The vertex of the graph is f(x) = |x-3|+6 is located at

The answer is -π

If you add π + (-π), you get 0 which is a rational number.

Adding 2 only results in changing the 3.14... to a 5.14... which is still an irrational number.

Adding 1/π only results in adding 1/3.14... to π which equals 3.45... which is still an irrational number.

Adding 0 doesn't change the original value at all so its still an irrational number.

Therefore, -π is the only logical answer.

Best of Luck!

Answer:

- pi

Step-by-step explanation:

Pi is an irrational number. We need to add an equal and opposite irrational number to get a rational number. pi +-pi = 0

That is rational

Adding anything else will still leave us with pi in our answer which is irrational

2+pi  

1/pi + pi =

0+pi

All have pi in the answer

To get an A, David must score at least 85 on the last test.

David has taken three tests so far, with scores of 89, 92, and 95. To find out what score he needs on the last test to achieve a total of at least 360 points, we first calculate the total points he has accumulated from the first three tests:

[tex]\[ 89 + 92 + 95 = 276 \][/tex]

Now, we subtract this total from the minimum total points required for an A:

Therefore, David needs to score at least 84 points on the last test to reach a total of 360 points. However, since test scores are whole numbers, we round up to the nearest whole number that David can actually achieve on the test. Thus, David needs to score at least 85 on the last test to ensure he gets an A.

Answer:

40 farms

Step-by-step explanation:

Given :

A mango farm contains 1250 mango trees.

Each tree produces an average of 160 mangoes .

To Find : No. of mango farms needed to produce 8,000,000 mangoes .

Solution :

1 farm contains 1250 mango trees

Each tree produces an average of 160 mangoes .

1250 trees produces mangoes = 1250 *160 = 200000.

⇒ 1 farm produces 200000 mangoes

Now to calculate  mango farms are needed to produce 8,000,000 mangoes .

No. of Farm produces 200000 mangoes = 1

So, farms needed to produce  8,000,000 mangoes  = 8000000/200000 = 40 farms.

Thus 40 farms are required to produce 8,000,000 mangoes during the summer.

Answer:

The decay factor is 0.88.

Step-by-step explanation:

The general form of an exponential decay function is

[tex]f(x)=ab^x[/tex]

Where, a is initial value and b is decay factor.

It is given a new truck that sells for $29,000 depreciates (decreases in value) 12% each year.

The initial value is $29,000 and decay factor is

[tex]1-r=1-\frac{12}{100}=1-0.12=0.88[/tex]

The exponential function is

[tex]f(x)=29000(0.88)^x[/tex]

Therefore the decay factor is 0.88.

The decay factor b for the truck, which depreciates 12% each year, is 0.88.

The decay factor, b, for the truck's depreciation can be calculated using the formula for exponential decay:

b = 1 - r

where r is the annual depreciation rate. In this case, the annual depreciation rate is given as 12%, or 0.12 in decimal form.

Now, let's calculate the decay factor:

b = 1 - 0.12

b = 0.88

So, the decay factor for the truck's depreciation is 0.88.

The decay factor is used to calculate the value of the truck after n years by raising b to the power of n and multiplying it by the initial value of the truck. The formula for the value of the truck after n years is:

[tex]\[ V(n) = P \cdot b^n \][/tex]

where P is the initial price of the truck, b is the decay factor, and n is the number of years.

In this case, the initial price P is $29,000, and the decay factor b is 0.88. If we want to find the value of the truck after, say, 5 years, we would use the formula:

[tex]\[ V(5) = 29000 \cdot (0.88)^5 \][/tex]

However, the question only asks for the decay factor, which we have already determined to be 0.88.

Option: B is the correct answer.

B.  The number of excluded values of a rational expression cannot exceed the degree of the denominator.

We know that a rational expression is a expression of the form:

[tex]\dfrac{p(x)}{q(x)}[/tex]

where p(x) and q(x) are polynomials.

Excluded value--

The excluded value of a rational expression are the values where the denominator of the expression is zero.

Also, the number of zeros of a polynomial is always less than or equal to degree of the polynomial.

Hence, the  number of excluded values of a rational expression cannot exceed the degree of the denominator.

         The answer is:

            Option: B

Final answer:

To find out how many pounds of untrimmed celery is needed to get 8 pounds of trimmed celery with a 75% yield, we divide the required trimmed weight by the yield percentage as a decimal. The calculation is 8 divided by 0.75, which equals approximately 10.67 pounds of untrimmed celery.

