A scuba driver wants to descend at an average rate of at least 7 feet per minute for 5 minutes. The table shows how many feet the scuba driver descends in the first 4 minutes. How many feet must the scuba driver descend in the fifth minute to meet the goal?

Final answer:

To find the equation of the circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). Using the distance formula, the radius is found to be 5. Therefore, the equation of the circle is [tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex].

Explanation:

To find the equation of a circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). We can use the distance formula to find the radius, which is the distance between the center and the point on the circle.

Using the distance formula, [tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex], we have:

[tex]d = \sqrt{((0 - 3)^2 + (2 - (-2))^2)} = \sqrt{((-3)^2 + (4)^2)} = \sqrt{(9 + 16)} = \sqrt{(25)} = 5[/tex]

So, the radius is 5. Therefore, the equation of the circle is

[tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex]

To find the equation of the circle with center at (3, -2) and passing through the point (0, 2), use the standard form and calculate the radius. Then, the equation is (x - 3)² + (y + 2)² = 25.

To find the equation of a circle with center at (3, -2) and passing through the point (0, 2), we can use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

Here, (h, k) is the center of the circle, and r is the radius. Given the center (3, -2), we substitute h = 3 and k = -2:

(x - 3)² + (y + 2)² = r².

Next, we find the radius by calculating the distance between the center (3, -2) and the point (0, 2) using the distance formula:

r = [tex]\sqrt{(0 - 3)^2 + (2 + 2)^2}[/tex]

= √(9 + 16)
= √(25)
= 5.

With r = 5, we can now write the full equation of the circle:

(x - 3)² + (y + 2)² = 25

To summarize, the equation of the circle with center at (3, -2) and passing through the point (0, 2) is (x - 3)² + (y + 2)² = 25.

Answer:

The answer is 231

Step-by-step explanation:

Answer:

231

Step-by-step explanation:

Answer:

4 > −3

Step-by-step explanation:

To find a number to the right of -3, it must be bigger than -3

The open part of the inequality faces the bigger number.

4 is bigger than -3

4>-3

Final answer:

The cabinet is 52 inches tall and the football team scored 5 field goals.

Explanation:

1)To find out how tall the cabinet is with 4 drawers each being 13 inches tall, you would multiply the number of drawers by the height of each drawer. So it would be 4 drawers into 13 inches per drawer.
2)For the football team scoring question, since a field goal is worth 3 points and the team scored 15 points from field goals, you would divide the points scored by field goals by the number of points a single field goal provides. It would be 15 points ÷ 3 points per field goal.

Answers:

1)The cabinet is 52 inches tall.

2)The team scored 5 field goals.

4x - 3y = 16

x + y = -3

Subtract y from both sides of the 2nd equation.

x = -3 - y

Now that we have a value of x, we can plug it into the first equation to solve for y.

4(-3 - y) - 3y = 16

Distributive property.

-12 - 4y - 3y = 16

Combine like terms.

-12 - 7y = 16

Add 12 to both sides.

-7y = 28

Divide both sides by -7.

y = -4

The value of y is -4, and now we can solve for the value of x.

Plug this value into either equation.

x + (-4) = -3

Add 4 to both sides.

x = 1

The value of x is 1.

To solve the linear equations 4x-3y=16 and x+y=-3, we can use substitution. The solution is x = 1 and y = -4.

To solve the linear equations 4x-3y=16 and x+y=-3, we can use the method of substitution or elimination. Let's use substitution:

From the second equation, we have x = -3-y. Now substitute this value for x in the first equation:

4(-3-y) - 3y = 16

-12 - 4y - 3y = 16

-7y = 28

y = -4

Substitute the value of y back into the second equation to find x:

x + (-4) = -3

x = -3 + 4

x = 1

Therefore, the solution to the linear equations is x = 1 and y = -4.

Answer:

2n/7=20

Step-by-step explanation:

let n be the number

Answer: 2x/7 =20

Step-by-step explanation:

Hi, to answer this question we have to write an equation.

Quotient means the result of the division of 2 numbers. In this case we have to divide twice a number (a number "x" multiplied by 2) by 7.

Mathematically speaking:

2x/7

That quotient is equal to 20.

So, the final equation is:

2x/7 =20

Feel free to ask for more if needed or if you did not understand something.

Answer:

D

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=2, b=16 and c=-9.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(16)+/-\sqrt{(16)^2-4(2)(-9)} }{2(2)}\\x=\frac{-16+/-\sqrt{256+72} }{4}[/tex]

We will now simplify and solve.

[tex]x=\frac{-16+/-\sqrt{328}}{4}\\x=-4+/-\sqrt{\frac{328}{16}}\\x=-4+/-\sqrt{\frac{41*8}{2*8}}\\x=-4+/-\sqrt{\frac{41}{2}}[/tex]

Answer:

[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]3\frac{1}{4}[/tex] is a mixed fraction and it can be written as

[tex]\frac{3*4+1}{4}=\frac{13}{4}[/tex]

13/4 can be break into

[tex]\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{1}{4}[/tex]

[tex]\frac{13}{4}[/tex] can be divided into [tex]\frac{3}{4}[/tex] and it is left with

[tex]\frac{1}{4}[/tex]

[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]

Answer:

Running rate of Destiny is 15 kmph

Step-by-step explanation:

Running rate of Destiny is the speed at which Destiny is running.

It can be calculated by finding the difference in the distance covered to the difference in the time taken.

So,

Running rate = Difference in distance covered / Difference in time taken

Difference in distance covered = 5-3 = 2 km

Difference in time taken = 10:44 am - 10:36 am = 44 -36 minutes = 8 mins =8/60 hour = 2/15 hour

Running rate = 2/(2/15) kmph =(2*15)/2 = 15 kmph

∴Running rate of Destiny is 15 kmph

Answer:

df/dx = e^x(1/x+ ln(x))

Step-by-step explanation:

f(x) = e^x * ln(x)

We can solve this by partial derivatives

df/dx = u dv + v du

let u = e^x and v = ln(x)

df/dx = e^x * 1/x + ln(x) * e^x

Factor out the e^x

df/dx = e^x(1/x+ ln(x))

Answer:

C. 81[-4/3]^n-1

Step-by-step explanation:

The explicit formula for a geometric sequence is given by a_n = a * r^(n-1). Using the provided values of a2 = 108 and a5 = 256, we can establish two equations to solve for 'a' and 'r'. This results in two possible explicit formulas for the sequence.

In a geometric sequence, each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. If we denote the first term of the sequence by 'a' and the common ratio by 'r', then the explicit formula of the sequence is: a_n = a * r^(n-1). Given that a2 = 108 (the second term is 108) and a5 = 256 (the fifth term is 256), we have two equations: a*r = 108 and a*r^4 = 256. Dividing the second equation by the square of the first equation, we get r^2 = 256/108^2 = 0.022. So, r is about +- 0.148. Substituting r into the first equation, we can solve for a. This gives us two possible explicit formulas for the sequence depending on whether we take the positive or negative value of r.

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Answer:

A. 54 tenths

Step-by-step explanation:

The 4 is in the tenths place. 54 is read as fifty-four, so it is 54 tenths.

Im not too sure, but C might work as an answer...

Sorry if it's wrong :(

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = -2/3 and the point (-9, 3). Substitute:

[tex]y-3=-\dfrac{2}{3}(x-(-9))[/tex]

[tex]y-3=-\dfrac{2}{3}(x+9)[/tex]      use distributive property

[tex]y-3=-\dfrac{2}{3}x-\dfrac{2}{3}\cdot9[/tex]

[tex]y-3=-\dfrac{2}{3}x-(2)(3)[/tex]

[tex]y-3=-\dfrac{2}{3}x-6[/tex]     add 3 to both sides

[tex]\boxed{y=-\dfrac{2}{3}x-3}[/tex]

[tex]\bf 3(x-1)^2+2x-7\implies \stackrel{\stackrel{x=3}{\cfrac{}{}}}{3[(3)-1]^2+2(3)-7}\implies 3[2]^2+6-7 \\\\\\ 3[4]+(-1)\implies 12-1\implies 11[/tex]

Answer:

