What two numbers multiple to 160, and add up to -4?
Answers
Let X be one number and Y be other number. Then, we can write
\(X\cdot Y=160\)and
\(X-Y=-4\)By moving -Y to the right hand side, we get
\(X=Y-4\)By substituting the last expression into the first one, we get
\((Y-4)\cdot Y=160\)which gives
\(\begin{gathered} Y^2-4Y=160 \\ Y^2-4Y-160=0 \end{gathered}\)So, we have a quadratic function, which we can solve by means of the quadractic formula:
\(Y=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(-160})}{2}\)which gives
\(\begin{gathered} Y=\frac{4\pm\sqrt[]{16+640}}{2} \\ Y=\frac{4\pm25.6}{2} \end{gathered}\)So, we have 2 solutions:
\(\begin{gathered} Y=\frac{29.6}{2}=14.8 \\ \text{and} \\ Y=\frac{-21.6}{2}=-10.8 \end{gathered}\)By substituting the fist solution into our first equation, we get
\(\begin{gathered} X\cdot(14.81)=160 \\ X=\frac{160}{14.8} \\ X=10.81 \end{gathered}\)Now, by substituting the second solution into our first equation, we h ave
\(\begin{gathered} X\cdot(-10.8)=160 \\ X=\frac{160}{-10.8} \\ X=-14.81 \end{gathered}\)Lets check one solution. For X=10.81 and Y=14.81 we have
\(\begin{gathered} (10.81)(14.8)\approx160 \\ \text{and} \\ 110.81-14.8\approx-4 \end{gathered}\)Now, lets chech the second solution. For X=-14.81 and Y=-10.81 we have
\(\begin{gathered} (-10.81)(-14.8)\approx160 \\ \text{and} \\ -14.81+10.81\approx-4 \end{gathered}\)They are correct !! So, one solution is X=10.81 and Y=14.8 and the other solution is X=-14.81 and Y=-10.81.
Related Questions
6.
(04.01 LC)
Evaluate cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5 . (5 points)
5 to the power of negative 5 over 6
5 to the power of 3 over 2
5 to the power of negative 1 over 6
5 to the power of 5 over 2
Answers
Answer:
A. 5 to the power of negative 5 over 6Step-by-step explanation:
\(\sqrt[3]{5} \sqrt{5} /\sqrt[3]{5^5} =\)\(5^{1/3+1/2-5/3}=\)\(5^{1/2-4/3}=\)\(5^{3/6-8/6}=\)\(5^{-5/6}\)plsss explain nd i’ll give brainliest answer
Answers
Answer: 118
Step-by-step explanation:
Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.
https://brainly.in/question/28196155#:~:text=Step%2Dby%2Dstep%20explanation%3A&text=1%20The%20corresponding%20angles%20are,alternate%20exterior%20angles%20are%20equal. See #5.
A piece of wire is 25 cm and has a weight of 10 grams. Another piece of the same wire is 30 cm long. Calculate the weight of the 30 cm piece of wire. working out please
Answers
Answer:
75 grams
Step-by-step explanation:
If 25 cm = 10 grams
Then 1 cm = 25/10
1 cm = 2.5 grams
To find 30 cm = 2.5 times 30 grams
30 cm = 75 grams
11. Jeff is taking his family and friends to the movies. Adult tickets, a, are $8 and child
tickets, c, are $5. He bought 11 total tickets for $64. Write the system of equations
necessary to compute how many adults and students were in the group.
Answers
Answer:
there are 3 adults and 8 children
Step-by-step explanation:
8*3 (3=Adults)=$24
5*8 (8 children)=$40
24+40=$64
Helppppp pleaseeeeee asapppp
Answers
(12)(4)+(2)(8)+(13)(7)
48+16+91
155
How do you solve this problem?
Answers
Answer: I don’t understand where the problem is? Can u show your whole paper so I can have a better understanding ?
Step-by-step explanation:
A 3-gallon container of disinfectant costs $36.24. What is the price per quart?
Answers
Answer:
10.74666666666667 per quart
Step-by-step explanation3 divided 36.24
Help me with this please
Answers
Answer
X= 1 over 7 hj + 27 over 7
Please help! The question is in the image.
