Answers
[tex]\begin{cases}2x+3y=12\\2x-2y=2\end{cases}\\ --------(-)\\2x-2x+3y-(-2y)=12-2\\\\5y=10\quad|:5\\\\\boxed{y=2}\\\\\\2x-2y=2\quad|:2\\\\x-y=1\\\\x=1+y\\\\x=1+2\\\\\boxed{x=3}[/tex]
so:
x + y = 5
Related Questions
pleaee solve this problem!!
Answers
Answer:
RHS=tanA/2
Step-by-step explanation:
LHS=1+sinA-cosA/1+sinA+cosA
=(1-cosA)+sinA/(1+cos A)+sinA
=2sin^2A/2+2sinA/2*cosA/2
_____________________
2cos^2A/2+22sinA/2*cosA/2
=2sinA/2(sinA/2+cosA/2)
___________________
2cosA/2(sinA/2+cosA/2)
sinA/2
=_____
cosA/2
= tanA/2 proved.
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle Identities:
sin 2A = 2cos A · sin A
cos 2A = 2 cos²A - 1
Use the following Quotient Identity: tan A = (sin A)/(cos A)
Use the following Pythagorean Identity:
cos²A + sin²A = 1 --> sin²A = 1 - cos²A
Proof LHS → RHS
Given: [tex]\dfrac{1+sin\theta - cos \theta}{1+sin \theta +cos \theta}[/tex]
Let Ф = 2A: [tex]\dfrac{1+sin2A - cos 2A}{1+sin2A +cos2A}[/tex]
Un-factor: [tex]\dfrac{\bigg(\dfrac{1- cos^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+sin\ 2A +cos\ 2A}[/tex]
Pythagorean Identity: [tex]\dfrac{\bigg(\dfrac{sin^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+cos\ 2A +sin\ 2A}[/tex]
Simplify: [tex]\dfrac{sin\ 2A}{1+cos\ 2A}[/tex]
Double Angle Identity: [tex]\dfrac{2sin\ A\cdot cos\ A}{1+(2cos^2 A-1)}[/tex]
Simplify: [tex]\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]
[tex]=\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}[/tex]
[tex]=\dfrac{sin\ A}{cos\ A}[/tex]
Quotient Identity: tan A
[tex]\text{Substitute} A = \dfrac{\theta}{2}}:\qquad tan\dfrac{\theta}{2}[/tex]
[tex]tan\dfrac{\theta}{2} = tan\dfrac{\theta}{2}\quad \checkmark[/tex]
La siguiente figura representa una torre de transmisión de energía eléctrica: ¿Mediante cual razón trigonométrica se puede determinar la altura de la torre? dejar procedimiento o justificación. A. sen α = BC/c B. sen α = BC/b C. sen α = c/b D. sen α = b/c
Answers
Answer:
B. sen α = BC/b
Step-by-step explanation:
Las identidades trigonométricas se utilizan para resolver problemas de ángulos rectos.
En un ángulo recto, el lado al que se hace referencia como opuesto es el lado opuesto al ángulo, el lado al que se hace referencia como adyacente es el lado siguiente al ángulo (entre el ángulo y el ángulo recto) mientras que la hipotenusa es el lado más largo (opuesto al ángulo recto)
De identidades trigonométricas:
[tex]sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} \\\\lado\ opuesto=BC=a\\\\hipotenusa=b\\\\sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} =\frac{BC}{b} \\\\sen\ \alpha =\frac{BC}{b}[/tex]
8. 1 Write a complex number to represent the impedance of each element. The voltage, V, is the real part, and the current, I, is the multiple of the imaginary unit i.
9. V = 34 volts: I = 3 milliamperes
10. V = 13 volts; I = 2.4 milliamperes
Answers
Given that,
Voltage = 34 volt
Current = 3i mA
We need to calculate the complex number to represent the impedance
Using ohm's law
[tex]V=IR[/tex]
[tex]R=\dfrac{V}{I}[/tex]
Where, V = voltage
I = current
R = impedance
Put the value into the formula
[tex]R=\dfrac{34}{0.003i}[/tex]
[tex]R=\dfrac{34}{0+0.003i}\times\dfrac{0-0.003i}{0-0.003i}[/tex]
[tex]R=\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]
(b). Given that,
Voltage = 13 volts
Current = 2.4 mA
We need to calculate the complex number to represent the impedance
Using ohm's law
[tex]R=\dfrac{V}{I}[/tex]
Put the value into the formula
[tex]R=\dfrac{13}{0.00024i}[/tex]
[tex]R=\dfrac{13}{0.00024i}\times\dfrac{-0.00024i}{-0.00024i}[/tex]
[tex]R=\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]
Hence, (a). The complex number to represent the impedance is [tex]\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]
(b). (a). The complex number to represent the impedance is [tex]\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]
Solve your equation from the first problem and pick the BEST interpretation for the solution. a \large h\approx2.9; The solution shows that it will take about three more hours to fill the pool. b \large h\approx1.8, The solution show that it will take two more hours to fill the pool. c \large h\approx2.9; The solution shows that it will take about 2 more hours to fill the pool. d \large h\approx4.2, The solution shows that it will take 4 more hours to fill the pool.
Answers
Answer:
The correct option is (a).
Step-by-step explanation:
The complete question is:
A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool.
Solution:
The first hose takes 6 hours to fill the pool.
So, work done per hour by the first hose is, 1/6.
Suppose the second hose takes x hours to fill the pool.
So, work done per hour by the second hose is, 1/x.
The work done per hour by the two hoses together is, [1/6 + 1/x] = (x + 6)/6x.
Together the two hoses can fill the pool in, 6x/(x + 6) hours.
It is provided that, the second hose needs 3 more hours to fill the pool than the two hoses combined.
That is:
6x/(x + 6) = x - 3
6x = (x - 3)(x + 6)
6x = x² + 3x - 18
x² - 3x - 18 = 0
x² - 6x + 3x - 18 = 0
x (x - 6) + 3 (x - 6) = 0
(x + 3)(x - 6) = 0
x = 6
Then the time taken by the two hoses together is,
6x/(x + 6) = x - 3 = 6 - 3 = 3 hours
So, each hose takes 6 hours and together they take 3 hours to fill the pool.
This implies that the second hose takes 3 hours more than the 3 hours together to fill the pool.
Thus, the correct option is (a).
Hector is flying a kite. He has let out 86 feet of string and is holding it 4 feet off the ground. If the string is at an angle of elevation of 42°15'30", how high is the kite?
Answers
Answer:
h = 61.83 feet
Step-by-step explanation:
length of string from Hector to kite = c = 86 feet.
and 4 feet off the ground.
angle A = 42° 15' 30"
req'd: how high is the kite?
angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')
angle A = 42.26
to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp
Sin(A) = a / c
Sin(42.26) = a / 86
a = Sin(42.26) * 86
a = 57.83 feet
therefore, the height of the kite from the ground = h = 57.83 + 4
h = 61.83 feet
7. Write the power as a product of factors: 97
Answers
Prime factorization: 97 is prime.
The exponent of prime number 97 is 1. Adding 1 to that exponent we get (1 + 1) = 2 Factors of 97: 1, 97.
Factor pairs: 97 = 1 x 97.
97 has no square factors that allow its square root to be simplified. √97 ≈ 9.8488578.
-2/3 + 4/5 + 5/8 Please help me :/
Answers
Answer:
91/120
Step-by-step explanation:
It might be convenient to use the form ...
(a/b) +(c/d) = (ad +bc)/(bd)
__
-2/3 +4/5 +5/8 = (-2/3 +4/5) +5/8
= (-10 +12)/15 +5/8
= 2/15 +5/8
= (16 +75)/120
= 91/120
A least squares regression line a. can be used to predict a value of y if the corresponding x value is given. b. implies a cause-and-effect relationship between x and y. c. can only be determined if a good linear relationship exists between x and y. d. ensures that the predictions of y outside the range of the values of x are valid.
Answers
Answer:
The correct option is (a).
