Find the point on the line 3x + y = 4 which is closest to the point (2, 1). Answer: Σ Note: Your answer should be a point in form (x-coordinate, y-coordinate)

A) A reasonable domain to plot the growth function is; d = 9.02

B) The y-intercept of the function is; 9

C) The average rate of change of the function f(d) from d = 3 to d = 9 is; 0.4477

We are given the equation that shows the radius of the algae, f(d), in mm, after d days as; f(d) = 9(1.04)^(d)

A) We are told that the radius is approximately 12.81 mm. Thus;

9(1.04)^(d) = 12.81

(1.04)^(d) = 12.81/9

(1.04)^(d) = 1.4233

d * log 1.04 = log 1.4233

d = 0.1533/0.017

d = 9.02

B) The y-intercept is obtained when the domain is zero. Thus;

f(0) = 9(1.04)^(0)

f(0) = 9

C) Average rate of change is given by the formula;

f'(x) = [f(b) - f(a)]/(b - a)

from d = 3 to d = 9. Thus;

f'(x) = (f(9) - f(3))/(9 - 3)

f'(x) = (9(1.04)^(9) - 9(1.04)^(3))/6

f'(x) = 0.4477

Read more about Domain of function at; https://brainly.com/question/10197594

#SPJ1

Answer:

Their total bill will be $83.78.

They will pay $20.95 each

Explanation:

Given;

Tom and his three friends went out to eat Their total bill T was $65.45.

The tax rate is 8% and they tipped the waitress 20%.

The total price they will pay is equal to the sum of the total bill, the tax and the tip.

Therefore, their total bill will be $83.78.

Assuming, each of them are to share the bill equally, then since there are 4 persons, The bill per person will be the total bill divided by 4;

So, they will pay $20.95 each

Answer:

a number plus 14

fourteen more than a number

a number increased by 14

Step-by-step explanation:

The phrases which can be represented by the algebraic expression x + 14 are

Let x = the unknown number

a number plus 14

= x + 14

fourteen more than a number

= x + 14

a number increased by 14

x + 14

Answer:

number plus 14

fourteen more than a number

a number increased by 1 :D

Step-by-step explanation:

The areas of the figures are 598.3125 sq ft, 960 sq in, 466 sq cm, 704 sq cm, 1920 sq m and 262.5 sq yd

Figure 1

The area is calculated as

Area = Rectangle + Semicircle

So, we have

Area = 15 * 34 + 1/2 * 3.14 * (15/2)^2

Area = 598.3125 sq ft

Figure 2

The area is calculated as

Area = Parallelogram * 2

So, we have

Area = 24 * (40/2) * 2

Area = 960 sq in

Figure 3

The area is calculated as

Area = Triangle 1 + Triangle 2

So, we have

Area = 1/2 * 38 * 14 + 1/2 * 40 * 10

Area = 466 sq cm

Figure 4

The area is calculated as

Area = Triangle + Square

So, we have

Area = 1/2 * 22 * (42 - 22) + 22 * 22

Area = 704 sq cm

Figure 5

The area is calculated as

Area = Trapezoid * 2

So, we have

Area = 1/2 * (20 + 40) * 64/2 * 2

Area = 1920 sq m

Figure 6

The area is calculated as

Area = Triangle 1 * 2

So, we have

Area = 1/2 * 35 * 15/2 * 2

Area = 262.5 sq yd

Read more about areas at

https://brainly.com/question/24487155

#SPJ1

Answer:

To find the product of 568.32 and \(10^{4}\), move the decimal point in 568.32 4 places to the right because \(10^{4}\) has 4 zeros.

Step-by-step explanation:

\(10^{4}\) = 10000

568.32 · 10000 = 5683200

the decimal point moved 4 places to the right because 10000 has 4 zeros.

hope this helps!

x/12 + 3 < 7 = x<48 this is the only one i can do because i cant do the others sorry

Answer:

5x

Step-by-step explanation:

The function S maps subsets of X to bit strings of length 3. For each element in X, if it belongs to the subset Y, the corresponding bit in the string is set to 0; otherwise, it is set to 1. The value of S(X) will provide the bit string representation of all elements in X.

Given the set X={a, b, c}, the function S maps subsets of X to bit strings of length 3. Let's determine the value of S(X).

For element a, since a∈X, the corresponding bit s1 is set to 0.

For element b, since b∈X, the corresponding bit s2 is set to 0.

For element c, since c∈X, the corresponding bit s3 is set to 0.

Therefore, the value of S(X) is 0, 0, 0; representing that all elements a, b, and c are present in the set X.

Learn more about Functions here : brainly.com/question/30721594

#SPJ11

Answer:

x=1/3,y=3

Step-by-step explanation:

y=7x+6_____equation1

5x+y=2_____equation2

substitute y into equation 2

5x+7x+6=2

12x+6=2

12x=2-6

12x=-4

x= -1/3

substitute X into equation 1

y=7x+6

y=7(-1/3)+6

y=-7/3+6

y=9/3

y=3

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

Learn more about simple interests here:

https://brainly.com/question/26457073

#SPJ9

the distance is 5 inche

beacuse they cant be to far away from eachoyher

For the given fraction x^2-8x+16/x^2-16 if x≠4 and x≠-4 the simplified fraction is (x-4)/(x+4).

Simplified fraction refers to the fractions in their lowest form which has been reduced and simplified. The numerator and denominator in the fraction are reduced in simplified fraction to the extent that the only common factor between them is 1.

In order to simplify the fraction (x^2-8x+16)/(x^2-16), first, we must factor the numerator and denominator of the fraction:

Numerator: x^2-8x+16 = (x-4)(x-4) = (x-4)^2

Denominator: x^2-16 = (x-4)(x+4)

So the fraction becomes:

(x-4)^2/(x-4)(x+4)

Next, we can simplify the fraction by canceling out the (x-4) term in the numerator and denominator:

(x-4)/(x+4)

Therefore, the simplified fraction is (x-4)/(x+4) if x≠4 and x≠-4.

Learn more about Simplified fraction:

https://brainly.com/question/15178106

#SPJ11

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to +1, where a value of -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

The correlation coefficient's sign will not change when the order of the variables in a correlation study is changed, but the coefficient's numerical value might. This is due to the symmetry of the correlation coefficient with regard to the two variables under comparison.

For instance, if you calculate the correlation coefficient between X and Y and the result is r = 0.7, it indicates that Y tends to rise as X does. The correlation coefficient between the variables Y and X will have the same sign (+ or -) but a different numerical value if the variables are computed in a different order.

For such more question on coefficient:

https://brainly.com/question/4219149

#SPJ4

Answer:

The radius and height of the cone are 3.41 cm and 20.46 cm respectively.

Step-by-step explanation:

Given that,

The volume of a conical candle is 250 cm³.

The height of candle is 3 times of its diameter.

h = 3d  (d = 2r, radius)

So,

h = 6r

The formula of volume of a cone is given by :

\(V=\dfrac{1}{3}\pi r^2h\\\\250=\dfrac{1}{3}\pi \times r^2\times 6r\\\\250=2\pi r^3\\\\r=(\dfrac{250}{2\pi })^{1/3}\\\\r=3.41\ cm\)

Height, h = 6r = 6(3.41) = 20.46 cm

Hence, the radius and height of the cone are 3.41 cm and 20.46 cm respectively.

Answer:

if it triples each time you will get 19683 pennies

Step-by-step explanation:

The equation represented by a graph that is centered at (-4, 5) and includes the point (-2, 5) is: (x+2)²+(y-5)² = 4

What is graph ?

In mathematics, a graph is a visual representation of a set of objects where some pairs of the objects are connected by links. The objects are often represented as points or vertices, and the links are represented as lines or arcs that connect the vertices. Graphs are used to model and analyze many real-world situations, such as social networks, transportation systems, and communication networks. They are also an important tool in various fields of mathematics, such as algebra, geometry, and topology.

According to the question:
The equation represented by a graph that is centered at (-4, 5) and includes the point (-2, 5) is:

(x+2)²+(y-5)² = 4

To see why, we can use the center-radius form of the equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

From the given information, we know that the center of the circle is (-4, 5) and that the circle passes through the point (-2, 5). Therefore, we can plug these values into the equation above:

(x - (-4))² + (y - 5)² = r²

(x + 4)² + (y - 5)² = r²

We now need to find the value of r, which is the radius of the circle. We know that the circle passes through the point (-2, 5), which is 2 units away from the center (-4, 5) along the x-axis. Therefore, the radius must be 2:

r² = 2²

r² = 4

Substituting r² = 4 into the equation above, we get:

(x + 4)² + (y - 5)² = 4

which matches the first option: (x+2)²+(y-5)² = 4. So, the answer is:

(x+2)²+(y-5)² = 4

To know more about graph visit:
https://brainly.com/question/13298277
#SPJ1

Answer:

He makes $324 more this week than last week.

Step-by-step explanation:

Answer:

$324 More

Step-by-step explanation:

Last week he made a total of $244 ($3 times 96)

This week he made a total of $612 ($3 times 204)

$612 minus $244 equals $324

The roots of the quadratic equation represented by the graph are;  x = -2.5 and x = 2.5.

The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.

The roots are located between -3 and 3.

Read more about Solution of Quadratic equations as; https://brainly.com/question/11347015https://brainly.com/question/12952549

#SPJ1

Answer:

3 and 4

Explanation:

The two perfect squares closest to √11 are √9 and √16, which are 3 and 4, respectively.

Hope this helps!

Check the picture below, I'll be referring to the material in the picture.

we know the outer cube has a surface area of 24, we also know is a cube, so it has 6 equal sides which are squares each, let's say the side of one of those squares in the cube is say of length "s", so the area of one square will just be  s², and for 6 squares that'll be an area of 6s², that is the area of the outer cube, which we know is 24.

