two show your work questions

[tex]f(x)=x^2-8\\\\g(x)=2x-5\\\\f(g(x))\to\text{instead of x write the equation of the function g(x)}\\\\f(g(x))=(2x-5)^2-8=(2x)^2-2(2x)(5)+5^2-8\\\\=4x^2-20x+25-8=4x^2-20x+17\\\\\text{used}\ (a-b)^2=a^2-2ab+b^2[/tex]

[tex]g(f(x))\to\text{instead of x write the equation of the function f(x)}\\\\g(f(x))=2(x^2-8)-5=(2)(x^2)+(2)(-8)-5=2x^2-16-5=2x^2-21[/tex]

Two-fifths of 1/4 acre is [tex]\(\frac{1}{10}\)[/tex]  acre planted in orange trees.

Sure, here's a detailed stepwise solution with explanation:

1. **Understand the problem**: The Avocados own a 1/4 acre orchard, and two-fifths of the orchard is planted in orange trees. We need to find the fraction of an acre planted in orange trees.

2. **Identify the fractions**: Let's represent the fractions given in the problem:

  - Fraction of the orchard planted in orange trees: [tex]\( \frac{2}{5} \) - Total acreage of the orchard: \( \frac{1}{4} \)[/tex]

3. **Multiply the fractions**: To find the fraction of an acre planted in orange trees, we multiply the fraction of the orchard planted in orange trees by the total acreage of the orchard.

4. **Perform the multiplication**: Multiply the fractions:

  [tex]\[ \frac{2}{5} \times \frac{1}{4} \] \[ = \frac{2 \times 1}{5 \times 4} \] \[ = \frac{2}{20} \][/tex]

5. **Simplify the fraction**: The fraction[tex]\( \frac{2}{20} \) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. \[ \frac{2}{20} = \frac{1}{10} \][/tex]

6. **Interpret the result**: The simplified fraction  [tex]\( \frac{1}{10} \)[/tex] represents one-tenth of an acre planted in orange trees.

7. **Conclusion**: Therefore, one-tenth of an acre is planted in orange trees in the Avocados' orchard.

The roots of a polynomial written in the form

[tex] (x-x_1)(x-x_2)(x-x_3)\ldots(x-x_n) [/tex]

Are exactly

[tex] x_1,\ x_2,\ x_3,\ldots x_n [/tex]

The multiplicity of a solution [tex] x_i [/tex] is how many times the parenthesis [tex] (x-x_i) [/tex] appears in the factorization of the polynomial.

So, if we write the powers explicitly, your polynomial is written as

[tex] (x + 5)^3(x - 9)^2(x + 1) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1) [/tex]

Which means that the solutions are:

The roots of  [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

The given function is:

[tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex]

The roots of the function [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are the values of x that makes f(x) to be zero

To find the roots of the function [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex], equate each of the terms to zero

The multiplicity of the roots is the power of the term from which the root is gotten

Equate each of the terms to zero

[tex](x+5)^3 = 0\\x + 5 = 0\\x = -5[/tex]

Since the power is 3, the multiplicity is 3

One root is -5 with a multiplicity of 3

[tex](x-9)^2 = 0\\x - 9 = 0\\x = 9[/tex]

Since the power is 2, the multiplicity is 2

One root is 9 with a multiplicity of 2

[tex](x+1)^2 = 0\\x +1 = 0\\x = -1[/tex]

Since the power is 1, the multiplicity is 1

One root is -1 with a multiplicity of 1

Therefore, the roots of  [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

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x + 5.39 > 4.48

   -5.39   -5.39

x            > -0.91

Answer: x > -0.91

Answer:

Option B is correct.

Step-by-step explanation:

Polyhedron is a solid figure which is entirely made up of polygons.

Means faces of the polyhedron are the polygons.

Minimum number of polygons required to for a polyhedron is 4 triangles.

Polyhedron made up of 4 triangles is known as Tetrahedron.

Tetrahedron has 6 edges.

Therefore, Option B is correct.

Hey there!!

Given equation :-

... [tex]\frac{2x}{7} + 2 = 5[/tex]

Subtracting 2 on both sides :

... [tex]\frac{2x}{7} = 3[/tex]

Multiplying 7 on both sides :

... [tex]2x = 21[/tex]

Dividing by 2 on both sides :

... [tex]x = \frac{21}{2}[/tex]

Hope my answer helps!!

As we already have the model that describes the change of the population in Italy in terms of the years that have elapsed, we only have to replace the conditions that are requested in that equation.

