please help, this is honors geometry, I need this done as soon as possible

Answer:-4,2

Step-by-step explanation:

a.

= (5x)² - 3 = 25x² - 3

- 5f(x) = 5(x² - 3) = 5x² - 15

b.

- f(x - 2) = (x - 2)² - 3 = x² - 4x + 1

- f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

a. To calculate f(5x), we substitute 5x into the function f(x) and simplify the expression.

  f(5x) = (5x)² - 3 = 25x² - 3

  To calculate 5f(x), we multiply the function f(x) by 5.

  5f(x) = 5(x² - 3) = 5x² - 15

b. To calculate f(x - 2), we substitute (x - 2) into the function f(x) and simplify the expression.

  f(x - 2) = (x - 2)² - 3 = x² - 4x + 4 - 3 = x² - 4x + 1

  To calculate f(x) - f(2), we evaluate f(x) and f(2) separately and then find their difference.

  f(x) = x² - 3

  f(2) = 2² - 3 = 4 - 3 = 1

  f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

For the difference quotient of f(x) = -7x² - 5x + 9, we can calculate it as follows:

Difference quotient = [f(x + h) - f(x)] / h

Expanding the function and substituting into the difference quotient formula, we have:

[f(x + h) - f(x)] / h = [-7(x + h)² - 5(x + h) + 9 - (-7x² - 5x + 9)] / h

Simplifying and expanding further:

= [-7(x² + 2hx + h²) - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-7x² - 14hx - 7h² - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-14hx - 7h² - 5h] / h

= -14x - 7h - 5

The difference quotient of f(x) = -7x² - 5x + 9 is -14x - 7h - 5.

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Answer:

3 and 5

Step-by-step explanation:

Alternate interior angles are the angles in between the two lines and on the inside

4 and 6

3 and 5

Answer:

∠3 and ∠5 are alternate interior angles

Step-by-step explanation:

By the definition, alternate interior angles are angles that are inside the lines and opposite sides of each other on the transversal.

The distance between town a and b is 175 mi.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, a map drawn move to the scale 2 cm : 100 mi. on the map town b is 3.5 centimeters from town a and town c is 2 centimeters past town b

Since, 2 cm = 100 mi

1 cm = 50 mi

Therefore, 3.5 cm = 50×3.5 = 175 mi

Hence, the distance between town a and b is 175 mi.

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(a) The cost function is given by C(x) = (7/100) ln|5x^2 + e| + 13000.

(b) The cost of producing 5 units is approximately $19,019.14, which is more than $19,000. Therefore, the company should seek a new source of investment income.

(a) To find the cost function C(x), we need to integrate the marginal cost function C'(x) and add the fixed cost of $13,000.

Integrating C'(x), we have:

∫ C'(x) dx = ∫ (70x / (5x^2 + e)) dx

To simplify the integration, we can use the substitution u = 5x^2 + e, which gives du = 10x dx. Rearranging the equation, we have dx = du / (10x).

Substituting these into the integral, we have:

∫ (70x / (5x^2 + e)) dx = ∫ (70 / u) (du / (10x))

Now, we can simplify the integral:

∫ (70 / u) (du / (10x)) = (7/100) ∫ du / u

Integrating this, we get:

(7/100) ln|u| + C

Substituting back u = 5x^2 + e, we have:

(7/100) ln|5x^2 + e| + C

Since the fixed cost is $13,000, we set C = 13000. Therefore, the cost function is:

C(x) = (7/100) ln|5x^2 + e| + 13000

(b) To determine if the company should seek a new source of investment income, we need to evaluate the cost of producing 5 units, which is C(5).

Substituting x = 5 into the cost function, we have:

C(5) = (7/100) ln|5(5)^2 + e| + 13000

C(5) = (7/100) ln|130 + e| + 13000

Calculating the value of C(5), we can determine if it is more than $19,000:

C(5) ≈ 19019.14

Since the cost of producing 5 units is more than $19,000, the company should seek a new source of investment income.

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Answer:

\(\frac{1}{24}\)

Step-by-step explanation:

La mitad es 1/2 y un tercio es 1/3. Como una persona se comió 1/2 y Ana 1/3, puedes determinar lo que se comieron sumando:

\(\frac{1}{2}\)+\(\frac{1}{3}\)=\(\frac{3+2}{6}\)=\(\frac{5}{6}\)

Como se comieron 5/6, puedes restar esto de 6/6 para determinar cuanto quedó de la tortilla:

\(\frac{6}{6}-\frac{5}{6}= \frac{6-5}{6} =\frac{1}{6}\)

De acuerdo a esto, quedó 1/6 de la tortilla. Luis tomó tres cuartas partes de lo que quedaba, lo que significa que quedó 1/4 de 1/6. Para encontrar la fracción de la tortilla que quedó puedes dividir 1/6 entre cuatro para saber a cuanto corresponde una cuarta parte de 1/6:

\(\frac{1}{6}\)÷4= \(\frac{1/6}{4}= \frac{1}{6*4}=\frac{1}{24}\)

De acuerdo a esto, la fracción de la tortilla que quedó al final del día es \(\frac{1}{24}\).

The height of the cube calculated from volume 48x⁶y⁵  cubic units, length 6x³y and breadth 4x²y³ is 2xy units.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

The Volume of the cube is 48x⁶y⁵  cubic units

The length of the cube is 6x³y unit

Breadth of the cube is 4x²y³ unit

The height of the cube be H

We know,

volume(V)  = length(L) * breadth(B) * height(H)

⇒ height = V/L*B = (48x⁶y⁵)/(6x³y)*(4x²y³)

⇒ height = (48x⁶y⁵)/(24x⁵y⁴) = 2xy

The height of the cube calculated from volume 48x⁶y⁵  cubic units, length 6x³y and breadth 4x²y³ is 2xy units.

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Check the picture below.

Answer:

Step-by-step explanation:

solving by elimination means to get rid of one of the variables,  pick either one,  X or Y  and use the other equation to make it zero.

3x - y = 5

4x + y = 9

+______  add the two equations, column for column,

7x + 0y = 14

now solve for x,  that is, get x by itself

7x / 7 = 14/7

x = 2

Now that you've solved for x,  plug that x into either equation.

3(2) - y = 5

6-y = 5

6-5 = y +5-5

1 = y

Now you have both :)

Answer:

The mean age of the frequency distribution for the ages of the residents of a town is 43 years.

Step-by-step explanation:

We are given with the following frequency distribution below;

    Age                      Frequency (f)               X                    

    0 - 9                            30                         4.5                   135

   10 - 19                           32                        14.5                  464

   20 - 29                         12                         24.5                 294

   30 - 39                         20                        34.5                 690

   40 - 49                         25                        44.5                1112.5

   50 - 59                         53                        54.5                2888.5

   60 - 69                         49                        64.5                3160.5

   70 - 79                          13                         74.5                968.5

   80 - 89                          8                          84.5                676        

   Total                            242                                              10389      

Now, the mean of the frequency distribution is given by the following formula;

                         Mean =  

                                    =    = 42.9 ≈ 43 approx.

Hence, the mean age of the frequency distribution for the ages of the residents of a town is 43 years

Answer:  5(11m + 6)

Step-by-step explanation:

We find the Greatest common factors to factor out:

55m + 30

= 5(11m + 6)

Answer:  8

Step-by-step explanation:

The formula for the sum of the angles of a polynomial is:

\(S_n=180(n-2)\)

1080 = 180(n - 2)

1080 = 180n - 360

1440 = 180n

8 = n

Answer:

8

Step-by-step explanation:

It's an octagon

Answer:

Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)

Range is the area covered vertically. Assuming it ends at 9.5 it would be        (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)

Neither.

Step-by-step explanation:

Domain is the area covered horizontally. Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)

Range is the area covered vertically. Assuming it ends at 9.5 it would be        (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)

It is neither because it is on the x-axis.

Answer:

d

Step-by-step explanation:

Answer:

its right

Step-by-step explanation:

Answer:

6+x

Step-by-step explanation:

sum means add

6+x

Hey there!

When you see/hear the word “sum” in mathematics.. it usually means “to add”.

So, we are adding 6 from the unknown number (the x-value)

Answer: 6 + x

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Where the above are given,

10. The nurse should give 2.45ml of the liquid medication.

11. The nurse can give 24ml of meperidine in 24 hours.

12. The patient should take 42 tablets of the antibiotic.

13. The IV rate is 100ml/hr at 1500gtt/min with a 15gtt/ml drip factor.

14. Each dose of codeine contains 15000mg.

15. The patient should be given 2.67oz (approximately) of the cough syrup.

10. To determine how much   of the liquid should be given, we can set up a  proportion

1g/3.5ml = 700mg/x

Cross-multiplying,

1g * x = 700mg * 3.5ml

x = (700mg * 3.5ml) / 1g

x = 2450mg*ml/g

Therefore, the amount of liquid to be given is 2.45ml.

11. The order states meperidine 75mg IM every 6 hours PRN pain, and the pharmacy sends a vial that contains 25mg/2ml. To calculate how many ml can be given in 24 hours, we need to consider the frequency and duration.

In 24 hours, there are 24/6 = 4 doses to be given. Each dose contains 75mg of meperidine.

To find the volume (ml) of each dose, we can set up a proportion  -

25mg/2ml = 75mg/x

25mg * x = 75mg * 2ml

x = (75mg * 2ml) / 25mg

x = 6ml

12.  To calculate the number of tablets the patient should take, we need to consider the dosage and the duration.

Each tablet contains 250mg of the antibiotic.

