One number is equal to the square of another. find the numbers if both are positive and their sum is 18921892.

Answer: The area of the new drawing is 240 in².

Step-by-step explanation:

Hi, to answer this we have to use ratios:

Since the ratios is 3:1, it means that 3 units are equal to 1: 3/1

So, 720 units will be equal to x : 720/x

3/1 = 720/x

Solving for x:

x = 720/ (3/1)

x = 720/3

x = 240 in²

The area of the new drawing is 240 in².

Feel free to ask for more if needed or if you did not understand something.

The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

[tex]\boxed{T_n = a + (n-1)d}[/tex]

[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]

[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Given:

This problem is about Geometric Sequence. Let's see why.

[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]

T₁ = [tex]\frac{1}{324}[/tex]

T₂ = [tex]\frac{1}{108}[/tex]

T₃ = [tex]\frac{1}{36}[/tex]

T₄ = [tex]\frac{1}{12}[/tex]

[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]

From the above results it can be concluded that this is Geometric Sequence.

The next number will be the fifth term and can be calculated as following.

[tex]T_n = a ~ r^{n-1}[/tex]

[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]

[tex]T_5 = \frac{1}{324} \times 3^4[/tex]

[tex]T_5 = \frac{1}{324} \times 81[/tex]

[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

Answer:

The density of the wood is, 0.64 [tex]g/cm^3[/tex]

Step-by-step explanation:

Using the density formula:

[tex]\text{density} = \frac{\text{mass}}{\text{Volume}}[/tex]         .....[1]

As per the statement:

If the volume of a cube of wood is 15.625 cm3 and its mass is 10.00 grams.

⇒Volume = 15.625 cubic cm and mass = 10 gram

Substitute the given values in [1] we have;

[tex]\text{density} = \frac{10}{15.625}[/tex]

Simplify:

density = 0.64 [tex]g/cm^3[/tex]

Therefore, the density of the wood is, 0.64 [tex]g/cm^3[/tex]

Note main rules:

[tex]1.\quad (a\cdot b)^n=a^n\cdot b^n,\\ \\2.\quad a^m\cdot a^n=a^{m+n},\\ \\3.\quad (a^m)^n=a^{mn}.[/tex]

1. Consider expression [tex](4xy^2)^3(xy)^5.[/tex] Using previous rules:

2. Consider expression [tex](2t^{-3})^3(0.4r)^2.[/tex]  Using previous rules:

Answer:

For the given case the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°. The correct option is (1).

The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.

The given problem can be solved as follows,

(4) The pair of angles can be named as below,

(1) The angles ∠1 and ∠6 are called consecutive angles.

(2) The angles ∠2 and ∠6 are called corresponding angles.

(3) The angles ∠3 and ∠5 are called consecutive interior angles.

(4)  The angles ∠4 and ∠5 are called alternate interior angles.

(5) The measure of ∠8 is given as below,

Since ∠4 and ∠8 are corresponding angles.

∠4 = ∠8 = 105°.

Hence, the names of the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°.

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△ABC has interior angles with measures x°, 100°, and 70°.

By using angle sum property, which states that the sum of measures of all three angles is 180 degrees.

[tex] x^{\circ}+100^{\circ}+70^{\circ}=180^{\circ} [/tex]

[tex] x^{\circ}=10^{\circ} [/tex]

Now, △DEF has interior angles with measures y°, 70°, and 20°.

By using angle sum property,

[tex] y^{\circ}+70^{\circ}+20^{\circ}=180^{\circ} [/tex]

[tex] y^{\circ}=90^{\circ} [/tex]

Now, we can say that,

"The two triangles are not similar because x≠y"

As one angle of measure 70 degree is common in both the triangles.

If 'x' would be equal to 'y' , then we could say that the triangles are similar by AA criteria.

Therefore, the two triangles are not similar because x is not equal to y.

Answer:

a

Step-by-step explanation:

Your answer should  be d

The equation of line is, y= -2x-9.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

slope= -2

points= (-5, 1)

Now, using slope intercept form

y= mx+ b

1 = (-2)((-5) + b

1= 10 + b

b= -9

Thus, the equation of line

y= mx + b

y= -2x- 9

Hence, the equation of line is, y= -2x-9.

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Final answer:

A recursive definition for the set of odd positive integers starts with a base case of 1 and uses a recursive step where each subsequent odd integer is obtained by adding 2 to the current odd integer.

Explanation:

To write a recursive definition for the set of odd positive integers, you can define a base case and a recursive step. The base case is the smallest odd positive integer, which is 1. The recursive step will then generate the next odd integer by adding 2 to the current odd integer. Here's how you can express it:

Base case: Let O1 = 1, which establishes that 1 is the first odd positive integer.

Recursive step: For every odd positive integer On, there exists an On+1 = On + 2. This means that if you have an odd positive integer, the next one in the set can be found by adding 2 to the current one.

This definition ensures that every number generated by the recursive step will be odd since adding 2 to an odd number always results in another odd number, and starting from 1, guarantees that all numbers will be positive.

The equation that could be used to find the slope of line AB is m = p/q.

Two triangles are said to be similar if they have congruent corresponding angles and their corresponding sides are in equal proportion.

Given that, is a graph showing two similar triangles, we need find the equation of the slope of the line AB.

So,

The slope = rise / run = Δy / Δx

Here, Δy / Δx = m/n

Since, the triangles are similar so, m/n = p/q

Therefore,

Δy / Δx = p/q

Hence, the equation that could be used to find the slope of line AB is m = p/q.

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It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.

To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:

Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.

To find the minimum number of years (t), we solve for t:

[tex]800 < 600(1 + 0.025)^t[/tex]

Solving for t gives us: t > ln(800/600) / ln(1.025).

Using a calculator, we find that t > 11.89.

Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.

Answer:

The correct options are A, C and D.

Step-by-step explanation:

The quadratic parent function is

[tex]f(x)=x^2[/tex]

The properties of quadratic parent function are:

1. It has one intercept, i.e, x- and y-intercept are at origin.

2. It has a vertex at (0, 0).

3. It is U-shaped.

4. Each image y has two preimage, except 0.

5. It opens up.

From the given option one the option B is incorrect because the quadratic parent function opens upward.

Therefore the correct options are A, C and D.

Answer:

∠C = 107°

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.

So, ABCD is cyclic quadrilateral.

∠A = 2x + 3

∠B = 2x - 4

∠D = 3x + 9

Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.

⇒ ∠B + ∠D = 180

⇒ 2x - 4 + 3x + 9 = 180

⇒ 5x = 175

⇒ x = 35

Now, ∠A = 73

Also, ∠A + ∠C = 180

⇒ ∠C = 180 - 73

⇒ ∠C = 107°

Answer:

(A) Use stratified random sampling

Step-by-step explanation:

Since, the population include all the citizens of that country so it is quite large data and working on this population is quite time taken and costly. Thus, Sample must be taken and it must be taken by appropriate sampling method.

 Here Stratified Sampling is used because by this sampling method peoples of every state, every cities, every village can be taken without much expense and in less time.

Further,

If the samples from the population are chosen randomly, where each and every unit has an equal chance of selection in a sample. This type of sampling is called Simple Random Sampling.

If the observers collect the sample as his\her convenience, then this type of sampling method is called Convenience Sampling.

In Cluster Sampling the population is distributed into a distinct group (clusters) and one or more groups (clusters) are chosen as a sample.

In Systematic Sampling the selection of sample is taken by some criteria . Like he\she is taken every 7th unit as a sample from the population.

Final answer:

The two numbers that multiply to -90 and add up to -8 are -10 and 2. This is found by factoring -90 and checking different factor pairs until the correct one is identified.

Explanation:

The student is asking for two numbers that when multiplied result in -90, and when added result in -8. This is a factorization problem that can be addressed by setting up a system of equations or by using intuition to guess and check pairs of factors. We are looking for a pair of numbers that have one positive and one negative number, because the product is negative (-90), and the sum is also negative (-8).

By listing out the factors of 90, we can test which pair of numbers, with one being negative, would multiply to -90 and add up to -8. After some trial and error, we find the pair that works are -10 and 9. -10 × 9 = -90 and -10 + 9 = -1. However, since the sum needs to be -8, then the correct pair is -10 and 2, because -10 × 2 = -20 and -10 + 2 = -8.