The difference between two natural numbers is 8. The product of these natural numbers is 345. Find these numbers.



Can someone please provide a good explanation?

To find the formula of an exponential function from a table, you need to identify two points that fall on the exponential curve, and then use them to find the function's base.

The first step is to identify two points that fall on the exponential curve. Look for two pairs of x and y values that are not too far apart. For example, (1, 2) and (2, 4) are good choices.

Next, you use these two points to find the base of the function, which is the number b in the equation y = b^x. To do this, you take the ratio of the y-values and the logarithm of that ratio with base b. The logarithm of the ratio is equal to the difference of the x-values.

For example, if you have (1, 2) and (2, 4) you can find the base by taking log2(4/2)=log2(2)=1, which means that the base of the function is 2.

Now you have the base you can write the formula of the exponential function as y = 2^x.

It is important to note that you can use the same process with other bases, such as base 10 or base e, depending on the problem and the logarithm function you have available.

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If the salesperson has the given the assets and liabilities. The value of the liquid assets is: D. $613,570.

Liquid assets can be defined as those assets that can be turn into cash with a short period of time.

Now let find the liquid asset using this formula

Liquid assets = Retirement Portfolio + Investment

Where:

Retirement Portfolio = $473,906

Investments = $139,664

Let plug in the formula

Liquid assets = $473,906 + $139,664

Liquid assets = $613,570

Therefore we can conclude that the correct option is D.

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Answer:

-36

Step-by-step explanation:

3*-12=-36

Answer: -36

Step-by-step explanation:

The value of the evaluated iterated integral is 6.667.

As per the given data the iterated integral is [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex]

Here we have to evaluate the given iterated integral to find the value of [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex] .

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval (a, b) is expressed as

[tex]$\int_a^b f(x) d x=\mathrm{F}(\mathrm{b})-\mathrm{F}(\mathrm{a})$[/tex]

Here,

[tex]$\int=$[/tex] Integration symbol

a - Lower limit

b - Upper limit

f(x) - Integrand

dx - Integrating agent

Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]& \int_2^3 \int_0^2 x y^2 d x d y \\[/tex]

Integrate the given iterated integral.

We get:

[tex]& \int_2^3 x d x \int_0^2 y^2 d y \\[/tex]

[tex]& =\int_2^3 x d x\left(\left.\frac{y^3}{3} \right|_0 ^2\right) \\[/tex]

Substitute the limits in y.

[tex]& =\int_2^3 \frac{8}{3} x d x \\[/tex]

[tex]& =\left.\frac{8}{3\times2} x^2\right|_2 ^3 \\[/tex]

[tex]& =\left.\frac{4}{3} x^2\right|_2 ^3 \\[/tex]

Substitute the limits in x.

[tex]& =\frac{4}{3} \times 9-\frac{4}{3} \times 4 \\[/tex]

[tex]& =\frac{20}{3}[/tex]

= 6.667.

Therefore answer is 6.667.

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The standard form of the equation Y=(x-2)² + 4 is written as y=x²-4x+6.

A standard form serves as a gauge for how widely scattered the data is in comparison to the mean.

The data are grouped around the mean when the standard deviation is low.

A parabola with the point at its vertex represents this equation (2,4). On a coordinate plane, the equation can be graphed, revealing a parabola that extends upwards and has a minimum value of 4 at the point (2,4).

The factored version of the equation

Y=(x-2)² + 4 is y =  (x-2) (x-2) + 4

This representation of the equation demonstrates that it is the result of two binomials. When the common element is eliminated, the equation can be made simpler (x-2).

The equation is now more easily expressed as

y = (x-2) (x-2) + 4 = (x-2)² + 4.

Expanded form of the equation

Y=(x-2)² + 4 is expressed as y = x² - 4x + 6.

This representation of the equation demonstrates that it is the outcome of expanding (x-2)².

You may use this equation to determine the vertex of the parabola, which is (2,4). The vertex is the location where the parabola's value is at its lowest.

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Answer:

No it is not

Step-by-step explanation:

Hope it helps!

Answer:

perpendicular slope to line k is 4

Step-by-step explanation:

calculate the slope of line k using the slope formula

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

with (x₁, y₁ ) = (4, 3 ) and (x₂, y₂ ) = (8, 2 )

m = [tex]\frac{2-3}{8-4}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{4} }[/tex] = 4

the slope of a line perpendicular to line k is 4

The exponential form of 72 can be written as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] . It can be written using the prime factorization of the number.

The exponential form is an easier way of writing repeated multiplication involving base and exponents. To write the exponential form we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.

72 = 2 × 2 × 2 × 3 × 3 =  [tex]2^{3}[/tex] . [tex]3^{2}[/tex]

Therefore, the exponential form of 72 can be expressed as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] .

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It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 4.5 and 3.5

4.5 + 3.5 > 6.4

8 > 6.4

Now we add 4.5 and 6.4

4.5 + 6.4 > 3.5

10.9 > 3.5

Now we add 3.5 and 6.4

3.5 + 6.4 > 4.5

9.9 > 4.5

It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.

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The function g in vertex form is g (x) = –5x^2 – 3.

In this case, the parent function is:

f (x) = x^2

First, after the reflection across the x-axis, we will get:

f (x) = –f (x)

And, the function will be:

g (x) = –x^2

Then, vertically stretched by a factor of 5, we will get:

g (x) = –5x^2

Last, translated 3 units down, we will get:

g (x) = –5x^2 – 3

Thus, the vertex form of the function g will be:

g (x) = –5x^2 – 3

In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.

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No. [tex]3x^{2}[/tex] is not an exponential function. It is a quadratic function. In this, exponent is not a variable.

There is a variable in the exponential function called exponent. 3x would have been an example of an exponential function. In this function, the exponent is not variable, it is 2. Therefore this is a quadratic function, not an exponential one. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.

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An inequality is a relationship that compares two numbers or other mathematical expressions in an unfair manner. When comparing the sizes of two numbers on the number line, it is most frequently used. The graph of each equation or inequality is given the attachment.

The graph, visual depiction of statistical information or a functional relationship between variables. Graphs serve a predictive purpose because they can highlight broad trends in the quantitative behaviour of data. However, they can be inaccurate and occasionally deceptive as mere approximations.

Most graphs have two axes: a horizontal axis for a set of independent variables and a vertical axis for a set of dependent variables. A broken-line graph is the most typical type of graph, with time usually acting as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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His hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.

Per annum denotes yearly or annually. It is a phrasing used frequently to describe interest rates. In sentences like "I have a 4% mortgage loan" or "This bond pays interest at a rate of 6%," "per annum" is frequently left out.

An illustration is when a supplier offers a credit customer a 2% early-payment discount for paying an invoice in 10 days as opposed to the full amount in 30. In this instance, the supplier forfeits 2% of the invoice amount in exchange for receiving payment 20 days early.

We recalculate the amounts and multiply both the "2%" and the "20 days" by 18 to get the rate per year. The annual rate that results is roughly 36%.

Isa works 34 hours a week

There are total 52 weeks a years

In a year the time he works is = 52 × 34 h

                                                  =  1768 hours

His annual salary is $32,500

Then his hourly rate of income = 32500/1768

                                                    = 32500/1768

                                                    = $18.38

Thus, his hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.

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fractions are a way of expressing the part of a whole.

3 3/4 = 15/4

22 1/2 = 90/4

90/4 ÷ 15/4 = 6

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On solving the quadratic function x²+6x+8, the solutions x = -4 and x = -2 are obtained.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is - x²+6x+8

To solve the function first multiply - 8 ×  x² = 8x²

Take the LCM of  8x².

8x² = 2 × 2x × 2x

Now, we need to form such two numbers that if added or subtracted gives 6x and when multiplied gives 8x².

8x² = 4x × 2x

6x = 4x + 2x

Factorize the equation using the numbers obtained -

= x²+6x+8

= x²+ 4x + 2x + 8

= x(x + 4) +2(x + 4)

= (x + 4)(x + 2)

This gives the value as x = -4 and x = -2.

Therefore, the solution points are x = -4 and x = -2.

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The type of water-based ecosystem that can be found in all regions of North Carolina are Ocean Pond

A tiny body of quiet, pure water is called a pond. It varies from a river or stream since there is no flowing water in it, and it differs from a lake because it is only a tiny area and only 1.8 meters deep.

About 71 percent of the surface of the Earth is covered by the ocean, a vast body of saltwater. Oceanographers and nations throughout the world have historically classified the planet's ocean into four separate regions: the Pacific, Atlantic, Indian, and Arctic seas.

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Answer:

5:9

Step-by-step explanation:

just divide both sides by 5 and then you get the ratio 5:9

Answer: 5/9 g

Step-by-step explanation:

Since the value of x cannot be negative x value that makes line RQ tangent to the circle P at point Q is 6.

From the circle P, if Q is the tangent, It implies that at the tangent line, it is perpendicular to the radius.

Using Pythagorean theorem;

PQ² + RQ² = PR²

Where PQ = 9

RQ = 12

PR = (x + 9)

Applying (x + 9) to the formula

(9)² + (12)² = (x + 9)²

Using algebraic expression; (a + b)² = a² + 2ab + b²

x² + 18x + 81 = 36 + 144

x² + 18x + 81 = 225

x² + 18x + 81 - 225 = 0

x² + 18x - 144= 0

By employing the quadratic formula,

[tex]x =\frac{ -b+/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 1, b = 18 and c = -144

[tex]x =\frac{ -18+/-\sqrt{18^{2} - 4(1)(-144)} }{2(1)}[/tex]

[tex]x =\frac{ -18+/-\sqrt{324 + 576} }{2}[/tex]

[tex]x =\frac{ -18+/-\sqrt{900} }{2}[/tex]

[tex]x =\frac{ -18+/- 30}{2}[/tex]

[tex]x =\frac{ -18 + 30}{2}[/tex]

[tex]x =\frac{ 12}{2}[/tex]

x = 6

[tex]x =\frac{ -18 - 30}{2}[/tex]

[tex]x =\frac{-48}{2}[/tex]

x = -24

Knowing that the value of x cannot be negative then, the quadratic equation that yielded 12/2 = 6 makes the value of x = 6.

The complete question is:

What value of x would make Line R Q tangent to circle P at point Q? x =

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Answer:

x = 6

Step-by-step explanation:

edg 23

Integer multiplication is equivalent to repetitive addition, which is adding an integer a predetermined number of times. For instance, adding 4 three times results in the number 12 (4 + 4 + 4).

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.

A straight line of numbers is shown visually as a number line.

This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.

The collection of integers can be shown on a number line much like other sets of numbers.

Hence, Integer multiplication is equivalent to repetitive addition, which is adding an integer a predetermined number of times. For instance, adding 4 three times results in the number 12 (4 + 4 + 4).

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No, not every number is a multiple of 8.

Multiple:

A multiple is a number that can be produced by multiplying another number by an integer.  

Integer:

An integer is a whole number with no fractional part.

For example, 1, 2, 3, 4, and 5 are integers. The number 0 is also an integer because it is not divisible by any whole number greater than 1. The largest integer that can be represented as a fractional value is called the fractional part of the value.

A multiple of 8 is a number that can be divided by 8 with no remainder.

For example, 8, 16, 24, 32, etc. are multiples of 8, but 7, 9, 15, etc. are not.

So, every number cannot be a multiple of 8.

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Answer:

32123456789098765443

As per the given percentage, the recommended daily amount is 30 grams.

The term percentage in math is defined as a portion of a whole expressed as a number between 0 and 100 rather than as a fraction

Here we have given that a cup of cereal has 12 grams of fiber, which is 40% of the recommended daily allowance.

Then the recommended daily amount is calculated as,

Let us consider that x be the recommended daily amount.

Then it can be written as,

=> 12/x = 40/100

When we cross multiply the terms, then we get,

=> 40x = 1200

Then the value of x is calculated as,

=> x = 30

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The end behavior of a polynomial function can be determined by looking at the degrees of the terms in the polynomial.

Generally, the highest degree term will indicate the end behavior of the function. For example, if the highest degree term is x^2, then the end behavior of the function will be that it will approach positive infinity as x approaches positive infinity and it will approach negative infinity as x approaches negative infinity. This can be illustrated by the following calculation:

f(x) = x^2 + 4x + 8

As x approaches positive infinity, the x^2 term will become much larger than the other terms, causing the polynomial function to approach positive infinity.

f(x) → +∞ as x → +∞

Similarly, as x approaches negative infinity, the x^2 term will again become much larger than the other terms, causing the function to approach negative infinity.

f(x) → -∞ as x → -∞

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Answer: In math, 3 2 would typically be written as 3^2, which means "3 raised to the power of 2" or "3 to the second power." It is the same as 3 multiplied by itself, which equals 9.

In some contexts, 3 2 could also be interpreted as "3, 2" which would be read as "3 and 2" and it can mean a collection of 3 and 2 items.

Step-by-step explanation:

Answer: Let's set up 1/5 and 1/4 side by side so they are easier to see:

[tex]\frac{1}{5} x\frac{1}{4}[/tex]

The next step is to multiply the numerators on the top line and the denominators on the bottom line:

1 x 1

5 x 4

From there, we can perform the multiplication to get the resulting fraction:

1 x 1

5 x 4 = [tex]\frac{1}{20}[/tex]

The complete answer is below (simplified to the lowest form):

1/20

Convert 1/5 times 1/4 to Decimal

Here's a little bonus calculation for you to easily work out the decimal format of the fraction we calculated. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:

[tex]\frac{1}{20}[/tex] = 0.05

Answer: How you can isolate the term f/3 is to

subtract 22 from both sides.

Step-by-step explanation:

calculating backwards :

12:39 pm minus 1 hour 13 minutes = 11:26 am

the cake needs to get into the oven latest at that time.

caucuses further backwards :

11:26 am minus 26 minutes = 11:00 am

Evan has to start latest at 11:00 am to have the cake ready at 12:39 pm.

Answer:

Step-by-step explanation:

1.75+x=-9/2

7/4+x=-9/2

x=-25/4

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Inequality is the absence of an equality link between two expressions or values. So inequality emerges from an imbalance.

a) inequality represents the solution to the given inequality

such as

3b > 48

3b /3 > 48/3

b>16

b) inequality represents the solution to the given inequality

such as

M/7 > -56

7 * M/7 > 7 * -56

m>-392

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