Step-by-step explanation:
The general least square regression line is given by,
[tex]\hat Y=a+bX[/tex]
Here,
X = independent variable
Y = dependent variable.
b = slope (or regression) coefficient
a = intercept
The main purpose of the least square regression line is to predict the value of the dependent variable when the independent variable is known.
So, the correct interpretation is:
A least squares regression line can be used to predict a value of y if the corresponding x value is given.
The correct option is (a).
Carl, Caitlyn, and Daryl are comparing their ages. Carl is two years older than Caitlyn. Daryl is five years older than Carl. The product of Carl and Daryl's ages is at least 160. If x represents Caitlyn's age, which inequality represents this situation?
Answers
Answer:
Step-by-step explanation:
If x represents Caitlyn's age, then can be used to represent Carl's age, and can be used to represent Daryl's age.
The product of Caitlyn and Daryl's ages is at least 160. Use this information to set up an inequality to represent this situation.
The answer is x squared +9x+14 is greater than or equal to 160.
The inequality that represents the given situation where x is the age of Caitlyn will be (X+2) (x+7) ≥ 160.
The inequality equation is a representation of the relation between two or more expressions that are not equal, not equal to, less than, or greater than.
Represented by:
greater than as >less than as <not equal to as ≠at least or, either equal or greater than as ≥Solution:
It is given that,
Caitlyn's age = x,
Carl's is two years older than Caitlyn, therefore,
Carl's age = x + 2
And, Daryl is 5 years older than Carl, therefore,
Daryl's age = Carl's age + 5
= (x + 2) + 5
= x + 7
The last condition is that the product of Carl and Daryl's age is at least 160, at least is represented as ≥ which mean that value either equal or greater than.
Therefore, the inequality would be (x+2) (x+7) ≥ 160
Learn more about inequality:
https://brainly.com/question/16826399
PLEASEEEE HELP ME!!!!!!! Write the quotient as a mixed number.
14 divided by 9 =1 R5
Answers
Answer:
1 5/9
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Write a word phrase for the expression: 13p + 12 12 more than the product of 13 and a number p The sum of p and 12 12 more than the quotient of 13 and a number p
Answers
Answer:
Add 12 to the product of 13 and a number p.
Step-by-step explanation:
Given expression: 13p + 12
In the expression, 13 is multiplied by a number p, and 12 is added to the result. Therefore, a simple word phrase for the given expression would be: Add 12 to the product of 13 and a number p.
i.e 13 × p = 13p
Then add 12,
= 13p + 12
MOD Pizza purchased a new brick-fired oven for $14,500. If they make a profit of $3 for every pizza they sell, how many pizzas must be in order to make their money back on the purchase of the oven?
Answers
Answer:
4,834
Step-by-step explanation:
$14,500/($3 / pizza) = 4833.3 pizzas
MOD Pizza must sell 4,834 pizzas to cover the cost of the oven.
Which expression does not represent "the sum of n and 6"?
1. 6+n
2. n+6
3. 6n
Answers
How much of a circle does a 100-degree angle turn through?
help pls
1. 1
2. 100/180
3. 50/360
4. 100/360
pls help!!!
Answers
Answer:
100/360
Step-by-step explanation:
A complete turn of a circle is 360 degrees
Therefore, 100 degrees turn is 100 out of 360
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $ 65 $65dollar sign, 65 along with an hourly rate of $ 28 $28dollar sign, 28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $ 250 $250dollar sign, 250, and he wonders how many hours of work he can afford. Let H HH represent the whole number of hours that the plumber works. 1) Which inequality describes this scenario? Choose 1 answer:
Answers
Answer:
Step-by-step explanation:
Basic Charge = $ 65
Rate per hour = $ 28
Number of hours = H
Rate for H hours = 28 *H = 28H
Equation:
65 + 28H ≤ 250
Anan consideration requires:
A plumber that charges an initial fee of = $65An hourly rate of = $28Anan doesn't want to spend more than = $250Requirements of the plumber
charges at a whole number of hour rate = HThus, to determine the number of how many hours Anan can afford for his total amount of $250, we have the following:
The initial fee + hourly rate ≤ 250
(why we use a less than or equal to sign is because Anan is not willing to spend more than $250)∴
$65 + $28 H ≤ 250
Therefore, we can conclude that the perfect inequality that describes Anan Scenario is: $65 + $28 H ≤ 250
Learn more about inequalities here:
https://brainly.com/question/20383699?referrer=searchResults
Find the midpoint of the segment with the given endpoints.
