Find the area of the figure

The two unknown integers can be found by graphing the given equations. The larger integer is 10, and the smaller integer is 8.

Let's represent the larger integer as 'x' and the smaller integer as 'y.' According to the given information, we have two equations:

Equation 1: 2x + 3y = 46

Equation 2: x^2 + 4x = 20y + 5

To solve this system of equations, we can graph both equations on the same coordinate plane. The point where the two graphs intersect will give us the values of 'x' and 'y' that satisfy both equations simultaneously.

For equation 1, we rearrange it to y = (46 - 2x)/3. Plotting this equation on the graph, we see a straight line.

For equation 2, we rearrange it to x^2 + 4x - 20y - 5 = 0. Plotting this equation, we get a quadratic curve.

By examining the graph, we can see that the two lines intersect at a point where 'x' is approximately 10 and 'y' is approximately 8. Therefore, the larger integer is 10, and the smaller integer is 8.

By substituting these values back into the original equations, we can verify that they satisfy both equations.

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The set of all partitions of a positive integer n, denoted as P(n), forms a partially ordered set (poset) under the relation of set inclusion (≤).

In part (a), we show that (P(n), ≤) satisfies the properties of a poset. In part (b), we draw the Hasse diagram for P(6) to illustrate the partial order. Whether (P(n), ≤) forms a lattice for all n depends on the specific values of n.

a) To show that (P(n), ≤) is a poset, we need to verify three properties:

Reflexivity: Every partition is included in itself, so for any partition A in P(n), A ≤ A.

Antisymmetry: If A ≤ B and B ≤ A, where A and B are partitions in P(n), then A = B.

Transitivity: If A ≤ B and B ≤ C, where A, B, and C are partitions in P(n), then A ≤ C.

These properties hold for the relation of set inclusion, thus establishing that (P(n), ≤) is a poset.

b) The Hasse diagram for P(6) represents the partial order of the partitions of 6. The partitions are depicted as nodes, with an upward-directed edge connecting A to B if A is included in B (A ≤ B). The diagram illustrates the hierarchy of partitions based on the inclusion relation.

Whether (P(n), ≤) forms a lattice for all n depends on whether it has both a least element (bottom element) and a greatest element (top element). For P(n), if n is greater than 1, there is no unique greatest element since there can be multiple ways to partition n. Therefore, (P(n), ≤) is not a lattice for all values of n.

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Step-by-step explanation:

Subtract

20

from both sides of the equation.

x

2

−

4

x

=

−

20

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of

b

.

(

b

2

)

2

=

(

−

2

)

2

Add the term to each side of the equation.

x

2

−

4

x

+

(

−

2

)

2

=

−

20

+

(

−

2

)

2

Simplify the equation.

Tap for more steps...

x

2

−

4

x

+

4

=

−

16

Factor the perfect trinomial square into

(

x

−

2

)

2

.

(

x

−

2

)

2

=

−

16

Solve the equation for

x

.

Tap for more steps...

x

=

2

±

4

i

Answer:

2.5mi

Step-by-step explanation:

?/20 = 1/8

^ If you turn into a percentage you get 1/8 = 12.5%

so now the question is v

what is 12.5 percent of 20?

which is 2.5

I WOULD CHECK FIRST, NOT 100 PERCENT SURE

Answer:

58-51

why to have the speed of a cucumber you need a potato on a skateboard at 1000kmh, ok?

Answer: 4 I think

on each side it has 4

Answer:

Step-by-step explanation:

the formula for a circle is pi(r^2) where r is the radius. the diameter is 16 so 16/2 =8. substitute 8 for the radius to get pi(8^2). 8^2=64 so you have pi(64).

pi(64)= approximately 201.06

Answer:

A & C

Step-by-step explanation:

If you substitute the first coordinate (which is the x coordinate) for x in the function and set it equal to the y, options A and C should satisfy the function.

Answer:

The multiplicative rate of change is 3/4

Step-by-step explanation:

Here, we want to get the multiplicative rate of change

In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change

mathematically, we have this as;

81/128 divided 27/32

= 81/128 * 32/27

= 3/4

Answer: Its y=-1.

Step-by-step explanation:

Answer:

8 hours of labor at 45 dollars an hour, plus the 98 dollars for parts equal 458

Answer:

No. of students enrolled in Health = 63

No. of students enrolled in P.E. = 181

Step-by-step explanation:

Given,

Total students in grade seven = 244 students

A.T.Q.

Let the number of students enrolled in Health be x

so, The number of students enrolled in P.E. = 3x - 8

As we know,

x + (3x - 8) = 244

4x = 244 + 8

x = 252/4

x = 63

Thus, the number of students enrolled in Health = 63

The number of students enrolled in P.E. = 3x - 8

= 3 * 63 - 8

= 189 - 8

= 181 students

Answer:

What

Step-by-step explanation:

I dont understand what you are asking

6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx. To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x).

To find a curve that passes through the point (1, 5) and has an arc length on the interval [2, 6] defined by the expression 6S²V1 + 16x dx, we can follow these steps:

Step 1: Determine the general form of the curve equation.

Step 2: Use the arc length formula to obtain an equation involving the curve's equation.

Step 3: Solve the resulting equation to find the specific curve.

Let's proceed with each step:

Step 1: Determine the general form of the curve equation.

Let's assume the curve equation is y = f(x), where f(x) represents the unknown function describing the curve.

Step 2: Use the arc length formula to obtain an equation involving the curve's equation.

The arc length formula for a curve defined by y = f(x) is given by:

S = ∫[a,b] √(1 + (f'(x))²) dx

We are given that the arc length on the interval [2, 6] is defined by the expression 6S²V1 + 16x dx. Substituting the formula for arc length, we have:

6∫[2,6] (√(1 + (f'(x))²))²dx + 16∫[2,6] x dx

Simplifying, we get:

6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx

Step 3: Solve the resulting equation to find the specific curve.

Since the expression 6S²V1 + 16x dx represents the arc length on the interval [2, 6], we need to equate it to the arc length formula obtained in Step 2.

6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx

To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x). Without such information, it is not possible to determine the specific curve. Please provide additional constraints or information if available to proceed further in finding the specific curve.

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Answer:

-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

-12 times 1/3.

It's pretty much just -12x1, then divided by 3.

-12x1 is equal to -12.

Your equation is now simplified, making it easier to solve.

Your equation is: [tex]\frac{-12}{3}[/tex]

-12 divided by 3 is -4, because when a negative number is divided (or multiplied) by a positive number, the quotient (or product) is negative.

-12 x (1/3) = -12/3 = -4.

Answer:

48 square units

Step-by-step explanation:

Each square on the grid is 2 units by 2 units.

Bases: AT = 8; RS = 4

Height: 8

area = (b1 + b2)h/2

area = (8 + 4)(8)/2

area = 48 square units

Answer:

The area of trapezoid is 48 sq units.

Step-by-step explanation:

According to the question,

➻ Trapezoid is consist of many square shapes. Each grid square equals 2 units. We need to find the area of trapezoid.

➻ To find area we need to find the length if base and height of trapezoid.

Calculate the square grids to find base and height. we get.

Base ; SR = 4 units and TA = 8units

Height = 8 units.

Finding the area of trapezoid.

We know that,

Area of trapezoid = ( Base1 + Base2 ) ×Height / 2

plug the values of both base and a height.

Area of trapezoid = ( 4 + 8 ) × 8 / 2

Add the numbers which are in bracket and multiply by 8.

Area of trapezoid = 12 × 8 / 2 = 96/2

Divide 96 by 2.

Area of trapezoid = 48 sq units.

Hence,

The area of trapezoid is 48 sq units.

Answer:

24

Step-by-step explanation:

Shiloh is building a tree house

It's measurement is 6ft by 4ft

Therefore the area can be calculated as follows

= 6×4

= 24

Hence the area of the rectangle is 24

Answer:

15ft

Step-by-step explanation:

Answer: no sol

Step-by-step explanation:

bro there is no pic to do so  im just going to say...

(1) x = -2 y = -8

(2) x = -1 y = -4

(3) x = 0 y = 0

(4) x = 1 y = 4

(5) x = 2 y = 8

Those are the answers for what y is so now i think you have to plug it in to the right side of the chart

Answer:

here go the answer hope it help

Step-by-step explanation:

The cook made 280 pieces of chicken altogether.

the diagram is  like this :

Grilled chicken: [#####] [#####] [#####] [#####] [#####] ,

Fried chicken:   [##] [##]  

The ratio of grilled chicken to fried chicken is 5:2, which means for every 5 pieces of grilled chicken, the cook made 2 pieces of fried chicken.

To model this ratio, we can use a bar diagram with five sections for the grilled chicken and two sections for the fried chicken,

If the cook made 80 pieces of fried chicken, we can use this ratio to calculate the number of pieces of grilled chicken.

First, we need to find out how many sets of 5:2 there are in 80. We can do this by dividing 80 by 2 and then multiplying by 5:

80 ÷ 2 = 40

40 × 5 = 200

So the cook made 200 pieces of grilled chicken.

To find the total number of pieces of chicken, we just need to add the grilled and fried chicken together: 200 + 80 = 280 .

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Answer: 0.3

Step-by-step explanation:

There are 20 practice jerseys in total.

Six of those 20 jerseys arrived late.

The fraction of jerseys that arrived late is therefore:

= 6 / 20 jerseys

Convert them to decimal form by dividing the numerator with the denominator:

= 6 ÷ 20

= 0.3

The shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.

When you slice a given object vertically (perpendicular to the ground level), then the sliced surface is called vertical cross section.

For a cylinder, usually it sits on its base and we take a right circular cylinder. When we slice it vertically, we obtain a rectangle, as shown in the figure attached below.

It can be proven that this shape is always going to be rectangular.

Thus, the shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.

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a) The mean and standard deviation need to be determined for the given data on the number of ways each sum can be obtained when rolling three dice.

b) A frequency polygon can be drawn to represent the data.

c) Whether the data has a normal distribution or not needs to be determined, and an explanation is required.

a) Mean and Standard Deviation: The mean can be calculated by summing up the products of each value and its corresponding frequency, then dividing by the total frequency. The standard deviation can be calculated by finding the square root of the variance, where the variance is the sum of the squared differences between each value and the mean, divided by the total frequency.

b) Frequency Polygon: A frequency polygon can be plotted by taking the sum values on the x-axis and the corresponding frequencies on the y-axis. Points are plotted for each sum value, and then lines are drawn to connect these points to form the polygon.

c) Normal Distribution: To determine if the data follows a normal distribution, one can visually analyze the frequency polygon. If the polygon displays a symmetric, bell-shaped curve, it suggests a normal distribution. However, if the polygon is skewed or does not exhibit a bell shape, the data is unlikely to have a normal distribution.

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Answer:

54 minutes

Step-by-step explanation:

3:14 = 3 × 60 = 180 + 14

= 194

2:20 = 2 × 60 = 120 + 20

= 140

194 - 140

= 54