Please help me solve this equation

Answer:

p = 20

Step-by-step explanation:

[tex]\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20[/tex]

The rate of change for cost is =  $2 per hour .

In the question ,

it is given that

the fixed rent for the bicycle is =$20

per hour charge of the bicycle is = $2

let the number of hours we rent a bicycle is = x

and let the total cost for renting the bicycle is = y

So , the equation to represent the cost becomes

y = 20 + 2x

to find the rate of change we differentiate the equation with respect to x .

we get

dy/dx = 2

Therefore , The rate of change is $2 per hour .

The given question is incomplete , the complete question is

You rent a bicycle for $20 plus $2 per hour. What is the rate of change of Cost ?

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a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3

b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3

c) The mistake she made throughout is not applying the basic rule of logarithm.

She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;

Step 1. 7 x 3^x = 189

Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.

Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3

Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;

x log 3 = 3log 3

Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3

Step 6. x = 9; This is wrong because x = 3

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Complete question is;

Mara solved an exponential equation by using logarithms. This is her work.

1. 7 x 3^x = 189

2. 3^x = 27

3. log^3 (^3) = log^27

4. xlog^33=9

5. x * 1 = 9

6. x = 9

Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)

a. Be sure to explain what she did and why it was correct or incorrect for Step 3.

b. Be sure to explain what she did and why it was correct or incorrect for Step 4.

c. Provide Mara with feedback on what the mistake was and how to fix it.

The probability of rolling a number that is less than 3 is P = 1/2.

A standard six-sided die has the following outcomes:

{1, 2, 3, 4, 5, 6}

The outcomes that are less than or equal to 3 are:

{1, 2, 3}

Assuming all the outcomes have the same probability, the probability of rolling a number less than or equal to 3 on a standard six-sided die will be equal to the quotient between the number of outcomes that meet the condition and the total number of outcomes.

It will give:

P = 3/6 = 1/2 = 0.5

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Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

Answer:

28, -27, 108, -42

Step-by-step explanation:

when x=2, 11x+6 = 22+6=28,

2x+28x+48= 30x+48=60+48=108

when x=-3, 11x+6 = -33+6=-27,

2x+28x+48= 30x+48=-90+48=-42

Answer:

I got 28, -27, 108, and -42. See explanation for the answer for which problems

Step-by-step explanation:

11x + 6 = ?

2x + 28x + 48 = ?

x = 2 and x = -3

Let's start with the first equation

Using x = 2

11(2) + 6 = ?

22 + 6 = 28

Using x = -3

11(-3) + 6 =?

-33 + 6 = -27

Second equation

Using x = 2

2(2) + 28(2) + 48 = ?

4 + 56 + 48 = 108

Using x = -3

2(-3) + 28(-3) + 48 = ?

-6 - 84 + 48 = -42

Answer:

its D

Step-by-step explanation:

calculator

The ratio of snakes to frogs is 1 : 2.

The ratio of frogs to animals is 2 : 3.

If 3 more snakes are added, the number of frogs that should be added to keep the ratio constant is 6.

Here are the completed tables:

TVs                   2        4       6

Computers       7       14        21

Trumpets   10       5          20           25

Drums         8         4         16             20

Books      0       40       100

Boxes      0        2        5

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained within other value(s).

The ratio of snakes to frogs can be determined by counting the number of snakes and frogs.

Number of snakes = 4

Number of frogs = 8

The ratio of snakes to frogs - 4 : 8 = 1 : 2

The ratio of frogs to animals = number of frogs : number of animals = 8 : 12 = 2 : 3.

Number of snakes if 3 more are added = 4 + 3 = 7

Ratio of snakes to frogs - 1 : 2  

Number of frogs that would keep the ratio constant = 7 x 2 = 14

Number of frogs that should be added = 14 - 8 = 6

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Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

Subtract 7 from both sides.

Subtract -7 from −3 to get −10.

Divide both sides by −2. Since −2 is negative, the inequality direction is changed.

Divide −10 by −2 to get 5.

Based on the data on the income statement, the amount of the tax equals to $27,000.

Generally, a taxes refers to those mandatory contributions levied on individuals or corporations by a government entity either from local, regional, or national government.

Given that: EBIT = $547,000 Interest expense = $94,000 Net income = $426,000

EBT = EBIT - Interest expense

EBT = $547,000 - $94,000

EBT = $453,000

The tax reported in Income statement:

= EBT - Net income

= $453,000 - $426,000

= $27,000

In conclusion, the 2021 taxes reported on the income statement equals to $27,000.

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By taking some products we will see that the total number of cupcakes ordered is 6 cupcakes.

Here we want to see how many cupcakes this person is ordering. We know that orders 9 halves of a cupcake for the family, plus a quarter of a cupcake for each of the 6 friends.

The total number of cupcakes is given by the order for the family plus the order for the friends.

The order for the familiy is given by the product:

9*(1/2) = 9/2 = 4.5

That is 9 times 1/2 of a cupcake, so for the family the person orders 4.5 cupcakes.

For the friends the person orders 6 times 1/4 of a cupcake, so now we have the product:

6*(1/4) = 6/4 = 3/2 = 1.5

If we add these two numbers we get the total number of cupcakes:

4.5 + 1.5 = 6

The person ordered 6 cupcakes.

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answer the answer is 200

Step-by-step explanation:

490-290

The numbers are plotted in the attached graph.

A number line is a representation of real numbers in the form of a graded straight line.

Note that 5/3 is approximately equal to 1.7.

Similarly, -5/3 is approximately equal to -1.7.

Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.

The numbers are plotted in the attached graph.

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The liquid that Richard used in the punch is 1 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Richard made punch for a party. He used 1/2 cup of pineapple juice, 1/2 cup of ginger ale, and 1/4 cup of white grape juice.

The total fraction will be:

= 1/2 + 1/2 + 1/4

= 1 1/4 cups.

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Answer: b

Step-by-step explanation:

The probability that the plant manufactures a part between 10.8 and 12.8 centimeters 13%

The probability is solved z scores, this measures the amount of standard deviation sample X is from mean. the formula is below

z = (X - μ) / σ

Definition of variables

mean, μ = 16.3 centimeters

standard deviation, σ = 2.5 centimeters

X = 10.8 and 12.8 centimeters

z score, z

substituting into the formula

for X = 12.8 centimeters

=  (X - μ) / σ

= (12.8 - 16.3) / 2.5

= -1.4

the p value for z of -1.4 = 0.161513

for X = 10.8 centimeters

=  (X - μ) / σ

= (10.8 - 16.3) / 2.5

= -2.2

the p value for z of -2.2 = 0.027807

the probability is calculated as below

0.161513 - 0.027807= 0.133706

= 0.13

=13%

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The expression will be; part (a) (f o g)(-2) = 2 and part (b) (g o f)(-2) = -95

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the functions as;

f(x)=4x-2

g(x)=5-x^2

We need to find (f o g)(-2)

So, first, we will find the function (f o g)(x) as follows:

[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]

Now, substitute with x = -2 then we get;

[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]

Thus, the answer to the part is (a) (f o g)(-2) = 2

b) (g o f)(-2)

We need to find (g o f)(x) as follows:

[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]

Now Substitute with x = -2, then we get;

[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]

Thus, the answer to the part (b) is (g o f)(-2) = -95

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Answer:

Step-by-step explanation:

3/5 pool/hr * 10hr = 6 pool

The domain of the function is [ - 6 , ∞ ]

A radical function is the one provided.

It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.

