A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t.

Explain how to write a composite function to find the area of the region at time t.

Answer:

The slope formed using points (4,6) and (8,0) is [tex]\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given as :

The points are (4,6) and (8,0)

([tex]x_1[/tex] , [tex]y_1[/tex]) = (4,6)

([tex]x_2[/tex] , [tex]y_2[/tex]) = (8,0)

Let The slope that formed = m

So,

slope = m = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

m =  [tex]\dfrac{0 - 6}{8 - 4}[/tex]

Or, m =  [tex]\dfrac{6}{4}[/tex]

∴ m = [tex]\dfrac{3}{2}[/tex]

So, The slope formed using points = m =  [tex]\dfrac{3}{2}[/tex]

Hence , The slope formed using points (4,6) and (8,0) is [tex]\dfrac{3}{2}[/tex] Answer

Answer:

-3

Step-by-step explanation:

[tex]4x + 2(x-3) = 3x + x-12\\4x+2x-6=4x-12\\2x=-6\\x=-3[/tex]

Answer:

Step-by-step explanation:

x + 24 > 4x

24 > 4x - x

24 > 3x

24/3 > x

8 > x or x < 8

so ur answer is : all numbers less then 8

Answer:

h(n+1) = h(n) - 7

Step-by-step explanation:

Our objective is to write the expression for h(n+1) in terms of h(n) which equals -31 -7(n-1)

So we use the given formula to find what h(n+1) is:

h(n+1) = -31 -7((n+1)-1)

h(n+1) = -31 -7(n+1-1)

we now re-arrange the order of terms inside the parenthesis without combining like terms:

h(n+1) = -31 -7(n-1+1)

and use distributive property to multiply "-7" times the "+1" term and get it extracted from inside the parenthesis:

h(n+1) = -31 -7(n-1) -7

Notice that this way we were able to preserve the form of the term h(n) "-31 -7(n-1)" , and see what is the modification introduced to it when finding the term h(n+1). We now replace "-31 -7(n-1)" by "h(n)" in the above equation:

h(n+1) = -31 -7(n-1) -7

h(n+1) = h(n) - 7

And this is the recursive formula that tells us how to construct the following term of a sequence by knowing the previous one.

Answer:

h(1)=-31

h(n)=h(n-1)+(-7)

Step-by-step explanation:

Answer:

21 lb

Step-by-step explanation:

Divide the amount of Ryan's pumpkin by 2 then multiply it by 3. Ryan's pumpkin weighs 14 lb divided by 2 is 7 then 7 multiplied by 3 is 21.

To find the weight of Felipe's pumpkin, we first determine that Meg's pumpkin weighs 7 pounds, which is half of Ryan's pumpkin's weight of 14 pounds. We then multiply Meg's pumpkin's weight by 3 to find that Felipe's pumpkin weighs 21 pounds.

The question asks to determine the weight of Felipe's pumpkin given the weight relationships between Felipe's, Meg's, and Ryan's pumpkins. We are told that Ryan's pumpkin weighs 14 pounds and that Meg's pumpkin is half the weight of Ryan's. This means Meg's pumpkin weighs 7 pounds (14 lb / 2). Since Felipe's pumpkin weighs three times as much as Meg's, we have to multiply Meg's pumpkin's weight by 3 to find the weight of Felipe's pumpkin: 7 lb x 3 = 21 pounds.

So, Felipe's pumpkin weighs 21 pounds.

Answer:

$420.8

Step-by-step explanation:

An employee deposits $400 of their paycheck into an investment account that earns 2.6% interest annually.

We assume that the investment account gives a simple interest against the deposits.

If there is no withdrawals or deposits in the account other than this, then after 2 years the sum in the account will be  

[tex]400(1 + \frac{2.6 \times 2}{100}) = 420.8[/tex] dollars (Answer)

Answer:

The amount in the account after 2 years is $421.04

Step-by-step explanation:

Given as :

The principal deposited into account = p = $400

The rate of interest applied = r = 2.6%

The time period = t = 2 year

Let The amount for 2 years in the account = $A

From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, $A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, $A = $400 × [tex](1+\dfrac{\textrm 2.6}{100})^{\textrm 2}[/tex]

Or, $A = $400 × (1.026)²

Or, $A = $400 × 1.0526

∴ A = $ 421.04

So, The amount =  A = $421.04

Hence The amount in the account after 2 years is $421.04 Answer

Answer:

The actual width is 26 feet.

Step-by-step explanation:

Elise made a scale drawing of a shopping center. The scale of the drawing was 1.5 inches : 3  feet = 1.5 inches : 36 inches = 1 : 24.

Now, in the drawing, a bakery in the shopping center is 13 inches wide.

