If an angle is bisected to form two new 20 degree angles, what was the measure of the original angle?

Answer:

Step-by-step explanation:

5) f(1)= 2x^3-3x^2-2x+a=-4

     2^3- 3^2-2+a= -4

      a=-1

6)b= 42

The constant of proportionality of y and x in the graph is given as follows:

k = 3/4.

In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:

k = y/x.

A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.

The marked point on the graph has the coordinates given as follows:

(4,3).

Meaning that the constant of proportionality of y and x in the graph is calculated as follows:

k = y/x = 3/4.

(division of the value of the y-coordinate by the value of the x-coordinate).

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

Natalie buys organic almonds priced at $77 from the grocery store. How much did she pay the cashier, if she received $23 in change? Let a = amount Natalie paid the cashier. a = 100 → Natalie paid the cashier $100.

Answer: a constant

Step-by-step explanation:

A constant is a numerical expression like 2, 0,78 etc .

A variable is a alphabetical expression that vary like a,b,c,d,x,y,z.

An expression can consists of both numerical and alphabets and also any arithmetic expression like x, 2abc, 6a+2c etc

A term consist of either numbers and variables multiplied together or only numbers or variable like 2xy, x, 2ab etc.

X is all (a term, a variable , an expression) except a constant because a constant is a numerical expression.

Answer: D, a constant

Step-by-step explanation: A constant is an expression without variables.

The stock price of Navel County Choppers, Inc. can be determined using the dividend discount model. With expected dividend growth of 18% for the next 11 years and a perpetual growth rate of 4%, and a required return of 10%, we can calculate the stock price.

To calculate the stock price, we need to find the present value of the expected future dividends. The formula for the present value of dividends is:

Stock Price = (Dividend / (Required Return - Growth Rate))

In this case, the dividend just paid is $1.94, the required return is 10%, and the growth rate is 18% for the first 11 years and 4% thereafter. Using these values, we can calculate the stock price.

Stock Price = ($1.94 / (0.10 - 0.18)) + ($1.94 * (1 + 0.04)) / (0.10 - 0.04)

Simplifying the equation, we find the stock price of Navel County Choppers, Inc.

Learn more about present value here: brainly.com/question/28304447

#SPJ11

The value of x is 35°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Angles on parallel lines can be ;

Corresponding to each other

Alternate to each other and

Vertically opposite to each other

In these cases , the angles are equal.

Therefore;

4x + 7 = 6x -63( corresponding angles)

collect like terms

4x - 6x = -63 -7

-2x = -70

divide both sides by -2

x = -70/-2

x = 35

Therefore the value of x is 35°

learn more about angles on parallel lines from

https://brainly.com/question/25770607

#SPJ1

Answer: the answer is B

Step-by-step explanation:

Answer:b

Step-by-step explanation:

The expression as limx→3​(x-3)(x+1)/ (x-3)Now cancel the common term (x-3) from numerator and denominator and we are left with limx→3​x+1 = 3+1 = 4. The trigonometric identity sin^2 x + cos^2 x = 1.  a. 4b. 1/12c. ∞d. ∞e. 0f. ∞g. -∞h. 0i. 0j. 1

The given indeterminate forms and L'Hospital's rule problems can be solved as follows :

a) We are given the limit as limx→3​x2−9x−3​. We can use factoring to solve it. By factoring, we can write the expression as limx→3​(x-3)(x+1)/ (x-3)Now cancel the common term (x-3) from numerator and denominator and we are left with limx→3​x+1 = 3+1 = 4.

b) Given limx→4​x−4x​−2​.

Applying L'Hospital's rule, we get the limit aslimx→4​1/(2x+4)On substituting the value of x in the above equation, we get the limit aslimx→4​1/(2x+4) = 1/12.

c) We are given the limit as limx→[infinity]​x2lnx​​. Applying L'Hospital's rule, we get the limit aslimx→[infinity]​2x/ x^-1 = limx→[infinity]​2x^2 = ∞.

d)

Given limu→[infinity]​u3e16π​​. Applying L'Hospital's rule, we get the limit aslimu→[infinity]​(3u^2/16π) e^16π = ∞

e) We have to find limx→[infinity]​x(tπx)2​. By dividing the numerator and the denominator by x^2, we get limx→[infinity]​tπ^2/ x^2. As x tends to infinity, the limit tends to 0.

f) Given limx→[infinity]​x​e2x​. Applying L'Hospital's rule, we get the limit as limx→[infinity]​e^2x/ x^-1 which is ∞.

g) We have to find the limit as limx→−[infinity]​xln(1−x1​). Let x = -t.

Now as t tends to infinity, the limit of the expression is equal to limt→[infinity]​tln(1+1/t). We can apply the expansion of log(1+x) which is equal to x - (x^2)/2 + (x^3)/3 - ...

On simplification, we get the limit as -∞.

h) Given limx→[infinity]​(x−lnx). Applying L'Hospital's rule, we get the limit aslimx→[infinity]​(1/x) = 0.

i) We have to find the limit as limx→0+​(1−cosx)sinx. We can apply the trigonometric identity sin^2 x + cos^2 x = 1. On simplification, we get the answer as 0.j) Given limx→0​(cosx). The limit is equal to 1.

Learn more about trigonometric identity here:

https://brainly.com/question/12537661

#SPJ11

Answer:

11

Step-by-step explanation:

3 + 5 = 8

8 + 9 = 17

17 - 6 = 11

Answer:

The probability is 0.5 tiles will be green

Step-by-step explanation:

Hope this helps

Answer:i cant see the picture, try re uploding it

Step-by-step explanation:

The total annual Expense for a car that drives 30,000 miles per year would be around $8500 ($2500 +           $1000 + $1500 + $3500).

If you drive 30,000 miles per year, the total annual expense for this car would depend on various factors.

take a look at some of the expenses you would need to consider:

Therefore, the total annual expense for a car that drives 30,000 miles per year would be around $8500 ($2500 +           $1000 + $1500 + $3500).

For more questions on Expense .

https://brainly.com/question/30967676

#SPJ8

Answer:

Yellow

Step-by-step explanation:

Answer:

its a right angle!

Step-by-step explanation:

<ABC is a complementary angle.

Courtney rides for two hours on a bicycle, traveling 24 miles from her home. She has ridden for nine hours and is now 101 miles away. Courtney travels at a speed of 6 mph.

Let x represent the duration in hours and y the distance in miles.

Courtney travels 24 miles from her home after a two-hour ride.

She has traveled 101 miles after riding for nine hours.

rate is the slope

We divide the change in hours by the change in miles to find the rate.

\(Slope=\frac{y_{2} - y_{1} }{x_{2}-x_{1} } \\Slope=\frac{101-24}{9-2} \\Slope= \frac{77}{7} \\Slope=11\)

Therefore, Courtney's speed is 11 mph.

The speed of something or someone is shown to us. If you know how far and how long it took, you can find the average speed of an object.

The distance covered in a given amount of time would also double if one were to speed up. We need to know how far an object has traveled in order to determine its speed, and the slowest speeds are measured over the longest time periods.

To learn more about speed, refer:-

https://brainly.com/question/28025358

#SPJ4

Answer:

\( \boxed{C}\)

The solution of the quadratic equation, -x²-3 x+7=0 are :  -1.54, 4.54.

Hence the correct option is C.

The given equation is,

-x²-3 x+7=0

To solve a quadratic equation of the form ax² + bx + c = 0,

Use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

In this case, we have the equation -x² - 3x + 7 = 0,

Where a = -1, b = -3, and c = 7.

Plugging these values into the quadratic formula, we get:

x = (-(-3) ± √((-3)² - 4(-1)(7))) / 2(-1)

Simplifying this expression, we get:

x = (3 ± √(9 + 28)) / (-2)

x = (3 ± √37) / (-2)

Now we can use a calculator to approximate the value of x to the nearest hundredth.

Using the "±" symbol, we can find the two solutions:

x ≈ -1.54 or x ≈ 4.54

Therefore, the answer is option c: -1.54, 4.54.

To learn more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ4

Answer:

D

Step-by-step explanation:

as we can easily see, the x-coordinates of all points increased by 7.

so, we need a solution with "x+7". that eliminates B and C.

with that transition (glide) the triangle moved to the right into the 4th quadrant.

and now, as a second step, it needs to move up, above the x-axis, into the 1st quadrant.

and that is a reflection across the x-axis.

a reflection across the y axis would bring it back into the 3rd quadrant, where it started.

so, it is D.

The equation of the set of all points equidistant from (4, 6) and (-2, 5) in the general form ax + by + c = 0 is:

-12x + 2y + 23 = 0.

To find the equation for the set of all points equidistant from (4,6) and (-2,5), we can use the distance formula. Let's denote an arbitrary point in the xy plane as (x, y).

The distance between (x, y) and (4, 6) is given by:

d1 = sqrt((x - 4)^2 + (y - 6)^2)

The distance between (x, y) and (-2, 5) is given by:

d2 = sqrt((x + 2)^2 + (y - 5)^2)

For the points equidistant from both (4, 6) and (-2, 5), we have d1 = d2.

Therefore, we can set up the equation as follows:

sqrt((x - 4)^2 + (y - 6)^2) = sqrt((x + 2)^2 + (y - 5)^2)

To simplify the equation, we can square both sides to eliminate the square roots:

(x - 4)^2 + (y - 6)^2 = (x + 2)^2 + (y - 5)^2

Expanding both sides of the equation, we get:

x^2 - 8x + 16 + y^2 - 12y + 36 = x^2 + 4x + 4 + y^2 - 10y + 25

Simplifying and rearranging terms, we obtain:

-12x + 2y + 23 = 0

Therefore, the equation of the set of all points equidistant from (4, 6) and (-2, 5) in the general form ax + by + c = 0 is:

-12x + 2y + 23 = 0.

Learn more about equidistant points: https://brainly.com/question/2286001

#SPJ11

Answer:

2^(n-1)

Step-by-step explanation:

To find the nth term of the sequence 1, 2, 4, 8, 16, 32, 64,..., we can observe that each term is obtained by multiplying the previous term by 2. Therefore, the pattern can be described by the formula:

nth term = 2^(n-1)

In this formula, n represents the position of the term in the sequence.

For example: I

If we want to find the 5th term, we substitute n = 5 into the formula:

5th term = 2^(5-1) = 2^4 = 16

So, the 5th term of the sequence is 16.

Answer:

A is not a right triangle

B is a right triangle

Step-by-step explanation:

A.

6^2 = 36
12^2 = 144.

36 + 144 = 180

15^2 = 225

180 ≠ 225, so it is not a right triangle

----------------------------------------------------------------------------

B.

5^2 = 25

12^2 = 144

25 + 144 = 169

13^2 = 169

169 = 169, so it is a right triangle

The location of Apollo's sigmoid flexure (the initial part of the sigmoid colon) would be reversed i.e., the sigmoid flexure would be found in the right lumbar region instead of the left lumbar region.

Situs inversus is a condition characterized by the reversal or mirroring of the internal organs' positions from their normal arrangement during embryological development.

In this condition, the major organs of the thoracic and abdominopelvic regions are affected. The sigmoid flexure, which is the initial part of the sigmoid colon, would also be reversed in its location.

Typically, the sigmoid flexure is located in the left lower quadrant of the abdomen.

However, in the case of situs inversus, the mirrored arrangement of the organs would result in the sigmoid flexure being located in the right lower quadrant instead of the left.

This reversal occurs due to the abnormal positioning of the internal organs caused by the abnormal cilia in individuals with primary ciliary dyskinesia (PCD).

It's important to note that situs inversus is a rare condition, and its presence can significantly alter the typical anatomical arrangement of organs.

In the context of Apollo's condition, with situs inversus and reversed organ positions, the sigmoid flexure would be found in the right lumbar region instead of the left lumbar region.

Learn more about situs inversus here:

https://brainly.com/question/28287242

#SPJ11

Answer:

15) CE= 14

16) BD= 15

Step-by-step explanation:

Please see the attached picture for the full solution.

The statement that is FALSE is option C: If f(x,y) has a saddle point at (a,b), then f(x,y) < f(a,b) on some points (x,y) in a domain near point (a,b).A saddle point is a critical point of a function where the function has both a maximum and a minimum along different directions.

At a saddle point, the function neither has a maximum nor a minimum. Therefore, option C is false because it states that f(x,y) is less than f(a,b) on some points in a domain near the saddle point (a,b), which is incorrect.

Option A is true because if a function f(x,y) has a maximum at the point (a,b), then (a,b) is a critical point since the derivative is zero or undefined at that point.

Option B is true because if f(x,y) has a minimum at the point (a,b), then the value of f(a,b) is positive since it is the minimum value of the function.

Option D is true because if (a,b) is one of the critical points of f(x,y), then the function f(x,y) may not be defined at that point.

To know more about saddle point refer here:

https://brainly.com/question/32594238#

#SPJ11

Answer:

Plug in numbers.

Step-by-step explanation:

using the equation of a line, y=mx+b, m is slope and b is the y-intercept. y and x are the coordinates. So graph the line first. It has a slope of one and the y-intercept is -1. Then plug in numbers for the equation. Make sure they are reasonable.

If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

To learn more about perimeter click on,

https://brainly.com/question/13203351

#SPJ4

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

To know more about Algorithm, refer to the link below:

https://brainly.com/question/21172316#

#SPJ11

The expression is f(y) = 80y.

We have a school canteen.

We have to write down an expression for the cost in pence of y cups of tea.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

Number of cups of tea = y

Cost of one cup = 80 pence.

Therefore, the function representing the cost in pence of y cups of tea =

f(y) = 80y

Hence, the expression is 80y.

To solve more questions on Expression modelling, visit the link below-

brainly.com/question/1833764

#SPJ1