A right rectangular pyramid is sliced parallel to the base as shown.

What is the area of the resulting two-dimensional cross-section?

A. 2
B. 3
C. 9
D. 12

Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition

x = 2 when y = 2

k = yx = 2 × 2 = 4, hence

y = [tex]\frac{4}{x}[/tex] ← equation of variation

Answer:

9.

The probabilities are the same

10.

1/3

Step-by-step explanation:

9.

Assuming the coin is fair;

The probability of getting heads in a single toss is, P(H) = 1/2

The probability of getting tails in a single toss is, P(T) = 1/2

Now, P(H,H,H) is the probability of obtaining 3 heads in the e tosses. Since each toss is independent of the others,;

P(H,H,H) = P(H)*P(H)*P(H)

              = 1/2 * 1/2 * 1/2 = 1/8

On the other hand, P(H,T,H) is the probability of obtaining a head followed by a tail followed by a final head. Using the independence property;

P(H,T,H) = P(H)*P(T)*P(H)

              = 1/2 * 1/2 * 1/2 = 1/8

Therefore, P(H,H,H) = P(H,T,H)

10.

We are informed that a coin is tossed and a number cube is rolled. We are to determine the following probability;

P(heads, a number less than 5)

Assuming the coin is fair;

The probability of getting heads in a single toss is, P(H) = 1/2

Assuming the number cube is fair as well, the probability of rolling a number less than 5 is;

4/6 = 2/3

This is because there are 4 numbers less than 5, (1, 2, 3, 4) while the cube has 6 sides.

P(heads, a number less than 5), the events presented here are independent since the outcome from tossing the coin does not in any way determine the outcome from rolling the number cube. Therefore,;

P(heads, a number less than 5) = P(heads)*P(a number less than 5)

                                                    = 1/2 * 2/3 = 1/3

Answer:

Blank 1 ⇒ supplementary

Blank 2 ⇒ complementary

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The tangent to a circle is a line touch the circle at one point

- The tangent and the radius of a circle are perpendicular to each

 other at the point of contact

- If the two angles are supplementary, then the sum of their measure

 is 180°

- If the two angles are complementary, then the sum of their measure

 is 90°

* Now lets solve the question

∵ CB and CA are two tangents to the circle O at B and A

∵ OB and OA are radii

∴ OB ⊥ BC at point B and OA ⊥ AC at point A

∴ m∠OBC = 90° and m∠OAC = 90°

- In figure CBOA is a quadrilateral

∴ The sum of the measures of its interior angles is 360°

∵ m∠CBO + m∠BOA + m∠OAC + m∠BCA = 360°

∵ m∠CBO = 90° , m∠OAC = 90°

∴ 90° + m∠BOA + 90° + m∠BCA = 360°

∴ 180° + m∠BOA + m∠BCA = 360° ⇒ subtract 180 from both sides

∴ m∠BOA + m∠BCA = 180°

∴ ∠BOA and ∠BCA are supplementary

- In Δ CBO

∵ The sum of the measures of the interior angles of any triangle is 180°

∴ m∠BOC + m∠BCO + m∠CBO = 180°

∵ m∠CBO = 90°

∴ m∠BOC + m∠BCO + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠BOC + m∠BCO = 90°

∴ ∠BOC and ∠BCO are complementary

Answer:

Blank 1: Supplementary

Blank 2:Complementary

Step-by-step explanation: I picked these and got it right

Answer:

The equation is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

The sum is:

[tex]S=\frac{211}{243}[/tex]

--------------------------------------------------------------------

If the sequence is infinite, the formula is:

[tex]S = \frac{a_1}{1-r}[/tex]

-------------------------------------------------------------------

Step-by-step explanation:

We must calculate the radius of the geometric series

[tex]r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}[/tex]

The first term of the series is: [tex]a_1=\frac{1}{3}[/tex]

The last term of the series is: [tex]a_n=\frac{16}{243}[/tex]

If the sequence is finite then the formula is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

[tex]S=\frac{211}{243}[/tex]

If the sequence is infinite then by definition as the radius  are [tex]0 <| r | <1[/tex] then the formula for the sum of the geometric sequence is:

[tex]S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1[/tex]

Answer:

A

Step-by-step explanation:

got it right on edge

The probability of drawing 3 oranges from a basket of 6 oranges and 4 tangerines is 1/6 or approximately 0.167.

This problem is a probability question in the field of mathematics. It is asking us to find the probability that all three fruits drawn from the basket are oranges. This can be solved using the concept of combinations from probability theory.

The total number of fruits in the basket is 10 (6 oranges and 4 tangerines). We want to draw a sample of 3 fruits. The number of ways to draw 3 fruits from a total of 10 (regardless of type) is given by the combination formula C(n, r), where n is the total number of items and r is the number of items to choose. So we have C(10, 3) = 120 possible ways.

Next, consider the scenario we're interested in--drawing 3 oranges. The total number of ways to draw 3 oranges from a total of 6 oranges is C(6, 3) = 20 possible ways.

So, the probability of drawing 3 oranges is the number of ways to draw 3 oranges divided by the total number of ways to draw 3 fruits. So, the probability is 20/120 = 1/6 or approximately 0.167.

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Final answer:

The probability of drawing 3 oranges from a basket containing 6 oranges and 4 tangerines is found using combinations. The calculation shows that the probability of selecting all oranges in a draw of 3 fruits is 1/6.

Explanation:

The question asks to find the probability that when three fruits are drawn from a basket containing 6 oranges and 4 tangerines, all three are oranges. This is a problem of probability without replacement, which can be solved using combinations.

To find the probability of drawing 3 oranges out of 3 fruits, we calculate the combinations of choosing 3 oranges from 6 and then divide it by the combinations of choosing 3 fruits from the total 10 fruits in the basket.

The number of ways to select 3 oranges out of 6 is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose. So, we have:

Ways to pick 3 oranges: C(6, 3)

Total ways to pick 3 fruits: C(10, 3)

Then the probability is calculated by:

P(all oranges) = C(6, 3) / C(10, 3)

Calculating the combinations, we have:

Thus, the probability that all three fruits are oranges is 1/6.

Answer:

The answer is 2.

Step-by-step explanation:

The equation for finding the axis of symmetry is:

x=-\frac{b}{2a}

Plug the numbers from the equation in:

a=1

b=-2

x=-\frac{-2}{2(1)}

Solve:

x=\frac{2}{1}

x=2

hope this helps :)

Step 1: Set the two equations equal to each other and solve for x.

3x -5 = 6x - 8

3x + (-5+5) = 6x -8 + 5

(3x - 6x) = (6x - 6x) - 3

-3x/-3  = -3/-3

x = 1

Step 2: To solve for y take one of the given equation of your choice (for the purpose of this explanation I will only do y = 3x - 5) and replace x with 1, then solve for y

y = 3(1) - 5

y = 3 - 5

y = -2

(1,-2)

Check:

-2 = 3(1) - 5 ---> - 2 = -2

-2 = 6(1) - 8 ---> -2 = -2

Hope this helped!

Answer:

x=1

and y= -2

Step-by-step explanation:

y=3x-5 y=6x-8

On equating the two equations:

3x-5= 6x-8

Taking terms of x on one side and constant terms on the other

6x-3x= 8-5

3x= 3

Dividing both sides by 3, we get

x=1

Now, putting value of x in y=3x-5, we get

y=3-5

 = -2

Hence, Solution is:

x=1 and y= -2

Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

A golden ticket costs $32. A regular ticket costs $24. A platinum ticket costs $64. Hope this helps!

Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

Step-by-step explanation:

ANSWER

The slope is 4

EXPLANATION

We want to find the slope of the line goin through (3,9) and (1,1)

We use the slope formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points into the slope formula to get;

[tex]m = \frac{1 - 9}{1 - 3} [/tex]

This simplifies to:

[tex]m = \frac{ - 8}{ - 2} [/tex]

[tex]m = 4[/tex]

Hence the slope of the line is 4.

Answer:

x = 3

x = -5

Step-by-step explanation:

(9)(x+1)(x+1) = 144

(9)(x²+2x+1) = 144

9x²+18x+9 = 144

9x²+18x = 135

x²+2x = 15

x(x+2) = 15

x = 3

x= -5

Answer: [tex]x_1=3\\x_2=-5[/tex]

Step-by-step explanation:

Divide boht sides of the eqeuation by 9:

[tex]\frac{9(x+1)^2}{9}=\frac{144}{9}\\\\(x+1)^2=16[/tex]

Remembert that:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Then, applying this, you get:

[tex]x^2+2(x)(1)+1^2=16\\x^2+2x+1=16[/tex]

Subtract 16 from both sides:

[tex]x^2+2x+1-16=16-16\\x^2+2x-15=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 2 and whose product be -15, then:

[tex](x-3)(x+5)=0\\x_1=3\\x_2=-5[/tex]

Answer:

4

Step-by-step explanation:

Final answer:

The expression equivalent to (X^3)^4 is X^12. You calculate this by multiplying the exponents, resulting in X raised to the power of 3 times 4, which equals 12.

Explanation:

The expression (X^3)^4 is equivalent to X^(3*4), which is X^12. This follows the rule that when you raise a power to a power, you multiply the exponents. A number raised to the fourth power, like in this case, means that number is multiplied by itself four times. Generalizing this, for any base 'n' and exponents 'a' and 'b', the expression (n^a)^b is equal to n^(a*b).

For example, similar to (5^3)^4 being 5^(3*4) or 5^12, which is twelve fives multiplied together. Therefore, our given expression simplifies to X multiplied by itself a total of twelve times.

x in (-oo:+oo)

2/7 = x/14 // - x/14

2/7-(x/14) = 0

2/7-1/14*x = 0 // - 2/7

-1/14*x = -2/7 // : -1/14

x = -2/7/(-1/14)

x = 4

x = 4

i hope this helps

Answer:

x*14 = 7*4

Step-by-step explanation:

I think the answer is 32,2000cm^3

Answer: C

Step-by-step explanation: i got 100% on test

Hello There!

To find a cylinder, we use the formula Pi*radius “squared” *height

First, let’s put in our values. Our radius is 5 but in our formula, we have to square 5 so we get a product of 25.

Then we multiply 25 by 9 because you will see in our formula we have to multiply by the height. 25*9 equals 225

Now, we are putting our value in terms of pi so our answer would be 225

Answer “C”

Answer:

175

Step-by-step explanation:

APEXX!!!!

Perimeter of a square = side*side

4*4=16cm^2

The perimeter of a square piece of plastic with each side measuring 4 centimeters is 16 centimeters.

The question is asking for the perimeter of a square piece of plastic with sides that are 4 centimeters long. To calculate the perimeter of a square, you multiply the length of one side by four. Since a square has four equal sides, the calculation in this case would be 4 cm (side length) times 4 (number of sides), which equals 16 cm. So, the perimeter of the square piece of plastic is 16 centimeters.

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Answer:

420 miles

Step-by-step explanation:

Distance = rate × time

Let's say that the distance is D and that John's speed is S.  We know that:

D = S × 6

When Elliot drives at speed S+14:

D = (S+14) × 5

Setting D = D:

S × 6 = (S+14) × 5

6S = 5S + 70

S = 70

Therefore, the distance D is:

D = 70 × 6

D = 420

The distance from John's house to Miami is 420 miles.

The distance from John's house to Miami, Florida is 420 miles, calculated by first determining John's speed using the given information and then applying the formula distance = speed times time.

To calculate the distance from John's house to Miami, Florida, we need to use the formula distance = speed times time. John's travel time is 6 hours. We are not directly given John's speed; instead, we know that Elliot drives 14 mph faster than John and it takes him 5 hours to cover the same distance. Let's denote John's speed as 's'. Therefore, Elliot's speed is 's + 14 mph'. Setting up an equation based on Elliot's travel information, we have distance = (s + 14 mph) times 5 hours.

Since they both travel the same distance, we can also write John's travel information as distance = s times 6 hours. Equating both expressions for distance, we get: s times 6 = (s + 14) times 5. Simplifying, we have 6s = 5s + 70, which leads to s = 70 mph. This means John's speed is 70 mph.

To find the distance to Miami, we return to the distance formula and substitute John's speed: distance = 70 mph times 6 hours = 420 miles. Hence, the distance from John's house to Miami, Florida is 420 miles.

Answer:

D

Step-by-step explanation:

Supplementary angles sum to 180°

Subtract the given angle from 180 for the supplement, that is

180° - 89° = 91° ← the supplementary angle

Final answer:

The supplement of an 89° angle is found by subtracting it from 180°, giving us 91°. Therefore, the correct answer is 91°, which is option D.

Explanation:

To find the supplement of an angle, we need to know that supplementary angles add up to 180 degrees. Given an angle that measures 89°, we can find its supplement by subtracting the given angle from 180°.

So, 180° - 89° = 91°.

The supplement of an angle that measures 89° is 91°, which corresponds to option D.

Answer:

12a−9

Step-by-step explanation:

Distribute:

=(3a)(3)+(3a)(−a)+(3)(a2)+(3)(−3)+3a

=9a+−3a2+3a2+−9+3a

Combine Like Terms:

=9a+−3a2+3a2+−9+3a

=(−3a2+3a2)+(9a+3a)+(−9)

=12a+−9

Answer:

3 (4 a - 3)

Step-by-step explanation:

Simplify the following:

3 a (3 - a) + 3 (a^2 - 3) + 3 a

3 a (3 - a) = 9 a - 3 a^2:

9 a - 3 a^2 + 3 (a^2 - 3) + 3 a

3 (a^2 - 3) = 3 a^2 - 9:

3 a^2 - 9 - 3 a^2 + 9 a + 3 a

Grouping like terms, 3 a^2 - 3 a^2 + 9 a + 3 a - 9 = (9 a + 3 a) - 9 + (-3 a^2 + 3 a^2):

(9 a + 3 a) - 9 + (-3 a^2 + 3 a^2)

9 a + 3 a = 12 a:

12 a - 9 + (-3 a^2 + 3 a^2)

3 a^2 - 3 a^2 = 0:

12 a - 9

Factor 3 out of 12 a - 9:

Answer:  3 (4 a - 3)

Answer:

1/6 * 1/6 = 1/36 or 0.027%

Step-by-step explanation:

This is because there is a 1/6 chance the cubes will land on 3. Sincer there is 2 of them, multiply them by each other. Do not add.

Hope this helps!

Answer:

40 cm

Step-by-step explanation:

Multiply the length, the width, and the height. You can multiply them in any order to get the same result. The formula for finding the volume of a rectangular solid is:

Volume = Length * Height * Width,

or V = L * H * W.

Answer:

-2

Step-by-step explanation:

2x + y = 10               Subtract 2x from both sides.

2x-2x + y = 10 - 2x  Combine the left.

y = 10 - 2x

The slope is the number in front of the x -- in this case - 2

The answer is - 2

Answer:

B. 28 minutes

Step-by-step explanation:

According to the given statement,

William weeds the whole garden in 45 minutes, then in one minute he will weed 1/45 of the garden

and

similarly, 1/75 of the garden in one minute.

When they both will work together, they will weed (1/45+1/75) of the garden in one minute

Solving the equation:

= [tex]\frac{1}{45}+ \frac{1}{75}\\= \frac{75+45}{3375}\\ =\frac{120}{3375}\\ = 0.036[/tex]

Garden weeded in one minute by both = 0.036

So, number of minutes to weed whole garden = 1/0.036

= 27.77 minutes

Rounding off will give us: 28 minutes

So,

Option B is the correct answer ..

Answer:

C.

Step-by-step explanation:

Answer:

The correct answer is C.

Step-by-step explanation:

We have given some pattern in the series.

We need to find the next step which follows and continue the series.

We know that, we have three given patterns in the question. In the first we have given a pattern which is made by the joining of three dots, and in the second pattern made by the joining of five dots and in the third pattern made by the joining of the five dots.

In the following way, we can say that the next step in the series and fourth pattern follows same pattern as given in the above. That's why next pattern made by the joining of seven dots, but in the following given options next to next pattern is given which is joining by nine dots, therefore we choose option which is the next step in the series.

The simplified form of ratio of  [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it.

Given that simplify 3 square root of 7 over 5 square root of 7 that is [tex]3\sqrt7 / 5\sqrt7.[/tex]

To find the ratio of  [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it by following steps:

Step 1: Factorize the numerator and denominator.

Numerator [tex]= 3\sqrt7 = 3(\sqrt7)[/tex]

Denominator [tex]= 5\sqrt7 = 5(\sqrt7)[/tex]

Step 2: Divide both numerator and numerator by common factor gives:

Ratio = numerator/denominator

[tex]= \sqrt7(3)/\sqrt7(5)[/tex]

Divide both numerator and numerator by [tex]\sqrt7[/tex] gives:

= 3/5.

Therefore, the simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it.

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The answer is:

The domain for the function is all the real numbers,

Domain:(-∞,∞)

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

[tex]f(x)=\frac{1}{x^{2}-5x+25 }[/tex]

Where, the denominator is given by the expression:

[tex]x^{2}-5x+25[/tex]

For the given expression (quadratic equation), we have that:

[tex]a=1\\b=-5\\c=25[/tex]

Calculating the discriminat of the quadratic function, in order to know if the denominator of the function has roots (zeroes) at the real numbers, we have:

[tex]Discriminant=b^{2} -4ac[/tex]

[tex]Discriminant=-5^{2} -4(1)(25)[/tex]

[tex]Discriminant=25 -100=-75[/tex]

Now, as we know, if the discriminant of a quadratic function is less than 0, the quadratic function has no roots in the real numbers.

Therefore, since the denominator (quadratic function) has no roots in the real numbers, the domain for the function will be equal to all the real numbers.

Domain:(-∞,∞)

Hence, the answer is the third option, the domain for the function is all the real numbers,

Domain:(-∞,∞)

Have a nice day!

Answer:

second choice

third choice

Step-by-step explanation:

righty whighty edg 2020

From the given diagram of triangle DEF:

Triangle DEF is shown in the image attached below/.

Triangle DEF has the following sides:

The triangle also shows that:

Also,

In summary, from the given diagram of triangle DEF:

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So, 1 cube equals 1/4 unit.

4 cubes will equal 1 whole unit.

If the volume of the rectangular prism is 3 cubic units, all you have to do is multiply.

4*3=12

So it would take a total of 12 cubes to fill the prism.

Hope this helps.

Answer:

x-6

Step-by-step explanation:

Let the number be x

Then the algebraic expression  “six less than a number” can be represented as:

x - 6

So, "six less than a number” can be represented as: x - 6

Answer:

Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.

Step-by-step explanation:

Mass of clown fish = 2.5 X 10 ^-1 kg

Mass of pilot whale = 3 X 10 ^ 3 kg

Find the ratio of Mass of pilot whale to the ratio of Mass of clown fish

Mass of pilot whale : Mass of clown fish

3 X 10 ^ 3 : 2.5 X 10 ^-1

It can be written as

3 X 10 ^ 3 / 2.5 X 10 ^-1

1.2 x 10^4

So, Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.