Find the equation of the line tangent to the curve defined by f(x) = x^2+1 / square root x at the point (1,2). Show all your work.

The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;

(a) The dimensions of the tiles are;

Width = 0.3 meters

Length = 0.8 meters

(b) 384 tiles are needed

(c) The fitting cost of the tiles is Kshs 51,000

An equation is a mathematical statement that consists of two expressions connected with an equals sign

Shape of the floor = Square

Shape of the tiles = Rectangular

Perimeter of the tiles = 220 cm = 2.2 m

The number of tiles in each row =  20 + The number of tiles in each column

Length of the floor = 9.6 m

(a) Let w represent the width of the tiles, the length l is found using the equation;

[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]

Let n represent the number of tiles in each row, which gives;

The number of tiles in each column = 20 + n

(20+n)·x = n·(1.1 - x)

Which gives;

[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]

The side length of the square floor, s = 9.6

(20+n)·x = n·(1.1 - x) = 9.6

Which gives;

[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]

Which gives;

0.55·n² - 1.4·n -96 = 0

n = 12 or n ≈ -14.5

The number tiles in each roe, n = 20

Which gives; n·(1.1 - x) = 9.6

20 × (1.1 - x) = 9.6

x = 0.3

The width of each tile, x = 0.3 m

The length of each tiles = 1.1 m - 0.3 m = 0.8 m

(b) The number of tiles in each row, n = 20

The number of tiles in each column = n + 20, which gives;

Number of tiles in each column = 12 + 20 = 32

The number of tiles needed = 12 × 32 = 384

(c) The cost of a dozen tiles = Kshs 1,500

The labour cost = Kshs 3,000

Number of dozens of tiles = 384 ÷ 12 = 32

The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000

The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000

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Answer:5/9

Step-by-step explanation:

Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.

Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.

The formula of compound interest is as follows,

[tex]A=p(1+\frac{r}{100} )^t[/tex]

Where P is the principal value, A is the amount, r is the rate and t is the time.

Here we have a principal value of £3,500 and a rate is 4.5%.

Now, finding the amount after 2 years by putting the values in the formula of compound interest,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]

So, After 2 years Josephine will have £3882.9.

Now, finding the amount after 3 years,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]

So, After 3 years Josephine will have £3994.9.

Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.

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The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.

A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.

y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.

y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.

y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.

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lynn got the better deal than Roger.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.

Convert 15% to decimal form

15%=15/100=0.15

0.15×120=18

So 15% of 120 is 18.

Iynn bought crash cymbal for her drum set is 120-18=102

Roger bought the same crash cymbal from another store for$130

Roger applied coupon of $25.

So 130-25=$105

When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.

Hence lynn got the better deal than Roger.

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Answer:

x= -2, -10

Step-by-step explanation:

(x+6)^2-16=0

(x+6)(x+6)-16=0

x^2+6x+6x+36-16=0

x^2+12x+20=0

10+2=12

10(2)=20

(x+2)=0

(x+10)=0

x= -2, -10

Answer:

4(67 + 22)

Step-by-step explanation:

1. Find the greatest common factor(in this case it is 4)

2. Divide both 268 and 88 by 4 and you get 67 and 22

3. Put it in the requested format and you are left with 4(67 +22)

The function notation when the function was shifted right 6 is f(x-6).

Given that, the function was shifted right 6 units.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

So, the transformation from the original function to new function is

f(x-6)

Therefore, the function notation when the function was shifted right 6 is f(x-6).

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Answer:

log4 (70)

Step-by-step explanation:

log4(7) + log4(10) = log4(7 * 10 ) = log4(70)

Step-by-step explanation:

"down by one" means that the y values (the function result values) are all decreased by 1.

so, k = -1

The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million

We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;

A(h) = -0.06h² + 2h + 4

where h is the time in number of hours after which the concentration is recorded.

Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;

A(4) = -0.06(4²) + 2(4) + 4

A(4) = -0.96 + 12

A(4) = 11.04 parts per million

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The expression that is equivalent to (f × g²) + 5 - (g² × f) is 5

The expression whose equivalence is to be determined is given as

(f × g²) + 5 - (g² × f)

To start with, we need to remove the brackets in the expression

So, we have the following representation

(f × g²) + 5 - (g² × f) = f × g² + 5 - g² × f

Evaluate the products

This gives

(f × g²) + 5 - (g² × f) = fg² + 5 - fg²

Next, we collect the like terms

So, we have

(f × g²) + 5 - (g² × f) = fg²  - fg² + 5

Lastly, we evaluate the like terms

So, we have

(f × g²) + 5 - (g² × f) = 5

The above expression cannot  be further simplified

Hence, the equivalent expression is 5

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Answer:

it's decimal value then it is 11.1803399.

The integer close to it is 11

Step-by-step explanation:

let's square this :

4² × 5 = 16 × 5 = 80

the closest squared integer is 81 (9²).

so, the closest integer to 4×sqrt(5) is 9.

Two heads in three tosses is 3/8, 3/8x713=267.375. 267.375×41=10,962.375.

5/8x713=445.62, 445.62×29=12,923.125

So 10,962.375-12,923.125=-1960.75

Therefore if you played this game, you would statistically lose $1960.75

The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

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The plan that fits to Landyn's budget is plan B

What is percentage and how to calculate it?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.

We are given that Landyn's current monthly net pay is $560

And he does not wish to spend more than 10% of his current net pay

That means not more that $56

Now we are given 3 choices

Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56

Consider the option B)

50 + 50(0.05)

= 52.5

Which is less than $56

Hence, The plan that fits to Landyn's budget is plan B

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Answer: 1.367

Step-by-step explanation:

csc47° = 1.3673 ≈ 1.367

The value of cosec 47° is 1.367.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cosec 47°

The value of cosec 47°.

= 1.367334

Rounding to the nearest thousandth.

= 1.367

Thus,

The value of cosec 47° is 1.367.

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Answer:

Step-by-step explanation:

solving 3x+4=2x-4

now 3x-2x=-4-4

⇒ x=-8

(c) x=8 here you have given it as O thank you

The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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Answer:

8×2+8×g

Step-by-step explanation:

78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.

What is the linear equation?

A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that the total number of meals is 169.

Assume that,

a = number of meals eaten in a restaurant

b = number of meals eaten in a car

c = number of meals eaten at home

a + b + c = 169 .....(i)

Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.

Thus b + c = a + 13 .....(ii)

Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.

a = 20 + c .....(iii)

Subtract equation (ii) from (i)

a + b + c - b - c = 169 - a - 13

2a = 156

Divide both sides by 2

a = 78

Substitute a = 78 in equation (iii)

78 = 20 +c

c = 58

Putting c =58  and a =78  in equation (ii)

b + 58 = 78 + 13

b = 33

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Question:

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.

The percentage of students in the tutor group that have attended at least one tutorial is 71%

The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:

= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%

Number of students who attended at least one tutorial = 21 students

Total number of students in tutor group = 15 students

The percentage is therefore:

= 15 / 21 x 100%

= 0.7142857 x 100%

= 71.42%

= 71%

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Answer:

Infinite solutions

Step-by-step explanation:

The equation is,

→ 8x + 16x - 12 = 24x - 12

Let's solve for the value of x,

→ 8x + 16x - 12 = 24x - 12

→ 24x - 24x = -12 + 12

→ [ 0 = 0 ]

Hence, it has infinite solution. Because, all the real numbers are suitable.

Answer:

infinite number.

Step-by-step explanation:

Comment

There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.

x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.

x^3 + x^2 + 4x + 9 would give 3 solutions.

Solution

8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.

For example let x = 10

The right side = 240 - 12 = 228

The left side = 8*10 + 16*10 - 12 = 228

You can't come up with a number that will make the left side unequal to the right side.

Answer:

x = √10,-√10

explanation:

5x2 + 1 = 51

you would carry the +1 to the other side making it

5x2=51-1

which is 5x2=50

this equation above can then be turned into

x2=50÷5

which goes on to form the equation

x2=10

this can then be turned into x=the square root of ten

and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer

but yeah I'm not smart or whatever but I hope this helps

not too sure it's correct though

Answer: The correct answer is 14/7

Step-by-step explanation: This is the correct answer because it's explaining how to do it

These are equivalent. I hope this helps a ton. I had this question on a test. Tell me if its wrong or not. <:

Answer:

Step-by-step explanation:

Correct answer is A 5

check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?

well, it means that if we evaluate f(5) our result should be 0, so

[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]