10. (2, -4); slope = -3

The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The water remaining is illustrated as y.

The time taken is t.

The appropriate equation will be:

y = 28 - (2 × t)

y = 28 - 2t

This illustrates the water remaining in the tank.

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The Recurrence interval for tornadoes in tuscaloosa county is 0.909

What is recurrence interval ?

The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence

Given that,

Total number of tornadoes is 77

Total time for Recurrence is 70 years

Using these data,

Recurrence = Total time for recurrence / Total number of tornadoes

Substituting we get,

Recurrence interval = 70/77

= (70/77)

= (0.909)

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The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13  .

In the question ,

the equation is given as

(x+yi)+(4+9i)=9-4i

to find the value of x and y , we solve LHS and RHS of the equation separately

So LHS =

(x+yi)+(4+9i)

x+yi+4+9i

Adding the real and imaginary terms , we get

(x+4)+(y+9)i which is equal to RHS that is 9-4i

So , on comparing , we get

x+4 = 9    and      y+9 = -4

x= 9-4      and      y = -4-9

x = 5       and       y = -13

Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .

The given question is incomplete , the complete question is

What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i  ?

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The formula to calculate the lateral area of a cone is given by

where

LA=10.5pi in2

r=2.1 in

l=? slant height

substitute given values

Answer:

x²[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

given

5[tex]\sqrt{20x^4}[/tex] - 3[tex]\sqrt{45x^4}[/tex]

simplify the 20 and 45 inside the radicals

[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]

[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]

Then

= 5(2[tex]\sqrt{5}[/tex] x² ) - 3(3[tex]\sqrt{5}[/tex] x² )

= 10[tex]\sqrt{5}[/tex] x² - 9[tex]\sqrt{5}[/tex] x²

= x²[tex]\sqrt{5}[/tex]

Answer:

The range is the allowed values of y.

Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}

Interval notation: [-9,0]

Hope that helps

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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The dimensions of building lot are 396 feet width and 1980 feet length.

Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.

18 acre = x×5x

Keep the value of acre in the above mentioned relation

18 × 43,560 = 5x²

Performing multiplication on Left Hand Side of the equation

784,080 = 5x²

Performing division by 5

x² = 156,816

Now taking square root to find the value of x

x = ✓156,816

x = 396 ft

Thus, the width of building lot is 396 feet

The length of building lot = 5×396

Performing multiplication

The length of building lot = 1980 feet

Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.

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The coordinates of the endpoint G is (0, 7).

The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -

Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)

Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].

(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)

Relating the x and y values -

x value :

3 = [tex] x_{1}[/tex] + 6/2

[tex] x_{1}[/tex] + 6 = 3×2

[tex] x_{1}[/tex] + 6 = 6

[tex] x_{1}[/tex] = 6 - 6

[tex] x_{1}[/tex] = 0

y value :

6 = [tex] y_{1}[/tex] + 5/2

[tex] y_{1}[/tex] + 5 = 6×2

[tex] y_{1}[/tex] + 5 = 12

[tex] y_{1}[/tex] = 12 - 5

[tex] y_{1}[/tex] = 7

Thus, the coordinates of point G from the line GH is (0, 7).

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This is because

distance = rate*time

Rate is another term for speed.

A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

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Answer:

x = 6

Step-by-step explanation:

180 = (8x - 18) + 110 + 40

180 = 8x + 132

48 = 8x

6 = x

If the measure of the angle is needed:

8(6) - 18 = 30

Hello!

Let's take this problem step by-step:

What is the formula for the circumference of a circle:

 [tex]\text{Circumference} = 2\pi *\text{radius}[/tex]

Since the circumference is 25 cm

  [tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]

Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]

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Out of the given integer(s), {−3} is the integer which will make the inequality 5x + 12 > 2x + 6 false.

As per the question statement, we are supposed to determine which integer will make the inequality 5x + 12 > 2x + 6 false

Let's solve the inequality for range of x first,

5x + 12 > 2x + 6

5x - 2x > 6 - 12

3x > -6

x > -2

So for all values of x > -2, the inequality 5x + 12 > 2x + 6 is true and for all values of x < -2, the inequality 5x + 12 > 2x + 6 false.

And out of the given options only x = -3 < -2

Hence, we accept {−3} as our required integer.