As a result, either the radicand of the provided function must be larger than or equal to zero, or:

Thus we can write it as

x + 6 ≥ 0

subtract 6 from both LHS and RHS

x + 6 - 6 ≥ 0 - 6

x ≥ - 6

Therefore the domain of the function is [ - 6 , ∞ ]

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Answer:272

Step-by-step explanation:

Answer: -4, -1, 1, 3, 3.9, 3.99, 3.999, 4

Step-by-step explanation:

That inequality symbol means less than or equal to. So that includes 4 and any number that precedes it on the number line.

Function g(x) is a translation of one unit to the left and 3 units down of f(x), then the correct option for the graph of g is B.

Here we start with a function f(x), and we also have the graph of this function.

And we want to find the graph of the function defined as:

g(x) = f(x + 1) - 3

Notice that:

g(x)=  f(x + 1)

Is a translation of one unit to the elft of f(x).

g(x) = f(x) - 3

Is a translation of 3 units down of the graph of f(x).

Then:

g(x) = f(x + 1)- 3

Is a translation of one unit to the left and 3 units down.

With that in mind, we can see that the correct option for the graph of g(x) is option B.

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how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?

A rate is a unique ratio where the two words are expressed in several units.

Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]

[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM

[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation

[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]

Hence the answer is   [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]

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A. The data modeling the relation is an exponential function.

B. The function is: y = 2^x.

C. The rate of change from x = 2 to x = 4 is of 4.

The definition of an exponential function is presented as follows:

[tex]y = ab^x[/tex]

In which the variables of the function are listed as follows:

From this data-set, when x increases by one, y is multiplied by 2, hence the rate of change is:

b = 2.

When x is increased by n, the rate of change is:

b^n = 2^n.

Hence, when x is increased by 2, from 2 to 4, in item c, the rate of change is:

2² = 4.

When x = 1, the output is the output at x = 0 multiplied by 2, hence the coefficient a of the function is given as follows:

a = 2/2 = 1.

Then the exponential function is:

[tex]y = 2^x[/tex].

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The value of the angle regarding the parallel lines are:

1. x = 14

2. x = 9

3. x = 17

4. x = 5

1. Lines 'l' and 'm' are the parallel lines and a transversal line is intersecting these  lines.

(9x + 13)° = (12x - 29)° [Alternate interior angles]

9x - 12x = -29 - 13

-3x = -42

Divide

x = 14

2). By substituting x = 14 in the box.

(13x + 5)° + (8x - 14)° = 180° [Consecutive interior angles]

21x - 9 = 180

21x = 189

Divide

x = 189/21

x = 9

3). By placing x = 9 in the box,

(5x + 52)° = (9x - 16)° [Corresponding angles]

5x - 9x = -52 - 16

-4x = -68

x = 17

4). By placing x = 17 in the box,

(10x + 17)° = (12x + 7)° [Alternate exterior angles]

10x - 12x = -17 + 7

-2x = -10

x = 5

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The length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, a chessboard is made using the ratio of square length to the king's height, 1.5 inches to 4.5 inches. If a chessboard is made with a king's height of 2.25 inches.

The square length will be calculated as,

Square length / Kings Height = 1.5 / 4.5

Square length = (King's height x 1.5 ) / 4.5

Square length = ( 1.5 x 2.25 ) / 4.5

Square length = 0.75 inches

Therefore, the length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

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The first person to get both integrity ticket and free water bottle is the person who comes 36th. This can be calculated by using L.C.M

What is L.C.M?

The value that's equally divided by 2 provided numbers is that the lowest common multiple of any two. Least common multiple is its full name. Another name for it's the Lowest common divisor (LCD)

Main Body:

According to question,

Every 4th person who walks into the dance gets a free water bottle

Every 9th person who walks in gets an integrity ticket.

so the L.C.M of 4 and 9 should be calculated.

L.C.M of 4 and 9 is 36.

Hence L.C.M is 36

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Answer:   6

Step-by-step explanation:   You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.

Answer:

18

Step-by-step explanation:

using bodmas rule by working out brackets first