A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long.

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 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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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: Richard =24 Teo = 8

Step-by-step explanation:

32-8 = 24

24-8 = 16

16/2= 8

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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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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In terms of this scenario, the point (9 , 1) means B. The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, you have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items.

Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy.

The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes. This can be illustrated as:

9($32) + 1($16)

= $282 + $16

= $298

The correct option is B.

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In order to build a cube with an edge length of b inches, b3 cubes with 1-inch edges are required.

A cube is a three-dimensional object with six square faces that are all the same size and form in mathematics. A cube has perpendicular sides and is symmetrical along all three axes. Finding the area of one of a cube's faces and increasing it to the third power yields the volume of the object. V=s3, where s denotes one of the cube's sides, is the formula for calculating a cube's volume. Cubes are frequently used in geometry and algebra, and they have a wide range of real-world uses, including volume measurement and the solution of mathematical equations.

How to solve?

The volume of a cube with an edge length of b inches is b3 cubic inches. For instance, if b=3, we would require 33=27 cubes with 1 inch-long edges, and the volume of a cube with a three inches edge would be 33=27 cubic inches.

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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:

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: y = -2x + 5

Step-by-step explanation: I think it's the same one...

The expression for 60 decreased by twice Jenny's score 60 - 2x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Let Jenny's score be x.

Twice Jenny's score will be 2x.

Therefore, the expression will be:

= 60 - 2x

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Answer:

distance ≈ 5.66 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = N (- 5, 7 ) and (x₂, y₂ ) = P (- 1, 3 )

d = [tex]\sqrt{(-1-(-5))^2+(3-7)^2}[/tex]

  = [tex]\sqrt{(-1+5)^2+(-4)^2}[/tex]

  = [tex]\sqrt{4^2+16}[/tex]

  = [tex]\sqrt{16+16}[/tex]

  = [tex]\sqrt{32}[/tex]

  ≈ 5.66 units ( to the nearest hundredth )

Answer:

90

I am not too sure but this question is VERY BRAIN-INTENSIVE

Sorry, if i am wrong

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:

Step-by-step explanation:

The rectangle is 4 feet long and 0.5 feet wide. l²+w² equals 16.25 feet².

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is a phrase used to describe how much room a 2D form or surface occupies.

Here,

Let l be the length and w be the width.

area=2

lw=2

w=2/l

2(l+w)=9

2l+2w=9

2l+2*2/l=9

2l²+4=9l

2l²-9l+4=0

l=0.5,4

w=4,0.5

l=4 and w=0.5

l²+w²=4²+0.5²

=16.25 feet²

The length of rectangle is 4 feet and width is 0.5 feet. The value of l²+w² is 16.25 feet².

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The required compound interest is $5,510.03

What is compound interest?

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.

Given, Principal = $9,000

Time = 4 years

Interest = 12% = 0.12

For compounded monthly, n = 12

The compound amount for monthly compounded is given by

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

or, A = [tex]9000(1 + \frac{0.12}{12} )^{12*4}[/tex]

or, A = 9000[tex](1+0.01)^{48}[/tex]

A = $14510.03

Compound interest = $14510.03 - $9,000 = $5,510.03

Hence, the required compound interest is $5,510.03

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Answer: asa

Step-by-step explanation: I just did this

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 :)

Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.

What is a chord of a circle?

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.

ΔABC is inscribed in O. If AB = 5, BC = 8, and AC =9.

Now if you look carefully at the given diagram, we can see that the perpendicular distance of chord AC from center O will be smaller than the perpendicular distance of chord AB from center O and the perpendicular distance of chord BC from center O.

Hence, Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.

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Answer:

idek

Step-by-step explanation:

In linear equation, 3 t is the maximum possible weight .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Assuming x to be lightest , y median and z the heaviest.

So according to given information average is 7 so total sum for three box = 21

thus x+y+z = 21

Given y=9 (median weight)

thus x+z = 12

For maximum possible value for x is 3 such that z= 9

if x=4 then Z= 8(this changes median to 8)

So maximum possible value for lightest box is 3

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Denise puts $67.50 in the savings account every week.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

To find out how much money Denise puts in the savings account each week, you need to multiply her weekly earnings by the percentage she puts into the savings account.

First, convert the percentage to a decimal by dividing by 100: 30% = 0.30

Then, multiply Denise's weekly earnings by this decimal to find the amount she puts into the savings account each week:

=$225 * 0.30

=67.50.

Hence, Denise puts $67.50 in the savings account each week.

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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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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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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

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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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.