Therefore, the actual width of the bakery in the shopping center will be the increased value of 13 inches in the ratio 1 : 24.

So, the actual width is (13 × 24) inches = 312 inches i.e. 26 feet. (Answer)

The actual width of the bakery is calculated using the scale factor from the drawing. This can be achieved by multiplying the drawn width of the bakery (in inches) by the scale factor to get the actual width (in feet). Thus, the actual width of the bakery is 26 feet.

The subject of this question is scale factor in mathematics, specifically in the context of real-world scenarios, like a scale drawing. The scale of the drawing is 1.5 inches: 3 feet, which represents a scale factor of 2 feet per inch (because 3 feet/1.5 inches = 2 feet per inch). In the drawing, the bakery is stated to be 13 inches wide.

To convert this to the actual width, one should multiply the width in the drawing (13 inches) by the scale factor (2 feet per inch). Hence, the actual width of the bakery is 26 feet (because 13 inches * 2 feet per inch = 26 feet).

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Answer:

Step-by-step explanation:

k² = -18 - 9k

k²  +9k + 18 = 0

k²  + 6k + 3k + 3*6 = 0

k(k + 6) + 3 (k + 6) = 0

(k + 6) (k + 3) =0

-2v²- v  +12 = -3v² + 6

-2v² - v + 12 + 3v² - 6 = 0

v² - v + 6 = 0

Answer:

The correct option is C).

Figure show the line with slope of -1/2 and a y-intercept of 3

Step-by-step explanation:

The equation of line is given by y=mx+c.

Where m is slope and c is y-intercept.

Given that line has slope

m=[tex]\frac{-1}{2}[/tex] and c=3

Thus equation of line will be

y=mx+c.

y=[tex]\frac{-1}{2}x+3[/tex]

To plot the line we need at least two points

Take x=0

y=[tex]\frac{-1}{2}x+3[/tex]

y=[tex]\frac{-1}{2}0+3[/tex]

y=3

The required point is A(0,4)

Take x=2

y=[tex]\frac{-1}{2}2+3[/tex]

y=2

The required point is B(2,2)

Using this points to graph the given equation of line

Figure show the line with a slope of -1/2 and a y-intercept of 3

The correct option is C).

Answer:

B

Step-by-step explanation:

I’m not sure but I put in c and got it wrong and that is the only other one that appears to be going on a negative slope

One song download costs $2 and one movie download costs $11.

Step-by-step explanation:

Let,

Price of one song download = x

Price of one movie download = y

According to given statement;

8x+9y=115     Eqn 1

15x+9y=129   Eqn 2

Subtracting Eqn 1 from Eqn 2

[tex](15x+9y)-(8x+9y)=129-115\\15x+9y-8x-9y=14\\7x=14[/tex]

Dividing both sides by 7

[tex]\frac{7x}{7}=\frac{14}{7}\\x=2[/tex]

Putting x=2 in Eqn 1

[tex]8(2)+9y=115\\16+9y=115\\9y=115-16\\9y=99[/tex]

Dividing both sides by 9

[tex]\frac{9y}{9}=\frac{99}{9}\\y=11[/tex]

One song download costs $2 and one movie download costs $11.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

Answer:

-4/15

Step-by-step explanation:

2/5-4/6=2/5-2/3=6/15-10/15=-4/15

Since m<A ≅ m<C, AB = BC.

And...

x+4=3x-8

-2x=-12

x=6

Since AC=x, AC=6.

answer: AC = 6

Answer:

Length of AC is 6

Step-by-step explanation:

he side AC = x ;we need to find x; since ∠A = ∠C , It's an isosceles triangle . i.e ,the sides opposite to the angles ( AB and CB ) are also equal. thus ,side AB = x+4 ;CB = 3x-8 ;thus AB = CB or ,x+4 = 3x-8 ,2x = 12 ,x = 6 ; therefore the side AC is 6.

hope this helped

Answer:

Angle C is equal to 30.

Step-by-step explanation:

To find angle C, we have to find all the other angles first. They tells us the B ~= BAD ~= ADC. So, if we find ADC, we've found B and BAD as well. ADC is just 180 - 70 (the angle of ADE), which is 110. So, ADC, BAD, and B are equal to 110.

Remember, angles in a quadrilateral add up to 360. So, add all of the values of angles be have now and subtract from 360:

360 - (110 + 110 + 110)

360 - 330 = 30

Angle C should be equal to 30.

Hope this helped!

The area of the parallelogram is equal to the product of its base and height, the area is the twice of πr,r or πr².

Step-by-step explanation:

The circumference of a circle = 2πr.

where r= radius of the circle.

If the circle is divided into equal sectors it will form a triangle.

If we arrange these triangle one by one we'll get a parallelogram. (refer the image).

Then the circumference of the circle becomes the base of the parallelogram and radius becomes the height.