\(24=6s^2\implies \cfrac{24}{6}=s\implies 4=s^2\implies \sqrt{4}=s\implies 2=s\)

now, we know the sphere is inscribed in the outer cube, so it's touching its edges, like you see in the picture in blue, so if we get a cross-section of the whole lot, we'd get the picture to the right of blue cube in the picture, an outer cube with a side of 2, and therefore an sphere with a diameter of 2, and thus a radius of 1, as you can see in the red triangle.

Let's notice that the red triangle is a 45-45-90 triangle, and thus we can use the 45-45-90 rule to get its sides, as you can see in the picture on the far-right, which gives us half of one side of the inner cube to be 1/√2.

\(\stackrel{\textit{half a side}}{\cfrac{1}{\sqrt{2}}}\qquad \stackrel{\textit{a full side}}{\cfrac{1}{\sqrt{2}}+\cfrac{1}{\sqrt{2}}}\implies \cfrac{2}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2}\sqrt{2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\)

now as you can see in the picture, the inner cube in orange, has 6 sides, each side is √2 long, so let's get the 6 squares area.

\(\stackrel{\textit{area of one square}}{\sqrt{2}\cdot \sqrt{2}\implies 2}\qquad \stackrel{\textit{area of all 6 sides of the inner cube}}{6\cdot 2\implies 12}\)

Apply the APR of 11.90% to the average daily balance. Multiply the average daily balance by 11.90% (or 0.119) to obtain the finance charge.

To determine Hannah's April finance charge on her credit card, we need to calculate the average daily balance and then apply the APR to that balance.

Step 1: Calculate the average daily balance by adding up the daily balances for each day in the billing cycle and dividing by the number of days.

Step 2: Calculate the daily balances by considering the transactions and their respective dates. The beginning balance of $322.95 on 4/1 remains the same until the first transaction occurs. After the first transaction on 4/10, the balance increases by $19.87. The payment on 4/14 reduces the balance by $50.00, and the subsequent purchase on 4/19 increases the balance by $71.21.

Step 3: Determine the number of days each balance is applicable for. From 4/1 to 4/10, the balance is $322.95 for 10 days. From 4/10 to 4/14, the balance is $342.82 for 4 days. From 4/14 to 4/19, the balance is $292.82 for 5 days. From 4/19 to the end of the billing cycle (4/30), the balance is $364.03 for 12 days.

Step 4: Calculate the average daily balance by summing up the (balance * number of days) for each period and dividing by the total number of days in the billing cycle (30).

Step 5: Apply the APR of 11.90% to the average daily balance. Multiply the average daily balance by 11.90% (or 0.119) to obtain the finance charge.

Step 6: Compare the calculated finance charge to the given choices (a, b, c, d) and select the closest match.

Therefore, by following these steps, you can determine Hannah's April finance charge on her credit card.

To learn more about balance click here:

brainly.com/question/28699225

#SPJ11

We will have the following:

From the polynomial we will have that:

*It falls to the left and rises to the right.

This can be seeing as follows:

Answer: 48

Step-by-step explanation:

The area of a triangle with the given set of vertices is 12 square units, which is obtained using the concepts of coordinate geometry and the area of triangles.

What is the area of a triangle?

The area of a triangle is defined as the total region bounded by the three sides of a triangle. For a right-angled triangle, the area is given by ½ * (base * height).

Calculation of the area of the given triangle

Given:

P(7,6), Q(1,6), R(4,2) be the three vertices of a triangle PQR

Let PQ be the base parallel to the x-axis

b = 7 - 1 = 6

And altitude is the difference of y coordinates of the point Q and R, h = 6 - 2 = 4

The area of triangle PQR is equal to half the product of base and height

Area = (6 × 4) / 2

        = 24 / 2

        = 12 square units

Hence, the area of the triangle with given vertices is 12 square units.

To learn more about the area of triangles, visit here:

https://brainly.com/question/17335144

#SPJ4

Answer:

g + 15 = 40

or

40 - 15 = g

Step-by-step explanation:

Answer:

jennifer

Step-by-step explanation:

Answer:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k

Step-by-step explanation:

hope it helps

The objective of keyword bidding is to d. get the best ranking for the lowest cost.

Keyword bidding is a practice used in online advertising, specifically in pay-per-click (PPC) campaigns, where advertisers bid on specific keywords to display their ads in search engine results. The objective of keyword bidding is to achieve the best possible ranking for their ads while keeping the cost as low as possible.

Option (a), obtaining the most profitable domain name, is not related to keyword bidding. Domain names refer to the website address or URL and are not directly associated with keyword bidding.

Option (b), limiting the amount of money the firm spends on search marketing, is partially correct but not the primary objective. While controlling costs is important, the main goal of keyword bidding is to optimize the ranking and visibility of ads.

Option (c), always being ranked first, is not feasible for every advertiser. Search engine rankings are determined by various factors, including bid amount, quality score, and relevance. It is not guaranteed that an advertiser will always secure the top position.

Learn more about Keyword bidding here:

https://brainly.com/question/9381008

#SPJ11

Number of boys = a - b

Number of children in the class = a

Number of girls in the class = b

Number of boys = Total - Girls

                              a - b

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

To learn more about algebraic expression, refer to the link-

https://brainly.com/question/2164351

#SPJ1