The other two zeros, which are x = 5 and x = -4.
To find the zeros of the polynomial f(x) = x³ − x² − 20x, we need to set the polynomial equal to zero and solve for x. This can be done by factoring out the common term x from each term of the polynomial:
f(x) = x(x² - x - 20) = 0
The zeros of the polynomial will be the values of x for which the product is zero. Since we already have x as one factor, one zero is x = 0. We then need to factor the quadratic, which is:
x² - x - 20
We can factor this quadratic to
(x - 5)(x + 4)
Thus, the other two zeros of the polynomial are x = 5 and x = -4.
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. C = 71°, a = 27, c = 26
We have
SinC/ c = Sin A / a
Sin 71/ 26 = Sin A / 27
Sin A = 27 Sin 71 / 26 = about .982
So°
Sin-1(.982) = A = 79. 08°
Then angle B = 180 - 71 - 79.08 = 29.92°
And b is given by
b/sin29.92 = 26/sin 71
b = 26sin29.92/sin71 = about 13.72
But A could also be an obtuse angle = 180 - 79.08 = 100.92°
So we have
B = 180 - 71 - 100.92 = 8.08°
And we have
b / sin 8.08 = 26/sin71
b = 26sin8.08/sin 71 = 3.865
Write the equation of a line perpendicular to the line 3x +7y =21 with a y-intercept of (0, 2). Write your answer in standard form. Please explain how I can solve this, please!
max is four years younger than his sister brenda. the total of their age is 16. write and solve an equation to find their ages.
If AB - 27 and BC=13 then find the length of AC
What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?
Answer:
Step-by-step explanation:
What you have todo is to multiply the length by the width
Which is 20×12 = 240
Then multiply 240 by 8.91
This should give you $2,138.4
Mindy is 36 years old. Mindy’s age is 3 years older than two times Jake’s age. Let j represent Jake’s age.
Find the quotient of the quantity negative 6 times x to the 2nd power times y to the 8th power plus 12 times x times y to the 3rd power minus 36 times x times y to the 2nd power all over 6 times x times y to the 2nd power.
Answer:
The quotient is:
[tex]xy^6+2y-6[/tex]
Step-by-step explanation:
We are asked to find the quotient of the mathematical expression which is given in terms of variable x and y is represented as:
[tex]=\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}[/tex]
Here the numerator is:
[tex]6x^2y^8+12xy^3-36xy^2[/tex]
and the denominator is:
[tex]6xy^2[/tex]
We can also represent our numerator term by the method of factoring it as:
[tex]6x^2y^8+12xy^3-36xy^2=6xy^2(xy^6+2y-6)[/tex]
Hence, our expression gets converted by replacing the numerator term to:
[tex]\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=\dfrac{6xy^2(xy^6+2y-6)}{6xy^2}\\\\\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=xy^6+2y-6[/tex]
Hence, the quotient is:
[tex]xy^6+2y-6[/tex]
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice all together
3/4 = 9/12
9/12 + 7/12 = 16/12 = 1 4/12 = 1 1/3 hours
help me pls I'm stuck......
subtracting the smaller number from the larger number
ex. 1+ -5 becomes 5-1 = 4, since the larger number is the negative, the answer is negatives oit is -4
ex2. -5+7 = 7-5 = 2, since the larger number is positive, the answer is positive 2
The question is above
The ratio of male students to female students is 4 to 5. if there is a total of 6192 students, find the number of male syudents to the number of female students
(a^2^n - a^n - 6) / (a^n + 8) That's a power of 2n the 2n is an exponent
For the above table:
x . 0.5 Y. 3 x.2 ,y 6, x 2, y 9 , x 2.5 y 12 , x 3, y 15
a. State the domain.
b. State the range.
c. Is this relation a function? Why or why not?
(2 points)
a) domain are the x's
so 0.5, 2, 2,2.5, 3
b) range is the y's so:
3, 6, 9, 12,15
c) it is not a function, since there are 2 x's that equal 2 but the 2 y's that go with them are different numbers (2,6) & (2,9)
Find the perimeter of △ABC with vertices A(−5, −5), B(3, −5), and C(−5, 1).
An airplane has a total of 414 packets of crackers, pretzels, and peanuts available for passengers.
There are n packets of crackers.
There number of packets of pretzels is 9 more than twice the number of packets of crackers.
The number of packets of peanut is 3 times the number of packets of pretzels.
