Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3

Answer:

y = 7/6x - 62/3

Step-by-step explanation:

The equation for slope:

y = mx + b

m is the slope and b is the y-intercept

y = 7/6x + b

-9 = 7/6(10) + b

-9 = 35/3 + b

-62/3 = b

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

⇒-8(x+13)=2(x-7)+4x

⇒-8x-13×8 = 2x-2×7+4x

⇒-8x-104=2x-14+4x

⇒-8x-104=6x-14

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).

Hence, option C is correct.

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Answer:

[tex]\huge\boxed{\sf L = 78\°}[/tex]

Step-by-step explanation:

Exterior angle of L = 5x + 12

M = 3x - 2

N = 50

So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.

Here,

Exterior angle of L = M + N

5x + 12 = 3x - 2 + 50

5x + 12 = 3x + 48

Subtract 12 to both sides

5x = 3x + 48 - 12

5x - 3x = 36

2x = 36

Divide 2 to both sides

x = 18

So,

= 3x - 2

= 3 (18) - 2

= 54 - 2

= 52°

Now,

We know that,

L + M + N = 180°

L + 52 + 50 = 180

L + 102 = 180

Subtract 102 to both sides

L = 180 - 102

L = 78°

[tex]\rule[225]{225}{2}[/tex]

[tex]h(x) = - x - 7 \\ \\ when \: x \: is \: - 2 \\ h(x) = - ( - 2) - 7 \\ h(x) = 2 - 7 \\ h(x) = - 5 \\ \\ when \: x \: is \: 0 \\ h(x) = 0 - 7 \\ h(x) = - 7 \\ \\ when \: x \: is \: 5 \\ h(x) = - 5 - 7 \\ h(x) = - 12[/tex]

After 7 days, the balance will be Rs. 628.

(A) The slope of the given function is 40.

(B) In point - slope form it is y - 600 = 40x

   In Slope - intercept form it is y = 40x + 600

   In Standard form it is 40x - y + 600 = 0

(C) g(x) = 4x + 600

(D) After 7 days, the balance will be Rs. 628

Let g(x) = y

(A) We know slope = change in y/change in x

                               = 720-600/3-0

                               = 120/3

                               = 40

Therefore, the slope of the given function is 40.

(B) We know that the equation of a line

in point - slope form is y - y₁ = m(x - x₁)

where ( x₁, y₁ ) is a point on the line

where m is the slope

Therefore, substituting the values, we get,

y - 600 = 40(x - 0)

=> y - 600 = 40x                                    --(i)

Slope - intercept form is y  = mx + b

where m is the slope

and b is the y-intercept

To find y intercept, we substitute x = 0 in equation (i)

=> 40*0 - y + 600 = 0

=> -y + 600 = 0

=> y = 600

Therefore, substituting the values, we get,

     y = 40x + 600

in Standard form is ax + by = c

where a, b, and c is constant

Converting the equation found above into the standard form

=> y = 40x + 600

=> 40x - y + 600 = 0

(C) As we had assumed g(x) to be y

=> From equation (i),

 y - 600 = 40x    

can be written as g(x) - 600 = 4x

=> g(x) = 4x + 600                                    --(ii)

(D) We need to find the balance in the bank account after 7 days

=> Balance [g(x)] when x = 7

Therefore, substituting the value of x in equation (ii)

=> g(x) = 4*7 + 600

          = 28 + 600

          = 628

Therefore, after 7 days, the balance will be Rs. 628.

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In the given equation, the value of x is approximately 75°

From the question, we are to determine the value of x

The given equation is

sin x ≈ 0.965926

If sin x ≈ 0.965926

Then,

x ≈ sin⁻¹(0.965926)

∴ x ≈ 75.0°

Hence, the value of x is approximately 75°

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Answer:

(3, -2)

Step-by-step explanation:

 We can view slope as: [tex]\frac{rise}{run}[/tex] (rise / run)

"rise" is the change in y from one point to another

"run" is the difference in x from one point to another

So, if the slope of a line is 2, it rises 2 every time it runs 1 (2 = 2/1)

So, we can find another point on the line by adding 2 to the y-value, and adding 1 to the x-value.

(x, y)  

          (2, -4)

         + 1  + 2

           (3, -2)

So, another point on this graph is (3, -2)

Answer:

60 minutes

Step-by-step explanation:

we can see that the number of minutes increases by 8 each day

(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)

So, because we have the value for the previous day (day 6) we know that we can simply add 8

52 + 8 = 60

So, the predicted number of minutes for day 7 is 60

hope this helps!!

The expected value of the winnings from the game is $4

The payout probability distribution is given as:

Payout ($) 2 4 6 8 10

Probability 0.5 0.2 0.15 0.1 0.05

The expected value is then calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05

Evaluate the expression

E(x) = 4

Hence, the expected value of the winnings from the game is $4

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Answer:

[tex]\huge\boxed{\sf x = -2/3}[/tex]

Step-by-step explanation:

3x + 2 = 0

Subtract 2 to both sides

3x = 0 - 2

3x = -2

Divide 3 to both sides

x = -2/3

[tex]\rule[225]{225}{2}[/tex]

Answer:

  (-1, -5)

Step-by-step explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

  (x, f(x) -2)

Then for x = -1, the point is ...