(10,5) and (-2, -10)
Answers
Answer:
The answer is
[tex] (4, - \frac{ 5}{2} )[/tex]Step-by-step explanation:
The midpoint M of two given points is given by
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(10,5) and (-2, -10)
The midpoint of points is
[tex]M = (\frac{10 - 2}{2} , \frac{5 - 10}{2} ) \\ = ( \frac{8}{2} , - \frac{5}{2} )[/tex]We have the final answer as
[tex]M = (4, - \frac{ 5}{2} )[/tex]Hope this helps you
PLZ HELP I CANT DO THIS QUESTION!!!!
Answers
Step-by-step explanation:
(A) (In the fig. triangle represented by small triangle with angle of elevation 30° and height h1 ) ( Using this explanation since the figure is not marked)
[tex]tan30 = \frac{h1}{40} [/tex]
[tex]h1 = \frac{40}{\sqrt{3} } m[/tex]
(B) (In the fig. triangle represented by small triangle with angle of depression 58° and height h2 )
[tex]tan58 = \frac{h2}{40} [/tex]
[tex]h2 = 64m[/tex]
(C)
[tex]Height \: of \: Building \: A = h2 = 64m[/tex]
[tex]Height \: of \: Building \: B = h1+h2 = (64 + \frac{40}{ \sqrt{3} } )= 87m[/tex]
Piz look at the pic
[tex]piz \: help \:me \: thx[/tex]
Answers
Answer:
-12a²+9a-5
Step-by-step explanation:
-7a²+3a-9 - (5a²-6a-4)=
-7a²+3a-9-5a²+6a+4=
-12a²+9a-5
You are painting your bedroom wall which is 9 feet high and 12 feet long, using paint that covers 50 square feet per gallon. How many gallons do you need to paint the wall?
Answers
Answer:
2.16 gallons
Step-by-step explanation:
Area to be painted:
9 ft × 12 ft = 108 ft²
Pain required:
50 ft² = 1 gallon ⇒ 1 ft² = 1/50 gallon108 ft² = ?108 × 1/50 = 2 8/50 = 2.16 gallonsWhich of the following is true of the data represented by the box plot
Answers
Answer:
The data is skewed to the bottom and contains an outlier.
Step-by-step explanation:
1. Test for outlier
An outlier is a point that is more than 1.5IQR below Q1 or above Q3.
IQR = Q3 - Q1 = 74 - 51 = 23
1.5 IQR = 1.5 × 23 = 34.5
51 - 15 = 36 > 1.5IQR
The point at 15 is an outlier.
2. Test for normal distribution
The median is not in the middle of the box.
Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.
3. Test for skewness
The longer part is to the left of the median, so the data is skewed left.
Could someone please help me!!!?? First answer gets brainliest.
Answers
Answer:
5A: All you got to do is put in the number of videos (v) and figure the equation out. For example, 40 x 20 + 3v = $803v.
I really hope this helps you!
2 less than the sum of x and y
Answers
Answer:
(x + y) - 2 or x + y - 2
Step-by-step explanation:
"sum of x and y"
may be expressed mathematically as (x + y)
"two less than sum of x and y", can thus be written:
(x + y) - 2 or x + y - 2
How far is a chord of length 8 cm from the centre of a circle of radius 5 cm
Answers
Answer:
3 cm
Step-by-step explanation:
A line from the centre of the circle at right angles to the chord is a perpendicular bisector.
Thus a right triangle is formed with legs d , the line from centre to chord and 4 , half the length of the chord. The radius 5 is the hypotenuse.
Using Pythagoras' identity in the right triangle.
