Rewrite using a single exponent.

The resulting perfect square using the given trinomial is found as (4y + 9)².

a²-2ab+b² or a²+2ab+b²

since:

a²-2ab+b²  = (a-b)²

and

a²+2ab+b² = (a+b)²

A trinomial is written as the square of the a binomial in the equations above.

Knowing that the aforementioned equations are correct, we may use the binomial that has been provided and proceed backwards from there:

= (4y)² +__+ (9)² ....eq 1

a = 4y and b = 9.

Thus, 2ab = 2(4y)(9) = 72y

Put in eq 1;

=  (4y)² + 72y + (9)²

The resulting perfect square:

= (4y + 9)²

Thus, resulting perfect square using the given trinomial is found as (4y + 9)².

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The theorem or principle that helps to solve the above is the properties of a parallelogram. On the basis of the same, we can state that the proof that Triangle ABC is congruent to Triangle ADC is the property that indicates that each diagonal of a parallelogram separates it into two congruent triangles. Hence, ΔABC ≅ Δ ADC.

There are six crucial parallelogram qualities to understand:

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The formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is a term in the sequence, and a(n - 1) is its previous term in the sequence

What is arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. For instance, the number sequence 5, 7, 9, 11, 13, and 15 has a common difference of 2 in arithmetic.

Sequences can in fact begin at any number that we choose. A sequence with the general word an is commonly notated as ann=1 a n n = 1.

or d = (an + 1 - an) (an – an-1). AP reduces if the common difference is negative. For instance, the AP drops in these numbers: -4, -6, -8.

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The solutions are that Two comparable triangles have proportional corresponding sides. And Two comparable triangles matching angles

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

For a regular polygon of any number of sides, therefore the sum of its exterior angle is 360°.

Given statements that the corresponding sides might be altered, they must still be proportionate.

The triangles will be congruent also, if they are.

But the angles must always line up otherwise the triangle's overall shape will change and it won't look the same.

Two comparable triangles must have proportional corresponding sides.

Two comparable triangles must matching angles match up.

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Answer:

Step-by-step explanation:

Answer: answer is b 12$.

Step-by-step explanation:

By using the functions we have found the value of x and it is found out to be as x = -20/3.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given data:

f(x) = -4x + 1, g(x) = x2 - 8x + 21, and h(x) = 19 - 3x and h(x) = 39.

By using the h(x) function, we can write

               h(x) = 19 - 3x

                39 = 19 - 3x

                3x = 19 - 39

                3x = -20

                  x = -20/3

Hence, by using the functions we have found the value of x and it is found out to be as x = -20/3.

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Answer:

c=65

Step-by-step explanation:

a=115

180-115=b

b=65

b=c

c=65

The number of fests of light that Mr Green needs 140 feet of lights

The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence.

From the formula for perimeter L x W which will give us.L being 5 and W being 3.5

The equation is 5 × 3.5 = 17.5.

With that being said I just need to multiply that answer by 8 which gives us 140. This means that he will need 140 feet of light in order to put light around each window.

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Answer: -9/50

Step-by-step explanation: It's asking you to give the answer of A (5/12) - B (3/5), how you do it is simple, you subtract 5/12 and 3/5 like so: 5/12 3/5 = -0.18 and -0.18 as a fraction is -9/50

So there is your answer :)

The translated points are A'(7, 9), B'(8, 8), and C'(4, 12) when they have been translated 6 units to the right and 10 units up.

A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.

The given points are,

A(1, -1), B (2, -2) and C(-2, 2).

When the points are translated 6 units to the right and 10 units up implies that,

There will be increase of 6 units in x coordinate and increase of 10 units in y coordinate

The point coverts as

A'(7, 9), B'(8, 8), and C'(4, 12)

The translated points are A'(7, 9), B'(8, 8), and C'(4, 12).

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Answer: 2/8

Step-by-step explanation: 2/16 can be simplified to 1/8, 1/8 + 5/8 = 6/8, since a whole bone is 8/8, or 1. 8/8 - 6/8 = 2/8

so, once more, the answer is 2/8.

Answer:

x = 100

Step-by-step explanation:

You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.

Answer:

21

Step-by-step explanation:

One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

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If the expected value of d is not equal to d, then the property that d hat exhibit is option (E) d hat is biased

Here a certain statistic d cap is being used to estimate a population parameter d

The central limit theorem states that "the distribution of sample means approximates a normal distribution as the sample size gets larger."

According to the central limit theorem,

The expected value is μ = p

Then the standard error will be

s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Here it is given that the expected value of d cap is not equal to d. So it is different from the expected value  μ = p.

Therefore, the d hat is biased

I have answered the question in general, as the given question is incomplete

The complete question is :

A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?

A. The sampling distribution of d hat is normal.

B. The sampling distribution of d hat is binomial.

C. The sampling distribution of d hat is uniform.

D. d hat is unbiased.

E. d hat is biased.

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Answer:

the answer is 306.25 feet and b is 8 sec

Step-by-step explanation:

Explanation

The height of the ball as a function of the time is given by the following formula:

A. Maximum height of the ball

To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:

Solving the last equation for t, we get time t when the height is maximum:

So the maximum height is given by the value of h(t) when t = 2.5:

The maximum height is 196ft.

