To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations and solve them using substitution or elimination.
Explanation:To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations. Let's assume the two numbers are x and y. From the given information, we have the following equations:
x - y = 2828
xy = 39003900
We can solve this system of equations by substitution or elimination. Let's use the substitution method:
From the first equation, we can express x as y + 2828. Substituting this into the second equation, we get (y + 2828)y = 39003900. Simplifying, we get y^2 + 2828y - 39003900 = 0.
Now we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula. Once we find the value of y, we can substitute it back into the first equation to solve for x. This will give us the two positive numbers.
Find the fifth term of an=2(-1) n
Answer:
The fifth term of [tex]a_n = 2(-1)^n[/tex] is, -2
Step-by-step explanation:
Given the sequence:
[tex]a_n = 2(-1)^n[/tex] .....[1]
where,
n is the number of terms.
To find the fifth term of the given sequence:
Substitute n = 5 in [1] we have;
[tex]a_5 = 2 \cdot (-1)^5[/tex]
⇒[tex]a_5 = 2 \cdot -1 = -2[/tex]
Therefore, the value of fifth term of [tex]a_n[/tex] is, -2
If the polynomial P(x) has roots −5, −1, 2, and 2, which of the following represents the factored form of function P(x)?
6 identical toys 1.8kg. B) what is the weight of one toy? give your answer in grams. C) what is the weight of 4 toys? give your answer in kilograms.
Total weight of six identical toys = 1.8 Kg
Therefore, the weight of one such toy = 1.8 kg/ 6 = 0.3 kg
Further, 1 kg = 1000 gms
Answer to Ques B-
Weight of one toy in grams = 0.3 * 1000 grams
= 300 grams
Answer to Ques C-
Weight of 4 toys in kilograms = 0.3 * 4 kilograms
= 1.2 kilograms
Hope this helps..!!
Thank you :)
Which of the polygons listed below have at least three angles?
I Triangles
II Quadrilaterals
III Pentagons
IV Hexagons
A. III and IV
B. II, III, and IV
C. I, II, III, and IV
D. IV
Find the general solution to y′′+7y′=0y′′+7y′=0. give your answer as y=..
The difference between two numbers is 66. The sum of the two numbers is 88. Find the greatest number
There are 203 apples in a basket. How many children can share these apples equally? How many apples would each child get?
Question#1: All possible numbers of children in ascending order are:
Question#2: All possible numbers of apples in descending order are:
please help!!!!!!!!!
Answer:
Question 1: 1, 7, 29, 203
Question 2: 203, 29, 7, 1
Step-by-step explanation:
Please help me with question 6
The formula V = πd2h 8 is used to find the volume of a parabolic cone. In the formula "d" represents the diameter of the cone and "h" represents the height. What is the volume of the parabolic cone that is 6 cm in diameter and 12 cm in height? A) 36π cm3 B) 48π cm3 C) 54π cm3 D) 60π cm3
Answer:
V = 54π cm³ ⇒ answer (C)
Step-by-step explanation:
∵ V = (πd²h)/8
∵ d = 6 cm
∵ h = 12 cm
∴ V = (π × 6² × 12) ÷ 8 = 54π cm³
Final answer:
To find the volume of a parabolic cone with a diameter of 6 cm and height of 12 cm using the formula V = πd²h/8, calculate the radius (3 cm), square it, multiply by the height, divide by 8, and then multiply by π, resulting in 54π cm³(Option C).
Explanation:
The student's question pertains to calculating the volume of a parabolic cone using a specific formula, which is V = πd²h/8, where d is the diameter and h is the height of the cone.
Given the cone's diameter (d) of 6 cm and height (h) of 12 cm, we can plug these values into the formula to find the volume:
First, calculate the radius (r) of the cone by dividing the diameter by 2: r = d / 2 = 6 cm / 2 = 3 cm.Next, plug the radius and height into the formula and calculate the volume:Therefore, the volume of a parabolic cone with a diameter of 6 cm and a height of 12 cm is 54π cm³.
Japan accounts for about 5.4% of the world's petroleum consumption. Write this percent as a fraction.