4² + d² = 5², that is
16 + d² = 25 ( subtract 16 from both sides )
d² = 9 ( take the square root of both sides )
d = [tex]\sqrt{9}[/tex] = 3
Thus the chord is 3 cm from the centre of the circle.
OB = 3 cm
Step-by-step explanation:AO = radius = 5 cm
AB = 8cm/2 = 4 cm
Pythagora
OB² = AO² - AB²
= (5cm)² - (4cm)²
= 25cm² - 16cm²
= 9 cm²
OB = √9cm²
= 3 cm
A coin is flipped 20 times. The results are 12 heads and 8 tails. Determine the theoretical probability of getting heads.
Answers
The theoretical probability of getting heads is; 12%
Theoretical Probability
We are given;
Number of times coin is flipped = 20 times
Number of heads gotten = 12 heads
Number of tails gotten = 8
Assuming the coin is fair, then;
p = 0.5 and q = 0.5
Using binomial probability formula we have;
P(getting heads) = ²⁰C₁₂ * 0.5¹² * 0.5⁽²⁰ ⁻ ¹²⁾
P(getting heads) = 125970 * 0.00000095367431640625
P(getting heads) = 0.12 or 12%
Read more about Theoretical Probability at; https://brainly.com/question/8652467
Find the smallest positive integer x which is greater than 1 and relatively prime to 120 (recall that relatively prime means that the GCD of x and 120 is 1)
Answers
Answer: 7
Explanation:
List out the factors of 120 until we hit a gap
1,2,3,4,5,6,8
Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.
Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime
Side note: The term "coprime" is sometimes used in place of "relatively prime"
my dudes could you help me cause im really bad at math heres the problem choose all the values that make the inequality true. 28-7x ≤ -4(-7x - 7) the options : -10 -5 0 5 10
Answers
Answer:
0, 5, 10
Step-by-step explanation:
You can solve the inequality to determine what values to select.
28 -7x ≤ -4(-7x -7) . . . . . . given
28 -7x ≤ 28x +28 . . . . . . eliminate parentheses*
-7x ≤ 28x . . . . . . . . . . . . . subtract 28 from both sides
0 ≤ 35x . . . . . . . . . . . . . . add 7x to both sides
0 ≤ x . . . . . . . . . . . . . . . . . divide by 35
So, all values that are 0 or greater will make the inequality true:
0, 5, 10
_____
* Parentheses are eliminated using the distributive property. The factor outside parentheses multiplies each of the terms inside. Pay attention to signs.
-4(-7x -7) = (-4)(-7x) +(-4)(-7) = 28x +28
Simplify 9^-8 × 1/9^3
Answers
Answer:
1/31381059609
Step-by-step explanation:
PLEASE HELP !!! Find the measure of y A. 43 B. 90 C. 53 D. 47
Answers
===============================================
Explanation:
Notice how inscribed angles x and y subtend (or cut off) the same minor arc measure. This means that x = y. So if we find x, we found y also.
The vertical line is a diameter of the circle. The blue angle marked in the diagram below is a right angle due to Thales Theorem, which is a special case of the inscribed angle theorem. Thales Theorem says that any inscribed angle in a semicircle is 90 degrees.
Therefore the triangle marked in red (same diagram) is a right triangle, allowing us to say
x+47+90 = 180
x+137 = 180
x = 180-137
x = 43
So y = 43 as well.
4. (x+ 2)(2x2 + 9x+8)
A.
2x3 + 13x2 + 26x+ 16
B.
16x3 + 728 + 46x - 16
C.
2x3 + 17x2 + 22x+ 16
D.
2x3 + 13x2 - 26x+ 16
Answers
Answer:
2x3+9x2+8x+4x2+18x+16
2x3+13x2+26x+16
What is the solution of StartRoot x squared + 49 EndRoot = x + 5?
Answers
Answer:
2.4
Step-by-step explanation:
√(x² +49) = x + 5(√(x² +49) )²= (x + 5)² ⇒ square of both sidesx² + 49 = x² + 10x + 25 ⇒ simplifying, x² get cancelled10x = 49 -2510x = 24x= 24/10x= 2.4Answer is 2.4
Answer:
12/5
Step-by-step explanation: