The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .

What is the equation of the circle in standard form?

Answer:

[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]

Step-by-step explanation:

Concept : We have to differentiate the given equation twice and then put the values of x and y at the given point.

The given point is (2,-5).

Given    xy - y = -5

Differentiating both sides,

[tex] x \times \frac{dy}{dx} + y - \frac{dy}{dx}[/tex] = 0

Substitute (x,y) as (2,-5)

[tex]2 \times \frac{dy}{dx} -5 - \frac{dy}{dx}[/tex] = 0

[tex]\frac{dy}{dx} = 5[/tex]

Differentiating again, we get

[tex]\frac{dy}{dx} + x \times \frac{ d^{2} y}{dx^{2} } + \frac{dy}{dx} - \frac{ d^{2} y}{dx^{2} } = 0[/tex]

Substitute values of x , y and \frac{dy}{dx} ,

[tex]5 + 2 \times \frac{ d^{2} y}{dx^{2} } + 5 - \frac{ d^{2} y}{dx^{2} } = 0[/tex]

[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]

Answer:

E(-5, - 6) D(5,-6) C(0,0)

Step-by-step explanation:

The strategy here is run then rise/fall

For example: for E, you run back - 5, then fall - 6

Answer:

They are actually equal.

Step-by-step explanation:

8.09 is equal to 8.090

They both have the same tenth(0) and the same hundredth(9).

A simple way to put this is to just add a zero to 8.09.

8.090

8.090

Answer:

false

Step-by-step explanation:

the only zero that matters is the one before the 9. so, if it was 8.009, ts smaller by one thousandth. if i had 8.09000000000, all the underlined zeros would mean nothing because they arent anything. they are the absence of a value.

The possible values of tutoring hours are 12 hours, 13 hours, 14 hours, 15 hours.

Given that, Nicole is working two summer jobs, making $10 per hour babysitting and making $20 per hour tutoring.  

In a given week, she can work at most 17 total hours and must earn a minimum of $250.  

Nicole worked 2 hours babysitting, then we have to determine all possible values for the number of whole hours tutoring that she must work to meet her requirements.  

Now, as she worked for 2 hours of babysitting, she will get 2 x $10 = $ 20  

Now, after this, she can work at most (17 - 2) = 15 hours for tutoring and she has to earn minimum of 250 – 20 = $230

Now, let the number of hours she tutored be "n"

Then, from above cases n ≤ 15  

And n x $20 ≥ 230

n ≥ 11.5  

Here we have to cases,  n ≥ 11.5 and n ≤ 15

So, the possible list of n values will be 12, 13, 14, 15

Hence, the possible values of tutoring hours are 12 hours, 13 hours, 14 hours, 15 hours.

The possible values for the number of whole hours tutoring that Nicole must work are: {12, 13, 14, 15} .

Given:

- Nicole can work at most 17 total hours: [tex]\( b + t \leq 17 \)[/tex].

- Nicole must earn a minimum of $250: [tex]\( 10b + 20t \geq 250 \)[/tex].

Nicole worked 2 hours babysitting, so ( b = 2 ).

Substituting ( b = 2 ) into the inequality [tex]\( b + t \leq 17 \)[/tex], we get:

[tex]\[ 2 + t \leq 17 \]\[ t \leq 17 - 2 \]\[ t \leq 15 \][/tex]

Now, let's find the minimum number of hours tutoring that Nicole must work to meet her requirements:

[tex]\[ 10(2) + 20t \geq 250 \]\[ 20 + 20t \geq 250 \]\[ 20t \geq 250 - 20 \]\[ 20t \geq 230 \]\[ t \geq \frac{230}{20} \]\[ t \geq 11.5 \][/tex]

Since Nicole must work a whole number of hours tutoring, the minimum number of hours tutoring she must work is 12 hours.

Answer:67.5 miles left

Step-by-step explanation:

15×30%= 4.5 then do 15×4.5= 67.5

The required distance of the trip is given as, 50 miles.

Jadas family has completed 30% of the trip. They have traveled 15 miles. How far is the trip is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the distance for the trip be x,
According to the question,
30% of x = 15
x = 15 / 30%
x = 1500 / 30
x = 50 miles

Thus, the required distance of the trip is given as, 50 miles.

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Answer:

slope is 1/2 or 0.5

Step-by-step explanation:

ΔX = 7 – -5 = 12

ΔY = 9 – 3 = 6

Answer:

I think that the answer is A

Step-by-step explanation:

Answer:

m=100-5c

Step-by-step explanation:

she starts with 100 bucks, and you take away 5 every time she buys a charm.

Answer:

A) 6/13 B) 7/40 C) 45/36 D) 37/43

Step-by-step explanation:

Answer: Graph A

Graph A: function f of x equals 5 multiplied by 2 to the power of negative x => f (x) = 5 (2)^-x

Graph B: function f of x equals 5 multiplied by 2 to the power of x => f (x) = 5 (2)^x

Graph C: function f of x equals 10 to the power of x => f (x) = 10^x

Graph D: function f of x equals 10 to the power of negative x => f (x) = 10^-x

 Therefore based on the mathematical interpretations above, only Graph A is similar to the given function. Hence the correct answer is:

Graph A

Answer:

The answer is A

Answer:

(2, 6)

Step-by-step explanation:

Because 8(2)-2(6)=16-12=4.

The ordered pair of the equation 8x - 2y = 4 is (2,6).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation is 8x - 2y = 4. The ordered pair will be calculated as,

8x - 2y = 4

( 8 x 2 ) - ( 2 x 6) = 4

16 - 12 = 4

4 = 4

Therefore, the ordered pair of the equation 8x - 2y = 4 is (2,6).

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The distance from home to second base in a slow pitch softball diamond is approximately 87.68 feet. This calculation is achieved through the use of the Pythagorean theorem, which utilizes the square lengths of the diamond sides to calculate the diagonal path between the bases.

The distance from home to second base in a slow pitch softball diamond can be calculated using the Pythagorean theorem, as the path forms a right triangle. The side lengths of the diamond are 62 ft, so we can use these as the legs of our right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, it's a^2 + b^2 = c^2, where c is the distance we want to find.

So, the calculation will be √((62ft)^2 + (62ft)^2). Simplifying this gives √(3844ft^2 + 3844ft^2), which is √7688ft^2. Which gives us approximately 87.68 ft. So, the distance from home to second base is approximately 87.68 feet.

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To find the distance from home to second base on a slow pitch softball diamond, use the Pythagorean theorem to calculate the diagonal of the square. With each side being 62 feet, the distance comes out to approximately 87.7 feet.

How to Find the Distance from Home to Second Base

In a slow pitch softball diamond, the bases form a square with each side measuring 62 feet.

We must compute the diagonal for the square in order to get the distance between home plate and second base.

This can be done using the Pythagorean theorem.

Step-by-Step Solution

Label the sides of the square. Each side is 62 feet.

Recall the Pythagorean theorem formula: a² + b² = c², where 'a' and 'b' are the legs of a right triangle, and 'c' is the hypotenuse (which, in this case, is the diagonal).

Here, both 'a' and 'b' are 62 feet because the square’s sides are equal.

→ Substitute the values into the formula: 62² + 62² = c²

→ Calculate the squares: 3844 + 3844 = c²

→ Combine the values: 7688 = c²

→ Take the square root to find 'c': c = √7688

The diagonal (distance from home to second base) is approximately 87.7 feet.

Therefore, the distance from home to second base is about 87.7 feet.

Step-by-step explanation:

Step 1: -x^2 is -1 because x is always 1.

Now that you found your first step take -1x+10=6. You're going to subtract 10 from both sides which leaves you with a sum of -4. So -1x= -4 now divide -4/-1x which gives you a positive number.

Answer:

x = -2 or 2

Step-by-step explanation:

-x² + 10 = 6

Move everything to one side.  I suggest moving the left side to the right so that the leading coefficient becomes positive.

0 = x² − 4

Factor the difference of squares:

0 = (x − 2) (x + 2)

Set each factor to 0 and solve.

x − 2 = 0

x = 2

x + 2 = 0

x = -2

Therefore, the solution is x = -2 or 2.

Answer:

2250

Step-by-step explanation:

From my understanding you have 450 packs to make and you need to put 5 tissue boxes in each one so we would just simply multiply 450 packages by 5 tissue boxes each package and get 2250

Answer:

Step-by-step explanation:

2 : 11 = 0 + r(2)

11 is 0 times in 2. The remainder of this division is 2.

Answer:

Answer. This is pretty tricky—if we have 2 divided by 11, the remainder is actually 2. The remainder is 2 because the quotient is 0 (11 goes into 2 zero times).

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

7 is higher than 4 so you round up one

A Whole number is any non-negative integer without a fractional or decimal portion. The whole number that is nearest to 15.74 is 16.

Any positive integer without a fractional or decimal portion is referred to as a whole number. This indicates that all whole numbers, such as 0-1, 2, 3, 4, 5, 6, and 7, are whole numbers.

If the number 15.74 is rounded to the nearest whole number, then the number that will be close to the number will be 16.

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Answers:

What is the ratio?         120:2

What is the unit rate?   60:1

What is the rate?          60 jumping jacks per minute

===================================================

Further Explanation:

To find the ratio of jumping jacks to minutes, you just write the two values 120 and 2 separated by a colon. That's how we get 120:2 as our first answer.

--------

Once we have 120:2, we divide both parts by 2 to get 60:1

120/2 = 60

2/2 = 1

The reason why we do this is so that the "2 minutes" turns into "1 minute". A unit ratio has the time value in unit increments so we can see how many jumping jacks Samuel can do. Writing "60:1" means "60 jumping jacks in 1 minute"

-------

Saying "60 jumping jacks in 1 minute" is the same as saying "60 jumping jacks per minute", which is similar to a car's speed of something like 60 miles per hour. The unit "X per Y" is the template for speed, where X is the number of items you get done and Y is the unit of time. In this case, X = 60 jumping jacks and Y = 1 minute.

Correct option is third [tex]\frac{2+3}{3}=\frac{x+y}{y}[/tex]

Given that:

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

Need to check which of the expression from given four expressions will be true.

Let's first try to eliminate wrong options.

If we observe carefully, we can say that option 2 that is [tex]\frac{3}{2}=\frac{x}{y}[/tex] is not correct as [tex]\frac{x}{y}[/tex] must be equal to [tex]\frac{2}{3}[/tex] and not [tex]\frac{3}{2}[/tex]

Lets now modify given expression that is:

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

On adding 1 to both sides we get

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

[tex]=>\frac{2+3}{3}=\frac{x+y}{y} \text { which is same as third option. }[/tex]

Hence correct option is third one that is [tex]\frac{2+3}{3}=\frac{x+y}{y}[/tex]

Answer:

abs(-1/4), abs(-0.5), abs(6/10), abs(6.25).

Step-by-step explanation:

abs(-1/4)=1/4=0.25

abs(6/10)=6/10=3/5=0.6

abs(6.25)=6.25

abs(-0.5)=0.5

-----------------------------------

abs(-1/4)=0.25 is the smallest, then comes abs(-0.5)=0.5, next comes abs(6/10), finally, comes abs(6.25).

8,653,972 rounded to the ten-thousands is 8,650,000.

Hope this helps!

8,653,972 rounded to the ten thousand is

8,650,000

Answer:

(- 5, 3 )

Step-by-step explanation:

Given the 2 equations

y = - 8x - 37 → (1)

x + 3y = 4 → (2)

Substitute y = - 8x - 37 into (2)

x + 3(- 8x - 37) = 4 ← distribute and simplify left side

x - 24x - 111 = 4

- 23x - 111 = 4 ( add 111 to both sides )

- 23x = 115 ( divide both sides by - 23 )

x = - 5

Substitute x = - 5 into (1) for corresponding value of y

y = - 8(- 5) - 37 = 40 - 37 = 3

Solution is (- 5, 3 )

Answer:

x = -5, y = 3 or you can write it as (-5, 3).

Step-by-step explanation:

y=-8x – 37

x+3y=4

From the second equation  x = 4 - 3y, so substituting in equation 1:

y = -8(4 - 3y) - 37

y = -32 + 24y - 37

-23y =  -69

y = 3

Now plug y = 3 into equation 1:

3 = -8x - 37

-8x = 40

x = -5.

Answer:

The height of the rock is 15 mm.

Step-by-step explanation:

Given : Cristian put a large rock on the bottom of the terrarium he made for his pet turtle.

To find : How high is the rock?

Solution :

The rock is a right rectangular prism 10 cm wide by 12 cm long.

Let the height be 'h'.

The volume of the right rectangular prism is [tex]V=L\times B\times H[/tex]

i.e. [tex]V=10\times 12\times h[/tex]

[tex]V=120h[/tex]

The rock displaces 1800 cm³ of water.

i.e. The volume of the right rectangular prism is equal to the rock displaces of water.

So, [tex]120h=1800[/tex]

[tex]h=\frac{1800}{120}[/tex]

[tex]h=15[/tex]

Therefore, the height of the rock is 15 mm.

The exact answer is going to be equal to 15mm

Hope this helped

Answer:

xy/2

Step-by-step explanation:

use m a t h w a y

Answer:

For [tex]x^2 - 4 = 0[/tex], x  = 2, or x = - 2.

Step-by-step explanation:

Here, the given expression is :

[tex]x^2 - 4 = 0[/tex]

Now, using the ALGEBRAIC IDENTITY:

[tex]a^2 - b^2 = (a-b)(a+b)[/tex]

Comparing this with the above expression, we get

[tex]x^2 - 4 = 0  = x^2 - (2)^2 = 0\\\implies (x-2)(x+2) = 0[/tex]

⇒Either (x-2) = 0 , or ( x + 2) = 0

So, if ( x- 2)   = 0 ⇒ x =  2

and if ( x + 2) = 0   ⇒ x = -2

Hence, for [tex]x^2 - 4 = 0[/tex], x  = 2, or x = - 2.

Answer:

Step-by-step explanation:

[tex]x^2-4=0\qquad\text{add 4 to both sides}\\\\x^2-4+4=0+4\\\\x^2=4\iff\sqrt{x^2}=\sqrt4\\\\|x|=2\Rightarrow x=\pm2[/tex]

Answer:

The measure of the three angles are 120°, 20° and 40°

Step-by-step explanation:

Let

x ----> the measure of the first angle

y ---> the measure of the second angle (smallest angle)

z ---> the measure of the third angle

Remember that

The sum of the angles in a triangle must be equal to 180 degrees

so

[tex]x+y+z=180[/tex] ----> equation A

[tex]x=y+100[/tex] -----> equation B

[tex]z=2y[/tex] ------> equation C

solve the system by substitution

substitute equation B and equation C in equation A

[tex](y+100)+y+(2y)=180[/tex]

solve for y

[tex]4y+100=180[/tex]

[tex]4y=180-100[/tex]

[tex]4y=80[/tex]

[tex]y=20\°[/tex]

Find the value of x

[tex]x=y+100[/tex]  ---- [tex]x=20+100=120\°[/tex]

Find the value of z

[tex]z=2y[/tex] ----> [tex]z=2(20)=40\°[/tex]

therefore

The measure of the three angles are 120°, 20° and 40°

Answer:

Step-by-step explanation:

120,20 and 40

Answer:

$9.35

Step-by-step explanation:

Tilapia: 1.5 * $3.88 = $5.82

Cod: 1 * 3.53 = $3.53

$3.53 + $5.82 = $9.35

Answer:

9.35

Step-by-step explanation:

3.88/2= 1.94 for every half pound of tilapia

1.94+3.88+3.53=9.35

Answer:

Cost of Tammy's lunch box before tax = $9.571

Step-by-step explanation:

Let the cost of Tammy's lunch box before tax be =$ [tex]x[/tex]

Sales tax charged = $0.727

Sales tax rate =7.596%

Sales tax charged in terms of  will be = 7.596% of the Original cost of lunch box[tex]=7.596\% \ of\ x =0.07596\ x[/tex]

So, we have,

[tex]0.07596\ x=0.727[/tex]

Dividing both sides by [tex]0.07596[/tex]

[tex]\frac{0.07596\ x}{0.07596}=\frac{0.727}{0.07596}[/tex]

∴ [tex]x=9.571[/tex]

∴ Cost of Tammy's lunch box before tax = $9.571

A Staghorn Coral can grow as much as 3.35 feet in 5 years under ideal conditions, assuming it grows at a fixed rate of 0.67 foot per year.

The question asks us to find out how much a Staghorn Coral, a type of branching coral, can grow in 5 years. Each year, the coral can potentially increase its size by 0.67 foot. To figure this out, we would use multiplication, a basic arithmetic operation.

First, we need to multiply the annual growth rate (0.67 foot) by the number of years (5). So, 0.67 * 5 equals 3.35 feet. This signifies that the Staghorn Coral can grow as much as 3.35 feet over the course of five years under optimal conditions.

Therefore, a Staghorn Coral can potentially add 3.35 feet to its branches during a 5 year span if it grows at the rate of 0.67 foot per year.

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