Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-halfx

y < One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.
(5, –2), (3, 1), (–4, 2)
(5, –2), (3, –1), (4, –3)
(5, –2), (3, 1), (4, 2)
(5, –2), (–3, 1), (4, 2)

Answer:

47 cents or $0.47

Step-by-step explanation:

1 dime = 10 cents (or $0.1)

1 quarter = 25 cents or ($0.25)

12 cents + 1 dime + 1 quarter = 12 + 10 + 25 = 47 cents

Both Roger and Jeff will have run a distance of 1/3 mile when Jeff catches up to Roger after 2 minutes.

To solve this problem, we can determine the relative speeds of Roger and Jeff.

Since Roger runs one mile in 9 minutes, his speed is 1/9 miles per minute.

Similarly, Jeff runs one mile in 6 minutes, so his speed is 1/6 miles per minutes.

Let's assume that Jeff catches up to Roger after t minutes.

In that time, Roger would have run (1/9) [tex]\times[/tex] t miles, and Jeff would have run (1/6) [tex]\times[/tex] t miles.

Since Jeff gives Roger a 1-minute head start, we can express their distances covered as:

Distance covered by Roger = (1/9) [tex]\times[/tex] (t+1) miles

Distance covered by Jeff = (1/6) [tex]\times[/tex] t miles

For Jeff to catch up to Roger, their distances covered must be equal. So we can set up the equation:

(1/9) [tex]\times[/tex] (t+1) = (1/6) [tex]\times[/tex] t

To solve for t, we can cross-multiply and simplify:

6(t+1) = 9t

6t + 6 = 9t

6 = 9t - 6t

6 = 3t

t = 2

Therefore, it will take 2 minutes for Jeff to catch up to Roger.

Substituting t = 2 back into the equations, we can find the distances covered by each:

Distance covered by Roger = (1/9) [tex]\times[/tex] (2+1) = 1/3 mile

Distance covered by Jeff = (1/6) [tex]\times[/tex] 2 = 1/3 mile

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The  system of equation: -x + 7 = -2x³ + 5x² + x - 2 has three solutions

The correct answer is option D.

To solve the system of equations:

-x + 7 = -2x³ + 5x² + x - 2

We need to simplify and rearrange the equation to find its solutions. Let's start by combining like terms:

-x + 7 = -2x³ + 5x² + x - 2

Simplifying the left side:

7 = -2x³ + 5x² - x - 2

Next, let's arrange the equation in descending order of the variable's exponent:

-2x³ + 5x² - x - 2 = 7

Now, let's move all terms to one side of the equation to set it equal to zero:

-2x³ + 5x² - x - 2 - 7 = 0

Simplifying further:

-2x³ + 5x² - x - 9 = 0

To determine the number of solutions, we can analyze the degree of the equation. Since it is a cubic equation, it can have a maximum of three real solutions.

The given system of equations is:

-x + 7 = -2x³ + 5x² + x - 2

To find the solutions, we need to set the equation equal to zero. Let's rearrange the terms:

2. -2x³ + 5x² - x - 9 = 0

Now, we can try to factor or use numerical methods to solve the equation. However, factoring a cubic equation can be complex and time-consuming. In this case, we'll use numerical methods to approximate the solutions.

One common numerical method is the Newton-Raphson method, which involves making an initial guess for the solutions and iterating to converge on a more accurate solution.

Using numerical software or calculators, we can find the approximate solutions of the equation as follows:

x ≈ -1.607, x ≈ 1.279, and x ≈ 3.328

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The equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b): Of(x) = (4x + 1)(4x - 1).

The correct answer to the given question is option a or b.

The given function is f(x) = 4x² - 1. We need to choose the equivalent function that best shows the x-intercepts on the graph.The x-intercepts are the points where the graph of a function intersects the x-axis. At the x-intercepts, the value of y is zero.

Therefore, to find the x-intercepts, we need to solve the equation f(x) = 0 for x. The function f(x) = 4x² - 1 can be factored as:(2x + 1)(2x - 1)

To find the x-intercepts, we set f(x) = 0:4x² - 1 = 0(2x + 1)(2x - 1) = 0So, either 2x + 1 = 0 or 2x - 1 = 0. Solving these equations, we get:

x = -1/2 or x = 1/2

These are the x-intercepts of the graph of f(x) = 4x² - 1.Now, let's look at the given options and determine which one shows the x-intercepts on the graph:

Option (a):

Of(x) = (4x + 1)(4x - 1)

This is the factored form of f(x) = 4x² - 1. It correctly shows the x-intercepts.

Option (b):

Of(x) = (2x + 1)(2x - 1)

This is the same as option (a) and correctly shows the x-intercepts.

Option (c): f(x) = 4(x² + 1)

This function does not have any x-intercepts. It has a minimum value of 4 at x = 0.

Option (d): f(x) = 2(x² - 1)

This function has x-intercepts at x = -1 and x = 1. It does not show the x-intercepts of the given function.

Therefore, the equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b):

Of(x) = (4x + 1)(4x - 1).

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Answer:

Step-by-step explanation:

Answer:

-27+15 (N-1)

Step-by-step explanation:

-27, -12, 3, 18

Take the second term and subtract the first term to find the common difference

-12 - (-27)

-12+27 = 15

The common difference is +15

We are adding 15 each time

The formula for an arithmetic sequence is

an = a1+d(n-1)

an = -27 +15(n-1)

Answer: -24

Step-by-step explanation:

To evaluate the expression, I guess we need to break it down into steps:

Expression: -3[-4(3-10)-12] / -2(-1)

Step1: Simplify the innermost parentheses Inside the square brackets: 3 - 10 = -7 Expression becomes: -3[-4(-7) - 12] / -2(-1)

Step2: Simplify the multiplication in square brackets: -4 * (-7) = 28. Expression becomes: -3[28 - 12] / -2(-1)

Step3: Simplify the subtraction inside the square brackets: 28 - 12 = 16. Expression becomes: -3[16] / -2(-1)

Step4: Simplify the multiplication outside the square brackets: -3 * 16 = -48. Expression becomes: -48 / -2(-1)

Step5: Simplify the multiplication inside the denominator: -2 * (-1) = 2 Expression becomes: -48 / 2

Step 6: Perform the division -48 divided by 2 is equal to -24

Therefore, the value of the expression -3[-4(3-10)-12] / -2(-1) is -24.

the answer is

w = -3/2 u + 2

Answer:

(3, -2) is the correct choice.

1. Using a calculator, we find that cos 10 ≈ 0.98.

2. Using a calculator, we find that sin 30 ≈ 0.50.

3. Using a calculator, we find that sin 20 ≈ 0.34.

4. Using a calculator, we find that tan 25 ≈ 0.47.

5. Using a calculator, we find that tan 48.5 ≈ 1.14.

Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:

Cos 10:

Using a calculator, we find that cos 10 ≈ 0.98.

Sin 30:

Using a calculator, we find that sin 30 ≈ 0.50.

Sin 20:

Using a calculator, we find that sin 20 ≈ 0.34.

Tan 25:

Using a calculator, we find that tan 25 ≈ 0.47.

Tan 48.5:

Using a calculator, we find that tan 48.5 ≈ 1.14.

These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.

Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.

It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.

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Answer:

p =1 0

Step-by-step explanation:

x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]

= (x - y)⁹(x - y)(x² + y² + xy)

= (x - y)¹⁰(x² + y² + xy)

where p = 10 and q = 1

Answer:

p = 10

Step-by-step explanation:

Given expression:

[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]

Factor out the common term (x - y)⁹:

[tex](x-y)^9(x^3- y^3)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]

Rewrite the second parentheses as the difference of two cubes.

[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]

[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]

[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]

[tex](x-y)^{10}(x^2+y^2+xy)[/tex]

Comparing the rewritten original expression with the given expression:

[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]

We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.

Therefore, we can conclude that p = 10.

Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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Part I- a) y = (x + 25)(x + 9)

b) y = x^2 + 34x + 225

c) y=  (x + 17)^2 - 64

d) The y-intercept is (0, 225), The y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.

g) y = 465 square yards

Part II- a) y = (6 + 2x)^2

b) 169 = (6 + 2x)^2

c) x = 3.5 feet

Part I:

y = (x + 25)(x + 9)

b) To rewrite the equation in standard form using the FOIL method:

y = x^2 + 9x + 25x + 225

= x^2 + 34x + 225

c) To rewrite the equation in vertex form by completing the square:

y = (x^2 + 34x) + 225

= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2

= (x^2 + 34x + 289) + 225 - 289

= (x + 17)^2 - 64

d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:

0 = (x + 17)^2 - 64

64 = (x + 17)^2

x + 17 = ±√64

x + 17 = ±8

x = -17 ± 8

x = -25, -9

Therefore, the x-intercepts are (-25, 0) and (-9, 0).

The y-intercept is obtained by setting x = 0 in the equation:

y = (0 + 17)^2 - 64

y = 17^2 - 64

y = 289 - 64

y = 225

Therefore, the y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.

g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).

h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:

y = (6 + 17)^2 - 64

y = 23^2 - 64

y = 529 - 64

y = 465 square yards

Part II:

a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:

y = (6 + 2x)^2

b) Substituting the area of the enclosed space (169 square feet) for y in the equation:

169 = (6 + 2x)^2

c) Solving the equation for x:

√169 = √((6 + 2x)^2)

13 = 6 + 2x

2x = 13 - 6

2x = 7

x = 7/2

x = 3.5 feet

Therefore, the width of the deck space around the hot tub is 3.5 feet.

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Given the information in the diagram, the theorem that best justifies why lines j and k must be parallel include the following: D. converse alternate exterior angles theorem.

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

In Mathematics and Geometry, the alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.

Since the alternate exterior angles are congruent, we can logically deduce the following based on the converse alternate exterior angles theorem;

93° ≅ 93° (lines j and k are parallel lines).

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Complete Question:

Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?

alternate interior angles theorem

alternate exterior angles theorem

converse alternate interior angles theorem

converse alternate exterior angles theorem

The area of the obtuse triangle is 34 square feet with a base of 10 ft and height of 6.8 ft.

To find the area of the obtuse triangle, we can use the formula A = (1/2) * base * height. Let's denote the unknown part of the base as x.

In the given triangle, we have the width of the obtuse angle triangle as 10 ft, the height (perpendicular) as 6.8 ft, and the unknown part of the base as x.

Using the formula, we can calculate the area as:

A = (1/2) * (10 + x) * 6.8

Simplifying this expression, we get:

A = 3.4(10 + x)

Now, we need to determine the value of x. From the given information, we know that the width of the obtuse angle triangle is 10 ft. This means the sum of the two parts of the base is 10 ft. Therefore, we can write the equation:

x + 10 = 10

Solving for x, we find:

x = 0

Since x = 0, it means that one part of the base has a length of 0 ft. Therefore, the entire base is formed by the width of the obtuse angle triangle, which is 10 ft.

Now, substituting this value of x back into the area formula, we have:

A = 3.4(10 + 0)

A = 3.4 * 10

A = 34 square feet

Hence, the area of the obtuse triangle is 34 square feet.

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Answer:

(x + 5)² + (y – 1)² = 25

Step-by-step explanation:

Note that the general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.

The circle is 10 units in diamater, so the radius is half this: r=10/2=5.

The circle goes from -10 to 0 along the x-axis, so the x-coordinate of its centre is halfway between this: h=(-10+0)/2=-10/2=-5

The circle goes from -4 to 6 along the y-axis, so the y-coordinate of its centre is halfway between this: k=(-4+6)/2=-2/2=1

Now that we know r, h, and k, we can sub these into the general formula to get our equation:

(x - (-5))² + (y – 1)² = 5²

(x + 5)² + (y – 1)² = 25

The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.

Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.

The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.

Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.

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Answer:

She willl be $1.40 under budget

Step-by-step explanation:

8% = 8/100 = 0.08

Adding this to 100% of the price of the shoes, we get 108% = 108/100 = 1.08.

We multiply the price of the shoes by this:

45*1.08 = 48.60

Subtract this from 50:

50 - 48.60 = 1.40

Answer:

D

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 16 and h = 8 , then

A = [tex]\frac{1}{2}[/tex] × 16 × 8 = 8 × 8 = 64 ft²

Answer:

be more clear of what u mean edit the question to explain more

Step-by-step explanation:

no explanation

Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Step-by-step explanation:

Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.

For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:

27x + 48y = 540 ...(equation 1)

For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:

50x + 24y = 416 ...(equation 2)

To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:

Multiplying equation 1 by 2 and equation 2 by 3, we get:

54x + 96y = 1080 ...(equation 3)

150x + 72y = 1248 ...(equation 4)

Now, subtracting equation 4 from equation 3, we have:

(54x + 96y) - (150x + 72y) = 1080 - 1248

-96x + 24y = -168

Dividing both sides of the equation by -24, we get:

4x - y = 7 ...(equation 5)

Now, we have a system of equations:

4x - y = 7 ...(equation 5)

50x + 24y = 416 ...(equation 2)

Solving this system of equations, we find that x = 8 and y = 5.

Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.

So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Answer:

Step-by-step explanation:

Total cost of hand towels for first hotel = 27 * $5 = $135

Total cost of bath towels for first hotel = 48 * $8 = $384

Total cost of hand towels for second hotel = 50 * $5 = $250

Total cost of bath towels for second hotel = 24 * $8 = $192

Total cost of all hand towels = $135 + $250 = $385

Total cost of all bath towels = $384 + $192 = $576

Total number of hand towels = 27 + 50 = 77

Total number of bath towels = 48 + 24 = 72

Average cost of one hand towel = $385 / 77 = $5

Average cost of one bath towel = $576 / 72 = $8

Answer:

ok t means some thing but zero and seven should be solved

A "⊂-maximal element" in set theory refers to an element in a set that cannot be strictly contained within any other element of the set, indicating a maximum extent or boundary within that set.

In the context of set theory and Tarski's notion of finiteness, a "⊂-maximal element" refers to an element within a set that cannot be strictly contained within any other element of the set. Let's break down the meaning of this term.

Consider a set S and a partial order relation ⊆ (subset relation) defined on the power set P(S) of S. A "⊂-maximal element" u of a set A ⊆ S is an element that is not strictly contained within any other element of A with respect to the subset relation. In other words, there is no element v in A such that u is a proper subset of v.

Formally, for any u ∈ A, if there is no v ∈ A such that u ⊂ v, then u is a ⊂-maximal element of A. This means that u is as large as possible within A and cannot be extended by including additional elements.

In the context of T-finite sets, the existence of a ⊂-maximal element in every nonempty subset of the set guarantees that the set has a well-defined structure and does not continue indefinitely without boundaries.

It ensures that there is a definitive maximum element within each subset, which is a key characteristic of finiteness.

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Answer: False

Step-by-step explanation:

Spherical geometry, on the other hand, is a type of non-Euclidean geometry that is specifically concerned with studying the properties of curved surfaces, such as spheres.

Hope this help! Have a good day!

Answer:

D

Step-by-step explanation:

to find the coterminal angles add/ subtract 360° to the given angle

- 255° + 360° = 105°

- 255° - 360° = - 615°