Therefore to find the population of Italy in the year 2000 (t = 10 years)  substitute t = 10 in the equation and have:

[tex]p = 56.8e^{0.0015*10}\\[/tex]

[tex]p=57.6584[/tex] million people

To find the population of Italy in 2008 (t = 18 years)

substitute t = 18 in the equation and have:

[tex]p=56.8e ^{0.0015*18}\\[/tex]

[tex]p=58.3545[/tex] million people

To predict the population in Italy for 2015 and 2020 with this model, we substitute in the equation t = 25 and t = 30

t = 25

[tex]p=56.8e^{0.0015*25}[/tex]

[tex]p=58.9704[/tex] million people

 t = 30

[tex]p=56.8e^{0.0015*30}[/tex]

[tex]p=59.4144[/tex] million people

Answer:

Option A is the correct answer.

Explanation:

 Let A be the base area and h be the height of prism.

 Volume of prism =  Base area x Height = a x h =ah

 Now we have base area of pyramid = Base area of prism = a ( both have same type of base)

Height of pyramid = 3 x height of prism = 3h

Volume of pyramid = 1/3 x Base area x Height = 1/3 x a x 3h = ah

Comparing both volumes, we will get Volume of prism = Volume of pyramid

So their ratio is 1.

Option A is the correct answer.

The volume of a pyramid with a height three times that of a prism's, but with the same base area, is equal to the volume of the prism, making the ratio 1.

To find the ratio of the volume of the pyramid to the volume of the prism with the same base area, we use the formula for the volume of a pyramid, which is Vpyramid = (1/3)Ah, where A is the area of the base and h is the height. The volume of a prism is given by Vprism = Ah.

Since we know the height of the pyramid is three times the height of the prism (3h), we can substitute in the formula: Vpyramid = (1/3)A(3h) = Ah, which simplifies to the same formula for the volume of the prism. This means that the volume of the pyramid is equal to the volume of the prism. Therefore, the correct ratio is Option A: 1.

y = 2x -5

y= -3x + 1

Here both the equations are in y = mx + b

where m is the slope and b is the y intercept

y =2x -5, the slope = 2  and b intercept = -5

y= -3x + 1, the slope = -3  and b intercept = +1

Both the equations have different slope. So there should be a single solution

Yes, the system of equations have a solution

Answer:

Answer is 225.

We have to find the sum of 15 terms of the series

sigma 1 to 15 (2n-1)

This can be split as per summation terms as

sigma 2n - sigma 1

sigma 2n can again be simplified by taking 2 outside

sigma 2n= 2 times sum of natural numbers of 1 to 15

= 2(15)(16)/2= 240

sigma 1= 1+1+...15 times= 15

Hence final answer is

= 2 times sigma n - (n) = 240-15 = 225.

Step-by-step explanation:

Step-by-step explanation:

Question 2) Answer

Use Arithmetic Series Formulas:

a) Nth term = F + (N - 1) x D, where F=First term, N=Number of terms, D=Common difference

6th row = 23 + (6 - 1) x -3

            = 23 + (5) x -3

            = 23 + (-15)

            = 8 - number of boxes in the top row.

b) Sum = N/2[2F + (N - 1) x D]

            = 6/2[2*23 + (6 - 1) x -3]

             = 3  [46  +    (5) x -3 ]

             = 3  [46  +      -15 ]

             = 3  [ 31 ]

             = 93 - total number of boxes in the entire display.

Question 3) Answer

Sum of the 8 first terms of the geometric progression with the first term 50 and the common ratio of 2:

=50 + 5*2 + 50*2^2 + . . . + 50*2^7

= 50*(1 + 2 + 2^2 + . . . + 2^7) = 50*(2^8-1)

= 50*(256-1) = 50*255

= 12750 Answer

I am also attached the solved question of this assignment please check and enjoy. Thanks

The answer is B I hope I helped

The measure of an interior angle of a regular septagon is approximately 128.6 degrees, calculated using the formula (((n-2) times 180) / n), where n is the number of sides.

To find the measure of an interior angle of a regular septagon (a seven-sided polygon), we can use the formula for finding the measure of an interior angle in any regular polygon: ((n-2) times 180) / n, where n is the number of sides in the polygon. For a septagon, n = 7.

Using the formula: ((7-2) times 180) / 7 = (5 times 180) / 7 = 900 / 7 ≈ 128.6 degrees.

