Solve the equation. Remember to check for extraneous solutions. (8)/(b^(2)-9)-(1)/(b+3)=(1)/(b^(2)-9)

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{2\sqrt{41}}\\ a=\stackrel{adjacent}{10}\\ o=opposite \end{cases} \\\\\\ o=\sqrt{ (2\sqrt{41})^2 - 10^2}\implies o=\sqrt{ (2^2)(\sqrt{41})^2 - 100 } \implies o=\sqrt{ (4)(41)-100 } \\\\\\ o=\sqrt{164-100}\implies o=\sqrt{64}\implies o=8[/tex]

The total fluid intake for the meal is 493.04 mL.

We first need to convert the volume of each beverage to ounces, and then to milliliters.

1/3 glass of orange juice = (1/3) x 8 oz = 2.67 oz = 79.01 mL (assuming 1 oz = 29.57 mL)

1/2 cup of tea = (1/2) x 6 oz = 3 oz = 88.72 mL

1/2 pt milk = (1/2) x 16 oz = 8 oz = 236.59 mL (assuming 1 pt = 16 oz and 1 oz = 29.57 mL)

1 popsicle (3oz) = 3 oz = 88.72 mL

The total fluid intake for the meal is

79.01 mL + 88.72 mL + 236.59 mL + 88.72 mL = 493.04 mL

Therefore, the fluid intake for the meal is approximately 493.04 mL.

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Answer is in a picture, so zoom in!

But overall, the answer is  below!

Answer:

  -119/169

Step-by-step explanation:

You want cos(2α) where cos(α) = 5/13 and 270° < α < 360°.

The desired function is ...

  cos(2α) = 2cos²(α) -1

In the given quadrant, sin(α) < 0. Since the sine is squared in the double-angle identity, whether it is positive or negative is irrelevant.

  [tex]\cos(2\alpha)=2\cos^2(\alpha)-1=2\left(\dfrac{5}{13}\right)^2-1=\dfrac{2(25)-169}{169}\\\\\boxed{\cos(2\alpha)=-\dfrac{119}{169}}[/tex]

The fraction of the euro is 8/100

one Euro will cost in 8 rands

When we talk about exchange rates, we're essentially talking about the value of one currency compared to another. In this case, we're comparing the South African rand to the euro.

We know that one South African rand is valued at 0.125 of one euro. To figure out what fraction of the euro one South African rand is worth, we can simply divide the value of one rand by the value of one euro:

1 rand ÷ 0.125 euro = 8/100 euro

So, one South African rand is worth 8/100 or 0.08 (which is equivalent to 8%) of one euro.

To calculate what one euro would cost in rands, we can use the inverse of the exchange rate we were given:

1 euro ÷ 0.125 rand/euro = 8 rand

So, one euro would cost 8 South African rand.

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Answer: A

Step-by-step explanation: 2/-3 means that the - sign should be brought up. So, A is correct.

Answer: 3.31662479036.

The  (√12 - √3)² = 6 according to the provided assertion.

Why do you use the word "binomial"?

A Binomial is a name for an algebraic equation with only two elements. It is a polynomial with two terms. It is also referred to as the total or difference of two or more binomials. It is a polynomial's most basic shape.

To expand and simplify the expression (√12 - √3)², we can use the formula for the square of a binomial:

(a - b)² = a²  + b² - 2ab

In this case, a = √12 and b = √3, so we have:

(√12 - √3)² = (√12)² - 2(√12)(√3) + (√3)²

To simplifying, we have:

(√12 - √3)² = 12 - 2√36 + 3

Since √36 = 6, we can simplify further:

(√12 - √3)² = 12 - 2(6) + 3 = 6

Therefore, the expanded and simplified equation (√12 - √3)² = 6.

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Part A: The function f(x) is an exponential function.

Part B: As x increases by 1, the value of f(x) increases by a factor of 6.

It is an exponential function because the function is of the form f(x) = a^(x-1), where a is a constant. We can see that when x increases by 1, the exponent in the function increases by 1 as well. So we have:

f(x+1) = a^x * a

f(x) = a^(x-1)

Therefore, the ratio of f(x+1) to f(x) is:

f(x+1)/f(x) = (a^x * a) / (a^(x-1)) = a

This means that as x increases by 1, the value of f(x) increases by a factor of a, which in this case is 6. Therefore, statement B supports the correct answer from Part A.

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The functiοn that gives the number οf illiterate peοple in Sylvania is

[tex]\mathrm{P(t) = 9000(2/5)^t}[/tex]

A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.

Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.

Sοlutiοn accοrding tο the questiοn:

Given, Tοtal number οf illiterate peοple = 9000

          Amοunt = 3/5

Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)

Nοw, fοr "t years":

P(t) = 9000(2/5)

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When lines A and B are cut by a transversal, then ∠1 and ∠4 fοrm a pair οf vertical angles.

In geοmetry, a transversal line intersects twο lines in the same plane at twο different lοcatiοns. In the Euclidean plane, transversals help establish the parallelism οf twο οr mοre οther straight lines. It crοsses twο lines at separate lοcatiοns. Transversal intersectiοn results in numerοus angles.

Twο parallel lines are A and B are drawn.

They are cut by a transversal C.

The angles ∠1 and ∠2 are fοrming a pair οf alternate exteriοr angles.

The angles ∠3 and ∠4 are fοrming a pair οf alternate interiοr angles.

The angles ∠2 and ∠3 are verticals angles.

Similarly, the angles ∠1 and ∠4 fοrm a pair οf vertically οppοsite angles.

Therefοre, the angles fοrm vertical pair.

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Answer:

C

Step-by-step explanation:

The proof that ∠B ≅ ∠C is:

D is the midpoint of of BC - Given...................(1)
Thus
BD = DC ................................................................(2)

∠EDC ≅ ∠FDB  - Given......................................(3)

DE ⊥ AB - Given...................................................(4)
DF ⊥ AC - Given ..................................................(5)
∠AED = ∠DEB = 90° - perpendicular bisector theorem  ....(6)

∠AFD = ∠DFC = 90° - perpendicular bisector theorem ....(7)
∠EAF = ∠EDF = 90° - Properties of the angles of a Quadrilateral

Since ∠EDC ≅ ∠FDB, as in   (3) above, and

Both comprise of ∠EDF,

thus,
(∠EDC - ∠EDF) ≅ (∠FDB - ∠EDF)

Since

∠EDB = (∠FDB - ∠EDF); and

∠FDC = (∠EDC - ∠EDF)

Thus,

∠EDB ≅ ∠FDC

thus,
∠EDB = ∠FDC = 45° (Sum of Angles on a Straight line) that is
∠EDB =  ∠FDC = (180° -∠EDF)/2

Since  ∠EDF = 90°
∠EDB =  ∠FDC = (180° -90°)/2

∠EDB =  ∠FDC = 90/2
∠EDB =  ∠FDC = 45°

Since
∠DEB = 90° (5); and

∠DFC = 90° (7)
ΔBED ≅ ΔDFC

Thus, by Sum of Angles in a Triangle,
∠B ≅ ∠C.

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Answer:

7:6

Step-by-step explanation:

...

Answer:

Below

Step-by-step explanation:

154 : 132      the GCF of these two numbers is 22.   Divide them both by 22

7:6    Done

[tex]PQ = 2 - (-3) = 2 + 3 = 5 \ cm[/tex]

[tex]RS = PQ \implies RS = 5 \ cm[/tex]

the perimeter of rectangle PQRS is 20 centimeters ⇒

[tex]QR = SP = 5 \ cm[/tex]

⇒ PQRS is square

[tex]x_{R} = x_{Q} - 5 = -1-5 = -6[/tex]

[tex]y_{R} = y_{Q} = 2[/tex]

[tex]\implies R(-6,2)[/tex]

[tex]x_{S} = x_{R} = -6[/tex]

[tex]y_{S} = y_{P} = -3[/tex]

[tex]\implies Q(-6,-3)[/tex]

Answer:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

The daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

Percentage decrease is the percentage by which a quantity οr value has decreased cοmpared tο its οriginal οr previοus value. It is calculated by taking the difference between the οriginal value and the new value, dividing that difference by the οriginal value, and then multiplying by 100 tο cοnvert the result intο a percentage. The fοrmula fοr percentage decrease is:

Percentage decrease = [(Original value - New value) / Original value] x 100%

The fοrmula fοr the amοunt οf radiοactive element remaining, r, in a 100-mg sample after d days is given as:

[tex]r = 100(1/2)^{(d/5)[/tex]

Tο find the daily percent οf decrease, we need tο find the difference between the amοunt οf the element at the start οf a day and the amοunt at the end οf that day, and then express this as a percentage οf the starting amοunt.

Let's assume that we start with 100 mg οf the radiοactive element. After οne day, the amοunt remaining is:

[tex]r = 100(1/2)^{(1/5)[/tex] ≈ 87.06 mg

The difference between the starting amοunt and the amοunt at the end οf the day is:

100 - 87.06 = 12.94

Tο express this as a percentage οf the starting amοunt, we divide this difference by the starting amοunt and multiply by 100:

12.94/100 * 100% = 12.94%

Therefοre, the daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

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Answer: bro hear me out rq in the explanation

Step-by-step explanation: Jim hands the cashier the $20 bill and, if necessary, provides his identification to purchase the item. The cashier will then record the purchase, give Jim his change, and thank him for his business.

The statement that explains how the bear population is changing is  A. The population is decreasing by 4% per year.

From the question, we have the following parameters that can be used in our computation:

N(t) = 850(0.96)^t

The rate factor of the above function is

Rate factor = 0.96

This is less than 1

So, we have

Rate = 1 - 0.96

Evaluate

Rate = 4%

Hence, the rate is 4%

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9 people can be seated at a round table is 8! = 40,320.

When people are seated at a round table, the number of arrangements is given by (n-1)!, where n is the number of people. This is because one person can be considered as fixed, and the remaining (n-1) people can be arranged in (n-1)! ways. So for 9 people, the number of arrangements is (9-1)! = 8! = 40,320.

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Answer:

To answer this question, we need to compare the number of men and women who like playing golf to the number of men and women who like running.

There are 14 men who like playing golf and 2 men who like running, so the ratio of men who like playing golf to men who like running is:

14 men / 2 men = 7 men who like playing golf for every man who likes running

There are 6 women who like playing golf and 18 women who like running, so the ratio of women who like playing golf to women who like running is:

6 women / 18 women = 1/3 or 0.333 women who like playing golf for every woman who likes running

Therefore, the correct statement is:

C. For every woman who likes running, 7 women like playing golf.

Answer:

m<BFC= 64°; m<AFB= 116°

Step-by-step explanation:

Using the Vertical Angle Theorem, in which "the opposing angles of two intersecting lines must be congruent, or identical in value"

m<AFE is congruent to m<BFC, therefore m<BFC is 64°

You can also use the straight angle theorem where BE is a straight line, and is therefore 180°. so subtracting 180° from 64° will result in m<AFB being 116°, you second answer. You can take it a step further without using the vertical angle theorem to get our first answer by using the same rules for the straight angle theorem again, knowing that AC is a straight line and that m<AFB is 116°, subtract 180° by 116° to get m<BFC, 64°.

Answer: Since lines l and m are parallel, we can use the fact that corresponding angles are congruent. Therefore:

m∠1 = m∠6 (corresponding angles)

m∠6 + m∠2 = 180° (supplementary angles, as angles 6 and 2 form a straight line)

m∠2 = m∠7 (corresponding angles)

m∠3 = m∠7 (alternate interior angles)

m∠1 + m∠4 = 180° (supplementary angles, as angles 1 and 4 form a straight line)

m∠3 + m∠4 = 180° (supplementary angles, as angles 3 and 4 form a straight line)

We know that m∠1 = 63°, so we can use the equations above to find m∠6 and m∠7:

m∠1 = m∠6, so m∠6 = 63°.

m∠6 + m∠2 = 180°, so m∠2 = 180° - m∠6 = 180° - 63° = 117°.

m∠2 = m∠7, so m∠7 = 117°.

m∠3 = m∠7, so m∠3 = 117°.

m∠1 + m∠4 = 180°, so m∠4 = 180° - m∠1 = 180° - 63° = 117°.

m∠3 + m∠4 = 180°, so m∠3 + 117° = 180°, which means m∠3 = 63°.

Therefore, the measures of the angles are:

m∠1 = 63°

m∠2 = 117°

m∠3 = 63°

m∠4 = 117°

m∠6 = 63°

m∠7 = 117°

Step-by-step explanation:

139

because you do 5 dollars times 11 cats equals 55 and 12 dollars times 7 dogs equals 84 add it together is 139

Answer:

Yes

What is horizontal distance ?

The distance between two points is understood to mean the horizontal distance, regardless of the relative elevation of the two points.

How to calculate horizontal distance?

Horizontal distance can be expressed as x = Vtx = Vtx=Vt. Vertical distance from the ground is described by the formula y = – 1 2 g t 2 y = – \frac{1}{2}g t^2 y=–21gt2, where g is the gravity acceleration, and h is an elevation.

Step by step explanation:

As long as the ramp is no more than .9965 feet high, then yes

If the ramp is .9965 feet high then its horizontal distance is 12 X .9965 feet or 11.958 feet

Using Pythagoras’ Theorem, the actual length of the ramp would be the square root of (11.958 X 11.958 + .9965 X .9965)

Or the square root of (142.9934 + .9930)

Or SQRT (143.987)

= 11.999 feet

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The LCM of the given polynomials is \[ (x+6y)(x+2y)(x-6y) \].

The LCM (Least Common Multiple) of two polynomials is the smallest polynomial that is a multiple of both of the given polynomials. To find the LCM, we need to factor the given polynomials and then take the product of the highest power of each factor.

Factoring the first polynomial: \[ x^{2}+8 x y+12 y^{2} = (x+6y)(x+2y) \]
Factoring the second polynomial: \[ x^{2}-36 y^{2} = (x+6y)(x-6y) \]

Now, we can take the product of the highest power of each factor to find the LCM:

\[ LCM = (x+6y)(x+2y)(x-6y) \]

So, the LCM of the given polynomials in factored form is \[ (x+6y)(x+2y)(x-6y) \].

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Answer:

Step-by-step explanation:

An example of a compound interest problem and the solution problem is:

"Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?"

Solution: Sarah will have $11,576.25 in the account after 3 years.

The compound interest on the same sum at the same rate for the same period, compounded annually, is:

$6,646.34

Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?

To solve this problem, we can use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years.

To find the compound interest on the same sum at the same rate for the same period, we can use the same formula for compound interest: A = P(1 + r)^n.

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Answer:

x=18

Step-by-step explanation:

Being that the angles are corresponding they are going to equal the same thing.

(7x+7)=133

Now just follow the laws of PEMDAS

7x+7=133

-7 -7

7x=126

÷7 ÷7

x=18

Answer: the meeting lasted for an hour and 5 min.

Step-by-step explanation:

Therefore, the meeting lasted for an hour and five minutes.