The solution of the system of equations is the point (-6, 6), so the correct option is B.
Which statements are correct about the system of equations?
Here we have the system of equations:
2x + 3y = 6
x + 3y = 12
First, let's write these two lines in the slope-intercept form:
y = (6 - 2x)/3 = 2 - (2/3)*x
y = (12 - x)/3 = 4 - (1/3)*x
Now, because "y" is the represents the same variable in both equations, we can write:
2 - (2/3)*x = y = 4 - (1/3)*x
Now we can solve that for x.
2 - (2/3)*x = 4 - (1/3)*x
2 - 4 = (2/3)*x - (1/3)*x
-2 = (1/3)*x
3*(-2) = x = -6
Now, to get the y-value of the solution we can evaluate any of the two lines in x = -6, evaluating the first we get:
y = 4 - (1/3)*x = 4 - (1/3)*(-6) = 4 + 2 = 6
Then the solution of the system is the point (-6, 6). Then the correct statement is B:
"The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is the solution."
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A rectangular tank measures 1.2m by 0.8m by 0.5m.
(a) Water flows from the full tank into a cylinder at a rate of 0.3m3
/min.
Calculate the time it takes for the full tank to empty.
Give your answer in minutes and seconds.
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
How to determine the draining time of a rectangular tank
In this question we must determine the draining time of a tank whose dimensions are known and whose water outflow is stable. The draining time is equal to the volume of the rectangular tank divided by outflow rate:
V = (1.2 m) · (0.8 m) · (0.5 m)/(0.3 m³/min)
V = 1.6 min
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
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anwer this question with full method please
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
The difference of the product of 3 and 6 minus the quotant of 6 / 2
Answer:
Answer:
(3*6) - (6/2) = 15
Step-by-step explanation:
3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.
The answer of the equation is 15.
"Systems of Linear Magic"
DIRECTIONS
You are given the following system of equations. Answer the questions
below using this system.
1st Equation: 4x + y = 7
2nd Equation: 2x + y = 11
1.) Solve the system of equations by using the elimination method.
2.) Following the steps described in the "How to Create a Magic Potion"
section on page 1, let's brew a magic potion! Answer the following
questions about your "magic potion"equation.
A.) What is the factor that you have multiplied the 2nd equation by?
C.) What is the magic potion equation you have created?
3.) Using your newly created "magic potion" equation along with the original
2nd equation, solve this new system of equations by using the elimination
method.
4.) Why do you think this "magic potion" method works mathematically to
give us the exact same solution? Use at least 2 complete sentences.
The solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a system of equations:
1st Equation: 4x + y = 7
2nd Equation: 2x + y = 11
Subtract equation 2nd from 1st
(4x + y) - (2x + y) = 7 - 11
2x = -4
x = -2
Now in equation 1st multiply by 2 and in equation 2nd multiply by 4
8x + 2y = 14
8x + 4y = 44
Subtract:
-2y = -30
y = 15
The factor is 2 and 4 for the 1st and 2nd equation respectively.
Thus, the solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.
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can anybody help meee
Answer:
a.) f(2) = 3
b.) if f(x) = 2
x=3
Step-by-step explanation:
Here you must notice that on the graph where x is 2, y or f(x) is at 3. This means that the answer where in the function of x, where the input 2, the output or y/f(x) is 3
And if the output is 2, the input is 3 as proven above.
Which term best describes the horizontal cross-sections of an oblique cone?
O A. Congruent discs
OB. Similar discs
OC. Similar polygons
O D. Congruent polygons
Answer:
B. Similar discs
Step-by-step explanation:
Definitions
Cone: A three-dimensional solid figure that has a circle at one end (the "base"), a point at the other end (the [tex]\sf a\:\!pex[/tex]), and a curved side.
Right Cone: A cone where the [tex]\sf a\:\!pex[/tex] is aligned on the center of the base.
Oblique Cone: A cone where the [tex]\sf a\:\!pex[/tex] is not centered over the base.
Horizontal Cross-section: The intersecting plane parallel to the base of the solid figure.
Congruent: The same shape and size.
Similar: When one shape can become the other after being resized, reflected, translated or rotated.
Disc: The region in a plane bounded by a circle.
Polygon: A two-dimensional closed shape with a minimum of 3 straight sides.
Therefore, the horizontal cross-sections of an oblique cone are similar discs.
Use the graphing calculator to graph the function f(x)=√x Which list contains three points that lie on the graph of
the function?
0(83) (42) (-11)
O (11 (42) (9. 3)
Answer:
The last option that starts with (1,-1)
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x+4)2 +4
B. F(x)=3(x-4)2 - 4
C. F(x)=-3(x+4)² +4
D. F(x) = -3(x-4)² +4
The equation of the function is F(x) = -3(x-4)² +4 , the correct answer is Option D
The missing graph is attached with the answer
What is a function ?A function is a law that relate the independent variable and the dependent variable.
It is given that
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed
From the graph, it is seen that,
G(x) when shifted by -4 on the negative x axis.
and graph shifted by +4 on the positive y axis.
F(x) is scaled by a factor of -⅓ of G(x)
it is reflected across the x-axis.
So the equation of the function is
F(x) = -3(x-4)² +4
Therefore , the correct answer is Option D.
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True or False: The minimum or maximum value on the graph of a quadratic function (parabola) is identified using the x-value of the vertex.
Find the length of segment AC if AB = 7.8 cm and BC = 25 mm. How many solutions are there in each case? Point B lies on line AC .
Answer:
103mm or 53mm
Step-by-step explanation:
--A------B------C--
AB=78mm BC=25mm AC=AB+BC=103mm
--A----C---B---
AB=78mm BC=25mm AC=AB-BC=53mm
-B---A---C-
is impossible because BA<BC but 78mm>25mm
3/5x + 3 = 6 whats is x?
Answer:
X = 3/53/5x + 3 = 6
3/5x = 6 - 5
3/5x = 1
Multiplying both the sides with 5x3/5x (5x) = 1* 5x
3 = 5x
3/5 = X
Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?
The shelter can house 15.6 cats because 15.6 < 28.
The shelter can house –8 cats because –8 < 28.
The shelter can house 17 cats because 17 < 28.
The shelter can house 28 cats because 28 < 28.
Answer:
The shelter can house 17 cats because
17 < 28.
Step-by-step explanation:
We cannot have fractions of cats, and we cannot have a negative number of cats. So the third statement is reasonable because c < 28.
a tissue box has a lentgh of 11 inches a width of 5 inches and a height of 4 inches
Use the graph of f(x) to find the indicated function values.
The indicated function values are f(0) = 2 and x = -1
How to determine the function values?The attached figure represents the missing piece in the question
From the attached figure, the function values to calculate are:
f(x) when x = 0 and x when f(x) = 0
From the figure, the graph crosses the y-axis at y = 2 and the x-axis at x = -1
This means that:
f(0) = 2 and f(-1) = 0
Hence, the indicated function values are f(0) = 2 and x = -1
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Selena is preparing for her eighth-grade graduation party. she must keep within the budget set by her parents. which is the best price for her to purchase ice cream? a. $3.99/ 24 oz carton b. $4.80/ one-quart carton c. $11.00 / one gallon tub d. $49.60/ five gallon tub
Answer:
Basically find the unit rate by doing 3.99/24 = $0.16625/1oz
1 quart = 32 ounces so 4.8/32 = $0.15/1oz
1 gallon = 153.722 ounces so 11/153.722 = 0.07
49.6/768.61 = 0.06
Step-by-step explanation:
D.
A couple plans to have 4 children. The gender of each child is equally likely. Design a simulation involving 55 trials that you can use to model the genders of the children. Write your answer as number
Answer:
4x55x2
Step-by-step explanation:
4 kids 55trys 50 50 odds
Toby has five coins. Three of the coins add up to 30p. Three of the coins add up to 40p. All the coins add up to 50p. List Tony's coins in ascending order of value.
Tony's coins in ascending order of value will be 5p, 10p, and 15p.
Definition of in Ascending order
Arranged in a series that begins with the smallest or least and ends with the largest or greatest The children were lined up in ascending order of height. Test score are listed in ascending order from lowest to highest.
How do depict the information?
Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.
In this case, 5p + 10p + 15p = 30p
10p + 15p + 15p = 40p
5p + 5p + 10p + 15p + 15p = 50p
Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.
