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For the given polynomial P(x) and c = -4, use the remainder theorem to find P(c). P(x) = (2x^4 + 4x^2 + 7) P(c) = (Simplify your answer. Type an integer or a fraction.)
1. A car travels 180 miles using 6 gallons of gasoline. What is the constant of proportionality? 2. Explain what the constant of proportionality means in Question 1. 3. Two stud...
Create two different equations that each have a solution of x = 1 by using the digits 0 to 9 only once. Explain what you notice about your equations.
Eureka is 14 years younger than Renton. In 5 years Renton will be three times as old as Eureka. Eureka's current age: Renton's current age:
A marble statue is 51 years old and a limestone statue is 123 years old. In how many years will the limestone statue be twice as old as the marble statue? Answer: ____
Eri is planting a rectangular garden with a perimeter of 120 feet. The width is three times the length. Find the dimensions of her garden. Length: ___ ft Width: ___ ft
Jeane worked 49 hours one week and earned a $856.00 paycheck. She earns time and a half (1.5 times her regular hourly wage) for the number of hours she works in excess of 40. Wh...
A second number is three times a first number. A third number is 15 less than the first number. If the sum of the three numbers is 190, find the numbers.
One number is six more than a second number. Twice the first number is five more than three times the second. Find the numbers.
The sides of a triangle have lengths 3z, 7z + 5, and 5z + 4. If the perimeter of the triangle is 150, what is the value of z?
Kirino and Ria start a 10 mile race at the same time. If Kirino ran the race at 5 miles per hour and finishes the race 45 minutes after Ria, how fast does Ria run? Answer: ___ m...
Alphonse is a salesman that earns a base salary of $1,550.00 per month and a commission of 10% on the amount of sales he makes. One month Alphonse received a paycheck for $2,596...
Clare borrowed money from her parents at 5.1% simple interest to help pay her tuition. At the end of 1 year, she owed a total of $2,205.00 in principal and interest. How much di...
A freight train leaves a station and travels due east at a speed of 40 mph. One hour later, a passenger train leaves the same station and travels due east on a parallel track at...
Two cyclists start at the same point and travel in opposite directions. One travels 5 mph slower than the other. In 3 hours they are 105 miles apart. Find how fast each cyclist ...
What quantity of 71% hydrochloric acid solution must be mixed with a 18% hydrochloric acid solution to produce 8877.5 mL of 20% solution? Answer: ____ mL
Ron invested a total of $5,200.00, part at 5.5% simple interest and part 4.5% interest. At the end of one year, the investments had earned $267.00 interest. How much was investe...
A triangle's area is 201.5 m². Its base is 31 m. Its height is ____.
Phyllis invested 38000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After one year the total intere...
What quantity of 65 percent acid solution must be mixed with a 30 percent solution to produce 945 mL of a 50 percent solution?
How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar? __ gallons. Hint: You want the final percentage of pure vinegar to be ...
How many cups of grapefruit juice must be added to 60 cups of a punch that is 6% grapefruit juice to obtain a punch that is 10% grapefruit juice? Amount (in cups):
The radiator in a car is filled with a solution of 75 per cent antifreeze and 25 per cent water. The manufacturer of the antifreeze suggests that for summer driving, optimal coo...
Evaluate the expression i^105 and write the result in the form a + bi. The real number a equals The real number b equals
Write the following numbers in a + bi form: (a) (2 - 5i)^2 = [ ] + [ ]i (b) i(π - 3i) = [ ] + [ ]i (c) (-5 + 3i) / i = [ ] + [ ]i
Evaluate the expression (-4 - 1i)(1i) / (1 - 1i) and write the result in the form a + bi. Then a = ___ and b = ___.
Evaluate the expression (-9 - 10i) / (4 + 7i), and write your answer in the form a + bi. a = ____ and b = ____
Express the complex fraction below in standard form: \( \frac{1 - 3i}{2 + i} = \_\_ + \_\_ i \).
Evaluate the expression (1 - 3i) / (2 - 4i) and write the result in the form a + bi. The real number a equals [ ]. The real number b equals [ ].
Evaluate the expression \( \frac{4 + \sqrt{-9}}{2 + \sqrt{-1}} \) and write the result in the form \( a + bi \). The real number a equals The real number b equals
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