Rectangles R and S are similar. If the area of rectangle R is 187, what is the area of rectangle S?

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.

The correct answer is a. A leading question.

A leading question is one that is designed to elicit a specific response or to influence the answer given by the respondent. In this case, the question is designed to lead the respondent to agree that they also liked the chocolate bar, as "most people" did. This type of question is often used in surveys and research studies to obtain desired results.

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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:

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  (√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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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 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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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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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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Answer is in a picture, so zoom in!

But overall, the answer is  below!

Answer:

4x + 14

Step-by-step explanation:

2 (3x2 - 4x + 7)

= 2 ( 6x - 4x + 7)

= 2 ( 2x + 7)

= 4x + 14

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:

  -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]

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:

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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There are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.

A permutation is to select an object then arrange it and it cares about the orders while a Combination is about only selecting an object without caring about the orders.

The number of ways to select the executive board is the number of permutations of 10 items taken 3 at a time.

That is:

P(10, 3) = 10!/(10-3)! = 10x9x8 = 720

Therefore, there are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.

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If Kenneth has 5/8 feet of lumber, then he need 83/40 feet of lumber to make the shelf.

First we convert the length of lumber in improper fraction form,

So, we convert 2(7/10) feet to an improper fraction,

⇒ 2(7/10) = (2×10 + 7)/10 = 27/10,

To find the length of lumber required we need to subtract the amount of lumber Kenneth has from the total length required,

Kenneth has a total of 5/8 feet of lumber,

Length of lumber required is = 27/10 - 5/8,

Taking LCM of 10 and 8 as 40 , and simplifying further,

We get,

⇒ 108/40 - 25/40

⇒ 83/40

Therefore, Kenneth needs 83/40 feet more lumber to make the shelf.

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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: the meeting lasted for an hour and 5 min.

Step-by-step explanation:

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

[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]

[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 simplified the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)) is (x+9)/(x+7).

To simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)), we can follow the following steps:

Step 1: Find the common denominator for the fractions in the numerator and denominator. In this case, the common denominator is (x+8).

Step 2: Multiply the numerator and denominator of the expression by the common denominator to get rid of the fractions. This gives us:

((x+8)(1+(1)/(x+8)))/((x+8)(1-(1)/(x+8)))

Step 3: Simplify the numerator and denominator by distributing and combining like terms. This gives us:

((x+8+1)/(x+8-1))/(x+8)

Step 4: Simplify the expression further by canceling out any common factors. In this case, we can cancel out the (x+8) terms in the numerator and denominator to get:

(x+9)/(x+7)

Therefore, the simplified expression is (x+9)/(x+7).

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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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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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Answer:

D

Step-by-step explanation:

Answer: 3.31662479036.

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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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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