How many more unit tiles must be added to the
function f(x)=x2-6x+1 in order to complete the square?
1
6
08
09

Answer:

-24x + 30y

Step-by-step explanation:

Step 1:

−4(x − 15y) + 5(−4x − 6y)

Step 2:

−4x + 60y + (−20x − 30y)

Step 3:

Combine like terms within each set of parentheses:

−4x + 60y − 20x − 30y

Step 4:

Combine like terms:

(-4x - 20x) + (60y - 30y)

Step 5:

Simplify:

-24x + 30y

Final result:

-24x + 30y

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The sum of the first 12 whole numbers of the sequence is 156.

Given that, the sum of the first n whole numbers is given by the expression (n²+ n).

Here, n=12

Substitute n=12 in the expression n²+ n, we get

12²+ 12

= 144+12

= 156

Therefore, the sum of the first 12 whole numbers of the sequence is 156.

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Option 4,option 6, and option 2 are the respective contrapositive to the statements given.

A contrapositive statement is obtained by interchanging both the hypothesis and conclusion of a given statement after contradicting them.

For "if p then q" the contrapositive is "if not-q, then not-p "

From the information given, we have;

Statement 1: If two figures are congruent, then their corresponding sides are equal.

Contrapositive: If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. (Option 4)

Statement 2: If two numbers are even, then their product is even.

Contrapositive: If the product of two numbers isn't even, then the two numbers aren't even. (Option 6)

Statement 3: If a figure is a pentagon, then the sum of its interior angles is 540°.

Contrapositive: If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon. (Option 2)    

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We can assume the age of the groom is represents by the variable "x."

According to the given tradition in the Pythagorean Planet, the sum of the square of the bride's age (33^2) and the square of the groom's age (x^2) must be equal to the square of the age of the bride's father (500^2).

Therefore, we can set up the equation:

[tex] 33^2 + 500^2 = x^2 \\ 1089 + x^2 = 250000 \\ x^2 = 250000-1089 = 248911 \\ x = \sqrt{248911} \approx 498.91 [/tex]

Therefore, the groom was approximately 498.91 years old when Juniper got married.

The scale factor represents the Ratio of the side lengths between the two similar figures. side length in triangle D' is four times larger than the corresponding side length in triangle D.

The scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

Triangle D has side lengths of 6, 8, and 10 units, while triangle D' has side lengths of 24, 32, and 40 units.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

For the first side, D' has a length of 24 units, while D has a length of 6 units.

24/6 = 4

For the second side, D' has a length of 32 units, while D has a length of 8 units.

32/8 = 4

For the third side, D' has a length of 40 units, while D has a length of 10 units.

40/10 = 4

Since all the ratios are equal to 4, we can conclude that the scale factor used to dilate triangle D to create triangle D' is 4.

The scale factor represents the ratio of the corresponding side lengths between the two similar figures. In this case, every side length in triangle D' is four times larger than the corresponding side length in triangle D.

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Answer: it is 4

Step-by-step explanation:

hope this helps

To convert litres to cm³, we need to multiply by 1000 since there are 1000 cm³ in 1 litre:

485 litres x 1000 cm³/litre = 485000 cm³

Therefore, the volume of concrete used to make the water trough is 485000 cm³.

Hello!

1L = 1dm³

so 485L = 485dm³

485dm³ = 485000cm³

the answer is 485000cm³

The closest time the temperature of the liquid reaches 90 degrees is (1) 25 minutes

From the question, we have the following parameters that can be used in our computation:

[tex]f(m) = 112e^{-0.058m} + 64[/tex]

When it reaches 90 degrees, we have

f(m) = 90

So, the equation becomes

[tex]112e^{-0.058m} + 64 = 90[/tex]

Subtract 64 from both sides

[tex]112e^{-0.058m} = 26[/tex]

Divide both sides by 112

[tex]e^{-0.058m} = 0.232[/tex]

Take the natural logarithm of both sides

m = ln(0.232)/(-0.058)

Evaluate

m = 25 (approx)

Hence, the closest time the temperature reaches 90 degrees is (1) 25 minutes

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There are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

To determine the number of ways the group of twelve people can take a ride on the roller coaster, we need to consider the different combinations of people that can fit in each train.

Let's analyze the possibilities:

If the train that can fit 8 passengers is chosen:

There are 12 people to choose from, and we need to select 8 of them to ride in this train.

The number of ways to choose 8 people out of 12 can be calculated using the combination formula, denoted as C(12, 8) or 12C8, which is equal to 12! / (8! × (12-8)!).

Simplifying this expression, we find that C(12, 8) = 12! / (8! × 4!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495.

If the train that can fit 7 passengers is chosen:

There are 12 people to choose from, and we need to select 7 of them to ride in this train.

