Answer:
Step-by-step explanation:
(x + y)^2 = 144
x^2 + y^2 = 80
----
x + y = 12 ---> y = 12 - x
x^2 + y^2 = 80
x^2 + (12-x)^2 = 80
2x^2 - 24x + 64 = 0
x^2 - 12x + 32 = 0
x = 4, x = 8
y = 8, y = 4
============================
x + y = -12 ---> y = -12 - x
x^2 + y^2 = 80
x^2 + (-12-x)^2 = 80
2x^2 + 24x + 64 = 0
x^2 + 12x + 32 = 0
x = -4, x = -8
y = -8, y = -4
-------------
One number is + or -4, the other is + or -8,
and the absolute value of the sum is 12.
Answer:
(4,8);(8,4);(-4,-8);(-8,-4)
Step-by-step explanation:
Ok, let's start writing down the two conditions:
[tex]\left \{ {(x+y)^2 = 144} \atop {x^2+y^2=80}} \right.[/tex]
Mumble. The second almost look like a square, if only there was the [tex]2xy[/tex] term. Let's add (and subtract, so we aren't creating something new) term to the second:
[tex](x+y)^2-2xy = 80[/tex] But we know what the first term is, it's 144. Let's replace and do some number tricks to get:[tex]144-2xy=80 \rightarrow 72-xy=40\\72-40=xy \rightarrow xy=32[/tex]
At this point, let' stare at it for a while. You can tell that the system is simmetrical (if you replace x with y you still get a solution). Moreover, x and y have the same sign: it means that if (a,b) is a solution, then also (b,a), (-a,-b) and (-b, -a) are solutions, and since it's a 4th degree system (the degree of a system is the product of the degrees of the single equations, and they're both quadratic) there are no other solution.
Let's find one pair then. We're tasked to find two numbers that sum to [tex]\sqrt{144} = 12[/tex] and whose product is 32. that is, the root of the polynomial
[tex]z^2+12z+32= (z+4)(z+8)[/tex] (or if you can't see the factors right away, bruteforce it with quadratic formula, it's always good practice). That tells us that one of the two is -4, and the other is -8. From what we said above, the solutions are by combining them with plus or minus.
[tex](4,8);(8,4);(-4,-8);(-8,-4)[/tex]
If it takes 7 people 8 days to dig a ditch, how many people would it take to dig the ditch in 1/2 day
Answer:
112
Step-by-step explanation:
8 days when fitted into a half (1/2) gives you 16
7 times 16 gives the answer of 112 (people needed)
Answer:
112 people to do it in 1/2 of a day
Step-by-step explanation:
7 · 8 = 56
56 ÷ ½ = 112 people to dig a ditch in 1/2 of a day
Given: ΔАВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 60° BC = 6 cm, find the length of AD
im not sure sorryyyyyyyyyyyyyyy
Bonie reduced the size of a photo to a height of 4 in. what is the new width if it was orginally 16 in tall and 8 in wide?
Answer:
i need help with this one too
Step-by-step explanation:
Answer:
2 inches
Step-by-step explanation:
I hope it helps you!
4,00
.
5. Mr. Brown has $410,000 in a retirement account that earns 3.85% interest each year. Find the
amount earned each year by his investment.
Answer:
9 dollars
Step-by-step explanation:
cuz 9 dollars
ℎ ℎ 22 2 22 2− 3 +10
Answer:
wouldn't the answer be 9
Step-by-step explanation:
Answer:
22h^2 + 33 (added) . h⋅h⋅22,2,22,2−3+10 (subtracted)
Step-by-step explanation:
I don't understand what you want so I will list lots of answers hopefully it helps. Please message under my answer for more solutions so I can help you but I hope this started to help you.
Please help I need the answer quickly.
