-16p+37=49-21p what is the answer

Answer:

y = 4

Step-by-step explanation:

1) Simplify [tex]3^5[/tex] to 243.

[tex]{9}^{y}=\frac{243\times {9}^{6}}{{27}^{3}}[/tex]

2) Simplify [tex]{9}^{6}[/tex] to 531441.

[tex]{9}^{y}=\frac{243\times 531441}{{27}^{3}}[/tex]

3)  Simplify  [tex]243\times 531441[/tex] to  129140163.

[tex]{9}^{y}=\frac{129140163}{{27}^{3}}[/tex]

4) Simplify  [tex]{27}^{3}[/tex]  to  19683.

[tex]{9}^{y}=\frac{129140163}{19683}[/tex]

5) Simplify  [tex]\frac{129140163}{19683}[/tex] to 6561.

[tex]{9}^{y}=6561[/tex]

6) Convert both sides to the same base.

[tex]9^y=9^4[/tex]

7)  Cancel the base of 9 on both sides.

[tex]y=4[/tex]

Cheers,

ROR

Answer:

y = 4

Step-by-step explanation:

Decompose  in base 3

[tex]9^{y} =\frac{3^{5} (3^{2})^{6} }{(3^{3})^{3} } =\frac{3^{5}3^{12} }{3^{9} } =\frac{3^{17} }{3^{9} } =3^{17-9} =3^{8}[/tex]

if

[tex]3^{8} =(3^{2} )^{4} =9^{4}[/tex]

then

[tex]9^{y} =9^{4}[/tex]

[tex]y=4[/tex]

Hope this helps

The domain that makes sense in this context will be (0, 10].

The domain means all the possible values of x and the range means all the possible values of y.

James can hike f(n) miles after building up n days of stamina, subject to a maximum of 10 days.

Then the domain that makes sense in this context will be (0, 10].

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Let's first gather all the information we have:

 [tex]\rm\hookrightarrow Center: (-3, 2)\\\rm \hookrightarrow Radius: 5[/tex]

Let's put that into standard form [tex](x-h)^2+(y-k)^2 =r^2[/tex]

              [tex]\rm \hookrightarrow Equation: (x+3)^2+(y-2)^2 = 5^2[/tex]

To put that equation into general form:

 ⇒ expand all the quadratics on one side and move the radius squared

      to the same side as the quadratics

           [tex](x+3)^2+(y-2)^2 = 25\\x^2+6x+9+y^2-4y+4=25\\x^2+y^2+6x-4y-12=0[/tex]

Answer: x² + y² + 6x - 4y - 12 = 0

Hope that helps!

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Answer:

DE

Step-by-step explanation:

........................

The equation which best represents the scenario is, x²/2=271

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Perimeter is a length of the boundary surrounding the area

Area of rectangle=length x Breadth

Perimeter=2(length+breadth)

length=x

breadth=x/2

Area=271ft²

Area=length x breadth

So, using the given value we can write

271=x²/2

⇒x=√542

      =23.28ft

Therefore, the equation which best represents the scenario is, x²/2=271

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The explicit formula for the sequence is 3n -10

An arithmetic sequence is a series of terms which have  common difference between its consecutive numbers.

The sequence given is

−7, −4, −1, 2, 5, …

The common difference between each term is d =3

-4-(-7) = 3

-1-(-4) =3

The nth term for a sequence is given by

[tex]\rm T_n = a +(n-1)d[/tex]

Here a is the first term = -7

n is the no. of terms  = n

d is the common difference = 3

Therefore the equation will be

[tex]\rm T _n = -7 + (n-1) * 3[/tex]

[tex]\rm T _n[/tex] = -7 +3n -3

[tex]\rm T _n[/tex] = 3n -10

Therefore the explicit formula for the sequence is 3n -10 .

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Answer:

B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .

this is possible IF thewheele consists of 24 parts

The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The diagram is given below.

The total number of the events will be

Total events = 24

Then the chance of landing on $500 will be

The number of favorable events will be

Favorable events = 3

⇒ 3/24

⇒ 1/8

Then the chance of the Lose A Turn will be

Favorable event = 1

⇒ 1/24

The chance of landing on $500 and then Lose A Turn will be

P = (1/24)(1/8)

P = 1/192

The chance of landing on $500 and then Lose A Turn will be 1/192.

Then the correct option is C.

The question was incomplete, but the complete question is attached below.

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The correct answer is option B which is (-4-√11) and (-4+√11).

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).

(-4 - √11)  = -4 -3.31 =-7.31

(-4 + √11) = -4 +3.31 = -0.68

Therefore the correct answer is option B which is (-4-√11) and (-4+√11).

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The cost of renting a community center for x guest is given as y = 10x + 100

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the y intercept.