∴Base= 2πr and Height=r.

The area of the parallelogram = Base×Height.

∴ The area for the circle turned parallelogram = 2πr×r.

⇒Area= 2πr².

In other words, twice the πr and r (or) πr².        

Thus area of a circle can be derived from the circumference formula.                                                            

Answer:

Product

Step-by-step explanation:

Answer:

[tex]\displaystyle [a - b][a^2 + 2ab + b^2][/tex]

Step-by-step explanation:

Use the Difference of Cubes to factor this polynomial.

I am joyous to assist you anytime.

Answer:

[tex]y=\sqrt x - 5[/tex]

Step-by-step explanation:

Given:

The range of the function includes the value '-4'.

The range of a function is the output of the function denoted by the variable 'y'. The input of the function is called the domain and is represented by the variable 'x'.

Here, the 'y' value is -4 which is a negative number.

The last two options given represent a square root function. We know that, the output of a square root function is always a positive number. So, for the last two options the range is always greater than or equal to 0. Thus, these two options are eliminated.

Now, if we consider the second option, let us replace 'y' by -4 and solve for 'x'. This gives,

[tex]-4=\sqrt x + 5\\-4-5=\sqrt x\\\sqrt x= -9[/tex]

But, we know that, the result of a square root function is never negative. Therefore, this option is also incorrect.

Hence, only the first function is correct which can verified below.

[tex]y=\sqrt x-5\\-4=\sqrt x-5\\\sqrt x=-4+5\\\sqrt x=1\\x=1[/tex]

So, we got a positive result without violating the definition of square root functions.

Therefore, the correct answer is [tex]y=\sqrt x-5[/tex]

Answer:

A. is the right answer on edge. 2020

Step-by-step explanation:

Answer:

35 ⋅ 104

(I hope this helped)

Answer:

35 ⋅ 104

Step-by-step explanation:

this was on my test and got it right. i hope this helped tho

Answer:

64

Step-by-step explanation:

f(-1)=-1-7=-8

g(f(-1))=(-8)^2=(-8)(-8)=64

Question is not proper; Proper question is given below;

Eliza and Jamie are making cupcakes for a bake sale at school.Eliza needs 2 1/3 cups of flour for her recipe, and Jamie needs 1 3/4 cups for her recipe. they have 4 cups of flour.Do they have enough flour for both of their recipes? explain.

Answer:

They do not have enough flour for both recipes.

Step-by-step explanation:

Given:

Amount of flour Eliza needs = [tex]2 \frac{1}{3}[/tex] cup

[tex]2 \frac{1}{3}[/tex] can be rewritten as [tex]\frac{7}{3}[/tex]

Amount of flour Eliza needs = [tex]\frac{7}{3}[/tex] cup

Amount of flour Jamie needs = [tex]1 \frac{3}{4}[/tex] cup

[tex]1\frac{3}{4}[/tex] can be rewritten as [tex]\frac{7}{4}[/tex]

Amount of flour Eliza needs = [tex]\frac{7}{4}[/tex] cup

Total Amount of flour they have = 4 cups

We need to find whether  they have enough flour for both recipes.

Total Amount of flour they need is equal to sum of Amount of flour Eliza needs and Amount of flour Jamie needs.

framing in equation form we get;

Total Amount of flour they need = [tex]\frac{7}{3}+\frac{7}{4}[/tex]

Now taking LCM for making the denominator common we get;

Total Amount of flour they need = [tex]\frac{7\times 4}{3\times 4}+\frac{7\times 3}{4\times3} = \frac{28}{12}+\frac{21}{12}= \frac{28+21}{12} = \frac{49}{12} \ cups \ \ \ \ \ OR \ \ \ \ \ 4\frac{1}{12} \ cups[/tex]

Now Since the Total amount of flour they need is [tex]\frac{49}{12} \ cups \ \ \ \ \ OR \ \ \ \ \ 4\frac{1}{12} \ cups[/tex] which greater than Total Amount of flour they have which is 4 cups.

Hence we can say that they do not have enough flour for both recipes.

Answer:

Step-by-step explanation:

Total number of guest = 182+18

= 200 guests

If 8 are using a table then the number of tables needed = 200/8

= 25tables

Answer: D

16*12 is 192. Plus the 6 for the bride and groom, and you get a total of 198.

Step-by-step explanation:

[tex]3 \times (3 \times 2) = 18 \\ 2 \times (3 \times 2) = 12 \\ 2 + (3 \times 2) = 8[/tex]

Answer:

Step-by-step explanation:

Let be "x" the unit price (price/ounce) of the soda in the 2-liter bottle and "y"  the unit price (price/ounce) of the soda in the case  of twelve 12 ounces cans.