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Answer:

S:{−3}

Step-by-step explanation:

Got it right on a test.

Answer:

113.85

Step-by-step explanation:

230*55% because 100%-45%=55% is 126.5

Then 126.5*90% because 100%-10%=90% which is 113.85

The Simplification of square root of three times square root of twenty one is; C: three square root of seven

The Laws of Exponents are;

We have the expression;

√3 * √21

= √3 * √3 * √7

= (√3 * √3) * √7

= 3√7

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The statement that best describes the total cost of the Screened Loam, Round stone, and Crushed stone is; D: The total cost is greater than $325

We are given the amount of each material required for the Landscaping Project as;

Screened Loam = 3.25 cubic yards

Round stone = 1.5 cubic yards

Crushed stone = 2.5 cubic yards

Likewise we are given the cost of each of these materials per cubic yard as;

Cost of Screened Loam = $26 per cubic yards

Cost of Round stone = $112.5 per cubic yards

Cost of Crushed stone = $37.5 cubic yards

Thus;

Total Cost = (26 * 3.25) + (112.5 * 1.5) + (37.5 * 2.5)

Total Cost = 84.5 + 168.75 + 93.75

Total Cost = $347

Looking at the given options, the most appropriate is option D

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Answer:

-130

Step-by-step explanation:

g(18)= -8(18)+14

=-144+14

=-130

Answer:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Step-by-step explanation:

Point slope form is shown below:

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

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

[tex](y--2)=\frac{2}{3} (x-5)[/tex]

Simplify:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Answer:

Yes, is a function

Step-by-step explanation:

it does not repeat x's

For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

As given in the question,

For the saving account,

Amount deposited is directly proportional to the number of weeks

Let y be the amount deposited and x be the number of weeks

y ∝ x

y = kx

'k' is the constant of proportionality

As per data unit rate is measured in dollars per week

For y = $14 then x = 2 weeks

14 = 2k

⇒ k = $7

For y = $35 then x = 5weeks

35 =5k

⇒ k = $7

Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

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Answer:

75 boxes

Step-by-step explanation:

If you divide 24000 bats by 50 boxes, you get 480. Then, if you divide the 36000 by 480, you will get 75

Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.

An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."

A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.

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Answer:

its 12

Step-by-step explanation:

Answer:

DF = 13

Step-by-step explanation:

Congruent triangles:

        In ΔABC & ΔDEF,

                     ∠A = ∠D

                     ∠C = ∠F

                      CB = FE

            ΔABC ≅ ΔDEF   {Angle Angle Side congruency}

              DF = AC = 13

The most appropriate choice for remainder theorem will be given by-

Quotient = [tex]-x^3-2[/tex]

Remainder = -3

What is remainder theorem?

When f(x) is divided by (x-a), the remainder will be f(a).

If the remainder is zero, (x-a) will become a factor of f(x)

Expression to be divided is called dividend, expression by which dividend is divided is called divisor, expression obtained on division is called Quotient and the other part is the remainder.

There is also a well known formula

Divisor x Quotient + Remainder = Dividend

Here,

P(x) = [tex]-x^4 +3x^3 -2x+3[/tex]

P(3) =  [tex]-(3)^4+3(3)^3-2(3)+3[/tex]

      = [tex]\\-81+81-6+3[/tex]

      = -3

So by Remainder theorem, remainder is P(3)

So, Remainder = -3

Let the quotient be q(x)

divisor = [tex]x - 3[/tex]

We know,

Divisor x Quotient + Remainder = Dividend

[tex](x-3) \times q(x) +(-3) = -x^4 +3x^3 -2x+3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+3 +3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+6\\q(x) = \frac{-x^4 +3x^3 -2x+6}{x -3}\\q(x) =\frac{ -x^3(x-3)-2(x-3)}{x-3}\\q(x) = \frac{(x-3)(-x^3-2)}{x-3}\\q(x) = -x^3-2[/tex]

So, Quotient = [tex]-x^3-2[/tex]

Remainder = -3

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Answer: x = -33

Explanation:

Given the following question:

x - 11 = -44

Step 1: collect the like terms

x = -44 + 11

x = -33

Therefore, x = -33

Answer:

C

Step-by-step explanation:

f(x) =0

when the curve intersects the x axis

goodluck :)