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]
Five numbers with mean 4, mode 3, and range 9
Answer:
6,6,6,6,6
Step-by-step explanation:
You’d have to have an odd number of 6s and more than one, so either 3 or 6 of the numbers will have to be 6s
6, 6, 6, 6, 6
5, 6, 6, 6, 7 (the 5 and 7 could be replaced by 4/8, 3/9, 2/10, or 1/11 - as long as balance is preserved)
A farmer has 24 bushels of apples and can harvest 22 bushels of apples each day?
Answer:
................ I don"t know sorry I hate you
Dave created a video that was originally 64 minutes long, but he ended up cutting it by 13%. How long was his video after he cut it?
Answer:
70 minute
it was help full
Find the unit rate for each problem.
Answer:
1. 11 players per team
2. 60 miles per hour
3. 25 games per season
4. 60 words per minute
Step-by-step explanation:
1) 132 players divided by 12 teams = # of players per team
132/12 = 11 players per team
2) 240 miles divided by 4 hours = # of miles per hour
240/4 = 60 miles per hour
3) 125 games divided by 5 seasons = # of games per season
125/5 = 25 games per season
4) 180 words divided by 3 minutes = # of words per minute
180/3 = 60 words per minute
Solve the equation for X:
4x2 + 15x = 4
Answer:
15x=-4
Step-by-step explanation:
Solve the inequality and enter your solution as an inequality.
X-4<6
Answer:
x < 10
Step-by-step explanation:
Given: x -4 < 6
Add four to both sides: x < 10
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Write a differential formula that estimates the change in volume of a sphere when the radius changes from
Answer:
d.
took the test
Step-by-step explanation:
I need help with this please.
1. Which value is the closest to 1/9 • 24/25 (fractions)
a. 0
b. 0.5
c. 1
d. 21/20 (fraction)
Explain your answer:
Answer:
Option A: 0
Step-by-step explanation:
Given the multiplication of fractions, [tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}}[/tex]:
Simply multiply the numerators (together), as well as the denominators.
In other words:
[tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}\:=\frac{1\:\times\:24}{9\:\times\:25}\:=\:\frac{24}{225}}[/tex]
Since 24 and 225 do not have common multiples, then we cannot simplify the fraction into its lowest terms.
Next, in order to find out which is the closest value to the product, [tex]\huge\mathsf{\frac{24}{225}}[/tex], divide the numerator by the denominator, which gives you the following quotient:
[tex]\huge\mathsf{\frac{24}{225}\:=\:24\:\div\:225\:=\:0.1067}[/tex] or 0.11.
We must compare this quotient with the other options:
Option A) 0: This is a possible answer, since rounding 0.11 to the nearest ones (whole number) is 0.
Option B) 0.5: Unlikely a valid answer, since the digit on the hundreths place is 0.11, and rounding it up to the nearest tenths will become 0.1.
Option C) 1: Definitely not a valid answer, according to the explanations provided in Options A and B.
For Option D) [tex]\huge\mathsf{\frac{21}{20}}[/tex] , we need to find its equivalent decimal form by dividing its numerator by the denominator: [tex]\huge\mathsf{\frac{21}{20}\:=\:21\:\div\:20\:=\:1.05}[/tex]. Hence, it is also not a valid answer, according to the explanations provided in Options A and B.
Therefore, the closest value to [tex]\huge\mathsf{\frac{24}{225}\:=\:0.11}[/tex] is Option A) 0.
State if the triangles are similar. If so, how do you know they are similar and complete the similarity
statement
STU ~
Answer:
b. not similar
Step-by-step explanation:
Side SC of the smaller triangle is ...
96 -57 = 39
So, the side lengths of the small triangle, shortest to longest, are ...
39, 40, 44
Side ST of the larger triangle is ...
44 +64 = 108
So, the side lengths of the large triangle, shortest to longest, are ...
96, 96, 108
These lengths do not have the same ratios as the lengths of the sides in the smaller triangle, so the triangles are not similar.
_____
Additional comment
The larger triangle is isosceles. The smaller triangle is not.
-5/6e-2/3=-24 what does e=
Answer:
-5e/6-2/3=-24
Step-by-step explanation:
Find the equation of the line.
Use exact numbers.
y = ___x + ___
Step-by-step explanation:
formula: y=mx+b
First you gotta find M witch is Slope.
B is the y-intercept which is -2
then you have to do rise/run
so up 2
right 3
= 2/3
so your answer would be
y=2/3-2 because you can't simplify 2/3
Please find the slope of these tables
Step-by-step explanation:
To calculate each slope, just take any two points from each table, and plug them into this formula:⤵⤵⤵
(It'll be a bit small btw)
[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]
Table 1: I chose points (13,1) and (5,21)
21 - 1 = 20
5 - 13 = -8
Simplified = -5/2 ⬅ Slope
Table 2: I chose points (4,16) and (9,19)
19 - 16 = 3
9 - 4 = 5
3/5 ⬅ Slope
Table 3: I chose points (0,6) and (9,0)
0 - 6 = -6
9 - 0 = 9
Simplified = -2/3 ⬅ Slope
Table 4: I chose points (-8,1) and (-8,17)
17 - 1 = 16
-8 - (-8) = -8 + 8 = 0
Undefined slope (meaning the line will just be verticle)
Table 5: I chose points (2,3) and (3,5)
5 - 3 = 2
3 - 2 = 1
Simplified = 2 ⬅ Slope
Hope this helps :)
What is the constant of proportionality in the equation
Below
Answer:
k = 9/2
Step-by-step explanation:
Constant of proportionality, k = y/x
given: x/y = 2/9
since k = y/x, therefore, k value will now be inverse of 2/9, which is 9/2
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
Can someone please give me examples of linear, quadratic, Absolute value, square root, cubic, cube root, exponential, logarithmic, and rational function (parent function) equations to help my friend? Please and thank you. I'll give brainliest to the first person who does all of them and get them right.
Answer:
Step-by-step explanation:
Consider the cube root parent function.
( graph in photo below )
Complete the statements to make them true.
A cube root function will ( 1 ) ________ have an x-intercept and ( 2 ) ________ have a y-intercept.
For the parent cube root function, ( 3 ) ____________ located at .
Answer:
1. always
2. always
3. both intercepts are
the explination photos below
Answer:
I got you
[tex]f(x)=3x+2[/tex]
[tex]f(x)=4x^2+3x+7[/tex]
[tex]f(x)=|x+4|[/tex]
[tex]f(x)=\sqrt{x+12}[/tex]
[tex]f(x)=6x^3+4x^2-3x-5[/tex]
[tex]f(x)=\sqrt[3]{3x-5}[/tex]
[tex]f(x)=2^x[/tex]
[tex]f(x)=log_3(x)[/tex]
[tex]f(x)=\frac{x+5}{x-3}[/tex]
Each function is respective to the order of the list given.
Let me know if you want the graphs
Which coin does Jeff have the most of in his collection?
nickel
penny
dime
Answer:
dimes
Step-by-step explanation:
Answer: dimes
Step-by-step explanation:
ANSWER FAST PLEASE !!
Use synthetic division and the remainder theorem to find P(a).
P(x) = x^3 + 5x^2 - 6x +6; a = 4
P(a) =
Simplify your answer
Answer:
[tex]1 + 2 = [/tex]
answer
Order the numbers from least to greatest.
1,553
1,347
1,644; 1,553; 1,347
b. 1,347; 1,553; 1,644
1,644
a.
C.
1,553; 1,347; 1,644
Please select the best answer from the choices provided
Ο Α
Ο Ο Ο
B
Answer:
b even though you made this hard to read lol, its b
Step-by-step explanation:
4x squared plus 20x minus 24 pls
The Answer will equal 4(x-1)(x-6)
Step by step explanation= 4x^2+20x-24, 16x+20x-24, 36x-24= 12x
Answer:
4(x-1) (x-6) as an evaluation OR 12x as the answer since you didn't include what it equals.
Step-by-step explanation:
4x^2+20x-24
16x+20x-24
36x-24
12x
1 Solve for the unknown variable:
Answer:
Hypotenuse^2 = Opposite^2 + Adjacent^2
Step-by-step explanation:
Here hypotenuse is c, opposite is a and adjacent is b.
c^2 = a^2 + b^2
16^2 = a^2 + 12^2
a^2 = 16^2 - 12^2
a^2 = 112
a = √112 or 10.58
As the question uses inches I think it would be better if you wrote 10.58 in.
Hopefully this helps!!
+ 1 x 4
2-
ax + b
can be written as a single fraction in the form
X2 x + 2
x² - 4
where a and b are integers.
x+ 2 x -
Work out the value of a and the value of b.
[tex]2 - \frac{x+1}{x-2} - \frac{x-4}{x+2} = \frac{2(x-2)(x+2)}{(x-2)(x+2)} - \frac{(x+1)(x+2)}{(x-2)(x+2)} - \frac{(x-4)(x-2)}{(x-2)(x+2)} \\= \frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)} \\= \frac{2x^{2} -8-x^{2}-3x-2-x^{2} +6x-8 }{x^{2} -4} \\=\frac{3x+(-18)}{x^{2} -4}[/tex]
so : a = 3 b = -18
ok done. Thank to me :>
(6x + 7) + (13x + 21) = 180
x =
Answer:
Step-by-step explanation:
x=4
Russell is eating at a restaurant. His total bill comes to $44.85. If Russell decides to leave a tip that is approximately 20% of the total bill, how much should he leave for the tip?
$9.00
$0.09
$54.00
$8.00
Answer:
I'm thinking is I'm not sure is is answer 0.9
Step-by-step explanation:
am not sure my answer guys because naka tulong din na man too
I dont know how to solve these still
Answer:
x = 20*
Step-by-step explanation:
180 - 110 = 70
90 - 70 = 20
x = 20*
reason is #5 Algebra
Have a nice day! :-)
A bread recipe uses 3 tablespoons of olive oil for every 1 clove of crushed garlic. Complete this table to show different-sized batches of bread that tastes the same as the recipe. number of batches olive oil (tablespoons) crushed garlic (cloves) 1 3 1 2
Question Blank
type your answer...
2 0.5 1.5
type your answer...
4
type your answer...
4
Answer:
What? I don't understand your question.
Step-by-step explanation:
just no just n oh yeah btw shoot some
what is the volume of the prism ?
Answer:
150 units squared
Step-by-step explanation:
would this be A? Im not too sure about this.
Answer:
You're correct
Step-by-step explanation:
Basically, just add the answers with the given 67° until you get 180°
Write the decimal as a fraction in simplest form.
5. -18.04
Answer: - [tex]\frac{451}{25}[/tex]
Step-by-step explanation:
3.
(03.06)
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
f(x) = (x −8)2
f(x) = (x −4)2−13
f(x) = (x −4)2 + 3
f(x) = (x −4)2 + 16
Answer: f(x) = (x −8)2
Step-by-step explanation:
Please help me this is due tomorrow.
Answer:
C
Step-by-step explanation:
The domain of a function is a set of values that make the function real and defined. No matter what number you substitute as x, the result is always real. Hence, the domain would be from negative infinity to positive infinity.
Answer: I think it’s D
Step-by-step explanation: