What is the surface area of the square pyramid?
(Figure is not drawn to scale.)

Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

Given that in quadrilateral ABCD, side AD is equal to side BC (AD = BC) and side AD is parallel to side BC (AD || BC), we can use these properties to prove that ABCD is a parallelogram.

Here is a step-by-step proof:

1. Definition of a parallelogram: A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.

2. Given: AD = BC (opposite sides are equal) and AD || BC (opposite sides are parallel).

3. To Prove: AB || CD and AB = CD (the other pair of opposite sides are also parallel and equal).

4. Proof:

   - Since AD = BC and AD || BC, we have one pair of opposite sides that are equal and parallel.

   - In a quadrilateral, if one pair of opposite sides is equal and parallel, the quadrilateral is a parallelogram (This is a theorem in Euclidean geometry).

   - Therefore, AB must be parallel to CD (AB || CD) because the opposite sides of a parallelogram are parallel by definition.

   - Also, in a parallelogram, opposite sides are equal (another property of parallelograms), so we can conclude that AB = CD.

5. **Conclusion**: Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

This logical sequence uses the properties of parallelograms and the given information to prove that ABCD must be a parallelogram.

Answer:

C) 13.75 dollars per month

Step-by-step explanation:

i took the test and got it right

Answer:

Parallel: [tex]m = 0[/tex] (Horizontal), Perpendicular: [tex]m = -\frac{1}{0}[/tex] (Vertical)

Step-by-step explanation:

The equation y = 1 is an horizontal straight line ([tex]y = 0\cdot x + 1[/tex]). The slope of a line parallel to it is [tex]m = 0[/tex]. The slope of line perpendicular to it is [tex]m = -\frac{1}{0}[/tex], since slope is represented by tangent function, which is undefined at [tex]\theta = \pm 0.5\pi[/tex].

4(x-7)=12=


4x-28=12 

add 28 to both sides

4x=40

x =40/4 = 10

x = 10

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

so

[tex]k=r'/r[/tex]  and [tex]k=h'/h[/tex]

The volume of the original cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

If the cylinder is scaled proportionally by a factor of k

then

the new radius is ------> [tex]r'=kr[/tex]

the new height is ------> [tex]h'=kh[/tex]

The volume of the scaled cylinder is equal to

[tex]V'=\pi r'^{2}h'[/tex]

substitute the values

[tex]V'=\pi (kr)^{2}(kh)[/tex]

[tex]V'=(k^{3})\pi r^{2}h[/tex]

Remember that

[tex]V=\pi r^{2}h[/tex]

so

substitute

[tex]V'=V(k^{3})[/tex]

The volume of the scaled cylinder is equal to the scale factor elevated to the cube multiplied by the volume of the original cylinder

The ladder is 29.9 feet long.

For solving this problem we have to use trigonometric ratio  

We need to use the tangent function:

[tex]tan (\theta) = opposite/adjacent[/tex]

[tex]tan 75 = opposite/8[/tex]

multiply both side by 8 so we will get,

Here, the opposite side is the length of the ladder and angle [tex]\theta =75^0[/tex]

Therefore by using the tan ratio we have,

[tex]8 * tan 75 = opposite[/tex]

[tex]29.8564065 = opposite[/tex]

Therefore, the ladder is 29.9 feet.

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Answer:

The correct answer is:

A) The food cans have a mean shelf life of 14 months.

Just took this quiz and this was the correct answer.

Step-by-step explanation:

Answer:

I'm a few years late, lol, but um the answer is 42 x [tex]10^{-3}[/tex] meters

For all the people who still need the answer.

Step-by-step explanation:

5 x [tex]10^{-11}[/tex] and 8.4 x [tex]10^{8}[/tex]

5 x 8.4 = 42  (multiply like terms)

[tex]10^{-11}[/tex] + [tex]10^{8}[/tex] = [tex]10^{-3}[/tex]  (add the exponents)

42 x [tex]10^{-3}[/tex]

The length in scientific notation is [tex]42\times10^{-7[/tex] meter.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].

Given that, the diameter of a hydrogen atom is about [tex]5\times10^{-15}[/tex] meter. Suppose 8.4×10⁸ hydrogen atoms were arranged side by side in a straight line.

Now, multiply the numbers

[tex]5\times10^{-15}[/tex]×8.4×10⁸

= [tex]42\times10^{-7[/tex] meter

Therefore, the length in scientific notation is [tex]42\times10^{-7[/tex] meter.

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The total number of nickels that can be collected is 17 and this can be determined by forming the inequality.

Given :

A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00.

The inequality can be formed in order to determine the total number of nickels that can be collected.

Let the total number of quarters be 'x' and the total number of nickels be 'y'. Then the inequality that represents the total number of quarters and nickels contained in the collection is at least 42 is given by:

x + y [tex]\geq[/tex] 42  --- (1)

The inequality that represents that the worth of the coins is at most $8 is given by:

0.25x + 0.5y [tex]\leq[/tex] 8   --- (2)

Now, according to the given data there are a total of 25 quarters in the collection, so, the number of nickels contained in the collection is:

x + y [tex]\geq[/tex] 42

25 + y [tex]\geq[/tex] 42

y [tex]\geq[/tex] 17

So, the total number of nickels that can be collected is 17.

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The collection can contain up to 35 nickels, given that it already includes 25 quarters and the total value does not exceed $8.00.

To determine how many nickels can be in the collection, we must first calculate the total value of the 25 quarters. Since each quarter is worth 25 cents, we multiply 25 quarters by 25 cents to get 625 cents, which is $6.25. The maximum value of the entire collection is $8.00. Thus, we subtract $6.25 from $8.00 to find the remaining value that can be occupied by nickels, which is $1.75. Each nickel is worth 5 cents, so we divide $1.75 by 0.05 (5 cents) to find the maximum number of nickels. $1.75 divided by 0.05 equals 35. Therefore, the collection can contain up to 35 nickels.

TRUE IVE GOT IT WRONG  ON MY ASSIGNMENT.

Answer:

True

Step-by-step explanation:

To find the geometric men you have to cross multiply the two given numbers and then find x squared for those numbers. So to find x squared you have to find the square root of the product from the two multiplied numbers.

8/x = x/2

8*2 = 16 = x squared

x= square root of 16 which equals 4

Answer:

Option (3) is correct.

(2,4) belongs to y ≥ 4x - 5

Step-by-step explanation:

Given : the point (2,4)

We have to find the equation of graph to which the point (2,4) belongs.

We will substitute the point in the  each given equation and for which the point satisfies will contain the point.

For 1) y ≥ x + 3

Put x = 2 and y = 4

⇒ 4 ≥ 2 + 3

⇒  4 ≥ 5 (false)

For 2) y ≥ -x + 8

Put x = 2 and y = 4

⇒  4 ≥ -2 + 8

⇒  4 ≥ 6 (false)

For 3) y ≥ 4x - 5

Put x = 2 and y = 4

⇒  4 ≥ 4(2) - 5 = 8 - 5

⇒  4 ≥ 3 (true)

For 4) y ≥ -2x + 9

Put x = 2 and y = 4

⇒  4 ≥ -4 + 9

⇒  4 ≥ 5 (false)

Since, the point (2,4) satisfies only inequality y ≥ 4x - 5.

Thus, (2,4) belongs to y ≥ 4x - 5

Final answer:

To achieve a 15 percent saline solution by mixing a 10 percent solution with a 25 percent solution, we calculate that we need to add 1.5 liters of the 25 percent saline solution to the initial 3 liters of the 10 percent solution.

Explanation:

To solve the problem, we need to calculate how much of a 25 percent saline solution should be added to 3 liters of a 10 percent saline solution to get a 15 percent saline solution. We'll use the concept of the conservation of mass of the solute (NaCl) and set up an equation to find the required volume of the 25 percent solution.

Let V be the volume of the 25 percent solution we need to add. The amount of NaCl in the 10 percent solution is (0.10)(3 L), and the amount of NaCl in the 25 percent solution is (0.25)(V). The resulting solution has a concentration of 15 percent, so the amount of NaCl in the final solution will be (0.15)(3 L + V).

Now we set up our equation based on the mass of NaCl being equal before and after the addition of the 25 percent solution:

(0.10)(3 L) + (0.25)(V) = (0.15)(3 L + V)

Solving this equation:

0.30 + 0.25V = 0.45 + 0.15V

0.25V - 0.15V = 0.45 - 0.30

0.10V = 0.15

V = 0.15 / 0.10

V = 1.5 L

Therefore, 1.5 liters of a 25 percent saline solution must be added to the initial 3 liters of a 10 percent solution to obtain a 15 percent saline solution.

A.

Its correct i got 100% on a test

The two numbers are 80 and 8.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero.

The substitution method can be defined as a way to solve a linear system algebraically. This method works by substituting one y-value with the other.

Let the two numbers be x and y.

According to the question.

x = 10y

And,

x - 10y = 72

Now, We have a linear equation in two variables. So, for finding the values of x and y we solve the above two equations by substitution method.

Substitute the value of x = 10y in x - y = 72

[tex]\implies 10y -y = 72 \\\implies 9y = 72\\\implies y = \frac{72}{9} \\\implies y = 8[/tex]

Therefore,

x = 10 × 8 = 80

Hence, the two numbers are 80 and 8.

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The number series 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46 has a pattern whereby each number doubles the previous number. However, 20 does not follow this pattern, and the correct number should be 32 (being double of 16). Therefore, 20 is the incorrect number in this series.

This question is a query regarding a number series, specifically asking for us to identify any number that does not fit the pattern of the series. The series given is: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46. By examining the series closely, we can observe a clear pattern: each number is doubling the previous number. So, after 2 we have 4 (2x2), then 8 (4x2), then 16 (8x2) and so forth.

However, at the fifth place, we have the number 20, which doesn't follow this pattern. If we were to follow the established pattern, the fifth number should be 32 (16x2), not 20. Therefore, the incorrect number in this series is 20, and the correct series should be 2 - 4 - 8 - 16 - 32 - 22 - 44 - 46.

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The incorrect number in the series is 20, and it should be replaced with 32. The accurate sequence is 2, 4, 8, 16, 32, 64, 128, 256.

Let's examine the sequence: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46.
At a glance, it appears each number is double its preceding number, except for a couple of deviations.

If we look at the pattern,

Here, we expect 32 instead of 20.
Therefore, 20 is the incorrect number in the series. When we continue correctly:

The correct sequence would be,
2 - 4 - 8 - 16 - 32 - 64 - 128 - 256.

So, the number that should be replaced is 20, and it should be 32.