what is thecentre and diameter of the circle with equation
[tex]x {2} + {y2} - 2y + 1 = 16[/tex]
​

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

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Answer:

A.

Step-by-step explanation:

hope its help^^

Answer:

.0214

Step-by-step explanation:

2.14 * .01 = .0214

to check:

.0214 * 100 = 2.14

Answer: 4 cups

Step-by-step explanation:

First, convert the 6 cups of water to fluid ounces:

6 cups (8 fluid ounces / 1 cup) = 48 fluid ounces.

Then, since each bowl took 4 fluid ounces, and there are 4 bowls, the total fluid ounces used must be 16.

Thus, if there was 48, and 16 were used, 32 fluid ounces must be left. Convert this to cups by dividing by 8 and getting 4 cups.

Answer:

$13,082.60 more

Step-by-step explanation:

Melanie:

[tex]A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36[/tex]

Amelia:

[tex]A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95[/tex]

Amelia-Melanie= $13,082.60

Answer:

App. 83.33 kg

Step-by-step explanation:

10/60=0.167 kg/minute

0.167/3=0.056 kg/minute/person

0.056 x 25 x 60= 83.33...6

Answer: y = 12.5x

Step-by-step explanation:

Because 250 bottles are filled every 20 minutes:

250/20=12.5

So, x=1, y=12.5

Hence, x=2 y=25

Because the number of bottles is directly proportional to the operation of the machine so:

12.5=a+b, 25.2a+b

a=12.5, b=0

Therefore, the equation is y = 12.5x

The Desmos graph of y = 12.5x is attached below

Answer:

7 feet

Step-by-step explanation:

60 inches is 5 feet add the 2 feet

Answer:

a=0.7

A Area

0.49

Using the formula

A=a2

Solving fora

a=A=0.49=0.7

Answer:

1207

Step-by-step explanation:

Total number of customers last week: 92 + 5 + 25 = 122

Number of customers who paid cash: 92

Percent of customers who paid cash last week: 92/122 × 100% = 75.4%

Next week:

Total number of customers: 1600

Expected number of customers paying cash:

75.4% of 1600 = 0.754 × 1600 = 1207

Answer:

the one you click is correct.

Step-by-step explanation:

Answer:

Mariah's investement is growing faster

Step-by-step explanation:

Here to find the rate at which the savings are growing at, we have to observe the slope of the line which describes the line representing the savings of each as a function of time.

The slope of a line is given by the relation;

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where m is the slope.

(x1,y1) is any point on the curve.

(x2,y2) is any other point on the curve.

Let's start of with Mariah by picking any 2 points from the table.

(0,150)

(1,159)

[tex]m(mar) = \frac{159 - 150}{1 - 0} = \frac{9}{1} = 9[/tex]

Let's move on to Mauricio's line and choose 2 points that lie on that line.

(0,190)

(1,195.7)

[tex]m(mau) = \frac{195.7 - 190}{1 - 0} = \frac{5.7}{1} = 5.7[/tex]

By looking at both slopes, we see that Mariah's growth rate (slope) 9>Mauricio's growth rate (slope) which is 5.7

Answer: A, C, F

Step-by-step explanation:

Answer:

4 quarters

Step-by-step explanation:

4 quarters = $1

14 nickels = $0.70

Answer:

no they dont form a Pythagorean triple

Step-by-step explanation:

a2 + b2 = c2

Answer:

1. (a. 8 b. 3 d. 6,6,12 e. 3,3,9) 2. (a. 2,3 b. 4,5 c. 6,6,2,3 d. 5,3,5) 3. (a.2/3 b.1/3 c.2/3 f.1/2 g.7/8 h.4/5)

Step-by-step explanation:

OK this is quite simple. Just multiply the top and bottom, otherwise known as the numerators and denominators, by whatever is next to it. In this case, 1a is [tex]\frac{2*4}{5*4}[/tex].

That would result in [tex]\frac{8}{20}[/tex]

Hey there!

In order to multiply fractions, we should multiply the numerator of the 1st fraction by the numerator of the 2nd fraction.

Same with denominators.

Let's multiply these fractions.

2/5=2*4/5*4=8/20

2/3=2*6/3*6=12/18

1/4=1*3/4*3=3/12

3/4=3*3/4*3=9/12

now divide:

10/15=10:5/15:5=2/3

12/18=12:6/18:6=2/3

12/15=12:3/15:3=4/5

15/25=15:5/25:5=3/5

Now, simplify the following fractions:

4/6

divide the top & bottom by 2:

2/3

next:

5/10

divide the top & bottom by 5:

1/2

next

5/15

divide the top & bottom by 5:

1/3

next:

12/18

divide the top & bottom. by 6

2/3

next

5/10

divide the top & bottom by 5

1/2

next

14/16

divide the top & bottom by 2

7/8

and then last but not least

28/35

divide the top & bottom by 7

4/5

And we're done!

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

Answer:

Left 2, up 1

Step-by-step explanation:

If you use slope, remember rise/run. You go up then left.

Answer: left 2 up 1

Step-by-step explanation: I did it by using the rule rise over run so it goes up then left . Hope it helps

Answer:

Formula for volume of hemisphere;

V = 2/3 * π * [tex]r^{3}[/tex]

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * [tex]r^{3}[/tex]

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.

Usando proporciones, hay que:

Una proporción es una fracción de la cantidad total.

En este problema, dos automovis, en sentidos opostos, salen al mismo tiempo. Por eso, su velocidad relativa es de 90 km/h + 80 km/h = 170 km/h.

La distancia es de 255 km, por eso, el tiempo en que se encontraran, en horas, es dado por:

t = 255/170 = 1.5h

La distancia recorrida por cada auto es dada por:

dA = 90 x 1.5 = 135 km.

dB = 80 x 1.5 = 120 km.

Puede-se aprender mas a cerca de proporciones en brainly.com/question/26425852

Answer:

15

Step-by-step explanation:

[tex]since \: \: \frac{5}{8} \times 40 \\ = 25[/tex]

[tex]those \: that \: did \: not \: sprout \: would \: be \\ \: equals \: to \: 40 - 25 \\ = 15[/tex]

Answer:

Step-by-step explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

⠀

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

⠀

✰ Solution :-

⠀

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

⠀

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

⠀

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

⠀

TSA = 2( lb + bh + hl )

⠀

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

⠀

Extra Credit Question.

⠀

Here, we can find out the total surface area by finding,

⠀

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

⠀

Now,

⠀

TSA = BA + 2 x S.A. + 2 x T.A.

⠀

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

After converting yards to miles:

2640 yards =  1.5 miles

Given,

2640 yards= ________ miles

Now,

To convert to yard to miles the conversion factor is 0.000568182.

So,

1 yard ⇒ 0.000568182 miles

Multiply 2640 on both sides,

2640 yards ⇒ 1.5 miles.

Therefore 2640 yards is equivalent to 1.5 miles.

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Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

I = PRT / 100

A = I + P

Where

A = P(1 + r/n)ⁿᵗ

Where

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

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Answer:

8/(x + 2) - 4/(x + 6)

Step-by-step explanation:

4x + 40 = Ax + 6A + Bx + 2B

Equating coefficients of x

4 = A + B      (1)

Equating constant terms:

40 = 6A + 2B    (2)

Multiply  equation (1) by -2:

-8 = -2A - 2B   .. (3)

Add (2) and (3):

32 = 4A

A = 32/4

A = 8.

4 = 8 + B

B = 4 - 8

B = -4.

The decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].

The partial fraction is the result of writing a rational expression as the sum of two or more fractions.

According to the given question.

We have a partial fraction

[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A}{(x+2)} +\frac{B}{(x+6)}[/tex]

We have to decompose the above partial fraction in terms of x.

The above partial fraction can be written as

[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A(x+6)+B(x+2)}{(x+2)(x+6)}[/tex]

⇒[tex]4x+40 = A(x+6)+B(x+2)[/tex]

⇒[tex]4x + 40 = Ax + 6A + Bx + 2B[/tex]

⇒[tex]4x + 40 = x(A+B) +6A + 2B...(i)[/tex]

On comparing the coefficient of x and the constant terms.

[tex]A+B = 4..(ii)[/tex]

⇒[tex]A = 4 - B[/tex]

and, [tex]6A+2B = 40..(iii)[/tex]

⇒[tex]2(3A+B) = 40[/tex]

Substitute the value of A in (iii)

⇒[tex]2(3A+B) = 40[/tex]

⇒[tex]3A+B = 20[/tex]

⇒[tex]3(4-B)+B = 20[/tex]

⇒[tex]12 - 3B +B = 20[/tex]

⇒[tex]12 - 2B = 20[/tex]

⇒[tex]-2B = 8[/tex]

⇒[tex]B = -4[/tex]

So, [tex]A = 4-(-4) = 8[/tex]

Substitute the value of A and B in the given partial fraction.

⇒[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex]

Hence, the decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].

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Answer:

[A] (4 ÷ 2)+(0.8 ÷ 2)

Step-by-step explanation:

Divide the 2 into each digit, which must be in the same spot it was before:

Knowing that 8 in 4.8 ⇒ 0.8

Thus, you can infer that [B] is wrong

You also infer that [D]  and [C] is wrong because 4 is a whole number.

Thus, that left us with [A] 4 ÷ 2+0.8 ÷ 2 which shows the quotient of 4.8 ÷ 2

Hence, [A] 4 ÷ 2+0.8 ÷ 2 is the answer.

~Learn with Lenvy~

Answer:

Option A

Simplification:

[tex]\rightarrow (4 + 0.8) \div 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{4.8 can also be written as 4 + 0.8}][/tex]

[tex]\rightarrow \dfrac{(4 + 0.8)}{2} = \dfrac{4 + 0.8}{2}[/tex]

[tex]\rightarrow \dfrac{4}{2} + \dfrac{0.8}{2}[/tex]

[tex]\rightarrow (4 \div 2) + (0.8 \div 2) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[Option A}}][/tex]

Answer:

hello

g (x)= x² - 5

g (3) = 3² - 5 =  9 - 5 =  4

Step-by-step explanation:

needless to say that the conversion from miles to kilometers uses a constant value, and therefore, they're directly proportional.

now, I could write the direct proportional relation blah blah but there's no need, we can simply squeeze it out of the table by simply checking how many kilometers there are in 1 mile.

well, we know that 11.0 miles give us 17.699 km, ok hmmm if we divide 17.699 ÷ 11 = 1.609.

if we do the same on table for 26 and 41.834, so 41.834 ÷ 26 = 1.609, and the next pair 54.706 ÷ 34 = 1.609, the value of 1.609 is consistent or constant, or namely that there are 1.609 kilometers in 1 mile.