Find the rate of change between the following points. (-1, -4) (3, 1)

It can be seen that the mistake that was made by Marvin was on line 1.

2x² - 8x + 5.... move the 5 to the other side

2x² - 8x = -5

Now divide by 2

x² - 4x = -5/2

x² - 4x + 4 = -5/2 + 4

(x - 2)² = -5/2 + 8/2

(x - 2)² = 3/2

x - 2 = (+-)sqrt 3/2

x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2

Therefore, he made his mistake on line 1.

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Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27

Answer:

[-3,∞)

Step-by-step explanation:

Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.

If there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

Given,

The conditions

We know

In multiple regression method the dependent variables are predicted by using the known independent variables. This method is usually used to analyze the relationship between multiple independent variables and one independent variables,

So here multiple regression method is using.

Hence, if there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

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Answer:

Kristen can ride the bike for 20 hours

Step-by-step explanation:

20 - 15 = 5

The rate is 0.25 an hour.

0.25 x 4 = 1 - Currently $4

0.25 x 4 = 1 - Currently $3

0.25 x 4 = 1 - Currently $2

0.25 x 4 = 1 - Currently $1

0.25 x 4 = 1 - No more

Add up all the 4's

She can ride the bike for 20 hours.

The answer is [tex]z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

What do you understand by differential equation?

An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.

Given equation:

[tex]$$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$[/tex]

[tex]$C=-1 / 7$[/tex]

[tex]$$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$[/tex]

[tex]$$e^{-7 z}=1-24.5 t^2$$[/tex]

[tex]$$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

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The area of the lawn is given as  50 . 24 m²

Area = πr² x θ/360

r = 12m

θ = 40 degrees

Area = 3.14 x 12² * 40/360

= 50.24

Hence the area is 50 . 24 m²

2 x 50.26

= 100.52

Area = πr² x θ/360

The value of  θ is not given

When we plug in the figures we would have

100.52 = πr² x θ/360

Then  θ = 100.53 x 360 / 3.14 x 12²

= 80 degrees

c. θ = 40 degrees

100. 53 =  πr² x 40/360

πr²  = 100.53 x 360 / 40

r = 16.97 m

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Answer:

6425

Step-by-step explanation:

12.85x500=6425

The total number of people who can go to the amusement park in the given scenario is 6. This problem is based on the basic mathematical formulae.

Formulae are mathematical statements comprising expressions, numbers, and variables to ease complex calculations.

Given that

The total amount for the expenditure = [tex]\[/tex]327.75.

Cost of parking per person = [tex]\[/tex]13.75,

Cost of tickets per person = [tex]\[/tex]39.25.

Total cost per person = Cost of parking per person + Cost of tickets per person

Total cost per person = [tex]\[/tex]13.75 + [tex]\[/tex]39.25

                                    = [tex]\[/tex]53

So,

Number of persons = [tex]\frac{The total amount for the expenditure}{Total cost per person }[/tex]

                                 = [tex]\frac{327.75}{53}[/tex] = 6.18.

So, 6 people can go to the amusement park.

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The measure of the angle the minute hand traces in 36 minutes is 3.77 radians

From the question, we are to determine the measure of the angle the minute hand traces in 36 minutes

The minute hand makes a complete rotation after 60 minutes.

Thus,

The angle the minute hand would have traced in 36 minutes is

36/60 × 360°

= 12960/60

= 216°

Now, convert to radians

216° = 216 × π/180 rad

= 3.77 rad

Hence, the measure of the angle the minute hand traces in 36 minutes is 3.77 radians

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a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).

The given equation of the circle is;

x² + y² = 26.

Th circle satisfies the line y = x + 4.

Thus, Put the value of y in the main equation.

x² + (x + 4)² = 26.

Simplify the equation;

x² + x² + 16 + 8x = 26

2x² + 8x - 10  = 0

Divide the equation by 2.

x² + 4x - 5  = 0  

Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

Part b: Now, do the factorization of x² + 4x - 5  = 0.

(x + 5)(x - 1) = 0

x = -5 and 1.

For x = -5; y = -1

Point P = (-5, -1)

For x = 1; y = 5

Point Q = (1, 5)

Thus, the requires points P and Q are obtained.

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The answer of 18 is y = 0.5x + 0

The answer of 22 is y =  -0.4x + 0

Step-by-step explanation:

c is constant, m is gradient

18. m = 1/2

     m = 0.5

     1 = 0.5(2) + c

     1 = 1 + c

     c = 0

     y = 0.5x + 0

22. m = 2/-5

      m = -0.4

      2 = -0.4(-5) + c

      2 = 2 + c

      c = 0

      y = -0.4x + 0

Answer:

b=8

Step-by-step explanation:

-4b + 5 = -27

Move the 5 to the right side by subtraction, subtract five from the right side as well.

Now you should have:
-4b = -32

Now divide by -4 to get ‘b’ isolated, do this on both sides.

You should be left with:
b=8

Answer:

The set of all whole numbers

Step-by-step explanation:

Real numbers, integers, and rational numbers can all contain negative numbers. Whole numbers include numbers from 0 and up.

Hope this helps!

Have a nice day

Answer:

π/2 and ³√4

also -4.8237 and π/2

Step-by-step explanation:

number 2 and 4 are automatically out since every integer is a rational number.

√25 = 5 and 5 + 4 = 9, 9 can be expressed as 9/1 which falls under rational numbers.

π/2 on the other hand is not rational same goes for -4.8237 and ³√4 because these numbers cannot be written as a fraction with integers.

for the above numbers π/4 and ³√9 are irrational.

On simplifying  the given expression the no. that goes in green box is -7

The rule of addition of two numbers

adding two positive integers result in positive integer.

adding two negative integers results in the sum with a negative sign.

addition of two different signed Integer will result in subtraction only and the sign of the result is same as the larger number sign.

so

2 + 16x - 9 - 10x

6x + [-7]                   HERE [ 2 + (-9) = -7 ]

On simplifying  the given expression the no. that goes in green box is -7

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The value are-

Now, for the given question.

Let the given angle be 'x'.

Then, the complement of the angle will be: 90 - x.

6 times the complement = 6(90 - x)

6 times the complement is 44 less; 6(90 - x) - 44.

Now, the supplement of the angle is; 180 - x.

Two time the supplement = 2(180 - x)

The equation will form as;

2(180 - x) = 6(90 - x) - 44

360 - 2x = 540 - 360 - 44

Simplifying the equation;

x = 34.

Thus, the original angle is 34°.

complement angle = 90 - x

= 90 - 34

= 56°

Thus, complement angle = 56°

supplement angle = 180 - x

= 180 - 34

= 146

supplement angle = 146°

Thus, the values of the angles are obtained.

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Answer:4 hours

Step-by-step explanation:

You have to figure out what times 5 would equal 20.

5x=20

5(4)=20

because 5*4=20, the answer is 4

Answer:1311

Step-by-step explanation:

2 digit long multiplication.
__________________________________________
Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large. If you take it step by step, though, you'll be able to do long multiplication in no time.

First, muiltiply the 3 by 5 and 7, and muiltiply the 2 by 5 and 7 as well.

[tex]\frac{\begin{matrix}\:\:&\:\:&5&7\\ \:\:&\times \:&2&3\end{matrix}}{\begin{matrix}0&1&7&1\\ 1&1&4&0\end{matrix}}[/tex]

(NOTE: Remember when you muiltiply two digit numbers, when you pass from the first digit to the other on the bottom side, you ALWAYS add a zero to the beginning of the result BEFORE multiplying the following digit)

Secondly, once you've multiplied, you add both results of the multiplication.

[tex]\frac{\begin{matrix}\:\:&\textbf{\:\:}&1&\:\:&\:\:\\ \:\:&\textbf{0}&1&7&1\\ +&\textbf{1}&1&4&0\end{matrix}}{\begin{matrix}\:\:&\textbf{1}&3&1&1\end{matrix}}[/tex]

[tex]=1311[/tex] <- This is your final answer.
___________________________________________
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10 combinations of two parts can be selected.

Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.

denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex]  ,

where n is the total number of elements in the set.

x is the number of selected objects.

According to the Question

Total number of elements = 5 = n

Number of objects to be selected = 2 = x

Substituting the values in the above formula

C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]

[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]

Therefore , 10 combinations of two parts can be selected.

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The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

What is the concept of time and work?

Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.

Calculation of the total time taken by the machines A and B working together

Given that Machine A completes the entire job in 12 minutes.

So, machine A completes 1/12 of the job in one minute.

Machine B takes 18 minutes to complete the entire job.

So, machine B completes 1/18 of the job in one minute

When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e.  (3 + 2) / 36 = 5/36 job in one minute     —---- 1

To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1

i.e. 36 / 5 minutes to complete the entire job

i.e. 7.2 minutes

Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

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The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

The distributive Property states in that it is necessary to multiply every one of the two numbers by the factor before performing the addition operation when a factor is multiplied by that of the sum or addition of two terms. The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.