Answer:
r = ± [tex]\sqrt{q^2-p^4[/tex]
Step-by-step explanation:
p² = [tex]\sqrt{q^2-r^2}[/tex] ( square both sides )
(p² )² = q² - r²
[tex]p^{4}[/tex] = q² - r² ( subtract q² from both sides )
[tex]p^{4}[/tex] - q² = - r² ( multiply through by - 1 )
q² - [tex]p^{4}[/tex] = r² ( take square root of both sides )
± [tex]\sqrt{q^2-p^4}[/tex] = r
b/4 + 2 = -1
Please help, I’ll give brainliest to whoever answers correct first.
Answer:
[tex]\frac{b}{4}+2=-1[/tex]
Subtract 2 from both sides:
[tex]\frac{b}{4}+2-2=-1-2[/tex]
[tex]\frac{b}{4}=-3[/tex]
Multiply 4 to both sides:
[tex]4*\frac{b}{4} =-3*4[/tex]
[tex]b=-12[/tex]
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD? Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit Reflection about the x-axis followed by a translation to the left by 1 unit Reflection about the y-axis followed by a translation to the right by 1 unit
PLEASE HURRY THIS IS TIMED !!!!
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What does the y-intercept represent in this situation? The weight of oats, in pounds, in the final mixture. The weight of hay, in pounds in the final mixture. The amount of protein the feed has if no oats are added. The amount of protein the feed has if no hay is added.
Your welcome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The y-intercept in the situation given represents: C. The amount of protein the feed has if no oats are added.
What is the Y-intercept of a Linear Function?The y-intercept of a linear function is the initial value or the value of y when x equals 0.
The initial value in this situation is the amount of protein in the feed when the amount of oats added is 0.
Therefore, the y-intercept represents: C. The amount of protein the feed has if no oats are added.
Learn more about the y-intercept on:
https://brainly.com/question/10700419
#SPJ6
Please help I’m begging you
Answer:
y = 9
Step-by-step explanation:
The line "y = 9" is parallel to the x-axis and passes through (0,9).
Write your answer as a decimal. If the decimal has more than 2 decimal places, round to 2 decimal places.
Charlie is flying a kite one afternoon and steps on the end of the string to have his
hands free to take a picture. The string is 135 feet long and forms a 68-degree angle
with the ground. How high is his kite at this time? Round to the nearest foot and
enter the number only.
I need the answer quick please!
Answer:
125.1698 Ft
Step-by-step explanation:
simplify the equation
Find the measures of the interior angles of the triangle.
Answer:
Imagine that scientists have just discovered a non-bird dinosaur skeleton. They want to know whether the dinosaur was closely related to birds. What features in ...
Step-by-step explanation:
What is the value of the rational expression when x = –3?
-1/12
0
1/6
undefined
Option D is correct, the value of the rational expression when x = –3 is undefined.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is x/x²-9
x divided by x square minus nine.
Now let us find the value of the expression when x is minus three,
Plug in x as -3 in the above expression.
-3/(-3)²-9
-3/9-9
-3/0
Anything divided by zero then the value is undefined.
Hence, Option D is correct, the value of the rational expression when x = –3 is undefined.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ7
What is the value of the rational expression x/x2-9 when x = –3?
A. -1/12
B. 0
C. 1/6
D. Undefined
What are the values of the two angles?
Answer:
the angle 3x is 42 degrees, the angle 12x-30=138 degrees
Step-by-step explanation:
first, write an equation to represent the problem.
3x+(12x-30)=180
3x+12x=210
15x=210
x=14
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.
We can solve this problem in 2 steps, one being Theory and the second being Solving. I'll start off with Theory.
Theory
There are many theorems in Geometry, from the very simple to the very complex, you also have got the standard information that is usually known by many people.
In this case, we can see that it is a Supplementary Angle. We know that Supplementary Angles add up to 180 degrees and Complementary Angles add up to 90 degrees.
Now that we know that we can solve the problem.
Solving
So, we know that both angles have to add up to 180 degrees because the line is a straight line and that means that the angles on it must be 180 degrees.
Since we know this, we can state the following equation:
[tex]3x+12x-30=180[/tex]
We can say this due to the rule of Supplementary angles adding up to 180 degrees.
