In boot camp, a cadet must use a rope swing to cross an obstacle without
falling into the water hazard below. Unfortunately, they miss the platform on
the other side and swing back to where they started. If it takes the cadet 4.5
seconds to swing from one side of the obstacle to the other and back, how
long is the rope swing? Use the formula:
T=2pie ,square root L over 9.8

([tex]x^{2}[/tex] + 4)([tex]x^{2}[/tex] - 4)

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(x^2 + 4)(x^2 - 4)

x^2 * x^2

x^4

Outside:

(x^2 + 4)(x^2 - 4)

x^2 * -4

-4x^2

Inside:

(x^2 + 4)(x^2 - 4)

4 * x^2

4x^2

Last:

(x^2 + 4)(x^2 - 4)

4 * -4

-16

Now combine all the products of the FOIL together like so...

x^4 - 4x^2 +4x^2 - 16

Combine like terms:

x^4 - 4x^2 +4x^2 - 16

- 4x^2 +4x^2 = 0

x^4 - 16 <<<This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

C. 28

EXPLANATION

The given expression is

[tex] {x}^{2} - 7x + 10[/tex]

We want to evaluate this function at x=-2.

We just have to substitute x=-2 into the given expression.

In other words, we have to replace x with -2 wherever we see x in the expression

[tex]{( - 2)}^{2} - 7( - 2) + 10[/tex]

We evaluate the exponent to get

[tex]4 - 7( - 2) + 10[/tex]

We multiply next to get:

[tex]4 + 14+ 10[/tex]

We now add to obtain:

[tex]28[/tex]

The correct answer is C

Answer:

positive association

linear association

Step-by-step explanation:

It is said that two variables A and B are related when the distribution of the values of one of the two variables differs according to the values of the other.

That is, when variable A grows then variable B also grows. This is known as positive correlation

When variable A grows then variable B decreases. This is known as negative correlation.

In the scatter plot you may notice that when variable A increases then variable B also increases, in an approximately linear relationship. Therefore it can be said that there is a positive and linear association.

The answer is the fourth and fifth option.

Answer:

The function is most likely inversely proportional

More input results in less output

Answer: y=-8-4/1

Step-by-step explanation:

Answer:

The slope is  m= 4.

Step-by-step explanation:

Do Rise over run method. Then divide the two numbers.

Answer:

Brown's experimental probability is closest to it's theoretical probability.

Step-by-step explanation:

Theoretical:

There are 5 colors so the probability of getting orange is 1/5

The probability of getting purple is 1/5

and so on... each color has the probability of 1/5 of being used

We just need to see what experimental probability is closest to .2

Experimental probability:

So Orange 118/625=.1888

Purple 137/625=.2192

Brown 122/625=.1952

Yellow 106/625=.1696

Green 142/625=.2272

So the closest from below .2 is .1952 (which is brown)

The closest from above .2 is .2192 (which is purple.

If you aren't sure which one is closer.. you can see which difference is closer to 0.

.2-.1952=.0048

.2192-.2=.0192

.1952 is the winner since .0048 is closer to 0 than .0192 is

So Brown !

Answer:

12 matches

Step-by-step explanation:

Hope this helps!

The number of matches that the team needs to win for the team to have a 55% success rate is approximately 16 matches.

A percentage is a number that tells us how much out of 100.

Given that, the tennis team has played 28 matches so far. If they've won 10 matches.

If 28 matches = 100%

10 matches = x %

x = (10×100)/28

x = 35%

So, we are left to determine (55% - 35% = 20%) the remaining 20% success rate;

28 = 100%

x matches = 20%

x = 5.6 matches

Thus, the total number of matches to be won to have a 55% success rate is:

= 10 matches + 5.6 matches

= 15.6 matches

≅ 16 matches

Hence, we can conclude that the total number of matches that the team needs to win for the team to have a 55% success rate is 16 matches.

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[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies 9=r \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies SA=4\pi (9)^2\implies \boxed{SA=324\pi }[/tex]

Answer:

20 rides.

The question:

"There have been two proposals for ticket sales. The first proposes a base fee of $5 for entry into the park and $0.50 per ride. The second plan has no base fee, but charges $0.75 per ride. After How many rides would the cost[s] be equal?"

Step-by-step explanation:

Assume that the two costs become equal after [tex]x[/tex] rides.

The two costs are assumed to be equal. That is:

[tex]5 + 0.50x = 0.75 x[/tex].

Subtract [tex]0.50x[/tex] from both sides of this equation:

[tex]5 = 0.25 x[/tex].

[tex]\displaystyle x = \frac{5}{0.25} = \frac{500}{25} = 20[/tex].

In other words, the two costs become equal after 20 rides.

Answer:

x =20

Step-by-step explanation:

We can use proportions to solve

$240         320

----------- = ------------

15                x

Using cross products

240x = 320 * 15

240x =4800

Divide by 240 on each side

240x/240 = 4800/240

x =20

By finding the cost per square yard from Joanna's initial purchase ($16 per sq yd), we can calculate that she can buy 20 square yards of carpet for $320.

To find out how many square yards of carpet Joanna can buy for $320 using the same rate, we first need to determine the cost per square yard based on her $240 purchase. She can buy 15 square yards for $240, so by dividing the total cost by the number of yards, we find the cost per square yard.

Cost per square yard = Total cost / Number of square yards = $240 / 15 sq yds = $16 per sq yd.

Now, we can use the cost per square yard to find out how many square yards she can get for $320. We divide the total amount she's willing to spend by the cost per square yard.

Square yards for $320 = Total amount to spend / Cost per square yard = $320 / $16 per sq yd = 20 sq yds.

Therefore, Joanna can buy 20 square yards of carpet for $320.

Answer:

5 years

Step-by-step explanation:

18= 9(1.15)^x

Divide each side by 9

18/9= 9/9 *(1.15)^x

2 = 1.15 ^x

Take the  log on each side

log (2) = log (1.15^x)

log 2 = x log 1.15

Divid each side by log (1.15)

log 2 / log 1.15 = x log 1.15/ log 1.15

log 2 / log 1.15 = x

4.959484455 = x

To the nearest year

5 years

Recall that

[tex]1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})[/tex]

So we have

[tex]x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1[/tex]

Then for any [tex]n[/tex], we have

[tex]x^{3n}=(x^3)^n=1^n=1[/tex]

The next step is to add (b/2a)^2 to both sides to complete the square, then balance the equation by adding the inverse of that value outside the parentheses.

The student has asked for the next step in solving the quadratic equation 0 = −2x2 + 2x + 3 by completing the square.

After rewriting the equation and factoring out the coefficient of the x2 term, the next step is to add a specific value to both sides to form a perfect square trinomial.

This value is found by taking (b/2a)2, where a is the coefficient of x2 and b is the coefficient of x. For this equation, we therefore add −(2/2*(-2))2 = 1 to both sides inside the parentheses.

The completed equation becomes −3 + 1 = −2*(x2 − x + 1/4). Finally, we must balance the equation by adding the inverse of −<strong>2*1/4</strong> outside the parentheses.

Then, we can continue solving for x.

Answer:

False

Step-by-step explanation:

y= mx+b

The x intercept is when y=0

0 = mx +b

Subtract b from each side

-b = mx+b-b

-b = mx

Divide each side by m

-b/m = mx/m

-b/m =x

The x intercept is -b/m

To maximize profit, the tailors' company should sew 14 skirts, achieving the optimal balance between fabric usage, production hours, and selling constraints.

To maximize profit, the tailors' company should determine the number of skirts and dresses to produce. Let's denote:

- x: Number of dresses to produce

- y: Number of skirts to produce

The constraints are:

1. Fabric usage: [tex]\(4x + 3y \geq 130\)[/tex] (at least 130 yards)

2. Selling constraint: [tex]\(y \leq 3x\)[/tex] (at most three times as many skirts as dresses)

3. Production hours constraint: [tex]\(10x + y \leq 286\)[/tex] (no more than 286 hours)

4. Non-negativity constraint: [tex]\(x \geq 0\)[/tex], [tex]\(y \geq 0\)[/tex]

The profit function to maximize is:

[tex]\[ \text{Profit} = 540x + 180y \][/tex]

We can solve this problem using linear programming. Here's the optimization model:

Objective function:

Maximize 540x + 180y

Subject to:

[tex]\[4x + 3y \geq 130\][/tex]

[tex]\[y \leq 3x\][/tex]

[tex]\[10x + y \leq 286\][/tex]

[tex]\[x \geq 0\][/tex]

[tex]\[y \geq 0\][/tex]

Using a linear programming solver, we can find the optimal values of x and y that maximize profit.

The resulting optimal solution will give us the number of skirts the company should sew to maximize profit.

Answer:

Westmoreland County, VA

For this case we must find the product of the following expressions:[tex](-2x ^ 2 + x-5) (x ^ 3-3x-4) =[/tex]

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

[tex]+ * - = -\\- * - = +[/tex]

[tex]-2x ^ {2 + 3} + 6x^{2 + 1} + 8x ^ 2 + x^{3 + 1} -3x^{1 + 1} -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

If we multiply[tex](x ^ 3-3x-4) (- 2x ^ 2 + x-5)[/tex] we would obtain the same result according to the commutative property of the multiplication:

[tex]a * b = b * a[/tex]

Answer:

[tex]-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]

Answer:

The CORRECT answer is  -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20

Step-by-step explanation:

I go to k12 and all the other answers are incorrect. I had this on my test.  

MY WORK:

-2x^6 + 6x^4 + 8x^3 + x^4 – 3x^2 – 4x – 5x^3 + 15x + 20

= -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20  

b) Yes, it would be equal because of the rule of the commutative property. (basically, the order in which you multiply won’t matter.)            

This took a little longer than expected but I hope this helps...                 Please leave a rating and a thanks

Sincerely, Another Brainly User

The given parallelogram is a rectangle when ΔZYX ≅ ΔWXY.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

In the given parallelogram WXYZ,

ZX ≅  WY.

For ΔZXY and ΔWXY,

ZX =  WY   (already given)

ZY = WX    (two opposite sides of the parallelogram WXYZ)

XY is the common side

Therefore, ΔZXY ≅ ΔWXY

Now, we can say, ∠ZYX = ∠WXY

For the given parallelogram, ∠ZYX + ∠WXY = 180°

ZYX = ∠WXY = 90°

Hence, the given parallelogram is a rectangle.

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HEYA MATE

YOUR ANSWER IS A.3/10,30%

BECAUSE SHADED SQUARES ARE 6

AND TOTAL SQUARES ARE 20

THAN APPLY THE FORMULA OF PERCENTAGE.

THAN WE GET

30%

[tex]<marquee><i><b>[/tex]THANK YOU

ANSWER

A. (4,12)

EXPLANATION

The equations are:

[tex]10x +2y = 64...(1)[/tex]

and

[tex]3x - 4y = -36...(2)[/tex]

To eliminate a variable we make the coefficients of that variable the same in both equations.

It is easier to eliminate x.

We multiply the first equation by 2 to get:

[tex]20x + 4y = 128...(3)[/tex]

We add equations (2) and (3).

[tex]3x + 20x + 4y - 4y = - 36 + 128[/tex]

[tex]23x = 92[/tex]

Divide both sides by 23

[tex] \frac{23x}{23} = \frac{92}{23} [/tex]

[tex]x = 4[/tex]

Put x=4 into equation (1).

[tex]10(4)+2y = 64[/tex]

[tex]40+2y = 64[/tex]

[tex]2y = 64 - 40[/tex]

[tex]2y = 24[/tex]

[tex] \frac{2y}{2} = \frac{24}{2} [/tex]

[tex]y = 12[/tex]

The solution is (4,12)

Answer:

Step-by-step explanation:

1 unit = 14 pence

and

1 times 942 = 942 so 14 times 942 = 13,188

therefore

942 units cost £131.88!!hope it help:):)

Final answer:

To calculate the total cost for 942 units at 14p each, multiply the cost per unit by the number of units [tex](942 imes 14p)[/tex]resulting in 13,188p, which is £131.88.

Explanation:

If each unit costs 14p, to find the total cost of 942 units, we need to multiply the cost per unit by the total number of units. The calculation is as follows:

[tex]942 units imes 14p per unit = 13,188p[/tex]

Since there are 100 pence in a pound, we need to convert pence into pounds:

[tex]13,188p \/ 100 = \£131.88\[/tex]

[tex]Therefore, the total cost for 942 units is \£131.88\.[/tex]

Answer:

B

Step-by-step explanation:

A. x^2 - 2x - 8 < 0

(x - 4)(x + 2) < 0

B. x^2 + 2x - 8 < 0

(x + 4)(x - 2) < 0

C. x^2 - 2x - 8 > 0

(x - 4)(x - 2) > 0

D. x^2 + 2x - 8 > 0

(x + 4)(x - 2) > 0

Since roots here are -4 and 2, the answer is either B or D.

When you test a point in the interval between -4 and 2, for example 0, it is negative.

So the answer is B.

Answer:

The answer is [tex]x^2+2x-8<0[/tex]

Step-by-step explanation:

In order to determine the answer, we have two alternatives:

In this case, we use the second option because it is easier to replace a value and solving basic math operations. Also, if we choose a good first value, we will eliminate immediately some options.

We can choose values between -4 and 2. Every time we could choose 0 value, we should do it.

First value: [tex]x=0[/tex]. Replacing:

[tex]-8<0\\-8<0\\-8>0\\-8>0[/tex]

We can see that the two first options are correct, the two last options are wrong.

Second value: [tex]x=-3[/tex]. Replacing:

[tex](-3)^2-2*(-3)-8<0\\9+6-8<0\\7<0\\\\(-3)^2+2*(-3)-8<0\\9-6-8<0\\-5<0[/tex]

We can see that the first option is wrong.

Finally, the correct option is the second one:

[tex]x^2+2x-8<0[/tex]

Answer:

A. Scalene since all sides have different lengths

E. Right since it has a right angle

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -4)\\(1,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 4)} {1-0} = \frac {4} {1} = 4[/tex]

So, the equation is of the form:

[tex]y = 4x + b[/tex]

We substitute a point to find "b":

[tex]-4 = 4 (0) + b\\-4 = b[/tex]

Finally, the equation is:

[tex]y = 4x-4[/tex]

Answer:

Option D

Answer: The approximate distance is 14.76

Step-by-step explanation:

You can use the following formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For the points (3, 5) and (-4, -8) you can identify that:

[tex]x_2=-4\\x_1=3\\y_2=-8\\y_1=5[/tex]

Now you need to substitute these values into the formula.

Therefore, the approximate distance between the given points is:

 [tex]d=\sqrt{(-4-3)^2+(-8-5)^2}\\\\d=\sqrt{(-7)^2+(-13)^2}\\\\d=\sqrt{49+169}\\\\d=\sqrt{218}[/tex]

[tex]d[/tex]≈[tex]14.76[/tex]

Final answer:

To find the distance between the points (3, 5) and (-4, -8), the distance formula is used, resulting in an approximate distance of 14.76 when rounded to the nearest hundredth.

Explanation:

To determine the approximate distance between two points with coordinates (3, 5) and (-4, -8), we use the distance formula which is derived from the Pythagorean theorem. The distance formula is: d = √((x2 - x1)² + (y2 - y1)²). Plugging in the values, we get d = √((-4 - 3)² + (-8 - 5)²) = √(7² + 13²) = √(49 + 169) = √218. The approximate distance is thus the square root of 218, which when calculated gives us approximately 14.76. This result should be rounded to the nearest hundredth, which would give us 14.76 as the final answer.

Answer:

D

Step-by-step explanation:

Given

- 1(x + 7)(x - 4)

each term in the second factor is multiplied by each term in the first factor, that is

leaving the multiplier of - 1 for the time being

x(x- 4) + 7(x - 4) ← distribute both parenthesis

= x² - 4x + 7x - 28 ← collect like terms

= x² + 3x - 28

Hence

- 1(x² + 3x - 28) = - x² - 3x + 28 → D

Answer:

D

Step-by-step explanation:

The expression below is the factorization of what trinomial?

-1(x+ 7)(x-4)

A. -x^2 + 3x+ 28

B. -x^2 + 3x-28

C. -x^2 - 3х - 28

D. -x^2 - 3x+ 28

Answer:

[tex]\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Step-by-step explanation:

We can simplify the expression under the root first.

Remember to use  [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]

Thus, we have:

[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}[/tex]

We know 4th root can be written as "to the power 1/4th". Then we can use the property  [tex](ab)^{x}=a^x b^x[/tex]

So we have:

[tex]\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}[/tex]

Option D is right.

Answer:

[tex]P(x\:<\:50)=0.0918[/tex]

Step-by-step explanation:

To  find the probability that a randomly selected test taker scored below 50, we need to first of all determine the z-score of 50.

The z-score for a normal distribution is given by:

[tex]z=\frac{x-\bar x}{\sigma}[/tex].

From the question, the mean score is [tex]\bar x=70[/tex], the standard deviation is, [tex]\sigma=15[/tex], and the test score is [tex]x=50[/tex].

We substitute these values into the formula to get:

 [tex]z=\frac{50-70}{15}[/tex].

 [tex]z=\frac{-20}{15}=-1.33[/tex].

We now read the area that corresponds to a z-score of -1.33 from the standard normal distribution table.

From the table, a z-score of -1.33 corresponds to and area of 0.09176.

Therefore the probability that a randomly selected test taker scored below 50 is [tex]P(x\:<\:50)=0.0918[/tex]

Answer:

D. All real numbers except 0.

Step-by-step explanation:

The figure show a particular case of a hyperbola, which is continuous for all values of x, except the value of x where discontinuity exists. Hence, the domain of the function is all real numbers except 0.

Answer:

The third option (C) Yes, because there is enough water in the cooler for about 81 cups total.Step-by-step explanation:

The radius and height of the cooler of 6 and 20 inches respectively, can

contain approximately only 81 cups, the correct option is therefore;

The dimensions of the cooler are;

Radius = 6 inches

Height = 20 inches

The possible dimensions of a cup are;

Diameter = 4.4 inches

Height = 5.5 inches

Required:

If each of the 38 players have 2 paper cups filled with water.

Solution;

The volume of the cooler, V₁, is found as follows;

V₁ = π × 6² × 20 = 720·π

The volume of the cooler, V₁ = 720·π in.³

The volume of the paper cup, V₂, is; [tex]V_2 = \dfrac{1}{3} \times \pi \times \left(\frac{4.4}{2} \right)^2 \times 5.5 = 8\frac{131}{150} \cdot \pi[/tex]

The volume of the paper cup, V₂ = [tex]8\frac{131}{150} \cdot \pi[/tex] in.³

The number of cups, n, in the cooler of water is therefore;

The number of cups of water in the cooler ≈ 81 cups

The number of cups required for each of the 38 player to have two full cups is, Cups = 38 × 2 = 76 cups

Given that the water available, (approximately 81 cups) is more than the

number of cups required (76 cups), the correct option is option;

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