Answer:
um... okie
Step-by-step explanation:
The square of the sum of two numbers is 144 and the sum of their squares is 80. Find the numbers.(Use completing the square method)
Please help me
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]
IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.
a) What is the difference between Einstein's IQ and the mean?
b) How many standard deviations is that?
c) Convert Einstein's IQ score to a Z-score
d) If we consider "usual IQ scores to be those that convert z-scores between -2 and 2, is Einstein's IQ usual or unusual?
Answer:
A) 60
B) Between 3 and 4
C) [tex] \frac{160 - 60}{16} [/tex]
D) Extremely unusual.
The difference between Einstein's IQ and the mean is 60. There are standard deviations between 3 and 4. Einstein's IQ score to a Z-score is 9.375. If we consider usual IQ scores to be those that convert z-scores between -2 and 2, is extremely unusual.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.
The difference between Einstein's IQ and the mean :
⇒ 160 - 100 = 60
There are standard deviations between 3 and 4.
Einstein's IQ score to a Z-score:
Here,
ц = 160
σ = 16
X = 100
⇒ z-score = (X-ц )/σ
Substitute the values,
⇒ z-score = (160- 10)/16
⇒ z-score = 150/16
⇒ z-score = 9.375
If we consider usual IQ scores to be those that convert z-scores between -2 and 2, is extremely unusual.
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HELP GIVING BRAINLIEST (NO LINKS) 50 POINTS
Expression A: 2(x + 1)
Expression B: 2x + 2
which statement does not show that these expressions are equivalent
A.subsitiuting any value of x makes the expressions equivalent
B. Both expressions involve addition
C. The expressions name the same number regardless of the value of x
D. 2(x +1) can be rewritten as 2x + 2 using the distributive property
Answer:
B. Both expressions involve additionStep-by-step explanation:
A. Substituting any value of x makes the expressions equivalent
FalseB. Both expressions involve addition
True. Both expressions involve multiplication tooC. The expressions name the same number regardless of the value of x
FalseD. 2(x +1) can be rewritten as 2x + 2 using the distributive property
FalseSolve for Y please help me
Answer:
y = j - rx/c
Step-by-step explanation:
Solve for r.
4r+10>6
71 points
Help Plslsspsl
Answer:
r > -1
Step-by-step explanation:
4r + 10 > 6
4r + 4 > 0
4 > -4r
-4 < 4r
-1 < r
r > -1
Answer:
r > - 1 or r ∈ (- 1, + ∞)Step-by-step explanation:
4r + 10 > 64r > 6 - 104r > - 4r > - 4/4r > - 1 or r ∈ (- 1, + ∞)Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
Here's a graph that shows a system of equations for this scenario where x is the number of books Aaden borrows and y is the total cost of the subscription.
A graph with two lines and a point. Line A is labeled y equals 96. Line B is labeled y equals 3 times x. Point S is below line B and above line A.
What does point SSS represent in this context?
Choose 1 answer:
(Choice A)
A
A number of books and their cost using the subscription that charges per book
(Choice B)
B
A number of books and their cost using the subscription with the annual fee
(Choice C)
C
A number of books and their cost where both subscriptions cost the same
(Choice D)
D
A number of books and their cost that is not possible with either subscription
I sent a screen shot of the graph
Answer:
A
Step-by-step explanation:
A number of books and their cost where the subscription with the annual fee costs less. hope it helps and take care ✌
Point S represents the number of books and their cost using the subscription that charges per book
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Based on the given graph, point S represents the number of books and their cost using the subscription that charges per book (Option A).
This is because point S is located below line B, which represents the total cost of the subscription with a variable cost per book, and above line A, which represents the total cost of the subscription with a fixed annual fee.
Therefore,
Point S represents a combination of a certain number of books borrowed and the corresponding total cost of the subscription using the variable cost per book option.
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16. A scuba diver started at sea level and dove 100 feet. The
diver then rose 25 feet. Write and evaluate an expression that
shows the diver's current elevation relative to sea level.
Math
Answer:
His realation to sea level would be -75 since he would be below the ground/ sea level
Step-by-step explanation:
Pls brainliest
Is 500 x 30 a good estimate for the number of tickets sold at the number of tickets sold at the theater in one month
Answer:
It depends if business is steady. If they make about 500 a day that is a fair estimate. Make sure that the month you are talking about has 30 days.
Find the slope of the line that passes through (10, 9) and (6, 18).
Answer:
M = -2 1/4
Step-by-step explanation:
You can use the formula y2 - y1 / x2 - x1 to get your answer.
y2 is 18 and y1 is 9. x2 is 6 and x1 is 10 so plugging that into the formula above you will get 18 - 9 / 6 - 10.
18 - 9 is 9 and 6 - 10 is -4
9/-4 = M (M is short for slope)
M = -2 1/4
Hope this worked for you.
The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 8 to 5. if there were 7332 total votes, how many no were there?
Answer:
2820 no votes
Step-by-step explanation:
The fraction of votes that were 'no' is ...
no/total = (5)/(8+5) = 5/13
The number of votes that were 'no' is ...
(5/13)(7332) = 2820 . . . no votes
Could you please help with this
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
If 5 boxes of cereal cost $27.50, how much does one box of cereal cost? a) $5.50 b) $5.05 c) $550 d) .55
}
Answer:B
Step-by-step explanation: I said that because you have 27 and 50 Cent so basically you won't have that $5 in that picture because you still going to have that $0.04 and then you still have to have that much so I I think I am right but if I'm not I'm so sorry but I'm taking not even to get I'm trying to get back on track but I think is b for a reason like I think you could be because you have 27 and 50 Cent so if you got twenty-seven fifty cents you just rounding it down
Answer:
ans is i think a) $5.50
Step-by-step explanation:
'cuz if 5 boxes cost $27.50
so it will be
[tex]27.50 \div 5 \\ = 5.50[/tex]
Please help! If it’s true then it’s 10 points. If it’s false then it’s 15. Don’t add up the numbers. I really appreciate it :)
1) True
2) True
3) False
4) False
5) False
6) True
7) True
8) False
The owner of a retail store is tracking his inventory for an annual report. The graph shows the remaining Inventory for a particular item and the
number of days that have passed since the stock was replenished.
Which type of function best models the relationship between the number of days and the inventory remaining?
Answer:
y = -2.8x +69.4
Step-by-step explanation:
Let y represent units of inventory, and x represent days since the last replenishment. We are given points (x, y) = (3, 61) and (13, 33). The line through these points can be described using the 2-point form of the equation of a line:
... y -y1 = (y2-y1)/(x2 -x1)(x -x1)
Filling in the given point values, we have ...
... y -61 = (33 -61)/(13 -3)(x -3)
Simplifying and adding 61, we get ...
... y = -2.8x +69.4
The linear function which best models the relationship between the number of days and remaining inventory is [tex]y = \frac{-35}{12}x + \frac{50}{3}[/tex] .
What is linear function?
A linear function refers to when the dependent variable (usually expressed by 'y') changes by a constant amount as the independent variable (usually 'x') also changes by a constant amount.
According to the given equation
We have a graph which shows the remaining inventory.
In which x represents the number of days and y represents the inventory remaining.
Let y = mx + b be the linear function which represents the relationship between the number of days and the inventory remaining.
Form the given graph if we choose two points (14, 30) and (2, 65) for finding the value of m and b.
Substitute y = 30 and x = 14 in y = mx + b
⇒ [tex]30 = m(14) + b...(i)[/tex]
Similarly,
substitute y =65 and x =2 in y = mx + b
⇒[tex]65 = 2m + b..(ii)[/tex]
From equation (i) and (ii)
[tex]m = \frac{-35}{12}[/tex]
and [tex]\frac{50}{3}[/tex]
Therefore, [tex]y = \frac{-35}{12}x + \frac{50}{3}[/tex]
Hence, the linear function which best models the relationship between the number of days and remaining inventory is [tex]y = \frac{-35}{12}x + \frac{50}{3}[/tex] .
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-7x > 10
Solve for x
Answer:
x > -10/7
Step-by-step explanation:
divide both sides by -7 and it will be x= -10/7
If you mix 0.02 litres of squash with 100 ml of water to make a drink, what is the total volume of drink that could be made with 1 litre of squash?
Give your answer in litres.
-4x + 60 < 72 or 14x + < -31
x=31/14
Step-by-step explanation:
I did the second one btw
-1/5 x 15/16 get 70 pts if u answer thisss tysmmm<3
Answer:
[tex]\frac{-3}{16}[/tex]
Step-by-step explanation:
[tex]\frac{-1}{5}[/tex] × [tex]\frac{15}{16}[/tex]
=> [tex]\frac{-15}{80}[/tex]
=> [tex]\frac{-3}{16}[/tex]
Hoped this helped.
Youssef paid AED 8 for 12 eggs.
Determine the cost of 3 eggs.
To solve this problem, you must first know how much 1 egg costs, for this we have to divide:
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace \sf 1,5\space\space\space\space\space\space\space\space\space\space\space\space\\ \sf 8\overline{|\smallspace \sf 12}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\underline{\sf 8}\\\sf 40\\\underline{\sf 40}\\(0)[/tex]
Now we know an egg costs $1.5, so:[tex]\sf 1,\:5\:+1,\:5+1,\:5=\boxed{\sf 4,5}\ll Eggs[/tex]
Okay?!Answer:
AED 2 for 3 eggs
Step-by-step explanation:
Price (p) is proportional to the number of eggs:
p/3 = 8/12
p = 3(8/12) = 8(3/12) = 8/4 = 2
The cost of 1/4 as many eggs will be 1/4 as much: AED 2 for 3 eggs.
What value would you need to multiply the top equation by in order to eliminate the y variable in the following system of equations?
Answer:
-3
Step-by-step explanation:
-3 would eliminate the y so you would solve for x.
Leave a comment if this doesn't make sense ;)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6
plz help!
1. (0, y) , (2, 7); m = 1/2
y = _____
2. (4, 2) , (5, y) m = 4
y = _____
Answer:
Step-by-step explanation:
y = mx + b, where m is the slope and y the y-intercept (the value of y when x=0).
(0, y) , (2, 7); m = 1/2
We can start with y = (1/2)x + b
To find b, use one of the two given points. I'll use (2,7), since (0,y) isn't helpful.
y = (1/2)x + b
7 = (1/2)*2 + b
7 = 1 + b
b = 6
The equation is y = (1/2)x + 6.
Now find (0,y) by using x = 0:
y = 6
The second point is (0,6)
============
2. (4, 2) , (5, y) m = 4
y = mx + b
y = 4x + b
Use (4,2) and solve for b:
2 = 4*4 + b
b = -14
The equation is y = 4x - 14
Now find (5,y):
y = 4x - 14
y = 4*5 - 14
y = 20 - 14
y = 6
The second point is (5,6)
Se attached graph.
--
4 divided by 2.48
Use long division
Answer:
Step-by-step explanation:
The quotient is 0.62 and the remainder is 0.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, 2.48 divided by 4.
Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.
Here,
4|2.48|0.62
24
24
_____
08
08
_____
0
So, quotient is 0.62 and remainder is 0.
Therefore, the quotient is 0.62 and the remainder is 0.
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PLEASE HELPPPP !! Which points have positive y coordinates?
A) A and F
B) A and B
C) F and H
D) B and F
all things algebra unit 5 homework 2
April borrows $60 from her grandmother to buy basketball shoes. At the end of the first week, April pays back $5. At the end of each of the following weeks, she pays back $3 more than she did the previous week. The arithmetic sequence 5, 8, 11, 14,. . . Can be used to represent this situation. In this sequence n represents what?.
Answer: Number of weeks
Step-by-step explanation:
Just did it on Ed
What percent of 80 is 112? Please hurry!
Answer:
140
Step-by-step explanation:
Here you go. Hope it helps you
i need help what is 7h+1−h+4?
Answer:
6h+5
Step-by-step explanation:
7h-h=6h
1+4=5
Hope this helps :)
Answer:
6h + 5 is the correct answer
Step-by-step explanation:
7h + 1 - h + 4
7h + 1 + 4 - h
7h + 5 - h
6h + 5
hope this helped!
mark me brainliest :D
a dress which sosts $180 is being sold at a discoundof 10% the amount of the discount is
Answer:
The discount is $18.
2.5x + 6 = 0.5x + 46
I’ll give brain whoever solves it
PLEASE DO IT STEP BY STEP
Answer:
x=20
Step-by-step explanation:
2.5x+6=0.5x+46
subtract 0.5x from both sides
2x+6=46
subtract 6 from both sides
2x=40
divide both sides by 2
x=20