ga rectangular enclosure at a zoo is 35 feet long by 18 feet wide. the zoo doubles the area of the enclosure by adding the same distance to the length and width. what are the new dimensions of the enclosure?

△DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the shapes have been flipped, turned, or rotated, the shape and size ought to remain constant.

1)  Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.

2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:

Preimage         Image

D (-3, -1)            D' (-3, 1)

E (2, -4)             E' (2, 4)

F (4, -4)             F' (4, 4)

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F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.003357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

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Answer: An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d.

Step-by-step explanation: Hope this was helpful

An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.

Example: 5, 7, 9, 11, 13, 15

Answer:

Mr. Callaway needs 120 ounces of seed to seed both lawns

Step-by-step explanation:

2400/40 = 60 ounces per square foot

3000 divided by 60 = 50 ounces

So, Mr. Callaway needs 50 ounces to cover a 3000-square-foot lawn

4200 divided by 60 = 70 ounces

So, Mr. Callaway needs 70 ounces to cover a 4200-square-foot lawn

50+ 70 = 120 ounces

So, Mr. Callaway needs 120 ounces to seed both lawns.

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Answer:

120 ounces pf grass seed

Step-by-step explanation:

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{3000}[/tex]  Cross multiply and solve for x

120000 = 2400x  Divide both sides by 2400

\[tex]\frac{120000}{2400}[/tex] = [tex]\frac{2400x}{2400}[/tex]

50 = x

It will take 50 ounces of grass seed to cover 3,000 square foot lawn.

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{4200}[/tex]  Cross multiply and solve for x

168000 = 2400x  Divide both sides by 2400

70 = x  

It will take 70 ounces of grass seed to cover 4200 square foot lawn.

50 + 70 = 120

Answer:

The figure below shows the graph of rational function f; It has vertical asymptotes x 2 andx = 4, and horizontal asymptote y = 0. The graph does not have an x-intercept, and it passes through the point (~3,-1). The equation for f (x) has one of the five forms shown below. Choose the appropriate form for f (x), and then write the equation: You can assume that f (x) is in simplest form_ 0 f() f() f ()

( g - 14)² is factor of equation .

What is factor ?

A number that divides another number by itself with no residual is known as a factor.The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8.

             In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Since the numbers we are multiplying are divisible by the product, they are factors of the product.

g2 − 28g + 196

= g² - 14g - 14g + 196

= g( g- 14 ) - 14( g - 14 )

= ( g - 14) ( g - 14)

= ( g - 14)²

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The complete question is -

One of the factors of g2 -28g + 196 is a. g-7 b. g-14 c. g+14 d. g+7

The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

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Answer:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

Step-by-step explanation:

Apply natural logarithm chain rule:

[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]

Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:

[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]

Now we have to derive quotient functions, we can use quotient rule for this:

[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

Where u and v are functions. Therefore, from numerator:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]

Derive using power rule and constant rule where:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]

Thus:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]

Therefore, we will now have:

[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]

Simplify expressions:

[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]

Therefore, the derived function is:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

The ratio of a : b : c in the linear equation is 2 : -1 : -1

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

ax + by + c = 0

The points on the line are given as

(2 ,3) and (8 , 15)

A linear equation is represented as

y = mx + c

Where

Slope = m

y-intercept = c

This means that

3 = 2m + c

15 = 8m + c

Subtract the equations

So, we have the following representation

6m = 12

Divide by 6

m = 2

Substitute m = 2 in 3 = 2m + c

3 = 2 * 2 + c

So, we have

c = -1

Substitute m = 2 and c = -1 in y = mx + c

y = 2x - 1

So, we have

2x - y - 1 = 0

Recall that

ax + by + c = 0

This means that

a : b : c = 2 : -1 : -1

Hence, the ratio is 2 : -1 : -1

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Answer:

The two numbers we are looking for are a rational number and an irrational number.

Step-by-step explanation:

To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can consider the prime factorization of 360. 360 can be written as 2^3 * 3^2 * 5, so the square root of 360 is equal to √(2^3 * 3^2 * 5) = 2√(3 * 5) = 2√15.

Now, suppose we want to find a rational number that is equal to x * √15. We can rewrite this expression as x * √(3 * 5) = x * √3 * √5. For this expression to be rational, both x and √3 must be rational or both must be irrational.

If x is rational, then the expression x * √3 * √5 is rational. Therefore, one of the two numbers we are looking for is x, which is a rational number.

If x is irrational, then the expression x * √3 * √5 is irrational. Therefore, the other number we are looking for is √3, which is an irrational number.

Therefore, the two numbers we are looking for are a rational number and an irrational number.

The values of x and y the triangles to the fight congruent are x = 3 and

y = 1.

What is congruent triangles?

Triangles with the same size and shape are said to be congruent. This implies that the corresponding sides and angles are both equal. Without comparing every angle and side of the two triangles, we can determine whether two triangles are congruent.

If given these triangles are congruent then all corresponding side must be equal

As we can see that both triangle are right triangle

Therefore hypotenuse of one triangle equal to another

x+1  = 4y   ..... (A)

And lenght ( height)  of one  must equal to another triangle

x = y +2          .... (B)

therefore

Plug the value of x = y + 2 in equation A

y + 2 + 1 = 4y

        3y = 3

          y = 1

and x = y+2

x = 1 + 2

x = 3

Hence, the values of x and y the triangles to the fight congruent are

x = 3 and y = 1.

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Complete question:

Complete question is attached below.

Answer: 6 pieces of candy

Step-by-step explanation:

Using the system of equation, the cost of one dinning table is 145 dollars.

James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.

The system of equation that represent the situation is as follows:

let

x = cost of one dinning room table

y = cost of one chair

Therefore,

x + 4y = 265

2x + 6y = 470

using substitution method,

x = 265 - 4y

2(265 - 4y) + 6y = 470

530 - 8y + 6y = 470

-2y = 470 - 530

-2y = -60

y = -60 / -2

y = 30

Hence,

x = 265 - 4(30)

x = 265 - 120

x = 145

Therefore,

cost of one dinning table  = 145 dollars

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The possible number of hours Henry could trim trees is t > 10.

The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.

Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:

6t – 4 > 56

Solving,

6t  > 56 + 4

6t  > 60

t > 10.

In order to earn at least $56, Henry must trim trees for at least 10 hours or more.

Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?

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Answer:

Step-by-step explanation:

40/20= 20

39/x=x

that woudl be how you would find it

Answer:10

Rewriting input as fractions if necessary:

3/5, 1/2

For the denominators (5, 2) the least common multiple (LCM) is 10.

LCM(5, 2)

Therefore, the least common denominator (LCD) is 10.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 2/2 = 6/10

1/2 = 1/2 × 5/5 = 5/10

Answer:

Step-by-step explanation:

1/2 + 3/5 = 5/10 + 6/10 = (5+6)/10 = 11/10 or 1 1/10 Your pair of fractions is 5/10 and 6/10

Answer:

here u go

Step-by-step explanation:

The diagram below shows ΔOAG, where RN¯, NE¯, and ER¯ are mid-segments of the triangle.

If OA=(4x+3) units, NE=(2.5x) units, RN=4.5 units, and ER=(2x) units, determine the measures below.

The length of NE¯ is units.

The length of GO¯ is units.

The length of AG¯ is units.

The perimeter of ΔOAG is units.

The distance between the 1st and the 3rd poles is 140 meters.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

ESB poles are placed along a road 70 meters apart.

So the distance between two poles is 70 meters.

So the distance between 1 and 3rd will be = 2*70 =140metets

Hence, the distance between the 1st and the 3rd poles is 140 meters.

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Complete Question:
Esb poles are placed along a road 70 metres apart. What is the distance between the 1st and the 3rd poles?

Answer:

y = -3x + 1

Step-by-step explanation:

The value c guaranteed by the Intermediate Value Theorem over the interval [0, 2], where f(0) = 2, and f(2) = 10 is c = 1.5, f(1.5) = 5

The inequalities, 0 < 1.5 < 2, f(0) < f(1.5) < f2), verifies the Intermediate Value Theorem.

The Intermediate value theorem states that a value p that is between the f(a) and f(b), such that f(a) < p < f(b) or f(a) > p > f(b), then a number, c, exists between a and b such that f(c) = p

The derivative of the function f(x), f'(x) = 4·x² - 4·x + 2

The interval over which the Intermediate Value Theorem is to be verified = [0, 2]

The value of the function at the boundaries of the domain [0, 2], are;

f'(0) = 4 × 0² - 4 × 0 + 2 = 2

f'(2) = 4 × 2² - 4 × 2 + 2 = 10

Therefore, the value, f(c) = 5, indicates that we get;

f'(0) < f(c) < f'(2), and 0 < c < 2

We get; 4·x² - 4·x + 2 = 5

4·x² - 4·x + 2 - 5 = 0

4·x² - 4·x - 3 = 0

Completing the square

4·x² - 4·x = 3

x² - x = 3/4

x² - x + (-1/2)² = 3/4 + (-1/2)²

(x - 1/2)² = 3/4 + (-1/2)² = 1

x - 1/2 = ± √1 = ±1

x = 1 + (1/2) = 1.5, and x = -1 + 1/2 = -1/2

A value of x that satisfies the equation, f'(x) = 4·x² - 4·x + 2, is x = 1.5

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Answer:

The sample midrange for the data is 559

What is Sample midrange?

