Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles.
if you know that 7 + 2i is a root of a polynomial function ,what is another root of that same function?
Answer: Another root of the same function is 7-2i.
Step-by-step explanation: Given that 7+2i is a root of a polynomial function.
We are to find the another root of the same function.
We know that
if a complex number a+ib is one of the roots of a polynomial function f(x), then the conjugate a-ib is another root of the same polynomial f(x).
According to the given information, the conjugate of 7+21, that is, 7-2i is another root of the same polynomial function.
Thus, another root of the same function is 7-2i.
find f when 27f=81 f=
A group of children each rode a horse to the bottom of the canyon. They had 20 eyes and 30 legs between them, how many horses were there
You can calculate that, since all children and horses have two eyes, and that children have two legs and horses have four, and the total number of eyes is 20 and the total number of legs is 30, there were 5 children and 5 horses.
Explanation:This problem can be solved using basic algebra. We need to count the numberOfChildren and numberOfHorses in a manner where each child and each horse contribute two eyes and with each child having two legs while each horse has four legs.
Let's make two assumptions:
numberOfChildren = number of children numberOfHorses = number of horsesSo, we can write two equations according to the question:
The total number of eyes = 20 (which implies that numberOfChildren + numberOfHorses = 10, because each creature, whether child or horse, has two eyes)The total number of legs = 30 (which implies that 2*numberOfChildren + 4*numberOfHorses = 30, as each child has two legs and each horse has four)By solving these two equations, we find that the numberOfChildren = 5 and numberOfHorses = 5.
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PLEASE PLEASE HELP ME 25 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Washington longed to retire to his fields at Mount Vernon. But he soon realized that the Nation under its Articles of Confederation was not functioning well, so he became a prime mover in the steps leading to the Constitutional Convention at Philadelphia in 1787. When the new Constitution was ratified, the Electoral College unanimously elected Washington President.
Which provides the best objective summary of this excerpt?
A.)
Even though he was unanimously elected to be president, Washington wished he could retire to Mount Vernon instead.
B.)
The Constitution probably would not have been ratified if Washington had retired early at Mount Vernon instead of attending the Constitutional Convention.
C.)
Washington played a major role in the events that led to the ratification of the Constitution and was elected to be the country’s first president.
D.)
Even though he wished to retire, George Washington knew that the nation needed help, so he put a lot of effort into helping to develop the Constitution. Eventually, the Constitutional Convention took place in Philadelphia in 1787, and the Constitution was approved. Then, Washington was elected president of the country. The entire Electoral College voted for him.
D
It provides concise information which is derived from the question.
Connie is a nurse and works a 12 hour shift if she worked 4 hours what fraction of her shift does she still have to work
In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He figures he has time to make, at most, 25 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $675.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit? A. define variables B. Write the constraint inequalities that represent the situation, and explain what each of the inequalities represents. (You should have four inequalities.) C. What are the vertices of the feasible region?
We have defined two variables, bookshelves (b) and tables (t), to reflect the number of each that Andrew can make. The constraints representing time and cost are given by two inequalities and these produce a feasible region of possible combinations of bookshelves and tables. Within this region, Andrew can determine the combination that gives maximum profit.
Explanation:Let's define the variables: Let's say 'b' is the number of bookshelves Andrew makes and 't' is the number of tables he makes.
B. The constraint inequalities are: b + t <= 25 due to the time constraint, and 20b + 45t <= 675 due to the cost constraint. These inequalities represent the limit on the number of pieces he can make due to time and the limit due to money available to buy materials.
C. In this system of inequalities, the feasible region would be determined by finding the intersecting points (vertices) of our inequalities. The feasible region is the set of all points that satisfy all the constraints of the problem.
To ascertain the maximum profits, Andrew should calculate his profit for each possible combination of bookshelves and tables within the feasible region to find the combination with the maximum profit.
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If the sles tax price je 162 and had a markdown of 1/4 what is the original price
if a triangle has side lengths of 22,32,and 55 units what type of triangle is it
acute,obtuse,right,no solution
A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.
Explanation:A triangle with side lengths of 22, 32, and 55 units is an obtuse triangle.
To determine the type of triangle, we can use the Pythagorean theorem. If the sum of the squares of the lengths of the two shorter sides is greater than the square of the length of the longest side, then the triangle is obtuse. In this case, 22^2 + 32^2 = 484 + 1024 = 1508, which is greater than 55^2 = 3025, so the triangle is obtuse.
An obtuse triangle is a triangle with one angle greater than 90 degrees. In this case, the angle opposite the longest side will be greater than 90 degrees.
If 5 lemons are used to make a gallon of lemonade,how many lemons are needed to make 3 gallons
If Mary deposits $275 in principal at an interest rate of 3.2 percent,how much interest will she earn in one year
Final answer:
Mary would earn $8.80 in interest after one year on her deposit of $275 at an annual interest rate of 3.2%, using the simple interest formula.
Explanation:
To calculate the amount of interest Mary would earn from her deposits of $275 at an annual interest rate of 3.2%, we can use the formula for simple interest, which is:
Interest = Principal × rate × time
In this case, Mary's principal is $275, the rate is 3.2% (or 0.032 when expressed as a decimal), and the time is 1 year. Plugging these values into the formula gives us:
Interest = $275 × 0.032 × 1
Interest = $8.80
Therefore, Mary would earn $8.80 in interest after one year.
A family's vacation destination is 850 miles from their home. They travel by car 6 hours on the first day of their trip. Their average speed is 45 mph. The next day they travel 7 hours, averaging the same speed. How many miles are left for the family to travel?
Answer:256
Step-by-step explanation:
Answer:
265 miles.
Step-by-step explanation:
Carl ran 27 miles last week. This is 3 times farther than Anna ran. Which equation can be used to find how many miles Anna ran?
which one is it. please answer
a salesperson has averaged $120 in commissions for each of the past ten days. For how many days must her commissions average $160 in order to bring her overall average to %150?
Robert plans to make a box-and-whisker plot of the following set of data. 27, 14, 46, 38, 32, 18, 21 Which of the following should Robert's box-and-whisker plot look like?
Tricia is baking a key lime pie for her friends. She is baking the pie in a pie dish that is 9 inches in diameter. What is the circumference of her pie?
Answer: 28.26 inches
Step-by-step explanation:
We know that the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.
Given: The diameter of pie dish (d)= 9 inches
Then the circumference of the pie dish is given by :_
[tex]\text{Circumference}=\pi (9)\\\\\Rightarrow\text{Circumference}=(3.14)(9)\text{Circumference}=28.26\ inches[/tex]
45 brainliest pts.
Plz answer...
Answer:
3360
Step-by-step explanation:
45 plus 50 plus 55 plus 60 equals 3360 !
Find the volume of the rectangular prism
23 in.3
297 in.3
318 in.3
159 in.3
Plz help!!
How many times larger is the value 0.75 than the value 0.0075? Please show how to solve the problem.
The value 0.75 is 100 times larger than the value 0.0075.
To solve the problem, we need to determine how many times larger 0.75 is compared to 0.0075. This can be done by dividing the larger number by the smaller number and then simplifying the result.
First, write both numbers as fractions to make the division easier:
[tex]\[ 0.75 = \frac{75}{100} \][/tex]
[tex]\[ 0.0075 = \frac{75}{10000} \][/tex]
Now, divide the fraction representing 0.75 by the fraction representing 0.0075:
[tex]\[ \frac{0.75}{0.0075} = \frac{\frac{75}{100}}{\frac{75}{10000}} \][/tex]
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
[tex]\[ \frac{\frac{75}{100}}{\frac{75}{10000}} = \frac{75}{100} \times \frac{10000}{75} \][/tex]
The 75s in the numerator and denominator cancel out:
[tex]\[ \frac{75}{100} \times \frac{10000}{75} = \frac{10000}{100} \][/tex]
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 100:
[tex]\[ \frac{10000}{100} = \frac{100 \times 100}{100} = 100 \][/tex]
Tickets are priced as follows:
Adult Tickets -£12
Child Tickets -£6
Cheryl rings the booking office to buy 6 adult tickets and 3 child tickets
She is told that a 10% booking fee will be added to the ticket price
2% will then be added if she is paying by credit card
Work out the total charge that Cheryl will have to pay if she uses her credit card to pay for the tickets
Answer:
down there
Step-by-step explanation:
£72 + £18 = £90
90 x 12%= £9 + £1.80
£90 + £10.80 = £100.98
Namely is putting up a fence in her yard to make a dog run the dog run is 20 feet long and 15 feet wide how much fencing does she need for the dog run
How many times can 3 go into 9
A computer company uses the linear model y = -21x + 13,082 to predict the decline in sales of a computer after it has been on the market more than one year. If x is the number of months after the first year and y is the number of computers sold during that month, how many computers will be sold 11 months after the first year?
(6.03) what is the coefficient of the variable in the expression 6-4x-8+2
Solve the equation
5m-10n=20
Is this right. If so what’s the correct answer
The arena intends to give a gift box to each company that hires a stand at the event. Select from the options below the nets which will fold up into a cube.
What is the product?
6(x – 1)^2
6(x^2 – 1)
(x + 1)(6x – 1)
(x – 1)(6x – 1)
A chef mixed oil and vinegar to make a salad dressing she made enough dressing to fill 6 plastic bottles each bottle has 4/8 cup of olive oil and 2/8 cup of vinegar what was the total amount in cups of salad dressing the chef made?