Answer:
the product of the 2 numbers is 22
Step-by-step explanation:
x² + y² = 80
(x - y)² = 36
=>
x - y = 6
or y - x = 6
let's start with the first one x-y=6
x = 6 + y
=>
(6+y)² + y² = 80
y² + 6y +6y + 36 + y² = 80
2y² + 12y + 36 = 80
2y² + 12y - 44 = 0
y² + 6y - 22 = 0
the solution of a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here we have an squadron in y.
a=1
b=6
c=-22
(-6 ± sqrt(36 + 4×22))/2 = (-6 ± sqrt(36+88))/2 =
= (-6 ± sqrt(124))/2 = (-6 ± sqrt(4×31))/2 =
= (-6 ± 2×sqrt(31))/2 = -3 ± sqrt(31)
y1 = -3 + sqrt(31)
y2 = -3 - sqrt(31)
=>
x1 = 6 + -3 + sqrt(31) = 3 + sqrt(31)
x2 = 3 - sqrt(31)
control :
(-3 + sqrt(31))² + (3 + sqrt(31))² = 80
9 - 3 sqrt(31) - 3 sqrt(31) + 31 + 9 +3 sqrt(31) + 3 sqrt(31) + 31 = 80
9 + 31 + 9 +31 = 80
18 + 62 = 80
80 = 80 correct
solving now for y-x=6
delivers exactly the same calculations, just with x and y trading places.
so, the resulting 2 number pairs are the same.
the product of the 2 numbers :
(3 + sqrt(31))(-3 + sqrt(31)) = -9 - 3 sqrt(31) + 3 sqrt(31) + 31 =
= -9 + 31 = 22
(3 - sqrt(31))(-3 - sqrt(31)) = -9 + 3 sqrt(31) - 3 sqrt(31) + 31 =
= 22
so, the product is the same in both cases.
59.73 - 21.876
can u help me
Answer:
37.854
Step-by-step explanation:
59.73-21.876=37.854
N is a number such that N ÷ 18= 16. What is the value of N?
Answer:
288 po
Step-by-step explanation:
288 divided by 18 is 16
PLEASE HELP WITH THIS GEOMETRY PROJECT IM GIVING ALL MY POINTS (45)
Answer:
YEAH!!!!!! ITS 45
Step-by-step explanation:
MHM!
Answer:
woooooooooooooooohoooooooooo points go brrrrrr
Step-by-step explanation:
!!
Ecuación ,me seria de mucha ayuda su respuesta
3x+1=5x+3=
Answer:
3x+5x=3-1
8x=2
X=8/2
X=4
Select the correct answer.
What is the solution for x in the equation?
-x + 3/7 = 2x - 25/7
Answer:
= 4/ 3
Step-by-step explanation:
-x+3/7=2x-25/7
We move all terms to the left:
-x+3/7-(2x-25/7)=0
We add all the numbers together, and all the variables
-x-(+2x-25/7)+3/7=0
We add all the numbers together, and all the variables
-1x-(+2x-25/7)+3/7=0
We get rid of parentheses
-1x-2x+25/7+3/7=0
We multiply all the terms by the denominator
-1x*7-2x*7+25+3=0
We add all the numbers together, and all the variables
-1x*7-2x*7+28=0
Wy multiply elements
-7x-14x+28=0
We add all the numbers together, and all the variables
-21x+28=0
We move all terms containing x to the left, all other terms to the right
-21x=-28
x=-28/-21
x=1+1/3
Answer:
x = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Given
- x + [tex]\frac{3}{7}[/tex] = 2x - [tex]\frac{25}{7}[/tex] ( multiply through by 7 to clear the fractions )
- 7x + 3 = 14x - 25 ( subtract 14x from both sides )
- 21x + 3 = - 25 ( subtract 3 from both sides )
- 21x = - 28 ( divide both sides by - 21 )
x = [tex]\frac{-28}{-21}[/tex] = [tex]\frac{4}{3}[/tex]
HELP!! I tried solving this and cant seem to get it right.
Answer:
x= 20
y = 10
Step-by-step explanation:
Angles 3x° and 60° are Corrosponding angles so they are equal:
[tex]3x = 60 \\ \frac{3x}{3} = \frac{60}{3} \\ x = 20[/tex]
Angles (5y-5)° and 135° are Cointerior so add to give 180°:
[tex]5y - 5 + 135 = 180 \\ 5y + 130 = 180 \\ 5y = 180 - 130 \\ \frac{5y}{5} = \frac{50}{5} \\ y = 10[/tex]
Substitute y and x into the respective formula's to get your angles.
How many one-to-one correspondences exist between A = {1, 2, 3, 4} and B = {a, b, c, d}
Answer:
There are 24 different correspondences.
Step-by-step explanation:
A one-to-one correspondence means that each element of A can be mapped into only one element of B, and we can't have two or more elements from A mapped into one element from B.
So, to count all the possible combinations, we need to find the number of possible options for each mapping
The first element from A, the 1, can be mapped into any of the four elements of B, so here we have 4 options.
The second element from A, the 2, can be mapped into any of the remaining elements from B, 3 of them (remember that one of the elements of B is taken).
The third element from A, the 3, can be mapped into any of the remaining elements from B, 2 of them now, so here we have 2 options.
The final element from A, the 4, can be mapped into the remaining element from B, so here we have only one option.
The total number of different correspondences (or combinations) is equal to the product between the numbers of options, this is:
Combinations = 4*3*2*1 = 12*2 = 24
There are 24 different correspondences.
Find the vertex and the axis of symmetry of the graph of f(x) = 1/4(x-6)^2
Answer:
The vertex of the graph is at (6,0) and the Axis of symmetry is at x= 6
Step-by-step explanation:
If you have to multiply the previous number by 2 in the y intercept in order to receive the next number, what would the equation be?
Answer:
Jsjsjsjsjwjwksjsjjsisisiwiw
Find the measures of a positive angle and a negative angle that are coterminal with each given angle
0=110
Answer:
Why was Mrs Hallette unhappy when people asked about her son?
Step-by-step explanation:
Find one value of x that is a solution to the equation:
(x^2+4)^2 – 11(x^2+4) + 24 = 0
Answer:
x = ±2
x = ±i
Step-by-step explanation:
(x^2+4)^2 – 11(x^2+4) + 24 = 0
Let m = x^2 +4
(m)^2 – 11(m) + 24 = 0
Solving this quadratic
What two numbers multiply to 24 and add to -11
-8*-3 =24
-8-3 = -11
(m-8)(m-3) =0
m = 8 m=3
Now substitute back
x^2 +4 = 8 x^2 +4 = 3
x^2 +4-4 = 8-4 x^2+4-4 = 3-4
x^2 = 4 x^2 = -1
Taking the square root
sqrt(x^2) = sqrt(4) sqrt(x^2) = sqrt(-1)
x = ±2 x = ±i
Answer:
one value of x = 2
Step-by-step explanation:
[tex](x^2 + 4 )^2 - 11(x^2 + 4 ) + 24 = 0\\\\x^4 + 16 + 8x^2 - 11x^2 -44 + 24 = 0\\\\x^4 - 3x^2 -4 = 0\\\\[/tex] ------ ( 1 )
[tex]Let \ x^2 \ = \ u[/tex]
( 1 ) => [tex]u^2 - 3u - 4 = 0[/tex]
[tex]u^2 -4u + u - 4 = 0\\\\u(u - 4) + 1 (u - 4) = 0\\\\(u + 1) (u - 4) = 0\\\\u = -1 \ , \ u = 4[/tex]
[tex]=> x^2 = - 1 \ and \ x^2 = 4[/tex]
[tex]x = \sqrt {-1} = i[/tex]
[tex]x = \sqrt{4} = \pm 2[/tex]
ill be giving brainlist:( please help
Answer:
Step-by-step explanation:
The translation vector < 4, - 2 > means each point is being moved 4 units to the right and 2 units down.
X(0, 3) ------> X' ( 0 + 4, 3 - 2 ) = X'(4, 1)
Y( - 1, 1) ------> Y' ( - 1 + 4, 1 - 2 ) = Y'(3, - 1)
Z( - 3, 4) -----> Z' ( - 3 + 4, 4 - 2 ) = Z'(1, 2)
Question 17 of 25
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
A. infinitely many
B. cannot be determined
C. O
D. 1
Answer:
A. infinitely many
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
If 2 lines are parallel (same slope, different y-intercept), they would have no solution.
If 2 lines were the same (same slope, same y-intercept), they would have infinite amount of solutions.
Susan buys the items listed below at a grocery store. 2 packages of chicken priced at $13.26 per package 1/2 pound of broccoli priced at $ 1.88 per pound 1 gallon of milk priced at $3.49 per gallon There is no sales tax on the food she buys. Susan pays for the items and receives $ 0.05 in change. What amount of money does Susan use to pay for the items?
Answer: $31.00
Step-by-step explanation:
The cost of the items bought will be:
2 packages of chicken priced at $13.26 per package = 2 × $13.26 = $26.52
1/2 pound of broccoli priced at $ 1.88 per pound = 1/2 × $1.88 = $0.94
1 gallon of milk priced at $3.49 per gallons = 1 × $3.49 = $3.49
Since Susan pays for the items and receives $ 0.05 in change, the the amount of money that Susan use to pay for the items will be:
= $26.52 + $0.94 + $3.49 + $0.05
= $31.00
The amount Susan uses in paying is $31.00.
5. There is a circular field of area of approximately
500 m2. How can you find its area accurately by
using a measuring tape?
Step-by-step explanation:
It is known that area of a circular is calculated as follows.
[tex]Area = \pi \times r^{2}[/tex]
So, when a circular field of area of approximately 500 [tex]m^{2}[/tex] is there then diameter of the field is calculated using the measuring tape from one side of the circular tape to the other. Now, to calculate the radius it is required to divide the diameter by 2.
Hence, put these values into the above formula to find out the area. In this way we can find out the area of given circular field accurately by using a measuring tape.
Which set of numbers is arranged in increasing order? A. , , , B. , , , C. , , , D. , , ,
Answer:
its B
Step-by-step explanation:
3.14 then pi (3.14159) then 22 ÷ 7 (3.1428) then square root of 10 (3.16)
Answer:
B
Step-by-step explanation:
pi=3.141592654
square root of 10=3.16227766
3.14=3.14
22/7=3.142857143
25.673 round off to the nearest hundredth
Answer:
25.67
Step-by-step explanation:
Look at the thousandth place. If it is 5,6,7,8 or 9 then add 1 to hundredth place. If it is less than 5, then write the hundredth place as it is
25.67
Which equation is equivalent to the given equation
X2-6x=8
Answer:
Step-by-step explanation:
x^2 －6x-8=0
PLEASE HELP ME!! its a pretty easy question
Answer:
V= 936m³
Step-by-step explanation:
Formula:
Volume = L * W * H
Volume1= L * W * H
= 16 * 9 * 6
= 864m³
Volume2= L * W * H
= 6 * 2 * 6
= 72m³
Add both volumes to get total volume.
= 864m³ + 72m³ = 936m³
Hope this helps!
Have a nice dayy! :)
4400 dollars is place in an account with annual interest rate of 8.25% How much will be in the account after 22years to the nearest cent
Answer: A = 4400(1 + 0.0825 x 22)
Step-by-step explanation:
A = accumulated amount
P = original amount unloaded- $4400
r = rate - 8.25% = 0.0825
t = years = 22
= 4400(1 + 0.0825 x 22)
Answer:
y = 25169.04
Step-by-step explanation:
An angle measuring 60 degrees is measured as 62 degrees. What is the percentage error correct to 3 significant figures?
error = 62-60 = 2°
% = (2×100)/60 = 100/30 = 10/3 = 3.333%
Fill in the blanks with the most appropriate words given below.
around, react, too, method, fields, on, plants,
together, is, family, planter, weeds, experience, talking
Ecology is the study of how (1)… ……………………, animals and people live (2)…… ………… and
help each other. But man sometimes forgets he (3) ……..……….. a part of the (4)……………….. of
all living things. Here is an example. A planter is (5)………………. about killing (6)… ……………
on his land. He remembers his first (7)……………….… with a weedicide. He was a (8)
………………….. then, working (9)………..………..a rubber plantation. He had a problem with
weeds. The cost of weeding of the (10)…….…………… by hand was getting (11)………..…………
high. So he used a new, cheap and effective (12)……………………, good old Sodium
Arsenate. He sprayed plenty of this (13)………………………… to kill the weeds. The first thing to
(14)…………………… were the frogs.
Answer:
1. plants
2. together
3. is
4. family
5. talking
6. weeds
7. experience
8. planter
9. on
10. fields
11. too
12. method
13. around
14. react.
Explanation:
The given passage talks about the impact of chemicals on the ecosystem. The speaker narrates how the ecology belongs to plants, animals, and humans, though man seemed intent to destroy it for himself.
The blanks in the given passage are filled with the appropriate words as follows-
Ecology is the study of how (1) plants, animals, and people live (2) together and help each other. But man sometimes forgets he (3) is a part of the (4) family of all living things. Here is an example. A planter is (5) talking about killing (6) weeds on his land. He remembers his first (7) experience with a weedicide. He was a (8) planter then, working (9) on a rubber plantation. He had a problem with weeds. The cost of weeding of the (10) fields by hand was getting (11) too high. So he used a new, cheap, and effective (12) method, good old Sodium Arsenate. He sprayed plenty of this (13) around to kill the weeds. The first thing to (14) react were the frogs.
Can someone helppppp and explain plsss:))
Answer:
Step-by-step explanation:
What is the answer to -4 + 10.
Negative 4 plus 10
Answer:
Six
Step-by-step explanation:
10 - 4 = 6
-4 + 10 = 6
Answer:
6
Step-by-step explanation:
[tex] - 4 + 10 = 6[/tex]
6
Please answer quickly
Answer:
10
Step-by-step explanation:
given :
length WX ≅ (congruent means equal) length XY
therefore , WX = 3
WZ = WX + XZ
WZ = 3 + 7
WX = 10
Add the following numbers. (-4) + (-9) =
Answer:
-13
Step-by-step explanation:
Adding a negative means that you subtract the number as + (-) = -
This means that the equation is -4-9=-13.
Answer:
-13
Step-by-step explanation:
25 points please explain it to me add the answer and the work since I’m so confused on when to subtract missing lengths where and when
9514 1404 393
Answer:
it depends on what the question is (no question is given)
Step-by-step explanation:
What you add or subtract will depend on the problem you're trying to solve, and how you're trying to solve it.
Perimeter
The two left-side vertical segments are 13 and 3. The right-side vertical segment is 16. As you can see, these have the same total: 16.
The top horizontal segment has a length of 21. The two bottom horizontal segments have lengths 16 and 5, for a total of 21—the same as the top segment.
For simple L-shaped figures like this, the overall horizontal lengths and the overall vertical lengths are the same as they would be for a rectangle that is 21 wide and 16 high.
P = 2(L+W) = 2(21+16) = 2(37) = 74 units
__
Area
The dashed lines divide this figure into 3 rectangles.
left side: 16 wide by 13 high
upper right: 5 wide by 13 high
lower right: 5 wide by 3 high
You can see that the vertical measures must "add up", as must the horizontal measures. This fact helps you determine the lengths of the unmarked sides.
You can compute the area from the three rectangles identified above, or any of several other ways. One of my favorite is to compute the overall area of the 21 wide by 16 high rectangle, then subtract the 16 wide by 3 high white space at lower left.
area = 21·16 -16·3 = 16·(21 -3) = 16·18 = 288 . . . . square units
Adding the 3 rectangles identified above gives ...
16·13 +5·13 +5·3 = 208 +65 +15 = 288 . . . . same area
Which statement can be represented by the equation 18 divided by m = 7.2?
A number, m, less than 18 is seven point two.
Eighteen decreased by a number, m, is seven point two.
A number, m, divided by 18 is seven point two.
Eighteen divided by a number, m, is seven point two.
Answer:
A number,m,is seven point two . Eighteen divided by a number,m,is seven point two
Answer:
its c
Step-by-step explanation:
just to make it easier for you:)
The measures, in degrees, of the three angles of a triangle are given by 2x+1, 3x - 3, and 9x. What is the
measure of the smallest angle?
Answer:
Step-by-step explanation:
27 degrees
Given the general form of the sinusoidal function, y = AsinB(x - C) + D, match the following items.
Answer:
[tex]\Delta y = A[/tex] (Amplitude) (Correct answer: 1)
[tex]\omega = B[/tex] (Angular frequency) (Correct answer: 2)
[tex]x_{o} = C[/tex] (Phase shift) (Correct answer: 3)
[tex]y_{o} = D[/tex] (Vertical shift) (Correct answer: 4)
[tex]\frac{2\pi}{\omega} = \frac{2\pi}{B}[/tex] (Period) (Correct answer: 5)
Step-by-step explanation:
The general form of a sinusoidal function is represented by the following characteristics:
[tex]y = \Delta y \cdot \sin \omega\cdot (x- x_{o}) + y_{o}[/tex] (1)
Where:
[tex]\Delta y[/tex] - Amplitude.
[tex]\omega[/tex] - Angular frequency.
[tex]x_{o}[/tex] - Phase shift.
[tex]y_{o}[/tex] - Vertical shift.
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
In addition, we know that the period associated with the sinusoidal function ([tex]T[/tex]) is:
[tex]T = \frac{2\pi}{\omega}[/tex]
By direct comparison, we get the following conclusions:
[tex]\Delta y = A[/tex] (Amplitude) (Correct answer: 1)
[tex]\omega = B[/tex] (Angular frequency) (Correct answer: 2)
[tex]x_{o} = C[/tex] (Phase shift) (Correct answer: 3)
[tex]y_{o} = D[/tex] (Vertical shift) (Correct answer: 4)
[tex]\frac{2\pi}{\omega} = \frac{2\pi}{B}[/tex] (Period) (Correct answer: 5)