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holii necesito ayuda lo más rápido posible x fiiiis
Utiliza la propiedad fundamental de las proporciones para determinar el valor p en la siguiente proporción.
p = p+2
6= 8
Usando proporciones, en conjunto con multiplicación cruzada, encontra-se que el valor de p es de 6.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
En este problema, relación es dada por:
[tex]\frac{p}{p+2} = \frac{6}{8}[/tex]
Aplicando multiplicación cruzada:
8p = 6(p + 2)
8p = 6p + 12
2p = 12
p = 12/2
p = 6.
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Select all the correct answers.
Which expressions are equivalent to this exponential expression? Please help
An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,
(6⁻¹⁰/6⁻⁴)
= 6⁻¹⁰ × 6⁴
= 6⁽⁻¹⁰⁺⁴⁾
= 6⁻⁶
= 1/6⁶
Hence, the correct options are A and C.
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How many grains of Fermiun will remain after 15 days? 50 25 12.5 6.25
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1
Question 2 multiple choice worth 1 points)
(01.02 lc)
solve for x: 6x + 3 = 5x - 8
0-11
11
0-5
5
[tex]6x+3=5x-8[/tex] (given)
[tex]x+3=-8[/tex] (subtract 5x from both sides)
[tex]x=\boxed{-11}[/tex] (subtract 3 from both sides)
Instruction: draw a line perpendicular to line AB at point C.
I have followed the steps, please tell me what have I done wrong? :)
(picture included of my answer)
Answer:
it’s correct
Step-by-step explanation:
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
When taking the perpendicular of the line, it should be done at the midpoint of the line. Hence, by taking arcs from both endpoints, it should be done. This is why this is incorrect.
Which point is on the graph of the inverse function h-¹(x)?
O (2,4)
0 (0)
O (0, 1)
O (-5, 1)
Answer: (0,1)
Step-by-step explanation:
If (x,y) lies on the graph of the original function, then (y,x) lies on the graph of the inverse.
Since (1,0) lies on the graph of h(x), (0,1) lies on the graph of its inverse.
(0, 1) point is on the graph of the inverse function h-¹(x).
What are inverse functions?Two functions f(x) and g(x) are inverses if their composition is equal to the identity.
Equation of line will be
y = -2x + 2 = h(x)
h⁻¹(x) will be calculated as:
x = -2y + 2
x - 2 = -2y
y = (2 - x)/2
So, y = h⁻¹(x) = (2 - x)/2
put x = 0 in the equation y = (2 - x)/2
y = 1
(0, 1) = (0, 1)
This, (0, 1) is the point on h⁻¹(x).
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find the area occupied by the base of a cylindrical bowl if the base is 9 cm?
Answer:
is it radius or diameter?
A rectangle swimming pool was 9 meters wide with an area of 90 square meters. What is the length of the pool?
Answer:
10 meters.
Step-by-step explanation:
The area of a rectangle formula is width multiplied by length. So, to find the length of the pool, simply divide the width from the area.
90/9=10
The length of the pool is 10 meters.
Hope this helps!
If not, I am sorry.
If the bearing of p from y is 048degrees what is the bearing of y from p
Step-by-step explanation:
see photo for detailed analysis
look at the attachments
the last one at the bottomm c is200
please i really need help its khan
Answer:
all I know is the second on about world population in 2014 which was c
7•10⁹
Answer:
B
B
Step-by-step explanation:
there are 9 steps for the second question so it 10^9
and if you times the 1st population size by 20 you get very close to the second population size.
Which of the following did you include in your response? Check all of the boxes that apply. the range, or spread, of the salaries whether most people make a very low salary and one or two people make a high salary the minimum salary, and whether that is an entry level or starting salary the maximum salary whether the maximum salary is a lot higher than the average and other salaries are a lot lower than the mean
Answer:
to be honest i don't know
Step-by-step explanation:
uh
Answer: its all
Step-by-step explanation:
it does not matter which one you pic, you just have to pick one.
Find the measure of a.
Answer:
10
Step-by-step explanation:
By the geometric mean theorem,
4/a = a/25100=a² (cross multiply)a=10 (square root both sides and take the positive solution)A bottle holds
5
55 milliliters of perfume.
How many bottles can we fill with
2
22 milliliters of perfume?
Answer:
0.4 bottles can be filled
Step-by-step explanation:
divide the amount that is present by the max amount
the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.
the amount that is present is 2.22 millimeters.
[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]
0.4 bottles
if the given values are 555 and 222 then the answer is still .4
Answer:
0.4 bottles can be filled
