Hegarty maths- Algebra Quadratic sequences & graphs 249 - Use the nth term of a quadratic sequence 1

Please help me TvT

Answer:

20xy^2 + 15x^2 + 10x

Step-by-step explanation:

Answer:

  7.8

Step-by-step explanation:

You want the distance between P(8, 2) and Q(3, 8).

The distance between points is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((3 -8)² +(8 -2)²) = √((-5)² +6²) = √61

  d ≈ 7.8

The distance between points P and Q is about 7.8 units.

__

Additional comment

You will notice that the desired distance is the length of the hypotenuse of a right triangle with legs that are 5 and 6. The Pythagorean theorem tells you that length is √(5² +6²) = √61, as above. The distance formula is based on the Pythagorean theorem.

You can find the relevant triangle leg lengths by counting grid squares on the graph. Of course, the distance formula does the same thing by subtracting coordinate values.

The critical t-distribution values converge to the critical z-distribution values as a particular family of t-distributions that t2 has 2 degrees of freedom (df) and t9 has 9 degrees of freedom.

The maximum number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom, also known as numerical freedom of variance, are the maximum number of logically independent values that can be present in sample data. Degrees of freedom are frequently brought up when discussing various mathematical hypothesis testing techniques, like the chi-square.

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The "average" of the "positive distances" of each point from the mean is the mean absolute deviation. There is more variability in the data the higher the MAD (the data is more spread out). The MAD aids in determining if the mean of the set serves as a reliable predictor of the values included therein.

Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. By using the formula |data value - mean|, determine the absolute value of each data value's variance from the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is. The mean absolute deviation may be calculated as shown below.

Step 1: First, determine the mean.

Step 2: Determine the positive distances between each data point and the mean. Absolute deviations are those.

Step 3: Combine those deviations.

Step 4. Multiply the total by the number of data points.

The simplest approach to learn about mean absolute deviation is probably to follow these steps in the example below, however here is a more formal method to express the stages in a formula:

GAD (Greatest Absolute Deviation) = ( ∑ | [tex]x_{i}[/tex] - [tex]x_{mean}[/tex] | ) / n

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From the given exponential function  y = 7.1(1.03)ˣ, the amount produced in 2006 was approximately 7.8 billion pounds and the estimated amount in 2014 will be approximately 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

x in 2006 = 3

x = 3

Insert the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

x in 2014 = 11

Insert in the value and solve

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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Answer:

293,000.

Step-by-step explanation:

Just round to the nearest thousandth, and add 500 since you originally had 292,500.

Answer:

Step-by-step explanation:

292500 to the nearest 1000 is 293000.

 In 14x¹³ ,  x¹³ is exponent with base x , power 13 and 14 as coefficient

Exponent is a method of expressing large numbers in terms of powers.

It means when a number is multiplied by itself many times we can express expressed it in exponent form .

The symbol used for representing the exponent is "^" .This symbol is known as carrot

Base is that number that is being multiplied.

tells how many times that number is multiplied.

In the given question,

14x¹³

Base = x

because x is multiplied 13 times

so, Power = 13

Exponent = x¹³

Coefficient = 14

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[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{14})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{r}) \hspace{5em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{14}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{-2} \\\\\\ \cfrac{r-14}{2+1}=-2\implies \cfrac{r-14}{3}=-2\implies r-14=-6\implies r=8[/tex]

Answer:

Connie - [tex]x^{2} + 10[/tex]

Step-by-step explanation:

10 more means that you are adding ten to the square of x

If the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.

It is given that, the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue.

If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present.

Thus, if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

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Answer:

A and D

Step-by-step explanation:

|3x + 4| − 9 = 0

|3x + 4| = 9

3x+4 = 9 v 3x+4 = -9

3x=5 v 3x=-13

x=⁵/₃ v x=-¹³/₃

x=1 ²/₃ v x=-4¹/₃

The answer of this 70/cos 20° round to 1 decimal place  is 74.5

To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.

From the simple calculator we can find the value of cos 20° which is 0.9397.

Now we use this value to solve the above equation.

70/cos 20°;

70/0.9397;

74.491.

written that we  have to round of the value to first decimal place, so the answer will become 74.5

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Answer:

y=-1,5x+17

Step-by-step explanation:

(10,2) => x=10, y=2

a - slope

a=-1,5

y=ax+b -linear equation

2=(-1,5)*10+b

2=-15+b

b=17

y=-1,5x+17

If the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour it is not possible.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

if the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour

Time = 2 hours

Distance = speed x time

Distance(for car ) = (65)(2) = 130 km

Distance(for bus ) = (75)(2) = 150 km

Total distance = 130 + 150 = 280 km

But the distance between car and bus is 350 km.

Thus, if the car's speed is 65 kilometers per hour if it possible that the bus speed 75 kilometers per hour it is not possible.

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Answer:

x = 12

Step-by-step explanation:

Given equation,

→ 6 + 12(x + 3) = 7x + 30 + 6x

Now the value of x will be,

→ 6 + 12(x + 3) = 7x + 30 + 6x

→ 6 + 12x + 36 = 7x + 30 + 6x

→ 12x + 42 = 13x + 30

→ 13x + 30 = 12x + 42

→ 13x - 12x = 42 - 30

→ [ x = 12 ]

Hence, the value of x is 12.

The coordinates of X’ is (4,12)

Dilation means changing the size of an object without changing its shape.

Given that, Line segment XY is located at X(2, 6) and Y(4,8). If the line segments are dilated by a scale factor of 2 with a centre of dilation of

T(0,0).

The rule for a figure dilated by a scale factor k with a centre of dilation (a, b) is;

(x, y) → (k(x-a) + a, k(y-b) + b)

The line segment is dilated by a scale factor of 2 with a centre of dilation of T(0,0)

According to the rule,

(x, y) → (2(x-0) + 0, 2(y-0) + 0)

(x, y) → 2x + 2y

The coordinates of X' are (2, 6)

X(2, 6) → (2*2, 2*6)

X(2, 6) → (4, 12)

Hence, The coordinates of X’ is (4,12)

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Answer:

[tex]x=-2\frac{9}{23} , y=\frac{16}{23 }[/tex]

Step-by-step explanation:

7x - 9y = -30 ------ equation (1)

-3x - 6y = 3 ------ equation (2)

From equation (2),

3x + 6y = -3

 x + 2y = -1

      ∴ x = -2y - 1 ------ equation (3)

Substitute equation (3) into equation (1):
7(-2y - 1) - 9y = -30

-14y - 14 - 9y = -30

             -23y = -16

               23y = 16

∴ y = [tex]\frac{16}{23}[/tex]

Substitute y = [tex]\frac{16}{23}[/tex] into equation (3):

x = -2([tex]\frac{16}{23}[/tex]) - 1

  = -[tex]\frac{32}{23}[/tex] - 1

  = -[tex]\frac{55}{23}[/tex] = -[tex]2\frac{9}{23}[/tex]

25 g of  5% ointment and the pure ingredient are needed to compound the prescription.

A ratio is a comparison of two or more numbers that indicates their relative sizes. When two or more ratios are multiplied termwise, the resulting ratio is known as a compound ratio. The first quantity in the ratio is known as the antecedent, and the second quantity is known as the consequent.

For example, the compound ratio of two ratios, a:b and m:n, is am: bn.

Given,

Prescription requirement 50g for 10% ointment

but pharmacist has 5% ointment and pure ingredient

then to compound the prescription pharmacist needs x g

calculation:-

[tex]50 : 10 :: x : 5\\\\\frac{50}{10}=\frac{x}{5}\\\\5=\frac{x}{5}\\\\x=25[/tex]

Thus, required quantity of ointment and pure ingredient is 25 g.

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The number of tickets sold at a regular price is 20.

The linear equation:

an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Let x be the number of regular admission and y be the number of students.

The first statement is 48 tickets are sold. By this we get the first equation:

x + y = 48 ----------(1)

The second statement is the total collection for the ticket is $300. Form this we get the second equation:

8x + 5y = 300 --------(2)

Multiplying the equation by 5 we have:

5x + 5y = 240 --------(3)

Now subtracting equation (3) from (2) we get:

3x = 60

x = 20

Therefore we get that the ticket sold at regular price is 20.

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Answer:

x=60

Step-by-step explanation:

180 = 100 + 20 + x

180 = 120 + x

-x = 120 - 180

-x = -60

x = 60

Answer:           bro you gotta figure dis out

Step-by-step explanation:hhahahahahahahahahahaahahhaha

Answer:

the conversion factor

Step-by-step explanation:

The equation for the logarithmic function that has the following transformation from the parent logarithmic function. The other factors are mentioned in the answer below.

An essential tool for arithmetic calculations is the logarithmic function. John Napier, a Scottish mathematician, physicist, and astronomer, made the discovery of logarithms in the 16th century. It has a wide range of uses in complex scientific and astronomical calculations. Exponential functions and logarithmic curves are closely related, and the latter is thought of as the inverse of the former.

Parent function is y = log x

1. Shifted 3 units left,

y = log (x+3)

2. The vertical compression by a factor of 2,

y = 2 log(x+3)

3. Reflection across the y-axis,

y = 2 log(-x+3)

4. Shifting down by 5 units,

y = 2 log(-x+3)-5

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For the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, Rasheed has two and three-fourths cups of berries. He uses four-sixths of a cup of berries to make a milkshake. He then uses one-half of a cup of berries.

The number of cups of berries will Rasheed has left is found by subtracting the total used amount from the total amount,

=2 3/4-(4/6+1/2)

=11/4-(4/6+1/2)

=11/4 - 7/6

=19/12

=1 7/12

1.58

Thus, for the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

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Answer:

n = 49

Step-by-step explanation:

49 has a factor of -7 which can also add up to -14

Eg : -7(-7) = 49, -7 + (-7) = -14

49

x²-14x+49=(x-7)²

An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial.

It is of the form (ax2 + bx + c).

Real numbers a, b, and c are present here, and a ≠0.

The given equation is x2 + 14x + c

To find the value of c

We can take half of the linear coefficient and square it

14/2 = 7

72 = 49

Therefore, the value of c is 49.

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Answer:

9

Step-by-step explanation:

3 x 3 = 9

4 x 4 = 16

16 - 11 = 5

11 - 9 = 2

2 is less than 5 which makes it closer to 11.

Answer:

Ans = 9

Step-by-step explanation:

3 x 3 =9

4 x 4 =16

2 x 2 =4