We can now use Algebra to simplify the equation:
[tex]3x+12x-30=180\\3x+12x=210\\15x=210\\x=14[/tex]
After doing algebra we can see that x s equal to 14 degrees, we can check our answers by putting that back into the equation.
[tex]3(14)+12(14)-30=180?\\42+168-30=180?\\210-30=180?\\180=180[/tex]
We have proven that our answer is correct, therefore the answer is [tex]x=14[/tex] degrees.
Cheers!
Dylan brought his DVD set of The Sleuth in the Shadows Saga to a secondhand store to sell. He was paid cash for all 4 DVDs in the set. Before he left, Dylan used $16.40 of his earnings to purchase a backpack. He had $3.60 remaining. How much did Dylan receive for each DVD in the set?
Answer: 5$
Step-by-step explanation:
In order to get the total, you would need to add the total spen on the backpack and the amount remaining and then you would divide that by 4 ( for all of the DVDs in the set)
A student solved a system of equations by elimination. The answer is not correct. Describe the error in the solution.
Original Problem:
3x−2y=8
x+y=2
Student Work:
3x−2y=8
2x+2y=2
5x=10
x=2
The student went from x+y = 2 to 2x+2y = 2, which is not correct. They multiplied the left side by 2, but forgot about the right hand side.
They should have gone from x+y = 2 to 2x+2y = 4 after multiplying both sides by 2.
So they should have this new equivalent system
[tex]\begin{cases}3x-2y = 8\\2x+2y = 4\end{cases}[/tex]
Add straight down and we end up with the new equation 5x = 12 which solves to x = 12/5 = 2.4
Use that x value to solve for y. You should get y = -2/5 = -0.4
Please help! I really need to get the answer correct
Answer:
x + 9y²
Step-by-step explanation:
A prime polynomial is simply an irreducible polynomial.
x + 9y² is a prime polynomial
First, we test the options.
x + 9y²
The above function cannot be reduced further.
Hence, x + 9y² is a prime polynomial
3m + 9n
Factor out 3
3 (m + 3n)
3m + 9n is not a prime because it can be factored as 3 (m + 3n)
8x^7 - 9x + 12x²
Factor out x
x(8x^6 - 9 + 12x)
8x^7 - 9x + 12x² is not a prime because it can be factored as x(8x^6 - 9 + 12x)
Hence, x + 9y² is a prime polynomial
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee (thank you :)
(cAt)
Answer:
answer is 2
Step-by-step explanation:
funny pic
Which pairs of numbers are equivalent?
Select each correct answer.
15/8 and 1 7/8
35/4 and 8 3/4
23/6 and 4 1/6
11/4 and 2 1/2
40/12 and 3 1/3
i need this fast
Answer:
4 an 5
Step-by-step explanation:
Answer:
15/8 and 1 7/8
35/4 and 8 3/4
40/12 and 3 1/3
Step-by-step explanation:
15/8 and 1 7/8:
Convert the improper fraction into a mixed number: [tex]\frac{8+7}{8}[/tex]
Calculate the sum or difference: [tex]\frac{15}{8}[/tex]
Check equivalency: True
Answer: True
=================================================================
35/4 and 8 3/4
Convert the improper fraction into a mixed number: [tex]\frac{8*4+3}{4}[/tex]
Calculate the product or quotient: [tex]\frac{32+3}{4}[/tex]
Calculate the sum or difference: [tex]\frac{35}{4}[/tex]
Check equivalency: True
Answer: True
================================================================
23/6 and 4 1/6
Convert the improper fraction into a mixed number: [tex]\frac{4*+1}{6}[/tex]
Calculate the product or quotient: [tex]\frac{24+1}{6}[/tex]
Calculate the sum or difference: [tex]\frac{25}{6}[/tex]
Check equivalency: False
Answer: False
===============================================================
40/12 and 3 1/3
Reduce the fraction: 10/3
Convert the improper fraction into a mixed number: [tex]\frac{3*+1}{3}[/tex]
Calculate the product or quotient: [tex]\frac{9+1}{3}[/tex]
Calculate the sum or difference: [tex]\frac{10}{3}[/tex]
Check equivalency: True
Answer: True
================================================================
11/4 and 2 1/2
Convert the improper fraction into a mixed number: [tex]\frac{2*+1}{2}[/tex]
Calculate the product or quotient: [tex]\frac{4+1}{2}[/tex]
Calculate the sum or difference: [tex]\frac{5}{2}[/tex]
Check equivalency: False
Answer: False
A yard is 33.22 m long and 17.2 m wide.
