Bob runs 5 miles in 38 minutes. at the same rate, how many miles would he run in 57 minutes?
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
1. 7, 1+i
2.
The polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros 7, 1 + i, and 1 - i is f(x) = x^3 - 9x^2 + 21x - 14.
Explanation:In mathematics, zeros are the x-values where a function touches or crosses the x-axis, or the values where f(x) = 0. When a polynomial has rational coefficients and you have a complex zero (a + bi), the conjugate of that zero (a - bi) also needs to be a zero of the polynomial. This is based on the Complex Conjugate Root Theorem. Hence, in this case, the other zero will be 1 - i.
Since you are given zeroes of 7, 1 + i, and 1 - i, the polynomial function of least degree is obtained by employing the Factor Theorem, which states that if k is a zero of a polynomial, then (x - k) is a factor of the polynomial.
Therefore, f(x) = (x - 7)(x - (1 + i))(x - (1 - i)) = (x - 7)(x^2 - 2x + 2). So, f(x) = x^3 - 9x^2 + 21x - 14 is the polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros.
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Three consecutive odd integers have a sum of 33 . find the integers.
Given the statement "If Jack’s pet is a pig, then Jack’s pet cannot fly,” which statement represents the converse?
q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly~q → ~p, where p = Jack’s pet cannot fly and q = Jack’s pet is a pig p → q, where p = Jack’s pet is a pig and q = Jack’s pet cannot flyq → p, where p = Jack’s pet is not a pig and q = Jack’s pet is a pig
the answer is A just had the practice quiz
Converse statement of "If Jack’s pet is a pig, then Jack’s pet cannot fly,” is given by " q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly."
What is converse statement?" Converse statement is defined as when the hypothesis and conclusion of a statement interchange or reversed."
According to the question,
Given,
p → q
Hypothesis of a statement 'p': If Jack’s pet is a pig
Conclusion of a statement 'q' : then Jack’s pet cannot fly
Converse of a statement is given by reversing hypothesis and conclusion we get,
q → p
Hypothesis of a statement 'q' : If Jack’s pet cannot fly
Conclusion of a statement 'p': then Jack’s pet is a pig
Hence, converse statement is given by q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly.
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Write an equivalent expression for 5x + 2y + 3x
The equivalent expression is 8x + 2y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
5x + 2y + 3x
Add like terms.
8x + 2y
Thus,
The final expression is 8x + 2y.
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Which is a correct expansion of (2x+3)(2x^2-5)
A. 2x•2x^2+2x•(-5)+3•2x+3•(-5)
B. 2x•2x^2+2x•(-5)+3•2x^2+3•(-5)
C. 2x•2x^2+3•2x^2+2x^2•(-5)+3•(-5)
Answer: B
2X.2X^2+2X.(-5)+3.2X^2+3.(-5)
Step-by-step explanation:
(2X+3) (2X^2-5)
Cross multiply (2X+3) by (2X^2-5)
2X*2X^2+
2X*(-5)+
3*2X^2+
3*(-5)
= 2X*2X^2+2X*(-5)+3*2X^2+3*(-5)
The petting zoo is not closed and the animals are not being fed by people.
write the statement that is logically equivalent to the statement
De Morgan's laws of distributing negation over disjunction and conjunction states that
A car traveled 360 km in 6 h. A train traveled 400 km in 8 h. A boat traveled 375 km in 5 h. Which has the fastest average speed
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
____ units
The other answer was using the formula correctly through most of the problem, but made a mistake when finding the last distance (#5). The person took away (-2-6 = - 4), which is incorrect. The correct answer is -8 because your adding two negatives. So, the correct answer for the whole problem is 24 units.
Good job to the person who answer they did the whole math problem - just made a little mistake at the end.
How to find third point between two points given coordinates?
A squirrel is traveling at a rate of 12 miles per hour. Write the rate in miles per minute.
1 hour = 60 minutes
12/60 = 0.2 miles per minute
A cylinder has a radius of 6 inches and a height of 2 feet. Which of the following should be done first in order to find the volume of the cylinder?
convert the radius and the height to the same unit
determine the diameter of the circle
calculate the circumference of the circle
multiply the circumference of the circle by the height of the cylinder
Which equation exemplifies the Associative property of addition?
