a pot of boiling soup cools at 80 degree in 12.5 minutes what is the average rate of temperature loss per minute

The equation of the circle in standard form is: (x + 2)² + (y - 1)² = 1

What is the equation of the circle?

The general form of the equation of a circle is:

(x - h)² + (y - k)² = r²

Where;

(h, K) is the coordinate of the center of the circle.

r is radius.

To find the equation of the circle in standard form, we need to determine the center and radius of the circle.

Since the center of the circle lies on the line y = 3x + 1 and is tangent to the x-axis at (-2,0), we can determine that the center of the circle is (-2,1) and the radius is 1.

Therefore, the equation of the circle in standard form is:

(x + 2)² + (y - 1)² = 1

Answer:

Domain:  -∞ < x < +∞

Range : 2 ≤ f(x) < +∞

Step-by-step explanation:

See the graph attached to this question.

The two arrow shows the graph of a function y = f(x).

Now, the value of x varies from +∞ to -∞.

So, the domain of the function is -∞ < x < +∞

Again from the graph the range of the function i.e. values of y varies from 2 to +∞ and including 2.

Therefore, the range of the function is 2 ≤ f(x) < +∞ (Answer)

Answer:

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Step-by-step explanation:

Let

x ----> pints of pure fruit juice at 70%

y ----> pints of pure fruit juice at 95%

we know that

[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation A

Remember that

[tex]70\%=70/100=0.70[/tex]

[tex]95\%=95/100=0.95[/tex]

[tex]80\%=80/100=0.80[/tex]

so

[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]0.70(110-y)+0.95y=0.80(110)[/tex]

solve for y

[tex]77-0.70y+0.95y=88[/tex]

[tex]0.25y=88-77[/tex]

[tex]0.25y=11[/tex]

[tex]y=44[/tex]

Find the value of x

[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]

therefore

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Answer:

Printer: $257, Computer: $771

Step-by-step explanation:

First you want to make a part to part diagram. It sounds stupid at first but trust me it works, We assume the both have the same amount. Now we draw 3 boxes for printer because it is 3 times as much. Now we have 4 boxes. divide 1028 by 4 and get 257. That is the amount for each box. You now know the printer is 257 dollars. Now multiply that by 3 to find cost of printer. 257x3=771.

Now you know the computer cost 771 dollars. You can check your work by adding them up. Hope this helped!!!!

Printer | []

Computer| [] [] []

The expression 56x+40y−48z can be rewritten as a product of the greatest common factor and one other factor, which is 8(7x+5y−6z). Therefore, the correct answer is A.

The expression 56x+40y−48z can be factored by identifying the greatest common factor (GCF). In this case, the GCF of 56, 40, and 48 is 8. Therefore, you divide each term in the expression by the GCF which will give you 7x+5y-6z. Hence, the expression can be rewritten as a product of the GCF and one other factor, which is 8(7x+5y−6z). So, the correct answer is A - 8(7x+5y−6z).

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Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.

Step-by-step explanation:

Length of garden = 9 ft

width of garden = 8 ft

Hence we will first find the total area of garden.

Total area of garden = length × width = [tex]8 \times 9 = 72ft^2[/tex]

He planted 1/2 of the garden with vegetables.

Hence.

Area of Vegetables garden = [tex]\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2[/tex]

He planted tomatoes in 1/3 of the vegetable garden and corn in the rest

Area in which tomatoes was planted = [tex]\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2[/tex]

Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = [tex]36ft^2-12ft^2=24ft^2[/tex]

Hence Area of vegetable garden in which corn was planted is 24 sq.ft.

Answer:

Let x be the number

5 times a number:

5x

The quotient of the number and 2.

5x / 2

Final answer:

The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.

Explanation:

The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.

Answer:

The segment area [tex]= 113.09\ unit^2[/tex]

Step-by-step explanation:

Area of the segment = [tex]\frac{(\theta)}{360} \times \pi r^2[/tex],where [tex]\theta[/tex] is the angle.

We can also say that [tex]90\ degrees[/tex] is covered with one segment and we have total [tex]4[/tex] segments (quadrants),so area of the circle divided by [tex]4[/tex] will give us the segement area of the arc.

