What is the factored form of 49b2 - 56b+ 16?

OA (4b-7)²
O B. (7b-4)²
O C. (7b-8)(7b-2)
O D. (8b-7)(2b-7)

Answer:

9

Step-by-step explanation:

If 'x' is equal to 1, then your need to multiply 1 by the number of x's. Now we have 2. If 'y' is equal to 3, then you need to multiply 3 by the number of y's.

Value of 'x' : 2

Value of 'y' : 9

9 + 2 = 11

9 - 2 = 9

This is the same as 3y.

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

Learn more about Congruent polygons here:

https://brainly.com/question/2096633

#SPJ1

We can be 90% confident that the true proportion of people who regularly have a dental checkup is between 0.797 and 0.843.

The proportion of people in the sample who regularly have a dental checkup is:

P = 2050/2500 = 0.82

The standard error of the sample proportion is:

SE = sqrt[(P\(\times\)(1-P))/n] = sqrt[(0.82\(\times\)0.18)/2500] = 0.014

Using a 90% confidence level, we find the critical z-value for a two-sided interval to be:

z_crit = 1.645

The 90% confidence interval for the true proportion of people who regularly have a dental checkup is:

P ± z_crit\(\times\)SE

0.82 ± 1.645\(\times\)0.014

= 0.82 ± 0.023

= [0.797, 0.843]

Therefore, we can be 90% confident that the true proportion of people who regularly have a dental checkup is between 0.797 and 0.843.

To learn more about  dental checkup visit: https://brainly.com/question/14704199

#SPJ11

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

y = -1x - 6

Slope (m) = 1-

The laser dot on the wall at point a moves at a pace of 6 times the circle's diameter, while the laser dot at point (ii) moves at 6π radians per minute.

i. The equation for linear speed, can be used to calculate the speed of the laser dot on the wall at point a. The distance in this instance is equal to the diameter of the circle created by the rotation of the laser, and the amount of time required to transit it is equal to one revolution, or 1/6 of a minute. The diameter of the circle is divided by 1/6 of a minute or six times the circumference of the circle.

ii. The equation for angular speed is used to calculate the speed of the laser dot on the wall at position b. In this instance, the angle is 2 radians, and it takes 1/6 of a minute to cross that angle. Therefore, 2 radians divided by 1/6 of a minute, or 6π radians per minute, is the speed of the laser dot on the wall at point b.

Learn more about linear and angular speed here:

https://brainly.com/question/29345009

#SPJ4

An exponential function can represent growth or decay.

The graph represents an exponential growth function is given by  \(y = ab^{x}\).

An exponential function is represented as:

\(y = ab^{x}\)

Where:

a represents any constant value.

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

Graph shown below represents an exponential growth function.

Hence, the graph representing an exponential growth function is graph traced by \(y = ab^{x}\).

Learn more about exponential functions at:

brainly.com/question/11464095

#SPJ4

The value of the line integral is (-16/3)cos(6) + (16/9)sin(6). Evaluating this integral, you will get the value of the line integral for the given curve.

To evaluate the line integral ∫c x sin yds, where C is the line segment from (0,3) to (4,6), we first need to parameterize the curve. We can do this by letting x = t and y = 3 + (3/4)t, where t goes from 0 to 4. This gives us the parametric equations x = t and y = (3/4)t + 3.

Next, we need to find ds, the length of the curve element. We can use the formula ds = sqrt(dx^2 + dy^2) to get ds = sqrt(1 + (3/4)^2)dt = sqrt(25/16)dt = (5/4)dt.

Now we can substitute in our parameterization and ds into the line integral to get ∫c x sin yds = ∫0^4 t sin((3/4)t + 3) (5/4)dt.

We can evaluate this integral using integration by parts. Let u = t and dv = sin((3/4)t + 3) (5/4)dt, then du/dt = 1 and v = (-4/3)cos((3/4)t + 3). The integral becomes:

∫0^4 t sin((3/4)t + 3) (5/4)dt = uv|0^4 - ∫0^4 v du/dt dt
= (-4/3)t cos((3/4)t + 3)|0^4 - ∫0^4 (-4/3)cos((3/4)t + 3) dt
= (-4/3)t cos((3/4)t + 3) + (16/9)sin((3/4)t + 3)|0^4
= (-16/3)cos(6) + (16/9)sin(6)

Therefore, the value of the line integral is (-16/3)cos(6) + (16/9)sin(6).