Therefore, the measure of an interior angle of a regular septagon is approximately 128.6 degrees. Hence, the correct answer is B.) 128.6.

Answer:

the answer would be c. 0.40x

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Before we can solve this problem we need to turn the percentage into decimal form. We do this by moving the decimal to digits to the left like so...

40.0%    ⇔    0.40

Now that we have the percent in decimal form we can create the algebraic expression. To be able to find the percent of a number, we have to multiply the decimal form of the percent by the given number. That being the case the expression would be....

[tex]0.40x[/tex]

Therefore, the answer would be c. 0.40x

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

56/7=8

Alexander was paid $8 per hour

Answer:

1/6

Step-by-step explanation:

sim[le thought

Staci has vacuumed 1/6 of the entire house tonight.

The student's question concerns the portion of housework completed by Staci. As one of her chores, Staci must vacuum 1/2 of the house. She has already vacuumed 1/3 of her share tonight. To find out what part of the entire house has been vacuumed, we multiply the two fractions together.

Staci's share to vacuum is 1/2 of the house.

She has completed 1/3 of her share, which is 1/3 of 1/2.

To calculate the portion she has vacuumed, we multiply 1/2 by 1/3:

(1/2) x (1/3) = 1/6.

Therefore, Staci has vacuumed 1/6 of the entire house tonight.

Answer:

The percent of change in quantity is 25%.

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You must use the following formula:

%[tex]change=(\frac{new-old}{old})(100)[/tex]

2. You have that the old quantity was 16 oz and the new quantity is 20 oz. Therefore, you only need to substitute these values into the formula shown above, as following:

%[tex]change=(\frac{20oz-16oz}{16oz})(100)=25[/tex]%

The quantity of the fruit drink sold has increased by 25% after changing from 16-ounce containers to 20-ounce containers.

To determine the percent of change in quantity for the fruit drink, you'll first need to ascertain the difference in size between the two containers. In this case, the original size was 16 ounces and the new size is 20 ounces. Thus, the change in size is 20 ounces - 16 ounces = 4 ounces.

To calculate the percent of change, we divide this change in size by the original size, and then multiply by 100 to convert to a percentage. This can be summarized by the formula: ((new size - original size) / original size) * 100.

Substituting the given values into this formula, we get: ((20 - 16) / 16) * 100 = 25%.

Therefore, the fruit drink has increased in quantity by 25%.

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Im not sure but i multiplied and got 1.134 for my answer

Answer:

8 cookies

Step-by-step explanation

We start with 9 cookies:

9

"Giving away" 8 means subtracting 8 from 9:

9 - 8 = 1

"Buying" 7 more means adding 7 to 1:

1 + 7 = 8

Therefore, the kid has 8 cookies.

For this problem, you don't need to know how much the pencils cost. You're only finding how much the 10 nickels are worth.

Start by knowing how much one nickel is worth. A nickel is worth five cents in US currency. Since you know the worth of one nickel, you can find the worth of ten nickels by multiplying ten nickels by five cents (0.05).

Multiply 10 by 0.05.

10 * 0.05 = 0.5

0.5 is equal to 50 cents in US currency, so this means that Ginger has 50 cents to spend to buy pencils at the school store.

Answer:

You should find the discounted price of the gear first.

The discount should be calculated on the original $100 price.

Step-by-step explanation:

Now let's check the answer options:

You can simplify the problem by calculating 33% of $100.

You should find the discounted price of the gear first.

The tax should be calculated on the original $100 price.

The discount should be calculated on the original $100 price.

Answer:

You should find the discounted price of the gear first.

The discount should be calculated on the original $100 price.

Step-by-step explanation:

Your Welcome;)

Answer:

4 pounds of ingredients are used in each batch.

Step-by-step explanation:

Amount of flour = [tex]21\frac{1}{2}pounds = \frac{43}{2}pounds[/tex]

Amount of butter = 8 pounds

Amount of sugar = [tex]18\frac{1}{2}pounds= \frac{37}{2} pounds[/tex]

So, the total amount of all ingredients will be:   [tex](\frac{43}{2}+\frac{37}{2}+8)pounds = (\frac{43+37+16}{2}) pounds= \frac{96}{2} pounds = 48 pounds[/tex]

Given that, she makes 12 batches of cookies using all the ingredients.