Let y represent the cost of renting a community center for x guest. Hence:

y = 10x + 100

The cost of renting a community center for x guest is given as y = 10x + 100

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Step-by-step explanation:

here is your answer. where are you from

The cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

For example, if you say 678, we must also know the whole number, but if you say 80%, it becomes evident. The percentage is the same as the amount of that value but ranges from 1 to 100.

Let's say

Cost of article = c

Given,

Marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894

1.4c - 0.15×(1.4c) = 26894

c = Rs 22600

So,

Marked price = 1.40c = Rs 31640

Profit percentage = ( 26894 - 22600)22600 = 19%.

Hence cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.

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Answer:

P= 2l + 2W

Step-by-step explanation:

(P-2W)/2= l

(P-2W)= 2l

P-2W= 2l

P= 2l + 2W

Answer:

5

Step-by-step explanation:

Count the digits.

Answer:

no they did not make enough money

Step-by-step explanation:

Glass: 35 ×0.50 = 17.5

plastic: 50 × 0.25 = 12.5

aluminum: 22 × 0.75 = 16.5

17.5 + 12.5 + 16.5 = $46.5

Answer:

B

Step-by-step explanation:

Answer:

a₃ = 1.25

Step-by-step explanation:

the sum to infinity is calculated as

S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]

a₁ is the first term and r the common ratio

given a₁ = 5 and S∞ = 10 , then

10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)

10(1 - r) = 5

10 - 10r = 5 ( subtract 10 from both sides )

- 10r = - 5 ( divide both sides by - 10 )

r = 0.5

then

a₂ = a₁ × r = 5 × 0.5 = 2.5

a₃ = a₂ × r = 2.5 × 0.5 = 1.25

Answer:

20 can be the answer of it

Answer:

3 is the smallest prime factor.

Step-by-step explanation:

ionk how to explain it but trust me its right.

Answer:

40 square units

Step-by-step explanation:

The question gives that both the large shape and the small missing shape are rectangles.  The formula for the area of a rectangle is [tex]A=bh[/tex] where "A" is the "Area", "b" is the "base" (bottom edge), and "h" is the height (side edge).

For rectangles, opposite sides (example: top & bottom) have the same length, so the top of the missing rectangle must also be 3.

To find the area of the figure, we must find the difference (subtraction) between the large rectangle (without a hole out of it) and the rectangular hole.

[tex]A_{\text{figure}}=A_{\text{large rectangle without hole}}-A_{\text{hole}}\\A_{\text{figure}}=(7)(7)-(3)(3)\\A_{\text{figure}}=49-9\\A_{\text{figure}}=40[/tex]

So, the area of the figure is 40 square units.

Answer:

40

Step-by-step explanation:

We can make a big square by making a line at the top open edge (as shown in the image attached below). We will first solve for [tex]A_{2}[/tex] and then [tex]A_{1}[/tex], and then finally solving for out answer by subtracting [tex]A_{1}[/tex] from [tex]A_{2}[/tex] .

[tex]A_{2}[/tex] is a square with side lengths of 7, so the area is 7 * 7 = 49.

[tex]A_{1}[/tex] is a smaller square with side lengths of 3, so the area is 3 * 3 = 9.

[tex]A_{2} - A_{1} = 49 - 9 = 40[/tex]

∴ Our final answer is 40

Answer:

$ 603.77

Step-by-step explanation:

Find unit rate of  dollars per hour :   359/22

   now multiply by hours :    359/22  * 37 = 603.77

Answer:

$603.77

Step-by-step explanation:

if they work 22 hours a week

and once a week they make $359

therefore divide to get the hourly rate

359/22 = 16.3181818182

they make 16.3181818182 per hour

then we have to multiply the hourly by the hours worked

16.3181818182 * 37 = 603.772727273

since this is in dollars ($) we round to the second decimal place (hundredths)

meaning we cut off the numbers after it

603.77║2727273

then, determine if the thousandths place is equal to or greater than five or less than five

since it is a 2 then the 7 stays the same

if it were a 5 or greater we would round up, making the 7 in the hundredth place turn into an 8.

therefore your answer is $603.77

hope this helps:)

Lets solve the question,

Given dimensions are:

Length = 26 feet

Width = 14 feet

concrete walkway with width = c

After installing the concrete walkway dimensions of the walkway will be,

Length = 26 + 2c

Width = 14 + 2c

She wants to build a wooden deck around the pool with a concrete walkway of width = w

Thus the dimensions of the wooden deck around the pool will be,

Length = [tex]26 + 2c + 2w[/tex]

Width = [tex]14 + 2c + 2w[/tex]

Now the perimeter of the wooden deck will be,

Perimeter = 2(length + width)

 [tex]= 2[(26 +2c + 2w) + 2(14 + 2c + 2w)] = 2(40 + 4c + 4w) = (80 + 8c + 8w)[/tex]

Therefore, perimeter of the wooden deck would be: 80 + 8c + 8w

Perimeter = (80 + 8c + 8w)

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The function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift:

Stretching:

The given function f(x) is needed to be stretched vertically by a factor of 2, therefore, the function can be written as,

g(x) = 2(x² - 7) = 2x² - 14

Now, the function is needed to be translated by 5 units in the downward direction, therefore,

p(x) = g(x)-5 = 2x² - 14 -5

p(x) = 2x² - 19

Hence, the function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.

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Answer:

26% increase

Step-by-step explanation:

Initial temperature= t

5% increase= t+ 5%= 1.05t

20% increase= 1.05t +20%= 1.05t*1.2= 1.26t

1.26 t= t + 26%

So temperature increased by 26%

The value of x for the equation to the true is 2/3

Given the following functions

f f(x) = −3x + 4 and;

g(x) = 2

If the functions are equal, then;

-3x + 4 = 2

Subtract 4 from both sides

-3x = 2 - 4

-3x = -2

x = 2/3

Hence the value of x for the equation to the true is 2/3

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Answer:

A

Step-by-step explanation:

(4x² + 2x - 3) + (3x² + 6)

= 4x² + 3x² + 2x - 3 + 6

= 7x² + 2x + 3

The expression is 17.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

10+(6-3) 22-4-1

Using the BODMAS rule,

First solve the bracket term

10+ 3 * 22 -4-1

Now, perform multiplication

10+66-4-1

Now, subtraction

10+66-5

=10+61

And lastly addition

=71.

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Answer:

17

Step-by-step explanation:

the answer is 17 :)

[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]

[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]

Answer:

a²​(a²​-a+2)

Step-by-step explanation:

Solution Given:

a⁴-a³+2a²​

first taking common a²​

we get

a²​(a²​-a+2) which is a required answer.

The percentage increase is 22.72%

The given parameters are:

Initial = 440 coins

Final = 540 coins

The percentage increase is calculated as:

%Increase = (Final - Initial)/Initial * 100%

So, we have:

%Increase = (540 - 440)/440 * 100%

Evaluate the difference

%Increase = 100/440 * 100%

Evaluate the quotient

%Increase = 0.2272 * 100%

Evaluate the product

%Increase = 22.72%

Hence, the percentage increase is 22.72%

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Answer:

The height of the balloon at 09 18 =  788.4 meters.

Step-by-step explanation:

As the hot air balloon is descending.

and the height of the balloon n minutes after it starts to descend is [tex]h_{n}[/tex]

meters.

The height of the balloon (n +1) minutes after it starts to descend, [tex]h_{n+1}[/tex]meters, is given by

[tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex] where K is a constant

Here the balloon starts to descend from a height of 1200 meters at 09 15

So [tex]h_{n}[/tex]=1200 meters

At 09 16 the height of the balloon is 1040 meters.

So  [tex]h_{n+1}[/tex]= 1040 meters

the height of the balloon at 09 18 = [tex]h_{n+3}[/tex] meters

now  [tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex]

k = [tex]\frac{h_{n+1 }-20 }{h_{n} }[/tex]

k= (1040 - 20) ÷ 1200

k = 0.85

Now [tex]h_{n+2}[/tex] = (0.85 × 1040) +20 =904 meters

Similarly  [tex]h_{n+3}[/tex] = (0.85 × 904) +20 = 788.4 meters.

Therefore the height of the balloon at 09 18 =  788.4 meters.

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A ratio shows us the number of times a number contains another number. The length of the pieces of wire are 200m, 250m, 300m, 350m, and 400m.

A ratio shows us the number of times a number contains another number.

Given the piece of wire are in the ratio 4:5:6:7:8. Therefore, the total length of the wire will be,

4x + 5x + 6x + 7x + 8x = 1500m

30x = 1500 m

x = 50 m

Now, the length of the wire will be,

4x = 4(50) = 200m

5x = 5(50) = 250m

6x = 6(50) = 300m

7x = 7(50) = 350 m

8x = 8(50) = 400 m

Hence, the length of the pieces of wire is 200m, 250m, 300m, 350m, and 400m.

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Answer:  [tex]\textsf{Slope = 6}[/tex]

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Given:  [tex]\textsf{f(x) = 6x + 7}[/tex]

Find:  [tex]\textsf{The slope of the equation}[/tex]

Solution: Looking at the equation it is in standard form which is y = mx + b where m is the slope and b is the y-intercept.  Looking at our expression we can see that m is equal to 6 which is our slope.

Therefore, the slope of our expression is equal to 6.