Write the equation of a circle with a diameter endpoints of 13 and -1 and 15 and 9

The selling price of the antique through an online auction website is $680.

Given that,

Kyle sold an antique through an online auction website.

The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.

After selling the antique, Kyle had to pay the website host $32.

Let x be the selling price of the antique.

We get an equation,

15 + (2.5% × x) = 32

15 + 0.025x = 32

0.025x = 17

x = $680

Hence the selling price is $680.

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Answer:

Each x is equal to 39.

Step-by-step explanation:

Well, all of the angles in a triangle would add up to 180 degrees. So since this is an isosceles triangle, we now know that the two base angles are going to be congruent. We would do 180 minus 102 and that would get us 78. So x would be 39 because of 78 divided by 2.

Hope this makes sense! :)

There is no proportional relationship between x and y.

No, all ratios yx are not equivalent.

We have,

"Two or more number or variable are said to be in proportion if the ratio between them are equivalent to each other."

According to the question,

Given x : 8 , 10, 12, 14

        y : 5, 7, 9, 11

Ratio between different values of x and y are not equivalent

( 8 /5) ≠ (10 / 7)≠ (12 /9) ≠(14 /11)

We conclude there is no proportional relationship between x and y.

Hence, Option(1) is the correct answer.

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complete question:

Is there a proportional relationship between x and y? Explain.

x 8 10 12 14

y 5 7 9 11

1. No; all ratios yx are not equivalent.

2.Yes; each x value and y value increases by 2.

3.Yes; the difference between each x value and y value is 3.

4.No; all ratios xy are greater than 1.

To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

On the second step when he multiplied distributed (x+1) (x+2) he forgot to multiply x*1 and x*2 (check red arrows in attachment below)

Step-by-step explanation:

i hope that helps please lmk if you need for help

Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)

The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).

Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:

a = -4.9

b = 11

Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:

t = -11 / (2 * -4.9)

t = -11 / -9.8

t ≈ 1.122

Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.

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If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

{-2,14}

Step-by-step explanation:

f(-4) = f(4) = 14

f(0) = -2

Answer:

X=4

Step-by-step explanation:

The solution is in the file

Answer:

Speed = 3.75 miles per hour.

Step-by-step explanation:

Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.

Mathematically, speed is given by the equation;

\(Speed = \frac{distance}{time}\)

\(S = \frac{d}{t}\)

Given the following data;

Distance, d = 3/4 miles

Time, t = 1/5 hour

Substituting into the equation, we have;

\(Speed, S= \frac{3/4}{1/5}\)

\(Speed, S = \frac{3}{4}*5\)

\(Speed, S = \frac{15}{4}\)

Speed, S = 3.75mph.

Therefore, Josie's speed is 3.75 miles per hour.

Answer:

The length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

Step-by-step explanation:

Given that the length of a rectangle is 3 yards more than twice the width, and the area of the rectangle is 54 yards, the following calculation must be performed to find the dimensions of the rectangle, knowing that the area of a rectangle arises from multiplying its base by its height:

2X + 3 + X = 54

3X + 3 = 54

3X = 54 - 3

X = 51/3

X = 17

(17 x 2) + 3 = 37

Therefore, the length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

answer is 13

I hope it helpful

Answer:

The value of p² + r³, when p = 2 & r = 3

(2)²+(3)³=4+27=31

the probability would be

1 in 6, 1/6, or 1:6

Answer:

Step-by-step explanation:

The answer is $26

Applying the steps, the result of the line integral is 99.

The curve is:

\(f(x,y,z) = xy i + 9y^2 j\)

The vector field is:

\(r(t) = (x(t), y(t)) = (16t^6, t^4)\)

Applying the vector field at the curve, we have that:

\(f(t) = (16t^{10}, 9t^8)\)

The derivative of the vector field is:

\(r^{\prime}(t) = (96t^5, 4t^3)\)

The dot product of the vector field along the curve with the derivative is:

\(f(t)r^{\prime}(t) = (16t^{10}, 9t^8)(96t^5, 4t^3) = 1536t^{15} + 36t^{11}\)

Hence, the line integral is:

\(I = \int_{0}^{1} (1536t^{15} + 36t^{11}) dt\)

\(I = 96t^{16} + 3t^{12}|_{t = 0}^{t = 1}\)

\(I = 96 + 3\)

\(I = 99\)

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To factor the expression, we need to identify any common factors that can be pulled out of the terms.

The terms g²r and 9²₂² have a common factor of g². The terms 6g²rs²t and -6g²rs²t have a common factor of -6g²rs²t. The term 5422 does not have any factors in common with the other terms.

Therefore, the expression can be factored as:

(-6g²rs²t)(g²r + 9²₂²) + 5422

This is the fully factored form of the expression.


????

We get that the cost of the battery is $ 8.24 per battery.

We are given that the cost of 88 batteries = $ 724.72

We need to find the cost of one battery.

We will do this by diving the cost of 88 batteries by 88.

Using division, we get that:

cost of one battery = $ 724.72 ÷ 88

Simplifying the expression, we get that:

cost of one battery = $ 8.24 per battery.

Therefore, we get that the cost of the battery is $ 8.24 per battery.

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Answer:

Explanation:

Angles 14 and 16 are corresponding angles; therefore,

since

which is our answer!

The equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

To rewrite the expression \(x^2 + 5x + 6\) in the form \(x^2 + rx + sx + 6\), we need to find values for r and s such that the coefficients of the x terms match.

Given expression: \(x^2 + 5x + 6\)

To factorize this expression, we need to find two numbers that multiply to give 6 and add up to 5. The numbers that satisfy these conditions are 2 and 3.

Now, let's rewrite the expression using these values:

\(x^2 + 2x + 3x + 6\)

By grouping the terms, we can rewrite it as:

\((x^2 + 2x) + (3x + 6)\)

Factoring out the common terms in each group:

x(x + 2) + 3(x + 2)

Now, notice that (x + 2) appears as a common factor in both terms. We can further simplify the expression:

(x + 2)(x + 3)

Thus, the equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

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Answer:

480.6 ; 440.5, 8 mode values

Step-by-step explanation:

Given that :

Given the data :

486, 358, 395, 759,496, 692, 353, 306

Rearranged data: 306, 353, 358, 395, 486, 496, 692, 759

The mean:

Σx/ n

n = sample size = 8

Σx = sum of all data values = 3845

Mean = 3845 / 8

Mean = 480.6

The median :

0.5(n + 1)th term

0.5(8 + 1) th term

0.5(9)th term

= 4.5term

(4th + 5th term) / 2

(395 + 486) / 2

= 440.5

The mode = most frequently occurring data value ; since all the data values have a frequency of 1, then the number of modes = 8.

Answer:

y = 50x

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

6x + 9 = 18

To find x, subtract 9 from both sides

6x + 9 - 9 = 18 - 9

6x = 18

divided both sides by 6

6x/6 = 18/6

x = 3

where we plug in x into 2x+3

2(3) + 3 = 6 + 3 = 9

\(\implies{6x + 9 = 18} \\ \implies{6x = 18 - 9} \\ \implies{6x = 9} \\ \\ \implies{x = \frac{9}{6} } \\ \\ \implies{x = \frac{3}{2} }\)

Now put x = 3/2 in 2x + 3 we get,

\(\implies{2x + 3} \\ \implies{2( \frac{3}{2} ) + 3} \\ \implies{3 + 3} \\ \\ \implies{6}\)