If m∠ABD=84°​, what are m∠ABC and m∠​DBC? D A B C (5x+1)° (6x-5)°

Answer:

★ GivEn :-

★ To Find :-

Step-by-step explanation:

→ Let the age of Sabita be x years.

→ Now, according to the question, Babita is 7 years older than Sabita.

→ Therefore, Babita's age is x + 7 years.

→ According to the given condition,

The sum of their ages is 33 years.

\( \sf \: x + (x + 7) = 33\)

\( \implies \sf \: x +x + 7 = 33\)

\( \implies \sf \: 2x + 7 = 33\)

\( \implies \sf \: 2x = 33 - 7\)

\( \implies \sf \: 2x = 26\)

\( \implies \sf \: x = \dfrac{26}{2}\)

\( \implies \boxed{ \red{\sf \: \therefore \: x = 13}}\)

Therefore, the age of Sabita is 13 years!

The age of Sabita is 13 years

If the sum of their ages is 33 years, then;

x + y = 33 .......................1

If Babita is now  than Sabita7 years older, then;

y = x + 7 ........................2

Substitute equation 2 into 1;

x + y = 33

x + x + 7 = 33

2x = 33  - 7

2x = 26

x = 13

Hence the age of Sabita is 13 years

Learn more on simultaneous equations here: https://brainly.com/question/16863577

A 30-year ARM mortgage loan means that the borrower will have a fixed interest rate for the first 30 years of the loan. After that, the interest rate will adjust annually based on the index and margin.

In this case, the start rate is 3.50%. This means that for the first year, the borrower will pay interest at a rate of 3.50%. At the end of the first year, the interest rate will adjust based on the index and margin.
The index used for this mortgage is MTA, which was 3.00% at the start of the loan. At the end of the first year, the MTA was 4.45%, and at the end of the second year, it was 4.50%.
To calculate the new interest rate at the end of each year, we need to add the margin to the current index rate. The margin is 3.00% and remains the same for the duration of the loan.

Let's calculate the new interest rate at the end of the first year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.45% + 3.00%
New Interest Rate = 7.45%

However, the rate caps limit how much the interest rate can increase or decrease. In this case, the rate caps are 3/2/6, which means that the interest rate can increase by a maximum of 3 percentage points after the first adjustment, 2 percentage points for subsequent adjustments, and 6 percentage points over the life of the loan.

Since the new interest rate calculated above (7.45%) exceeds the rate cap of 3 percentage points for the first adjustment, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the first year will be 6.50%.

For subsequent adjustments, the interest rate can increase by a maximum of 2 percentage points. Let's calculate the new interest rate at the end of the second year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.50% + 3.00%
New Interest Rate = 7.50%

Since the new interest rate calculated above (7.50%) exceeds the rate cap of 2 percentage points, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the second year will be 6.50%.

To Know More about index and margin visit:

brainly.com/question/30907031  

#SPJ11

The equation of the line that meets the following conditions are as follows;

5. y + 2 = 3(x - 4).

6. y - 7 = -3/2(x + 5)

7. y + 8 = -20/7(x - 4).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (4, -2) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3(x - 4)

Part 6.

At data point (-5, 7) and a slope of -3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = -3/2(x + 5)

Part 7.

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (12 + 8)/(-3 - 4)

Slope (m) = -20/7

At data point (4, -8) and a slope of -20/7, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 8 = -20/7(x - 4).

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

To learn more about economy click here: brainly.com/question/30131108

#SPJ11

The directional derivative of the function f(x, y) = 3ex sin(y) at the point (0, π/3) in the direction of the vector v = (-5, 12) is ∂vf(0, π/3) = -60eπ/3.

The directional derivative measures the rate at which a function changes at a given point in a specific direction. To compute it, we need to take the dot product between the gradient vector (∇f) and the unit vector in the direction of v.

First, we need to find the gradient of f(x, y) by taking the partial derivatives with respect to x and y. The partial derivative with respect to x is ∂f/∂x = 3ex sin(y), and the partial derivative with respect to y is ∂f/∂y = 3ex cos(y).

Next, we evaluate the gradient at the point (0, π/3) by substituting x = 0 and y = π/3 into the partial derivatives. We obtain ∂f/∂x = 3e^0 sin(π/3) = (3/2)√3 and ∂f/∂y = 3e^0 cos(π/3) = (3/2).

To find the directional derivative, we take the dot product between the gradient vector (∇f) and the unit vector in the direction of v, which is v/|v|. Since v = (-5, 12), we normalize it to obtain the unit vector (-5/13, 12/13).

Finally, we compute the directional derivative as ∂vf(0, π/3) = (∇f) · (v/|v|) = [(3/2)√3, (3/2)] · (-5/13, 12/13) = -60eπ/3. Therefore, the directional derivative of f(x, y) at (0, π/3) in the direction of v is -60eπ/3.