"The correct fraction representing Japan's petroleum consumption as a percentage of the world's total is [tex]\(\frac{5.4}{100}\).[/tex]
To express the given percentage as a fraction, one must divide the percentage by 100, since percentages are parts per hundred. T
hus, 5.4% can be written as a fraction by placing 5.4 over 100, which gives us [tex]\(\frac{5.4}{100}\)[/tex].
Finally, this fraction can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 2 in this case, yielding the simplified fraction [tex]\(\frac{27}{500}\).[/tex]
When reduced to a fraction without a decimal, [tex]\(\frac{27}{500}\)."[/tex]
Evaluate the function at the indicated value of x. Round your result to three decimal places
F(x)=500e(0.05)^x with a value x=2
The given function is represented below:
F(x)=500e^(0.05)x with a value x=2
or, F(x) = 500 * e^(0.05*2)
( putting the value of x as 2 )
or, F(x) = 500 * e^(0.1)
or, F(x) = 500 * e^0.1
or, F(x) = 500 * e^(0.1)
or, F(x) = 500 * 1.10517092
or, F(x) = 552.585459
The value of the function at x = 2, rounded off to 3 decimal places is given by 552.585
Hope this helps..!!
Thank you :)
What is the area of this trapezoid? Enter your answer in the box. units2 A rectangle with a length of 10 and a height of 9 has two right triangles on each side of it with short leg lengths of 9.
In a factory a manager tests 250 products and find defcts in 7 of them how many defcts are likely going to be in 10000 unit order
There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 2?
The probability that a spinner with 14 equal areas lands on a multiple of 5 or a multiple of 2 is 4/7, after identifying the unique numbers from 1 to 14 that fit the criteria and dividing by the total number of possible outcomes.
The student is asking about the probability of an event occurring after spinning a spinner with 14 equal areas numbered 1 through 14. Specifically, the question seeks the probability that the result is either a multiple of 5 or a multiple of 2 when the spinner is spun once.
To solve this, first identify the multiples of 5 and 2 between 1 and 14: for 5, the multiples are 5 and 10; for 2, the multiples are 2, 4, 6, 8, 10, 12, and 14. Here, the number 10 is a multiple of both 5 and 2, so it should only be counted once. In total, there are 8 unique numbers that are multiples of 2 or 5 on the spinner. Since there are 14 possible outcomes, the probability is:
Probability = Number of favorable outcomes / Total number of outcomes = 8 / 14 = 4/7.
Thus, the probability that the spinner lands on a multiple of 5 or a multiple of 2 is 4/7.
a cylinder shaped drum is used as a garbage container. The drum has a height of 4 ft and a radius of 1.25 ft how many cubic feet of garbage does the drum hold ? enter your answer as a decimal rounded to the nearest hundreth
Answer:
19.63
Step-by-step explanation:
The price of a shirt was $38. It was reduced by 20% and then again by 10%. What would the price of be if it were reduced by 30% from the original
Original Price of the shirt is $38.
Double discount :
Given that it was reduced by 20%, means
[tex] \\ Cost \; of \; Shirt\; after\; 1^{st}\; discount (20\%)\\ \\= \; (100\; - \; 20) \%\; of \; Original Price=\; 80\%\; of\; \$38\\ \\ = \frac{80}{100} \times 38\; =\; \frac{3040}{100}\; =\; \$30.40\\ \\ Cost \; of \; Shirt \; after\; 2^{nd}\; discount(10\%)\\ \\ (100 - 10)\%\; of\; $30.40=90\%\; of\; \$30.40\\ [/tex]
[tex] =\frac{90}{100} \times 30.40 = \frac{2736}{100}= \$27.36 \\ \\ After \; double \; \; discount,(20\%\; of\; Original\; Price, again\; 10\%\; reduced\; )\\\\ Double \; Discounted \; Price = \$ 27.36\\ \\ But \; After\; single \; discount\; of\; 30\%\; of\; Original \; Price, \; we\; get\\ \\ (100-30)\%\; of \; \$38=70\% \times \$38=\; \frac{70}{100} \times 38 =\frac{2660}{100}=\$26.6 [/tex]
Megan buys 3 bracelets and 3 necklaces. Each bracelet costs 5. Megan pays on 40 and gets 4 change. what is the cost of one necklace?
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The area of a circle is 113.04 in. 2. What is the radius of the circle? 36 inches 18 inches 12 inches 6 inches
evaluate if hj + h if h = 6 and j = 8
What is three fourths multiplied by 24
a collection of dimes and nickels is worth $8.40 there are 106 coins how many of each are there
Convert 30 gallons to liters using an equivalent rate
the distance around a circle (the circumference) is about 3.14 times the diameter. If a circulares table has a diameter of 3 feet What is the circumference can somebody please help me I'm stuck xD
Please help me questions 9 and 10
Use the distributive property to simplify the expression. 8(3 + 4) = 24 +
If a ploynominal has four terms 3x^3+5x+6x^2+10 which factoring method can be considered
Answer:
(c) Factor by Grouping
(−6)∙(a+2b−3c−4d)−(−2)∙(−4a−3b+2c+d)
Answer:
-14a-18b+22c+26d
given the input in the table which function rule produces the output?
Answer: b) [tex]f(x)=4x+2[/tex]
Step-by-step explanation:
The given table :-
Input 4 5 7 8
Output 18 22 30 34
Let's check all the options
a) [tex]f(x)=5x-2[/tex]
At x= 4, [tex]f(4)=5(4)-2=18[/tex]
At x= 5 , [tex]f(5)=5(5)-2=25-2=23\neq22[/tex] , thus it not the correct function.
b) [tex]f(x)=4x+2[/tex]
At x= 4 , [tex]f(4)=4(4)+2=18[/tex]
At x= 5 , [tex]f(5)=4(5)+2=22[/tex]
At x= 7 , [tex]f(7)=4(7)+2=30[/tex]
At x= 8 , [tex]f(8)=4(8)+2=34[/tex] , thus it is the function rule that produces the output.
c) [tex]f(x)=3x+6[/tex]
At x= 4 , [tex]f(4)=3(4)+6=18[/tex]
At x= 5 , [tex]f(5)=3(5)+6=21\neq22[/tex] , thus it not the correct function.
d) [tex]f(x)=2x+10[/tex]
At x= 4 , [tex]f(4)=2(4)+10=18[/tex]
At x= 5 , [tex]f(5)=2(5)+10=20\neq22[/tex] , thus it not the correct function.
Hence, the correct function rule that produces the output = b) [tex]f(x)=4x+2[/tex]
Lalo has 1500 minutes per month on his cell phone plan. How many more minutes can he use if he has already talked for 785 minutes? What is the interpretation?
Calculate the resistance of a piece of aluminum wire with a diameter of 100 mils and a length of two miles, at 68°F. Hint: Be sure to first convert mils to cmils and use the K value for aluminum found in the reference. (Round the FINAL answer to two decimal places.)
This answer calculates the resistance of an aluminum wire of specific dimensions. It begins by determining the cross-sectional area of the wire, then uses a formula incorporating resistivity, length, and area to calculate resistance. The final resistance of the wire is approximately 0.037 Ohms.
Explanation:To calculate the resistance of a piece of aluminum wire, we first need to figure out the cross-sectional area of the wire. As given, the diameter of the wire is 100 mils. To convert mils to cmils (circular mils), we square the diameter, thus 100^2 = 10,000 cmils is the cross-sectional area.
Next, we use the formula for resistance: R = ρL/A, where R is the resistance, ρ (Rho) is the resistivity of the material (aluminum, in this case), L is the length in feet, and A is the cross-sectional area in circular mils (cmils).
We need to convert the length from miles to feet (1 mile = 5,280 feet), so 2 miles = 10,560 feet. The resistivity of aluminum at 68°F is approximately 10.75 nanoOhms*meter, to convert this to Ohms*foot we multiply by 3.281, so ρ becomes approximately 35.28 nΩ/ft.
The resistance R can then be calculated as follows: R = ρL/A = (35.28 x 10^-9) x 10,560 / 10,000 = 0.037 Ohms, rounded to two decimal places.
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