The system is:
[tex]\frac{x}{y}=2x + 4[/tex]
[tex]\frac{x-3}{y-3}=\frac{2}{3}[/tex] (y musn't be 3).
Solving for y in the first equation gives you:
[tex]y=\frac{x}{2x+4}[/tex]
Simplify the second equation to:
[tex]2(y-3)=3(x-3)[/tex]
Insert y you solved in first equation to second equation to get:
[tex]\frac{x}{x+2}-6=3x-3[/tex]
Further simplification gets you to quadratic equation:
[tex]x=(3x+3)(x+2)\implies x=3x^2+9x+6[/tex] [tex]3x^2+8x+6=0[/tex].
Solving quadratic equation using quadratic formula gives you two solutions of x in complex plane:
[tex]x_1=\boxed{-\frac{8}{6}+\frac{\sqrt{8}}{6}i}[/tex]
[tex]x_2=\boxed{-\frac{8}{6}-\frac{\sqrt{8}}{6}i}[/tex]
Insert the found x-es into first equation to find the y-s:
[tex]y_1=\boxed{-\frac{1}{2}+\frac{\sqrt{2}}{2}i}[/tex]
[tex]y_2=\boxed{-\frac{1}{2}-\frac{\sqrt{2}}{2}i}[/tex]
So there are two solutions (points) [tex]P_1(x_1,y_1),P_2(x_2,y_2)[/tex] both in [tex]\mathbb{C}[/tex] plane.
And the two fractions are:
[tex]\frac{-\frac{8}{6}+\frac{\sqrt{8}}{6}i}{-\frac{1}{2}+\frac{\sqrt{2}}{2}i}[/tex].
[tex]\frac{-\frac{8}{6}-\frac{\sqrt{8}}{6}i}{-\frac{1}{2}-\frac{\sqrt{2}}{2}i}[/tex].
Hope this helps.
when 5 times a number is added to twice the number the result is 10. what is the number?
Answer:
10/7
Step-by-step explanation:
5x+2x=10
7x=10
x=10/7
three times the sum of d and 4 is 32
Answer:
d=6 2/3 or 6.6666
Step-by-step explanation:
3(d+4)=32
3d+12=32
3d=32-12
3d=20
d=6 2/3 or 6.6666
Convert 2 3/8 to a decimal
Answer:
[tex] \huge \boxed{ \bold{2.375}}[/tex]Step-by-step explanation:
[tex] \mathsf{2 \frac{3}{8} }[/tex]
Convert mixed fraction to improper fraction
⇒[tex] \mathsf{ \frac{2 \times 8 + 3}{8} }[/tex]
⇒[tex] \mathsf{ \frac{16 + 3}{8} }[/tex]
⇒[tex] \mathsf{ \frac{19}{8}} [/tex]
Calculate
⇒[tex] \mathsf{2.375}[/tex]
Learn more:
How to convert mixed fraction into improper fraction?
https://brainly.com/question/11500334
Hope I helped!
Best regards!
Linda scored a total of 265 points in mathematics, physics and English. She scored 7 more marks in mathematics than in English and she scored 5 more marks in physics than in mathematics. Find her scores in all three subjects.
Answer: E 265 M 272 P 277
Step-by-step explanation:
English 265
math 265+7=272
Physics 272+5=277
Elena drank 3 liters of water yesterday. Jada drank 34 times as much water as Elena. Lin drank twice as much water as Jada. Did Jada drink more or less water than Elena? Explain how you know. Did Lin drink more or less water than Elena? Explain how you know.
Complete question :
Alana drink 3 Liters of water yesterday Jada drank 3/4 times as much water as Elena. Lin drank twice as much water as Jada.
Did Jada drink more or less water than Elena? Explain how you know
Did Lin drink more or less water than Elena? Explain how you know.
Answer:
Kindly check explanation
Step-by-step explanation:
Amount of water drank:
Elena = 3 litres
Jada's consumption = 3/4 times Elena's consumption,
Hence Jada's consumption = (3 * 3/4) = 9/4 litres = 2 1/4 litres
Lin drank twice as much water as Jada, Hence,
Lin's consumption = (2 * 9/4) = 18/4 litres = 4 1/2 litres
Did Jada drink more or less water than Elena?
Jada drank less than Elena.
Explain how you know:
Jada drank 2 1/4 litres compared to Elena, who drank 3 litres
Did Lin drink more or less water than Elena?
Lin drank more than Elena
Explain how you know.
Lin drank 4 1/2 litres, which is greater than the 3 litres drank by Elena.
Simplify: 2 - 6x + 8x3 + 1 = 23
the answer x=8.5
if ur trying to solve for x
3. Compare the function y = tanx and its reciprocal. Identify two similarities and two
differences between the functions.
Answer:
The similarities are;
1) The tangent slope of the tangent graph and the cotangent graph are always the same sign through out
2) The period of each trigonometric ratio cot and tan is π/2
The differences are;
1) The sign of tangent function always positive while that of the cotangent function always negative
2) Where the value of cot x ranges from undefined to 0, the value of tan x ranges from 0 to undefined in the same domain
Step-by-step explanation:
Find the derivative of Y=2xcos2x
Answer:
Y' = -xsin(2x) + 2cos(2x)
Step-by-step explanation:
For this problem, we will need to use the product rule since you have two terms that contain the variable x.
The product rule is simply as follows:
The derivative of the function is the product of the first term times the derivative of the second term plus the derivative of the first term times the second term.
Note the derivative of 2x with respect to x, is 2.
Note the derivative of cos(2x) with respect to x is (-1/2) sin(2x).
With this in mind, let's find the derivative of our function with respect to x.
Y = 2xcos2x
Y = 2x * cos(2x)
Y' = 2x * (-1/2)sin(2x) + 2 * cos(2x)
Y' = (2x * -1 / 2) sin(2x) + 2 * cos(2x)
Y' = (-x)sin(2x) + 2cos(2x)
So the derivative of our function is Y' = -xsin(2x) + 2cos(2x) according to the application of the product rule.
Cheers.
i need help asap someone pleae help me
Problem 1
We have two possible answers here.
Either AC = DF is needed, or AB = DE is needed
We can't use BC = EF, as that would be ASA. The sides cannot be between the marked angles. With AAS, the sides are not between the angles.
Note: AC pairs up with DF because both segments have an endpoint at an angle with one arc marking. AB pairs up with DE because one endpoint has a double arc marking.
==========================================
Problem 2
We have a pair of congruent sides (due to the tickmarks) and a pair of congruent angles. We need another pair of angles. We can't pick angle B = angle E, as that would give us ASA. So we must pick the other pair of angles
angle A = angle D
If angle A = angle D, then we have enough to use AAS.
I will give you 30 points ? Need it quick please
Answer:
x = 4
Length = 19 feet
Width = 11 feet
Step-by-step explanation:
Area = Length x Width
Area = 209 ft²
Length = (4x + 3)
Width = (4x - 5)
Find:
x
Length
Width
Area = Length x Width
209 = (4x + 3) * (4x - 5)
209 = 16x² - 8x - 15
16x² - 8x - 15 = 209
16x² - 8x - 15 - 209 = 209 -209
16x² - 8x - 224 = 0
use quadratic equation to solve x:
-(-8) + sqrt( -8² - 4 * 16 * (-224))
x = --------------------------------------------
2 * 16
x = 4, x = -(7/2) ----therefore use x = 4
solve for L:
Length = (4x + 3)
Length = (4 * 4 + 3)
Length = 19 feet
solve for W:
Width = (4x - 5)
Width = (4 * 4 - 5)
Width = 11 feet
check:
Area = Length x Width
209 = (4x + 3) * (4x - 5)
Area = Length x Width
209 = 19 * 11
209 = 209 ----- OK
What’s an algebraic expression for 8 increased by three times a number
Answer:
3x + 8
Step-by-step explanation:
Number: x
Three times a number: 3x
Eight increased by three times a number: 3x + 8
Answer:
[tex]\huge\boxed{ 8 + 3x}[/tex]
Step-by-step explanation:
Let the number be x
So, three times x will be => 3x
Increases by 8 means adding 8 So, the final expression will be:
=> 8 + 3x
what is the solution to 6x − 8 > 4x + 26
Answer:
x > 17
Step-by-step explanation:
Combine like terms, We get:
2x > 34, or
x > 17
PLEASE HELP IM STUCK
Answer: The table on the top right corner
Answer: Answer in the steps
Step-by-step explanation:
x y
0 3
1 1
2 -1
3 -3
This a linear function because as the y values decrease by a constant amount the x values also increase by a constant amount.
Higher Order Thinking Describe the
transformation g of f(x) = |x| as a stretch and
as a compression. Then write two equations
to represent the function. What can you
conclude? Explain.
Answer:
Step-by-step explanation:
An absolute value function f when stretched or shrink vertically,
1). If a function f(x) = |x| is stretched vertically by a factor 'k',
g(x) = k[f(x)] = k|x| [where k > 1]
2). If the same function is vertically compressed by a factor 'k',
g(x) = k[f(x)] = k|x| [where 0 < k < 1]
Following these rules we can define a vertical stretch or compression of any function.
how does brainstorm,decide,work,enjoy help with motivation?
Answer:
It helps because it gets you thinking. Personally, it would motivate me because that process itself is very helpful. Brainstorm will get you your idea, you can decide if you want to do it or not, then you work on it, and because you have the right attitude towards whatever you are working on, you'll enjoy it!
Eloise scored a total of 268 points during the basketball season. Of her total points, l points came from left handed shots. She scored 225 points from right handed shots write an equation to describe the situation and find the value of l for left handed shots
Answer:
[tex]\bold{268=225+}l[/tex]
43
Step-by-step explanation:
Given that:
Total points scored in basketball season, T = 268
Points scored from right handed shots, R = 225
Points scored from left handed shots = [tex]l[/tex]
To find:
To write an equation to describe the situation and find the value of [tex]l[/tex] for left handed shots ?
Solution:
We know that the points can be scored in basketball either by right hand shots or by left hand shots.
In other words, we can say that:
Total points scored in basketball season = points scored from right handed shots + points scored from left handed shots
i.e.
[tex]T = R + l\\\Rightarrow \bold{268=225+}l[/tex]
So, the equation is:
[tex]\bold{268=225+}l[/tex]
Now, let us find the value of [tex]l[/tex] from the above equation:
[tex]l=268-225\\\Rightarrow \bold{l = 43}[/tex]
Number of points scored from left handed shots = 43
Identity the property shown in the example below.
-8+8= 0
Answer:
Commutative Property
Step-by-step explanation:
-8+8 = 0
0 = 0
Which equation can be used to find the length of AC?
A
10 in.
b
40°
C
B
CU
O (10)sin(40°) = AC
O (10)cos(40°) = AC
1
= AC
sin(40)
10
cos(40
= AC
Answer:
AC = 10sin40°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] , then
sin40° = [tex]\frac{AC}{10}[/tex] ( multiply both sides by 10 )
10sin40° = AC
The length of the side AC of the triangle is AC = 10 ( sin ( 40 )° )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ABC = 40°
The height of the triangle AC = b
The base of the triangle BC = a
The hypotenuse of the triangle AB = 10 inches
Now , for a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
And , the trigonometric relation is
sin 40° = opposite side / hypotenuse
sin ( 40 )° = AC / 10
Multiply by 10 on both sides , we get
AC = 10 ( sin ( 40 )° )
Hence , the measure of the hypotenuse of triangle is AC = 10 ( sin ( 40 )° )
To learn more about triangle click :
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(2t-3)^3, can you help me?, please?
Answer:
8t^3-36t^2+54t-27
Step-by-step explanation:
(2t-3)^3
(2t-3)(2t-3)(2t-3)
Multiply the first two terms
(4t^2 -6t -6t+9)(2t-3)
Combine like terms
( 4t^2 -12t +9) ( 2t-3)
Multiply
2t*( 4t^2 -12t +9) -3 ( 4t^2 -12t +9)
Distribute
8t^3 -24t^2 +18t-12t^2 +36t-27
Combine like terms
8t^3-36t^2+54t-27
Answer:
8t³ - 36t² + 54t - 27
Step-by-step explanation:
(2t - 3)³
(2t - 3)(2t - 3)(2t - 3)
FOIL the first two binomials - first - outer - inner - last
(2t - 3)(2t - 3)
= 4t² - 6t - 6t + 9
= 4t² - 12t + 9
multiply this polynomial by the last binomial
(4t² - 12t + 9)(2t - 3)
distribute 2t
2t • 4t² = 8t³
2t • -12t = -24t²
2t • 9 = 18t
distribute -3
-3 • 4t² = -12t²
-3 • -12t = 36t
-3 • 9 = -27
combine
8t³ - 24t² + 18t - 12t² + 36t - 27
simplify
8t³ - 36t² + 54t - 27
A park is a rectangle a fence runs along all four sides the area of the park is 5,400 yards squared the length is 1.5 times longer then the width what is the perimeter of the park
In a camp, 16.1 kg of rice is cooked each week. Find the quantity of rice cooked in the month of October.
Answer:
Quantity of rice cooked in October = 71.3 kg
Step-by-step explanation:
Given:
Quantity of rice cooked per week = 16.1 kg
Number of days in a week = 7
Number of days in October = 31
Find:
Quantity of rice cooked in October
Computation:
Quantity of rice cooked in October = [Number of days in October / Number of days in a week] Quantity of rice cooked per week
Quantity of rice cooked in October = [31 / 7]16.1
Quantity of rice cooked in October = 71.3 kg
WILL MARK THE BRAINLIEST!! PLEASE HELP If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1. Question 5 options: A) 27° B) 63° C) 61° D) 9°
Answer:
A. 27°
Step-by-step explanation:
Given that s is perpendicular to r, and <1 = 3x, <2 = 5x + 18, therefore:
m<1 + m<2 = 90°
3x + (5x + 18) = 90°
Solve for x using this equation
3x + 5x + 18 = 90
8x + 18 = 90
Subtract 18 from both sides
8x + 18 - 18 = 90 - 18
8x = 72
Divide both sides by 8
x = 9
Find m<1
m<1 = 3x
Plug in the value of x
m<1 = 3(9) = 27°
25 precent of this square is shaded. What present of the square is not shaded
Answer:
75%
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
I'm sure you meant "percent," not "present."
If 25% of the square is shaded, then the percent that is not shaded is 75%.
If (5 t the power of 4)m = 5 to the power of 12, what is the value of m? (4 points) 2 3 5 8
Answer:
m = 3
Step-by-step explanation:
Given
[tex]5^{4m}[/tex] = [tex]5^{12}[/tex]
Since the bases on both sides are equal ( both 5) the equate the exponents.
4m = 12 ( divide both sides by 4 )
m = 3
how do you simplify ratios
Answer: Simplifying ratios is just like simplifying fractions. Think of ratios as fractions. You divide a number that both numerator and denominator can be divided by.
Example
5/10 = 1/2
How did we get 1/2? Simple! You divide the numerator and denominator by 5.
5/10÷5/5=1/2
You do the same for ratios but the only difference is instead of putting a fraction bar (/) you put a colon (:)
Let's try another example but with a ratio!
Example
5:10 = 1:2
How did we get 1:2? Simple! Again we divided by 5 just like we did with the fraction example! So really ratios are just like fractions!
5:10÷5:5=1:2
Remember
The fraction bar is /
The ratio bar is :
Ratios are just like fractions but the symbol can sometimes trick people.
Nanette has 5 dimes and 5 pennies in her
pocket. What's the probability that Nanette
pulls out a dime and then a penny from
her pocket? (Assume that she doesn't put
the first dime back in her pocket.)
Answer:
2/9
Step-by-step explanation:
5 dimes and 5 pennies = 10 coins
P( dime) = number of dimes / total
=5/10 = 1/2
keep the dime
4 dimes and 5 pennies = 9 coins
P( penny) = number of penny / total
=4/9
P( dime, keep, penny) = 1/2 * 4/9 = 2/9
=================================================
Explanation:
There are 5+5 = 10 coins total, of which 5 are dimes. The probability of selecting a dime is 5/10 = 1/2.
The coin is not put back, so we have 10-1 = 9 coins overall. Of this, 5 are pennies. The probability of pulling a penny out is 5/9. Note how this is dependent on the first event above.
From here, multiply the two probabilities
(1/2)*(5/9) = 5/18
The rule used here is
P(A and B) = P(A)*P(B given A)
where A and B are the events "pulling out a dime on the first selection" and "pulling out a penny on the second selection"
Determine three consecutive odd integers if the square of the largest integer is 33 less than the sum of the squares of the two smaller integers.
Factor the trinomial below.
x2 + 3x - 18
A. (x + 6)(x-3)
B. (x+9)(x-2)
C. (X-9)(x+2)
D. (x-6)(x+3)
Answer:
A
Step-by-step explanation:
Given
x² + 3x - 18
Consider the factors of the constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3, since
6 × - 3 = - 18 and 6 - 3 = + 3, thus
x² + 3x - 18 = (x + 6)(x - 3) → A
Answer:
( x+6) ( x-3)
Step-by-step explanation:
x^2 + 3x - 18
What 2 numbers multiply to -18 and add to 3
6*-3 = -18
6+-3 = 3
( x+6) ( x-3)
Mr. Noel borrowed money from his cousin at a rate of 10% simple interest. After 1 year, $440
paid off the loan. How much did Mr. Noel originally borrow?
Answer:
$400Step-by-step explanation:
Using the formula for calculating the simple interest expressed as;
Simple Interest = Principal * rate * time/100
Note that the principal is the amount he originally borrowed
I = PRT/100 ............ 1
Amount paid off A = Principal+Interest
A = P+I ............ 2
From equation 2; I = A-P......... 3
Substitute equation 3 into 1;
A-P = PRT/100
Given A = $440, R = 10%, Time = 1year
Substitute the given parameters into the resulting equation;
440 - P = P*10*1/100
440-P = 10P/100
440-P = 0.1P
440 = 0.1P+P
440 = 1.1P
Divide through by 1.1;
1.1P/1.1 = 440/1.1
P = $400
Hence the amount Mr Noel originally borrow is $400
if i=√-1 , what is i^2 equal to ?
Answer:
-1
Step-by-step explanation:
If i = √-1, then i^2 = -1.