Answers
Answer:
Step-by-step explanation:
Simplify (2^5/3^2)^4 I need help asap within 10 min
Answers
Answer:
\(\frac{2^{20} }{3^{8} }\)
Step-by-step explanation:
Exponent Multiplication Rule :
\((\frac{x^{a} }{y^{b} } )^{c} = \frac{x^{ac} }{y^{bc} }\)
=============================================================
Solving :
⇒ \((\frac{2^{5} }{3^{2} } )^{4}\)
⇒ \(\frac{2^{5(4)} }{3^{2(4)} }\)
⇒ \(\frac{2^{20} }{3^{8} }\)
Geometric Probability
Find the probability that a point chosen randomly inside the larger rectangle is in each given smaller shape. Round to the nearest percent. PLEASE HELP!
1) The circle
2) The smaller rectangle
3) Not the circle or smaller rectangle
Answers
Answer:
Step-by-step explanation:
1) P= Area of Circle/ Area of large rectangle
Area of the circle = pi·r² = pi·2²=4 pi ft.²
Area of large rectangle= l·w -12·10 =120 ft.²
P = 4pi/120 rewrite 120 as 4·30
P= 4 pi/4*30 = pi/30 = 3.14/40 ≈ .1047 ≈10% (because .1047·100 =10.47≅10)
2) P = Area of smaller rectangle/ Area of large rectangle
Area of smaller rectangle = l·w = 2·4 =8 ft.²
Area of large rectangle=l·w = 12·10=120 ft²
P= 8/120 ≅ .0666≅ 7% (because .0666·100 =6.66≅7)
3) P= Not the circle or smaller rectangle/ Area of large rectangle
Not the circle or smaller rectangle area
= Area of large rectangle - Area of circle -Area of smaller rectangle
= 120 -4·pi -8 = 120 - (4· 3.14) -8 = 99.4362939 ft²
Area of large rectangle = l·w = 12·10 =120 ft²
P = 99.4362939 /120 ≅ .8286 ≅83% (because .8286·100 =82.86≅83)
how do you evaluate 2x + Y when x = 4 and y=2
Answers
Answer:
10
Step-by-step explanation:
When given variables, plug them into the equation. When x = 4 and y = 2, than 2x + Y would equal 2(4) + 2.
Answer:
10
Step-by-step explanation:
when x=4 and y=2, you would evaluate like so:
2(4) + 2 = 10
use PEMDAS to solve! :]
Ephemeral services corporation (esco) knows that nine other companies besides esco are bidding for a $900,000 government contract. each company has an equal chance of being awarded the contract. if esco has already spent $100,000 in developing its bidding proposal, what is its expected net profit?
a. $10,000
b. $0
c. $100,000
d. $90,000
Answers
Answer:
c. $100,000
Step-by-step explanation:
Calculation of the expected net profit of Ephemeral services corporation
Since we are been told that 9 other companies besides esco are as well bidding for the $900,000 government contract, it means we have to find the expected net profit by dividing 1 by 9×$900,000 .Thus ESCO can only expect to cover its sunk cost.
Hence ,
E(X) = (1/9) × $900,000
E(X)=0.111111111×$900,000
E(X)= $100,000
Therefore the expected net profit would be $100,000
A car can go 420 miles on a tank of gas (15 gallons in a tank). How many kilometers can this car go on 6.5 gallons
Answers
Answer:
182 miles
Step-by-step explanation:
15 gallons ------------------------- 420 miles
1 gallons --------------------------- 420/15 miles
1 gallons --------------------------- 28 miles
6.5 gallons -------------------------- 6.5 × 28 miles
6.5 gallons -------------------------- 182 miles
The car can go 182 miles on 6.5 gallons.
It is given that the a car can go 420 miles on a tank of gas of 15 gallons in a tank.
It is required to find the how many kilometers can this car go on 6.5 gallons.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.
We have a car can go 420 miles on 15 gallons gas.
A car can go on 1 gallon = \(\frac{420}{15}\) = 28 miles ie.
A car can go on 1 gallon = 28 miles
On 6.5 gallons car can go = 6.5×28
= 182 miles
Thus, the car can go 182 miles on 6.5 gallons.
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Pineapple Street intersects Plum Street and Apple Street at their midpoints. Your home is at point P. You leave your home and jog down Plum Street to Kiwi Street, over Kiwi Street to Apple Street, up Apple Street to Pineapple Street, over Pineapple Street to Plum Street and then back home up Plum Street. How many miles did you jog?
Answers
Answer:
7.125 miles
Step-by-step explanation:
Using the triangle midsegment theorem:
Distance of pineapple street = 1/2(distance of kiwi street) = 0.5 * 1.4 = 0. 7 miles
Distance of plum Street = (2 * distance of P to Pineapple street) = 2 * 1.3 = 2.6 miles
Distance from Kiwi to pineapple = 1/2 * distance of apple Street = 0.5 * 2.25 = 1.125 miles
1.3 + 1.3 + 1.4 + 1.125 + 0.7 + 1.3
Find the inflation rate from 1992 to 1993 . Assume that all prices have risen at the same rate as the CPI.
The inflation rate was about
nothing%.
Answers
69,420
69,420
69,420
69,420
69,420
69,420
69,420
69,420
69,420
69,420
69,420
69,420|
69,420
Find the number of foreign mammals.
Answers
Explanation:
The total mammals = 314
Number of mammals in US = 63
Number of foreign mammals = A
Total mammals = Number of mammals in US + Number of foreign mammals
314 = 63 + A
subtract 63 from both sides:
314 - 63 = 63 - 63 + A
251 = 0 + A
A = 251
Hence, the number of foreign mammals is 251 (option B)
как решить это уравнения,,×-3=6
Answers
Answer:
9
Step-by-step explanation:
Данный,
=> x - 3 = 6
=> x = 6 + 3
=> x = 9 (Отвечать)
What is the absolute
value for:
| +98|
Answers
Answer:
The absolute value of +98 is simply 98. So, | +98| = 98.
Step-by-step explanation:
Answer:
98
Step-by-step explanation:
The absolute value of a number is its POSITIVE distance from 0, so as +98 is 98 away from 0, then |+98| = 98.
Help pleaseeeee!!!!!!
Answers
Answer:
0.05m^2
Step-by-step explanation:
5 divided by 100
A grocery store sells a bag of 8 oranges for $4.40. How much would it cost for 9 oranges?
Answers
To solve this exercise, we apply the rule of three:
Oranges......................Price
8.................................$4.40
9.......................................x
We solve as follows:
\(\boldsymbol{\sf{x=\dfrac{9\times4.40}{8}=\dfrac{39.6 }{8}=4.9 }}\)
Therefore, 9 oranges would cost $4.9.
{ Pisces04 }The required cost of the amount of 4.95 dollars would be for 9 oranges.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have been given that a grocery store sells a bag of 8 oranges for $4.40.
We have to determine the cost for 9 oranges.
Let's assume x dollars would it cost for 9 oranges.
As per the given condition, we can write the ratio as:
8 oranges : $4.40 = 9 oranges : x dollars
⇒ 8 / 4.40 = 9 / x
Cross multiplication and rearrange the terms of the above equation,
⇒ 8x = 4.40×9
Divide by 8 into both sides of the equation,
⇒ x = (4.40×9)/8
⇒ x = (39.6)/8
⇒ x = 4.95
Therefore, the cost of the amount of 4.95 dollars would for 9 oranges.
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What is g please help!!!!
Answers
Answer:
g = - 3
Step-by-step explanation:
\(\sqrt[n]{a}\) = \(a^{\frac{1}{n} }\)
\((a^{m})^n\) = \(a^{mn}\)
~~~~~~~~~~~~~~
∛g × ∛g × ∛g = - 3
\((g^{\frac{1}{3} })^3\) = - 3
\(g^{\frac{3}{3} }\) = - 3
g = - 3
The price of a gift plus 14% delivery charge comes to a total cost of $19.38. What was the price of the gift? Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity.
Answers
Answer:
$16.67
Step-by-step explanation:
$19.38*14%=$2.71
$19.38-2.71=$16.67
Mr. DeWitt carved a wooden boat for his granddaughter. He began with a piece of wood that was 20.3 centimeters long. The boat is 16.7 centimeters long. How many centimeters did Mr. DeWitt carve off the length of the piece of wood when he made the boat?
Answers
In the word problem , the length of wood Mr. DeWitt carved off is 3.6cm.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
According to the given ,
Length of wood = 20.3 cm
The length of boat = 16.7 cm.
Now Length of wood he carved off is,
=> Length of wood - length of boat
=> 20.3 - 16.7
=> 3.6 cm.
Hence the length of wood Mr. DeWitt carved off is 3.6cm.
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Whats (c) ????????????? ????
Answers
Answer:
11
Step-by-step explanation:
yeah-ya............ right?
Check the picture below.
Please review the following sets of sentences and select the one that contains filler.
A. This Star Wars LEGO set has 305 pieces and includes two minifigures and two droids you can battle against each other.
B. Your kids will love the LEGO Star Wars Republic Fighter Tank and spend hours building it to completion.
C. The set features an opening top hatch with a cockpit where you can place the included Clone Trooper Gunner figure to ready for battle.
D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes.
Answers
The sentence that contains filler is: D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes. Option D
In this sentence, the phrase "also includes heroes like Obi-Wan Kenobi and Anakin Skywalker" acts as a filler. The main purpose of this phrase is to provide additional information about the set and highlight the inclusion of popular characters from the Star Wars franchise. It doesn't directly contribute to the core information about the set's features or components.
The other sentences (A, B, and C) provide specific details and descriptions about the LEGO set, such as the number of pieces, minifigures, droids, and features like the opening top hatch and cockpit. They directly convey important information about the set itself without any filler or additional unnecessary information.
In marketing or promotional contexts, fillers are often used to enhance the appeal of a product or create excitement by mentioning well-known or desirable elements that may not be directly relevant to the core features. The filler in sentence D serves to attract fans of Obi-Wan Kenobi and Anakin Skywalker by emphasizing their presence in the set and the inclusion of their iconic weapons and attire.
Option D
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Answer:D
Step-by-step explanation:
Prove that if an integer n is the sum of two squares (n = a2+ b2 for a, b Z) then n = 4q or n= 4q+1 or n= 4q + 2 for some qЄ Z. Deduce that 1234567 cannot be written as the sum of two squares.
Answers
The number 1234567 cannot be written as a sum of two squares.
Let q = x^2+y^2,
Let a and b be two even numbers, such that
a= 2x and b = 2y
then
n = (2x)^2 + (2y)^2 = 4 (x^2+y^2)
implies n = 4q
Let a and b be two odd numbers, such that
a = 2x+1 and b = 2y+1
then
n = (2x+1)^2 + (2y+1)^2 = 4x^2+4y^2+1 = 4q+2
Let a be an even number and b be an odd number, such that
a= 2x and b = 2y+1
then
n = (2x)^2 + (2y+1)^2 = 4q+1
But, the given number 1234567 = (4×308641)+3 which is of the form 4q+3, hence it cannot be written as the sum of two squares.
To know more about the even numbers
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Write the letter of the definition next to the matching word as you work through the
lesson.
Answers
Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.
What is Hypotenuse?In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.
According to question:Altitude: In a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.Geometric mean: for two positive numbers, a and b, the positive number x that satisfies a/x = x/b.Hypotenuse: The side of a right triangle that is opposite the right angle and is always the longest side of the triangle.Leg: In a right triangle, either of the two sides forming the right angle.One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.
The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.
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Emily and Andy each go to a hardware store to buy wire.The table shows the relationship between the cost and the length of wire.
a. Emily needs 22 feet of wire. How much will she spend on wire?
b.Andy needs 15 yards of wire.How much will he spend on wire?
Inches. PLEASE HELP ME
Answers
Answer:
For part A-Emily would spend $22.70 on 22 feet of wire. For part B- Andy would spend $2.30 for 15 yards of wire.
Step-by-step explanation:
The cost is going down 10 cents by the foot, so getting 22 feet into 264 inches then having 165 into 164 and going up by the ten ending the number in four. Same with the yards in feet then the feet into yards and going down by 10. Hope it helps and makes sense.
Which of the following is true of points on the line y=5/3 x + 1/2? (1) For every 3 units that increases, y will increase by 5 units. (2) For every 5 units that x increases, y will increase by 2 units. (3) For every 2 units that x increases, y will increase by 1 unit. (4) For every 1 unit that x increases, y will increase by 2 units.
Answers
4) For every 1 unit that x increases, y will increase by 2 units.
1) For the function y=5/3x +1/2
If we remember that "rise over run" mnemonics, that'll make it easier to memorize it.
2) Plotting the graph of this function. Look at point A (1,2)
Counting from bottom to up (2 units "rise" on the y-axis, point A is 1 unit to right "run". So, For every 1 unit that x increases, y will increase by 2 units.
