An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,

where h(x) gives the height of the water jet, in feet, x feet from its starting point.

The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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A 45-degree triangle is called a right-angle triangle.

A 45-degree angle is exactly half of a 90-degree angle formed between two rays.

It is equal to half of a straight angle or a 90-degree angle. An angle bisector of a 90-degree angle creates two equal 45-degree angles. The 45-degree angle can be found in many everyday objects, such as scissors, doors, and windows. It is also known as the angle created by a square's diagonal and its sides.

It is an acute angle and two angles measuring 45 degrees form a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex.

Thus, A 45-degree triangle is called a right-angle triangle.

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The side length of square C is given as follows:

5 ft.

The area of a square of side length is given as follows:

A = s².

Hence the side length of A and B are given as follows:

Then the side length of square C is the hypotenuse of a right triangle, and applying the Pythagorean Theorem, it's length is obtained as follows:

C² = 3² + 4²

C² = 25

C = 5 ft.

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Answer:

12,34

Step-by-step explanation:

For 'a'

8x=(2x+72) [vertically opposite angle]

8x-2x=72

6x=72

x=72/6

x=12

For 'b'

4x+20+x-10=180° [ being straight angle ]

4x+x+20-10=180°

5x+10=180°

5x=180-10

x=170/5

x=34

Answer: The answer Is 9f

Step-by-step explanation:

The scale factor used to produce the second triangle is 5/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size. For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given that, a triangle with base length of 3 units is transformed into a second triangle with a base length of 5 units,

Therefore, the scale factor = 3/5

Therefore, to produce Figure 2 from Figure 1 we will multiply it by 5/3

Hence, the scale factor used to produce the second triangle is 5/3.

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Answer:

If ur options are  one sixth

6

one half

2

then the correct answer is 2

Step-by-step explanation:

I took the quiz and got it right.

The slope of the line is -10, and the y-intercept is 1.

Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

x is the x coordinate on the line that corresponds with the y coordinate in the equation,b is the y-intercept of the line

So for the equation y=-10x+1:

comparing the above equation with  y=mx+b we get,

m=-10 and b=1 so the slope of the line is -10, and the y-intercept is 1.

Thus, The slope of the line is -10, and the y-intercept is 1.

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The rate he would he earn for 9 h will be 83.25

Your pay for each hour of labor is expressed as an hourly rate. You might need to estimate your income for other applications or change your own budget after comparing the hourly and salaried pay rates.

The sum of money charged, received, or earned for each hour of work: Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.

Noah earns 37 for 4 hr of babysitting.

so if you divide 37 by 4 you get the rate per hour

which is 9.25 so if you multiply 9 times 9.25

The rate he would earn for 9 h will be

you would get 83.25.

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The recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.

What is geometric ?

A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is always the same, this common ratio is denoted by "r" and the first term of the sequence is denoted by "a1". A geometric sequence can be represented by the following formula

a_n = a_1 * r^(n-1)

Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:

r = a5 / a2 = 768 / 12 = 64

To find the 8th term of the geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where a1 is the first term, r is the common ratio, and n is the position of the term.

Given the 8th term, we can substitute the values

a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7

To find the recursive formula, we can use the formula:

an = a(n-1) * r, where a(n-1) is the previous term of the sequence

So the recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.

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A geometric sequence is a set of numbers where any two consecutive terms' quotients are always the same. The first term in the series is indicated by the letter "a1," and the common ratio is indicated by the letter "r". The following formula can be used to describe a geometric sequence.

Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:

r = a5 / a2 = 768 / 12 = 64

To find the 8th term of the geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where a1 is the first term, r is the common ratio, and n is the position of the term.

Given the 8th term, we can substitute the values

a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7

The first step in determining whether a linear system is inconsistent is to identify whether the lines are parallel. Check to see if the lines have a y-intercept in common, if so.

This result establishes an inconsistent system due to the fact that two parallel lines with distinct y-intercepts will never intersect.

If there is at least one solution to a linear equations system, it is said to be a consistent system. The system is regarded as inconsistent if there is no solution.

When the lines are parallel to one another, a system of linear equations cannot become inconsistent in any other way. The slope of parallel lines is the same. Therefore, comparing the slopes is a good way to ascertain whether the system is inconsistent. The comparison is simple if the linear equations are written in the point-slope or slope-intercept form. In order to determine the coefficient of x and compare slopes, it is a good idea to solve for y on all equations that are in a different form and express them in the slope-intercept form. The equation system is inconsistent if the slopes are equal to one another.

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The length of the rectangle side x is equal to 35.33 cm approximately to 2 decimal place using the trigonometric ratio of tangent.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the intercept of the diagonal lines in the rectangle with O so that we consider the right triangle ∆AOx, then we solve for the length of Ax and multiply the result by 2 to derive the value of x as follows:

angle 54 and m∠AOD are supplementary so;

m∠AOx = (180 - 54)/2 {m∠AOD/2}

m∠AOx = 63°

tan 63° = (x/2) ÷ 9

tan 63° = x/2 × 1/9 {change division to multiplication}

tan 63° = x/18

x = 18 × tan 63° {cross multiplication}

x = 35.3270

Therefore, 35.33 cm approximately to 2 decimal place is the length of the rectangle side x using the trigonometric ratio of tangent.

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The sum of the polynomial is obtained by adding the terms with the same power and variable together.

The steps to determine the sum of the polynomial :

Step 1: Arrange each polynomial with the term with the highest degree first then

in decreasing order of degree.

Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.

Step 3: Simplify by combining like terms.

For example, (2x² + 6x +5) +(-2x + 3x²- 1)

and we have determine sum of polynomial. Follows the above steps :

=> (2x² + 6x +5) + ( 3x²– 2x – 1)

2x² + 3x² + 6x – 2x + 5 -1

= 2x² + 3x² + 6x – 2x + 5 -1

= 5x² + 4x + 4

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Answer:

Obtuse angle

Step-by-step explanation:

Angles greater than 90 degrees are obtuse angles, angles less than 90 degrees are acute angles, and angles at 90 degrees are right angles.

Answer:

3 ⁴√-1

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
[tex]R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=[/tex]
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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The GCD is 30 and the LCM is 13860 for the numbers 420, 630, and 330 .

The highest factor among two or more numbers is the greatest common denominator (GCD).

The lowest common multiple (LCM) is another name for the least common multiple in mathematics. The least common multiple of two or more numbers is the smallest of all the common multiples of the numbers provided.

Take all three numbers and their factors to determine the greatest common divisor.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are the factors for 420.

The factors for 630 are as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630, and 330 are as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.

Of the three, 30 is the common factor with the highest value.

Take all three numbers and their prime factors to determine the lowest common multiple.

The prime factors for 420 = 2 × 2 × 3 × 5 × 7

The prime factors for 630 = 2 × 3 × 3 × 5 × 7

The prime factors for 330 = 2 × 3 × 5 × 11

The LCM of 420,630,330 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.

Therefore, the GCD and LCM is 30 and 13860 respectively.

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The scale factor in the dilation can be found by comparing the coordinates of the original image (A) and the new image (B). The coordinates of A and B must be provided in order to determine the scale factor.

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Answer:

36-12s=y

s=3

thats with it all the way simplified

First convert the distance she ran from a mixed number to a improper fraction:

• 4-1/2 equals 9/2.

Since this a unit rate problem divide the km by the time traveled.

• 9/2 (km) ÷ 3/4 (hour). When you divide a number by a fraction use (Keep-Change-Flip).

• 9/2 × 4/3 = 36/6 miles/hour.

That's means 36/6 = 18/3 = 6 km/ hour.

A 30-60-90 triangle has one right angle, with the other two angles measuring 30 and 60 degrees. The shortest side is half as long as the hypotenuse, while the middle side is equal to the shortest side multiplied by the square root of 3. The area can be found using (1/2) x base x height, with the perimeter equal to the sum of all three sides.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The number of students who prefer summer is equal to 60 students.

In order to determine the number of students who prefer summer, we would multiply the total number of students in Bowling Green middle school by the number of students in Aiko’s class who prefer summer to spring.

Mathematically, an expression which models the number of students who prefer summer is given by;

Number of students who prefer summer = 6/10 × 600

Number of students who prefer summer = 0.6 × 600

Number of students who prefer summer = 60 students.

Based on these results, we can logically conclude that 60 students in Aiko’s class who prefer summer to spring.

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Complete Question:

Bowling Green middle school has 600 students. in Aiko’s class, 6 out of 10 students prefer summer to spring. Based on these results, how many students prefer summer?

The relation that is a function is

{(1, 2), (2, 3), (3, 4), (4, 5)}

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function can have different inputs but the same output.

i.e many to one.

But a function can not same input and different output.

i.e one to many.

Now,

{(1, 2), (2, 3), (3, 4), (4, 5)}

This is a function because each input has a different output.

This is a one-to-one function.

{(1, 2), (3, 4), (5, 6), (1, 8)}​

This is not a function because 1 has different outputs 2 and 8.

{(1, 2), (2, 1), (1, 3), (3, 1)}

This is not a function because 1 has different outputs 2 and 3.

{(0, 2), (0, 4), (0, 6), (0, 8)

This is not a function because 0 has different outputs 2, 4, 6, and 8.

Thus,

{(1, 2), (2, 3), (3, 4), (4, 5)} is a function.

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The algebraic expression y = $2x + $10 represent the cost of each ATM transaction for the month where x is the cost of transaction during the month. And $20 is the total cost of 5 ATM transactions with the expression y = $2(5) + $10.

We shall represent the total cost of ATM transaction in a the month with the letter y and the cost of a transaction with the letter x so that we have an algebraic expression as follows:

y = $2x + $10

using the algebraic expression to evaluate for the total cost of 5 ATM transaction, we have;

y = $2(5) + $10

y = $10 + $10

y = $20

Therefore, the algebraic expression y = $2x + $10 can be used to represent the cost of each ATM transaction for the month. And the expression y = $2(5) + $10 with the result $20 represent the total cost of 5 ATM transaction during the month.

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Answer:

See the image attached.

Step-by-step explanation:

x    y

0    -1

1     -2

Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.

Three equations that can be used to solve for y, the length of the room are:

y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.

750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.

(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.

Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.

The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.

Step-by-step explanation:

So, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

A root of an equation is a value that satisfies the equation when it is set equal to zero. In other words, a root of an equation is a solution to the equation of the form x = constant.

The equation x^2 - kx - 5 = 0 is a quadratic equation, which can be factored into (x - r1)(x - r2) = 0 where r1 and r2 are the roots of the equation.

In this case, we can use the fact that 1/2 is a root of the equation x^2 - kx - 5 = 0

We can use the factored form of the equation and substitute x = 1/2

(x-1/2) (x-r2) = 0

Then, we can set each factor equal to zero and solve for r1 and r2:

x - 1/2 = 0 and x - r2 = 0

x = 1/2 and x = r2

We can use the quadratic formula to find the value of r2:

x = (-b ± √(b^2 -4ac) ) / 2a

We can substitute the values in the equation x^2 - kx - 5 = 0

x = (-(-k) ± √((-k)^2 - 41(-5)) ) / 2*1

x = (k ± √(k^2 + 20) ) / 2

x = (k ± √(k^2 + 20) ) / 2

r2 = (k + √(k^2 + 20) ) / 2

Now we have two values of x that satisfies the equation x^2 - kx - 5 = 0

x = 1/2 and x = (k + √(k^2 + 20) ) / 2

We can use the first value x = 1/2 and substitute it back into the original equation:

(1/2)^2 - k(1/2) - 5 = 0

1/4 - k/2 - 5 = 0

k/2 = 6 - 1/4

k = 12 - 1

k = 11

Therefore, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

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The cross product of A & B (A × B) is |A| |B| Sin θ, where θ is the angle between A and B.

The vector product or cross product of two vectors, A and B, is denoted by A × B, and its resultant vector is perpendicular to the vectors A and B.

The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.

The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions.

If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:

|A| |B| Sin θ

--The given question is incorrect; the correct question is

"What is the cross product of A & B?"--

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(9cm + 12cm) =15cm

21cm = 15cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The experimental probability of spinning red and spinning blue is 4 and 2.8.

What is the experimental probability?

Experimental probability is a type of probability that is determined by conducting an experiment and observing the outcomes. It is also known as empirical probability.

It is calculated by counting the number of times an event occurs in a set of trials and then dividing that number by the total number of trials.

The experimental probability of spinning red.

P(red) = 20/5 = 4

The experimental probability of spinning blue

P(red) = 20/7 = 2.8

Hence, The experimental probability of spinning red and spinning blue is 4 and 2.8.

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