Given point O(0, 1) and point P(5, 3), what is the slope of the line that passes through points P and Q

The transformation h(x)=3x^2-7 will cause the graph of f(x)=x^2 to stretch vertically by a factor of 3 and shift 7 units downward.

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

f(x) = x^2

h(x) = 3x^2 - 7

This means that

h(x) = 3f(x) - 7

This in other words, the transformation "stretches" the graph of f(x) = x^2 vertically by a factor of 3 and "translates" it vertically by shifting it downward by 7 units.

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[(x₁ + x₂)/2, (x₁ + x₂)/2] is the formula to find: B. the midpoint.

[(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)] is the formula to find: A. the point that partitions a segment into a ratio of m : n, where m : n is not 1 : 1.

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

In Mathematics, a line ratio can be defined as the set of points that partitions a line segment into a ratio of m : n and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

where:

m : n is not 1 : 1.

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The solution is Option C.

The value of the equation is y' = y/2x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y² = cx   be equation (1)

Now , dividing by x on both sides of the equation , we get

c = y²/x

Differentiating the equation with respect to x , we get

0 = ( x ( 2yy' ) - y² ) / x²

Multiply by x² on both sides of the equation , we get

x ( 2yy' ) - y² = 0

Adding y² on both sides of the equation , we get

y² = x ( 2yy' )

Divide by 2xy on both sides of the equation , we get

y' = ( y² ) / 2xy

y' = y/2x

Hence , the equation is y' = y/2x

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After putting the first 2 terms together and the second 2 terms together, what needs to be in the middle is; Parenthesis around all 4 terms

Factorization by grouping in algebra simply means that we need to group the terms with common factors before factoring.

Now, some of the steps to take in this regards are;

- From the groups of the given expression a factor can be taken out from each group.

- Factorize each group

- Now take out the factor common to group formed.

Thus, from the above after grouping the terms together, the next thing to be in the middle is to put parentheses around the 4 terms.

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The transformations to prove the relationships between the angles formed by parallel lines and a transversal are as follows

10. A translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] and rotation of the image, indicates that the alternate interior angles ∠3 and ∠6 are congruent

11. The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex], and the linear pair angles, ∠3 and ∠1, indicates that the same-side interior angles ∠3 and ∠5 are supplementary

Alternate interior angles are angles formed in the interior part but on opposite side of the common transversal to (two) parallel lines.

10. To prove that alternate interior angles are congruent using (rigid) transformations, the specified parameters for the parallel lines [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex], are used as follows;

[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]

The alternate interior angles are ∠3 and ∠6

A transformation that can be used to prove that the alternate interior angles, ∠3 and ∠6 are congruent is the translation of the line [tex]\overleftrightarrow{BF}[/tex] along the transversal [tex]\overleftrightarrow{AB}[/tex] to coincide with the line [tex]\overleftrightarrow{AD}[/tex], such that the the image of angle ∠3 following the translation is angle ∠7

Angle ∠3 is then indicated to be congruent to ∠7

∠3 ≅ ∠7

Rotating the resulting figure, 180°, we get, the image of angle ∠3, (∠7) is congruent to ∠6, ∠7 ≅ ∠6

Therefore, by transitive property of congruency, ∠3 is congruent to ∠6

11. The parallel sides are; [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex]

[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]

The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] indicates that ∠1 is congruent to ∠5

∠1 ≅ ∠5

∠1 = ∠5, (definition of congruency)

∠3 and ∠1 are linear pair angles, therefore, angle ∠3 and ∠1 are supplementary angles

∠3 + ∠1 = 180° (definition of supplementary angles)

∠3 + ∠5 = 180° (substitution property)

Therefore, Same-side interior angles, angle ∠3 and angle ∠5 are supplementary angles by definition of supplementary angles

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The number of chalkboards that the school will be able to give away is 89.

In order to determine how many chalkboards the school can give away, the mathematical operation that would be used is division.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Number of chalkboards the school can give away = total amount the school has to spend / cost of each chalkboard #

$3,293 / $37 = 89

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12 is the  missing number of the unit rate 36/3=\1.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the missing number be x in the given equation

36/3=x/1

36 and 3 are the multiples of 3 so divide numerator and denominator by 3

36 divided by 3 is equal to twelve

so the value of x is 12

Hence, 12 is the  missing number of the unit rate 36/3=\1.

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Answer: 0>-6

Step-by-step explanation:

2x+8>2x+2     Distribute and subtract numbers.

2x+8-8 > 2x+2-8  Subtract eight from both sides.

2x > 2x-6  Then, simplify the expression. Subtract the numbers.

Answer: 0>-6

Hoping this helps!

This question is based on the concept of statistics. Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion p=0.05. For samples of size 100.

According to the question of statistics,

Mean of  sampling distribution of the sample proportion = p (Population proportion.)

It is given that, the population proportion of those who make donation when contacted by phone is known to be p=0.05.

Thus, Mean = p = 0.05

Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

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A researcher should follow all of the rules when presenting quantitative data with a histogram. This includes starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals.

When creating a histogram, there are several important rules to follow in order to ensure that the data is accurately presented. These rules include starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals. Additionally, the bin width should be uniform and the x-axis should have a label. Furthermore, the histogram should have a title that describes the data being presented. Finally, the researcher should be sure to include a legend that explains the different colors and symbols used in the histogram. Following these guidelines will ensure that the data is accurately and effectively presented.

The complete question is :

When presenting quantitative data with a histogram, which of the following rules should a researcher follow? Start the frequency/proportion at zero. Put a break in they-axis. Put gaps between intervals. All of the above. None of the above.

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The term of the sequence is Tn = 200[(e^0.09959)^1/12]^(n-1)

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

200 + 200(e^0.09959)^1/12 + 200(e^0.09959)^2/12 + 200(e^0.09959)^3/12 + ... + 200(e^0.09959)^58/12 + 200(e^0.09959)^59/12

In the above sequence, we have

T1 = 200

T2 = 200(e^0.09959)^1/12

So, the common ratio (r) is

r = 200(e^0.09959)^1/12/200

Evaluate

r = (e^0.09959)^1/12

The sequence is then calculated as

Tn = T1 * r^(n - 1)

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

Tn = 200[(e^0.09959)^1/12]^(n-1)

Hence, the term is Tn = 200[(e^0.09959)^1/12]^(n-1)

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The percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base will be ~43.30%

Given that the normal tetrahedron's (Vt) side-S volume,

Vt = S3/(6*(square(2))

Considering a regular tetrahedron with side S and the radius (r) of a sphere,

the proportion of the total volume of four identical spheres stacked in a tetrahedral pattern with a triangular base

r = (S) / (2 + (2*sqrt(6))

S =[tex](2 + 2(sqrt(6)*r)[/tex]

S = r times 6.898979486

for S = 1

r = ~0.144948974

Sphere volume = (4*pi*r3)/3

Vsphere = 0.012756574 (Vs).

Vs = [tex]((2+(2*sqrt(6)/(2+(2*sqrt(6)3/3[/tex]

Vs equals 0.012756574 when S = 1.

4 spheres' volume equals 0.051026296.

Tetrahedron volume = Vt = S3/(6*(sqrt(2))

When S = 1, Vt equals 0.11785113.

4Vs/Vt = ~0.432972475

4Vs/Vt = ~43.30%

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The complete question:

What is the percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base, inscribed within a regular tetrahedron, to the volume of the tetrahedron?

Answer:

1. Rational

2. False

Step-by-step explanation:

1. You will always get a rational number when you add, subtract, multiply, or divide rational numbers.
2. All whole numbers, integers, and natural numbers are rationals, but not all rational numbers are integers, natural numbers, or whole numbers.
Hope it helps!

The coordinates for hector's position are (137.78, 47.72) for (x, y)

Tre's position as the point on the pitcher's mound (42.78, 42.78). Hector is approximately 95 feet away from the pitcher's mound horizontally (x axis).

We must solve for the correct x-coordinate because we already have the correct y-coordinate.

Now all that is required of you is to write down the coordinates.

The coordinates of Hector are (137.72, 47.78).

The coordinate values of a point on a graph can be represented by (x, y), with x being referred to as the abscissa, indicating the horizontal distance from the origin or x-axis, and y being referred to as the ordinate, signifying the vertical distance from the origin or the x-axis.

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Complete Question:

Hector was standing halfway between first and second base, at the grass line. The

grass line is 95 feet from the pitcher's mound.

6. Calculate the coordinates for Hector's position. [Note: We can assume that 95

feet is an approximately horizontal distance from the pitcher's mound to the grass

line.] (2 points: 1 for x, 1 for y)

Hector was standing at the coordinate ( __, _).

Answer:

11

Step-by-step explanation:

find ratio of girls to boys

22:11 divide by 11

2:1

2girls and 1boy in every boy makes 11 groups

The lenght of the dotted line in the given diagram is 5.92

The dotted line in the given diagram is the diagonal of the rectangle. The lenght of diagonal can be calculted using phytagoras theorem:

diagonal² = length² + wide²

From the diagram, we know that the wide of the rectangle is 1, however we have no information about the length of the rectangle yet. If we look to the attached triangle, we can know that the lengt of rectangle is actually the hypotenuse of the triangle.

We can find the hypotenuse of the triangle using the phytagoras theorem:

hypotenuse² = base² + height²

hypotenuse² = 3² + 5²

hypotenuse² = 9 + 25

hypotenuse² = 34

We can use the value of squred hypotenuse as the squared length to find the length of the diagonal:

diagonal² = length² + wide²

diagonal² = hypotenuse² + wide²

diagonal² = 34 + (1)²

diagonal² = 35

diagonal = 5.92

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The largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet

Let the width of the rectangle be x. Then, the height of the rectangle is (43 - 2x)/2, and the radius of the semicircle is x. The area of the Norman window is then given by:

A = x * (43 - 2x)/2 + (π/4) * x^2.

We want to maximize A subject to the constraint that the perimeter is 43 feet, which we have expressed as:

x + (43 - 2x)/2 = 43/2.

Solving for x, we find x = 12. The height of the rectangle is then 15.5, and the area of the Norman window is:

A = 12 * 15.5 + (π/4) * 12^2 = 180 + 144π.

So the largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet.

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Answer:

school who study French also study Japanese, do more students at the school study french than Japanese? (1) 16 students at

well, the quadratic function is simply a parabola that looks like a bowl with a "minimum" at its vertex, so

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10.5}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{10.5}{2(1)}~~,~~20-\cfrac{10.5^2}{4(1)} \right)\implies \left( -\cfrac{10.5}{2}~~,~~20-\cfrac{110.25}{4} \right) \\\\\\ \left( -5.25~~,~~20-27.5625 \right) ~~ \approx ~~ \boxed{(-5.25~~,~-7.56)}[/tex]

The function 4^n + 15n - 1  is divisible by 9 if n is a natural number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The given number = 4^n + 15n - 1

so we are going to test different natural numbers as n, to check if the resulting number is divisible  by 9.

let n = 1

4^(1) + 15(1) - 1 = 4 + 15 - 1 = 18

sum of 18 = 1 + 8 = 9

9 is divisible by 9

let n = 2

4^(2) + 15(2) - 1 = 16 + 30 - 1 = 45

sum of 45 = 4 + 5 = 9

9 is divisible by 9

Thus, if is proved that 4^n + 15n - 1 is divisible by 9 if n is a natural number. ​

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The time needed when the bacteria count reaches 8621 is approximately 19.97 hours.

The composite function of the bacteria count in a refrigerated food product with respect to time can be found by combining the two functions given. The first function is the number of bacteria in the food, which is given by , where is the temperature of the food. The second function is the temperature of the food when it is removed from the refrigerator, which is given by , where is the time in hours. Combining these two functions, we can form the composite function , where is the number of bacteria and is the time in hours.

To find the time when the bacteria count reaches 8621, we can rearrange the composite function to solve for . Doing this gives us , which can be solved for to obtain . Therefore, the time needed when the bacteria count reaches 8621 is approximately 19.97 hours.

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1. The ordered pair (1, 5) is a solution to the system of equations.

2. The ordered pair (-2, 0) is NOT a solution to the system of equations.

To determine if the ordered pair (1, 5) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

-5(1) + 6(5) = 25

25 = 25 (holds true)

-7(1) + 8(5) = 33

33 = 33 (holds true)

Since both equations hold true for the values of m=1 and n=5, we can conclude that the ordered pair (1, 5) is a solution to the system of equations.

To determine if the ordered pair (-2, 0) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

8(-2) - 3(0) = -16

-16 = -16 (holds true)

-9(-2) - 2(0) = 50

4 ≠ 50 (does not hold true)

Since one of the equations does not hold true for the values of x=-2 and y=0, we can conclude that the ordered pair (-2, 0) is NOT a solution to the system of equations.

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The length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle ABC, by sine rule;

a/sinA = b/sinB = c/sinC

We first derive the angle A as follows:

75° + 35° + A = 180° {sum of interior angles of a triangle}

A = 180° - 110°

A = 70°

Thus by sine rule;

b/sin75° = 12/sin35°

b = (12× sin75°)/sin35° {cross multiplication}

b = 20.21

a/sin70° = 12/sin35°

a = (12× sin70°)/sin35° {cross multiplication}

a = 19.67

Therefore, the length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

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The length of side BD is, 40

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In figure,

⇒ AB = 20

⇒ BC = 10

In triangle ABC;

We can find the side AC by using Pythagoras theorem as;

⇒ AB² = AC² + CB²

⇒ 20² = AC² + 10²

⇒ 400 - 100 = AC²

⇒ AC² = 300

⇒ AC = 10√3

Now, By using proportional relationship in triangles ABC and triangle ACD;

⇒ Hypotenuse / Short

⇒ AB / BC = AD / AC

Substitute all the values, we get;

⇒ 20 / 10 = AD/10√3

⇒ 2 × 10√3 = AD

⇒ AD = 20√3

In triangle ACD;

We an find CD by using Pythagoras theorem as;

⇒ AD² = AC² + CD²

⇒ (20√3)² = (10√3)² + CD²

⇒ 1200 - 300 = CD²

⇒ CD² = 900

⇒ CD = 30

Hence, Length of BD is,

⇒ BD = BC + CD

⇒ BD = 10 + 30

⇒ BD = 40

Thus, The length of side BD is, 40

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The percent increase in the collections is 40%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %.

Percent increase = (increase in the number of collections / initial collections) x 100

Increase in collections = 14 - 10 = 4

= (4/10) x 100 = 40%

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The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

Let P(F) be the prior probability of a sensor fault and P(M|F) be the probability of measurements below 1m given a faulty sensor. Then, the posterior probability of a sensor fault given N consecutive measurements below 1m is given by

P(F|M1 ,M2 ,...,MN )=P(F)P(M1|F)P(M2|F)....P(MN |F)/P(M1 ,M2 ,...,MN )

P(M1 ,M2 ,...,MN ) = P(M1)P(M2)....P(MN) = (1/3)^N

Therefore,

P(F|M1 ,M2 ,...,MN )=P(F)(1/3)^N

For N = 1,2,...,10

P(F|M1 ,M2 ,...,MN ) = 0.01 (1/3)^N

For N = 1, P(F|M1)= 0.01/3

For N = 2, P(F|M1,M2)= 0.01/9

For N = 3, P(F|M1,M2,M3) = 0.01/27

Similarly, for N= 4,5,6,7,8,9,10

P(F|M1,M2,M3,M4,M5,M6,M7,M8,M9,M10) = 0.01/81, 0.01/243, 0.01/729, 0.01/2187, 0.01/6561, 0.01/19683, 0.01/59049 respectively.

The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

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1) Completing the square is a good solving option when b is an even number.

2) The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.

What is discriminant?

The discriminant of a polynomial is a number that depends on the coefficients and allows some properties of the roots to be deduced without having to compute them.

1) Completing the square is a good solving option when b is an even number.

Completing the square is a technique used to solve quadratic equations of the form ax² + bx + c = 0 by rewriting the equation as a perfect square. This technique is particularly useful when b is an even number because it makes it easier to recognize the perfect square pattern.

For example, if b = 2, then the equation can be written as ax² + 2x + c = 0. By adding and subtracting the same term, this equation can be rewritten as a(x + 1)² + (c - a) = 0, which is a perfect square. Solving the equation then becomes a matter of finding the square root of the constant term.

If b is an odd number, the equation can still be solved using the completing the square technique, but it may require more steps.

Hence, Completing the square is a good solving option when b is an even number.

2) The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by b² - 4ac. In this case, a = 1, b = 4, and c = 4, so the discriminant is b² - 4ac = 4² - 4 * 1 * 4 = 16 - 16 = 0.

A positive discriminant means that the equation has two real and distinct roots, a negative discriminant means that the equation has two complex roots, and a zero discriminant means that the equation has one real root (a double root).

Hence, The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.

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The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.

Now, radius = 3/2 =1.5 feet

We know that, the formula to find the volume of a cylinder is πr²h.

Here, 3.14×1.5²×4

= 28.26 cubic feet

In gallons = 28.26×7.48

= 211.38 gallons

Therefore, option C is the correct answer.

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The correct option is C, 211.38. Hope this helps :)

Answer:

x = 3/2  or x = -1

Step-by-step explanation: