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.
in a sale, normal prices are reduced by 10%
nathalie bought a pair of shoes in the sale for £54
what was the original price of the shoes
in a sale, normal prices are reduced by 10%
nathalie bought a pair of shoes in the sale for £54
what was the original price of the shoes
Answer[tex]x = 60[/tex]
Explanation
[tex] \sf based \: on \: the \: given \: conditions \: write : x = \frac{54}{ 1 - 01} [/tex]
[tex] \sf calculate \: the \: sum \: difference: x = \frac{54}{0.9} [/tex]
convert decimal to fraction: x= 54 / 9 / 10
[tex] \sf \: divide \: a \: fraction \: by \: multiplying \: its \: reciprosal : x = 54 \times \frac{10}{9} [/tex]
[tex] \sf \: write \: as \: a \: single \: fraction : x = \frac{54 \times 10}{9} [/tex]
[tex] \sf \: reduce \: fraction \: to \: the \: lowest \: term \: by \: cancelling \: the \: greatest \: [/tex]
[tex] \sf \: common \: factor : x = 6 \times 10[/tex]
[tex] \sf \: calculate \: the \: product \: or \: quotient : x = 60 [/tex]
[tex] \sf{ \boxed{answer : x = 60}}[/tex]
The isosceles triangle theorem says "If two sides of a triangle are congruent,
then the angles opposite those sides are congruent."
If you are using this figure to prove the isosceles triangle theorem, which of
the following would be the best strategy?
S
Answer:
Draw QS so that S is the midpoint of PR, then prove ΔPQS is congruent to ΔRQS using SSS.
Step-by-step explanation:
Explanation,
(For Proper Question And Diagram Please Find In attachment)
Draw QS, so that S is the midpoint of PR .Solution,
Now, We know that PS = SR ( S is Midpoint of PR)QS = QS (Common Side) and PQ=QR (given Isosceles Triangle)then triangles are congruent and thus ∠QPS equals to ∠QRS.Thus, the triangle PQR is then the isosceles Triangle.I need help with this question
Answer:
38°.
Step-by-step explanation:
A triangle adds up to 180°.
CAB= 78°
But we minus 78° from 46°:
32°.
As a triangle adds up to 180°,
110+32= 142°.
180-142= 38°.
To see if we are correct:
38+32+110= 180°.
Hope this is okay!
An aeroplane flies 1860 miles in 4 hours. What is its average speed?
Answer:
The average speed is 465 mph
Step-by-step explanation:
1860/4 = 465
Answer:
The average speed is 465 mph
Step-by-step explanation:
Average speed = distance/time
1860 miles / 4 hours = 465 mph
10. Volume =
pls help me i wanna go home ;(
Answer:
1248 cm^2
Step-by-step explanation:
Volume = Length · Width · Height
Volume = 24 · 6 · 5
Volume = 720 cm^2
Volume = Length · Width · Height
Volume = 8 · 6 · 11
Volume = 528 cm^2
528 + 720 = 1248
Answer:
1248 cm³
Step-by-step explanation:
V = lwh
V = 24 cm × 6 cm × 5 cm
V = 720 cm³
V = lwh
V = 8 cm × 6 cm × 11 cm
V = 528 cm³
720 cm³ + 528 cm³
1248 cm³
Michael is going to the amusement park, where he has to pay a set price of admission
and another price for tickets to go on each of the rides. The total amount of money
Michael will spend is given by the equation y = 3x + 28, where y represents the
total amount of money, in dollars and cents, and a represents the number of rides
Michael goes on. What could the number 3 represent in the equation?
cant figure it out. pls help
[tex]\longrightarrow{\green{x\:=\:6}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
➝[tex] \:\frac{3x + 2}{4} = \frac{x + 4}{2} [/tex]
➝[tex] \: 2(3x + 2) = 4(x + 4)[/tex]
➝[tex] \: 6x + 4 = 4x + 16[/tex]
➝[tex] \: 6x - 4x = 16 - 4[/tex]
➝[tex]\:2x = 12[/tex]
➝[tex] \: x = \frac{12}{2} [/tex]
➝[tex] \: x = 6[/tex]
Therefore, the value of [tex]x[/tex] is 6.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
➪ [tex] \: \frac{3x + 2}{4} = \frac{x + 4}{2} [/tex]
➪ [tex] \:\frac{3 \times 6 + 2}{4} = \frac{6 + 4}{2} [/tex]
➪ [tex] \:\frac{18 + 2}{4} = \frac{10}{2} [/tex]
➪ [tex] \:\frac{20}{4} = 5[/tex]
➪ [tex] \: 5 = 5[/tex]
➪ [tex] \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{❦}}}}}[/tex]
an angle is 21 degree more than twice its complement find it
QUICK
ASAP now before tomorrow Please
Answer: 67°
Step-by-step explanation:
Complementary angle refers to the angle that when added together will be equal to 90°.
Let the measurement of the angle's complement be x.
Therefore, the angles are x and 2x + 21. Since it's a complementary angle, therefore,
x + 2x + 21 = 90
3x + 21 = 90
3x = 90 - 21
3x = 69
x = 69°/3
x = 23°
Therefore, the angle will be:
= 2x + 21
= 2(23°) + 21°
= 46° + 21°
= 67°
The angle is 67°.
Explain two procedures that you can use to draw two adjacent complementary angles. Then draw a pair of adjacent complementary angles so that one angle has a measure of 30°.
Answer:
Complementary angle of 30° is 60°.
Step-by-step explanation:
The complementary angles are the angles whose sum is 90.
If one angle is x then the other angle is 90 - x, they both are complementary to each other.
One angle is 30°, so the other angle is 90° - 30° = 60°
What is the area of ABC?
This value is approximate.
=========================================================
Work Shown:
area = 0.5*side1*side2*sin(included angle)
area = 0.5*AB*AC*sin(A)
area = 0.5*11*18*sin(55)
area = 81.0960523846101
area = 81.1 cm^2
The cm^2 refers to "square cm".
Notice that the angle must be between the two sides, hence the "included".
in trapezium abcd diagonals ac and bd intersect at o ar(COD) = 24cm² ar( AOB) = 96 cm² find the area of trapezium
Answer:
The area of the trapezium is 216 cm²
Step-by-step explanation:
The parameters of the trapezium are;
The point of intersection of the diagonals ac and bd = point o
The area of ΔCOD = 24 cm²
The area of ΔAOB = 96 cm²
Let h represent the height of the trapezium and let x represent the height of triangle ΔCOD, we have;
The height of ΔAOB = h - x
Therefore;
The area of ΔCOD = (1/2) × The length of CD × x = 24
∴ The length of CD = 24/((1/2) × x) = 48/x
The area of ΔAOB = (1/2) × The length of AB × (h - x) = 96
The length of AB = 96/((1/2) × (h - x)) = 192/(h - x)
The area of the trapezium, A = ((48/x + 192/(h - x))/2) × h
We note that ΔCOD ~ ΔAOB, therefore;
(AB)²/(CD)² = (h - x)²/x² = (arΔAOB)/(arΔCOD) = 96/24 = 4
∴ √((h - x)²/x²) = (h - x)/x = √4 = 2
∴ h - x = 2·x
h = 2·x + x = 3·x
A = ((48/x + 192/(h - x))/2) × h
∴ A = ((48/x + 192/(2·x))/2) × 3·x = ((48 + 192/(2))/2) × 3 = 216
The area of the trapezium, A = 216 cm².
Helpppp
Will
Give Brainlist
:)))
Answer:
3.14 million
Step-by-step explanation:
I already answered it on the 1st post
Answer:
3.14 million is the correct answer
Help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4/8 = 1/2
Step-by-step explanation:
hope it thepled u
Express in simplest form -45%
Answer: hello, your answer is -0.45
I know the answer but yes here points
Whats the greater number 1.32 or 1.34
1.34
Step-by-step explanation:
1.34 1.34 1.34 1.34 1.34
Please help. I only have a little bit of time left. Find the volume of this sphere. Round to the nearest tenth. 7 in Formulas for Spheres S.A. = 40 V = [?] in3
Answer:
V = 1436.0 in ^3 with 3.14 for pi
or
V = 1436.8 in ^3 with the pi button
Step-by-step explanation:
V = 4/3 pi r^3
The radius is 7
V = 4/3 pi (7)^3
V = 4/3 ( 3.14) (7)^3
V =1436.02666 in ^3
V = 1436.0 in ^3
If you use the pi button
V = 4/3 pi 7^3
V = 1436.75504
V = 1436.8 in ^3
GIVEN: f(x)=3x-7, g(x)=2x^(2)-3x+1, h(x)=4x+1, k(x)=-x^(2)+3
FIND: (hg)(x)
a. 2x^2+x+2
b. none of these answers
c. 32x^2+4x
d. 8x^2-12x+5
Answer:
32x^2+4x
3x-7, g(x)=2x^(2)-3x+1, h(x)=4x+1, k(x)
Name the marked angle in 2 different ways
Answer:
∠TSR ∠S
Hope this helps! :)
the question how old is my mathematics teacher is an example of non statistical question which of the following make it a statistical question?
Include options please
The statistical question is "What is the typical age of the grade 7 Mathematics teacher?"
How to determine the statistical question?The question is given as:
"how old is my mathematics teacher?"
A statistical question is such that requires statistical data to be answered or completed.
A statistical question for "how old is my mathematics teacher?" could be "What is the typical age of the grade 7 Mathematics teacher"
Read more about statistical question at:
https://brainly.com/question/15980493
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (- 1, - 1)?
Answer:
y=-1x-1
Step-by-step explanation:
it should be this
Answer:
D. y+1=3(x+1)
Which numbers are written in scientific notation? Check all that apply.
–10.8 × 104
2.7 × 10–3
6.1 × 105
9.582 × 106
21.5 × 10–11
Answer:
[tex]2.7 \times 10^{ - 3} [/tex]
[tex]6.1 \times 10^{5} [/tex]
[tex]9.582 \times 10^{6} [/tex]
Step-by-step explanation:
-
Answer:
B,C,D
Step-by-step explanation:
hi dev lol hahahahhahahahahahahahahahahahahaha
Answer: hi
Step-by-step explanation: siodrifjojseidufjsoidhfidshiufhoiersdnfiojdriofjoiedsjfpoiejdpoigheroiuhgoiutrhfbiukghvioruefdhgbiuktrhdfiougkhneoiuwhsrdtifu[tex]\lim_{n \to \infty} a_n \geq \alpha \leq \sqrt{x} \\ \pi \geq \lim_{n \to \infty} a_n \left \{ {{y=2} \atop {x=2}} \right. x^{2} \frac{x}{y} \frac{x}{y}[/tex]
Answer:
oh no
Step-by-step explanation:
⇔⇔∈∈ω∵↑↑±±±±±±±[tex]\lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \neq \neq \neq \neq \neq \neq \neq x^{2}[/tex]←⊂∈∈∈∈∈ωωωωωωωωωωωωωωωω∧∨∧∧∧∧Find the greatest number of student among whom 120 oranges and 130 apples can be divided equally.
Answer:
10
Step-by-step explanation:
We need to find the greatest number of student among whom 120 oranges and 130 apples can be divided equally.
It means we need to find the HCF of 120 and 130.
HCF is highest common factor.
The HCF of 120 and 130 is 10.
So, the greatest number of student is 10.
which numbers are the extremes of the proportion shown below [tex]\frac{4}{7} =\frac{20}{35}[/tex]
9514 1404 393
Answer:
4 and 35
Step-by-step explanation:
Written as 4/7 = 20/35, the extremes are the outside numbers: 4 and 35.
This is math all right.
Answer:
1 and 3
Step-by-step explanation:
find the next two terms in this sequence
0.1, 0.02, 0.004, 0.0008, 0.00016 ___ ___
Answer:
0.000032 and 0.0000064
Work out m and c for the line:2y+3x=5
Answer:
[tex]{ \tt{2y + 3x = 5}} \\ { \tt{2y = - 3x + 5}} \\ { \tt{y = - \frac{3}{2} x + \frac{5}{2} }} \\ { \boxed{ \bf{general \: equation : { \tt{y = mx + c}}}}} \\ by \: relation : \\ { \tt{m = - \frac{3}{2} }} \\ \\ { \tt{c = \frac{5}{2} }} \\ \\ { \underline{ \blue{ \tt{becker⚜jnr}}}}[/tex]
So sánh √144 và √169
Answer:
Step-by-step explanation:
√144 < √169
Answcăn169
Step-by-step explanat
ion:cvăn 144
PLEASE HELP QUICK, NO FAKE ANSWERS
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation.
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Step-by-step explanation:
(A) We can shift f(x) to the left or up, both resulting in a transformation to g(x) if the values are right.
If we shift all of the values of f(x) to the left, forming a horizontal translation, we can get g(x)
Similarly, if we shift all of the values of f(x) up, forming a vertical translation, we can get g(x)
(B) k represents how much a graph is shifted up or down. In a horizontal translation, we do not shift k up or down, making it 0
In our second, we can make k 10 as the values of g(x) are 10 steps higher than
(C) First, we can see that the values of g(x) are two steps to the left of f(x). As shifts a graph to the left h units, we can turn into to get g(x)
Next, as stated previously, we can see that the values of g(x) are 10 steps higher than f(x). As fx* + k shifts a graph up k units, we can turn into +10 to get g(x)
* this is f(x), needed to bypass content filter
solve for x and y x+y/ху=1 and x-y/xy = 5
Answer:
(x, y) = (-1/2, 1/3)
Step-by-step explanation:
Given the simultaneous equation
x+y/ху=1. ...1
x-y/xy = 5 .... 2
From 1; x+y = xy ...3
From 2; x - y = 5xy ...4
Substituting 3 into 4
x - y = 5(x+y)
x - y = 5x + 5y
x - 5x = 5y + y
-4x = 6y
-2x = 3y
x = -3y/2 ... 4
Add 3 and 4
2x = 6xy
2 = 6y
y = 2/6
y = 1/3
x = -3(1/3)/2
x = -1/2
Hence (x, y) = (-1/2, 1/3)