How do I algebraically solve this? (solve for x)

Answer 81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

the dimensions are 9x + 2y and 9x - 2y

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81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

The dimensions of the rectangle with an area of (81x² - 4y²) square units are (9x + 2y) and (9x - 2y) units, as the area expression is a difference of squares that has been factored accordingly.

The area of a rectangle is given by the expression (81x² − 4y²) square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

Therefore, the dimensions of the rectangle can be 9x + 2y and 9x - 2y units.

Answer: try A I took the same test earlier

Step-by-step explanation:

Answer:

[tex]\boxed{\text{16 ft}}[/tex]

Step-by-step explanation:

h(x) = -2x² + 4x + 16

At the time the ball is thrown,

x = 0

h(0) = -2 × 0² + 4 × 0 + 16 = [tex]\boxed{ \textbf{16 ft}}[/tex]

Answer:

The height of the ball at the time it is thrown is 16 meters.

Step-by-step explanation:

To find the height of the ball at the time it is thrown, we have that we set the time accordingly. So the height of the ball at the time it is thrown is given by h(0) since the ball was thrown at second 0.

Now that we know the time, which is our x, we set all of our x's to 0.

[tex]h(0)=-2(0)^{2} +4(0)+16[/tex]

Next we solve,

      [tex]=0+0+16[/tex]

      [tex]=16[/tex]

In conclusion, the height of the ball at the time it is thrown is 16 meters.

Solved and got it right on Khan Academy!

Answer: it’s 200ft

Step-by-step explanation:

Answer:

1. Not Independent

2. Independent

3. Not Independent

4. Independent

Step-by-step explanation:

Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.

Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.

1. A jar contains twenty coins. Two coins are picked randomly without replacement.

Not Independent because if coins are not replaced the outcome of next event will be effected.

2. A coin is flipped three times.

Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again

3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

Not Independent because if balls are not replaced the outcome of next event will be effected.

4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again

The correctcorrect probabilityprobability conditiony for each of the given situation as regards independent or not are;

A) Not Independent

B) Dependent

C) Not Independent

D) Dependent

An independent event is one that doesn't depend on the probability of another one happening while a dependent event is one that depends on the probability of another one happening.

A) A jar contains twenty coins. Two coins are picked randomly without replacement; This is not independent because when we do not replace a selected coin, it affects the outcome of the next choice.

B) A coin is flipped three times; This is dependent because a flip doesn't depend on another flip.

C) A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement; This is not independent because when we do not replace a selected ball, it affects the outcome of the next choice.

D) A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice; This is independent because spinning doesn't affect the outcome of the next spin.

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Answer:

The 3rd person who drove 500 miles in 8 hours drove the fastest.  

Step-by-step explanation:

1st person : 60.5 mph

2nd person : 62.14 mph

3rd person : 62.5 mph

4th person : 43 mph

you simply divide the total miles driven by the amount of time and then you get the miles per hour.

Hope this helps!

Answer:

C) weak negative association

Step-by-step explanation:

As X increases, Y generally decreases.  So this is a negative association.  Because the points are widely scattered, it is also a weak association.  So the answer is C.

the answer is c because the graph is going down

Answer:

196

Step-by-step explanation:

The probability of rolling a sum of 2 with two dice is 1/36. This is calculated by determining the independent probabilities of rolling 1 on each die and multiplying these probabilities together.

Explanation:

The subject of this question is probability in mathematics, specifically involving the numbers on two rolled dice. The only way two dice (number cubes) can add up to 2 is if both rolled dice shows 1. Each die has 6 sides, so the probability for each dies rolling 1 is 1/6.

The probability of two independent events both occurring is founding by multiplying the probability of each event. As the two dice is rolled independently, the probability of both are showing 1 (and hence their sum is being 2) is (1/6) x (1/6), which simplifies to 1/36. Therefore, the probability that the sum of the numbers rolled on two dice is 2 1/36.

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[tex] \sqrt{ - 75} = \sqrt{ - 1 \times 75} = \sqrt{ {i}^{2} \times 75 } = 5i \sqrt{3} \\(therefore \: {i}^{2} = - 1)[/tex]

Answer:

[tex]\large\boxed{\sqrt{-75}=5\sqrt3\ i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\\\\\sqrt{-75}=\sqrt{(25)(3)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{25}\cdot\sqrt3\cdot\sqrt{-1}=5\cdot\sqrt3\cdot i=5\sqrt3\ i[/tex]

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.

Answer:

6

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude (in this case, j) is equal to radical(g*f).

Therefore, j=√(g*f), j=√(3*12), j=6

Answer:

[tex]\boxed{6}[/tex]

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it creates.

Thus, in your triangle,

j = √(fg)

If f = 12 and g = 3,

j = √(12 × 3) = √ 36 = 6

[tex]\boxed{j = 6}[/tex]

Answer:

12 pack for $15.00

Step-by-step explanation:

4 pack for $7.00:  7 ÷4  = 1.75

6 pack for $10.25:  10.25 ÷6 ≈ 1.71

10 pack for $13.00:  13 ÷10  = 1.30

12 pack for $15.00:  15.00 ÷12 = 1.25

25 pack for $32.50:  32.50 ÷25 = 1.30

Answer:

d. [tex]1.82\: or\:4.46[/tex]

Step-by-step explanation:

The given trigonometric equation is;

[tex]\sec \theta=-4.0545[/tex]

Recall that;

[tex]\cos \theta=\frac{1}{\sec \theta}[/tex]

[tex]\implies \cos \theta=\frac{1}{-4.0545}[/tex]

[tex]\implies \cos \theta=-0.2466[/tex]

The cosine function is negative in the second and third quadrant.

[tex]\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)[/tex]

[tex]\theta=1.82\: or\:4.46[/tex]

    A)

No solution--

No solution is obtained when there is a condition such that the equation gives a absurd condition.

Hence we write our equation as:

        2x+9+3x+x=6x+1

 Hence, we have:

          6x+9=6x+1

i.e. we have:   9=1

which is a contradiction.

Hence, we get no solution.

B)

         One solution--

One solution or unique solution is obtained when we obtain a unique value for our given variable.

i.e. if we write our equation as:

             2x+9+3x+x=5x+1

i.e. 6x+9=5x+1

i.e. x= -8

Hence, we get a unique value for x.

C)

            Infinite many solution--

The infinite many solution is where we get a condition such that we could not get a unique value for x but the equation is true.

Hence, we have:

                     2x+9+3x+x=6x+9

i.e.   6x+9=6x+9

as left hand side of equation is equal to right hand side of the equation for every ''x'' Hence, we get infinite many solution.

Answer:

1. 6x+1

2. 5x+1

3. 6x+9

For angles between 180° and 360°, only cosine (cos) and cosecant (csc) may yield a positive value. This is because these angles fall in the third and fourth quadrants of the unit circle where only certain functions yield positive results.

In the trigonometric functions, the sign of the function's result can vary depending on the size of the angle. For angles between 180° and 360°, only cosine (cos) and cosecant (csc), which is the reciprocal of sine, may have positive values.

In mathematics circle, these angles are in the third and fourth quadrants. In the third quadrant (180° ≤ θ < 270°), only the function tangent (tan) and its reciprocal cotangent (cot) can be positive. While in the fourth quadrant (270° ≤ θ < 360°), the functions cosine (cos) and its reciprocal secant (sec) can be positive.

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Answer:

4

Step-by-step explanation:

The value of Side DC is 4.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

We have three similar triangles because each has a right angle and shares an angle.   Let's write the angles in order: opposite to the short leg, long leg, and the hypotenuse.

CAB ≡ BAD ≡ CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

Let CD = x

(5 +x )/6 = 6/x

(5+x)*x = 6*6

5x + x² = 36

x² + 5x - 36 = 0

x² + 9x -4x -36 = 0

x(x+9 ) -4 (x +9 ) = 0

(x-4)(x+9) = 0

x= 4, -9

We reject the negative root and conclude x=4

Therefore, Side DC is 4.

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Answer:

Option B: y = -2x + 17.

Step-by-step explanation:

Lets calculate values for option B:

x = 2 , y = -4+17 = 13   ( B gives the value 12)

x = 4, y = -8+17 = 9   (10)

x = 5, y = -10+17 = 7  (6)

x = 6, y = -12+17 = 5 (6)

x = 8, y = -16+17 =- 1  (1)

Sum of the differences =  1 + 1 + 1 + 1 = 4.

These values are close to the ones given in the question.

Option A  y = 6, 10, 12, 14, 18 -  some of the values of y are  a lot different than the given values.

Option C:

Working them out we get y =  14, 10, 8, 6, 2. which are not quite as good as Option B values The total difference is 5 compared with 4 for option B.

Option D.

y =  12.4,  9.8, 8.5, 7.2, 4.6 where some of  the differences are large.

Answer:

P ≈ 56 million

Step-by-step explanation:

Your question is attached in the picture below.

The exponential formula for these cases is

P = Po*e^(kt)

Where,

Po = initial population

k = is a constant used to define the growth rate

t = time transcurred since the time of the initial population

For this exercise,

Po = 50 million

Year 2002

2002 - 1992 = 10

53 million = 50 million *e^(k*10)

(53/50) = e^(k*10)

k*10 = ln(53/50)

k = 0.005827

The equation results

P = 50 million *e^(0.005827*t)

Year 2010

2010-1992 = 18

P = 50 million *e^(0.005827*18)

P = 50 million *(1.11058)

P = 55.53 million

P ≈ 56 million

Answer:

the answer is 56 just got it right

if you need population in 2010

Step-by-step explanation:

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

Answer:

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

Step-by-step explanation:

The question in English is

6 pounds of coffee and 5 pounds of sugar cost 227 pesos and 5 pounds of coffee and 4 pounds of sugar (at the same prices) cost 188 pesos Find the price of one pound of coffee and one pound of sugar.

Let

x-----> the price of one pound of coffee

y-----> the price of one pound of sugar

we know that

6x+5y=227 -----> equation A

5x+4y=188 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (32,7)

see the attached figure

therefore

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

Answer:

6 hazelnut

4 almond

Step-by-step explanation:

Answer:

Samantha should make six hazelnut chocolate boxes and four almond chocolate boxes in order to maximize the number of chocolates she gives to her friends.

Step-by-step explanation: This is the right answer

=================================================

Explanation:

The base is 10 and the height is 6. So b = 10 and h = 6.

We don't use the 7 at all.

Let's use those b and h values into the formula below

A = b*h/2

A = 10*6/2

A = 60/2

A = 30

Answer:

30 square units

Step-by-step explanation:

Always remember that the equation for the area of a triangle is 1/2 times base times height. With an obtuse triangle, you must always ignore the slant. So, half of the base, which is 10, is equal to 5 and 5 times 6 is 30. Also, remember you can multiply in whichever order and the answer will always be the same because of the commutative property.

Answer:

Domain = (-∞,∞)

Range: [0,∞)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=|2x|-sin(x)

From the graph we can see that

- the domain is equal to all real numbers.

- The range goes from [0,∞)

The correct answer is option d, but bear in mind that the range includes zero as well, so it would be Range: [0,∞)

Answer:

Answer is D!!!

Step-by-step explanation:

Final answer:

The practical domain of the function f(x), representing the height of a model rocket after launch, is [0,4], including the launch at time x=0, reaching the maximum height at x=2 seconds, and landing at x=4 seconds.

Explanation:

The practical domain for the function f(x), which represents the height of a model rocket x seconds after launch, refers to the interval of time during which the rocket is in flight. Since the rocket is launched at time x=0, reaches its maximum height at x=2 seconds, and hits the ground at x=4 seconds, the practical domain of f(x) is [0,4].

This domain includes all times from the launch to when the rocket lands, as the function's values will only be meaningful or defined within this interval.

Answer:

the number if different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards.

Step-by-step explanation:

this is a valid answer for e2020

Final answer:

In poker, the number of microstates when dealing with five cards from separate decks is 52^5, and the probability of getting 5 queens of hearts is (1/52)^5. The probability of drawing any specific hand is also 1 in 380,204,032. Poker hand values are inversely proportional to their entropy, with rarer hands having greater value.

Explanation:

Calculations Involved in Poker Probabilities

The game of poker involves a combination of skill and luck, with probabilities playing a significant role in the strategy. To answer the student's questions regarding probabilities in poker, we need to delve into some detailed calculations.

In analyzing poker hands and their respective values, we find that the value of a hand is typically inversely proportional to its entropy, meaning a less likely hand equates to a higher value.

Pascal's Wager as applied to gambling is not directly related to poker probabilities, but it is an interesting philosophical approach to decision-making under uncertainty. Rather than calculating monetary risk, it assesses the existential gamble of believing in a deity.

Understanding probabilities like these allows gamblers, politicians, teachers, doctors, and individuals in many other fields to make more informed decisions about probable outcomes.

Answer:

[tex](1-\sqrt{2})a^2[/tex]

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

[tex]PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a[/tex]

Thus,

[tex]MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a[/tex]

Consider isosceles triangle MSC. In this triangle

[tex]MS=MC=(\sqrt{2}-1)a.[/tex]

The area of this triangle is

[tex]A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}[/tex]

Consider right triangle PTS. The area of this triangle is

[tex]A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}[/tex]

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

[tex]A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2[/tex]

Answer:

2nd table

Step-by-step explanation:

Because it’s split into 3 equal sections so each region is one third

Answer:  d) 4/9, 4/9, 1/9

Step-by-step explanation:

Let's look at all of the possible combinations of 1st spin & 2nd spin:

AA        BA         CA

AB        BB         CB

AC        BC         CC

P (X=0): how many times is A not in the combination? 4 out of 9

P (X=1): how many times is A in the combination once? 4 out of 9

P (X=2): how many times is A in the combination twice? 1 out of 9

Answer:

  $4140

Step-by-step explanation:

For each of the amounts, the final balance is ...

  A = P(1 +rt)

Filling in the given numbers, we can add the final balances:

  900(1 + 0.06·4) + 900(1 + 0.06·3) + 900(1 + 0.06·2) + 900(1 + 0.06·1)

  = 900(4 + 0.06(4 +3 +2 +1)) = 900·4.60

  = 4140

The amount withdrawn is $4140.

Answer:

The function is f(n) = 10n - 13 ⇒ answer A

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms, n is the position of the

  term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13

Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).

Looking at the functions provided:

Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.