Elyis saving for a vacation. He can put $150 a month into a savings account. He already has $200 in the account and needs a total of $1,550. Write an equation that can be used to determine how many months Ely will need to save money to reach his goal. In one sentence, describe what the variable means in your equation.

The expression for  a and b of AM, fully simplified, is:

AM = x/2 = √(64a² + 116b² - 64ab)/2

The perimeter of an equilateral triangle is the sum of its three sides. P = 3a is the basic formula for calculating the perimeter of an equilateral triangle, where "a" means one side of the triangle. The sum becomes a + a + a = 3a, because all three sides of an equilateral triangle are equal. Height = √3a/ 2.  Since M is the midpoint of AC, we have:

To find AM, we can use the midpoint formula, which states that the coordinates of the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) are:

M = ((x1 + x2)/2, (y1 + y2)/2)

In this case, we know that M is the midpoint of AC, so we can use the coordinates of A and C to find the coordinates of M. Let's assume that A has coordinates (0, 0) and C has coordinates (x, 0), where x is the length of AC. Then, we can find the coordinates of M as follows:

M = ((0 + x)/2, (0 + 0)/2) = (x/2, 0)

Now, we can use the distance formula to find the length of AM. The distance formula states that the distance between two points with coordinates (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, we want to find the length of AM, so we can use the coordinates of A and M to find the distance between them. Using the coordinates we found for A and M, we get:

d = √((x/2 - 0)² + (0 - 0)²)

Simplifying this expression, we get:

d = √(x²/4) = x/2

Therefore, the length of AM is x/2. To find x, we can use the fact that BC has length 10b and that the triangle ABC is a right triangle (since AC is the hypotenuse). Using the Pythagorean theorem, we can write:

AC² = AB² + BC²

Substituting the given values, we get:

x²= (8a - 4b)² + (10b)²

Simplifying, we get:

x² = 64a² - 64ab + 16b² + 100b²

x² = 64a² + 116b² - 64ab

Taking the square root of both sides, we get:

x = √(64a² + 116b² - 64ab)

Therefore, the length of AM is:

AM = x/2 = √(64a² + 116b² - 64ab)/2

This is the fully simplified expression for AM in terms of a and b

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If a is a non-zero, real number and equation a(x − 3)² − b = c then x = 3 ± √b+c/a and  the condition on c that restricts the solutions for x to real numbers is c ≥ -5.

To prove that x = 3 ± √(b+c)/a, let's start with the given equation: a(x - 3)² - b = c.

Add b to both sides of the equation to isolate the quadratic term:

a(x - 3)² = c + b.

Divide both sides by 'a' to obtain the quadratic term by itself:

(x - 3)² = (c + b)/a.

Take the square root of both sides to solve for x:

x - 3 = ±√(c + b)/a.

Add 3 to both sides to isolate x:

x = 3 ± √(c + b)/a.

Therefore, we have proven that x = 3 ± √(b+c)/a.

Now, let's consider the case where a = 2 and b = 5.

Substituting these values into the equation x = 3 ± √(b+c)/a, we have:

x = 3 ± √(5 + c)/2.

For the solutions to be real numbers, the expression under the square root (√(5 + c)) must not be negative. In other words, (5 + c) ≥ 0.

Therefore, the condition on c that restricts the solutions for x to real numbers is c ≥ -5.

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Answer:

3y

Step-by-step explanation:

The volume of the prism will be reduced to 1/512 of its original size

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. If the dimensions of a prism are multiplied by 1/8, then the new dimensions are 1/8 of the original dimensions. Therefore, the new base area is 1/64 of the original base area, and the new height is 1/8 of the original height.

Substituting these values into the formula for the volume of a prism, we get:

V' = (1/64)Bh(1/8)

Simplifying, we get:

V' = (1/512)Bh

Therefore, the new volume of the prism is 1/512 of the original volume of the prism.

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Answer:

The quadratic equation that represents this problem is

4x² + 56x - 165 = 0

Step-by-step explanation:

The dimensions of the picture are 16 length and 12 width both in inches

The area of the picture without frame = 16 x 12 = 192 square inches

Let the frame have a width of x inches. The frame surrounds the picture on both sides of the length and both sides of the breadth

Then the length with the frame = x + 16 + x = 2x + 16  inches

The width of the frame = x + 12 + x = 2x + 12 inches

The area of the painting with the frame
= (2x + 16)(2x + 12)

Using the FOILmethod to multiply these two expressions we get
(2x + 16)(2x + 12) = (2x)(2x) + 2x(12) + 16(2x) + 16 x 12

= 4x² + 24x + 32x + 192

= 4x² + 56x + 192

The area of the frame by itself is the area with frame - area of picture alone

Area of frame = 4x² + 56x + 192 - 192

=>  4x² + 56x

We are given the area of frame is 165 square inches
Hence we get
4x² + 56x = 165

To represent as a quadratic equation move 156 from the right side to the left side to get 0 on the right side

4x² + 56x - 165= 0

ANSWER

Solving a system of equations we can see that she has 6 $50 bills and 5 $100 bills.

Let's define the variables.

x = number of $50 bills.

y = number of $100 bills.

We know that there are 11 in total, and the value in total iis $800, then we can write the system of equations:

x + y = 11

x*50 + y*100 = 800

Let's isolate x in the first equation:

x = 11 - y

Replace that in the second one:

(11 - y)*50 + y*100 = 800

550 - y*50 + y*100 = 800

550 + y*50 = 800

y*50 = 800 - 550

y*50 = 250

y = 250/50 = 5

And then:

x = 11 - y = 11 - 5 = 6

These are the numbers.

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Answer:

Side = 2/5 cm

Step-by-step explanation:

Area of square = side²

(4/25) cm² = side²

√((4/25)cm²) = √(side²)

√(4cm²) / √(25cm²) = side

(2 / 5) cm = side

side = 2/5 cm

The first four terms of the sequence are 1, 2, 3, and 4.

An ordered list of numbers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. Every number in the sequence is referred to as a term, and its location in the sequence is referred to as its index or subscript. The total of the terms in a sequence, on the other hand, makes up a series. In other words, a series is created by adding up each phrase in a sequence. In other terms, a series is a single number that represents the total of a sequence of numbers, whereas a sequence is a list of numbers.

The given sequence is represented by the pattern:

an = n​

Substituting values of n starting from 1 we have:

a1 = 1

a2 = 2

a3 = 3

a4 = 4

Hence, the first four terms of the sequence are 1, 2, 3, and 4.

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a. 5/36

count how many sets add up to 6 and then put that number over the total number of sets

So there are 5 sets that add to 6 and 36 total sets so the answer is 5/36

Hope this helps!

The triangles ΔABC and ΔDEF are similar triangles and DE = 1.52

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

And , they are similar triangles

Now , the measure of sides of the triangle ABC are

AB = 11

BC = 7.9

AC = 7.6

And , the measure of side ED = 2.2

Now , corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their

So , AB / DE = k

k = 11 / 2.2 = 5

So , the measure of length of side DF = AC / ( 5 )

DF = 7.6 / 5

DF = 1.52

Hence , the measure of length DF of triangle is 1.52

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The height of the tree was 4.8 m after 2 years its height increased by 12.5 percent then 5.1m is the  height after 1 year if its height is increased with the same ratio.

Given that the height of the tree was 4.8 m

After 2 years the height increased by 12.5 %

Let us find the 12.5% of the tree height

12.5% of 4.8

12.5/100×4.8

0.125×4.8

0.6m

In two years the height is increased by 0.6m

In one year 0.3m is increased.

Now the total height of tree after one years is 4.8+0.3 which is 5.1 m

Hence, the height of the tree was 4.8 m after 2 years its height increased by 12.5 percent then 5.1m is the  height after 1 year if its height is increased with the same ratio.

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The height of the tree was 4.8 m after 2 years its height increased by 12.5 percent. What is its height after 1 year if its height is increased with the same ratio

Answer:

The surface area of the square pyramid is approximately 864.2 square centimeters.

Step-by-step explanation:

To solve for the surface area of a square pyramid, you need to find the area of the base and the area of each of the four triangular faces.

The area of the base is simply the square of the length of one side. So, for a base with edge lengths of 15 centimeters, the area of the base is:

15^2 = 225 square centimeters.

To find the area of each of the four triangular faces, you need to use the formula:

(area of triangle) = 1/2 x (base of triangle) x (height of triangle)

For a square pyramid, the height of each triangular face is equal to the slant height of the pyramid, which can be found using the Pythagorean theorem:

(hypotenuse)^2 = (height)^2 + (1/2 x base)^2

In this case, the height is given as 20 centimeters and the base is half of the base edge of the pyramid, or 7.5 centimeters. So, the slant height is:

hypotenuse = sqrt(20^2 + 7.5^2) = 21.3 centimeters

Now you can use this slant height to find the area of each triangular face:

(area of triangle) = 1/2 x (base of triangle) x (height of triangle)

= 1/2 x (15) x (21.3)

= 159.8 square centimeters

So, the total surface area of the square pyramid is:

225 (area of base) + 4 x 159.8 (area of each triangular face)

= 225 + 639.2

= 864.2 square centimeters.

Therefore, the surface area of the square pyramid is approximately 864.2 square centimeters.

To find the limit of (x + x²)/(6 − 5x²) as x approaches infinity, we can first simplify the expression and then apply l'Hospital's Rule if necessary.

1. Factor x out of the numerator: x(1 + x)/(6 - 5x²).

2. Divide both the numerator and the denominator by x²: lim (x→∞) (1 + x)/(6/x² - 5x²/x²) lim (x→∞) (1/x + 1)/(6/x² - 5)

3. Now apply the limit: lim (x→∞) (1/x) = 0 and lim (x→∞) (6/x²) = 0.

So, we have: lim (x→∞) (0 + 1)/(0 - 5) = 1/(-5)

The limit of the function as x approaches infinity is -1/5.

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We can begin our task by relocating the tinted triangle along a vector perpendicular to one of its sides, constructing a second copy adjacent to the primary figure. We may replicate the translation process to produce a third and fourth duplicate so that four facets mirroring each other occupy the square design.

Once we have four comparable figures in a square style, reflections can be employed to generate the left-out triangles which culminate the conception. In order to accomplish this, each of the constructed four can be mirrored across a diagonal spanning the square. This will fabricate four additional replicas, thus fully forming the square.

An alternate way to create the remaining four shapes is through rotations. By spinning each of the first four triangles 90 degrees around the center of the form, four further copies are created, fulfilling the completion of the square design.

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The routing algorithm would then iteratively update these distances based on new information from the network until convergence is reached.

I am an AI language model and I need more information about the context and specific details regarding the algorithm and network topology in order to provide an accurate answer.
When an algorithm converges, it means that it has reached a stable state and no more changes are expected. In this context, it usually refers to a routing algorithm that has calculated the shortest paths between routers. The distance vectors from router 'X' to all routers would be the final set of shortest distances to each of the other routers in the network. These can be represented as UVWXy, where U, V, W, and y are the distances from router 'X' to routers U, V, W, and y, respectively.
For the initial distance vectors for router 'W', we would consider the direct connections between router 'W' and its neighboring routers at the beginning of the algorithm. The initial distance vectors would be the distances from router 'W' to its neighbors before any routing updates occur. The routing algorithm would then iteratively update these distances based on new information from the network until convergence is reached.
Please provide more details about the network, and I can give you a more specific answer.

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To determine the distance vectors from router 'X' to all routers when the algorithm converges, I would need more information about the specific routing algorithm being used.

Different routing algorithms, such as Distance Vector or Link State, have different convergence behaviors and update mechanisms. If you can provide the details of the routing algorithm, I can help you determine the distance vectors.

Regarding the initial distance vectors for router 'W', again, it depends on the specific network configuration and the routing algorithm being used. In most routing algorithms, the initial distance vectors are typically set to some predefined values. It could be a cost of infinity for unreachable destinations or a cost based on the direct links to neighboring routers. Without more information about the network topology and routing algorithm, I cannot provide the specific initial distance vectors for router 'W'.

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The fourth roots of cos20+sin20 are 0.9421925652434.(cos5 + isin5).

This theorem states that if z is a complex number and n is any positive integer, then zⁿ = (rⁿ)(cosnθ + isinnθ), where r is the modulus of z and θ is the argument of z.

The fourth roots of cos20+sin20 can be found using De Moivre's Theorem.

In this case, z = cos20+sin20 and n = 4.

First, we need to determine the modulus of z. This can be found using the Pythagorean Theorem, which states that r² = (cos20)² + (sin20)². Plugging in the values we get:

r² = (cos20)² + (sin20)²

= (0.93969262)²+ (0.34202014)²

= 0.88772683.

Taking the square root of both sides gives us

r = √0.88772683

= 0.9421925652434.

Now that we have the modulus, we can use De Moivre's Theorem to find the fourth roots of z.

We have z⁴ = (r⁴)(cos4θ + isin4θ).

Plugging in the values we get:

(0.9421925652434)⁴ = (r⁴)(cos4(20) + isin4(20)).

Taking the fourth root of both sides gives us r = 9421925652434.

Finally, we can solve for the fourth roots of z.

We have [tex]z^{^(1/4)}[/tex] = (0.9421925652434)(cos(20/4) + isin(20/4)).

Plugging in the values we get:  [tex]z^{^(1/4)}[/tex] == (0.94409403)(cos5 + isin5). Therefore, the fourth roots of cos20+sin20 are 0.9421925652434.(cos5 + isin5).

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The probability they are both seniors is 0.194

There are a total of 22 possible options to select.

The probability of ranomly selectinga senior is equal to the quotient between the number of seniors and the total number of options, so for the first selection the probability is:

P = 10/22

For the second selection there are 9 seniors and 21 options, so the probability here is:

Q = 9/21

The joint probability is the product of these two, so we get:

p = 10/22*9/21 = 0.194

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Answer:

Step-by-step explanation:

It would take Max and Jan 30 minutes to mow the lawn together.

It will take Max 45 minutes to mow the lawn alone, and it will take Jan twice as long, so it will take her 90 minutes to mow the same lawn alone. Working together, we can use the equation 1/45 + 1/90 = 1/t to solve for t, where t is the number of minutes it would take to mow the lawn together.

First, we need to simplify the equation:

1/45 + 1/90 = 1/t

2/90 + 1/90 = 1/t

3/90 = 1/t

1/30 = 1/t

Now we can solve for t by cross-multiplying:

1/30 = 1/t

t = 30

So, it will take Max and Jan 30 minutes to mow the lawn together.
To find how long it would take Max and Jan to mow the lawn together, we can solve the equation 1/45 + 1/90 = 1/t for t.

First, find a common denominator for the fractions, which in this case is 90. Then, rewrite the equation as: (2/90) + (1/90) = 1/t.

Next, add the fractions on the left side: 3/90 = 1/t.

Now, to solve for t, take the reciprocal of both sides: t = 90/3.

Finally, simplify: t = 30.

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The amount of compound interest that was earned more than simple interest after 45 years is about 485 dollars

From the question, we are to determine how much more compound interest than simple interest is earned after 45 years

In order determine how much more compound interest is earned than simple interest after 45 years, we will determine the simple interest earned in any year after the 45th year. We will also determine the corresponding compound interest for the particular year.

Finally, we will determine the difference of the interests.

From the graph,

The interests around the 46th year are:

Compound interest = 1200 dollars

Simple interest = 715 dollars

Thus,

Difference = 1200 dollars - 715 dollars

Difference = 485 dollars

Hence,

The amount of compound interest that was earned more than simple interest is about 485 dollars

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The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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Answer:

$6,578

Step-by-step explanation:

((5500 * 0.028) * 7) + 5500, where parentheses is the interest rate

(5500 * 0.028) * 7

154 * 7

1078

1078 + 5500

6578

Brainliest? ;)

It helps me a lot!

The first transformation for this composition is a reflection across line n followed by a 270° rotation about point P.

When we convert a point across a line y = x then x-coordinate and y-coordinate change.

Also when we reflect a point across the line y = -x then signs exist changed and both coordinates change places.

When transformation maps X"Y" Z" .Then the first transformation for this composition exists, and the second exists at 90° rotation about point X'.

Therefore, the correct answer is option B. first transformation across the line n.

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Tanya has captured many purple-footed bog frogs. She weighs each one and then counts the number of yellow spots on its back. This trend line is a A. strong fit for these data.

A trend line's ability to accurately predict one variable based on the values of another is directly correlated with how closely it follows the overall pattern of the data points. Essentially, a well-fitted trend line indicates a high degree of correlation between the variables being analyzed.

Looking at the trend line for Tanya's data, we can see that the trend line is a strong fit because the points around it are very close to it which means it can predict values better.

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If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased.

When there are omitted variables that are correlated with the variable of interest (in this case, years of schooling), the OLS estimator becomes biased. This means that the estimate of the effect of years of schooling on income is no longer accurate or unbiased. Therefore, researcher B's regression results may not provide a true estimate of the effect of education on wages due to the potential bias caused by the omitted variables.

Your answer: If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased. This is because the unobserved factors like motivation and work_ethic would be correlated with the variable of interest, educi, which can lead to biased estimates in the regression analysis.

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The notation for the given compositions of transformations is R180∘[tex]R_x[/tex]=2.

The composition of a reflection across the line x=2, followed by a rotation of 180 degrees about the origin, can be represented using function notation as follows:

                                        R180∘[tex]R_x[/tex]=2

Where:

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Answer:

Step-by-step explanation:[tex]2\frac{4}{3}.a\frac{4}{3}[/tex]

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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