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the horizontal asymptote as x tends to infinity that is  approaches positive infinity of \sqrt{4x^2+ 9x} - \sqrt{4x^2 +x} is 2

What do the asymptotes mean?

Definition of asymptote

a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the

slope of the line

[tex]f(x)=\sqrt{4x^2+9x}-\sqrt{4x^2+x} \\\\f(x)=2x(1+\frac{9}{4x}) ^{\frac{1}{2} } -2x(1+\frac{1}{4x})^\frac{1}{2}[/tex]

[tex]f(x)=2x( 1+\frac{1}{2} .\frac{9}{4x} +...... -1 -\frac{1}{2} .\frac{1}{4x} - ......)[/tex]

all the other terms involve 1/powers of x which vanish as x tends to infinity

[tex]f(x)=\frac{9}{4} -\frac{1}{4} +...[/tex]

Hence

[tex]\lim_{x \to \infty} f(x)=2[/tex]

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assume that y is normally distributed n​ (​, 2​). moving from the mean ​(​) 1.96 standard deviations to the left and 1.96 standard deviations to the​ right then P( -1.96 ≤ Z≤ 1.96) = 0.95

assume that y is normally distributed n​ (​, 2​). moving from the mean ​(​) 1.96 standard deviations to the left and 1.96 standard deviations to the​ right

Given that the z -scores -1.96 and 1.96

we have to find   Probability( -1.96 ≤ Z≤ 1.96)

Probability( -1.96 ≤ Z≤ 1.96) = |A(1.96)+A(-1.96)|

= |A(1.96)+A(-1.96|   (∵A(-Z) = A(Z))

=  0.4750+0.4750

= 2×0.4750

= 0.95

The probability lies between  -1.96 to 1.96

P( -1.96 ≤ Z≤ 1.96) = 0.95

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Answer:

500 divided by 2/3 = 500 * 3/2= 750

Step-by-step explanation:

If the length of a rectangle is 19 feet longer than the width. If the perimeter is 46 feet, The equation for this scenario where "x" represents the width is 2x + 2 (x +19 ) = 46  and the width is 2 feet.

Given data :

Length of a rectangle = 19 feet

Perimeter = 46 feet

Perimeter formula: 2l+2w=P

Let x represent the width

Hence,

2x + 2 (x +19 ) = 46

2x + 2 x +38 = 46

Collect like terms

4x  = 46 -38

4x = 8

Divide both side by 4x

x = 8/4

x = 2 feet

Therefore the equation that was used to find the width  is  2x + 2 (x +19 ) = 46  while the width is 2 feet.

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A line with slope m then the slope of a line perpendicular to it is ;M = -2/3

A straight line of the form  y = mx + c has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

To find the slope m of the given line using the slope formula

[tex]m = \dfrac{y-q}{x-p}[/tex]

with (p, q ) = (1, 0) and (x₂, y₂ ) = (x, y)  2 points on the line

m =  (3 -0)/(3-1)

m = 3/2

ALso it is given that a line with slope m then the slope of a line perpendicular to it is ;

M = -2/3

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The list which orders the numbers from least to greatest is π, √15, 4.1, 4. 85, √30.

To find the list which orders the numbers from smallest to largest we need to find the values of the respective numbers,

In the first list, we have the numbers √13, 2.1, 5.4, √/17, π. The value of √13 = 3.6 and the next term is 2.1. As 2.1 < 3.6, the list does not arrange numbers in increasing order.

In the second list, we have the numbers π, 3.2, 6.3, √17, √20. The value of π is 3.14 and the next terms are 3.2 and 6.3 which are more than the former. But the value of √17 is 4.1 which is less than the previous number 6.3.

In the third list,√23, 2.6, 1.3, √30, π the numbers are not arranged in increasing order as √23's value is 4.8 more than the second number.

In the fourth list, π,√15, 4.1, 4. 85, √30 the numbers are arranged in increasing order when calculated. The value of π is 3.1, of √15 is 3.8, then there are 4.1 and 4.85, and at last, is √30 whose value is 5.5.

Hence, π <√15 < 4.1 < 4. 85 <√30 is the list in the increasing order.

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Given,

No. of photos Marcus took on his cell phone = 18

Ratio of photos took by Marcus and Maribel = 3:4

Let the no. of photos took by Maribel be [tex]x[/tex].

∴ [tex]\frac{18}{x} = \frac{3}{4}[/tex]

⇒[tex]3x = 72[/tex]

⇒ [tex]x = \frac{72}{3} = 24[/tex]

Hence, Maribel took 24 photos.

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Answer:

31

Step-by-step explanation:

9+10

19

4+8

12

19+12= 31

The change in temperature was 25 F - (-8F) = 33 F.

Answer:

Explanation:

The change in temperature is the difference between the two temperatures. In our case this is 25 F - (-8F) = 33 F. Notice that the subtracting the negative number changes the sign of the operation and turns it into an addition problem25 F+ 8 F = 33 F.

The number that is less than a whole, in 3 decimal places and when rounded to the nearest tenth is 0.78 will be 0.775.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position. The word decimus, which means tenth in Latin, is derived from the base word decem, or 10.

It should be noted that 0.775 is in 3 decimal places. In this case, the last 5 will be converted and this will become 0.78.

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Answer:

C (50, - 40 )

Step-by-step explanation:

C is the midpoint of AB

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (0, - 80 ) and (x₂, y₂ ) = B (100, 0 ) , then

C = ( [tex]\frac{0+100}{2}[/tex] , [tex]\frac{-80+0}{2}[/tex] ) = ( [tex]\frac{100}{2}[/tex] , [tex]\frac{-80}{2}[/tex] ) = (50, - 40 )

Answer:

0.87 cent

if i did this right.

Step-by-step explanation:

17.50 divided by 2 = 8.75

8.75 divided by 10 = 0.87

We have a horizontal translation of 2 units to the right, so the correct option is B.

"The graph of y = f(x) will shift right 2 units."

For any function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, the translation is to the left.

if N < 0, the translation is to the right.

In this case we have the function written as:

y = f(x - 2)

So we have N = -2, which means that we have a translation of 2 units to the right.

Then the correct option is B.

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Answer:

The error is in line A. f(x), not x, is equal to 21.

f(x) = 2x - 1 = 21

2x = 20, so x = 10.

The price in which Evan bought the car for in 2008 is 75 percentage or £14000

What is Percentage ?

Percentage (%), which is a relative figure used to denote hundredths of any quantity. One percent is represented by the symbol 1%; hence, 100 percent denotes the entire amount, and 200 percent designates double the amount.

Given,

Loss% = 25%

Profit% = 45%

selling price = £15,225

The price of the car before getting the profit of 45%

= 15225 / 145 x 100

= 105 x 100

= 10500

The price of the car before getting the profit of 45% is  £10500

Now, he had a loss of 25%

=100% - 25%

= 75%

So, the price will be

= 10500 / 75 x 100

= 14000

Hence, Evan bought the car for £14000 in 2008

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∠ AEC = ∠ DEB by using the property of the straight lines.

We are given the two lines AB and CD.

We are given that they intersect at point E and both are the straight lines.

Now, we know that, the sum of angles of a straight line will be equal to 180° (straight line property).

Now, For line AB, we get that:

∠ AED + ∠ DEB = 180°    …(1)

For line CD, we get that,

∠AED + ∠ AEC = 180°   … (2)

Now, we will subtract (1) from (2) and we get that:

∠ AED + ∠ DEB - ∠AED - ∠ AEC = 180° - 180°

∠ DEB - ∠ AEC = 0

∠ DEB = ∠ AEC

∠ AEC = ∠ DEB

Hence proved.

Therefore, we get that, ∠ AEC = ∠ DEB by using the property of the straight lines.

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Answer:(a+1) (ba+b−5)

Step-by-step explanation:

The number of baby camels at the zoo is 44.

Given: The number of adult camels is 6 and the number of baby camels is 5 for every 6 camels respectively.

To find :We have to find how many baby camels are at the zoo.

Explanation:

Step 1:The ratio of adult camels and baby camels is 6:5

Step 2:Let the number of adult camels = 6x .

Step 3:Let the number of baby camels = 5x

Step 4:It is given that the total number of adult camels and baby camels is 44 at the zoo. So According to the questions,

⇒6x+5x=44

⇒11x=44

⇒x=44/11

⇒x=4

∴The number of adult camels = 6×4

                                               = 24

And the number of baby camels at the zoo.

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Answer:x^2*y/(4/5)

Step-by-step explanation:

That's the equation. Your question is the word form.

Answer: the number in question is 5.5

Step-by-step explanation: brainliest please? i could really use it

Answer:

D. 0 ≤ x ≤ 10

Step-by-step explanation:

I took the quiz.

The domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

It is given that:

A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m.

The function is:

f(x) = 20(2)ˣ

The value of x represents the domain of the exponential function.

The domain of the function is:

0 ≤ x ≤ 10

Thus, the domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.

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Answer:

60 minutes

Step-by-step explanation:

    Number of problems done, and the time taken to finish them are in proportion.

Let the time taken to finish 40 problems = 'x'

30 : 45 = 40 : x

Product of extremes = 30 *x = 30x

Product of means = 45 * 40

Product of extremes = Product of means

                30 *x    = 45 * 40

                          [tex]\sf x = \dfrac{45*40}{30}[/tex]

                         x = 15 * 4

                          x = 60 minutes

If ratio of m to n is equal to 5 then, m = 5n

Ratios :- The quantitative relation between two amounts showing the number of times one value contains or is contained within the other are known as ratios.

m/n = 5

m = 5    

Therefore, option b is correct i.e. m = 5.                                    

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3x - y = -7 is the required equation of the line, which will bisect the line segment with endpoints (-7, 6) and (5,2).

the equation for the perpendicular bisector of the line  with end points [tex](x_{0},y_{0})\\[/tex] and [tex](x_{1},y_{1})[/tex] are given by:

[tex]2(x_{1} - x_{0})x+2(y_{1}-y_{0})y = x^{2} _{1}-x^{2} _{0}+y^{2}_{1}-y^{2}_{0}[/tex]

in the given case we have,

[tex](x_{0},y_{0})\\[/tex] = (-7,6)

and

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

now substituting the given values in the above equation we get,

2(5-(-7))x + 2(2-6)y = 5²- (-7)² + 2²- 6²

= 24x - 8y = 25 - 49 + 4 - 36

= 24x - 8y = -56

on simplifying by dividing the LHS and the RHS by 6 we get our equation to be,

3x - y = -7

What is a perpendicular bisector?

A line or segment that is perpendicular to another segment and passes through its midpoint is called a perpendicular bisector.

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The numerical expression for model the number of miles to Masha runs, jogs or walks will be;

⇒ 1 + 11 + 2

⇒ 14

What is Addition?

Addition in math is the process of combining two or more numbers. Addends are the numbers added, and the result or the final answer.

Now,

Masha is training for marathon.

Masha jogs 1 mile.

And, runs at a fast pace for 11 miles.

And, For finishing by walking she walk 2 miles to cool down.

Now,

The numerical expression for model the number of miles to Masha runs, jogs or walks will be;

⇒ Miles in jogs + miles in runs + miles in walk

⇒ 1 + 11 + 2

⇒ 14 miles.

Therefore,

The numerical expression for model the number of miles to Masha runs will be;

⇒ 1 + 11 + 2

⇒ 14

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As per the given question;

The coordinates of the original triangle ABC with vertices is ;

A(-4, 1), B(-1, 1), and C(-1, 3)

For the first reflection along y-axis, the coordinates of y will remain same and x will reverse to positive.

Y-axis reflection: A(4, 1), B(1, 1), and C(1, 3)

Now, the triangle is again reflected along x-axis.

Thus, for the first reflection along x-axis, the coordinates of x will remain same and y will reverse to positive.

x-axis reflection: A(4, -1), B(1, -1), and C(1, -3)

Rotation: The circular motion of an item around a center is referred to as rotation.

The rotation of triangle ABC 180° about the origin.

Rule for Rotation 180° (Clockwise and Counterclockwise);

(x, y)   ----- > (-x, -y)

A(4, -1)  ------> A(-4, 1)

B(1, -1) ------>  B(-1, 1)

C(1, -3) ------>  C(-1, 3)

Rotation 180° = A(-4, 1), B(-1, 1) and C(-1, 3)

Thus, the result of the coordinates of the new triangle with vertices are found.

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[tex]a = l \times w \\ a = (10y + 4w)(10y - 4w) \\ a = 10y(10y - 4w) + 4w(10y - 4w) \\ a = 100 {y}^{2} - 40wy + 40wy - 16 {w}^{2} \\ a = 100 {y}^{2} - 16 {w}^{2} [/tex]

ATTACHED IS THE SOLUTION

1. The amount donated by the people with same ratio is $40.

2. The amount greater is $40.

From the information, there's a total of $160 in donations from three people and the three donations are in the ratio 5 : 5 : 10.

It should be noted that the amount donated by the people with same ratio will be:

= 5/(5 + 5 + 10) × $160

= 5/20 × $160

= $40

The amount donated by the person with largest ratio will be;

= 10/20 × $160

= $80

Therefore, the difference will be:

= $80 - $40

= $40

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Answer: N > -4

Step-by-step explanation:

Cuz It's Right

The solution for inequality  is n < -4.

The given inequality is −2(n − 3.5) > 15

An inequality will have the sign < , > , ≥ or ≤ instead of an equality in an equation. That is, an inequality compares two quantities on either sides of the inequality sign.

We are asked to solve the inequality  −2(n − 3.5) > 15. That is, to find the possible values for n.

−2(n − 3.5) > 15

Dividing throughout by 2,

-(n - 3.5) > 15/2

⇒ -n +3.5 > 7.5

Subtracting 3.5 from both sides,

⇒ -n > 7.5 - 3.5

⇒ -n > 4

Multiply -1 on both sides of the inequality and the inequality will be reversed,

⇒ n < -4 is the solution for n.

The solution is the values of n less than -4.

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