the numbers are 23 and 15.
Let's assume the two natural numbers as x and y.
Given:
The difference between the two numbers is 8: x - y = 8
The product of the two numbers is 345: xy = 345
From the first equation, we can express x in terms of y:
x = y + 8
Substituting this value of x in the second equation, we get:
(y + 8)y = 345
Expanding the equation:
y^2 + 8y = 345
Rearranging the equation to form a quadratic equation:
y^2 + 8y - 345 = 0
To solve this quadratic equation, we can factorize or use the quadratic formula. In this case, let's factorize it:
(y + 23)(y - 15) = 0
Setting each factor to zero, we have:
y + 23 = 0 --> y = -23
or
y - 15 = 0 --> y = 15
Since we are looking for natural numbers, we discard the negative value. Therefore, y = 15.
Now, substituting this value of y back into the equation x = y + 8:
x = 15 + 8 = 23
So, the two natural numbers are x = 23 and y = 15.
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What strategy do you use to multiply integers?
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).
What is an integer ?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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due tonight help please
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
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.
What is graph?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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y=(x-2)^2+4 standard form
The standard form of the equation Y=(x-2)² + 4 is written as y=x²-4x+6.
Definition of standard formA 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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Which water-based ecosystem can be found in all regions of North Carolina?
Salt marsh
Estuary
Ocean
Pond
The type of water-based ecosystem that can be found in all regions of North Carolina are Ocean Pond
What is pond in short answer?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.
What is ocean in short answer?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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What value of x would make Line R Q tangent to circle P at point Q?
x =
Since the value of x cannot be negative x value that makes line RQ tangent to the circle P at point Q is 6.
How to find x value?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
What is the exponential form of 72?
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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Write to ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
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:
How can you isolate the term ?
3
f
3
+22=17
?
?
on both sides.
Answer: How you can isolate the term f/3 is to
subtract 22 from both sides.
Is 3x 2 exponential?
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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Evaluate the iterated integral. The first integral is 0 to 2 and the second integral is 2 to 3. xy^2 dx dy. Please show step by step with detail. integral 0 to 2 xy^2 dxdy
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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Line k passes through points (4, 3) and (8, 2). What is the slope
of a line perpendicular to line k?
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
Isa earns a salary of $32,500 per annum. If he works an average of 34 hours a week calculate his hourly rate of pay
His hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.
What does per annum mean?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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What does 3 2 mean in math?
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:
Is every number a multiple of 8?
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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A cup of cereal ha 12 gram of fiber, which i 40% of the amount of fiber Jared’ doctor recommend he conume each day. How much fiber doe Jared’ doctor recommend he conume each day?
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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Can anyone help with 1/4 of what is 1/5?
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
Can the length 4.5 cm 3.5 cm 6.4 cm be the dimensions of a triangle?
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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Evan is going to make a cake for his mother's birthday. It will take 26 minutes to make the cake batter, and the cake needs to bake in the oven for 1 hour and 13 minutes. If Evan wants the cake to be out of the oven by 12:39 P.M., what is the latest time he can start making the cake batter?
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.
-4(1.75+x)=18. ;;;;;;;;;;;;;;;;
Answer:
Step-by-step explanation:
1.75+x=-9/2
7/4+x=-9/2
x=-25/4
y=x^2+6x+8 solve by completing the square.
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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In a company, 65% of the workers are women. If 945 people work for the company who aren't women, how many workers are there in all?
Answer:
32123456789098765443
6) Which inequality represents the solution to the given inequality? State the letter of the correct answer.
3b > 48
A.b>144
B. b ≤144
C. b≤ 16
D. b>16
Which inequality represents the solution to the given inequality? State the correct answer.
M/7 > -56
A) m>-8
B) m<-392
C) m>-392
D) m<-8
What is inequality?
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>16 is represents the solution to the given inequality.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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How to find the formula of an exponential function from a table?
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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7 less than 2 times a number is 3. what is the number?
Han is traveling at a speed of -12 miles per hour. If he starts at a position of zero, what will his position be after 3 hours?
Answer:
-36
Step-by-step explanation:
3*-12=-36
Answer: -36
Step-by-step explanation:
Is 2x3 is an exponential function?
Answer:
No it is not
Step-by-step explanation:
Hope it helps!
How can we determine the end behavior of a polynomial function?
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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The assets and liabilities of a salesperson are listed below.
Home Value $264,500
Retirement Portfolio $473,906
Credit Card Balances $58,236
Bank Loan $35,275
Mortgage $187,632
Car Value $22,750
Investments $139,664
Home Furnishings $23,100
What is the value of the liquid assets?
$139,664
$264,500
$473,906
$613,570
If the salesperson has the given the assets and liabilities. The value of the liquid assets is: D. $613,570.
What is liquid assets?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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The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 5, and translated 3 units down to create g. Identify g in vertex form.
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
What is translation?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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What fraction of 3 3/4 is 22 1/2
30 points
fractions are a way of expressing the part of a whole.
What is the fraction?To answer this question, we need to first convert both fractions into the same denominator. The fraction 3 3/4 can be converted to 15/4, and 22 1/2 can be converted to 45/2.Once both fractions are in the same denominator, we can divide the numerators by the denominators to get the solution. When we divide 15/4 by 45/2, the answer is 1/3. Therefore, 22 1/2 is one third of 3 3/4. To explain this in more depth, In the fraction 3 3/4, the numerator 3 is the number of parts of the whole, and the denominator 4 is the number of equal parts that make up the whole.Therefore, 3 3/4 can be expressed as 3 parts out of 4 parts, or 3 out of every 4. Similarly, 22 1/2 can be expressed as 22 parts out of 2 parts, or 22 out of every 2. When we divide 15/4 by 45/2, we are essentially asking what fraction of 3 3/4 is 22 1/2. To get the answer, we divide 15, the numerator of 3 3/4, by 45, the numerator of 22 1/2. This gives us the answer of 1/3. In other words, 22 1/2 is one third of 3 3/4.3 3/4 = 15/4
22 1/2 = 90/4
90/4 ÷ 15/4 = 6
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