8+2=2+8
4+(2+1) = (4+2)+1
4+5=1+8
9(5•6)=(9•5)6
Answer:
Equation which exemplifies the associative property of addition is:
4+(2+1) = (4+2)+1
Step-by-step explanation:
The associative property of addition says that:
if a,b and c are the three terms
Then,
a+(b+c)=(a+b)+c
which is given in the equation:
4+(2+1) = (4+2)+1
Hence, equation which exemplifies the associative property of addition is:
4+(2+1) = (4+2)+1
A stock market analyst observes the following for the price of two stocks that he owns, one of which is increasing at an exponential rate (geometric) and the other is increasing in a linear fashion (arithmetic).
Stock A: Equation: an = 15n + 130, where an is the value of the stock and n is the number of years.
Year Price
1 $145.00
2 $160.00
3 $175.00
4 $190.00
5 $205.00
Stock B: Equation: an = 36(1.09)n − 1, where an is the value of the stock and n is the number of years.
Year Price
1 $36.00
2 $39.24
3 $42.77
4 $46.61
5 $50.82
Assuming these stock values continue to increase in the same manner until retirement, which stock option is worth more in 50 years and how much more is this stock worth per share?
OPTIONS:
A) Stock B is worth more in 50 years, $1,575.84 more per share
B) Stock A is worth more in 50 years, $1,364.08 more per share
C) Stock B is worth more in 50 years, $1,796.87 more per share
D) Stock A is worth more in 50 years, $880.00 more per share
Stock B is worth more in 50 years, $1,575.84 more per share.
Explanation:To determine which stock option is worth more in 50 years, we need to find the value of each stock after 50 years.
For Stock A, we have the equation: an = 15n + 130. Plugging in n = 50, we get a50 = 15(50) + 130 = $880.
For Stock B, we have the equation: an = 36(1.09)n - 1, where n is the number of years. Plugging in n = 50, we get a50 = 36(1.09)^50 - 1 = $2,455.84.
Therefore, Stock B is worth more in 50 years, $1,575.84 more per share.
On a clear day you can see about 27 miles from the observation deck of the Empire State Building in New York City. Using the formula below, estimate the height in feet ,h, of the observation deck.
Answer:
Step-by-step explanation:
Alright, lets get started.
Distance we can see from the building d is given as 27 miles.
We are asked to find height of the building h
The formula is given as [tex]d=\frac{5}{6}\sqrt{h}[/tex]
Plugging the value of d
[tex]27=\frac{5}{6}\sqrt{h}[/tex]
Cross multiplying
[tex]\sqrt{h}=\frac{6}{5}*27[/tex]
[tex]\sqrt{h}=32.4[/tex]
Taking square root on both sides
[tex]h=1049.76[/tex]
So, the height of the observation desk is 1050 feet. : Answer
Hope it will help :)
Mari has a part time job. She earns $7 an hour. She makes at most $143.50 a week. What is the greatest number of hours that she works?
Mari works at most 20 hours per week.
Explanation:To find the greatest number of hours that Mari works, we can divide her total weekly earnings by her hourly wage. In this case, we divide $143.50 by $7. The result is approximately 20.5. Since Mari cannot work a fraction of an hour, we round down to the nearest whole number. Therefore, the greatest number of hours she works is 20 hours.
A survey at your school found that 792 in 1,220 students have a cell phone. what percent of the students in school has a cell phone? round to the nearest hundredth where necessary.
64.84% of the students in the school have a cell phone.
To find the percentage of students with cell phones, divide the number of students with cell phones by the total number of students, then multiply by 100.
Find the fraction of students with cell phones: [tex]\( \frac{792}{1220} \)[/tex].
Divide to get the decimal: [tex]\( \frac{792}{1220} = 0.6484 \)[/tex].
Multiply by 100 to get the percentage: [tex]\( 0.6484 \times 100 = 64.84\% \)[/tex].
at a local pizza parlor, patrons have 2 choices of cheese and 14 choices of topping. in how many different ways can a patron choose 1 type of cheese and 1 type of topping?
30
28
16
2
HELP PLEASE!!!!!!!
Simplify 6r · s · 4rt.