B

Step-by-step explanation:

f(x) = [tex]x^{2} -8x+3[/tex]

=> f(x)= [tex]x^{2} -2(x)(4)+4^{2}-4^{2}+3[/tex]

=> f(x) = [tex](x-4)^{2}-4^{2}+3[/tex]

=> f(x) = [tex](x-4)^{2}-16+3[/tex]

=> f(x) = [tex](x-4)^{2}-13[/tex]

Answer:

f(x) = (x - 4)² - 13

Step-by-step explanation:

f(x) = x² − 8x + 3

x² − 8x + 3 = 0

x² - 8x = -3

x² - 8x + 4² = -3 + 4²

x² - 8x + 4² = -3 + 16

x² - 8x + 4² = 13

(x - 4)² = 13

(x - 4)² - 13 = 0

The vertex form of a quadriatic function  f(x) = x2 − 8x + 3 is;

f(x) = (x - 4)² - 13

Answer:

As you did not provide any "next steps", I would do it this way:

2q - 4 = 20 // add 4 to both sides

2q = 24 // divide both sides by 2

q = 12

Answer:

2q-4=20

Step-by-step explanation:

Counting in early childhood settings is best described as the D) basic ordering of numbers and identification by written number.

The question relates to the concepts children learn during their early mathematical development. The answer to the question is Basic ordering of numbers and identification by written number. This encompasses the fundamental process of recognizing numerical order and associating the spoken number with its written symbol. Counting in the early childhood setting involves learning the sequence of numbers, recognizing the relationship between the number and the quantity it represents, and connecting spatial understanding with numerical concepts.

Activities such as playing numerical board games, like Chutes and Ladders, are particularly beneficial as they involve working with numbers in a variety of ways - verbally, spatially, kinesthetically, and concerning time. This multisensory approach supports the development of numerical magnitudes, which are crucial for later mathematics achievement. The cognitive development in the area of mathematics reveals that engaging in numerical activities helps bridge the mathematical knowledge gap often observed between children from different socioeconomic backgrounds.

Answer:

Step-by-step explanation:$18,500 × .04=

$740×5= $3,700 + $18,500=

$22,200 for total loan

[tex]sin30^o=\frac{9}{a}\\\frac{9}{a}=\frac{1}{2}\\a=2\cdot9\\a=18[/tex]

Answer:

B. 18  

Step-by-step explanation:

We have been given a diagram of a right triangle and we are asked to find the value of a.

Since we know that Sine relates the opposite with hypotenuse of a right triangle.  

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

Upon substituting our given values we will get,

[tex]sin(30^o)=\frac{9}{a}[/tex]

Upon substituting [tex]sin(30^o)=\frac{1}{2}[/tex] in above equation we will get,

[tex]\frac{1}{2}=\frac{9}{a}[/tex]

Now let us cross multiply our equation to solve for a.

[tex]1\cdot a=9\cdot 2[/tex]

[tex]a=18[/tex]

Therefore, the value of a is 18 and option B is the correct choice.

Answer:

[tex]a= \frac{-52-b}{4}[/tex]

Step-by-step explanation:

Rearrange the equation so b is the independent variable.

To get 'b' as a independent variable , we need to get 'a' alone

WE need to solve for 'a' so that 'a' depends on variable b and 'b' becomes independent variable

4a+b=−52

To get 'a' alone , subtract 'b' from both sides

4a = -52-b

Divide by 4 on both sides

[tex]a= \frac{-52-b}{4}[/tex]

Answer:

a=-13-1/4b

Step-by-step explanation:

I got it on khan academy I didn’t get what the guy before got but sorry if it’s wrong

Answer: $9.75

Step-by-step explanation: I think this is how you do it. 20h=195 so you divide 195 by 20 to find our how much he gets an hour.

Answer:

9.75

Step-by-step explanation:

You have to divide the both by 20 since there is any like terms or anything to use, but you can use division on both sides since its 20h = 195.

20h   =    195

20            20

h       =     9.75

Answer:

The rangers

Step-by-step explanation:

Their number of wins didn't go up. In fact their wins decreased the most.

Answer:

D

Step-by-step explanation:

Improvement means positive change. The one with the least positive difference is the Rangers because they became WORSE by more than 10, which is bigger than even the Jets' negative amount.

Answer:

they are different numbers

Step-by-step explanation:

when you subtract 35-15 it comes out to 20 and the other one comes out to 17

Answer:

see below  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

14% ÷ 12 (MONTHS IN THE YEAR) = 1.16666667

If rounding to the nearest 10th of a percent the answer is 1.2% increase per month.

Answer:

1.1%

Step-by-step explanation:

Annual rate: 14 % = [tex]\frac{14}{100}  = 0.14[/tex]

Monthly rate  = [tex](1 + r )^{\frac{1}{12} } - 1[/tex]

=   [tex](1 + 0.14 )^{\frac{1}{12} } - 1[/tex]

=   [tex](1.14 )^{\frac{1}{12} } - 1[/tex]

= 1.01097 - 1

= 0.01097

In percent it becomes: 0.01097 * 100 = 1.097%

Rounded to the nearest tenth: 1.1%

Answer:

[tex]A=\frac{C^2}{4\pi ^2}[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. We will also need the formula for the area of a circle which is [tex]A=\pi r^{2}[/tex]. Since the area formula is in terms of r we will use the second formula for circumference.

We start by solving for r in the Circumference formula.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex]. We input this value of r into the area formula.

[tex]A=\pi r^{2} \\A=\pi (\frac{C}{2\pi })^2\\A=\pi (\frac{C^2}{4\pi ^2 })\\A=\frac{C^2}{4\pi ^2}[/tex]

The formula for the area of a circle in terms of its circumference is A = (C²) / (4π), by substituting the expression for the radius r = C / (2π) into the area formula A = πr².

The student has asked how to use the formula for the circumference of a circle to write a formula for the area of a circle in terms of its circumference. The formula for the circumference (C) of a circle is C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle.

To write the formula for the area (A) in terms of the circumference, we first solve the circumference formula for r: r = C / (2π). Then we substitute this expression for r into the formula for the area of a circle, which is A = πr². This gives us A = π (C / (2π))², simplifying, we get A = (C²) / (4π).

Thus, the formula for the area of a circle in terms of the circumference is A = (C²) / (4π).

Answer:

$29.02    

Step-by-step explanation:  

We will use compound interest formula to find the amount of interest after 3 months.

[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,

A= Amount after T years.

P= Principal amount.

r= Annual interest rate in decimal form.

n=  Number of times interest is compounded per year.

T= Time in years.

Let us convert our given interest rate in decimal form.

[tex]3.55\%=\frac{3.55}{100}=0.0355[/tex]

Let us convert our given time in years.

[tex]3\text{ months}=\frac{3}{12}\text{ years}=0.25\text{ years}[/tex]

Let us substitute our given values in above formula.

[tex]A=3260(1+\frac{0.0355}{12})^{12\times 0.25}[/tex]

[tex]A=3260(1+0.0029583333333333)^{3}[/tex]

[tex]A=3260(1.0029583333333333)^{3}[/tex]

[tex]A=3260\times 1.0089012810988858948[/tex]

[tex]A=3289.018176382368017048[/tex]  

We will use formula [tex]A=P+I[/tex] to find the amount of interest.

[tex]3289.018176382368017=3260+I[/tex]

[tex]3289.018176382368017-3260=I[/tex]

[tex]29.018176382368017=I[/tex]

[tex]I\approx 29.02[/tex]

Therefore, the total interest earned by the end of the third month will be $29.02.

Answer:

$28.59

Step-by-step explanation:

GradPoint doesn't seem to have the correct answer. THe closest I could get was to take 3,260 x .0355 x 90/365 = 28.54

Answer:

0.8

Step-by-step explanation:

We can solve P(A or B) by using the following:

[tex]P(AorB)=P(A)+P(B)-P(AandB)[/tex]

Since we know P(A) = 0.6, P(B) = 0.3 and P(A and B) = 0.1 we obtain:

[tex]P(AorB)=0.6+0.3-0.1=0.8[/tex]

Answer: 0.8

Step-by-step explanation: