Write each equation in slope-intercept form. Under line the slope and circle the y-intercept in each equation.


5x+3y=30

This is one RSM


The y-intercept is (_,_)

The total amount in the bank account after 7 years will be $1490

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. The principal amount in simple interest is constant.

The formula for simple interest = (P*R*T)/100

where P = principal amount

R = rate of interest

T = time in years

As per the question,

P = 1000

R = 7%

T = 7 Years

Simple interest will be = (1000*7*7)/100 = $490

The amount of money in the savings account at the end of 7 years will be $1000 + $490 = $1490

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Answer:

(-2,9)

Step-by-step explanation:

2-4=-2

7+2=9

The solution is A' ( -2 , 9 )

The translation of the point A ( 2 , 7 ) to left 4 units and up 2 units is given by A' ( -2 , 9 )

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the first point be represented as A

Now , the coordinates of point A = A ( 2 , 7 )

The point A is translate to left by 4 units and up by 2 units

So , the new point be represented as A'

Translation is 4 units left , means there is change in x coordinate by -4

( x - 4 , y ) = A' ( 2 - 4 , y )

( x - 4 , y ) = A' ( -2 , y )

And , Translation is 2 units up , means there is change in y coordinate by 2

( x , y + 2 ) = A' ( -2 , 7 + 2 )

( x , y + 2 ) = A' ( -2 , 9 )

The value of A' = A' ( -2 , 9 )

Hence , the coordinates of translated point is A' ( -2 , 9 )

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Answer:

( x,y)

the 1st Q: A (-4.5,3); B (0,-2.5)

2nd:A(-4.5, -1.5);B(2.5,-4.5)

Answer:

Step-by-step explanation:

y-8

Answer:

y - 8

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

y = x² - w / 2z (D)

Step-by-step explanation:

w = x² - 2yz

w - x² = - 2yz

multiply both sides by -1

-1(w - x²) = -1 (-2yz)

-w + x² = 2yz

x² - w = 2yz

2yz = x² - w

divide both sides by 2z

y = x² - w / 2z

The value of  fog= gof is x² - 5x = 0

Functions are rules or expressions showing the relationship between an independent and dependent variable.

Given the functions:

fog(x) and gof(x) are both known as composite functions

If fog(x) = gof(x)

Then , we have

\(\frac{x - 2}{x -2 + 3} = \frac{x}{x + 3} -2\)

solve the fractions

\(\frac{x-2}{x -1} = \frac{2x - 2x +6}{x+3}\)

\(\frac{x -2}{x -1} = \frac{6}{x + 3}\)

cross multiply

(x -2) ( x+ 3) = 6 ( x -1)

expand the bracket

x²+ 3x - 2x - 6 = 6x - 6

collect like terms

x² - 5x + 0 = 0

x² - 5x = 0

Thus, the value of  fog= gof is x² - 5x = 0

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the average waiting time cannot be determined when all five checkout lanes are being used.

To calculate the average waiting time when all five checkout lanes are being used, we can use queuing theory and the Little's Law formula.

Little's Law states that the average number of customers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time a customer spends in the system (W).

L = λ * W

Given:

Number of checkout lanes (m) = 5

Average checkout time per customer (μ) = 3 minutes (since each clerk takes 3 minutes on average to checkout a customer)

Arrival rate (λ) = 70 customers per hour

First, we need to calculate the arrival rate per lane when all five lanes are being used. Since there are five lanes, the arrival rate per lane will be λ/m:

Arrival rate per lane = λ / m

= 70 customers per hour / 5 lanes

= 14 customers per hour per lane

Next, we can calculate the average time a customer spends in the system (W) using the formula:

W = 1 / (μ - λ)

where μ is the average service rate and λ is the arrival rate per lane.

W = 1 / (3 - 14)

W = 1 / (-11)

W = -1/11 (since the service rate is smaller than the arrival rate, resulting in negative waiting time)

However, negative waiting time is not meaningful in this context. It indicates that the system is not stable or the service rate is insufficient.

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Answer:

145600000

Step-by-step explanation:

Please mark as branliest !

The sum of the angles in a triangle is 180°, If I remember correctly.

Answer:

Hybrid basis

Step-by-step explanation:

There are different methods of accounting used by businesses depending on their peculiar needs. Below are the type of accounting methods:

- Cash basis is when revenues and expenses are recognised when cash is recieved or paid out.

-Accrual basis is when revenue and expenses are recognised when they are earned. For example if services are rendered to a client that will pay in a week's time, since service has already been given it is considered that the future payment has been earned.

- Modified basis combines elements of cash and accrual basis. For example considering short term assets like accounts receivable and accounts payable as cash items. Long term assets are recorded on accrual basis.

- Hybrid basis is used when cash and accrual methods are used for various expenses and tax. Mostly it is used for internal accounting purposes.

In this scenario Hariette would like to review the income and expenses that were actually paid last month. This requires a cash basis that shows actual amount recieved and paid last month. Account receivable and payable are not considered.

In setting aside money for tax she will employ accrual basis accounting. It is an expense that is estimated for future use.

So the hybrid basis is the method that will be most suitable.

Homoscedasticity refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.

Regression line is defined as the line which is used to estimate the unknown relationship between two variables and the relationship is linear.

The equation of this line is used to find or predict the value of one of the variable from the other.

Homoscedasticity is something which assumes that the variances are equal for different groups.

So, this refers to the pattern of covariation that is constant around the regression line, whether the values are small, medium, or large.

Hence the correct term is Homoscedasticity.

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To find the cross product of two vectors, we can use the determinant method. The formula for the cross product of two vectors a and b is given by a × b = |i  j  k|, where the coefficients of i, j, and k are the determinants of the 2x2 matrices formed by excluding the row and column that correspond to that variable.

Using this formula, we can find the cross product of a and b as follows:

a × b = |i  j  k|
      |1  0   -1|
      |0  10 -1|

= i(0+10e^(-t)) - j(e^(-t) -0) + k(e^(-t)-0)

= 10i + (1-e^(-t))j + e^(-t)k

The cross product of two vectors is a vector that is perpendicular to both the vectors and has a magnitude equal to the product of their magnitudes multiplied by the sine of the angle between them. In three-dimensional space, the cross product is used to determine the orientation of two vectors in relation to each other.

In this problem, we are given two vectors a and b, and we need to find their cross product. We can use the determinant method to find the cross product as shown above.

The cross product of a and b is 10i + (1-e^(-t))j + e^(-t)k.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The limit of the given sequence does not exist, it can be concluded that the sequence En=1 3 n³+4n+1 does not converge. Therefore, the sequence is divergent.

The given sequence  En=1 3 n³+4n+1 can be written as

En=1 3 n³(1+4/n²+1/n³)

The limit of the given sequence can be evaluated by using limit rule of sequence,

lim En=1 3 n³(1+4/n²+1/n³)

=lim 1+4/n²+1/n³ × lim 3 n³

On applying the limit rule,

= lim 1+4/n²+1/n³

= 1+0+0

= 1 and,

lim 3 n³ = ∞

Since the limit of the given sequence does not exist, it can be concluded that the sequence En=1 3 n³+4n+1 does not converge. The sequence is divergent. Thus, it can be concluded that the sequence En=1 3 n³+4n+1 does not converge.

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its B 15 divide by 3 is 5 because 2 - 5 is -3 - 15 is 5

Answer:

Slope Intercept Form: y=3x-10

Step-by-step explanation:

First, we need to solve the slope.

The formula: y2-y1/x2-x1 = m

Coordinate Points:

(2, -4) ; (4,2)

Do 2 - (-4) for the y's and 4-2 for the x's

Formula: 2-(-4)/4-2

2 - (-4) is a positive answer since the negatives cancel to a positive.

That shall be 6.

4-2 = 2

Now we have 6/2 which means 6 divided by 2 which is 3.

Our slope is 3.

Slope-Intercept Formula: y=mx+b

Our "m" is 3

y = 3x + b

Our b which is the y-intercept is undefined.

We need to plug one of the coordinates into the formula to find it.

Plug (2,-4) into the formula.

-4 = 3(2) +b

Do 3 x 2 first

-4 = 6 + b

Now subtract 6 on both sides

-6-4 = b

Our y-intercept is -10 because negative subtracted by negatives is an addition number followed by the greater number's sign.

Formula: y=3x-10

Answer:

y = 3x - 10

Step-by-step explanation:

To determine the line that passes through the points (2, -4) and (4, 2), we need to determine the slope of the line. Then, using the slope of the line and any point, we can determine the equation of the line using point slope form.

How to determine the slope of the line?

The slope of the line can be determined by using the formula (y₂ - y₁)/(x₂ - x₁), where x₂ and y₂ are the coordinates of the second point; x₁ and y₁ are the coordinates of the first point.

\(\implies\large\text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

In this case, our first point and second point are (2, -4) and (4, 2) repectively as stated in the question. Therefore,

When we substitute the following into the formula, we obtain;

\(\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 }\)

When we perform subtraction, we obtain;

\(\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 } = \dfrac{2 + 4}{2 } = \dfrac{6}{2}\)

Which when simplified, we get;

\(\implies\large\text{Slope} = \dfrac{6}{2} = 3\)

As said above, to determine the equation of the line with the slope and a point given, we can use point slope form. The chosen point must be on the line. The question states that "the line that passes through the points (2,-4) and (4, 2)". Therefore, we can tell that (2,-4) and (4, 2) are points that are on the line. Let's choose (4, 2) as our chosen point.

Now, let's substitute the slope of the line and the coordinates of the chosen point in the point slope form equation.

Finally, let's simplify the point slope equation and convert it into slope intercept form (as stated in question).

The slope intercept form states that;

We can see that the "y" variable is isolated on one side of the equation [y = (m)x + (b), Slope intercept form equation]. Thus, we need to isolate the y-variable in y - 2 = 3x - 12 to obtain our equation in slope intercept form. This can be done by adding 2 to both sides of the equation.

Therefore, the equation in slope intercept form is y = 3x - 10.

\(10 + x^2\) Will be greater than \(2^x\)for certain values of x, specifically when x is approximately less than

0.543 and between 4.337 and 5.172.

Set up the inequality: \(10 + x^2 > 2^x\)

Since there's no algebraic method to solve this inequality directly, we can analyze it graphically.

Plot the two functions,\(y1 = 10 + x^2\) and\(y2 = 2^x\), on a graph.

Find the points where the two graphs intersect.

If there's a region where the graph of y_1 is above the graph of y_2, that means \(10 + x^2 > 2^x\) in that region.

When analyzing the graphs, you'll find that\(10 + x^2 > 2^x\) for x approximately less than 0.543 and x approximately

between 4.337 and 5.172.

In these regions, the inequality holds true.

In conclusion,  \(10 + x^2\)  will be greater than  \(2^x\) for certain values of x, specifically when x is approximately less than 0.543 and between 4.337 and 5.172.

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If we allow the number of edges between any two nodes to be more than two, we would need to use the adjacency matrix to accurately store that graph information.

The adjacency matrix is a matrix representation of a graph where the rows and columns represent the vertices and the values in the matrix represent the number of edges between two vertices.

In this case, we could have values greater than 1 in the matrix to represent multiple edges between two vertices.

On the other hand, the adjacency list data structure would not be able to accurately store this information, as it represents each vertex and its adjacent vertices in a linked list format.

It would be difficult to represent multiple edges between two vertices using this data structure.

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The trigonometric relations from the triangles are

a) tan A = 5/12

b) sin C = 3/5

c) cos X = 3/5

d) sin Z = 4/5

e) tan Z = 4/3

f) tan X = 12/5

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

a)

The triangle is ΔABC

tan A = opposite side / adjacent side

Substituting the values in the equation , we get

tan A = 10/24

tan A = 5/12

b)

The triangle is ΔABC

sin C = opposite side / hypotenuse

Substituting the values in the equation , we get

sin C = 24/40

sin C = 3/5

c)

The triangle is ΔXYZ

cos X = adjacent side / hypotenuse

Substituting the values in the equation , we get

cos X =21/35

cos X = 3/5

d)

The triangle is ΔXYZ

sin Z = opposite side / hypotenuse

Substituting the values in the equation , we get

sin Z = 32/40

sin Z = 4/5

e)

The triangle is ΔXYZ

tan Z = opposite side / adjacent side

Substituting the values in the equation , we get

tan Z = 28/21

tan Z = 4/3

f)

The triangle is ΔXYZ

tan X = opposite side / adjacent side

Substituting the values in the equation , we get

tan X = 12/5

Hence , the trigonometric relations are solved from the triangles

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Answer:

Step-by-step explanation:

all values are true

Answer:8 feet

Step-by-step explanation:

The perpendicular bisectors of a triangle are concurrent lines that intersect at a single point, known as the circumcenter.

The perpendicular bisector of a line segment is a line that is perpendicular to the line segment and passes through its midpoint. For a triangle, the perpendicular bisectors of the three sides are constructed, and these lines intersect at a single point. This point is known as the circumcenter of the triangle.

The circumcenter is equidistant from the three vertices of the triangle, and it lies on the perpendicular bisectors of the sides. The circumcenter plays an important role in the geometry of triangles, as it is the center of the circumcircle, the circle that passes through all three vertices of the triangle.

The proof of the concurrency of the perpendicular bisectors is based on the fact that any two distinct points in a plane determine a unique perpendicular bisector, and that the three perpendicular bisectors of a triangle must intersect at a single point because they cannot be parallel (since they are perpendicular to different sides) and they cannot intersect in more than one point (because two distinct points determine a unique line).

In conclusion, the perpendicular bisectors of a triangle are concurrent lines that intersect at a single point, known as the circumcenter. This property is unique to triangles and plays an important role in the geometry of triangles.

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Answer:

Domain: -5, -3, -2, 1, 3

Step-by-step explanation:

Find all the points on the x-axis that line up with the line shown on the graph.

Yes because sometimes the new number can be over double or triple times larger or smaller than the original number so the percentage change would be greater than 100%

Answer: x=2

Step-by-step explanation: refer to image

From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.

Hence, from the histogram in this distribution, it is found that:

75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

The complete problem is given by the image at the end of the answer.

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