Explanation:

To determine the amount of untrimmed celery needed when a recipe requires 8 pounds of trimmed celery with a 75% yield, we use the yield percentage to find out how much the weight reduces during trimming. Yield percentage tells us how much of the original, or untrimmed, product remains after trimming. In this case, a 75% yield means that 75% of the untrimmed celery's weight will be left after trimming.

To find the amount of untrimmed celery, we set up the equation using the yield percentage (Y) of the untrimmed weight (U) that will result in the desired trimmed weight (T). The equation is T = U * Y/100. We can rearrange the equation to solve for U using the given values. So U = T / (Y/100), which gives us U = 8 / (75/100), resulting in U = 8 / 0.75.

After completing the division, we find that U equals 10.67. This means we need approximately 10.67 pounds of untrimmed celery to get 8 pounds of trimmed celery. Always remember to round according to the context, in most recipes a little more celery wouldn't be a problem, but it depends on the precision needed for the specific recipe.

The equation which is not necessarily true is that G'H' = 8 units.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraint.

Given that a polygon of GHIJ translates 8 units to the left to form polygon G 'H 'I 'J ' in the option it is necessary because GH is a side and G'H' will still be a side so they will be the same.

In option b G'G will be  8 units because the entire figure has shifted towards the left.

And the correct answer will be that G'H' = 8 units which are not true.

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Answer:

59 ft

Step-by-step explanation:

Given;

Then Darren's plane must have flown (2 × 20ft) = 40 ft

Amanda's plane would have flown (40ft + 19ft) = 59 ft

Amanda's plane flew 59 ft far.

The distance of the paper plane thrown by Amanda is given by the equation A = 59 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance of the paper plane thrown by Amanda be A

Now , the equation will be

The distance of the paper plane thrown by Rachel R = 20 feet

The distance of the paper plane thrown by Darren D = 2 x distance of the paper plane thrown by Rachel R

Substituting the values in the equation , we get

The distance of the paper plane thrown by Darren D = 40 feet

And , Amanda plane flew 19 ft farther than Darren plane Darren plane

Substituting the values in the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + distance of the paper plane thrown by Darren D

On simplifying the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + 40

The distance of the paper plane thrown by Amanda A = 59 feet

Hence , the distance is 59 feet

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A bar graph would be the best way to summarize this information for display the data.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Andrea surveyed her classmates asking what type of pets they have.

Hence To show this on graph bar graph would be the best way to summarize this information for display the data.

Because, Bar graphs show comparisons between distinct categories and display changes over time.

Thus, A bar graph would be the best way to summarize this information for display the data.

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The equation of the line is y + 2 = −3 (x − 1). The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The points from which the line passes are ( 0,1) and (1,-2). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2 - 1 ) / ( 1 )

Slope = -3

The equation of the line will be written as,

y - y₁ = m ( x - x₁ )

y +2 = -3 ( x - 1 )

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Answer:

false

Step-by-step explanation:

Number of days Julia took to learn 145 word is 21 days.

Given that, Julia knows 19 latin words. Each day, she learns 6 new words.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

Here, 145-19=126

Number of days = 126/6

= 21

Therefore, number of days Julia took to learn 145 word is 21 days.

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Option: A is the correct answer.

              The axis of symmetry is:

                      A.    x=3/2      

We are given a graph as:

[tex]y+3x-6=-3(x-2)^2+4[/tex]

and

[tex]y=-3(x-2)^2+4+6-3x[/tex]

and

[tex]y=-3[(x-2)^2+x]+10\\\\i.e.\\\\y=-3[x^2+4-4x+x]+10\\\\i.e.\\\\y=-3[x^2-3x+4]+10[/tex]

This equation could also be written in the form:

[tex]y=-3[x^2-3x+4-\dfrac{9}{4}+\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+4-\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+\dfrac{7}{4}]+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2-3\times \dfrac{7}{4}+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2+\dfrac{19}{4}[/tex]

Now, we know that for any general equation of the type:

[tex]y=a(x-h)^2+k[/tex]

The axis of symmetry of the graph of the equation is:

[tex]x=h[/tex]

Here we have:

[tex]h=\dfrac{3}{2}[/tex]

            Hence, the answer is: Option: A