10rst
10r2st
24r2st
Answer:
24r^2*s*t
Step-by-step explanation:
We can simply the following expression by looking at the which terms are common:
[tex]6*r*s*4*r*t[/tex]
We have two of r and according to the product rule we can add there exponents:
[tex]r*r=r^(1+1)=r^2[/tex]
Therefore the expression can be simplified as:
[tex]=6*4*s*t*r^2=24*s*t*r^2[/tex]
The measure of each interior angle of a regular polygon is eleven times that of an exterior angle how many sides does the polygon have
The polygon would have 24 sides.
[tex]\frac{180n - 360}{n}[/tex] ≈ [tex]\frac{360}{n}[/tex] ([tex]\frac{11}{1}[/tex])
[tex]\frac{180n - 360}{n}[/tex] = [tex]\frac{3960}{n}[/tex]
180n - 360 = 3,960
180n = 4,320
n = 24
The lengths of the sides of a triangle are 8, 15, and 17. if the longest side of a similar triangle is 51, what is the length of the shortest side?
he length of the shortest side is 32
Similar triangles and scale factorsGiven the length if the sides of the triangle to be 8, 15 and 17. If the longest side of a similar triangle is 51, then the scale factor will be expressed as:
Scale factor = 51/17
Scale factor = 4
For the shortest side;
Length = 8 * scale factor
Length = 8 * 4
Length = 32
Hence the length of the shortest side is 32
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k + k divided by 2 when k = 20
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven. You drove 15 miles over to your grandma house . How many cups of oil did your car leak ?
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven. You drove 15 miles over to your grandma's house. Therefore, it would be 2 cups and 4 oz leaked out.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven. You drove 15 miles over to your grandma's house.
There are 8 oz in a cup
So,
8 x 3 = 24 which is too high
So,
8 x 2 = 16 leaving about 4 oz left
Therefore, it would be 2 cups and 4 oz leaked out.
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What geometric term does the flight path of a plane on radar represent?
A line B plane C angle D point
the answer is A. Line
The Geometric Term that best approximates this reality is option A (A line).
Planes usually travel in a straight Line at constant Speed, Flight Path represents the Trajectory taken by the Plane and shown on radar, which can be either a Line or a Curve.
Hence, the Geometric Term that best approximates this reality is option A (A line).
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Yulian works at the zoo feeding the animals. He puts water in the elephant habitat at the beginning of the day. This table shows how much water, in gallons, remains at different times during the day. Time (h) 2 4 6 8 Water remaining (gal) 43 36 29 22 What is the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water? Enter your answer in the boxes. y−29=___ (x−___ )
How to find the rate of change of the volume of cone?
Select the equation that most accurately depicts the word problem.
The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.
68 = 9L + 2
68 = 2L + 2(9)
68 = 9(L + 2)
68 = + 2(9)
68 = +
68 = 2(L - 9)
Answer:
68 = 2L + 2(9)
Step-by-step explanation:
How is 10 ounces written using apothecary abbreviations?
Apothecary abbreviations or apothecary symbols are usually found in medical recipes. For this case, we are to write 10 ounces into apothecary symbols. In this abbreviation, numbers are written in Roman Numeral and the unit precede the number, hence:
oz x
10 ounces can be written as 10 oz in apothecary abbreviations.
Explanation:To write 10 ounces using apothecary abbreviations, we need to convert ounces to the appropriate apothecary unit. In the apothecary system, 1 ounce is abbreviated as oz. So, 10 ounces would be written as 10 oz in apothecary abbreviations.
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Find the derivative of f(x) = 7 divided by x at x = 1.
The solution is, the derivative of f(x) = 7 divided by x at x = 1 is -7.
What is derivative?A derivative is described as either the rate of change of a function, or the slope of the tangent line at a particular point on a function.
here, we have,
given that,
the derivative of f(x) = 7 divided by x at x = 1.
so, we get,
F(x) = 7/x
Same as..
F(x) = 7x^-1
we know that,
d/dx (x^n) = n*x^n-1
so, using this, we get,
Take derivative..
F'(x) = -7x^-2
Plug in x = 1
F'(1) = -7(1)^-2
F'(1) = -7
Hence, The solution is, the derivative of f(x) = 7 divided by x at x = 1 is -7.
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3(6/8−1/2)+0.25 Please help with fractions