B. Time until the ball hits the ground

The ball will hit the ground when h(t) = 0. So we must find the value of t such that:

Solving this equation is equivalent to finding the roots of a second-order polynomial:

Where:

• a = -16,

,

• b = 80,

,

• c = 96.

The roots of this polynomial are given by the following formula:

s

Answer

A. The maximum height of the ball is 196 ft.

Answer:

  12

Step-by-step explanation:

You want a 2-digit number that rounds to 10 and has 2 as one of its digits.

The integers that round to 10 are in the rangle 5–14. The only one of these that has a digit of 2 is 12.

The 2-digit number is 12.

Answer: Richard =24 Teo = 8

Step-by-step explanation:

32-8 = 24

24-8 = 16

16/2= 8

Answer:

(4,12) Quadrant l

(-5,2) Quadrant ll

(-9,-4) Quadrant lV

(3,-3) Quadrant lll

Step-by-step explanation:

hope this helps!

The equation of parabola will be;

⇒ y = 4 ( x + 4)² - 8

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The vertex = (- 4, - 8)

And, The focal diameter = 16

Now,

Since, The vertex (h, k) = (- 4, - 8)

And, The focal diameter (4a) = 16

⇒ 4a = 16

⇒ a = 4

Hence, The equation of parabola with vertex (h, k) will be;

⇒ y = a (x - h)² + k

Substitute all the values, we get;

⇒ y = 4 (x - (-4))² + (-8)

⇒ y = 4 ( x + 4)² - 8

Thus, The equation of parabola will be;

⇒ y = 4 ( x + 4)² - 8

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Answer:

z = 7

Step-by-step explanation:

We know that, sum of the exterior angles of a quadrilateral is added up to 360°.

Accordingly,

115 + 7z + 12z + 16z = 360

Combine like terms.

115 + 35z = 360

Subtract 115 from both sides.

35z = 360 - 115

35z = 245

Divide both sides by 35.

z = 7

Answer:

-12.5 -10.5n

Step-by-step explanation:

Use distributive property to solve:

1. -2.5 x -3 = 7.5

2. -2.5 x 4.2n = -10.5n

3. -2.5 x 8 = -20

Simplify:

7.5-20= -12.5

-12.5 -10.5n

Answer: asa

Step-by-step explanation: I just did this

Answer: 8.8 (-8.8'F)

Step-by-step explanation:

What we know:

Temperature started as 7.2

Temperature ended as -1.6

We need to find the difference

How to solve:

By doing simple subtraction, we can solve this.

Process:

Write equation                                                   7.2 - (-1.6) = ?

Simplify                                                               7.2 + 1.6 = ?

Solve                                                                                 = 8.8

Solution:  {8.8 (-8.8'F)}

The temperature decreased by 8.8'F, but it increased/changed by -8.8'F.

The slopes of the segments can be the same as long as the change in y divided by the change in x of both segments is the same. This means that the two segments are parallel.

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.

Hence, given two points on a line, the slope is calculated by the division of the change in y divided by the change in x.

As long as the changes are the same, two different segments can have the same slope, which is the case when they are parallel, meaning that they meet only at infinity.

One possible example of two parallel segments is given as follows:

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The solution to the following functions are 1) 6x5-3x4, 3x4+1, 6x5-3x4, 3x4 / (2x-1),  2)(x-1)/x3, (x-1)/x2 - 1/x,  (x-1)/x3, x-1

The relationship between two sets of numbers is described mathematically by a function. It is a mathematical equation that assigns a unique output value to each input value inside a specific domain. Functions are frequently expressed by a letter, such as  F(x) = 3x+ 4 or g(x), where the letter indicates the function and the input value is represented by the variable x.

Functions can be either linear or nonlinear, and they can have a single or numerous outputs for each value of the input. They are frequently employed to simulate real-world situations and generate predictions based on available information. Functions can be graphed on a coordinate plane to visualise their behavior, and they can be combined or transformed using various mathematical operations.

How to solve?

1)a. (fg)(x) = (3x4)(2x-1) = 6x5-3x4

b. (f-g)(x) = (3x4) - (2x-1) = 3x4+1

c. (f *g )(x) = (3x4) * (2x-1) = 6x5-3x4

d. (f/g) (x) = (3x4) / (2x-1) = 3x4 / (2x-1)

2)a. (fg)(x) = (x-1/x2) * (1/x) = (x-1)/x3

b. (f-g)(x) = (x-1/x2) - (1/x) = (x-1)/x2 - 1/x

c. (f *g )(x) = (x-1/x2) * (1/x) = (x-1)/x3

d. (f/g) (x) = (x-1/x2) / (1/x) = (x-1)/x2 / (1/x) = (x-1)/x2 * x = x-1

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Answer:

582.1

Step-by-step explanation: