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The graph y > x-2 and x + 2y 4 represents the system of linear inequalities.

A mathematical expression that compares two expressions to use the inequality symbol is known as a linear inequality. The expression may be a numerical expression, an algebraic expression, or both.

y > x - 2

x - 2y < 4

The line y = x - 2 in the graph, which is a boundary line because it excludes the line's points, stands in for the first inequality, y > x - 2, which is shown as y > x - 2. The area that is coloured above the line denotes all the locations where y exceeds x - 2.

The graph y > x-2 and x + 2y 4 represents the system of linear inequalities.

formula for a line

Y = mx + b is the formula for determining a line's equation.

The slope is m.

the y-intercept is b.

About the dotted line (4, 0) and (0,2)

Slope = 2/-4

Slope = -1/2

Y = -1/2 x + 2 = 2y = -x + 4 is the equation.

The inequality formula is x + 2y 4.

The graph y > x-2 and x + 2y 4 represents the system of linear inequalities.

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Complete question -

Which system of linear inequalities is represented by the graph?

y > x-2 and x – 2y < 4

y > x + 2 and x + 2y < 4

y > x-2 and x + 2y < 4

y> x-2 and x + 2y ​

9514 1404 393

Answer:

  1. asymptotes: x=-6, x=6, y=0; zero: x=0

  2. 20 blue fish

Step-by-step explanation:

1. The vertical asymptotes are where the denominator is zero. It factors as (x-6)(x+6), so will have zeros at x=-6 and x=6.

The horizontal asymptote is at the limit when x goes to infinity. Here, the ratio of highest-degree terms is 6/x, so the value goes to zero as x gets large.

The zero is where the numerator is zero, at x=0.

In summary:

__

2. 60% are red, so 40% are blue. The difference in percentages is 60%-40% = 20%. The percentage of blue fish (40%) is twice the difference (=2×20%), so the number of blue fish is twice the difference in numbers.

  blue fish = 2×10 = 20 fish

Check

There are then 20+10=30 red fish, so 20+30=50 fish total. Reds are 30/50 = 60% of the total.

Additional comment

I find it often works well to work with ratios, which I can often do in my head. Other folks like to see equations. Here, we could write equations like ...

  r = 60%(r + b) . . . . reds are 60% of the total

  r - b = 10 . . . . . . . . 10 more reds than blues

We want the value of b, so we can eliminate r by substituting for it:

  r = 10 + b . . . . from the second equation above

  (10 +b) = 0.60((10 +b) + b) . . . . substitute for r

  10 +b = 6 + 1.2b . . . simplify

  4 = 0.2b . . . . subtract b+6

  20 = b . . . . . . multiply by 5 (there are 20 blue fish)

Using the slope formula, the lines are:

1. Neither

2. Perpendicular

3. Neither

The slope formula is given as, m = change in y / change in x.

Slope of lines that are parallel are the same while slope of perpendicular line will give a product of -1.

1. Slope of L1 (m) = change in y / change in x = (6 - 0) / (0 - (-2))

m = 6/2

m = 3

Slope of L2 (m) = change in y / change in x = (3 - 3) / (0 - 1)

m = 0/-1

m = 0

Both lines are neither.

2. Slope of L1 (m) = change in y / change in x = (-2 - 2) / (8 - 6)

m = -4/2

m = -2

Slope of L2 (m) = change in y / change in x = (0 - 1) / (3 - 5)

m = -1/-2

m = 1/2

Both lines are perpendicular because (-2)(1/2) = -1

3. Slope of L1 (m) = change in y / change in x = (4 - (-1)) / (4 - (-5))

m = 5/9

Slope of L2 (m) = change in y / change in x = (10 - (-7)) / (8 - 4)

m = 17/4

The lines are neither.

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The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

THE ANS IS 0<-23

Step-by-step explanation:

4(X+3)< 7x-3x-11

4x+12< 4x-11

4x will be cancelled,

So we get,

4x-4x< -11-12

0 < -23

Thank YOU AND PLZ MARK AS BRAINLY AND GIVE RATING ALSO

A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.

In other words, prime numbers are the numbers

divisible by 1 and the number itself.

For example, let us take 2.

2 has only two factors and those are 1 and 2 so it's prime.

Similarly, 7 is also a prime number because it has only two factors

and these are 1 and the number itself which is 7.

Answer:

A number that is only divisible by itself and 1

Step-by-step explanation:

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Based on the diagram, the true statement is "If a student is an honor student, then he/she may also be a band member."

It shows the intersection between two groups:

This intersection implies some band members are honor students and vice versa. However, not all band members are honor students and not all honor students are band members.

A correct conclusion is that an honor student may also belong to the band.

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If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Option A

Using points (1,20) and (2,40) from the graph:

Option B

Using points (-1,6) and (1,10) on the table:

Option C

We have the points (4,12) and (6,18).

Option D

Comparing y=3x+7 with the slope-intercept form:

Thus, the first graph (option A) has the greatest rate of change.

Answer:

which ever diagram with 11.6 at the starting point

Answer:

14.66 or 14.7

Step-by-step explanation:

if we solve the equation we get 14.6666 but since it goes on and on we round and put it on 14.7

Answer:

Step-by-step explanation:

11 ÷ 3/4 = \(11 * \frac{4}{3}\)

             \(=\frac{44}{3}\\\\=14\frac{2}{3}\)

Answer:

267.5 miles

Step-by-step explanation

65×2.5=162.5                

70×1.5=105

162.5+105=267.5

The answer is -3.

If m = 4 and n = -7, we can evaluate the expression by substitution.

m + n

4 + (-7)

-3

❄ H there,

evaluate this expression by substituting the provided parameters –

\(\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}\)

That's it!

❄

The probability that, 1.5 years from now, he will still have a usable pick without having had to order more is 0.1898, and the expectation of the time in months is 20 months.

Here, we have to find the standard deviation of time.

T is a random variable denoting the life of the pick chip. Then it will be an exponentially distributed random variable i.e.

\(f_{T}\) (t) = λe^(-λt)

\(F_{T}\) (t) = 1- λe^(-λt)

Here, given the average to shop is 3 times a year. Then λ = 1/3.

There is a total of 5 picks of chips available.

Total number of picks = 5

Expected time to break 5 picks  = 5 x 12/3 = 20 months.

Then T5 denotes the random variable that represents the life of all five chips.

The distribution of T5 = P.

\(F_{T}\) (5) = P (T5≤t) = P (T1 + T2 + T3 + T4 + T5 ≤t)

Now, T1 is governed by an exponential distribution. Then the sum of the exponential distribution is the Erlang distribution. Thus, distribution T5 is given by

\(f_{T}\) (5) = λ^5 x t^4 x e^(-λt) /T(5)

Mean is given μ = 5λ = 5 x 3 = 15

Then σ = (5λ^2)^1/2 = \(\sqrt{5(3)^2}\) = \(\sqrt{45}\)

Here, probability has usable picks means 4 available picks have failed.

∵ Life of picks is exponentially distributed, a number of failures of picks that failed in a given time are Poisson distribution.

P (X= x) = (μt)^x . e^(-μt)/x!

Thus μ = 3. So, here the probability have 4 failed after 5 years of

P (x=4) = (3 x 1.5)^4 . e^(-3 x 1.5)/4!

P (x=4) = 0.1898

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

We can add the two similar terms on the right side of the inequality:

now we can move all the terms with p to the left side of the inequality, and all the constants to the right side:

since the coefficient of the term 2p is positive, we can move it to the opposite side dividing without changing the inequality sign:

therefore, p is greater or equal to 11

Answer:

a = 8 m

Step-by-step explanation:

Since, given is an isosceles right triangle.

So, by Pythagoras theorem:

\( {a}^{2} + {a}^{2} = {(8 \sqrt{2} )}^{2} \\ \\ 2 {a}^{2} = 128 \\ \\ {a}^{2} = \frac{128}{2} \\ \\ {a}^{2} = 64 \\ \\ a = \sqrt{64} \\ \\ a = 8 \: m\)

The expression for the total amount of sales the store makes will be:25s + 28.8p

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandal.

Let sneakers = s

Let sandals = p

An expression for the total amount of sales the store makes will be: 1/2(50s) + 0.8(36p).

= 25s + 28.8p

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Mean (X + Y) = Mean (X) + Mean (Y).

The above statement is false.

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Probability Distributions of Discrete Random Variables:

Probability distributions of discrete random variables list the probabilities associated with each possible outcome. Also called probability function or probability mass function.

The probability of a discrete random variable is between 0 and 1. Also, the sum of the probabilities of a discrete random variable is equal to 1. The probability distribution of discrete random variables resembles the normal distribution.

Example:

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X goes from result 1 + 1 = 2 to 2 and the maximum value goes from result 6 + 6 = 12 to 12. Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

Discrete random variables should not be confused with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. However, a discrete random variable can have a range of possible values ​​that result from experimentation.

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Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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The value of x in the triangle ABC is 25.

The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.

The exterior angle of the triangle is given as m∠ACD = 5x.  

The sum of angle in a triangle is equals to 180 degrees. Therefore,

3x + 50 + (180 - 5x)  = 180

3x + 50 - 5x + 180 = 180

3x - 5x + 50 + 180 = 180

-2x + 230 = 180

subtract 230 from both sides

-2x + 230 - 230 = 180 - 230

-2x = -50

divide both sidesby -2

-2x / -2 = -50 / -2

x = 25

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The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.

Answer:

A = 26.6°

Step-by-step explanation:

To obtain the measure of angle A :

We use the trigonometric relation :

Tan A = opposite / Adjacent

Tan A = 6 / 12

Tan A = 1/2

A = tan^-1(1/2)

A = 26.565°

A = 26.6°

1. A, as A is the shared vertex of both triangles. and 2. The original is ABC, and the dilated version is AED. as triangle ABC's half is represented by triangle AED.

The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.

A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.

The center, which may be found within, outside, or on a figure, is the only invariant (constant) point under a dilation (k 1).

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The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Answer:

10:4 and 20:8 are equivalent to 15:6.

Step-by-step explanation:

15/6 = 2.5

10/4 = 2.5 yes

7/2 = 3.5 no

20/8 = 2.5 yes