Tristan wants to build a square garden in his backyard that will cover an area of 75ft(squared). If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain

Answer:

#4:    7.5

#5:    28

Step-by-step explanation:

Polygon in #4

is a triangle
base = 1 - (-2)  = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5

Area of a triangle with base b and height h = (1/2)b.h

So area of this triangle = (1/2) (3) (5) = 15/2 = 7.5

Polygon in #5
is a rectangle with length = 7 - (-7) = 7 +7 = 14

and width = 5-3 = 2

Area of a rectangle with length l and width w = lw

Area of this rectangle = 14 x 2 = 28

Hope that helps

The area of the polygon for exercise 4 is 7.5 square units and for exercise 5 the area is 28 square units.

The space occupied by the object in two-dimensional space is called as the area.

For a triangle, the area will be calculated as,

base = 1 - (-2)  = 1+2 = 3

height = 1-(-4) = 1 + 4 = 5

Area of a triangle with base b and height,

h = (1/2)b.h

Area of this triangle,

A = (1/2) (3) (5) = 15/2 = 7.5

Rectangle with length = 7 - (-7) = 7 +7 = 14

Rectangle width = 5-3 = 2

Area of a rectangle with length l and width w = lw

Area of this rectangle = 14 x 2 = 28 square units

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Answer:

a) algebraic expression

b) equation

c) numerical expression

Step-by-step explanation:

Hope this helps......if not then sorry for wasting your time and may God bless you<3

Since in the image above angle 3 is 79 degrees, angle 11 is also equal to 79 degrees based on the vertical angles theorem.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the interior angles that are formed on the same side of the transversal are supplementary angles, which makes:

Angle 3 = Angle 14

Angle 14 = Angle 9

Angle 3 ≅ Angle 9 (Congruent angles or supplements of the same angle)

By applying the vertical angles theorem, we have:

Angle 9 ≅ Angle 11 = 79 degrees.

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Answer:

This equation has one solution I believe if you substitute the variable 68.3375

Step-by-step explanation:

Based on the word problem, the number is 9

This refers to the type of number that is expressed as the ratio of two integers that has a non-zero denominator.

Let the numerator be x

Let the denominator be x+2

If 5 is subtracted from the numerator

x - 5

If 5 is added to the denominator

x +2 + 5

x-5/x+7= 1/4

Cross multiply the values

It becomes

4x- 20 = x+ 7

3x= 27

x= 9

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The value of the expression xy + z is 26 when x = 6, y = 4, and z = 2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

xy + z

The values are given as

x = 6, y = 4, and z = 2

The expression can then be represented as

xy + z = 6 * 4 + 2

Evaluate the product

So, we have

xy + z = 24 + 2

Evaluate the sum

So, we have

xy + z = 26

Hence, the value of the expression xy + z is 26 when x = 6, y = 4, and z = 2

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Equation that describes the relationship between a and c is c = 750 / a

The domain of the function is - 5 ≤ a ≤ 50

The range of the function is - 50 ≤ c ≤ 150

Given,

Total money spent is = $750

Thus, our equation become,

ca = 750

solving for c,

c = 750 / a

The domain and range of function is -

a ≤ 5

Now, each award should be less than 50.

= 50 ≤ c

using equation, ac = 750

maximum value for a = 75.

we can say that domain is

5 ≤ a ≤ 50

Finally, by substituting a = 5 we can see that the maximum for c is 150.

This gives range for c as -

50 ≤ c ≤ 150

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The solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7

The expression is given as

3 - 1/2d = 3/2d + 4 - d.

Multiply through the expression by 2

So, we have

6 - d = 3d + 8 - 2d

Evaluate the like terms

6 - d = d + 8

Evaluate the like terms

2d = -14

Divide by 2

d = -7

Hence, the solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7

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The sides of angle 4 will be side CD and side DG.

We are given a ray diagram.

We need to tell the sides or the rays of the angle 4.

an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

Here, angle 4 has the sides as CD and DG.

Therefore, the sides of angle 4 will be side CD and side DG.

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Using given algebraic equation, Keelan collected 431 tokens.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic statement is 2(x + 8y).

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic statement. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we may substitute those values for the original variables before evaluating the expression.

Given,

p=20x+75

p = 8695

8695 = 20x + 75

x = 8695 - 75 / 20

x = 431

Therefore Keelan collected 431 tokens.

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The absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).

It should be noted that from the information, we are to write an absolute value equation representing all numbers x whose distance from 5 is 3 units.

Therefore, the absolute value equation representing all numbers x will be illustrated as:

x - 3 = 5.

It should be noted that we will solve for x

Therefore, x - 3 = 5

Collect like terms

x = 5 + 3.

x = 8

Therefore, the absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).

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As A and B are vertical angles, the measures of angle A and B is 98° each.

When two lines collide, vertical angles are created. The angles that are directly opposite one another, out of the four that are generated, are vertical angles. Additionally, they are known as "vertically opposed angles." All of these angles are equal.

Vertical angles are created when two straight lines cross. Angles vertically are consistently congruent and equal. As the two sets of non-adjacent angles created by crossing two lines superimpose on one another, vertical angles are congruent.

As A and B are vertical angles,

6x - 16 = 4x + 22

⇒ 2x = 38

⇒ x = 19

Measure of Angle A is 98°

Measure of Angle B is 98°

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Answer:

d-(8,15)

Step-by-step explanation:

69497694646946464646463434644

Answer:

0.41

Step-by-step explanation:

The total number of half-dollar coins are in $28 given to children who come into your store is 56.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

You have $28, and you want to get half-dollar from the bank to give to children who come into your store.

According to given question we have

Half-dollar from the bank= $28

1/2 =28

1=28*2

1=56

So, the total number of half-dollar coins given to children who come into

your store is 56.

Therefore, the total number of half-dollar coins are in $28 given to children who come into your store is 56.

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Answer:

x=12

Step-by-step explanation:

Our equation: 3x + 4= 40

40-4=36. 36/3 = 12

The probability that at least one ball of each color is chosen is 105/8568.

Given that:-

Number of red balls in the urn = 5

Number of white balls in the urn = 6

Number of blue balls in the urn = 7

We have to find the probability that at least one ball of each color is chosen.

Let us consider the that 1 ball of each color has been chosen.

Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.

Now we have to choose 2 balls from them.

Hence,

Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = [tex]^{15}C_2=105[/tex]

Total number of ways in which we can choose 5 balls from 18 balls =

[tex]^{18}C_5=8568[/tex]

Hence,

Probability that at least one ball of each color is chosen = 105/8568

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Answer:

3872

Step-by-step explanation:

10,000 - 6,128 = 3872

use calculator man

Answer: The answer is B

The perimeter of the polygon is 12.

The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.

The distance between the two points A(x, y) and B(x₁, y₁ ).

AB = √ [ (x₁ - x)² + (y₁ - y)² ]

Consider the vertices U ( -1, 4), V (3, 4), W (3, 1).

Then,

UV = √ [ ( 3 +1)² + (4 - 4)² ] = √4² = 4

VW = √ [ ( 3 - 3)² + ( 1 - 4)² ] = √(- 3)² = 3

UW = √ [ ( 3 + 1)² + ( 1 - 4)² ] = √ [ ( 4)² + (-3)² ] = √ [ 16 + 9 ] = √25 = 5

Then the perimeter of the polygon will be:

perimeter = UV + VW + UW

perimeter = 4 + 3 + 5 = 12

Hence, the perimeter of the polygon is 12.

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Answer:

3

Step-by-step explanation:

11 = 3x+2
9 = 3x
x = 3

The point of discontinuity for y= x²-x-2 / 3 x²-7 x+2 is x= 1/3 and x= 2.

What is discontinuous function?

Mathematics, functions, and applications all place a premium on continuous functions. But not every function is continuous. A function is said to have a discontinuity there if it is not continuous at that point in its domain.

Given,

y = x²-x-2 / 3 x²-7 x+2

It can be expressed in the form of -

⇒ y = (x-2) (x+1) / (3x-1) (x-2)

The function will be undefined if the denominator will be 0

⇒ 3x-1 = 0

⇒ x = 1/3

⇒ x-2 = 0

⇒x = 2

So, we can conclude that the given function will be having points of discontinuity as x = 2, 1/3

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The mass ratio of the rocket is 10.8468 kg/C.

Given:

To find: Mass ratio (R) = ?

Finding:

On substituting the values of 'c', 't', 'v', we get:

6.9 = - 0.0098 (50) + 3.1 (ln (R) )

=> 6.9 + 0.49 = 3.1 (ln (R) )

=> 7.39 =  3.1 (ln (R) )

=> ln (R) = [tex]\frac{7.39}{3.1}[/tex]

=> R = [tex]e^{\frac{739}{310}}[/tex] ≈ 10.8468

Hence, the mass ratio of the rocket is 10.8468 kg/C.

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1) The converse of the function is; If not q, then p

2) The Inverse of the function is; If not p, then q.

3) The contrapositive of the function is; If q, then not p

Suppose we have a conditional statement, If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then; If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.

The conditional statement is given as;

If p, then not q.

1) The converse of the function is; If not q, then p

2) The Inverse of the function is; If not p, then q.

3) The contrapositive of the function is; If q, then not p

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The answer of the logarithmic form is -2 .

We have given an equation [tex]log_2\frac{1}{4}[/tex]   ..... (1)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{loh_ax}[/tex]  in equation (1) ,we get

     [tex]log_2\frac{1}{4}=\frac{log\frac{1}{4} }{log2}[/tex]                      ..(2)

[tex]log\frac{1}{4}[/tex] can be written as [tex]log1-log4[/tex] using property [tex]log\frac{a}{b} =loga-logb[/tex] whereas [tex]log1=0[/tex]

Then , the equation (2) becomes

       [tex]log_2\frac{1}{4}=\frac{log1-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{0-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{-log4 }{log2}[/tex]

[tex]log4[/tex] can be written as [tex]log2^2[/tex]

The equation (2) becomes

                    [tex]log_2\frac{1}{4}=\frac{-log2^2 }{log2}[/tex]                

   using property [tex]loga^b=bloga[/tex]

           [tex]log_2\frac{1}{4}=\frac{-2log2 }{log2}\\log_2\frac{1}{4}=-2[/tex]

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The measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.

Parallel segments are defined as lines on a plane that never meets.

The properties of parallel segments include:

Given the angles;

We can see that the two angles are vertically opposite angles and thus equal.

Then,

m∠JKL  = m∠PLK

substitute the values

10x + 5 = 12x - 1

collect like terms

10x - 12x = -1 - 5

-2x = - 6

Make 'x' the subject of formula

x = 3

But:

m∠JKL = (10x + 5)° = 10(2) + 5 = 25°

m∠PLK = (12x - 1)° = 12(2) - 1 = 23°

Thus, the measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.

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The inequality that represents the given situation is 13x - 9 > 4.5x + 8

From the question, we are to determine the inequality that represents the given situation

From the given information, we have that

The length of the laptop is given by 13x - 9 units

and

The width of the laptop is given by 4.5x + 8 units

If the length is greater than the width, then we can write that

13x -9 > 4.5x + 8

Hence, the inequality is 13x - 9 > 4.5x + 8

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