According to the data provided in the exercise, you know that:

1. The 2-liter bottle of soda  is equal to 67.6 ounces.

2. That bottle costs  $1.89

Then, the unit price is:

[tex]x=\frac{1.89}{67.6}\\\\x\approx0.028[/tex]

3. There are 12 ounce  cans in the case. Then the total ounces is:

[tex]12\ oz*12=144\ oz[/tex]

4. It costs $2.99.  So the unit price is:

[tex]y=\frac{2.99}{144}\\\\y\approx0.021[/tex]

Since:

[tex]y<x[/tex]

The better bargain is the case of 12 ounce cans.

Answer:

A could work

Step-by-step explanation:

Because it is a square, all angles should be 90 degrees

Answer:Try B

Step-by-step explanation:

If its right please give me brainiest

The division problem 123 divided by 5 equals 24r3 is about arranging 123 objects into equal groups of 5. There will be 24 groups with 3 objects remaining that can't be added into any group.

In the division problem 123 divided by 5 equals 24r3, we're dividing the number 123 into equal groups of 5. When you divide 123 by 5, the quotient (or answer) is 24 and the remainder is 3. This means you can make 24 equal groups of 5 from the number 123, and you would have 3 left over which couldn't form a complete group of 5.

So, in terms of equal groups, you can say: '123 objects can be arranged into 24 equal groups of 5, with 3 objects remaining that cannot be added into any group because it would make that group unequal to the others.'

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Answer:

There are 9 terms, and the common difference is 11.

Step-by-step explanation:

The sum of the first n terms of an arithmetic sequence is:

S = n (a₁ + aₙ) / 2

where a₁ is the first term and aₙ is the last term.

252 = n (-16 + 72) / 2

n = 9

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n−1)

where d is the common difference.

72 = -16 + d (9−1)

d = 11

There are 9 terms, and the common difference is 11.

To find the number of terms and the common difference of an arithmetic progression, you can use the formulas for the sum of an arithmetic progression and the last term. In this case, there are 10 terms in the AP and the common difference is 8.

The first step is to understand that the sum 'S' of the first 'n' terms of an arithmetic progression (AP) can be given by this formula: S=n/2(2a+(n-1)d). Here 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.

From the question, we know that S=252, a=-16, and the last term is 72. The last term can be expressed as a+(n-1)d, hence 72=-16+(n-1)d.

Solving these two equations we get n=10, meaning there are 10 terms in the AP, and d=8, the common difference.

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Answer:

Cost of a coffee is $2.5 and cost of a latte is $4.25.

Step-by-step explanation:

Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.

Given:

4 coffees and 12 lattes cost $61.

12 coffees and 7 lattes cost $59.75.

∵ 1 coffee cost = [tex]c[/tex]

∴ 4 coffees cost = [tex]4c[/tex] and 12 coffee cost = [tex]12c[/tex]

∵ 1 latte cost = [tex]l[/tex]

∴ 12 lattes cost = [tex]12l[/tex] and 7 lattes cost = [tex]7l[/tex]

Now, as per question:

[tex]4c+12l=61-----1\\12c+7l=59.75----2[/tex]

Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,

[tex]-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25[/tex]

Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,

[tex]4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5[/tex]

Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.

A system of linear equations can determine the cost of a coffee and a latte, which are found to be $2.50 and $4.25 respectively.

To solve the question how much does a coffee and a latte cost, we can treat it as a system of linear equations problem. We have the following two equations based on the given information:

4 coffees + 12 lattes = $61

12 coffees + 7 lattes = $59.75

Let's denote the cost of one coffee as c and the cost of one latte as l. We can now rewrite the equations as:

4c + 12l = 61

12c + 7l = 59.75

Multiplying the first equation by 3 gives us:

12c + 36l = 183

Now we can subtract the second equation from this new equation to find the cost of lattes:

(12c + 36l) - (12c + 7l) = (183 - 59.75)

29l = 123.25

l = 123.25 / 29

l = $4.25

Having found the cost of a latte, we can now substitute this back into the first original equation to find the cost of a coffee:

4c + 12(4.25) = 61

4c + 51 = 61

4c = 10

c = 10 / 4

c = $2.50

Therefore, a coffee costs $2.50 and a latte costs $4.25.

Answer:

y=5

Step-by-step explanation:

5(8)-2y=30

40-2y=30

2y=40-30

2y=10

y=10/2

y=5

Answer: A. 1cm=0.3937 inch

              B. 61.417inch

               C. 5.1 ft

Step-by-step explanation:

A.

1inch=2.54cm

1/2.54=0.3937 inch

1cm=0.3937 inch

B. 156cm*0.3937=61.417 inch

C: 1 ft=12 inch

1:12=X:61.417

61.417 =12x

x=5.1 ft