The following generic form can be used to specify the distribution property:

a(b+c) = ab + bc

the following expression:

6(24)

We can observe the following by contrasting this to the general form:

a = 6

b + c = 24

Consequently, we must identify two integers from the options whose sum is 24.

These numbers, out of the options provided, are 20 and 4.

The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

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Option D is the correct answer (We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%)

Since the confidence interval is calculated for population proportion (parameter) based on sample data.

Because the figure is based on a sample of the population you are investigating; there is always uncertainty when you generate an estimate in statistics, whether it be a summary statistic or a test statistic. The confidence interval is the range of values. If you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time. The alpha value determines the confidence level, the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

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Jarome can make 6 whole pizzas with the leftover cheese.

Given that Jarome uses 2 1/2 cups of cheese for every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the bag.

We need to determine the number of pizza pies can he make with the leftover cheese.

To find out how many pizza pies Jarome can make with the leftover cheese, we need to determine how many sets of 2 3/4 pizzas can be made using 6 1/4 cups of cheese.

Let's start by finding the number of sets of 2 3/4 pizzas that can be made from 6 1/4 cups of cheese:

Number of sets = Total cheese available / Cheese per set

Number of sets = 6 1/4 cups / 2 1/2 cups per set

To make the calculation easier, let's convert all the mixed numbers to improper fractions:

6 1/4 cups = (4 x 6 + 1) / 4 = 25/4 cups

2 1/2 cups = (2 x 2 + 1) / 2 = 5/2 cups

Number of sets = (25/4) / (5/2)

Now, to divide fractions, we invert the divisor (5/2) and multiply:

Number of sets = (25/4) x (2/5)

= (25 x 2) / (4 x 5)

= 50/20

= 5/2

So, Jarome can make 5/2 sets of 2 3/4 pizzas with 6 1/4 cups of cheese.

Now, let's see how many pizzas he can make with the leftover cheese:

To calculate the number of pizzas in 5/2 sets, we multiply it by the number of pizzas per set (2 3/4 pizzas):

Number of pizzas = (5/2) x (2 3/4)

Again, let's convert all the mixed numbers to improper fractions:

2 3/4 pizzas = (4 x 2 + 3) / 4 = 11/4 pizzas

Number of pizzas = (5/2) x (11/4)

Now, when multiplying fractions, we simply multiply the numerators together and the denominators together:

Number of pizzas = (5 x 11) / (2 x 4) = 55/8

So, Jarome can make 55/8 pizzas with the leftover 6 1/4 cups of cheese.

Now, let's simplify the fraction:

55/8 = 6 7/8

Therefore, Jarome can make 6 7/8 pizzas with the leftover 6 1/4 cups of cheese.

Since we can't make a fraction of a pizza, he can make 6 whole pizzas with some cheese left over.

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The pan that comes closest in area is the 8-inch square pan.

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 22/7

R = radius = diameter / 2 = 9/2 = 4.5 inches

22/7 x 4.5² = 63.64 in²

A square is a quadrilateral with four equal sides.

Area of a square = length²

8² = 64 in²

9² = 81 in²

10² = 100 in²

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In roughly 127 hours the prices of the two stocks will be the same.

So, if we count the hours (x) after 9 a.m., the stock prices will be:

The value of x when A = B can be calculated using:

A = B

Therefore, in 127 hours roughly the prices of the two stocks will be the same.

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Answer:

yes

Step-by-step explanation:

if (a,b) is on the graph of f(x) then (-a,-b) is on the graph of f^-1(x)

debt-equity ratio is 0.92.

A firm's total liabilities and shareholder equity are compared using the debt-to-equity (D/E) ratio, which may be used to determine how heavily reliant a company is on debt. D/E ratios vary by sector and are most useful for comparing a firm to its closest rivals or tracking changes in its reliance on debt over time. When comparing similar organizations, a larger D/E ratio denotes greater risk, whereas a very low one can signify that a company is not utilizing debt funding to grow. Since long-term debt entails greater risk than short-term commitments, investors frequently change the D/E ratio to simply take it into account.

Debt-equity ratio is computed as follows:

= total debt ratio / (1 - total debt ratio)

= 0.48 / (1 - 0.48)

= 0.48 / 0.52

= 0.92

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The value not in the solution is x = -10.2

The inequality expression is given as:

-4x - 6.8<34

Add 6.8 to both sides of the inequality

So, we have:

-4x < 40.8

Divide both sides by -4

x > -10.2

This means that only values greater than -10.2 are in the solution set

Hence, the value not in the solution is x = -10.2

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