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Answer:

  r = 5

Step-by-step explanation:

Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.

The attached shows that the value of r that makes both sides of the equation have the same value is r = 5.

Check:

  √(5·5 -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . true

Solution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.

We can add 3, square the equation, then isolate the radical and square again:

  [tex]\displaysyle \sqrt{5r-9}-3=\sqrt{r+4}-2\\\\\sqrt{5r-9}=\sqrt{r+4}+1\qquad\text{add 3}\\\\5r-9=(r+4)+2\sqrt{r+4}+1\qquad\text{square both sides}\\\\(4r-14)^2=4(r+4)\qquad\text{subtract $(r+5)$ and square again}\\\\16r^2-116r+180=0\qquad\text{rewrite in standard form}\\\\4(4r -9)(r -5) = 0\qquad\text{factor}\\\\r=\{\dfrac{9}{4},\ 5\}\qquad\text{solutions to the factored form}[/tex]

Trying these values in the original equation, we get ...

  √((5(9/4) -9) -3 = √(9/4 +4) -2   ⇒   1.5 -3 = 2.5 -2 . . . . . false

  √(5(5) -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . . . true

The solution is r = 5.

The partial sums are correct are  That is:  (2) and (28/9).

A partial sum would be:

2 + (2/3).

In this case, thus,

Series 1 = 2  - This is correct.

Series 2 = 2 + (2/3) = 8/3 - incorrect

Series 3 = (8/3) + (4/9) = (28/9) Correct

Series 4 = (28/9) + (8/27) = (92/27)

Series 5 = (92/27) + (16/81) = 292/81

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Answer:39084620

Step-by-step explanation:

New questions in Mathematics

19 ft 4 ft l Find l. l = √ [?] ft

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?

Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.

Solve the equation 7/4x-2=-5x+1

How to Convert 11010112 to base 10?

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)

Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)

The probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

We know that 40% of the counters are red or white. Then 60% of the counters are blue or green.

Now we know that the ratio of red to white is 3:5

Then the percentage of red counters is:

(3/8)*40% = 15%

And the ratio of blue to green is 3:2

Then the percentage of red counters is:

(2/5)*60% = 24%

Then the percentage of counters that are either red or green is:

15% + 24% = 39%

Then the probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

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Answer:

a = 2

b = 11

c = 11

d = -2

Step-by-step explanation:

[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]

   [tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]  

On comparing to right side, we get,

 22a + 6b = 110

Divide the entire equation by 2

   11a + 3b = 55  ------------(I)

 11a   - 9b  = -77  -------------(II)

Subtract equation (II) from (I)

       11a + 3b = 55

       11a - 9b = -77

      -      +        +     {Now subtract}

               12b = 132

                 b = 132/12

[tex]\sf \boxed{\bf \ b = 11}[/tex]

Substitute the value of b in eqaution (I)

  11a + 3*11 = 55

  11a + 33   = 55

             11a = 55 - 33

             11a = 22

               a = 22/11

      [tex]\sf \boxed{\bf \ a = 2}[/tex]

           22c + 6d = 230

Divide by 2

           11c + 3d = 115  -----------------(III)

           11c - 9d  = -139 ------------------(IV)

Subtract (IV) from (III)

           11c + 3d  = 115

           11c - 9d  = 139

           -     +         -      

                  12d  =  -24

                      d = -24/12

                     [tex]\sf \boxed{\bf \ d = -2}[/tex]

Plugin d = - 2 in equation (III)

    11c + 3*(-2) = 115

     11c  - 6      = 115

                11c  = 115 + 6

               11c = 121

                  c = 121/11

                 [tex]\sf \boxed{\bf \ c = 11}[/tex]

Answer:

Please see the answer below.

Step-by-step explanation:

The average rate of change of credit card is $ 401.79 /year.

Solution

The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625

The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14

average rate of change of credit card debt with respect to time = [tex]\frac{difference of credit card debt}{difference of years}[/tex]

average rate = [tex]\frac{5625}{14}[/tex] = $ 401.79 / year

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The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]

Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]

[tex]\frac{1}{2 - \sqrt{3} }[/tex]  x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Equating,

a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Comparing the variables,

a = 2,   b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1

The ratio, a: b = 2:1

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The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = aeˣ

Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:

p = 14.63 × 0.8^a

Next, we would evaluate as follows;

At a = 0, we have:

p = 14.63 × 0.8^(0)

p = 14.63 psi.

At a = 1, we have:

p = 14.63 × 0.8^(1)

p = 11.704 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(2)

p = 9.3632 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(3)

p = 7.4906 psi, and this is 20% less than a mile before.

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Complete Question:

Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?

p = 14.63 × 0.8^a

A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.

B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

D. For each mile that the altitude increases, the atmospheric pressure increases 20%.

From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).

Notice that the question states:  △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,

under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,

△A'B'C' is in the same position with △ABC.

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Answer: D: 60 degrees

Step-by-step explanation:

khan

The total amount of Chandra's investments after 8 years exists $110.03.

The formula for calculating the compound interest exists defined as;

[tex]$A = P(1+r/n)^{nt[/tex]

where, P exists the amount invested = $75

r exists the rate. = 0.048

t exists the time = 8 years

n = 12 (monthly)

The formula for calculating the compound interest,

[tex]$A = P(1+r/n)^{nt[/tex]

Substitute the value in the above equation, and we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years exists $110.03

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The equation that represents the relation is y = 8 - 0.5x

The given parameters are:

Start = 8m

Rate = 1/2 m/s

The linear equation that represents the submarine movement is:

y = Start - Rate * x

This gives

y = 8 - 1/2 * x

Evaluate

y = 8 - 0.5x

Hence, the equation that represents the relation is y = 8 - 0.5x

See attachment for the graph

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The linear equation is 45x+50

Linear equation is the equation having the degree 1

Given that the charge per computer repair service  is $50

The charge per hour of work is $ 45

We need to show the linear equation that  expresses the total amount of money Charlie earns per computer is y

So , Let the number of hours be x

Therefore, the Charlie working hours charge will be 45x

The total amount of money Charlie earns per computer is y

Therefore the linear equation will be

y = 50+45x  

Where y = Total amount of money

x =  number of hours

Hence the linear equation is y = 45x+50

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Answer:

Quadrant III

Step-by-step explanation:

Top-right quadrant = QI

Top-left quadrant = QII

Bottom-left quadrant = QIII

Bottom-right quadrant = QIV

It is not too many reds, but it is also not a perfectly balanced roulette wheel.

It is given that the red numbers should come up 18 times when the roulette wheel is played 38 times.

Therefore, the ratio of red numbers to the total number of plays is = 18:38

It is also given that a casino tests the wheel with 3800 plays and noticed that the red numbers came up 1890 times.

The ratio is given as 1890:3800.

We have to simplify this.

1890/3800 = 18.9/38

If the roulette wheel was perfect, it should've been 18:38.

Therefore, we can say that the roulette wheel is not perfectly balanced.

Therefore we have found that it is not too many reds, but it is also not a perfectly balanced roulette wheel.

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Applying the trigonometry ratios, the correct option is: B. none of these are correct.

The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.

Use the trigonometry ratio to find out which option is correct.

Cos Z = adj/hyp = 61/CZ, so option A is incorrect.

Sin Z = opp/hyp = 73/CZ,  so option C is incorrect.

Tan Z = opp/adj = 73/61,  so option D is incorrect.

Thus, the answer is: B. none of these are correct.

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Answer:

9 x 9 = 81

Step-by-step explanation:

area = width x height

Since it's a square, width = height

1. The semi inter quartile range is 10

2. The coefficient of quartile deviation is 0.2

1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40

3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60

Semi inter quartile range = (Q₃ - Q₁) / 2

Semi inter quartile range = (60 - 40) / 2

Semi inter quartile range = 10

Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)

Coefficient of quartile deviation = (60 - 40) / (60 + 40)

Coefficient of quartile deviation = 0.2

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Answer:

7

Step-by-step explanation:

this is probably a 45-45-90 triangle if its both legs

Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

The inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

The equation is given as:

y = x^2 + 9

Subtract 9 from both sides

x^2 = y - 9

Take the square root of both sides

[tex]x = \sqrt{y - 9[/tex]

Hence, the inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

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Answer:

e) B. 45°

f) A. 30°

Step-by-step explanation:

e) sec theta = 1/ cos theta

the value of cos theta is 1/√2 at 45°

so , sec 45° = √2 and theta = 45°

f) cot theta = 1/ tan theta

the value of tan theta is 1/ √3 at 30°

so, cot 30° = √3 , theta = 30°

The answers are :

e) B

f) A

For part (e), convert into terms of cosθ.

For part (f), convert into terms of tanθ.

The expression which can be used to represent the total amount llean earned last week is 75 + 18x

An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)

= 75 + (18 × x)

= 75 + 18x

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The coordinates of the fourth vertex are (6, -2)

The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).

Calculate the slope of the first two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

d = (7 - 5)/(3 + 3)

Let the fourth coordinate be (x, y)

Calculate the slope of the other two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

m = (y + 4)/x

Equate both slope equations

(y + 4)/x = (7 - 5)/(3 + 3)

Simplify the fraction

(y + 4)/x = 1/3

Cross multiply

x = 3y + 12

Let y = -2

So, we have:

x = 3 *-2 + 12

Evaluate

x = 6

Substitute x = 6 and y = -2 in (x, y)

This gives (6, -2)

Hence, the coordinates of the fourth vertex are (6, -2)

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Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.

According to this question, a 2-column table with 5 rows is given.

If y varies directly with x, the mathematical representation is as follows:

y = kx

Since y = 3, when x = 1

3 = k × 1

k = 3

The relationship between x and y is as follows: y = 3x

Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.

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Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].

The range of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it can take as input.

Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.

The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.

Therefore, the domain of the function is  [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].

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Jessica purchased a DVD that was on sale for 12% off.

The sales tax in her county is 3%.

Let, y represent the original price of the DVD.

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will form an algebraic expression, according to the given data.

So,

The original price of the DVD = y

Discount on the original price :

y * 12/100

=3y/25

Price after discount :

y - 3y/25

=25y - 3y/25

=22y/25

Sales tax amount :

22y/25 * 3/100

11y/25 * 3/50

=33y/1250

Final price including the sales tax :

22y/25 + 33y/1250

1100y + 33y/1250

1133y/1250

(This will be considered as the final result.)

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Answer:

502.4 ft²

Step-by-step explanation:

To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.

Area (White Circle)

radius = 1/2 diameter

radius = (1/2) x 36 ft

radius = 18 ft

Area = πr²

Area = π(18 ft)²

Area = π(324 ft²)

Area = 1017.36 ft²

Area (White Circle + Ring)

radius = 1/2 diameter + width of ring

radius = (1/2 x 36 ft) + 4 ft

radius = 22 ft

Area = πr²

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft²

Area (Ring)

Area (Ring) = Area (White Circle + Ring) - Area (White Circle)

Area (Ring) = 1519.76 ft² - 1017.36 ft²

Area (Ring) = 502.4 ft²