(a) What length of fence must be purchased to enclose the entire yard?
(b) What area must be covered if the yard is to be fertilized? PLEASE HELP FOR A TEST
Answer:
A. = 100.84 m
B. 571.384 cubic m
Step-by-step explanation:
a.
33.22+33.22+17.2+17.2 =100.84m
b.
33.22x17.2 = 571.384 m2
Which variable expression represents the following word phrase?
four times the sum of five and a number
Answer:
c
Step-by-step explanation:
c represents adding 5 and n together, and multiplying it by four.
Four times the sum of five and a number equivalent expression is 4(5 + n) which is the correct answer would be an option (C).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs arithmetic operations is called arithmetic operator.
Operators let do basic mathematical calculations.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
Let the number be n
To determine the four times the sum of five and a number
The sum of five and a number as
⇒ 5 + n
So, four times the sum of five and a number as
⇒ 4*(5 + n)
Hence, four times the sum of five and a number equivalent expression is 4(5 + n).
Learn more about the expressions here :
brainly.com/question/21751419
#SPJ2
What is the range
of 98, 99, 100,
90, 98, 100?
Answer:
10
Step-by-step explanation:
Increasing order:-
90,98,98,99,100,100Range = Highest term - Lowest term
Range = 100 - 90
Range = 10
Hence,
Range of the given term is 10
Answer:
10Step-by-step explanation:
The data set in ascending order:
90, 98, 98, 99, 100It has min = 90, max = 100
The range is the difference between min and max:
100 - 90 = 10if i can get 4 tastykake snack cakes. 4 for $5.00 how much would it be if i get 2 tastykake snack cakes?
Answer:
2.50
Step-by-step explanation:
If 4= $5.00
then divided 5.00 by 4=1.25
so 1 = 1.25
1.25x2=2.50
Therefore 2 tastykake snack cakes = $2.50
Answer:
The answer is 2.5
Step-by-step explanation:
5 divided by 4 = 1.25
1.25 times 2 = 2.5
brainliest :)
I need help i will give brainly
A grain silo on a farm holds 500 pounds of grain. The equation shown represents the total amount of grain, y, remaining in the silo x minutes after the farmer begins to release the grain.
y=−5x+500
What does the -5 represent in the equation in reference to this situation?
Answer:
the negative 5 is showing that you are losing grain in the silo because you are letting some out.
Factor the following polynomial completely. x2n – y2n
Answer:
(x/y)^2n-2n
(x/y)⁰
=1
since any number raised to power of 0 is 1
it takes 3 brick layers 2 hours to build a wall how long would it take 4 brick layers
please show steps in ratio
Answer:
Ratios are basically proportions so in this scenario
We can make it…
brick layers : hours
We’re given the first one which is
3:2
Whilst the one we need to find is only given for brick
For the unknown hours we can make it “x”
4: x
Now we have 2 ratios
3:2
4:x
Now these are fractions and we can make them equal to each other by
3/2 = 4/x
Now cross multiply to solve for x
3x=8
2 2/3 = x
So 2 2/3 hours
ABC is a triangle
AB = AC and BA is parallel to CD
Work out the size of the angle marked x
Step-by-step explanation:
so as ∆BCE is a right angled triangle
angle BEC = 90°
angle CBE = 22° (given)
apply angle sum property of triangle
so according to that
BCE + CBE + ECB = 180
22° + 90° + ECB = 180
102° + ECB = 180
ECB = 180 - 102
ECB = 78°
and also we know, that exterior angle of a triangle is equal to 2 interior angle of triangle,
so ,
x = 78°
hope this answer helps you dear! take care