The number of ways to choose 7 people out of 12 can be calculated using the combination formula as well, denoted as C(12, 7) or 12C7, which is equal to 12! / (7! × (12-7)!).

Simplifying this expression, we find that C(12, 7) = 12! / (7! × 5!) = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1) = 792.

Therefore, the total number of ways the group can take a ride on the roller coaster is the sum of the possibilities from both scenarios:

495 (for the train fitting 8 passengers) + 792 (for the train fitting 7 passengers) = 1287.

Hence, there are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

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Answer:

D

Step-by-step explanation:

[tex]\sqrt{x}[/tex] ≤ 2  is the graph D.  Only values greater than or equal to 0 and less than or equal to 4 satisfy this inequality.  

Answer:

  c = (7/2)√3

  a = (3/2)√2

Step-by-step explanation:

You want the length of the adjacent side in the special right triangles shown.

The unknown side in each triangle is the side adjacent to the angle. The known side is the hypotenuse. This tells us we can make use of the relation ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos

The ratios of side lengths in these triangles are ...

  30°-60°-90° triangle: 1 : √3 : 2   ⇒   cos(30°) = (√3)/2

  45°-45°-90° triangle: 1 : 1 : √2   ⇒   cos(45°) = 1/√2 = (√2)/2

  c = 7 · cos(30°)

  c = (7/2)√3

  a = 3 · cos(45°)

  a = (3/2)√2

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The required angle measures 73°

Given are two angles which is vertically opposite to each other, the one angle is x and the other is 73°.

We need to find the value of angle x,

So, we know that,

Vertically opposite angles are a pair of angles formed by two intersecting lines. When two lines intersect, they create four angles at the intersection point. Vertically opposite angles are formed by the opposite pairs of these angles.

In simpler terms, when two lines cross each other, the angles that are opposite to each other, or directly across from each other, are called vertically opposite angles.

Vertically opposite angles are always equal in measure. This means that if you know the measurement of one of the vertically opposite angles, you automatically know the measurement of the other angle.

Hence the required angle measures 73°

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The value of length of VW is,

⇒ VW = 43.2

We have to given that,

Two triangles VXY and VWZ are shown in figure.

Now, By using definition of proportionality we get;

⇒ VW / (99 - 55)  = 72 / 55

Solve for VW as,

⇒ VW / 33 = 72 / 55

Cross multiply we get;

⇒ 55 VW = 33 × 72

⇒ VW = 33 × 72 / 55

⇒ VW = 3 × 72 / 5

⇒ VW = 43.2

Therefore, The value of length of VW is,

⇒ VW = 43.2

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The modulus value function is solved and the minimum value of d is 5 more than the maximum value of c

Given data ,

Let the modulus function d be represented as d ( x )

where the value of d ( x ) is plotted on the graph

The function c ( x ) is represented by the table of values as

x = { -5 , -4 , -3 , -2 , -1 }

And , the output is c ( x ) = { -4 , -3 , -4 , -5 , -6 }

So, the maximum value of the function c ( x ) = -3

And , the modulus function on the graph is d ( x )

So, the minimum value of the function is d ( x ) = 2

And , d = 5 + c

2 = 5 + -3 = 2

Therefore , the minimum value of d is 5 more than the maximum value of c

Hence , the modulus function is solved.

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To solve this problem, we can use the formula for the sum of a geometric series:

S_n = a(1 - r^n)/(1 - r)

where S_n is the sum of the first n terms of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $334, the common ratio is 1.17 (since profits increase by 17% each week), and there are 16 terms (since we want to find the total profits over 16 weeks).

Plugging these values into the formula, we get:

S_16 = 334(1 - 1.17^16)/(1 - 1.17) ≈ $20,205.46

Therefore, Buffy's total profits over 16 weeks will be approximately $20,205.46.

The function is continuous at every x for a = 0 and b = 1.

For the function to be continuous at every x, the left-hand limit must equal the right-hand limit at every x. That is, for every x in the domain,

lim x→x- f(x) = lim x→x+ f(x)

In other words,

ax - b - 1 = ax + b - 1

Solving the above equation for a and b, we get

a = 0 and b = 1

Therefore, the function is continuous at every x for a = 0 and b = 1.

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Answer:

The unit rate is also 18 feet per second.

Step-by-step explanation:

To express the rate, we can use the formula:

rate = distance / time

Using the values given in the problem:

rate = 540 feet / 30 seconds

Simplifying this equation:

rate = 18 feet per second

Therefore, the rate at which the bicyclist is traveling is 18 feet per second.

To express this as a unit rate, we simply divide the distance and time by the same value. In this case, we can divide both by 30 seconds:

unit rate = 540 feet / 30 seconds ÷ 30 seconds / 30 seconds unit rate = 18 feet / second

The unit rate is also 18 feet per second.