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]
pls answer. and show your solution.
Answer:
23, - 46, 57, 10, 12
Step-by-step explanation:
(a)
2x + 5 = 2(9) + 5 = 18 + 5 = 23
(b)
4x - 2 = 4(- 11) - 2 = - 44 - 2 = - 46
(c)
x² + 21 = (- 6)² + 21 = 36 + 21 = 57
(d)
[tex]\sqrt{x}[/tex] - 1 = [tex]\sqrt{121}[/tex] - 1 = 11 - 1 = 10
(e)
[tex]\frac{x}{8}[/tex] + [tex]\sqrt[3]{x}[/tex] = [tex]\frac{64}{8}[/tex] + [tex]\sqrt[3]{64}[/tex] = 8 + 4 = 12
Part A
In "Primary Lessons" from Silent Dancing: A Partial Remembrance of a Puerto Rican Childhood, what can the reader infer about how the narrator will ultimately feel about going to school?
She will misbehave there constantly to punish her mother for sending her.
She will become used to it, knowing everyone must go.
She will become an academic herself as she begins a lifelong quest for learning.
She will remain upset and fight her mother every single day.
Question 2
Part B
Which sentence in the text best supports the answer in Part A?
"It was my final argument, and it failed miserably because I was shouting my defiance in the language I claimed not to speak."
"How could she send me to school to learn Spanish when we would be returning to Paterson in just a few months?"
"I guess most children can intuit their loss of childhood’s freedom on that first day of school."
"The sight of my cousins in similar straits comforted me."
Answer:
a) she will become used to it, knowing everyone must go.
b) i guess most children can intuit their loss of childhood's freedom on that first day of school.
Explanation: i took the quiz
show that 296 not not a perfect number
Step-by-step explanation:
in which the sum of all it's factor are twice of that no... factor of 296 =1,2,4,8,37........easy will give brainlest no files.
Answer:
can u give better picture
Answer:
Remain the same.
Step-by-step explanation:
When you are translating a figure, nothing changes expect for its location. It's shape and orientation stay the same. Hope this helped, and please let me know if you have any further questions. :)
There are 50 sheets of scrapbook paper in a pack, and 20% of them are striped. How many sheets of scrapbook paper are striped? Pick the model that represents the problem. How many sheets of scrapbook paper are striped?
Answer:
10 sheets of paper are striped
Step-by-step explanation: Make a proportional relationship.
20% as a fraction is 20/100
Make 50 into a fraction using a variable. For example, x/50
Cross multiply 20 and 50. That equals 1000.
Then divide 1000 by 100 and that equals 10. So 10 sheets of paper are striped.
Hope this helps!
onique bought 2 hot dogs and 1 large soda. She spent $7. Scott
bought 4 hot dogs and 1 large soda. He spent a total of $12.
What is the cost of one hot dog and one large soda?
After Gwen, Tristan, and Keith finish exercising, they go to the fair. At the fair, they each pay the entry fee and also buy tickets they can use for food or rides. Gwen pays the entry fee and buys 10 tickets. It costs her a total of $30. Tristan pays the entry fee and buys 15 tickets. It costs him a total of $40. Keith pays the entry fee and buys 10 tickets. It costs him a total of $30. In this task, you will create a system of equations and find the cost of each ticket. Let x represent the entry fee and y represent the cost of each ticket in dollars.
Part B
Write an equation representing how much Tristan paid.
Part C
Write an equation representing how much Keith paid.
Part E
Solve the system you found in Part D. Did you use elimination or substitution? What was the entry fee, and how much did each ticket cost?
Part F
What do you need to do to the equations so you can put them into the Graph tool? Put the equations into the Graph tool. To create the graph, select the correct relationship and then enter the values for the variables. Paste a screenshot of your graph in the space provided. Do you get the same solution as when you solved it algebraically?
Answer:
Let x represents the entry fees
y represent the cost of each ticket
Gwen equation
x + 10y = 30 ... (i)
Tristan equation
x + 15y = 40 ...... (ii)
Keith equation
x + 10y = 30 .......... (iii)
By solving eq. (ii) and (iii), we get
x = 10
y = 2
Hence entry fees = $10
cost of each ticket = $2
PLEASE MARK ME AS BRAINLIEST AS IT WILL HELP ME IN ACHIEVING NEXT LEVEL.
THNX IN ADVANCE
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represents the entry fees
y represent the cost of each ticket
Gwen equation
x + 10y = 30 ... (i)
Tristan equation
x + 15y = 40 ...... (ii)
Keith equation
x + 10y = 30 .......... (iii)
By solving eq. (ii) and (iii), we get
x = 10
y = 2
Hence entry fees = $10
cost of each ticket = $2
A line that includes the points ( – 4, – 6) and (5,v) has a slope of – 2/9 . What is the value of v?
Answer:
v is -8
Step-by-step explanation:
The form of a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
We are given the slope, so let's write:
y = -(2/9)x + b
We can find b by using the one fully given point, (-4, -6).
y = -(2/9)x + b
-6 = -(2/9)(-4) + b
b = -6 - (8/9)
b = -(62/9)
Now we have y = -(2/9)x - (62/9)
We want the value of y when x is 5 to find v in (5,v):
y = -(2/9)x - (62/9)
y = -(2/9)(5) - (62/9)
y = -(10/9) - (62/9)
y = -(72/9)
y = -8
v is -8
Determine the corresponding general form of each of the following vertex form
1. y = (x– 1)2
A. y = x2+ x + 1
B. y = x2 – 2x – 1
C. y = x2 – 2x + 1
2. y = (x + 4)2– 5
A. y = x2+ 8x – 11
B. y = x2+ 8x – 21
C. y = x2+ 8x + 21
3. y = -(x + 9)2– 10
A. y = -x2– 18x + 91
B. y = -x2– 18x – 91
C. y = -x2– 18x – 71
4. y = 3(x + 2)2– 18
A. y = 3x2+ 12x – 6
B. y = 3x2+ 12x + 6
C. y = 3x2+ 12x – 14
5. y = -2(x + 1)2– 16
A. y = -2x2– 4x – 18
B. y = -2x2– 4x – 2
C. y = -2x2– 4x – 14
6. y = 5(x + 5)2
A. y = 5x2+ 50x + 125
B. y = 5x2+ 50x + 25
C. y = 5x2+ 25x + 125
7. y =1/2(x + 8)2– 8
A. y = 1/2x2 + 8x + 24
B. y= 1/2x + 8x – 40
C. y = 1/2x2 + 16x + 24
8. y = (x + 3/2)2 + 3/4
A. y = x2+ 3x + 2
B. y = x2 + 6/4x + 12/16
C. y = x2 + 3x + 3
9. y = 2(x + 8)2– 5x
A. y = 2x2 + 32x + 59
B. y = 2x2 + 27x + 128
C. y = 2x2+ 37x + 64
10. y = -5(x – 4)2+ 15
A. y = -5x2+ 40x – 65
B. y = -5x2 – 40x – 65
C. y = -5x2+ 40x + 65
Answer:
Step-by-step explanation:
(a + b)² =a² + 2ab + b²
(a -b)² = a² - 2ab + b²
1) y = (x -1)²
y= x² - 2*x*1 + 1
y = x² - 2x + 1
Ans: C
2)y = (x +4)² + 5
y = x² +2*x*4 + 4² + 5
= x² + 8x + 16 + 5
y = x² + 8x + 21
C
3) y = -(x + 9)²- 10
y = - [x² + 18x + 81] - 10
= -x² - 18x - 81 - 10
y =-x² - 18x - 91
B
4) y = 3(x + 2)² - 18
y =3 [x² + 4x + 4] - 18
y = 3x² + 12x + 12 - 18
y =3x² + 12x - 6
A
5) y = -2(x + 1)² - 16
= -2[x² + 2x + 1] -16
= -2x² - 4x - 2 - 16
y = -2x² - 4x - 18
A
6) y = 5(x + 5)²
=5[x²+ 10x + 25]
y = 5x² +50x + 125
A
7)y = (1/2)(x + 8)² - 8
y = (1/2) (x² + 16x + 64) - 8
[tex]y = \dfrac{1}{2}*x^{2}+ \dfrac{1}{2}*16x + \dfrac{1}{2}*64 -8\\\\\\y =\dfrac{1}{2}x^{2}+8x +32 - 8\\\\\\y=\dfrac{1}{2}x^{2} +8x + 24[/tex]
A
8) y = (x + 3/2)² + 3/4
[tex]y = x^{2} +2*x*\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{3}{4}\\\\y=x^{2}+3x+\dfrac{12}{4}\\\\\\y=x^{2}+3x + 3[/tex]
C
9) y = 2[x² + 16x + 64] - 5x
y = 2x² + 32x + 64 - 5x
y =2x² + 27x + 6
what would the answer be
Answer:
60
Step-by-step explanation:
If a 12-foot-tall object casts a 9-foot shadow, how long a shadow would a 4-foot-tall object cast at the same time and place
Answer:
I think it is 3 feet
Step-by-step explanation:
12:9 is equal to 4:3
4:? should also be equal to 4:3, so ?=3
Hope this helps
let me know if it does and if it is right
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
Answer:
15
Step-by-step explanation:
Find x. Isosceles triangle theorems.
Answer:
x = 70°Step-by-step explanation:
If two sides of a triangle are congruent, then angles opposite those sides are congruent.
the sum of the interior angles in a triangle is 180°
(180 - 40) : 2 =
70
x = 70°
----------------------------
check
70 + 70 + 40 = 180°
the answer is good
The line given by y=2x+1,and the circle given by (x+1)^2+y^2=1 are graphed.
Answer:hhfff
Step-by-step explanation:
The required solutions to the line intersecting the circle at the points are x = -1, y = -1, and x = -0.2; y =0.6.
What is the equation of a circle?The equation of a circle with center (h,k) and radius r is :
r² = (x−h)² + (y−k)²
The graph correctly defines one solution.
The straight line intersects the circle at point A in the third quadrant.
The coordinates of point A are (-1,-1).
Hence, the solution is: x = -1,and y = -1
(x+1)² + y² = 1 and y=2x+1
Solving for 'x'
(x+1)² + (2x+1)= 1
x²+1+2x + 4x² + 1 + 4x =1
5x² + 6x + 1 = 0
(x+1/5)(x+1) = 0
(x+1/5) = 0 and (x+1) = 0
x = -1/5 and x = -1
For x = -1
y = 2(-1) +1 = -2+1 = -1
For x = -1/5
y = 2(-1/5) +1 = -2/5 + 1 = 3/5
Hence, the solution is : x = -0.2 and y =0.6
Learn more about the equation of a circle here:
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The question seems to be incomplete the missing part has been attached below
A square solar panel has an area of 16 square feet. Write the area as a power. Then find the side lengths of the panel.
The area of the solar panel written as power is
square feet.
The side lengths of the solar panel are
feet.
Answer:
area = 4^2
side lengths 4 ft
Step-by-step explanation:
I really really really need help with this please I’ll give brainlist
Roy works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 1 kilogram each, and are shipped in a container that weighs 6 kilograms. Large ones, on the other hand, weigh 2 kilograms apiece, and are shipped in a container that weighs 5 kilograms. If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight. How many helicopters would fit in either container? What would the total weight be
for the small one there would be six small helicopters and two big ones
and the total weight would be 11 for the two containers like one container of large helicopters and one container of small helicopters
if it's wrong i'm very sorry i'm bad at word problems
Comepare and order the following numbers from least to greatest. 5.2 -5.666 3.9 ✔️21
Answer: 1st -5.666 2nd 3.9 3rd 5.2 4th21
Step-by-step explanation:
you don't have to worry about the .9 and .2 in 3.9 and 5.2 just look at it as 3 and 5. 5 is greater so it comes first and 21 is the greatest and -5.666 is negative so -5.666 is the least
please help me with this 2
What is the
leasure of Z?
x
У
4.
9
Z=
=
= [?]V
Give your answer in simplest form.
Answer:
z = 3√13
Step-by-step explanation:
The length of z is the geometric mean of the segments of the longest side that share a common point with z. The shorter of those is 9; the longer one is 4+9 = 13. Then ...
z = √(9(13))
z = 3√13
__
Additional comment
In like fashion, ...
x = √(4(13)) = 2√13y = √(4·9) = 6.__
These relations come about because all of these right triangles are similar. That means their side lengths are proportional.
long side/hypotenuse = z/13 = 9/z ⇒ z = √(9·13)
short side/hypotenuse = x/13 = 4/x ⇒ x = √(4·13)
short side/long side = 4/y = y/9 ⇒ y = √(4·9)
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
110
(216)
-6+
O x = 2
O x = 6
-2-
to 6t 22
6 8 10
х
O y = 2
O y = 6
(-8-4
(84)
-6
-8
10
Answer: what are the choices?
Step-by-step explanation:
2x+5+2x+3x in One sloution, and no solution.
- BRAINLIEST answerer
PLEASE HELP
Find the current value of a car bought for new at $18300 which depreciates at 8% per annum over 4 years
Answer:
12, 444
Step-by-step explanation:
•First find out what is 8% of 18300
=8\100 ×18300\1 = 146400\100 =1464. [\ means ÷]
• Next multiply 1464 by 4 years =5,856
•Finally calculate 18300- 5856 = 12,444 (we are saying 18300 - 5856 because the money
decreased & 5856 represnt 8% of 18300 in 4 years)
Note :~ Appreciation is when money increases
~Deperciation is when money decreases
Hope this helps !!!Plsss some one help with this
Answer:
the answer is c and the entire equation means that the tickets each cost $15 and the service fee is $12
Seven times the sum of a number and three is equal to four times the number, decreased by eight. If X represents the number, which equation is correct
A- 7(X + 3) = 4X - 8
B- 7(X + 3) = 4(X - 8)
C- 7X + 3 = 4X - 8
Answer:
A. 4(x + 3) = 4x - 8.
Step-by-step explanation:
Which ordered pairs are on the line with the equation y+3.5=0.75(x−2)? Select each correct answer. A. (4, −2) B. (1, 1.75) C. (7, 5.5) D. (−4, −8)
Answer:
A
Step-by-step explanation:
Answer: 4, -2
Step-by-step explanation: I just visualized the graph in my head and went from there
Evaluate the formula χ2=
(n−1)s2
σ2 when σ=1.61, n=39, and s=3.79.
Work Shown:
[tex]\chi^2 = \frac{(n-1)s^2}{\sigma^2}\\\\\chi^2 = \frac{(39-1)(3.79)^2}{(1.61)^2}\\\\\chi^2 = \frac{38*14.3641}{2.5921}\\\\\chi^2 = \frac{545.8358}{2.5921}\\\\\chi^2 \approx 210.57667528259\\\\\chi^2 \approx 210.577\\\\[/tex]
Find the inverse function in slope-intercept form (mx+b):
f(x) = -x - 5
Answer:
In order to find the inverse of a function, we flip it over the line y=x, or we switch the x and y values in the equation and solve it for y. So let's do the latter:
m(x) = 5x - 5
y = 5x - 5
x = 5y - 5
5y = x + 5
y = (x + 5)/5
Step-by-step explanation:
hope this is helpful
Answer: f ^−1(x)=x+5
If x=4 then 2(x-4) equals
Answer:
0
Step-by-step explanation:
Need to plug in the x to the 4 then u get 2(4-4)
After that it will equal to 0 the 4-4
2(0)=0
The selling price of an item is $550 it’s marked down by 20% but the sale price is still marked up from the cost of $400 find the markup from cost to sale price
STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system.
Gustavo used 8 round tables and 6 rectangular tables.
Since Gustavo sets up tables for a caterer on weekends, and each round table can seat 8 people while each rectangular table can seat 10 people, and one weekend, his boss asked him to set up tables for 124 people, and he uses 2 more round tables than rectangular tables, to find the number of round tables and rectangular tables Gustavo used the following calculation must be performed:
10 x 8 + 8 x 10 = 160 8 x 8 + 6 x 10 = 124
Therefore, Gustavo used 8 round tables and 6 rectangular tables.
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