Although the sample midrange only uses a small fraction of the data, outliers can have a significant impact on it. It offers details on the distribution's skewness and heavy tails, which are identical to those of the random variable's distribution. Although the structure of this distribution is not obvious, with large sample sizes, the central limit will cause it to resemble a normal distribution.

According to question:

Minimum value: 34

Maximum values:  1084

The sample midrange can be computed as:

(Minimum value + Maximum value) / 2

⇒ (34+1084)/2

⇒ (1118)/2

⇒ 559

Hence, the sample midrange is 559

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The Complete Question is

a) Natural number: [tex]12[/tex]

b) Integer that is not a natural number:[tex]-8[/tex]

c) Rational number that is not an integer: [tex]\frac{5}{10} or 0.5[/tex]

d) An Irrational number: [tex]\sqrt{3}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5,6[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or [tex]0[/tex]. Examples of integers are: [tex]-5,0,1,5,10.[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]-\frac{1}{2},\frac{3}{4},0.75, etc.[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi (3.14), \sqrt{2}, etc.[/tex]

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a) Natural number: 12

b) Integer that is not a natural number:-8

c) Rational number that is not an integer: [tex]\frac{5}{10}[/tex]

d) An Irrational number: [tex]\sqrt{5}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or 0. Examples of integers are: [tex]-1,5, etc[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]\frac{1}{2} ,0.5[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi ,\sqrt{6}[/tex]

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Answer: Hugo should buy car A

Step-by-step explanation:

Car A

Take 702 divided by 12 = 58.5 miles per gallon of gas

Car B

Take 873 divided by 15 = 58.2 miles per gallon of gas.

So Hugo should buy car A

At some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards.

We are going to use 50, 8 and 10 to find are answer.

Therefore, we are going to divide the numbers:

[tex]\boxed{50/10}[/tex]

First, we need to figure out 50/10:

[tex]\boxed{50/10=5}[/tex]

[tex]\boxed{8x5=40}[/tex]

[tex]5=40\\(50/10=5=8x5=40)[/tex]

Therefore, at some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Answer:

40

Step-by-step explanation:

Answer:

Option D: 7/3x

Step-by-step explanation:

Because this line passes through the origin (0,0), we know that there is know b-value according to the equation y = mx + b. To figure out the equation, we must first calculate the slope of the linear function.

Slope = △y/△x

△y (change in y) = -7

△x (change in x) = -3

Therefore, the slope is 7/3 and the equation is y = 7/3x.

Answer:

Step-by-step explanation:

b(x)=6x^2

That is the same as b(x)=6*x*x

when x=16

b(16)=6*16*16=1536

The xx-value on the line when y=29 represents the length in inches of the catfish that would have a weight of 29.

Measuring is the act or process of determining the connection between two numbers. The act of measuring is the practice of putting a number on a characteristic of an object or event so that it can be compared to other things and phenomena. Calculating something's size or magnitude is what it is.

Comparing unknown amounts to known quantities is made easier by measurement. Measurement enables us to establish quantitative claims about the size, length, and speed of objects. Without measurement, the result will be inaccurate. Examples: Vehicle speed is measured using a speedometer.

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The evaluation of the given fraction expression is 1 11/16. The correct option is the last option

From the question, we are to evaluate the given expression.

The given expression is

[tex]12 \div (2+\frac{2}{3})^{2}[/tex]

Evaluating the expression

[tex]12 \div (2+\frac{2}{3})^{2}[/tex]

[tex]12 \div (\frac{8}{3})^{2}[/tex]

[tex]12 \div (\frac{8^{2}}{3^{2}})[/tex]

[tex]12 \div \frac{64}{9}[/tex]

= [tex]12 \times \frac{9}{64}[/tex]

= [tex]\frac{108}{64}[/tex]

= [tex]\frac{27 \times 4}{16 \times 4}[/tex]

= [tex]\frac{27}{16}[/tex]

= [tex]1\frac{11}{16}[/tex]

Hence, the fraction is 1 11/16

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a) The mean of the sampling distribution of p is of 0.2.

b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.

c) The shape of the sampling distribution of p is approximately normal.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:

The parameters for this problem are given as follows:

p = 0.2, n = 300.

The 10% condition is given as follows:

Then the standard error of the sampling distribution of p is calculated as follows:

[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]

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