The perimeter of a rectangular garden is 40 it. The length is 2 ft more than the width. Find the length and the width of the garden.

Answer:

1 5/6

Step-by-step explanation:

1 1/3 = 4/3

4/3 + 1/2 = 8/6 + 3/6 = 11/6 =1 5/6

Answer:

the answer I got is 25/6

Step-by-step explanation:

22/6+3/6 since 22/6 and 3/6 have the same denominator add them by adding their numberators

22+3/6 add 22 and 3 to get 25

25/6

Answer:

-107, -14, -9, 16, 34, 87, 147

Answer:

−107,−14,−9,16,34,87,147

With the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects.

Circles that overlap share certain characteristics, whereas circles that do not overlap do not.

Venn diagrams are useful for showing how two concepts are related and different visually.

When two or more objects have overlapping attributes, a Venn diagram offers a simple way to illustrate the relationships between them.

Venn diagrams are frequently used in reports and presentations because they make it simpler to visualize data.

So, we need to find:

A ∪ B

Now, calculate as follows:

The collection of all objects found in either the Blue or Green circles, or both, is known as A B. Its components number is:

8 + 7 + 14 + 6 + 1 + 8 = 44

n(A∪B) = 44

Therefore, with the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

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Answer:

16800

Step-by-step explanation:

The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

The roots of the given quadratic equation are 5 and -4

Quadratics are the polynomial equation which has the highest degree of 2. Also, called quadratic equations.

Given is an equation 3x²-13x-10 = 0, we need to solve by using completing the square method,

The given equation is =

3x²-13x-10 = 0

3(x²-13x/3-10/3) = 0

3(x²-2x·13x/6-10/3) = 0

Adding and subtracting (13/6)²

3(x²-2x·13x/6+(13/6)²-(13/6)²-10/3) = 0

3[(x-13/6)²-169/36-10/3] = 0

3[(x-13/6)²-289/36] = 0

(x-13/6)²-289/36 = 0

(x-13/6)² = 289/36

Taking roots,

x-13/6 = ±17/6

x = 17/6+13/6

x = 5

Or,

x = -17/6+13/6

x = -4

Hence, the roots of the given quadratic equation are 5 and -4

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The domain of the function consists of all real numbers greater than 0.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Next, we would determine the function which models the amount of gas as follows:

Function, f(x) = rate × x

Function, f(x) = 2.25 × x

Function, f(x) = 2.25x

Based on the function above, we can reasonably and logically deduce that the amount of gas cannot be negative. Therefore, the domain of this function is given by:

Domain = [0, ∞]

In conclusion, the domain is equal to all real numbers that are greater than zero (0).

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Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

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Answer:

4, 15, 16, 17, 19, 21, 22

Step-by-step explanation:

The length of the pen is 2√3 feet

The formula for calculating the area of a rectangle is expressed according to the formula below:

Area of a right triangle = 1/2 * base * height

A = 1/2 bh

Given the following parameters

Area = 20 square feet

If the height is five times the length, then;

h = 5b

Substitute

A = 1/2 bh

A = 1/2(b)5b

30 = 1/2(5b²)

60 =5b²

b² = 12

b = 2√3

Hence the length of the pen is 2√3 feet

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Answer:

18cm

Step-by-step explanation:

Given:

- The length of AB is 9 centimeters

- A dilation with a scale factor of 2

The length of the image AB after the dilation is applied:

9 x 2 = 18

dilation is used to make an image or in this case AB, with a scale factor of 2 means that its doubling in size. If the scale factor was 1/2 that it would be decreasing in size since it will be half of the original size

The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

(6/6) x (7/7) + (6/7) x (6/6) / 2

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer:X= 6X-14

Step-by-step explanation:

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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So, first we have to put in an equation

9/20+ 2 9/10

multiply 9/10 by 2

So you get 9/20+ 2 18/20

Add the fractions together and you'll get 26/20

since their isn't a whole number a whole number it's just 2 and 26/20 reduce it to

2 and 9/5

I hope this is right. This is how I was taught.

Answer:

D

Step-by-step explanation:

i did the assignment.

The correct solution of the system of the equation is -3y = 3.

The correct option is D.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x – 5y = 6    {equation 1}

–x + 2y = –3    {equation 2}

In order to solve the equations, using linear combination method.

Combining the two equations 1 and 2 to eliminate one of the variables x.

Adding both the equations,

-3y = 3

y = -1.

Therefore, –3y = 3 is the solution.

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Answer:

Step-by-step explanation:

Solve for the equation equal to y

\(3x+4y=12\\4y=-3x+12\\y=\frac{-3}{4}+\frac{12}{4}\)

The slope here is -3/4. The slope of a line perpendicular to the original has a negated and inverted slope. Therefore the slope is 4/3

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

\(1. \: 405352 \: cm = 4.05352 \times {10}^{5} \: cm\)

___o___o___

2. 7.6352 x 10-3 kg ( This is scientific notation) [ If you want —> Standard notation]

7.6352 x 10^ -3 kg = 0.0076352 kg

__o_o___

\(3. \: \: 3.1 \times 10 ^{4} mm + 4.87 \times {10}^{5} \: mm \\ 0.31\times 10 ^{4} mm + 4.87 \times {10}^{5} \: mm \\ = 5.18 \times {10}^{5} \: mm\)

____o___o___

\(4. \: \: (4.8 \times {10}^{5} \: km) \times (2.0 \times {10}^{3} \: km ) \\ = 9.6 \times {10}^{8} \: km\)

____o____o____

\(5.(3.3 \times{10}^{ - 4}\: ml)\div(1.1 \times {10}^{ - 6}\: ml) \\ \\ \frac{3.3 \times {10}^{ - 4} \: ml}{1.1 \times {10}^{ - 6} \: ml} = \frac{33 \times {10}^{ - 4} \: ml}{11 \times {10}^{ - 6} \: ml} \\ \\ = \frac{33 \times {10}^{ - 4 + 6} }{11} ml \\ \\ = 3 \times {10}^{2} \: ml\)

I hope I helped you^_^

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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The radius of the circle, marked p on the diagram, is approximately 5.8 cm.

Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.

The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.

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The value of x which is the dimension of the eternal part of the secant segment is 4.

The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment".

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the diagram:

tangent segment = 6

External part of the secant segment = x

Secant segment = ( 5 + x )

Plug the given values into the above formula and solve for x.

( tangent segment )² = External part of the secant segment × Secant segment.

( 6 )² = x × ( x + 5 )

36 = x² + 5x

x² + 5x - 36 = 0

Using AC method:

( x - 4 )( x + 9 ) = 0

( x - 4 ) = 0 or ( x + 9 ) = 0

x = 4 or x = -9

Since we are dealing with dimensions, we take the positive value.

Hence:

x = 4

Therefore, the value of x is 4.

Option D) 4 is the correct answer.

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Answer: C=40

Step-by-step explanation: X=40 APPLES PER BOX.  

PROOF:

2+.25*40=12

2+10=12

12=12

Answer:

Step-by-step explanation:

You want to identify the given shapes as a regular or irregular polygon, or neither.

A regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.

Polygon E is a regular polygon.

A polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.

Any simple polygon that is not a regular polygon is an irregular polygon.

Polygons A, B, D are irregular polygons.

A circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.

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Answer:

m = 5

Step-by-step explanation:

A quadratic function is in the form \(ax^{2} +bx+c\).

To factor an equation, you are looking for two numbers that multiply to c (are factors of c), and add to b. In this case, c = -15, and b = 2.

The factors of -15 include 1, 3, 5, 15, -1, -3, -5, and -15.

After looking through the possible combinations, we can come to the conclusion that the only factors that multiply to -15 and add to 2 are 5 and -3, as 5 x -3 = -15, and 5 + -3 = 2.

You can now plug these numbers into the factored form (x + factor1)(x + factor2).

This then becomes (x + -3)(x + 5) or (x - 3)(x + 5).

Therefore, m = 5.

Answer:

12

Step-by-step explanation:

n(AUB) = n((A) + n(B) – n(AnB)

Step 1:

Identify the values for each function of the formula. n(A) = 10, n(B) = 5, n(AnB) = 3

Step 2:

Replace each function with its values

n(AUB) = n(A) + n(B) – n(AnB)

n(AUB) = 10 + 5 – 3

Step 3:

Carry on the simple arithmetic

n(AUB) = 10 + 5 – 3 (follow the BODMAS method)

= 15–3

= 12

Therefore, the n(AUB) is 12

The unit of the rate of change is (b) dollars per month

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

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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