Here are the first 7 terms of a quadratic sequence.
(a) Find an expression, in terms of n, for the nth term of this sequence.
6 11 18 27 38 51

Answer:

Step-by-step explanation:

The answer is 3, if you did 4-7 it would be -3, but since both -4-(-7) are negative it's a positive 3.

Ignore the parentheses, is just there so you don't mix the negative sign up with the subtraction sign.

To write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.

Given that expression is log₅4 - log₅6.

We have to tell the name of the property of logarithm which will help us to express the expression in a single logarithm.

The quotient rule for logarithms tells us that the logarithm of a quotient is equal to a difference of logarithms. Just as with the product rule we  use the inverse property to derive the quotient rule.

Division of logarithm says that log(m/n)=log m-log n.

The expression is  log₅4 - log₅6.

log₅4 - log₅6=[tex]log_{5}[/tex](4/6)

=[tex]log_{5}[/tex] 0.67

Hence to write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.

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The equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).

Variables, which are alphabets represents unknown values and can be used in creating equations that model a scenario.

For example, in the model shown in the image, x represents the weight of each triangle while y = the weight of each square.

From the first balance, we can rearrange the squares and triangles to create hanger B.

The first equation is: 3(2x + y) = 9y + 3x

The second equation that can be created using the set of shapes would be:

6x + 3y = 3(3y + x)

Therefore, the equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).

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Answer: 2x+y=3y+x

Step-by-step explanation:

Shape C is different from shape A and B.

Here, we are given 3 shapes as shown in the image below.

Let us look at each of the shapes one by one.

Shape A-

The height of shape A is 4

The width of shape A is 5

The ratio of width and height = 5/4

Shape B-

The height of shape B is 10

The width of shape B is 8

The ratio of width and height = 8/10 or 4/5

Shape C-

The height of shape C is 10

The width of shape C is 6

The ratio of width and height = 6/10 or 3/5

Thus, we can see that the ratio of width and height is equal for shape A and B. Thus, C is different.  

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Your question was incomplete. Check for the missing image below.

The equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.

We are given that:

To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².

Also, V₁=V₂

So, we get that:

1 / 2 (4 / 3 π r₁³) = 12 π r₂².

4 / 3 π r₁³ = 24 π r₂²

r₁³ = 18 r₂²

r₂ = √ ( r₁³ / 18)

r₂ = r₁ / 3 √r₁ / 2

Now, r₁³ = 18 r₂²

r₁ = ∛ 18 ₂²

Therefore, the equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.

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now, the assumption is that, "x" is a simple variable whilst "y" is a function in x-terms, so

[tex]e^{\frac{x}{y}}=3x-y\implies \stackrel{\textit{\LARGE chain~rule}}{e^{\frac{x}{y}}\stackrel{quotient~rule}{\left( \cfrac{1\cdot y-x\cdot \frac{dy}{dx}}{y^2} \right)}} =3-\cfrac{dy}{dx} \\\\\\ \cfrac{ e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \frac{dy}{dx}}{y^2}=3-\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}=3y^2-y^2\cfrac{dy}{dx}[/tex]

[tex]e^{\frac{x}{y}}y-3y^2=e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}-y^2\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-3y^2= \cfrac{dy}{dx}\left( e^{\frac{x}{y}}x-y^2 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \cfrac{e^{\frac{x}{y}}y-3y^2}{e^{\frac{x}{y}}x-y^2}=\cfrac{dy}{dx} \end{array}}~\hfill[/tex]

Based on the information given, the values are:

1. 80 rides

2. 53. 3%

3. 56. 6%

4. 30 students

Percentage can be defined as the ratio of a number to 100.

It is denoted with the symbol, '%'

How to determine the values;

1.. 24 rides = thirty percent of the total rides

Total rides = 24 rides/ 30%

Total rides = 24/ 30/ 100 = 24/ 0. 3 = 80 rides

2.  There are 14 Apple computers

16 PC computers

% of PC computers = 16/ 16 + 14 × 100/ 1

% of PC computers  = 16/ 30 × 100

% of PC computers  = 0. 53 × 100 = 53. 3

3.  3 out of 30 are not working

% of the working computers = 30- 3/ 30 × 100

% of the working computers = 17/ 30 × 100

% of the working computers = 56. 6

4.

If 12 students = 0. 4

Then x students = 1 - 0. 4 = 0. 6

cross multiply

x = 18 students

Total number of students = 40% + 60% of students = 18 + 12 = 30

Thus, the values are 80 rides, 53. 3%, 56. 6% , 30 students respectively.

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Answer:

Step-by-step explanation:

To graph any point (±x, ±y) we must follow the steps as illustrated below.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, The points (- 4,- 4.5), (1, 2.5), and (- 2, - 0.5).

Now, To graph the point (-4, - 4.5) we should move 4 units left along the x-axis and down 4.5 units along the y-axis.

Similarly, for points (1, 2.5) and (- 2, - 0.5) we must follow the exact steps.

The graph of the points is shown in the attached image.

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Answer:

10 Dimes, 5 quarters, and 7 Nickels

Step-by-step explanation:

10 Dimes - 1 dollars

5 Quarters - 1.25 dollars

7 Nickels - 35 cents

1 + 1.25 = 2.25

2.25 + 35 = 2.60

The amount Charlie and Kathy would pay interest on the loan of $20,000 is $6,344.80.

An ordinary annuity is payment of level cash flows for a defined period of time, in this case, a fixed monthly payment would be made for 10 years, hence, using the present value formula of an ordinary annuity we can determine the monthly payment:

[tex]PV=PMT*(1-(1+r)^{-N/r}[/tex]

Where:

[tex]PMT*(1+1+0.00479166666666667)^-120/0.00479166666666667\\PMT=$219.54[/tex]

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Answer: 1. (21/10 or 2.1). 2. (3/2 or 1.5)

Step-by-step explanation:

1. Let's take the first equation as an example (5 1/4 ÷ 2 1/2)

2. First, make both fractions improper (21/4, and 5/2)

3. Next, multiply the first fraction by the reciprocal (numerator and denominator swapped) of the second fraction. This is because, to keep the equation mathematically the same, we need to turn the division question into a multiplication question. In this case, it is 21/4 x 2/5 which answers 21/10, or 2.1.

4. Using the same method, we get 7/2 x 3/7, which is 3/2 (simplified), or 1.5.

I didn't want to give the answers for all the equations, but I hope this method is clear and concise for figuring out the answer for the rest of the equations.

The inequality that is represented by the given graph is; y ≤ (3/4)x - 2

From the given inequality graph, we see that;

Slope; m = 3/4

x-intercept = -2.5

y-intercept = -2

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, our graph is ordinarily;

y = (3/4)x + (-2)

y =  (3/4)x - 2

However, it is an inequality that is shaded at the bottom with a thick line and so the inequality becomes;

y ≤ (3/4)x - 2

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Answer:

1) 34

2) 282.4

3) $183.70

4) 0.324

Answer:

yes, each input (x) has only one output (y)

Step-by-step explanation:

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}} \implies \cfrac{12}{10}\implies {\LARGE \begin{array}{llll} \cfrac{6}{5} \end{array}}[/tex]

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

We have to find the value of x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

First take squares on both sides, then,

⇒ x² = 2 + [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

As the terms inside the square roots are non terminating, we can substitute x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] into the above equation.

i.e.,  x² = 2 + x

⇒ x² - x -2 = 0

This is a quadratic equation which can be solved using factorization.

⇒  x²+(-2+1)x +(-2.1) = 0

⇒ (x-2)(x+1) = 0

So x = 2 or -1

But here the value of √2 is positive and square root of sum of positive numbers will always be positive.

So we can conclude that

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

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Answer:

b = 16

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the angles and equate to 180

b + 15 + 8b - 18 + 39 = 180

9b + 36 = 180 ( subtract 36 from both sides )

9b = 144 ( divide both sides by 9 )

b = 16

Answer:

11.9a − 3

Step-by-step explanation:

Answer:

-120

Step-by-step explanation:

According to the given question -12 [tex]\times[/tex] 2/3 is equal to -8.

There are certain rules to solve this question.

multiply -12 × 2 = -24

And,

then divide it by 3 as stated in the denominator.

[tex]\frac{-24}{3}[/tex] = -8

This is how we solve this equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

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The value of x is 13.

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

We have,

Two lines m and n are parallel.

Two angles (7x -1)° and (8x - 14)° are corresponding angles.

We know that corresponding angles are equal.

We can write as:

7x - 1 = 8x - 14

We will find the value of x.

We will keep the like terms on one side.

14 - 1 = 8x - 7x

13 = x

x = 13

Therefore the value of x is 13.

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Answer:m= 83 degrees

Step-by-step explanation: the sum of all three corners will always add up to 180 so adding 31 and 66 together is 97 an then 180-97 is 83.brainliest?

The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

The similarity between the characteristics of exponents linear logarithms can be used to find the property for a quotient's logarithm. To create multiple numbers with the same base using exponents, add the exponents. Subtraction of exponents is used to split two numbers having the same base.

logb(xy) = logbx + logby.

logb(x/y) = logbx - logby.

logb(xn) = n logbx.

logbx = logax / logab.

log₅ 1/ 125 given

log₅ 1/ 125 applying the log property (log[tex]_a[/tex]ᵇ = log b/log a)

(log 1 - log 125)/ log 5

(log 1 - log 5³)/ log 5

(log 1 - 3log 5)/ log 5

((log1)/log 5 )) - 3

log₅¹ - 3

The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

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A. 559 meters Is the answer

Yes , the toll company is correct to give the teacher a ticket.

Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.

(i) f(x) is continuous on [a,b].

(ii) f(x) is differentiable on (a,b).

(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).

In the given question

Speed Limit = 60 mph

Time of entrance on toll road = 6:00

Time of exit from toll road = 7:00

Total time on toll road  = 1 hr

Mile marker on entry in toll road = 15 mile

Mile marker on exit from toll road = 100 mile

Total distance travelled on toll road = 100-15= 85 miles

[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]

Substituting the values we get .

Avg Speed = 85/1 = 85  mph

Overspeed = Avg Speed - Speed Limit

=85-60

=25 mph

The teacher over speed by 25 mph.

Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.  

By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .

Therefore , Yes , the toll company is correct to give the teacher a ticket.

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Answer:

the phothois not clear pls incorrectly I can't understand