To find the number of tablets for the total dosage, we can set up a proportion  -

250mg/1 tab = 0.75g/x

250mg * x = 0.75g * 1 tab

x = (0.75g * 1 tab) / 250mg

x = 0.003 tab

Since we cannot take a fraction of a tablet, the patient should take 1 tablet every 4 hours for 7 days, resulting in a total of 1 * 6 * 7

= 42 tablets.

13.  To determine the IV rate, we need to calculate the number of drops per minute.

The formula to calculate the IV rate in drops per minute (gtt/min) is -

IV rate (ml/hr) = Total volume (ml) / Total time (hr)

IV rate (gtt/min) = IV rate (ml/hr) * Drop factor (gtt/ml)

IV rate (ml/hr) = 1000ml / 10hr = 100ml/hr

IV rate (gtt/min) = 100ml/hr * 15gtt/ml =

1500gtt/min

Therefore, the IV rate is 100ml/hr at 1500gtt/min.

14. To determine the   amount of milligrams of  codeine in each dose, we need to convert grams to milligrams.

1  gram (g) = 1000   milligrams (mg)

15 grams (gr) = 15 * 1000mg = 15000mg

Therefore, each dose contains 15000mg of codeine.

15. To calculate how much cough syrup should be given in ml's, we can set up a proportion -

225mg/1oz = x ml/600mg

225mg * x = 1oz * 600mg

x = (1oz * 600mg) / 225mg

x = 2.67oz

Therefore, 2.67oz of cough syrup should be given in ml's.

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Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

b > - 9

Step-by-step explanation:

i hope i did okay i try my best

Answer:

x = -9

Step-by-step explanation:

5 + 3x = -22

1.) Subtract 5 from itself, then from -22. That then cancels out the 5 on the left and gives you -27 on the right

3x = -27

2.) Divide 3x and -27 by 3 which is the coefficient in this problem.

x = -9

Answer:

10 units.

Step-by-step explanation:

In order to solve this, we first need to know the distance of the points by using rise and run. Then we will be able to find the hypotenuse. This is pretty much gonna make a triangle.

Run = 6

Rise = 8

We can use Pythagorean Theorem to solve for the hypotenuse since this forms a right triangle.

6² + 8² = c²

36 + 64 = c²

100 = c²

10 = c

Therefore, the distance between the two points is 10 units.

Answer:

10

Step-by-step explanation:

\(8^{2}\) + \(6^{2}\) = \(\sqrt{100}\) = 10

Each side of the playground is 10\(\sqrt{2}\) m.

We know that in a square,

                               d = \(\sqrt{2}\) a

            where, d = diagonal of the square

                         a = side of the square

Now, according to the question the walkway forms a diagonal and is 20 meters long.

  So, d = 20 m

        a = ?

          d = \(\sqrt{2}\) a

        20 =   \(\sqrt{2}\) a

          a  =  20/ \(\sqrt{2}\)

              =  \(\frac{10\sqrt{2}*\sqrt{2} }{\sqrt{2}}\)

              = \(10\sqrt{2}\)

Hence, the side of the playground is \(10\sqrt{2}\) meters long.

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Step-by-step explanation:

a= 1/3 + 3/5

= 5+9/15

= 14/15

b=6/7-2/5

=30-14/35

= 16/35

Answer:

Bodmas in full is Bracket Of Division

Bracket Of Division Multiplication Addition and Subtraction

\(2 + 4 \times 6 \div 3\)

\(2 \div 3 \times 6 + 4\)

\(0.66666 \times 6 + 4\)

\(4 + 4\)

\( = 8\)

hope that helps you

Answer:

The vertex is (4,-3)

Step-by-step explanation:

P.S. you got the 2nd last one wrong.

When x>4 y increases as x increases

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4). 4a2 + 3a. -11c2 - 4c. 3. x(2x - 5). 4. 2y( y - 4).

Step-by-step explanation:

Answer: (I REDID THIS ANSWER)

$128

Step-by-step explanation:

20% off of $16,000 = $3,200

20% off of $3,200 = $640

20% off of $640 = $128

Answer= $128

If function  f: R → R , then  |f(x) - f(1)| > 1/2

Given:

f: R → R

f(x) is

1 when x ∈ Q

0 when x ∉ Q

Then,

Right hand limit,

\(\lim_{h \to \ 0} f( 1+h ) = 0\)   [ 1 + h∈ Q  ]

Left hand limit,

\(\lim_{h \to \ 0} f( 1-h ) = 0\)  { 1-h ∉ Q }

From the definition of continuity ,

|f(x) - f(a)| < ∈

But ,

f(1) = 1

\(\lim_{x \to \ 1} f(x) \neq f(1) = 1\)

Thus f(x) is not continuous at x = 1

|f(x) - f(1)| = |f(x) - 1|

Assume ∈ = 1/2

Then,

|f(x) - f(1)| > 1/2

Hence proved ,

|f(x) - f(1)| > 1/2

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The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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