A very high powered microscope would allow us to see the smallest unit of a bar of gold as shown below.

What is the smallest unit found in the bar of gold?

cell

O atom

element

O nucleus

If the explicit formula is in the form of Formula 2, we can consider p to be (35 + √(1213))^n and c to be (35 - √(1213))^n.

To find the explicit formula for the given recurrence relation, we need to solve the characteristic equation associated with the recurrence relation and determine the form of the explicit formula.

The given recurrence relation is:

an = 70n-1 - 12an-2

To find the characteristic equation, we assume the solution of the form an = r^n and substitute it into the recurrence relation:

r^n = 70(r^(n-1)) - 12(r^(n-2))

Dividing both sides by r^(n-2), we get:

r^2 = 70r - 12

This is the characteristic equation. We can rearrange it to:

r^2 - 70r + 12 = 0

To solve this quadratic equation, we can use the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = -70, and c = 12. Plugging in these values, we get:

r = (70 ± √(70^2 - 4*1*12)) / (2*1)

r = (70 ± √(4900 - 48)) / 2

r = (70 ± √(4852)) / 2

r = (70 ± √(4 * 1213)) / 2

r = (70 ± 2√(1213)) / 2

r = 35 ± √(1213)

So the roots of the characteristic equation are r1 = 35 + √(1213) and r2 = 35 - √(1213).

Now, we consider the explicit formula in the form of Formula 2: an = px^n + cy^n, where T and y are the roots of the characteristic equation.

Since the roots of the characteristic equation are r1 = 35 + √(1213) and r2 = 35 - √(1213), we have:

an = p(35 + √(1213))^n + c(35 - √(1213))^n

Note that the coefficients p and c depend on the initial conditions a1 = 17 and az = 59. We would need to use these initial conditions to determine the values of p and c.

Therefore, if the explicit formula is in the form of Formula 2, we can consider p to be (35 + √(1213))^n and c to be (35 - √(1213))^n.

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Answer:

Step-by-step explanation:

The chosen topic is not meant for use with this type of problem. Try the examples below.

|−4|+|−4|3+i+(3−2i)(y−3)(y+3)

Option B is correct. The relationship is: H0 = 0 there is no linear association between calories and sodium content H1  ≠ 0 there is a linear association between colones and sodium content

The test statistic is 3.75

The test statistics can be gotten from the data that we already have available in this question

The coefficient is given as 2.235

The Standard error of the coefficient is given as 0.596

The formula used is given as

Such that t = coefficient /  Standard error

where the coefficient = 2.235

The standard error = 0.596

Then when we apply the formula we have

2.235 / 0.596

t statistic = 3.75

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The number of sides of the polygon is denoted by n

.Then we have the relation

On solving this,

Then,

Hence the number of sides is 20.

Answer:

(-14,36)

Step-by-step explanation:

We know the midpoint, so we can substitute for that. The formula for midpoint is (x1+x2)/2 ; (y1+y2)/2 =(Midpoint). We can make the equation:

(-2+x)/2=-8      and      (-20+x)/2=8

To get rid of the division, multiply both sides by 2, and you get:

-2+x=-16          and       -20+x=16

Isolate x:

-2+x=-16           and           -20+x=16

+2      +2                            +20     +20

__      __                            ___      ___

0         -14                             0          36

So, you end up with (-14,36)

Hope this helped!

Answer:

x < -1 3/7

Step-by-step explanation:

-7x > 10

Divide each side by -7, remembering to flip the inequality

-7x/-7 < 10/-7

x < -10/7

x < -1 3/7

The value of x for the given inequality -7x > 10 can be simplified as a set of all values of x such that x < -1.4286.

Given an inequality:

-7x > 10

It is required to find the value of x.

In order to find the value of x, it is required to process the inequality in such a way that the variable x lies on one side isolated and constants on the other side of the inequality.

Consider:

-7x > 10

Divide both sides by 7.

\(-\text{x} > \frac{10}{7}\)

\(-\text{x} > 1.4286\)

Divide both sides by -1. The inequality sign changes since the division is by a negative number.

x < -1.4286

Hence the solution is x < -1.4286.

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Answer:

12.9

Step-by-step explanation:

cos 72 = 4/x

x = 4/cos72

x = 12.9

we need to standardize the value of 24 months using the given mean and standard deviation there is a 22.66% chance that a randomly selected customer will require a replacement within 24 months due to the battery no longer working.

Z = (x - μ) / σ
where x is the value we want to standardize (24 months), μ is the mean (30 months), and σ is the standard deviation (8 months).
Z = (24 - 30) / 8 = -0.75
Now we can use a standard normal distribution table or calculator to find the probability of a Z-score less than -0.75.
P(Z < -0.75) = 0.2266
Therefore, the probability that a customer who purchases the warranty will require a replacement within 24 months from the date of purchase because the battery no longer works is approximately 0.2266 or 22.66%.
To answer your question, we will use the normal distribution, mean, and standard deviation. The mean life span of the new battery is 30 months, with a standard deviation of 8 months. You want to know the probability that a customer will require a replacement within 24 months.
First, we need to find the z-score, which is the number of standard deviations away from the mean a given value is. The formula for the z-score is:
z = (X - μ) / σ
where X is the value we're interested in (24 months), μ is the mean (30 months), and σ is the standard deviation (8 months).
z = (24 - 30) / 8
z = -6 / 8
z = -0.75
Now we need to find the probability associated with this z-score. You can use a z-table or an online calculator to find the probability. For a z-score of -0.75, the probability is approximately 0.2266.

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Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

Answer:

It's......................

Hope this will help you.

Given matrices A and B as A = -7 -7 2 0 BA = [] and B = 1 2. To find the matrix BA, we need to ensure that the number of columns in matrix A is equal to the number of rows in matrix B. In this case, the number of columns in A is 2 and the number of rows in B is also 2. Hence, matrix BA is defined. Let's find BA as follows: $$
BA = \begin{b matrix}

\(-7 & -7\\2 & 0\(-7)(1) + (-7)(2)\\(2)(1) + (0)(2)\\\)

\end{b matrix} = \begin{b matrix}
\(-21\\2\\\end{bmatrix}\)rix BA is [-21, 2].

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Answer:

The word sentence you are looking for is:

n + 4.1 ≤ 7

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

1. 11/2

2. -1/2

3. 17/20

Step-by-step explanation:

Step-by-step explanation:

Factor, in mathmatechis, a number or algebric expression that divides another number or expression evenly.

For example, 3 and 6 are factors of 12 because 12 divided by 3 equals 4 exactly and 12 divided by 6 equals 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Answer:

y = 2x + 3

Step-by-step explanation:

First things first we have to find the slope. To do so you simply choose two of the ordered pairs and use the formula:

y2 - y1 / x2 - x1

I will use (0, 3) and (2, 7).

7 - 3 / 2 - 0

4 / 2

2

let’s double check by using the other set of ordered pairs.

(-1, 1) and (5,13)

13-1 / 5 + 1

12 / 6

2

Our slope is 2!

Next we will use the point-slope formula:

y - y1 = m (x - x1)

we will do this with one of the ordered pairs, since they all lie on the same line the answer will be the same each time.

I will use (2, 7).

y - 7 = 2(x - 2)

distribute:

y - 7 = 2x - 4

add 7 to both sides:

y = 2x + 3

Just to be sure that i didn’t make any mistakes i will double check by using another ordered pair.

I will use (-1, 1)

y - 1 = 2 (x + 1)

distribute:

y - 1 = 2x + 2

add 1 to both sides

y =2x + 3

There we have it! The answer is:

y = 2x+ 3

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

See below.

Step-by-step explanation:

Triangle ADC is congruent to triangle ADB because

____A. reflecting____

B. rotating

C. translating

continuing sentence:

triangle ADC

A. Across line segment AD

____B. to the right____

C. 90 degrees clockwise

D. across line segment AD

maps it onto triangle ADB.

Triangles ADC and ADB are congruent based on the SAS congruence theorem, and by reflection, one triangle can be carried onto the other triangle.

What is angle of reflection ?

The angle of reflection simply means the angle that's formed between the normal ray and the reflected ray. It's the line that's perpendicular to the resulting surface at the point of incidence.

Recall:

The diagram shows the congruence theorem that can prove that two triangles are congruent.

Two triangles that are reflection of each other can also be said to be congruent triangles.

Thus:

The image of both triangles given shows that they have two pairs of angles and an included side, which means that the SAS Congruence Theorem can be used to prove their congruency. Therefore,

Therefore, the transformation that can justify that triangles ABC and ADC are reflection across line segment AD maps it onto triangle ADB.

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The area of trapezoid $ABCD$ is $\frac{1}{2}h(a+b)$, where $h$ is the height of the trapezoid and $a$ and $b$ are the lengths of the bases $\overline{AB}$ and $\overline{CD}$, respectively.

To find the area of trapezoid $ABCD$, we need to know the lengths of the bases and the height. Let's assume that the lengths of the bases are $a$ and $b$, where $a > b$. The extensions of the legs of the trapezoid intersect at point $P$.

To calculate the area of the trapezoid, we need to find the height. Let's consider triangle $APB$ formed by the extension of the leg $\overline{AB}$, the extension of the leg $\overline{CD}$, and the line segment $\overline{AP}$. Since $\overline{AB}$ and $\overline{CD}$ are parallel, triangle $APB$ is similar to triangle $CPD$.

Using the similarity of triangles, we can set up the following proportion: $\frac{h}{a} = \frac{h+x}{b}$, where $x$ is the length of $\overline{PD}$. Cross-multiplying gives us $bh = ah + ax$. Rearranging the equation, we have $ax = (b-a)h$. Dividing both sides by $a$, we get $x = \frac{b-a}{a}h$.

Now, the height of the trapezoid, $h$, is the sum of the lengths of $\overline{AP}$ and $\overline{PD}$: $h = \overline{AP} + \overline{PD} = x + \frac{b-a}{a}h$. Simplifying the equation, we have $\frac{a}{a}h = x + \frac{b-a}{a}h$, which gives us $\frac{h}{a} = x + \frac{b-a}{a}h$.

Substituting the value of $x$, we have $\frac{h}{a} = \frac{b-a}{a}h + \frac{b-a}{a}h$. Simplifying further, we get $\frac{h}{a} = \frac{2(b-a)}{a}h$. Dividing both sides by $\frac{2(b-a)}{a}$, we find that $h = \frac{a}{2(b-a)}h$.

Finally, we can substitute the value of $h$ in the formula for the area of the trapezoid to find:

$[ABD] = \frac{1}{2}h(a+b) = \frac{1}{2}\left(\frac{a}{2(b-a)}h\right)(a+b) = \frac{a(a+b)}{4(b-a)}$.

The area of trapezoid $ABCD$ with bases $\overline{AB}$ and $\overline{CD}$ is given by $\frac{a(a+b)}{4(b-a)}$, where $a$ and $b$ are the lengths of the bases and $h$ is the height of the trapezoid.

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Answer:

3 cm

Step-by-step explanation:

Find the value of x:

\(5-2x=-4x+9\)

\(-2x+4x=-5+9\)

\(2x=4\)

\(x=4/2\)

\(x=2\)

Find one side of the triangle by adding 2 as the value x:

\(=5-2x\)

\(=5-2(2)\)

\(=5-4\)

\(=1\)

Perimeter of the triangle:

1 × 3 = 3cm

Step-by-step explanation:

the answer is b

Answer: The answer is B, use the distributive property on each side of the equation.

Answer:

x=2

Step-by-step explanation:

-2(1-4x)=3x+8

-2*1 and -2*-4x

-2+8x=3x+8

+2  -3  -3 +2

5x=10

/5.  /5

x=2

Answer:

I believe the answer is d

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

In this case, since \(\sqrt{81}\) can be simplified to 9 and 9 can be written as a fraction (9/1) it is a rational number.

Answer:

B: y = 5x + 30

Step-by-step explanation:

Answer:

$421.74

Step-by-step explanation:

The x-intercept of the linear equation is (7, 0).

Here we have the following linear equation:

y = x - 7

We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.

0 = x - 7

Solving that, we get:

7 = x

Then we conclude that the x-intercept of the linear equation is (7, 0).

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Answer:

The answer is d

Step-by-step explanation:

simplyfied into the simpiliest form possible

Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

The general solution of the given differential equation `2y′ y = 5t²` and using it to determine how solutions behave as t is discussed below:Solving the differential equation:

Separating the variables of the differential equation `2y′ y = 5t²` we get:dy/y = (5/2)t² dtIntegrating both sides, we have:ln|y| = (5/6) t³ + C1

Taking the exponential of both sides, we get:y = Ke^(5t³/6) , where K = ± e^(C1) is a constant of integration.

The general solution of the given differential equation is given by `y = Ke^(5t³/6)` where `K` is a constant of integration.

How solutions behave as `t`:When `t → ∞` (i.e., as t grows large), `e^(5t³/6) → ∞`. So solutions of the given differential equation `y′ y = 5t²` grow exponentially as `t → ∞`.

When `t → -∞` (i.e., as t gets very negative), `e^(5t³/6) → 0`. So solutions of the given differential equation `y′ y = 5t²` approach `y = 0` as `t → -∞`.

Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

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Answer:

9+(c*2)

im pretty sure this is correct, sorry for misreading it at first <3