Where is the vertex of the graph of the quadratic function f/x )= x² located?.

The general form of a perfect square trinomial is (x + y)², where x and y are the roots of the trinomial. It can also be written as x² + 2xy + y² or x² + (2xy)x + y².

The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.

It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.

Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.

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The equation connecting U,S and M is K = U√M/S

The value of M when U=110.5 and S=32 is 4.32

From the information given, we have that U partly varies directly as S and partly inversely as the square root of M.

This is represented mathematically as;

U ∝S/√M

To determine the constant of the variation, we have;

U = KS√M

Now, make 'K' the subject of formula;

K = U√M/S

Substitute the values

K = 124.6 √25/86.75

Find the square root

K = 7. 18

To determine the value of M, we have;

KS/U = √M

substitute the values

√M = 7.18(32)/110. 5

√M = 2. 08

find the square of both sides

M = 4. 32

Hence, the value is 4.32

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When  P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.

In the given question, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then we have to find the remainder.

The given equation is

P(x) = [tex]x^3-3x^2+4x+32[/tex]

We have to divide this equation by x+2.

To find the remainder we firstly equate x + 2 equal to zero to find the value of x.

x + 2 = 0

Subtract 2 on both side, we get

x = -2

Now we put x value in the given equation to find the remainder.

The equation

P(x) = [tex]x^3-3x^2+4x+32[/tex]

Put x = -2

P(x) = [tex](-2)^3-3(-2)^2+4(-2)+32[/tex]

Simplify

P(x) = -8 - 3×4 + (-8) + 32

P(x) = -8 - 12 - 8 + 32

P(x) = 4

Hence, when  P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.

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The complete question is:

When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2. The remainder is?

An angle bisector of a triangle is a line segment that divides an angle into two congruent angles. In an equilateral triangle, all angles are congruent (60 degrees), so any line segment that divides an angle into two congruent angles is also an angle bisector.

To find the angle bisector of an equilateral triangle, you can use the following method:

Draw an equilateral triangle.

Choose an angle and draw the angle bisector from the vertex of the angle to the midpoint of the opposite side.

Since all the angles of an equilateral triangle are congruent, the angle bisector that you drew bisects any angle of the triangle.

Alternatively, you can use the following method:

Draw an equilateral triangle.

Connect the midpoint of one side of the triangle to the opposite vertex.

The segment that you drew bisects the angle of the triangle.

It is important to note that in an equilateral triangle, all medians, altitudes, angle bisectors, and perpendicular bisectors are congruent, they all divide the triangle in the same ratio, so they all meet at the same point, called the centroid, which is 2/3 of the distance from each vertex to the midpoint of the opposite side.

Answer:

Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).

To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.

The postulates are:

SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.

ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.

SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.

AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.

HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.

From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.

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Location of the negative make value different from each other that is  5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])  

According to this rule, if the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.

The negative exponent rule is given as:

   5. 3 x 10^-4

=  5.3/10^4                 (1)

-5. 3 x 10^4

-(5.3 * [tex]10^{4}[/tex])                  (2)

from equation 1 and 2 these two equations are different from each other.

location of the negative make value different from each other that is  5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])  

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A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

MEAN =Sum of observations/Total number of observations.

MEDIAN= If n is odd, then the following formula is used: Value of (n+1/2th observation. If n is even, then the following formulae is used: {Value of (n/2) th observation + (n/2 +1)th observation/2}

MODE= Most number of times occurring value in the data

Note that your information wasn't properly written and a overview was given.

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The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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The slope intercept form of the following equation 6x - 2y = 18 is y = 3x - 9

We knwo that the slope intercept form of equation of line is y = mx + b, where m is the slope and b is the y-intercept.

Consider given equation,

6x - 2y = 18

6x - 2y - 6x = 18 - 6x          .......(Subtract 6x from each side)

- 2y = 18 - 6x

- 2y × (-1) = (18 - 6x) × (-1)       ......(Multiply each side by -1)

2y = -18 + 6x

2y/2 = (-18 + 6x)/2                   ..........(Divide each side by 2)

y = -18/2 + 6x/2

y = -9 + 3x

y = 3x - 9              

This equation is in the form y = mx + b

Here, slope m = 3 and the y-intercept b = -9

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The complete question is:

What is the slope intercept form of the following equation 6x - 2y = 18?

The remote interior angles of ∠1 are 34° and the right angle. The amount of m∠2 is 56°.

∠1 is an exterior angle because it is located outside the triangle. It has 2 remote interior angles. Remote interior angles are the angles with no shared vertex with the exterior angle. In this case, the remote interior angle of ∠1 is angle 34° and the right angle.

m∠1 can be measured by adding the remote interior angles:

m∠1 = 34° + 90°

m∠1 = 124°

Since m∠1 share a vertex with m∠2, then the total of both angles should be equal to 180° (a straight line). Hence:

m∠1 + m∠2 = 180°

Using the value of m∠1 known above, we can find the value of m∠2:

m∠1 + m∠2 = 180°

124° + m∠2 = 180°

m∠2 = 56°

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Answer:

The square root of 3 is an irrational number

Step-by-step explanation:

A rational number is defined as a number that can be expressed as the division of two integers, i.e. p/q. where q is not zero.

√3 = 1.7320508075688772...and keeps getting longer. √3 is an irrational number because the decimal point does not end or repeat.

Answer: 7.9524 m^

Step-by-step explanation:

The square with the least area can only be formed when we take LCM of the dimensions of the rectangular tile I.e. 54 CM × 30 CM

LCM = 270

This means that a square of length 270 CM will be formed when we take least no. of tiles.

Also given in question, 6cm is left around the square that means 12cm is added on every side to make the floor with minimum area = 282 × 282 cm^2

minimum area = 79524 cm^

in m^2 = 79524/10000 = 7.9524 m^

The balance on the card, rounded to the nearest penny $15350.92..

The correct option is D.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.

Formula of continuous compound interest rate;

P(t) = P₀[tex]e^{rt}[/tex]

where P₀ is the principal amount, r is the interest rate and t is the time period.

A customer uses a store credit card to purchase a boat for $10,500.

The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.

That means,

P₀ = $10500, r = 18.99 and t = 2.

So,

P(t) = P₀[tex]e^{rt}[/tex]

Substituting the values,

P(t) = (10500)

P(t) = (10500)(1.46199)

P(t) = 15350.917

P(t) = $15350.92

Therefore, the final amount is $15350.92.

The balance on the card, rounded to the nearest penny $15350.92.

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Cameron can download 4 movies with his $66. He can solve an equation of 14.50x + 22.50y = 66 and x + y = 4

14.50x + 22.50y = 66

14.50x = 66 - 22.50y

14.50x = 43.50

x = 3 (43.50/14.50)

x + y = 4

3 + y = 4

y = 1

Cameron wants to download some movies and an ebook with his $66. To figure out how many movies he can download, he needs to solve an equation. The equation is 14.50x + 22.50y = 66, where x is the number of movies and y is the number of ebooks. By solving for x, he can figure out how many movies he can get, which is 3 (43.50/14.50). To find the number of ebooks, he can solve for y in the equation x + y = 4, which is 1. Therefore, Cameron can download 4 movies with his $66.

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a. Even numbers are numbers that are divisible by 2

b. prime number is the number that has two factors by 1 and itself, all even numbers are divisible by 2 hence any other even number aside 2 will be divisible by 1, 2 and itself and this does not define a prime number any more

A prime number is a positive integer greater than 1 that is only divisible by 1 and itself. In other words, a prime number has exactly two positive integer divisors: 1 and itself.

For example, the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. The number 2 is the only even prime number, and all the other prime numbers are odd.

Prime numbers are important in mathematics because they play a crucial role in various fields such as number theory, cryptography, and coding theory. They are also used as basic building blocks for constructing larger composite numbers.

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The length of the rectangle is 74 yard.

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is

P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.

The perimeter of rectangle is given by  2 ( l + b)

where l is length of rectangle and b is width of the rectangle

given that perimeter of rectangle is 274

so 2 (l+b)= 274

=>  l+b= 137   ---(i)

so l = 137 -b

=> l = 137 - 63

=> 74

so the lenth of rectangle is 74 yard.

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If cos x = 3/5 then the value of b = 4

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin(tetha) = opp/hyp

cos ( tetha) = adj/hyp

tan ( tetha) = opp/ adj

In the triangle adj = 3b and hyp = 20

cos x = 3b/20

cos x = 3/5

therefore 3/5 = 3b/20

multiply both sides by 20

3/5×20 = 3b/20 × 20

3b = 12

divide both sides by 3

b= 12/3 = 4

therefore the value of b is 4

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Answer:A: b = 4

Step-by-step explanation:

A magnitude 8 on the Richter scale is 100 times more ground shaking than one that measures 6 on the Richter scale.

The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to a scale by the seismometer. The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. We have, maganitude of two earthquakes, 8 and 6 Let the magnitude of first earthquake be A and second be B . So, A = 8 , B = 6 , to compare two earthquakes in terms of shaking, you subtract one magnitude from the other and raise 10 to that power, 10⁽ᴹ ⁻ ᴹ´⁾

=> 10ᴬ⁻ᴮ = 10⁸⁻⁶ = 10² = 100

Hence, the magnitude 8 of one quakehas has shake the ground 100 times than the other with magnitude 6.

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Answer:

7.2 because 72 / 10 = 7.2

hope this helps!!!

The ratio which can be used to calculate the height of the building would be [tex]\frac{8}{4}=\frac{x}{15}[/tex].
Option (B) is correct.

What is the triangle similarity test?

The triangle similarity test is a method used to determine whether two triangles are similar or not. Similar triangles are triangles that have the same shape but different sizes. They are similar if their corresponding angles are congruent and their corresponding sides are in proportion. There are several ways to test for similarities, such as the side-side-side (SSS) test, the angle-angle-side (AAS) test, and the side-angle-side (SAS) test.

In the given figure, triangle KLM is similar to Triangle ORS.

and by the property of similar triangles, sides of similar triangles are in proportion:

so we can write:

LM/RS = KL/OR

15/4  = x/8
[tex]\frac{15}{4}=\frac{x}{8}\\\\\frac{8}{4}=\frac{x}{15}[/tex]

Hence, the ratio which can be used to calculate the height of the building would be [tex]\frac{8}{4}=\frac{x}{15}[/tex].

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Jayden makes 3 trays of dog treats for his puppy Spot

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem, we have to do the conversion of units with the given information:

Information about the problem:

By converting the unit from quart to ounce, we have:

1 quart * (32 ounce / 1 quart) = 32 ounce

Calculating the total of ingredients Jayden mixed we have:

Total ounces = Yogurt + peanut butter + honey

Total ounces = 32 ounces + 10 ounces + 6 ounces

Total ounces = 48 ounces

Calculating the number of tray that Jayden can make we have:

No. trays = Total ounces / tray capacity

No. trays = 48 ounces / 16 ounces/ tray

No. trays = 3 trays

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Answer:

28.6%

Step-by-step explanation:

10 minute difference, 10 is 28.6% of 35.

Answer:

sea grass red algae green seaweed mangrove or -20 3/4, -15 1/2, -14 3/4, -1/4

Step-by-step explanation:

negatives switch around the rules of positive so the one with the number tat is bigger when not negative is the lowest when negative

The situation in which the quantities combine to make 0 is "On Monday, Huang withdraws $30 from a bank account. On Friday, she deposits $30 into the account".

For two quantities two make 0, it is necessary to add two numbers with the same value but different sign (positive or negative). Here is an example:

For example if you buy 10 apples but use 10 apples to make a pie.

Based on this, the correct situation is "On Monday, Huang withdraws $30 from a bank account..." as -30 + 30 = 0.

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The values within the range of the piecewise-defined function are

y = -6,  y = -4, y = 1 and y = 3.

A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.

Given f(x) = 2x + 3,   if x < -3

f(x) = x, if  x = -3

f(x) = -x - 2, if  x > -3

the function will be at x ≤ -3 and x ≥ -3

We now wish to determine which values fall within this function's range. Keep in mind that the set of possible outputs from a function constitutes its range.

The range of the first part of the function f(x) = 2*x + 2 has an upper bound at x = -3

f(-3) = 2*-3 + 2 = -6 + 2 = -4

Then the range of the first part is (-∞, -4)

Notice that the actual value -4 belongs to the range because x is smaller than and equal to -3.

The range of the second part has a lower bound for x = -3, the lower bound is:

f(-3) = -(-3) - 2 = 1

Then the range of this part is (1, ∞)

Then the range of the piecewise function is:

(-∞, -4) U (1, ∞)

and including -4 and 1

y = -6,  y = -4

y = 1,     y = 1

Hence values in the range are y = -6,  y = -4, y = 1, and y = 3.

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Answer:

The linear speed (V) is equal to 7 in/s.

The angular speed in rpm is equal to 4.77 rpm.

The angular speed in deg/s is equal to 28.65 deg/s.

Step-by-step explanation:

Co-prime numbers are those numbers that have only one common factor, namely 1.

Coprimes are pair of numbers that have no common factor other than 1. There should be at least two numbers to form a set of coprimes. Such numbers have only 1 as their highest common factor, for example (4 and 7), (5, 7, 9) are co-prime numbers. It should be noted that concurrent primes need not always be primes. If the only common factor of two numbers a and b is 1, then a and b are coprimes. In this case, (a, b) is considered a prime pair. Minor primes are also referred to as relatively primes. To determine whether any two numbers are co-prime, we first find their greatest common factor (GCF). If their GCF is 1, we can say they are co-prime. Consider the two numbers 5 and 9. The factors of 5 are 1 and 5. The factors of 9 are 1, 3, and 9. The factor that is common to both 5 and 9 is 1. The GCF of (5, 9) = 1. Thus, (5 , 9) is a co-prime pair.

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So, the gradient of y = -3x^1 is -3.

The gradient of a function y = f(x) with respect to x is the derivative of the function with respect to x, denoted by dy/dx or f'(x).

In the case of y = -3x^1, the gradient is -3.

It is a constant function, thus, the slope is always the same and equal to the coefficient of the x term, which in this case is -3.

The gradient of a function tells us the rate of change of the function with respect to x. In other words, it tells us how steep the function is at any given point. A positive gradient means that the function is increasing, while a negative gradient means that the function is decreasing.

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