which polynomial is prime?
a) x^3+3x^2-2x-6 b)x^3-2x^2+3x-6 c)4x^4+4x^3-2x-2
d)2x^4+x^3-x+2

Answer:

c

Step-by-step explanation:

There are 6 red and 2 black balls.

The total number of balls = 2 + 6 = 8

The probability of drawing a black ball first is 2/8 = 1/4

The probability of drawing a red ball second is 6/7

P(black, red)=1/4 * 6/7 = 6/28 = 3/14

C

Answer:

The answer is F: 108

Step-by-step explanation:

144 - 108 = 36

108 ÷ 3 = 36

Answer:

giytg8h0ygrubigrfbk

Step-by-step explanation:

Answer:

It could be anywhere from eight to 15 members.

Step-by-step explanation:

Answer:

A. Count the members on each team

   Hurdles  = ⅜ × 40 = 3 × 5 = 15

Long jump = ⅘ × 40 = 4 × 8  = 32

Let's look at the two extremes.

B. Most people will compete in only one event

Then the teams will overlap by seven members (Figure 1).

C. All those in Hurdles compete in the Long Jump

Then 15 members will compete in both Hurdles and Long Jump (Figure 2).

Answer:

12 do both hurdles and long jump

Step-by-step explanation:

3/8 of the team does hurdles, so that number is 3/8·40 = 15.

Of those 15, 4/5 do long jump, so there are ...

4/5·15 = 12 . . . hurdlers who do long jump

Answer:

19.87 Pizzas are left

Step-by-step explanation:

To solve, just take 35 the number of starting pizzas and then subtract the number pizzas both of them consumed. So, 35 - 6.8 given 4/5 converts to 0.8 this leaves use with Bob's pizza consumption only at 28.2 pizza's left. Next, we are going to take 28.2 - 8.33 given 1/3 is .3333 repeating this then gives us the answer with having 19.87 pizzas left - although if it asks how many whole pizzas you would say 28 given you can't have .87 of a pizza.

A fraction is a way to describe a part of a whole. The amount of pizza left is 19 13/15.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given the total number of pizzas is 35. Also given, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. Therefore, the amount of pizza both together eat are,

Amount of pizza Bob and Dave eat = 6 4/5 + 8 1/3

                                                           = 34/5 + 25/3

                                                           = 102/15 + 125/15

                                                           = (102+125)/15

                                                           = 227/15

Amount of pizza left = 35 - 227/15

                                  = (525 - 227)/15

                                  = 298/15

                                  = 19 13/15

Hence, the amount of pizza left is 19 13/15.

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Answer:

343.7 ft

Step-by-step explanation:

The wire is anchored 190 -13 = 177 ft from the ground. That distance is opposite the given angle (31°). The measure you want is the hypotenuse of the triangle with that side and angle measures.

The mnemonic SOH CAH TOA reminds you that the relation between the opposite side, hypotenuse, and angle is ...

Sin(angle) = Opposite/Hypotenuse

Filling in the given information, you have ...

sin(31°) = (177 ft)/hypotenuse

Solving for hypotenuse gives

hypotenuse = (177 ft)/sin(31°) ≈ 343.7 ft

The length of the guy wire should be 343.7 ft.

To find the length of the guy wire attached 13 feet from the top of a 190-foot tall tower at an angle of 31° with the ground, we can use the sine function and trigonometry. The length of the guy wire is approximately 380.8 feet.

To find the length of the guy wire, we can use trigonometry. The guy wire, the height of the tower, and the distance from the top of the tower to the attachment point form a right triangle. We can use the sine function to find the length of the guy wire: sin(31) = height of the tower / length of the guy wire. Rearranging the equation gives us length of the guy wire = height of the tower / sin(31). Plugging in the values, we get length of the guy wire ≈ 190 / sin(31) ≈ 380.8 feet. Therefore, the guy wire should be approximately 380.8 feet long.

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The answer would be 9,631.473. Since there is a 5 after the two, you round up one value. Hope this helps!

Answer:

9,631.473

Step-by-step explanation:

The five would make 2 into a 3.

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}f(1)=5\\f(n)=f(n-1)\cdot(-2)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]f(n)=5\cdot(-2)^{n-1}\\\\f(1)\to\text{put n = 1 to the equation of}\ f(n):\\\\f(1)=5\cdcot(-2)^{1-1}=5\cdot(-2)^0=5\cdot1=5\\\\\text{calculate the common ratio:}\ \dfrac{f(n+1)}{f(n)}\\\\f(n+1)=5\cdot(-2)^{(n+1)-1}=5\cdot(-2)^{n+1-1}=5\cdot(-2)^n\\\\r=\dfrac{f(n+1)}{f(n)}=\dfrac{5\!\!\!\!\diagup^1\cdot(-2)^n}{5\!\!\!\!\diagup_1\cdot(-2)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=(-2)^{n-(n-1)}=(-2)^{n-n+1}=(-2)^1=-2\\\\\text{Therefore}\\\\f(n)=f(n-1)\cdiot(-2)[/tex]

Answer:

135

Step-by-step explanation:

[tex]\frac{5}{9}\times243=\frac{5\times243}{9}=

\frac{1250}{9}=\boxed{135}

[/tex]

ANSWER

84%,0.82,¾,⅓

EXPLANATION

Convert everything to decimals.

[tex] \frac{3}{4} = 0.75[/tex]

[tex] 84\% = 0.84[/tex]

[tex] \frac{1}{3} = 0.333....[/tex]

The last one is already in decimals.

[tex]0.82[/tex]

We can now see clearly, that

[tex]0.84 \: > \: 0.82 \: > \: 0.75 \: > \: 0.3333...[/tex]

This implies that,

[tex]84\% \: > \: 0.82 \: > \: \frac{3}{4} \: > \: \frac{1}{3} [/tex]

Hence from highest to least, we have

84%,0.82,¾,⅓

387 customers or 930 customers

(27+12)x10x3 and 1,170

Answer:

pennies/first offer

Step-by-step explanation:

you would be rich

1x2=2  2^364= a lot of pennies

the pennies gives u the most money

It’s -125 and you welcome

the diameter is 2. GJ as it goes across the whole circle

Answer:

GJ

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

Diameter = Any straight line segment that passes through the centre of the circle.

Answer: ($2.50k) + $5

The distance you can ride is 6 kilometers.

($2.50 x 6) + $5 = $20

Answer:

[tex]2.50d+5\leq 20[/tex]

Step-by-step explanation:

Let d represent distance in kilometers.

We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.

We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.

You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.

We can represent this information in an inequality as:

[tex]2.50d+5\leq 20[/tex]

Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].

27\1000 is your rational form.

To simplify (9/100)^3/2, cube 9/100 to get 729/1000000 and then take the square root, which simplifies to 3/100 in rational form.

To simplify (9/100)^3/2 in rational form, we first understand that the exponent 3/2 can be broken down into two steps: first cubing the number, then taking the square root. Cubing 9/100 gives us (9^3)/(100^3), or 729/1000000. Then, taking the square root of this result and multiplying by the convenient factor of 1 in the form of 100/100, we simplify to 3/100, which is the result in rational form.

The official formula is 2B+ Ph

where B is the area of a base of the prism, P is the perimeter of a base, and h is the height of the prism (distance between the two bases)

However, length x width x height can also be used

Answer:

204

Step-by-step explanation:

First you divide 612 by 9 (612÷9) which gives 68.

Then multiply 68 by 3 (68×3) giving the answer 204.

Answer:  

3/9 of 612 = 204

Step-by-step explanation:

Step 1: convert 3/9 into a decimal so that its easier to work with, that will be 0.3333333333

Step 2: since we know that "of" means "X" in math, we times it by 612 to get the answer of 204

Martin's drink equation = option b, 11.99 + d = 14.48

Nora's calzone equation = option a, c - 3 = 9.49

Hope this helps

10/12 for 1. 12/10 for 2

Answer:

Look at explanation

Step-by-step explanation:

1. How many miles does the herd travel in an hour? : 10 divided by 12 and 10 divided by 1/12

2. How many hours does it take the herd to go 1 mile? : 12 divided by 10 and

1/10 x 12

This answer works on Imagine Math

Answer:

The first choice is correct;

(-∞,∞)

Step-by-step explanation:

We have been given the following functions;

[tex]f(x)=x^{2}-1\\\\g(x)=2x-3[/tex]

We are to determine the domain of (fog)(x).

The composite function, (fog)(x) is obtained by substituting g(x) in place of x in the function f(x);

(fog)(x) = f[g(x)] = [tex](2x-3)^{2}-1[/tex]

Clearly the function will be defined everywhere on the number line since it has no undefined points or domain constraints. The domain is thus;

(-∞,∞)

For this case we have the following functions:

[tex]f (x) = x ^ 2-1\\g (x) = 2x-3[/tex]

We must find [tex](f_ {0} g) (x):[/tex]

By definition of composite functions we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {0} g) (x) = (2x-3) ^ 2-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 9-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 8[/tex]

The domain of the function is given by all the values for which the function is defined.

The function is defined for all real numbers.

Answer:

Domain: (-∞,∞)

Answer: 1

Step-by-step explanation: the cosine function oscillates between the values -1 to 1

The amplitude of this particular function is understood to be 1

The maximum value that a graph of y = cos(x) assumes is y = 1.

In a triangle, the cos function (or cosine function) is the ratio of the base side to the hypotenuse.

cos(0°) = 1

cos(30°) = √3/2

cos(45°) = 1/√2

cos(60°) =  1/2

cos(90°) = 0

Cosine function is a periodic function and the value repeat themselves at an interval of 2π. The maximum value the cosine function achieves is y=1. The graph of the function is shown below:

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Answer:

Step-by-step explanation:

Look at the picture.

ΔABC and ΔACD are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]

We have:

[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]

Substitute:

[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex]           cross multiply

[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=4[/tex]

Answer:

the solution is the last one.

Step-by-step explanation:

We know that for a second grade equation of the type:

ax^2 + bx + c = 0

The solution will be given by the quadratic formula, which states that:

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x2 = [-b - sqrt(b^2 - 4ac)]/2a

So, according to the solution, we have:

x1 = [-5 + 2sqrt(7)]/3

Then:

2a = 3

-b = 5

b^2 - 4ac = 28

Solving each equation:

a = 2/3

b= -5

c = 9/8

None of the alternatives equals the values obtained before. So we can say that the expression is simplified.

Now we knoe what the first and second equation are wrong because b is not equal to -5.

So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:

then:

2a = 6

b= -10

b^2 - 4ac = 112

Then b=-10, a = 3 and c=-1

So the solution is the last one.

Final answer:

The correct quadratic equation with the solutions x = 5 ± 2√7 / 3 is 3x² - 10x - 1 = 0, determined by matching the given solution to the quadratic formula.

Explanation:

The student is asking which of the given quadratic equations has the solutions x = 5 ± 2√7 / 3. The correct equation that yields these solutions must be in the form ax² + bx + c = 0, where a, b, and c are constants.

To determine the right equation, we can work backwards from the given solutions using the quadratic formula:

x = ∛( -b ± √(b² - 4ac) ) / 2a

Comparing the solutions to the standard form obtained by the quadratic formula, we need to match the coefficients such that:

After testing each equation, we find that:

The discriminant for the last equation is (10)² - 4×3×(-1) = 100 + 12 = 112, which is 4×7, confirming that x = 5 ± 2√7 / 3 are indeed the solutions.

For this case we must find the inverse of the following function:[tex]f (x) = 4x[/tex]

We follow the steps below:

We change f(x) to y:

[tex]y = 4x[/tex]

We exchange the variables:

[tex]x = 4y[/tex]

We solve for and:

[tex]4y = x[/tex]

We divide between 4 on both sides of the equation:

[tex]y = \frac {x} {4}[/tex]

then y  by [tex]f ^ {-1} (x):[/tex]

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

ANswer:

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

Answer:

[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]

Step-by-step explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

[tex]V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r[/tex]

Therefore:

[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]

Answer:

The formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

Step-by-step explanation:

It is given formula for volume of sphere.

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

To find the radius r of sphere

Volume V =  4/3 πr³

r³ = 3V/4π

r = ∛(3V/4π)

Therefore formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

For this case we must simplify the following expression:

([tex](-6 ^ {\frac {1} {3}}) ^ {- 2}[/tex]

So, by definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]\frac {1} {(- 6 ^ {\frac {1} {3}}) ^ 2} =\\\frac {1} {(- 6 ^ {\frac {1} {3}}) * (- 6 ^ {\frac {1} {3}})} =\\\frac {1} {(6 ^ {\frac {1} {3}}) * (6 ^ {\frac {1} {3}})} =\\\frac {1} {6 ^ {\frac {2} {3}}}[/tex]

ANswer:

[tex]\frac {1} {6 ^ {\frac {2} {3}}}[/tex]

4*2=8

4*1.5=6

2*1.5=3

8*2=16

2*6=12

2*3=6

16+12+6=34 ft

Total surface area is sum of area of all parts of surface. The surface area of the box is 34 squared feet.

The area of surface of a figure is sum of area of all sub-parts of it. It is because we want to get the total area of its surface.

For the given case, the box given has:

(its all because of assuming box is cuboid or say  rectangular prism)

Thus,

Surface area of box = twice of (area of top + area + left side + area of back)

Calculating these sub areas:

Area of top = [tex]2 \times 4 = 8 \: \rm ft^2[/tex]

Area of back = [tex]1\dfrac{1}{2} \times 4 = \dfrac{2+1}{2} \times 4 = 6 \: \rm ft^2[/tex]

Area of left side: [tex]1\dfrac{1}{2} \times 2 = \dfrac{2+1}{2} \times 2 = 3 \: \rm ft^2[/tex]

Thus,

Surface area of box = [tex]2(8 + 6 + 3) = 2 \times 17 = 34 \: \rm ft^2[/tex]

Thus,

The surface area of the box is 34 squared feet.

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Answer:

Step-by-step explanation:

1/2 over 4 = 15/4 over x

4/1=/15/4= 60/4*2/1=120/4=30

repeat the step but instead of 15/4 to 21/4

anyways it's 72

Final answer:

The actual distance the Patel family will travel from Smithville to Clarksville is approximately 282.66 miles.

Explanation:

The scale on the map is 12 inches equals 4 miles. To find the actual distance the Patel family will travel from Smithville to Jonesville, we can set up a proportion:

12 inches / 4 miles = 334 inches / x miles

Cross multiplying, we get:

12x = 1336

Dividing both sides by 12, we find that x = 111.33 miles. So, the Patel family will travel approximately 111.33 miles from Smithville to Jonesville.

Similarly, to find the actual distance they will travel from Jonesville to Clarksville, we can set up another proportion:

12 inches / 4 miles = 514 inches / y miles

Cross multiplying, we get:

12y = 2056

Dividing both sides by 12, we find that y = 171.33 miles. So, the Patel family will travel approximately 171.33 miles from Jonesville to Clarksville.

Therefore, the total actual distance the Patel family will travel by the time they reach Clarksville is approximately 111.33 miles + 171.33 miles = 282.66 miles.

Answer:

[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]

[tex]tan(x) =\±\sqrt{2}[/tex]

Step-by-step explanation:

By definition we know that:

[tex]sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = \frac{sin(x)}{cos (x)}[/tex]

in this case we know that

[tex]cos(x) =\frac{1}{2}[/tex]

So how:

[tex]sin ^ 2(x) = 1-cos ^ 2(x)[/tex]

Substitute the values of cosine in the function

[tex]sin ^ 2 (x) = 1-\frac{1}{2}[/tex]

[tex]sin ^ 2 (x) = \frac{1}{2}[/tex]

[tex]sin(x) =\±\sqrt{\frac{1}{2}}[/tex]

[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]

Then how:

[tex]tan(x) = \frac{sin(x)}{cos (x)}[/tex]

Substitute the values of sine and cosine in the function

[tex]tan(x) = \±\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}=\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=x^2-2x\\\\g(x)=6x+4\\\\\text{Substitute:}\\\\(f+g)(x)=(x^2-2x)+(6x+4)=x^2-2x+6x+4\\\\\text{combine like terms}\\\\(f+g)(x)=x^2+(-2x+6x)+4=x^2+4x+4\\\\(f+g)(x)=0\Rightarrow x^2+4x+4=0\\\\x^2+2x+2x+4=0\\\\x(x+2)+2(x+2)=0\\\\(x+2)(x+2)+0\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\\\x=-2[/tex]