8 6 points Create an equation that represents the relationship between x and y in the table. HAAA #1 X y 488.8 -1 -2 10 y = 8 Answer -8 0 8 X + 2 6 Answe 4 4​

y = 3(x-1)^2 - 8

y = 3(x^2 - 2x + 1) - 8 [Using the identity (a-b)^2 = a^2 - 2ab + b^2]

y = 3x^2 - 6x + 3 - 8 [Distributing the 3]

y = 3x^2 - 6x - 5 [Simplifying]

*IG:whis.sama_ent

Answer:

y=3x^(2)-6x-5

[tex]y=3x^2 -6x-5[/tex]

hope this helps ;)

We are given the system of equations:

y = 3x

y = 6x + 3

We can use substitution to solve this system. Since both equations are equal to y, we can set them equal to each other:

3x = 6x + 3

Subtracting 3x from both sides, we get:

0 = 3x + 3

Subtracting 3 from both sides, we get:

-3 = 3x

Dividing both sides by 3, we get:

x = -1

Now that we know x, we can use either equation to find y. Let's use the first equation:

y = 3x = 3(-1) = -3

Therefore, the solution to the system of equations is (-1, -3).

To check our solution, we can substitute these values back into both equations:

y = 3x gives us -3 = 3(-1), which is true

y = 6x + 3 gives us -3 = 6(-1) + 3, which is also true

Therefore, our solution is correct.

We can also plug in the other given points to check that they do not satisfy both equations, which means they are not solutions to the system.

The angle that is vertical to angle DEB is A.

A vertical angle is an angle formed by two intersecting lines or planes that are perpendicular to each other. Specifically, it is the angle between two straight lines or planes that intersect each other and are perpendicular to the horizontal plane.

The measure of a vertical angle is always the same as the measure of the other vertical angle formed by the same two intersecting lines or planes. This is because vertical angles are always congruent, meaning they have the same size and shape. Vertical angles are commonly used in geometry and trigonometry to solve problems involving angles, lines, and plane.

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The piecewise function graphed is defined as follows:

C)

A piecewise function is a function that is defined by multiple equations, each of which applies to a specific interval or set of inputs. The equations are pieced together to form a single function that describes the behavior of the function over its entire domain.

The intervals for this problem are given as follows:

For the first interval, we have a linear function with a slope of 1/2 and an intercept of 2, hence:

y = 1/2x + 2, x ≤ -1.

For the second interval, we have a quadratic function with a vertex of -1, hence:

y = 1/2x² - 1, x > -1.

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there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

How to solve the question?

The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:

C(52, 7) = 52! / (7! * (52-7)!)

where "!" represents the factorial function.

To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.

Using this property, we can rewrite the above expression as:

C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying this expression, we get:

C(52, 7) = 133,784,560

Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.

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A quadratic model for the data is y = -0.0076x² + 0.6915x + 14.711.

The fuel economy at 80 mph is 21.39.

In this scenario, the speed (x) would be plotted on the x-axis of the scatter plot while the fuel economy (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the speed (x) and fuel economy (y), a quadratic model for the line of best fit is given by:

y = -0.0076x² + 0.6915x + 14.711

When the speed (x) = 80 mph, the fuel economy (y) is given by;

y = -0.0076(80)² + 0.6915(80) + 14.711

y = 21.39

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Answer:

what brand

Step-by-step explanation:

The new mixture contains 34% peanuts.

Using a weighted average approach.

Let x be the percentage of peanuts in the new mixture. Then we can set up the following equation:

(0.16)(4) + (0.40)(12) = x(4 + 12)

simplifying the equation, we get:

0.64 + 4.8 = 16x

5.44 = 16x

x = 0.34 or 34%

Therefore, the new mixture contains 34% peanuts.

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Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%

Step-by-step explanation:

Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Answer:

9/13

Step-by-step explanation:

P(odd or less than 5) = number of odd cards + number of cards less than 5 / total number of cards

P(odd or less than 5) = (20 + 16) / 52

P(odd or less than 5) = 36 / 52

P(odd or less than 5) = 9 / 13

Therefore, the probability of picking an odd card or a card less than 5.

Answer is 9/13

Answer: B

Step-by-step explanation: You can subtract 21 from 245 11 times but some will remain

1. The value of Angle STR is 19°

2. The value of arc ST is 134°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Part of circle theorem states that: The angle in the same segment are equal.

1. Therefore the value of angle STR is calculated as;

= 180- ( 90+71)

= 180- 161

= 19°

2. The value of arc ST is calculated as;

Since arc SR = QR = 46°

representing the value of arc ST by x

therefore,

46+46+x+x = 360

92 +2x = 360

2x = 360-92

2x = 268

divide both sides by 2

x = 268/2

x = 134°

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Answer:

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

We can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=xWe can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=x

Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

To find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.

To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).

This gives us:

1 part of the ratio = 1225 / 35 = 35

To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.

For the part that corresponds to 8, we have:

8 parts of the ratio = 8 x 35 = 280 items

For the part that corresponds to 27, we have:

27 parts of the ratio = 27 x 35 = 945 items

Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

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The x-intercept represents:

"The number of hours the taxi was driven before running out of fuel"

In standard notation, the variable x is the independent variable in the horizontal axis, here we can see that in the horizontal axis we are measuring the time (in hours) that the taxi was driving.

Then the x-intercept (the time when y = 0) is the number of hours until the fuel is down to zero, then the correct option is B i guess, but it should be worded as:

"The number of hours the taxi was driven before running out of fuel"

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The conclusion of the given hypothesis is: we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

The parameters given are:

Population mean: μ = 12

Sample mean: x' = 12.5

Population standard deviation; σ = 3.5

Sample size: n = 35

Let's define the hypotheses:

Null Hypothesis: H₀: μ = 12

Alternative Hypothesis: Hₐ: μ ≠ 12

Let us find the z-score from the formula:

z = (x' - μ)/(σ/√n)

z = (12.5 - 12)/(3.5/√35)

z = 0.845

The p-value from online p-value from z-score calculator using two tailed hypothesis and a significance level of 0.1 gives:

p-value = 0.398

The p-value is greater than the significance value and we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

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a. The exponential model representing the situation is S (t) = 6.26 * [tex]1.04^{t}[/tex]. The number of subscribers in 2016 is 7.32 billion.

b. In the year 2015, the number of cell phone subscribers were about 7 billion.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference.

a. Since, during next 5 years there is increase by 4% so, we get the base using the addition operation as:

1 + 4% = 1.04

The exponential model comes out to be

y = 6.26 * [tex]1.04^{t}[/tex]

Now, the number of cell phone subscribers in 2016 is:

y = 6.26 * [tex]1.04^{4}[/tex]      (This is because t = 4)

y = 7.32 billion

b. We are given y = 7 billion.

So, we get

⇒ 7 = 6.26 * [tex]1.04^{t}[/tex]

⇒ 1.12 = [tex]1.04^{t}[/tex]                           (Using the division operation)

⇒ t = 2.8

So, in 2015, the number of cell phone subscribers were about 7 billion.

Hence, the required solutions have been obtained.

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Answer:5,4

Step-by-step explanation:

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

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Answer:

7.D

8.A

Step-by-step explanation:

For the function f(x) = √x+2+5:

(D) D= {x|x≥2}, R= {y|y≥5}

The domain is restricted to x values greater than or equal to 2 because the function contains the square root of x+2, which cannot be negative. The range starts at y = 5 because the lowest possible output of the function is √2+2+5 = 5.

(A) f(x)+∞o as x→ +∞o; f(x) +∞ as x――∞

As x approaches positive infinity, the output of the function approaches infinity as well. As x approaches negative infinity, the function is undefined since it involves taking the square root of negative numbers. However, the limit of the function as x approaches negative infinity from the right is positive infinity.

Answer: Correct answer is pie/2 or A

Step-by-step explanation:

r = -5sinθ + 4θ has symmetry with respect to the line θ = π/2.

To demonstrate this, we can apply the third symmetry test for polar equations:

Symmetry with respect to the line θ = π/2: Replace θ by π - θ and see if the equation remains the same. If it does, the equation has symmetry with respect to the line θ = π/2.

r = -5sin(π/2 - θ) + 4(π/2 - θ) = 5cosθ + 2π - 4θ

r = 5cosθ + 2π - 4θ is the same as the original equation, so there is symmetry with respect to the line θ = π/2.

Therefore, the correct answer is θ = π/2.

Answer: C

Step-by-step explanation: C



The value of x unknown for the given shape with given measurements 131°, 122°, 125°, 148°, 107°, 126° is equal to 141°.

The attached figure is seven sided polygon.

Seven sided polygon is called Heptagon.

Sum of all the interior angles of seven sided polygon = 900 degrees

Measurements are,

131°, 122°, 125°, 148°, 107°, 126°

Measurement of seventh angle is unknown.

let the measure of seventh angle be x°

⇒ x° + 131° + 122° + 125° + 148° + 107° + 126° = 900°

⇒ x° + 759° = 900°

⇒ x° = 900° - 759°

⇒ x° = 141°

Therefore, the value of x for the given shape with measurements is equal to 141°.

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The above question is incomplete , the complete question is:

what is the value of x if a shape has sides measuring 131, 122, 125, 148, 107, 126.

Attached figure.

The equivalent expressions is solved to give the quantity four ninths end quantity to the power of x. Option C

An algebraic expression can be described as an expression that is made up of terms, factors, coefficient, variables and constants.

These expressions are also composed of mathematical operations.

Also note that index forms are mathematical forms used to represent numbers too large or too small.

From the information given, we have that;

(2/3)²⁽ˣ⁾

expand the bracket, we get;

(2/3)²ˣ

Find the square of both the numerator and denominator, we get;

(4/9)ˣ

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The area the grass seed needs to cover is 7,425 square meters.

To find the total area of the lawn excluding the pool, we first need to calculate the area of the pool. Using the formula for the area of a rectangle, we multiply the length and width of the pool together to get:

= 7.5 m x 3.25 m

= 24.375 square meters

Next, we can find the total area of the lawn by subtracting the area of the pool from the total area of the rectangle formed by the lawn:

= 50 m x 150 m

= 7,500 square meters

So, the area the grass seed needs to cover is:

= 7,500 square meters - 24.375 square meters

= 7,425 square meters.

Full question" Marcos wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 7 1/2 m by 3 1/4 m. Find the area the grass seed needs to cover. The dimensions of the lawn are 50 m x 150 m.

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Answer:

1600

Step-by-step explanation:

The answer you tried is equivalent.

If the width of a rectangle with perimeter P is 6 units, its length would be equal to L = P/2 - 6.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + 6)

P = 2L + 12

P - 12 = 2L

L = (P - 12)/2

L = P/2 - 6.

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The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

The measure of  m∠STR is calculated as;

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

The measure of arc QT is calculated as;

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

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