Learn more about gradient vector here:

https://brainly.com/question/29751488

#SPJ11

Answer:

6 months

Step-by-step explanation:

Let m be the number of months.

\(115 + 3m = 145 - 2m\)

\(115 + 5m = 145\)

\(5m = 30\)

\(m = 6\)

The 5 students walked a total of 15 miles all together.

The duration of running races and distances for land transport, such as walking or driving, are frequently measured in miles. Miles are the unit of measurement for distance in the aviation and nautical fields.

We can easily calculate the total distance walked by all 5 students if they collectively walked 3 miles during a walk-a-thon by multiplying the distance travelled by the number of students.

Total distance walked by all 5 students = 3 miles/group x 5 students = 15 miles

Therefore, the 5 students walked a total of 15 miles all together.

Learn more about miles here : brainly.com/question/24937565

#SPJ1

Answer:

C

Step-by-step explanation:

if you plug in the X values, you get the corresponding Y values.

Answer:

a=m+4

a=3+4

a=7

Step-by-step explanation:

hope it helps

mark as brainlist

Answer:

a = 7

Step-by-step explanation:

a = 3 + 4

Answer:

f(1)=8

Step-by-step explanation:

f(1)= 7(1-1)+8

f(1)= 7(0) +8

f(1)= 0+8

f(1)= 8

The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

More on  tangent line: https://brainly.com/question/28994498

#SPJ11

Answer:

1.6

Step-by-step explanation:

Answer:

1.6 degrees

Step-by-step explanation:

The Algorithm for a time complexity of O(n) is given at the end.

The algorithm with a time complexity of O(n) to solve the problem:

1. Initialize two variables: "min_price" to store the minimum price encountered so far and "max_profit" to store the maximum profit found so far. Set both variables to infinity or a very large number.

2. Iterate through the given prices from left to right, for each day i:

  - Update min_price as the minimum between min_price and prices[i].

  - Calculate the potential profit as prices[i] - min_price.

  - Update max_profit as the maximum between max_profit and the potential profit.

3. After the iteration, max_profit will contain the maximum profit that can be obtained by buying on one day and selling on a later day.

4. In this case, return a suitable message indicating that there is no profitable opportunity.

5. If max_profit is positive, it represents the maximum profit that can be obtained. To find the specific days i and j, iterate through the prices again and find the day i where the profit is equal to max_profit. Then, continue iterating from day i+1 to find the day j where the price achieves the maximum profit (prices[j] - prices[i]). Return the pair of days (i, j).

The Python code implementing the algorithm:

def find_optimal_days(prices):

   n = len(prices)

   min_price = float('inf')

   max_profit = 0

   buy_day = 0

   sell_day = 0

   for i in range(n):

       min_price = min(min_price, prices[i])

       potential_profit = prices[i] - min_price

       max_profit = max(max_profit, potential_profit)

       if potential_profit == max_profit:

           sell_day = i

   if max_profit <= 0:

       return "No profitable opportunity."

   for i in range(sell_day):

       if prices[sell_day] - prices[i] == max_profit:

           buy_day = i

           break

   return buy_day, sell_day

# Example usage:

prices = [7, 1, 5, 3, 6, 4]

result = find_optimal_days(prices)

print(result)

This algorithm has a time complexity of O(n), where n is the number of days (length of the prices list). It iterates through the prices list twice, but the overall complexity is linear.

Learn more about Time Complexity here:

https://brainly.com/question/30227527

#SPJ4

the missing term is 5

Hi there !

12x² - 75 =

= 3(4x² - 25)

use formula a² - b² = (a - b)(a + b)

= 3(2x - 5)(2x + 5)

= 3(2x + 5)(2x - 5)

the missing term is 5

Good luck !

A

Step-by-step explanation:

ik trust me

Answer:

A. The prepaid phone plan will have a steeper line and lower y-intercept.

Step-by-step explanation:

did it on edge 2020

The number of people in a household with 2.5 pounds of waste are = 11

and we calculate this on the basis of question below

Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5

pound    0.27  ,1.41,  2.19  ,2.83  ,2.19  ,1.81  ,0.85,  3.05  

people      2          3      3       6        4        2        1       5

so now the question is complete

in pound section we have to take care which value are greater than 2.5

so 2.83 and 3.05 is greater than 2.5 so here  number of people who's home have greater than 2.5 pound of waste are 6+6=11

and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15

so final ans is 11.

so this question was in complete and this ans is valid for this Question only.

For more about pound question click here

https://brainly.com/question/7828343

#SPJ4

Answer:

(option 1) 1 unit up and 5 units right

Step-by-step explanation:

the x value represents horizontal shifts (left<-->right)
The y value represents vertical shifts (up<---->down)
a positive change in the x or y value is seen as going right or up, respectively. Since a positive value change is seen in both the x and y values, we can eliminate all the options except for option 1.
We can also subtract the initial point from the new point in order to find the exact shift (even though we already narrowed down to our answer).
x(A'-A)=3-(-2)=+5=right 5
y(A'-A)=3-2=+1=up 1

The cost price of cloth that John bought per meter is Php 46.00 (Option C). To find the cost price per meter, divide the total cost by the number of meters of cloth.

In this case, the total cost is Php 425.50 and the number of meters is 9.25. By dividing the total cost by the number of meters, we get Php 46.00 per meter. This means that John paid Php 46.00 for every meter of cloth he bought. This is the cost price per meter and it is option C, Php 46.00.

The specific value that corresponds to the unit price that was purchased is reflected in retail systems by the cost price. In some stock market theories, this value is used to determine the value of stock holdings, and it is used as a key factor in determining profitability.

Learn more about Cost:

https://brainly.com/question/29509552

#SPJ4

Answer:

50 ft

Step-by-step explanation:

Answer:

Answer            2

Step-by-step explanation:

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Using the slope intercept form of the line, cost per night (m) is 75 and the initial fee (b) that the cabin charges is 50.

Equation of a line in slope intercept form is

y = mx + b

Here m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

The cabin that Jake and his friends are staying at charges an initial fee plus the cost per night.

Given graph is a linear relationship between the total cost, y, and number of nights, x.

Let initial fee be b and cost per night be m.

So the equation will be of the form,

Total cost = Initial fee + (cost per night × number of nights)

y = b + mx

Comparing this with slope intercept form, initial fee is the y intercept and cost per night is the slope.

From the graph, we have a point (0, 50).

y intercept = 50

So initial fee = 50

Consider (0, 50) and (2, 200).

Slope = (200 - 50) / (2 - 0) = 75

So cost per night = 75

Hence cost per night is 75 and the initial fee is 50.

Learn more about Slope Intercept form here :

https://brainly.com/question/19998530

#SPJ9

The probability that a randomly selected player has fair potential for improvement 21/65 and the probability that a randomly selected player has average current ability or has good potential for improvement is 227/390.

In the given question,

Potential for improvement

Current Ability        Excellent     Good     Fair     Total

Above Average          62               71         70      203

Average                      33               50         45      128

Below Average          20               28         11         59

Total                           115               149         126    390

a) We have to find the probability that a randomly selected player has fair potential for improvement.

Probability of player having fair potential for improvement

P(F) = Total player having fair potential for improvement/Total player

From the table we know that,

Total player having fair potential for improvement = 126

Total Player = 390

P(F) = 126/390

Simplifying the ratio

P(F) = 21/65

Hence, the probability that a randomly selected player has fair potential for improvement is 21/65.

b) We have to find the probability that a randomly selected player has average current ability or has good potential for improvement.

Probability of player having average current ability or having good potential for improvement.

P(C or G) = P(C) + P(G) − P(C ∪ G)................(1)

P(C) = Probability of Player having average current ability

P(G) = Probability of Player having good potential for improvement

P(C ∪ G) = Probability of Player having average current ability and having good potential for improvement.

Firstly we finding the value of each term.

P(C) = Player having average current ability/ Total number of player

From the table we know that

P(C) = 128/390

Now finding the value of P(G)

P(G) = Player having good potential for improvement/ Total number of player

From the table we know that

P(G) = 149/390

Now finding the value of P(C ∪ G)

P(C ∪ G) = Player having average current ability and having good potential for improvement/Total number of player

From the table we know that

P(C ∪ G) = 50/390

Now putting the value in the Equation (1)

P(C or G) = 128/390 + 149/390 − 50/390

Simplifying

P(C or G) = (128+149−50)/390

P(C or G) = 227/390

Hence, the probability that a randomly selected player has average current ability or has good potential for improvement is 227/390.

To learn more about probability link is here

https://brainly.com/question/11234923

#SPJ4

The true statement about the function of area of by rectangle and width of rectangle are:

The correct answer option is options A and D

A rectangle is a quadrilateral having opposing sides parallel and four right angles.

At point (x, y) = (10, 100) the area is maximum.

This means that the area of the rectangle is maximum when width is 10m.

If the width of the rectangle is more than 10m, the area reduces or decreases.

Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.

The statement "To get the greatest area, the width should be 20" is false.

Complete question:

Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).

Wlhich of these statements are true?

A. Greater width relates to greater area as long as the width is less than 10.

B. Greater width relates to greater area as long as the width is more than 10.

C. To get the greatest area, the width should be 10

D. To get the greatest area, the width should be 20

Read more on area of rectangle:

https://brainly.com/question/15066985

#SPJ1

The mistake made is the error in finding the value of the slope, m, of the line.

The error can be corrected by plugging in m = 6/3 = 2 in the equation; y = m·x + b

The slope of a line is the ratio of the rise to run of the points on the graph of the line.

The points on the graph of the line are; (0, -2), and (3, 4)

The slope of the line, m, can be found using the formula;

m = (y₂ - y₁)/(x₂ - x₁)

Where for the line in the question, we get;

Therefore;

Slope, m = (4 - (-2))/(3 - 0) = 6/3 = 2

The slope of the line = 2

The equation of the line in point-slope form is therefore;

(y - 4) = 2·(x - 3)

y = 2·x - 6 + 4 = 2·x - 2

y = 2·x - 2

The equation can also be found using the x-intercept as follows;

At the x-intercept, x = 0. The x-intercept is therefore, the point (0, -2)

The equation of the line in the slope-intercept form is, y = m·x + b, where b is the y-value at the x-intercept is therefore;

y = -2, when x = 0

-2 = 2×0 + b

b = -2

y = m·x + b, therefore; y = 2·x - 2

The mistake of the student is therefore;

y = m·x + b

4 = 2·(3) + b

4 = 6 + b

-6 \({}\)  -6

-2 = b

y = 2·x - 2

Learn more about the equation of a straight line here: https://brainly.com/question/29266581

#SPJ1

If corresponding elements of matrices are equal, the matrices are equal.

Choose the correct term to complete each sentence. If corresponding elements of matrices are equal, the matrices .

Matrices are mathematical structures that consist of rectangular arrays of numbers or elements. They are widely used in various fields, including mathematics, physics, computer science, and engineering, to represent and manipulate data.

A matrix is defined by its dimensions, which are given by the number of rows and columns it has. For example, a matrix with 3 rows and 4 columns is called a 3x4 matrix or simply a 3-by-4 matrix.

learn more about matrices here:

https://brainly.com/question/30646566

#SPJ11

Answer:

it will take about 1/3 of the time (10 minutes)

Step-by-step explanation:

Answer:

Step-by-step explanation:

t/30+t/30+t/60=1

2t/60+2t/60+t/60=1

5t/60=1

5t=60

t=12 minutes

The total surface area of the figure shown as a rectangular prism is 208. 6 cm

The formula for calculating the total surface area of a rectangular prism is expressed as;

TSA =  2 (lh +wh + lw )

Such that the parameters are;

Now, substitute the values, we have;

TSA = 2(2(9) + 7.9(9) + 2(7.6)

expand the bracket, we have;

TSA = 2(18 + 71.1 + 15.2)

add the values

TSA = 2(104. 3)

TSA = 208. 6

Learn about rectangular prism at: https://brainly.com/question/24284033

#SPJ1

\(x^2+12x+35\\\\=x^2 +5x +7x +35\\\\=x(x+5) +7(x+5)\\\\=(x+7)(x+5)\\\\\\3x+15 = 3(x+5)\)

Answer:

D due to the calculation conducted

The part, dividing, and multiplying by 100 remain the same percentages involves expressing a Fraction or portion of something as a percentage out of 100.

Percentages is a fundamental mathematical skill that is used in a variety of contexts, from calculating grades to figuring out discounts while shopping. In this response, I will explain the basic principles of how to work out percentages.

A percentage is simply a way of expressing a fraction or portion of something as a portion out of 100. For example, if you have a bag of 20 apples and 5 of them are rotten, you can express the percentage of rotten apples as:

(5 rotten apples / 20 total apples) x 100% = 25%

To calculate a percentage, you need to follow a few simple steps:

1. Identify the total amount or whole. This is the quantity that you will be expressing a portion of.

2. Identify the part or portion. This is the quantity that you will be expressing as a percentage of the whole.

3. Divide the part by the whole. This will give you a decimal or fraction.

4. Multiply the result from step 3 by 100. This will give you the percentage.

Here's an example to illustrate these steps:

Suppose you have a test with 40 questions, and you got 32 of them correct. To calculate your percentage score, you would do the following:

1. The whole is 40 questions.

2. The part is 32 questions.

3. Divide the part by the whole: 32/40 = 0.8

4. Multiply by 100: 0.8 x 100 = 80%

Therefore, your percentage score on the test is 80%.

There are many other applications of percentages in math, including calculating percentage change, percentage increase or decrease, and percentage of a total. However, the basic principles of identifying the whole and the part, dividing, and multiplying by 100 remain the same calculating percentages involves expressing a fraction or portion of something as a percentage out of 100. The process involves identifying the whole and the part, dividing, and multiplying by 100. With practice, working out percentages becomes a quick and easy task.

To know more about Fraction .

https://brainly.com/question/78672

#SPJ11

A percentage is calculated as the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

Hence the rule is given as follows:

P = a/b x 100%.

For example, if 3 out of 8 people have green eyes, the percentage is given as follows:

P = 3/8 x 100%

P = 37.5%.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1