Thus, the amount of ingredients used in each batch [tex]=\frac{48}{12} pounds = 4 pounds[/tex]

36 times 0.25 is 9

9+36=45

The original price was $45

Answer:

A

Step-by-step explanation:

Hope this helps

We are given

The average income, I, in dollars is

[tex]I=-425x^2+45500x-650000[/tex]

(a)

now, we are given

average income is $275000

so, [tex]I=275000[/tex]

now, we can set them equal

and then we can solve for x

[tex]275000=-425x^2+45500x-650000[/tex]

[tex]-425x^2+45500x-925000=0[/tex]

we will have to use quadratic formula

[tex]x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}[/tex]

[tex]x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}[/tex]

we get

[tex]x=27.28199[/tex]

[tex]x=79.776[/tex]

we need to find youngest age

It means that we need to choose smallest value

so,

[tex]x=27[/tex]............Answer

(b)

we are given

x=40

so, we can plug it and find I

[tex]I=-425(40)^2+45500(40)-650000[/tex]

[tex]I=490000[/tex]..............Answer

To find the youngest age for an average income of $275,000 for a lawyer, one would solve the quadratic equation formed by setting the income function equal to $275,000 and choosing the positive solution. The predicted average annual income of a 40-year-old lawyer is calculated by plugging 40 into the income function and rounding to the nearest dollar.

The student asked two questions about a quadratic function representing the average income of a lawyer by age.

Finding the youngest age for a certain average income

To find the youngest age at which the average income of a lawyer is $275,000, we set the quadratic income function I = -425x^2 + 45,500x – 650,000 equal to $275,000 and solve for x. After simplifying, we get a quadratic equation that can be solved using factorization, completing the square, or applying the quadratic formula. Once we find the values for x, we select the positive solution since age cannot be negative, and round it to the nearest year.

Predicted average annual income for a 40-year-old lawyer

To determine the average income for a 40-year-old lawyer, we substitute x = 40 into the given income model and calculate the value of I. The result will be the predicted average annual income of a 40-year-old lawyer, rounded to the nearest whole dollar.

So here are the rules of horizontal asymptotes:

Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that this function has no horizontal asymptote.

The two points (0,0) and (4,5) are on the line. The points are marked in blue in the attached image below.

Use the slope formula to get

m = (y2-y1)/(x2-x1)

m = (5-0)/(4-0)

m = 5/4  <----- this is the answer in fraction form

m = 1.25 <----- this is the answer in decimal form

The idea of the slope formula is we're subtracting the y values together, then subtracting the x values together in the same order, finally we divide the two results and reduce if possible to get the fraction form. Use long division or a calculator to find the decimal form of the fraction. In this case, the rise is 5 and the run is 4. Meaning we go up 5 units and over to the left 4 units to go from (0,0) to (4,5).

We need to construct an equilateral triangle inscribed in a circle, two congruent circles are created such that the center of each circle is also a point on the other circle.

Following would be correct directions:

A. Using a straightedge draw a line segment between the endpoint of the diameter of the circle that is not also the radius of the second circle and the bottom point of intersection of the two circles.

B. Using a straightedge draw a line segment between the endpoint of the diameter of the circle that is not also the radius of the second circle and the upper point of intersection of the two circles.

D. Using a straightedge draw a line segment between the top intersection point of the two circles and the radius of the first circle.

Therefore, incorrect direction would be

C. Using a straightedge draw a line segment between the two intersection points of the two circles.

Option D is incorrect because drawing a line segment between the top intersection point of the two circles and the radius of the first circle does not necessarily form the side of an equilateral triangle inscribed in a circle.

To determine which of the given directions for constructing an equilateral triangle inscribed in a circle does not work, we need to visualize the basic properties of such a triangle and its relationship to the circles. An equilateral triangle inscribed in a circle has all its vertices on the circumference of the circle, and the sides of the triangle are equal in length.

Option A suggests drawing a line segment from the endpoint of the diameter of the first circle that is not also the radius of the second circle to the bottom point of intersection of the two circles. This is one correct method to form the side of an equilateral triangle. Similarly, option B, which involves drawing a line segment between the endpoint of the diameter and the upper intersection point of the two circles, also forms a side of the equilateral triangle correctly.

Option C suggests drawing a line between the intersection points of the two circles. This will correctly create the base of the equilateral triangle. However, option D is incorrect because it states to draw a line segment between the top intersection point of the two circles and the radius of the first circle. This would not generally create the side of an equilateral triangle unless the radius mentioned coincidentally falls on another vertex of the triangle, which typically is not the case. Therefore, option D would not represent directions to construct the sides of the equilateral triangle.