Part B
The airplane has seats for 144 passengers. The seats are arranged in 48 rows, with 3 seats in each row.
There are 132 passengers on a certain flight.
There are exactly 2 passengers in x rows.
There are exactly 3 passengers in y rows.
Write a system of linear equations that can be used to model the situation. Use your system to determine the number of rows with exactly 2 passengers and the number of rows with exactly 3 passengers. Show your work.
A system of linear equations can be used to model the given situation. The number of rows with exactly 2 passengers can be found by solving the equation 2x = 12, and the number of rows with exactly 3 passengers can be found by solving the equation 3y = 12.
Explanation:To write a system of linear equations, we need to translate the given information into algebraic expressions.
Let n be the number of packets of crackers.
According to the problem:
The number of packets of pretzels is 9 more than twice the number of packets of crackers: p = 2n + 9The number of packets of peanuts is 3 times the number of packets of pretzels: pn = 3(2n + 9)To determine the number of rows with exactly 2 passengers and 3 passengers:
Let x be the number of rows with exactly 2 passengersLet y be the number of rows with exactly 3 passengersThere are 48 rows and 3 seats in each row, so the total number of seats is 48 * 3 = 144132 passengers are on the flight, so there are 144 - 132 = 12 unoccupied seatsEach row with exactly 2 passengers contributes 2 unoccupied seats, so 2x = 12Each row with exactly 3 passengers contributes 3 unoccupied seats, so 3y = 12The system of linear equations is:
p = 2n + 9
pn = 3(2n + 9)
2x = 12
3y = 12
We can solve this system of equations to find the values of x and y.
Suppose M is the midpoint of FG. Use the given info. to find the missing measure or value. FM=3X-4, MG=5X-26, FG=?
Answer:FG=29+29
Step-by-step explanation:
A cube has eight congruent faces.
true
false
Deangelo has $7 worth of dimes and quarters in a jar. He has 7 more quarters than dimes.
How many of each coin does he have?
How does the value of 2 dimes compare to the value of 2 dollars
Answer:
[tex]\text{2 Dimes}< \text{2 Dollars}[/tex]
Step-by-step explanation:
A dime has a value of 10 cents. It is a 10 cent coin.
So, the value of 2 dime = [tex]2\times10 = 20 \text{ cents}[/tex]
Now, 1 dollar consist of 100 cents.
1 dollar = 100 cents
so, the value of 2 dollars = [tex]2\times100 = 200\text{ cents}[/tex]
Comprinf, 2 dimes and 2 dollars, we have,
[tex]\text{2 Dimes}< \text{2 Dollars}[/tex]
as
[tex]\text{20 Cents}< \text{200 Cents}[/tex]
If the measure of Angle AXC=8x-7 and Angle AXB = 3x+10 find the measure of ANGLE AXC
To find the measure of ANGLE AXC, we assume Angle AXB is supplementary to Angle AXC. Solving the supplementary angle equation with the given expressions, we find x = 16. Substituting x back into the expression for Angle AXC, we determine its measure to be 121 degrees.
The question asks to find the measure of ANGLE AXC given that the measure of Angle AXC is represented by the expression 8x-7 and Angle AXB is represented by the expression 3x+10. Without additional context, it is not clear whether Angle AXB is related to Angle AXC in a way that would allow us to solve for x. However, if we assume Angle AXC and Angle AXB are supplementary angles (which sum to 180 degrees), we could set up the equation 8x - 7 + 3x + 10 = 180. If we solve this equation, we get:
Combine like terms: 8x + 3x - 7 + 10 = 180Simplify: 11x + 3 = 180Subtract 3 from both sides: 11x = 177Divide by 11: x = 16Once we have found that x = 16, we can substitute it back into the expression for Angle AXC:
AXC = 8x - 7 = 8(16) - 7Calculate the value: AXC = 128 - 7Simplify: AXC = 121 degreesTherefore, the measure of ANGLE AXC is 121 degrees.
A student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of
b. devon's grades on the first four tests were 92%, 82%, 88%, and 92%. what range of grades on the fifth test would give him a b in the course?
The requried, Devon needs to score between 46% and 95% on the fifth test to receive a final grade of a B in the course.
To find the range of grades Devon needs on the fifth test to receive a final grade of a B (between 80% and 90% inclusive), we need to consider the average of all five tests.
Let's denote the grade on the fifth test as "x" (in percentage).
The average of the five tests will be:
Average = (92% + 82% + 88% + 92% + x) / 5
To achieve a final grade of a B, the average must be greater than or equal to 80% but less than 90%:
80% ≤ Average < 90%
Now, substitute the given grades and the variable "x" into the average equation:
(92% + 82% + 88% + 92% + x) / 5 ≥ 80%
(92 + 82 + 88 + 92 + x) / 5 ≥ 80
(354 + x) / 5 ≥ 80
354 + x ≥ 400
x ≥ 400 - 354
x ≥ 46
Now, for the upper limit:
(92 + 82 + 88 + 92 + x) / 5 < 90
(354 + x) / 5 < 90
354 + x < 450
x < 450 - 354
x < 96
So, Devon needs to score between 46% and 95% on the fifth test to receive a final grade of a B in the course.
Learn more about averages here:
https://brainly.com/question/28883997
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Devon must score between 46% and 91% on his fifth test to achieve a B average in the course.
Explanation:To determine the range of grades on the fifth test that would give Devon a final grade of B, we need to calculate the average of the five test scores. For an average to fall between 80% and 90%, the total sum of the five test grades must be between 400% and 449%, since 5 tests × 80% = 400% and 5 tests × 89% (just below 90%) = 445%. Devon's current grades add up to 92% + 82% + 88% + 92% = 354%. Therefore, to achieve a B, his fifth test score needs to be between 400% - 354% = 46% and 445% - 354% = 91%.
Which equation can be used to solve this problem?
Molly bought 6 packs of trading cards. Each pack cost $3. She also bought 1 pack of gum. It cost $2. How much did Molly spend altogether?
A.
6 ÷ 2 × 3 = x
B.
6 + 3 × 2 = x
C.
6 × 3 ÷ 2 = x
D.
6 × 3 + 2 = x
Two cars start at the same time, but travel in opposite directions. one car's average speed is 20 miles per hour (mph). at the end of 4 hours, the two cars are 320 miles apart. find the average speed in mph of the other car. (enter an exact number.)
Final answer:
The question asks for the average speed of the second car given that two cars travel in opposite directions and the total distance between them after 4 hours. By calculating the distance one car traveled at 20 mph after 4 hours, it's possible to determine that the other car must have traveled at an average speed of 60 mph to cover the remaining distance.
Explanation:
The student's question is a problem involving distance, speed, and time, which are fundamental concepts in mathematics. To find the average speed of the other car, we can use the formula distance = speed times time. Since the two cars travel in opposite directions, their distances add up to the total separation distance after a certain time.
In this case, one car travels at 20 mph, so in 4 hours it covers 20 mph times 4 h = 80 miles. The total distance between them after 4 hours is 320 miles. Therefore, the distance covered by the second car is 320 miles - 80 miles = 240 miles. To find the average speed of the second car, we divide the distance it covered by the time it traveled which is 240 miles / 4 h = 60 mph. Hence, the average speed of the other car is 60 mph.
Find the value of x if B is between A and C AB=4x-9 BC= 3x+5 and AC = 17
Chris went to the store to purchase 6.5 gallons of milk. When he got to the store, he noticed that the milk was no longer sold in gallons but in liters. Which of the following shows the number of liters, with the correct number of significant digits, Chris needs to buy in order to have 6.5 gallons of milk? (1 liter = 0.26418 gallon)
6.5 gallons = 24.6052 liters
6.5 has 2 significant figures, so it would need to be 25 liters
Using radicals what is an equivalent expression of y 1/5
You are making gift baskets. each basket will contain three different types of candles: tapers, pillars ad jar candles. tapers cost $1 each, pillars cost $4 each, and jar candles cost $6 each. you put 8 candles costing a total of $24 in each basket, and you include as many tapers as pillars and jar candles combined. how many of each type of candle will be in a basket?
Please explain the answer.
Give an example of two numbers that differ by an order of magnitude
Final answer:
The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. For example, 10¹, 10², 10³, and so forth are all different orders of magnitude.
Explanation:
The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. For example, 10¹, 10², 10³, and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of 10 are said to be of the same order of magnitude. For example, the number 800 can be written as 8 x 10², and the number 450 can be written as 4.5 x 10². Thus, the numbers 800 and 450 are of the same order of magnitude: 10². Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10⁻⁹ m, while the diameter of the sun is on the order of 10⁹ m.
Marcus has $40 in his pocket. Joseph has twice as much as Marcus; Jenna has half as much as Marcus, and Sam has 1/3 as much as Marcus. Order the individuals based on the amount of money they have from least to greatest