Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed. y ≥ 0 y < x x + y < 6

Answer:

[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex]

or

[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]

Step-by-step explanation:

we have

[tex]f(x)=8x^{2}-4x+11[/tex]

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

[tex]f(x)=8(x^{2}-\frac{1}{2}x)+11[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}[/tex]

[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}[/tex]

Rewrite as perfect squares

[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex] ----> equation in vertex form

or

[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]

The vertex is the point  (0.25,10.5)

Answer:

14.1cm (3s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

sine angle= opp/hyp

cosine angle= adj/hyp

The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle ⇒ D

Step-by-step explanation:

The Pythagorean triple is:

A. 12, 16, 20

∵ 20 is the greatest number

∵ (12)² + (16)² = 144 + 256 = 400

∵ (20)² = 400

∴ (20)² = (12)² + (16)²

∴ The set of integers 12, 16, 20 is a Pythagorean triple

∴ 12, 16, 20 are the side lengths of a right triangle

B. 10, 24, 26

∵ 26 is the greatest number

∵ (10)² + (24)² = 100 + 576 = 676

∵ (26)² = 676

∴ (26)² = (10)² + (24)²

∴ The set of integers 10, 24, 26 is a Pythagorean triple

∴ 10, 24, 26 are the side lengths of a right triangle

C. 14, 48, 50

∵ 50 is the greatest number

∵ (14)² + (48)² = 196 + 2304 = 2500

∵ (50)² = 2500

∴ (50)² = (14)² + (48)²

∴ The set of integers 14, 48, 50 is a Pythagorean triple

∴ 14, 48, 50 are the side lengths of a right triangle

D. 27, 32, 45

∵ 45 is the greatest number

∵ (27)² + (32)² = 729 + 1024 = 1753

∵ (45)² = 2025

∴ (45)² ≠ (27)² + (32)²

∴ The set of integers 27, 32, 45 is NOT a Pythagorean triple

∴ 27, 32, 45 are NOT the side lengths of a right triangle

The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle

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To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication. The equivalent expression is 56x^2 + 59xy + 15y^2.

To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication over addition.

This means that each term in the first expression is multiplied by each term in the second expression.

Here are the steps:

Apply the distributive property to multiply 7x by each term in the second expression: 7x * 8x + 7x * 5y

Apply the distributive property to multiply 3y by each term in the second expression: 3y * 8x + 3y * 5y

Simplify each term: 56x^2 + 35xy + 24xy + 15y^2

Combine like terms: 56x^2 + 59xy + 15y^2

Therefore, the expression (7x + 3y)(8x + 5y) is equivalent to 56x^2 + 59xy + 15y^2.

Answer:

y=4x-1

Step-by-step explanation:

4x-y=1

4x=y+1 then negative Y becomes positive after going to the other side of the equal sign.

4x-1=y the positive 1 becomes negative after going to the other side of the equal sign.

Answer:

y = 4x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

4x - y = 1 ( subtract 4x from both sides )

- y = - 4x + 1 ( multiply through by - 1 )

y = 4x - 1 ← in slope- intercept form

Answer:

look down + pls give me brainiest

Step-by-step explanation:

Let x = number of people when she got on.

x -4+3 -5+1 -1 = 4

x -6 = 4

Solve for x to get x=10.

So there were 10 people when Paulina got on (including herself).

Answer:

The area of the orange ​band is 576 + 48x square inches

Step-by-step explanation:

Step 1: Area of the green square

The area of the green square =[tex]side^2[/tex]

The area of the green square  =  [tex]x^2[/tex] square inches

Step 2: Area of the orange square

The area of the orange square =[tex]side^2[/tex]

The side of the orange square  =  12+12 + x = 24 +x

Now the area of the orange square  =[tex](x+24)^2[/tex]

Step 3: The area of the orange ​band

Area of the orange ​band =  area of the orange square - area of the green square

Area of the orange ​band =   [tex](x+24)^2 - x^2[/tex]

expanding and solving the equation we get

[tex]x^2 + 24^2 +48x - x^2[/tex]

[tex]576 + 48 x[/tex] square inches

Final answer:

The area of the orange band surrounding the central green square on the rug is found by subtracting the area of the green square from the area of the entire rug. The formula for the area of the orange band is 48x + 576 square inches, where x represents the side length of the green square.

Explanation:

To find the area of the orange band on the rug, we need to calculate the area of the entire rug and subtract the area of the central green square. The width of the orange band is given to be 12 inches. Therefore, each side of the orange rug is increased by 2 times 12 inches (for both the left and the right side of the green square), making the total length of the rug's side x + 2(12) inches.

The area of the entire rug, which is a larger square, is[tex](x + 24)^2[/tex] square inches. The area of the central green square is [tex]x^2[/tex]square inches. To find the area of the orange band, we subtract the area of the green square from the area of the entire rug which is: [tex](x + 24)^2 - x^2[/tex].

Expanding the squared term we get: [tex]x^2 + 48x + 576 - x^2[/tex], which simplifies to 48x + 576 square inches. That's the area of the orange band surrounding the green square.

Answer:

x=-11/6, y=7/6. (-11/6, 7/6).

Step-by-step explanation:

-2x+2y=6

4x+2y=-5

-----------------

2(-2x+2y)=2(6)

4x+2y=-5

----------------------

-4x+4y=12

4x+2y=-5

----------------

6y=7

y=7/6

4x+2(7/6)=-5

4x+14/6=-5

4x=-5-14/6

4x=-30/6-14/6

4x=-44/6

x=(-44/6)/4

x=(-44/6)(1/4)

x=-44/24

simplify

x=-11/6

Answer:

The correct answer is 1 and 1/2  

Trust Me

Answer:

The correct option is A

Step-by-step explanation:

quiz

Answer:

x=4

Step-by-step explanation:

2(x+2)+2(x+4)=28

Simplify the equation

2x+4+2x+8=28

4x+12=28

4x=16

x=4

Answer:

Divide each side of the equation by 2.

Step-by-step explanation:

(I took the test so i know its right) Basically, when doing the this by completing the square we need y^2 by itself, so we divide 2y^2-16y=6 by two first.

Answer:

Divide each side of the equation by 2.

Step-by-step explanation:

2y² – 16y = 6

Divide both sides by 2

y² - 8y = 3

Answer:

a^2b^2 - 3ab + 3ab - 9

a^2b^2 - 9

Step-by-step explanation:

Answer:

(2,-5)

Step-by-step explanation:

P(2,5)

(x,y)

Reflection over x-axis so the x coordinate stays the same while the y coordinate changes from a positive to a negative.

The point P(2, 5) reflected over the x-axis will have coordinates (2, -5), as the x-coordinate remains unchanged and the y-coordinate becomes negative.

When the point P(2, 5) is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Therefore, the coordinates of the resulting point, P', after reflection would be (2, -5). This is because reflecting over the x-axis means that we keep the horizontal position of the point the same (same x-coordinate), but flip the vertical position (change the sign of the y-coordinate).

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Final answer:

The volume of the refrigerator is factored by dividing with the given height, resulting in a quadratic polynomial that provides the other two dimensions. Upon factoring, we discover that the other dimensions are x - 6 and x + 1, corresponding to option D.

Explanation:

The volume of the refrigerator is given by the polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex]. To find the other two dimensions of the refrigerator, we need to factor this polynomial using the given height of the refrigerator, which is x + 2. The goal is to divide the volume polynomial by the height polynomial to get the product of the remaining two dimensions.

We proceed with polynomial division or factoring:

Divide the volume polynomial by x + 2 using synthetic division or long division.

The result should be a quadratic polynomial that further factors into the product of two linear factors corresponding to the unknown dimensions.

Factor the quadratic polynomial to find the two missing dimensions.

In this case, the volume polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex] can be divided by x + 2 to yield [tex]x^2 - 5x - 6[/tex], which can then be factored into (x - 6)(x + 1). Hence, the other two dimensions are x - 6 and x + 1, making option D correct.

Answer:

A: -0.3 and C: 1/6

Step-by-step explanation:

Step 1. Since 1/6 is positive it is greater than all negative numbers including -0.33

Step 2. -0.33 and -0.3 have the same numbers they are both negative but in -0.33 there are more hundred.

-0.3 >- 0.33

Step 3. -3/9= 0.33333..... -0.33 and -3/9 have the same number of units, tenths  and hundredths and both are negative but, -3/9 has more thousandths, so it's farther below 0.

-3/9 < -0.33

Final Step 4. -0.3 and 1/6 are greater than-0.33

The correct options are A.-0.3 and C. 1/6

In mathematics, an interval can be defined as a set of real numbers that contains all real numbers lying within any two specific numbers of the set R.

Given here: -0.33  which is equivalent to -1/3

The numbers greater than -1/3 lie in the interval (-1/3, ∞)

Clearly out of the given options only -0.3 and 1/6 lie in this interval.

Hence, The correct options are A.-0.3 and C. 1/6

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Answer:

answer is b

Step-by-step explanation:

look at the picture

Yo sup??

slope=y2-y1/x2-x1

just take any value of x1 x2 y1 and y2

let x1,y1=2,1

and

x2,y2=4,-2

plugging in the values

slope=-2-1/4-2

=-3/2

therefore your answer is option 2

Hope this helps

45 gallons of water used per person each month

Solution:

Given that,

The town of new London uses about 2,750,000 gallons of water each month

The population of new London is approximately 61,000

To find: Number of gallons of water used per person each month

From given,

Total gallons of water each month = 2750000

Population = 61000

Therefore,

[tex]Gallons\ of\ water\ per\ person = \frac{\text{Total gallons of water each month}}{population}[/tex]

[tex]Gallons\ of\ water\ per\ person = \frac{2750000}{61000}\\\\Gallons\ of\ water\ per\ person = \frac{2750}{61}\\\\Gallons\ of\ water\ per\ person =45.08 \approx 45[/tex]

Thus 45 gallons of water used per person each month

Answer: Angle X = 30

Step-by-step explanation: First and foremost, we should recognize that an isosceles triangle has two sides equal and the two angles subtended by the two equal sides are also equal in measurement.

This means. In the diagram on the left, line DE = line DF and that is 10cm.

The similar angles are the ones subtended by the lines identified as being equal, that is

Angle E = angle F and that is 75. If both angles measure a combined total of 150 the third angle can be derived simply as

180 - (75+ 75)

{Sum of angles in a triangle = 180}

180 - (150)

= 30

Therefore angle D = 30.

However having been given in the question that both triangles are similar and are isosceles, then

Angle D = Angle X and that is 30

Answer:

Answer:

What

Step-by-step explanation:

What is the missing variables

Final answer:

To simplify the expression 24 - 4.57 + (-4.62), add the negative numbers together and then subtract the sum from the positive number, resulting in a simplified answer of 14.81.

Explanation:

The question involves simplifying an expression, which is a basic arithmetic operation in mathematics. We are given the expression 24 - 4.57 + (-4.62). To simplify, we need to combine like terms and perform the addition and subtraction.

First, let's combine the positive and negative numbers separately:

Positive number: 24

Negative numbers: -4.57 and -4.62

We add the negative numbers together: -4.57 + (-4.62) = -9.19

Now, we subtract this sum from the positive number:

24 - 9.19 = 14.81

Therefore, the simplified result of the expression 24 - 4.57 + (-4.62) is 14.81.

Answer:

First term: 5

Fourth term: 5 1/2

Tenth term: 6 1/2

Step-by-step explanation:

Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:

A(n) = 5 + (n-1) (1/6)

First term:

A(1) = 5 + (1-1) (1/6)

A(1) = 5 + (0) (1/6)

A(1) = 5

Fourth term:

A(4) = 5 + (4-1) (1/6)

A(4) = 5 + (3) (1/6)

A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)

Tenth term:

A(10) = 5 + (10-1) (1/6)

A(10) = 5 + (9) (1/6)

A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)

Answer:

  f(x) = x² +2

Step-by-step explanation:

x-values are evenly spaced, and y-values decrease to a minimum of 2, then increase again. First differences are -1, 1, 3, 5, and second differences are constant at 2. This means that a 2nd degree polynomial can be used for the rule.

The minimum of f(x) occurs at x=0, so there is no horizontal shift of the vertex of the quadratic function. f(1) -f(0) = 1, so the vertical scale factor for the quadratic is 1.

The quadratic with a vertex of (0, 2) and a vertical scale factor of 1 is ...

  f(x) = 1·(x -0)² +2

  f(x) = x² +2 . . . . . . simplified

_____

Comment on differences

"First differences" are the differences between successive "y" values when the "x" values are evenly spaced. Here, they are 2-3 = -1, 3-2 = 1, 6-3 = 3, 11-6 = 5. These are not constant, so the function is not a linear function.

"Second differences" are the differences between successive first differences. Here, they are 1-(-1) = 2, 3-1 = 2, 5-3 = 2. These are constant, so the function is a quadratic (2nd-degree). When n-th differences are constant, the sequence can be modeled by a polynomial of degree n.

__

Comment on determining the rule

Once you know the rule is 2nd-degree, there are a number of ways you can find out what it is. One way is to write it as ...

  f(x) = ax^2 + bx + c

and fill in three different values for x and f(x). This will give you three linear equations in a, b, and c, which can be solved by any of the usual means for solving systems of linear equations.

Fortunately, this set of data includes the vertex of the function, making it easy to start with the vertex form:

  f(x) = a(x -h)^2 +k

where (h, k) is the vertex (minimum, in this case), and "a" is the vertical scale factor. The value of "a" is easily determined as being the difference between f(h+1) and f(h). Here, h=0, so that is f(1) -f(0) = 3-2 = 1.

Answer:

x² +2

Step-by-step explanation:

Answer:

es mi amigos senior le si nueve diez veite treinta Cien si onu fose locas

Step-by-step explanation:

gregory is 19 years old  and daisy is 21 because 21 is two more that 19 but 19 +21=40

The correct answer is:

Gregory is 19 years old  and daisy is 21

Let,

Age of Gregory = x years

Age of Daisy = (x+2) years

An equation in term of x

x + (x+2) = 40

2x + 2 = 40

2x = 40 - 2

x = [tex]\frac{38}{2}[/tex]

x = 19

∵ 19+21=40

⇒ Gregory is 19 years old

⇒ daisy is 21 years old

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Step-by-step explanation:

Given,

The product of two numbers = a

To find, the both numbers = ?

Let the two numbers = x

∴ x × x = a

⇒ [tex]x^{2}[/tex] =  a

⇒ [tex]x^{2} =\sqrt{a}^2[/tex]

Comparing the powers, we get

⇒ x = [tex]\sqrt{a}[/tex]

∴ First number = [tex]\sqrt{a}[/tex] and Second number = [tex]\sqrt{a}[/tex]

Thus, the product of two numbers is a,  [tex]\sqrt{a}[/tex] of both numbers.

Answer:

Step-by-step explanation:

(f-g)(x)​ = f(x)- g(x)

= 3x - 1 - ( x + 2)

=3x - 1 - x - 2

= 2x - 3

The proportion that could be used to solve for the variable is [tex]\frac{16}{40}=\frac{3}{h}[/tex] ; h = 7.5 ⇒ answer b

Step-by-step explanation:

A proportional relationship: one variable is always a constant value times the other, that constant is called the constant of proportionality

The number of walls and the number of hours are increased or decreased together

∴ The number of walls and the number of hours are proportion

∵ 16 walls in 40 hours

∵ 3 walls in h hours

- By using the second rule above

∴ [tex]\frac{16}{40}=\frac{3}{h}[/tex]

The proportion that could be used to solve for the variable is  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

Let us solve it to find h

∵  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

- By using cross multiplication

∴ 16 × h = 3 × 40

∴ 16 h = 120

- Divide both sides by 16

∴ h = 7.5

The value of h is 7.5 hours

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Answer:

425

Step-by-step explanation:

just subtract, 750-325

You subtract 750 - 325 = 425. Your answer is 425.

Hope this helps!!!!!

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