  (-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

_____

Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.

The correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.

Therefore the correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

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Assuming that both lines are parallel, we conclude that C = 74°.

Here we can see that both of the lines that go upwards are parallel lines. This means that C and the 74° angles are opposite angles.

Then if we say that x is the angle at the right of the 74°, we must have that:

x + 74° = 180°

x = 180° - 74° = 106°

And we also must have that:

x + C = 106° + C = 180°

Solving for C:

C = 180° - 106° = 74°

C = 74°.

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Answer:

13×13×13=2197 that is the answer

Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.

In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.

When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.

Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.

Hence option D is correct.

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Answer:

no correlation

Step-by-step explanation:

Step-by-step explanation:

solution:

here,

x/2+4

= 6/2+4 ( x = 6 )

= 3+4

= 7

Answer:

7

Step-by-step explanation:

x/2 + 4

=> 6/2 + 4 (x=6)

=> 3 + 4

=> 7

Answer:

(5,2)

Maximum

5

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\texttt{\:Coordinates of vertex = (5,2)}[/tex]

[tex]\texttt{The graph has a maximum} [/tex]

[tex]\tt \: Axis\:\: of \:\; symmetry : x = 5\ [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Coordinate of vertex is the point where there's a unique (only one) value of y for x :

[tex]\qquad \tt \rightarrow \: (5,2)[/tex]

Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]

and hence, it has a maximum, at the vertex.

Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.

it is the line passing through vertex and parallel to y - axis.

[tex]\qquad \tt \rightarrow \: x = 5[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

y = 7 x - 13. y=7x−13. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side.7x-13=y. 7x−13=y. Add 13 to both sides. ... 7x=y+13. 7x=y+13. Divide both sides by 7. ... \frac{7x}{7}=\frac{y+13}{7} 77x​=7y+13​ Dividing by 7 undoes the multiplication by 7.

Step-by-step explanation: hope this helps

Answer:

-7

Step-by-step explanation:

In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.

In this question we need to analyze an exponential function of the form:

y = a · (1 + r)ˣ      (1)

Where r is the growth rate. Please notice that there is a decay for r < 0. Thus, we find the following finding by comparing the given expression to (1):

y = 0.84 · (1 + 1/6)ˣ

In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.

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Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:

D(n) = 30n.

She has n = 8 gallons, hence the distance is given by:

D(8) = 30 x 8 = 240 miles.

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The answer is no solution

Explanation:

it depends on how you interpret what's written. The way I initially interpreted it*, I was able to use the quadratic formula to find :

[tex]x=\frac{1}{4}-i\frac{\sqrt{455}}{20},\:x=\frac{1}{4}+i\frac{\sqrt{455}}{20}[/tex]

*I interpreted it as: [tex]x\left(x+3\right)-2\left(-5x+1\right)x=x^2-3\left(4-2x\right)[/tex]

but I don't want to say that this is your correct answer, because there are multiple interpretations (like a lot of interpretations)

{this is mostly in response to other answers}

The number of answers that were incorrect will be 7.

From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:

3 - x = -4

where x = incorrect answer

3 - x = -4

-x - 4 - 3

-x = -7

x = 7

In conclusion, the number of answers that were incorrect will be 7.

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The number of postage stamps in John’s collection is 27.

We have given that,

John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Johan and Jonathan have the same number of stamps.

Let x be the Johan and Jonathan postal stamps.

Let y be the John postal stamps.

Two times Johan’s collection is eleven less than five times John’s collection.

2x = 5y - 11............(1)

Three times Jonathan’s collection is three less than seven times John’s collection.

3x = 7y - 3............(2)

Multiply equation 1 with 3

3(2x = 5y - 11)

⇒ 6x = 15y - 33.........(3)

Multiply equation 2 with 2

2(3x = 7y - 3)

⇒ 6x = 14y - 6.............(4)

Subtract equation 4 from equation 3

⇒ 6x - 6x = 15y - 33 - (14y - 6)

⇒ 0 = y - 27

⇒ y = 27

Hence, the number of postage stamps in John’s collection is 27.

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Answer:

[tex]\boxed {D) -\frac{2y}{x}}[/tex]

Step-by-step explanation:

Solving :

[tex]\implies \mathsf {\frac{(-2xy^{2})^{3}}{4x^{4}y^{5}}}[/tex]

[tex]\implies \mathsf {\frac{-8x^{3}y^{6}}{4x^{4}y^{5}}}[/tex]

[tex]\implies \mathsf {\frac{-2y}{x}}[/tex]

The area of the octagon having an apothem of 6 meters and a side length of 7 meters is 168 meter square

Using the formula:

Area of an octagon = perimeter * apothem / 2

Note that perimeter of an octagon = 8 a

where a is the length of it's side

Perimeter = 8 * 7

Perimeter = 56 meters

Apothem = 6 meters

Substitute into the formula

Area = 56 * 6/ 2

Area = 336 / 2

Area = 168 meter square

Thus, the area of the octagon is 168 meter square

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