So area [tex]\frac{\pi r^2 }{4} =\frac{\pi(12)^2}{4} = 113.09\ units^2[/tex]

So the area of the segment [tex]= 113.09 \ units^2[/tex]

Answer:

14b - 10ab + 34a²b - 64a²b²

Step-by-step explanation:

We have to simplify the expression

2ab + 3b + 7b + 3a × 3a × b + 4b - 8ab × 8ab + 5a × 5a × b - 12ab

= 2ab + 3b + 7b + 9a²b + 4b - 64a²b² + 25a²b - 12ab

{Since (3a × 3a × b) = 9a²b, (8ab × 8ab) = 64a²b² and (5a × 5a × b) = 25a²b}

= 2ab + 10b + 9a²b + 4b - 64a²b² + 25a²b - 12ab  

= 14b - 10ab + 34a²b - 64a²b² (Answer)

Answer:

The answer would be 18/16 or 1 1/8.

Final answer:

The costs for members and nonmembers of a local fitness center will be the same after attending 6 aerobics classes. Members have an initial $12 membership fee plus $2 per class, while nonmembers pay $4 per class.

Explanation:

To find the number of aerobics classes for which the cost for members and nonmembers will be the same, we need to set up an equation that compares the two cost structures. For members, the cost is a $12 membership fee plus $2 per class, which we can express as Cm = 12 + 2n, where Cm is the cost for members and n is the number of classes. For nonmembers, the cost is $4 per class, so we can express that as Cnm = 4n, where Cnm is the cost for nonmembers.To find the number of classes where costs are the same, we set Cm equal to Cnm:

Subtract 2n from both sides: 12 = 2n

Divide both sides by 2: n = 6

Therefore, the costs for members and nonmembers will be the same when they attend 6 aerobics classes.

Answer:

27/12

Step-by-step explanation:

6 3/4=27/4

(27/4)/3

(27/4)(1/3)=27/12

Answer:

The range of a set of data is the difference between the highest and lowest values in the set

Step-by-step explanation:

Answer:

point blank range is the range at which you don’t need to aim high or low to hit your aiming point. Maximum Point Blank Range (MPBR) is simply the farthest end of that distance.

Step-by-step explanation:

[tex]\bf 18-\sqrt{-25}\implies 18-\sqrt{-1\cdot 25}\implies 18-\sqrt{-1}\cdot \sqrt{25}\implies 18-5i[/tex]

Answer: 18-5i

Step-by-step explanation:

Answer:

From given option ,  the equation of parabola is                                            y = negative x² divided by 12

Step-by-step explanation:

Given as for parabola :

The focus is at (0 , - 3)

The directrix equation is y = 3

Now, equation of parabola parallel to y-axis is

( x - h )² = 4 p ( y - k )

where focus is ( h , k+p )   and  directrix equation is y = k - p

So, from equation

h  = 0     and   k + p = - 3

And y = k - p   i.e k - p = 3

Now solving  ( k + p ) + (  k - p ) = - 3 + 3

or, 2 k = 0  ∴ k = 0

Put the value of k , k + p = - 3

So, 0 + p = - 3    ∴ p = - 3

Now equation of parabola with h = 0  , k = 0  , p = - 3

( x - h )² = 4 p ( y - k )

I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )

Or, x² = - 12 y   is the equation of parabola

Hence  From given option ,  the equation of parabola is                                y = negative x² divided by 12       Answer

Answer:

Step-by-step explanation:

A) 1/7, 3/7, 9/7, 27/7,81/7

Explanation: actually in it we simply multiply the nominator with 3.

B) 24,12,6,3,1.5

Explanation: In this we simply half the value or we can say that divided by 2.

Answer:

$697

Step-by-step explanation:

25% × 4 = 100%

174.25 × 4 = 697

Answer:

174.25

Step-by-step explanation:

174.25 × 4 = 697

697 × 0.25 = 174.25

Answer: 174.25

Answer:

x=-1 and x=-2

Step-by-step explanation:

Given

[tex]f(x)=\dfrac{1}{(x+1)(x+2)}[/tex]

This function is undefined when the denominator becomes 0. Find values of x for which the denominator is 0:

[tex](x+1)(x+2)=0\\ \\x+1=0\ \text{or}\ x+2=0\\ \\x=-1\ \text{or}\ x=-2[/tex]

Thus, the lines with equations [tex]x=-1[/tex] and [tex]x=-2[/tex] represent vertical asymptotes (see attached graph)

Answer: -1 and -2

Step-by-step explanation:

Answer:

w=4

Step-by-step explanation:

10+15(w-2)=40

distribute the 15

10+15w-30=40

combine like terms

-20 + 15w = 40

15w=60

w=4

Answer:

y = -2

Step-by-step explanation:

to do this, you have to plug in -8 for x

7(-8) - 2y = -52

-56 - 2y = -52

+56          +56

-2y = 4

/-2     /-2

y = -2

Answer:

The linear equation is 1.25x + 0.5x = y

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Price of ride ticket at country fair = US$ 1.25

Total spent by Tom for rides and admission= US$ 43.75

Number of ride tickets bought by Tom = 25

Price of admission is the same for everyone

Total cost = y

Number of tickets = x

2. Let's find out the cost of the admission:

Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission

Replacing with real values:

1.25 * 25 + Cost of admission * 25 = 43.75

31.25 + 25 * Cost of admission = 43.75

25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)

25 * Cost of admission = 12.50

Cost of admission = 12.50/25 (Dividing by 25 at both sides)

Cost of admission = 0.50

3. Let's write a linear equation to determine the cost for rides tickets and admission:

Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission

Total cost = y

Number of tickets = x

1.25x + 0.5x = y

Answer:

The measure of angle F is m∠F=130°

Step-by-step explanation:

step 1

Find the measure of angle E

we know that

An isosceles triangle has two equal sides and two equal interior angles

In this problem

DF=EF ----> given problem

so

Triangle DEF is an isosceles triangle

m∠D=m∠E

we have

m∠D=25°

substitute

m∠E=25°

step 2

Find the measure of angle F

we know that

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

so

m∠D+m∠E+m∠F=180°

substitute the values

25°+25°+m∠F=180°

50°+m∠F=180°

m∠F=180°-50°

m∠F=130°

Answer:Can You please like this I want to rank up

Step-by-step explanation:

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The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

Step-by-step explanation:

The recursive formula of the sequence is

[tex]a_{1}=6[/tex] and [tex]a_{n}=\frac{4}{3}*a_{n-1}[/tex]

To find the first five terms do that:

∵ [tex]a_{1}=6[/tex]

∴ [tex]a_{2}=\frac{4}{3}*6[/tex]

∴ [tex]a_{2}=8[/tex]

∵ [tex]a_{2}=8[/tex]

∴ [tex]a_{3}=\frac{4}{3}*8[/tex]

∴ [tex]a_{3}=\frac{32}{3}[/tex]

∵ [tex]a_{3}=\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{4}{3}*\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{128}{9}[/tex]

∵ [tex]a_{4}=\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{4}{3}*\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{512}{27}[/tex]

The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

Learn more:

You can learn more about sequences in brainly.com/question/1522572

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Answer:

The absolute value of a number is its distance from zero on the number line. For example, -7 is 7 units away from zero, so its absolute value would be 7

|-4|=4

|1|=1

Step-by-step explanation:

the absolute value of - 4.5 = | - 4.5 | = + 4.5

the absolute value of 1 = | 1 | = + 1

Answer: 42 pages

Step-by-step explanation: 6 pages x 7 days= 42 pages

Answer:

12.  x = 50

13.  m∠M = 34°

Step-by-step explanation:

12.

Since the triangles are congruent, the sides' lengths are proportional. We can set up a ratio and solve for x.

Side JG corresponds to Side KM

Side HG corresponds to Side LM

Now, we can set up a ratio, cross multiply, and solve for x. Shown below:

[tex]\frac{35}{70}=\frac{25}{x}\\35x=70*25\\35x=1750\\x=\frac{1750}{35}\\x=50[/tex]

Thus, the value of x is 50

13.

The triangles are similar, so sides are proportional and angles are not related in the same way. Angles are same for both.

We want the value of Angle M, that angle corresponds to Angle G of the left triangle.

It is given that Angle G = 34, so Angle M would be the same degree measure as well.

Hence,

m∠M = 34°

Answer:

1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]

2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]

3. The x-intercept of the linear model is [tex]d = x = 12[/tex]

Step-by-step explanation:

Given:

[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]

Where,

[tex]P_{2}[/tex] is the number of phones.

d is the number of days he has worked that week.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

[tex]y = mx + c[/tex]

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

[tex]m = \frac{-25}{3}\\\\c = 100[/tex]

So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].

and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]

For finding x-intercept put y = 0

Here,[tex]P_{2}(d) = 0[/tex]

[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]

So, the x intercept of the linear model is [tex]d = x = 12[/tex]

Answer:

Option 4 : 19

Step-by-step explanation:

For trapezoid ABCD : AB = 16 and CD = 28

E and F are midpoints of the legs

So, EF = (AB + CD)/2 = (16+28)/2 = 44/2 = 22

GH be the median of ABFE

So, GH = (AB + EF)/2 = (16+22)/2 = 38/2 = 19