇒ f (4) = f (4 - 1) - 60

⇒ f (4) = f (3) - 60

⇒ f (4) = 0 - 60

⇒ f (4) = - 60

Thus, The next two term are 0 and - 60.

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Answer: Yes

Step-by-step explanation

Since the number being divided has a 0, it can be divided by 2

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

Now, According to the question:

Finding Slope From Two Points Formula

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,

m = slope of the line

x₁ = the x-coordinate of the first point

y₁ = the y-coordinate of the first point

x₂ = the x-coordinate of the second point

y₂ = the x-coordinate of the second point

Then rise from A to B = y₂ - y₁

Run from A to B = x₂ - x₁

Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)

Hence, we derived the slope formula.

Here are the steps to find the slope of a line given two points on it.

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The difference in the volumes of the sphere is 410.29 inches³.

A sphere is a three dimensional circle in which each point on the circumference is equidistant from its center. The volume of a three-dimensional object is the amount of space in the object.

The formula for the volume of the sphere = 4/3πr³

Where:

Difference in the volumes = volume of the larger sphere - volume of the smaller sphere

(4/3 x 5³ x 3.14) - (4/3 x 3³ x 3.14)

523.33 - 113.04 = 410.29 inches³

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The surface area of the pyramid is 568  square inches.

The surface area of the square pyramid is defined as the total area covered by the surfaces required to make the square pyramid. The area is the space occupied by the square pyramid in two-dimensional planes.

The formula to calculate surface area will be calculated by the formula below,

SA=B+12(P × l)

Here, B is the area of the base, P is the perimeter of the base, and l is the slant height.

SA = ( 8 x 8 ) + 12 ( 8 x 4 + 10 )

SA = 64 + 12 ( 32 + 10 )

SA = 64 + 12 x 42

SA = 568 square inches

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The graph of y is a straight line parallel to the x−axis through the point (0,1)

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The equation is Y = 1

A straight line in slope (m) and intercept (c) form is:

y = mx + c

y is a straight line of slope 0 and y- intercept of 1

y = 0.x + 1

y = 1

Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)

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Answer:

1. 6
2. 15

Step-by-step explanation:

4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48

- He sold: 120 : 8 = 15 pumpkins that day

Answer:

3$:4

Step-by-step explanation:

12/3= 4  9/3= 3

3$:4

The time taken for his return flight, in hours could be  4 hours.

What is time ?

Time is defined as the sequence of events that occurs which can be from past through present or to future.

Given,

Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose to Chicago.

If Benji's flight from Chicago to San Jose was 4.5 hours long

let,

chicago to san jose = san jose  to chicago+0.5

4.5 - 0.5  = san jose to chicago

san jose to chicago  = 4 hours

Hence,  How  long was his return flight, in hours is 4 hours.

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The sum of the natural numbers is (a) 25

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

Number type = natural number

Condition = 5 times bigger than their last digit

This means that

Number = 5 * Last digit

Because the number is a natural number, then the number cannot end in 0

This is so because 0 is not a natural number

Solving further, the last digit of the number is at most, 9

Using the above as a guide, we have the following:

The number is at most 45 i.e. 5 * 9

Also, it means that it can not have more than 2 digits.

The above highlights in a nutshell is that the number is a multiple of 5 that does not end in 0 and the last digit is 5

Since the last digit is 5, then we have the number to be 25 i.e. 5 * 5

Hence, the number is (a) 25

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The block weighed 8 grams. The other two blocks average have weighed the same amount as the first block, so they also weighed 8 grams each.

1. Joe has three metal blocks.

2. The weight of each block is the same.

3. Joe weighed one of the blocks against 8 grams.

4. The block weighed 8 grams.

5. The other two blocks must have weighed the same amount as the first block, so they also weighed 8 grams each.

Joe had three metal blocks that all weighed the same. He weighed one of the blocks against 8 grams, and it weighed exactly 8 grams. This meant that the other two blocks must also have weighed 8 grams each, since the weight of all three was the same. Joe was able to determine the weight of all three blocks with just one measurement.

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The triangles can be proved congruent by SAS theorem.

Two or more triangles are said to be congruent if and only if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.

To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.

Therefore. in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;

It can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.

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Answer:

15w^2

Step-by-step explanation:

The reason being is note how it says portrait, so assume the shape of a square, because it says 3 inches on all sides, and it also mentioned 1.5 times w, so in turn, 15w^2

Refer to the attached image.

Answer: There are three 0s

240 x 25 = 6000 and there are three 0s in 6000

Edna's phone can operate for up to 12 more hours without running out of battery. ​

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

fully charged

T = 18Hr

It has been 6 hours since Edna's phone was fully charged.

remaining battery =18- 6= 12Hr

x=12Hr

6 + x < 18

6 +x > 18

neither nor.

both equations are wrong.

6 +x = 18

Edna's phone can operate for up to 12 more hours without running out of battery. ​

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A logarithmic function is a type of inverse function.

A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).

The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y

One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.

Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.

It is also important to note that logarithmic function have some key characteristics such as:

The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.

The range of a logarithmic function is all real numbers.

The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.

A logarithmic function is increasing over its domain and concave down.

The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.

Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.

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Answer:

128cm²

Step-by-step explanation:

Formula to find area of rectangle is l×b

In order to find the area of the rectangle we need to apply that formula

[tex]A =lb[/tex]

[tex]A = 16[/tex]×[tex]8[/tex]

[tex]A = 128[/tex][tex]cm[/tex]²

Hence ,  the area of the given rectangle is 128cm²

The diameter of Mars is 6825 kilometers.

First we quantify angular size a = 8. 0 arcseconds in radians.

a = ( 8/ 3600) × (π/180)

a = 0.000039 radians

also, the distance from Earth to Mars in kilometres is 175,000,000 km

So, r = 175,000,000 km

We use the formula S = r x a to find the diameter of Mars

Substitute r = 175,000,000 and a = 0.000039 in above formula

S = 175,000,000 × 0.000039

S = 6825 km

Therefore, the diameter is 6825 km

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The slopes of function 1 and function 2 are respectively; -4 and 2. Thus, function 1 has a negative slope

The slope is simply defined as the change in the y-values divided by corresponding change in x-values.

1) Now, the formula for the slope between two coordinates is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Let us take two coordinates from the table as;

(0, 50) and (1, 46). Thus;

Slope = (46 - 50)/(1 - 0)

Slope = -4

2) The general equation for equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, we are given the equation as;

c = 2d + 10

Comparing to the standard form, we have;

Slope = 2

Thus, function 1 has a negative slope

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Answer:

From Least to Greatest

-9, 1/25, 0.25, 9/20, 11/20, 9

Step-by-step explanation:

Answer:

-9, 0.25, 9/20, 11/20, 9, 9 1/25

Step-by-step explanation:

You can convert everything in decimals or into fractions with a common denominator. Using what you have, you then put them in order.

I converted them all into decimals, getting:

-9, 0.55, 0.25, 0.45, 9, 9.04

Then I put them in order

-9, 0.25, 9/20, 11/20, 9, 9 1/25

a) A function w(t) to represent the amount of water in the pool using the two functions is w(t) = -3t + 5.

b) The pool will leak out the water when w(t)=0.

c) It will take 1.67 hours to leak out all the water from the pool.

d) Yes, functions f(t) and d(t) will intersect on the graphs when the pool stops leaking all the water out.

e) The domain of the functions  f(t), d(t) and w(t) are 0 ≤ t ≤ 1.67.

What are functions?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Subtract the amount flowing into the pool by the amount being drained out the pool to get the amount of water in the pool .

The given functions are -

Flowing: f(t) = t² + 8t + 9.

Draining: d(t) = t² + 11t + 4.

The amount of water in the pool is -

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Therefore, the function obtained is w(t) = -3t + 5.

When the condition is w(t) = 0 then, the pool will have leaked all the water.

Plugging in the values -

-3t + 5 = 0.

3t = 5

t = 1.67.

Therefore, the pool will leak all the water in 1.67 hours.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked. The graph is shown below.

The domain of a function is the set that contains all input values of the function. The input is the time in the given situation, so -

Time cannot be negative, hence t ≥ 0.

When all the water has been drained, everything stops, hence t ≤ 1.67.

Therefore, the domain of the function is 0 ≤ t ≤ 1.67.

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As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.

No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."

Here,

one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:

Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over

It can be shown that the halting problem cannot be resolved since it is indecisive.

As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.

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Answer:

the answer is neither

Step-by-step explanation:

An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is neither positive nor negative. Two integers that are the same distance from the origin in opposite directions are called opposites.

The linear functions for each situation are given as follows:

Makayla is closer than Addision when:

x < 5.

The linear functions in slope-intercept format for this problem are given as follows:

y = mx + b.

In which:

Hence the functions are defined as follows:

Makayla is closer when:

290 - 40x < 345 - 51x

11x < 55

x < 5.

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No, 8, 15, 17 are not Pythagorean triples.

No, 8 15 17 are not Pythagorean triples. A Pythagorean triple is a set of three positive integers a, b, and c such that a2 + b2 = c2. In other words, the sum of the squares of two integers must equal the square of the third integer.

In the case of 8 15 17, if we calculate the sum of the squares of the two smaller integers, 8 and 15, we get

[tex]8^2 + 15^2 = 64 + 225 = 289[/tex].

This does not equal the square of the third integer,

[tex]17^2 = 289,[/tex]

so 8 15 17 are not Pythagorean triples.

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Using the slope of the least-squares regression line, the interpretation will be: C) The slope is 0. 50, which means for each additional pound in weight, the child’s height will increase by 0. 5 inches.

A linear approach is linear regression, which is used to represent the relationship between a scalar answer and one or more explanatory factors in statistics. When there are many explanatory factors, multiple linear regression is employed; otherwise, simple linear regression is utilised. It is possible to predict the value of one variable using linear regression analysis and the value of another variable.

Predicting the dependent variable is what you want to do. The variable you are using to anticipate the value of the other variable is the one you are utilising as an independent variable. Lines of best fit are another name for regression lines. To demonstrate how several graph points might be connected, a line of best fit is used.

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Parallel lines are those lines that lie in the same plane and never intersect each other. They are equidistant from each other at every point and have the same slope.

Two lines are stated to be parallel when they do not meet at any point in a plane. This means that lines which do not have a common intersection point and never cross paths with each other are parallel to each other. The symbol used for representing parallel lines is ‘||’.

Two parallel lines are represented as:

AB║CD

That is line AB is parallel to CD.

The perpendicular length between the two parallel lines is always constant.

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The sum of the three sides of the triangle is 24.

The sum of three sides of a triangle is calculated using the formula S = a + b + c, where a, b, and c are the lengths of each side of the triangle.

To calculate the sum of three sides of a triangle, first measure the lengths of each side and assign a value for each side. For example, if the lengths of the sides are 6, 8, and 10 respectively, then the values for each side would be a = 6, b = 8, and c = 10.

Next, plug in the values of the sides into the formula S = a + b + c to calculate the sum:

S = 6 + 8 + 10

S = 24

Therefore, the sum of the three sides of the triangle is 24.

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