Choosing from the binomial factors shown below, write the equation of the parabola to the left in factored form. (please help)

1. The Pythagoras theorem is (6+r)² = r²+9²

2. 36+12r+r² = r²+9²

3. The value of r is 3.75

Pythagoras theorem states that; the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

This means that, c² = a² + b²

In the triangle, 6+r is the hypotenuse, 9 and r are the other two legs.

therefore;

(6+r)² = r²+9²

= (6+r)(6+r) =r²+9²

36+6r+6r+r² = r²+9

36+12r+r² = r²+9

Collecting like terms

12r+r²-r²= 81-36

12r = 45

r = 45/12

r = 3.75

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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A linear equation in slope intercept form for each of this line are as follows;

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (2, 7) and a slope of -7, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 7 = -7(x - 2)  

y - 7 = -7x + 14

y = -7x + 21

y = 5x - 6

At data point (-1, -7) and a slope of 1, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - (-7) = 1(x - (-1))  

y + 7 = x + 1

y = x - 8

At data point (6, 7) and a slope of 1/2, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 7 = 1/2(x - 6)  

y - 7 = x/2 - 3

y = x/2 + 4

At data point (9, 0) and a slope of -2/3, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 0 = -2/3(x - 9)  

y - 0 = -2x/3 + 6

y = -2x/3 + 6

At data point (5, 19) and a slope of 5, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 19 = 5(x - 5)  

y - 19 = 5x - 25

y = 5x - 6

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The number of article sold for Rupees 20 to gain a profit of 20% is equal to 4.

Number of article sold for Rupees 20 = 6

Percent of loss in selling 6 article for Rupees 20 = 20%

Let us start by finding the cost price of one article.

We know that if 6 articles are sold for 20 rupees,

then the selling price of one article is equal to,

Selling price of 1 article = 20/6

⇒ Selling price of 1 article = 3.33 rupees

There was a loss of 20% when 6 articles were sold for 20 rupees.

This means that the cost price of 6 articles is equal to,

Cost price of 6 articles

= Selling price of 6 articles / (1 - Loss%)

= 20 / ( 1 - 20% )

= 20 / (1 - 0.2)    

= 25 rupees

To gain 20% profit, the selling price of the articles should be equal to,

Profit% is 20% = 0.2

Selling price of 6 articles

= Cost price of 6 articles × (1 + Profit%)

= 25 × (1 + 0.2)  

= 30 rupees

Now , the selling price of one article to calculate how many articles can be sold for 20 rupees,

Selling price of 1 article

= Selling price of 6 articles / 6

= 30 / 6

= 5 rupees

This implies,

The number of articles that can be sold for 20 rupees to gain a 20% profit is equal to,

Number of articles

= 20 / 5

= 4 articles

Therefore,  4 articles must be sold for 20 rupees to gain a 20% profit.

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The triangle with the side length of 4.8, 28.6 and 29 is a right triangle.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

The sides of a right angle triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, lets check if the triangle is a right triangle using Pythagoras's theorem as follows:

4.8² + 28.6² = 29²

23.04 + 817.96 = 841

841 = 841

Therefore, the triangle is a right triangle.

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The Greatest common Factor of 16 and 32 is 16

Greatest common factor is the largest factor that all the numbers share. For example, 12, and 18 have three common factors: 2, 3and 6 the greatest is 6.

Similarly the factors of 16 and 32 are shown below;

factors of 16 are : 2,4,8,16

factors of 32 are : 2,4,8,16,32

The common factors are: 2,4,8,16

and the largest number among the common factors is 16

Therefore the greatest common factor of 16 and 32 is 16

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Answer: 1

Step-by-step explanation:

you can create a ratio because they are similar you can see that if you multiply 8 by 2 you get 16 so you divide 2 by 2 and you get x

Answer:

Rice:Water = 1:2

Step-by-step explanation:

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

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The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.

B

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular.

An equilateral triangle can never be obtuse. 

Answer: The second candle can burn for 20 hours before its length is zero inches.

Step-by-step explanation:

If the second candle is 8 inches in length and burns down at a rate of 2/5 inches per hour, we can use a simple formula to find how long it can burn before its length is zero inches:

Number of hours = Length ÷ Rate of burn

Number of hours = 8 inches ÷ (2/5 inches per hour)

Number of hours = 8 inches × (5/2) hours per inch

Number of hours = 20 hours

Therefore, the second candle can burn for 20 hours before its length is zero inches.

Answer:

k = 1

Step-by-step explanation:

given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0

here the polynomial is divided by (x + 1)

then substitute x = - 1 into the polynomial and equate to zero

k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0

- k + 1 + 5 - 5 = 0

- k + 1 = 0 ( subtract 1 from both sides )

- k = - 1 ( multiply both sides by - 1 )

k = 1

The measure of angle A in triangle ABC is approximately 113.8 degrees.

To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:

c² = a² + b² - 2ab*cos(C)

where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.

In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:

cos(A) = (b² + c² - a²) / 2bc

Plugging in the values we have:

cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)

cos(A) = -0.3694

Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:

A = cos⁻¹(-0.3694)

Using a calculator, we get:

A ≈ 113.8 degrees

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The unknown measure in the line segment is as follows:

∠x = 141 degrees

When line segment intersect, angle relationships are formed such as vertical angles, adjacent angles etc.

Therefore, let's find the angle x in the line intersection as follows:

Therefore, the angle x comprises of angle 90 degrees and angle 50 degrees.

The sum of angle 90 degrees and 50 degrees is equals to angle x

Hence,

x = 51 + 90

x = 141 degrees

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Answer:

câu này là 500 nhen

The equation that shows the total number of miles Jill walked, w, on Tuesday and Wednesday is w = 3 + 2

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

Tuesday = 3 miles

Wednesday = 1 less than Tuesday

This means that

Wednesday = 3 miles - 1 mile

Evaluating the like terms, we have

Wednesday = 2 miles

The equation shows the total number of miles Jill walked, w, on Tuesday and Wednesday is represented as

w = Tuesday + Wednesday

Substitute the known values in the above equation, so, we have the following representation

w = 3 + 2

Evaluate

w = 5

Hence, the equation is w = 3 + 2 and the number of miles s 5

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The percentage of saline solution in brand B is 3%.

Let x be Percentage of saline solution in brand B

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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The area of the desktop is 307.72 square inches.

Remember that the area of a semicircle of radius R is given by the formula:

A = (pi/2)*R²

Where pi = 3.14

Here we know that the diameter is 28 inches, then the radius is:

R = 28in/2 = 14 inches

Replacing that in the formula for the area we will get:

A=  (3.14/2)*(14 in)²

A = 307.72 in²

That is the area of the desktop.

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The volume of the file cabinet in this problem is given as follows:

V = 8 and 7/10 cu ft.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

2.167 ft, 1.5 ft and 2.67 ft.

Hence the volume of the prism is given as follows:

V = 2.167 x 1.5 x 2.67

V = 8.7 ft³.

As a mixed number, the volume is given as follows:

V = 8 and 7/10 cu ft.

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The rules for the two graphs above are: A. first graph: y = 3 + x; second graph : y = 6 + x.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of graph 1;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 3)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 3) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 1(x - 0)  

y = x + 3

Next, we would determine the slope of graph 2;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 - 6)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 6) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 1(x - 0)  

y = x + 6

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Answer:

[tex] - 8(45) + 482 = - 360 + 482 = 122[/tex]

An expression that represents the amount of canned food collected so far by the three friends is 8x² + 2xy - 4.

An expression that represents the number of cans the friends still need to collect to meet their goal is 4x² - 4xy + 2.

From the information provided above, we can logically deduce the following number of canned food collection expressions for each friend:

Jessa; 3x²

Tyree: 5x² - 8

Ben: 2xy + 4

Canned food collection goal: 12x² - 2xy - 2

Therefore, an expression that represents the total amount of canned food collected so far by the three friends can be calculated and written as follows;

Total amount collected so far = 3x² + 5x² - 8 + 2xy + 4

Total amount collected so far = 8x² + 2xy - 4

In order to meet the goal, they need to collect this amount:

Remaining canned foods = 12x² - 2xy - 2 - (8x² + 2xy - 4)

Remaining canned foods = 12x² - 2xy - 2 - 8x² - 2xy + 4

Remaining canned foods = 4x² - 4xy + 2

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The transformation sequence of the function is:

The function is first shifted to the left, then vertically stretched, and finally vertically shifted up and down to get the final graph.

We have,

The transformations of f(x) = 2^x to get to g(x) = -5 + 2^{x + 6} + 3 are as follows:

Translation:

f(x) is translated 6 units to the left, which gives 2^{x+6}.

Vertical stretch/compression:

The entire function is multiplied by 2, which makes it taller.

Vertical shift:

The entire function is shifted up 3 units and down 5 units, which raises the entire graph 3 units and then lowers it 5 units from its original position.

Thus,

The function is first shifted to the left, then vertically stretched, and finally vertically shifted up and down to get the final graph.

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Answer:

Step-by-step explanation:

To find the median of a set of data, we first need to arrange the data numbers from smallest to largest. The median is the middle data number in the list.

Given:

5, 0, 1, 3, 9, 0

Arrange the numbers:-

0, 0, 1, 3, 5, 9

Median = 1, 3

Since there are even amount of numbers, the median will be the average of the two middle data numbers.

To find the median, we'll add the numbers 1 + 3 and then divide them by two. (since they are 2 set numbers):-

Therefore, the median of this set of data is 2.

__________________________

Hope this helps! :)