Which of these correctly explains the solution of the system of equations shown
below?
2x + 3y = 6
x+ 3y = 12
O A The equations have x-intercepts at 3 and 12; therefore, (3, 12) is the
O
B. The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is
the solution.
O
C. The lines representing the equations intersect at x= 1 and y = o; therefore,
(1, 0) is the solution.
The equations have v-intercents at 2 and 4: therefore
the solution

Answer:

3/5x + 3 = 6

3/5x = 6 - 5

3/5x = 1

3/5x (5x) = 1* 5x

3 = 5x

3/5 = X

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.

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

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]

[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)

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

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.

Answer:

The last option that starts with (1,-1)

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.

Learn more about coins on: brainly.com/question/2974216

#SPJ10

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).

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).

Learn more about this concept here:

https://brainly.com/question/17780415

#SPJ1

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.

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.

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.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

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.

Answer:

is it radius or diameter?

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.

Usando proporciones, en conjunto con multiplicación cruzada, encontra-se que el valor de p es de 6.

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.

Puede-se aprender más a cerca de proporciones en https://brainly.com/question/24615636

#SPJ1

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.

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.

To learn more on draining processes: https://brainly.com/question/15840655

#SPJ1

An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.

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.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ1

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.

Answer:

10

Step-by-step explanation:

By the geometric mean theorem,

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

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.

To know more about Function

https://brainly.com/question/12431044

#SPJ1

The indicated function values are f(0) = 2 and x = -1

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

Read more about functions at

https://brainly.com/question/12518981

#SPJ1

Step-by-step explanation:

see photo for detailed analysis

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.

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.

Answer:

0.00305 (rounded)

Step-by-step explanation:

this is a geometric sequence so the formula is

an=a×r×n-1

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.

Answer:

4x55x2

Step-by-step explanation:

4 kids 55trys 50 50 odds