To evaluate the line integral ∫c x sin y ds, where C is the line segment from (0, 3) to (4, 6), you first need to parameterize the curve C.

A possible parameterization is r(t) = (1-t)(0, 3) + t(4, 6) = (4t, 3+3t), with t ∈ [0, 1]. Then, compute the derivative dr/dt = (4, 3).

Now, find the integrand by replacing x and y with the parameterized curve components: x sin y = (4t) sin(3 + 3t).

Next, find the magnitude of the derivative: |dr/dt| = √(4² + 3²) = 5.

Finally, compute the integral:

∫[0, 1] (4t sin(3 + 3t))(5) dt.

Evaluating this integral, you will get the value of the line integral for the given curve.

Learn more about derivative at: brainly.com/question/29144258

#SPJ11

Answer:

(1,4)

Step-by-step explanation:

Solve top equation for x:

x = 5 – y

Sub into bottom equation:

–3(5 – y) + 2y = 5

–15 + 3y + 2y = 5

5y = 20

y = 4

Backsolve in top equation:

x + 4 = 5

x = 1

Answer: (x, y) = (1, 4)

The solution to the given system of equation is (1, 4)

System of equations are equations made up of several equations and unknowns. Given the following equations:

x + y = 5

–3x + 2y = 5

Using substitution method

Fro equation 1, x = 5 - y

Substitute into 2

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

-15 + 3y + 2y =5

5y = 20

y = 4

Substitute y = 4 into x = 5 - y

x = 5 - 4

x = 1

Hence the solution to the given system of equation is (1, 4)

Learn more on system of equation here: https://brainly.com/question/847634

#SPJ9

Answer:

Root:  x = 0

Step-by-step explanation:

We can find the roots by setting the equation equal to 0 and simplifying:

Step 1:  Raise both sides to the 4th power:

\((\sqrt[4]{16x^4})^4=0^4 \\16x^4=0\)

Step 2:  Divide both sides by 16:

\((16x^4=0)/16\\x^4=0\)

Step 3:  Take the fourth root of both sides to solve for x:

\(\sqrt[4]{x^4}=\sqrt[4]{0}\\ x=0\)

Thus, the root is = 0.

Answer:

12

Step-by-step explanation:

f(x)=16x-30

g(x)=14x-6

f(x) - g(x) = 16x-30 - (14x-6)

               = 16x - 30 - 14x +6

                = 2x -24

Set this equal to zero

2x-24 = 0

Add 24 to each side

2x-24 +24 = 0+24

2x = 24

Divide by 2

2x/2 =24/2

x = 12

x=12

Answer:

Solution given:

f(x)=16x-30 and g(x)=14x-6

(f-g)(x)=0

or

f(x)-g(x)=0

16x-30-14x+6=0

2x-24=0

2x=24

x=24/2

x=12

Answer:

A- The point-slope form of a line parallel to another line is given by y - y1 = m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line parallel to x+2y=6 through (8,3) is y - 3 = -1/2 (x - 8), which can be written in standard form as -2x + y = -11.

B- The point-slope form of a line perpendicular to another line is given by y - y1 = -1/m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line perpendicular to x+2y=6 through (8,3) is y - 3 = 1/2 (x - 8), which can be written in standard form as 2x + y = 15.

C- To graph the three lines, we can plot the x- and y-intercepts of each line and then draw a line through the points.

The x-intercepts are (-11/2,0), (0,-15), (0,-11) and the y-intercepts are (0,3), (0,7.5) and (0,5.5) respectively.

For a more detailed graph you can use a graphing software or calculator.

The linear lines y = 3x - 7 and y = 3x + 1 are parallel.

A linear equation is simply an euqation of a straight line.

A linear graph shows equation in two variables and also the linear association between two quantities.

Given the two linear equations;

y = 3x - 7

y = 3x + 1

Two lines are perpendicular if their slopes are negative reciprocals of one another.

y = 3x - 7 and y = 3x + 1 have the same slope.

Hence, they are not perpendicular.

Two lines are parallel if they have the same slope.

Since y = 3x - 7 and y = 3x + 1 have the same slope

They are parallel.

Therefore, the linear lines are are parallel.

Learn more about linear equation here: https://brainly.com/question/29739212

#SPJ1

The person swims approximately   \(30\) meters.

To find out how far the person swims, w  have to use trigonometry.the distance the person swims “d”, and let's call the angle between the person's path and the perpendicular to the river “θ”.

the sine function to relate the opposite side (which is d) to the hypotenuse (which is the distance from A to B).

sin(θ) = opposite/hypotenuse

The Pythagorean theorem can be used to determine the hypotenuse, which is the distance from A to B, and the opposite side, which is d:

distance from \(A to B = \sqrt(50^2 + 30^2) \approx 58.31 m\)

To rewrite the equation

\(\sin(\theta) = d/58.31\)

To solve for d, and multiply both sides by 58.31:

\(d = 58.31 \times \sin(\theta)\)

Angle is equal to the angle formed by the individual's path and the river's perpendicular.

those tangent is equal to the ratio of the opposite side (which is 30 m, the width of the river) to the adjacent side (which is the distance from A to B along the river bank).

tan(θ) = opposite/adjacent = 30/50 = 0.6

So we can take the arctangent of 0.6 to find θ:

\(\theta = arctan(0.6) \approx 30.96 degrees\)

Now we can substitute this value of θ into the equation we found earlier:

\(d = 58.31 \times sin(30.96) \approx 30 m\)

Therefore, the person swims approximately 30 meters.

Learn more about trigonometry here:

https://brainly.com/question/29002217

#SPJ1

Answer:

6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

B=40°

Step-by-step explanation:

Sum of angles in a triangle =180°

90°+50°+x°=180°

140°+×°=180°

Collect like terms

x°=180°-140°

x°=40°

Assuming the premises (-p^g) ^ (rp) ^ (→→s) ^ (st), we can simplify and apply the rules of inference to conclude that the expression implies t.



To prove (-p^g) ^ (rp) ^ (→→s) ^ (st) → t using the rules of inference, we can start by assuming the premises:

1. (-p^g) ^ (rp) ^ (→→s) ^ (st)    (Assumption)

We can simplify the premises using conjunction elimination and implication elimination:

2. -p ^ g                  (simplification from 1)

3. rp                      (simplification from 1)

4. →→s                   (simplification from 1)

5. st                       (simplification from 1)

Next, we can use modus ponens on premises 4 and 5:

6. t                          (modus ponens on 4, 5)

Finally, we can use conjunction elimination on premises 2 and 6:

7. t                          (conjunction elimination on 2, 6)

Therefore, we have proved (-p^g) ^ (rp) ^ (→→s) ^ (st) → t using the rules of inference.

To learn more about inference click here

brainly.com/question/14303915

#SPJ11

Answer:

7.50 + 14x < 60

x < 3.75

Step-by-step explanation:

Let

x = number of pizzas ordered

Delivery fee = $7.50

Cost per pizza = $14

Total cost should be less than $60

The inequality

7.50 + 14x < 60

14x < 60 - 7.50

14x < 52.5

x < 52.5/14

x < 3.75

Jerry wants to know what would have a bigger impact on the value of his car long-term, an increased purchase price or decreased depreciation

From the graph, we can see that the blue line (purchase price of $50,000 and 20% depreciation) starts higher on the y-axis than the red line (purchase price of $35,000 and 17% depreciation). This means that initially, the car with the higher purchase price will have a higher value.

However, the blue line has a steeper negative slope, which means that the car's value decreases more rapidly over time. On the other hand, the red line has a shallower negative slope, which means that the car's value decreases more slowly over time.

To determine which factor has a bigger impact on the value of the car long-term, we need to look at the point where the two lines intersect. From the graph, we can see that the two lines intersect at approximately (4.25, $23,075).

This means that after about 4.25 years, the two cars will have the same value of approximately $23,075. After this point, the car with the lower purchase price and slower depreciation (red line) will have a higher value than the car with the higher purchase price and faster depreciation (blue line).

Therefore, in the long-term, a lower purchase price and slower depreciation have a bigger impact on the value of the car than a higher purchase price.

For more details regarding depreciation, visit:

https://brainly.com/question/30531944

#SPJ1

Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

There are 11 animals on a farm, some of which are goats, while others are ducks. The total number of legs on the ducks and goats is 34.

An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.

In mathematics, an expression is referred to as an algebraic expression if it contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are made up of multiple terms.

Functions, variables, and numbers make up an expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.

There are 11 animals, and they have a combined total of 34 legs.

Set G and D to the number of goats and ducks, respectively.

Consequently, G = 11 - D when G + D = 11, and vice versa.

therefore 4G + 2D = 34

Using the value as a stand-in for G, we obtain 4(11 - D) + 2D = 34.

By expanding, we have 34 - 44 - 4 + 2D.

The answer is D = 5. Thus, G equals 6.

Proof (5 x 2) plus (6 x 4) equals 34.

To learn more about Expression refer to:

https://brainly.com/question/1859113

#SPJ4

Answer:

$54.19

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the probability of choosing two caramels candies without replacement, we need to know the total number of candies and the number of caramels.

Let's say we have a bag with 10 candies, and 4 of them are caramels. The probability of choosing a caramel on the first draw is 4/10, or 2/5.

Now, let's assume that we don't replace the first candy back into the bag. This means that there are now only 9 candies left in the bag, with only 3 caramels left. So, the probability of choosing a second caramel is 3/9, or 1/3.

To find the probability of both events happening, we need to multiply the probabilities:

P(both caramels) = P(first caramel) x P(second caramel after first caramel was not replaced)

P(both caramels) = (4/10) x (3/9)

P(both caramels) = 12/90

P(both caramels) = 2/15

Therefore, the probability of choosing two caramels candies without replacement from a bag of 10 candies with 4 caramels is 2/15.

Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.

1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.


To know more about binary search visit :-

https://brainly.com/question/15178888

#SPJ11

Answer:

Line A

Step-by-step explanation:

Line A is the line of best fit because it intersects the point (10,3) on the graph while the others do not.

(a) The chance that the sum of the draws will be more than 1,500

(b) The chance that there will be fewer than 90 occurrences of the number 3.

(a) To estimate the chance that the sum of the draws will be more than 1,500, we need to consider the possible combinations and their probabilities. Since there are four numbers in the box, each with an equal chance of being drawn, we can calculate the mean and standard deviation of the draws. With this information, we can use statistical methods such as the normal distribution to estimate the probability of the sum exceeding 1,500.

(b) To estimate the chance that there will be fewer than 90 occurrences of the number 3, we need to calculate the probability of drawing a 3 in each individual draw and then consider the distribution of the number of 3's over the 400 draws. Using statistical techniques such as the binomial distribution, we can estimate the probability of having fewer than 90 occurrences of 3 in the 400 draws.

Both estimations involve applying statistical methods to analyze the probabilities of specific events occurring in the random drawing process. The precise calculations and estimations would require detailed information about the probabilities of drawing each number and the distribution of these numbers in the box.

Learn more about binomial distribution here:

https://brainly.com/question/29163389

#SPj11

Answer:

8

Step-by-step explanation:

22-12+4-6 = 8

So, the area of the figure is 54.5 square miles.

In mathematics, the area is the measurement of the size of a two-dimensional surface or region, usually expressed in square units. It is a quantity that expresses the extent of a two-dimensional shape or figure in a plane. The area of a figure is calculated by multiplying the length and width of the shape, in the case of a rectangle, or by using the appropriate formula for other shapes such as triangles, circles, or irregular polygons.

Here,

The area of rectangle R1 is:

Area of R1 = 5 mi x 2 mi

= 10 square miles

The area of rectangle R2 is:

Area of R2 = 2 mi x 14 mi

= 28 square miles

The area of the triangle TRI is:

Area of TRI = (1/2) x base x height

           = (1/2) x 11 mi x 3 mi

           = 16.5 square miles

Therefore, the total area of the figure is:

Area of figure = Area of R1 + Area of R2 + Area of TRI

              = 10 + 28 + 16.5

              = 54.5 square miles

To know more about area,

https://brainly.com/question/13194650

#SPJ1

Hey does this help you by any chance