In the parallelogram below, find the length of the segment GM.

Answer:

20

Step-by-step explanation:

A=a+b

2h=6+2

2·5=20

Answer:

16.4

Step-by-step explanation:

Separate it into a triangle and a rectangle.

The rectangle will be 2, 5 and the triangle will be 4, 5, and x with a right angle.

The area of the rectangle section is 10, and the area of the triangle is 6.4.

6.4 + 10 = 16.4.

Answer:

3

Step-by-step explanation:

Since you need to find the y value when x = -1, go to -1 on the x axis, and find where the green line crosses. The green line goes through the point (-1,3), or one box to the left and three boxes up, so the y value is 3.

Hopefully this helps- let me know if you have any questions!

Answer:Find the point in which the x = 1, and the y  point meets.

When x = 1, y = 2

2 is your answer for y

hope this helps

Step-by-step explanation:

The fractions in the options are equivalent to the fraction 18/8, except the option

D; 6/4

A fraction is a representation of a part of an item, by the expressing the proportion consisting of a numerator, divided by a numerator, between which is the divisor bar.

The fraction is; 18/8

Therefore, we get; 18/8 = (2 × 9)/(2 × 4)

The like terms indicates that we get;

(2 × 9)/(2 × 4) = 9/4

Therefore; 18/8 = 9/4

The above fraction is an improper fraction, therefore, we get;

9/4 = (2 × 4 + 1)/4 = 2 1/4

However; 18/8 = (2 × 18)/(2 × 8) = 36/16

Therefore, the numbers in the options A, B, and C are equivalent to the fraction 18/8

The fraction 6/4 is not equivalent to the fraction 18/8

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Hi there!

\( \large{tan35\degree = \frac{x}{16} }\)

We can also use the other angle but I will focus on 35°.

The reason why we use the equation above because tan is equivalent to opposite/adjacent

From the picture, the opposite is x-term while the adjacent is 16 if we focus angle 35°.

Define theta = 35°. Thus, the equation would be tan35° = x/16.

Solving the equation, you might want to bring open Trigonometric Table or a calculator to calculate tan35°. You should get 0.7 (rounded)

\( \large{0.7 = \frac{x}{16} }\)

Then solve the equation for x-term.

\( \large{0.7 \times 16 = x} \\ \large{x = 11.2}\)

Hence, the value of x is 11.2

Answer

Questions about the problem be asked through comment.

Furthermore, you can also use the other angle. If we use 55° instead, the equation would be tan55° = 16/x. The outcome would be the same.

Hope this helps, and Happy Learning! :)

The area of a regular octagon with sides 1/3 the length of sides of the larger octagon is 173.82 ft sq.

The area of a polygon = n side^2 / (4 tan(180/n))

where "n" is the number of sides

To calculate area for side = 2

area = 8 x 2^2 / (4  tan(180/8))

area = 32 / (4  tan(22.5))

area = 32 / 4 x 0.41421

area = 19.3138746047

To calculate area for side = 6

area = 8*6^2 / (4 * tan(180/8))

area = 288 / 1.65684

area = 173.824871442

173.824871442 / 19.3138746047 =  9

So, the area would be 9 times larger.

Therefore, if we increase the side length is increased by 1/3, then the area increases by 1/9.

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Answer:

36b + 30n

Step-by-step explanation:

1. solve your like terms inside the parentheses to get 6(6b + 5n)

2. distribute the 6 on the outside, to get 36b + 30n

:)

Answer:

1.

x=3,y=0

2.

x=-3,y=3

3.

x=-9,y=-9

Step-by-step explanation:

1.

y=x-3

or

x-y=3   ...(1)

y=-2x+6

2x+y=6   ...(2)

(1)+1(2) gives

3x=9

x=9/3=3

y=3-3=0

2.

-x+5y=18  ...(1)

x+4y=9   ...(2)

(1)+1(2) gives

9y=27

y=27/9=3

x+4(3)=9

x=9-12=-3

3.

3x+5y=-72   ...(1)

2x+3y=-45

2(1)-3(2) gives

6x+10y-6x-9y=-144+135

y=-9

2x+3(-9)=-45

2x=-45+27=-18

x=-18/2=-9

Answer: I believe your answer is the median.

Step-by-step explanation:

Answer:

C: median

hope this helps

Step-by-step explanation:

BCE+DCE=90

BCE WHICH IS 21

So, 21+DCE=90

GROUPING OF LIKE TERMS

DCE=90-21

DCE=69

The slope of the line passing through the points (4, -2) and (6, -8) is -3.  A slope of -3 means that the line is steeply downward-sloping, slanting from the point (4, -2) towards the point (6, -8).

To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), we can use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Let's apply this formula to the given points (4, -2) and (6, -8):

x₁ = 4, y₁ = -2

x₂ = 6, y₂ = -8

Substituting these values into the slope formula, we have:

m = (-8 - (-2)) / (6 - 4)

Simplifying the numerator and denominator:

m = (-8 + 2) / 2

m = -6 / 2

m = -3

The slope represents the rate of change of the line. In this case, a slope of -3 means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 3 units. This indicates a downward or negative slope.

We can also interpret the slope as the ratio of the vertical change (change in y) to the horizontal change (change in x) between the two points. In this case, for every 2-unit increase in the x-coordinate, there is a 6-unit decrease in the y-coordinate.

It's important to note that the slope is a measure of the line's steepness and direction but does not provide information about the line's position or length.

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If the first-year teacher wants to retire in 40 years and plans to invest in an account with a 5.67% annual interest rate compounded continuously, retiring with at least $100,000 in the account, they must initially invest A) $10,352 (present value).

The present value for continuous compounding is given by the formula: P = A / e^rt.

This present value that is required to earn a future value of $100,000 can be determined using an online finance calculator as follows:

Total P+I (A): $100,000.00

Annual Rate (R) = 5.67%

Time (t in years): 40 years

Result:

P = $10,351.9

= $10,352.

Thus, to have $100,000 in 40 years, the teacher should invest $10,352 now.

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Answer:

Ah Thanks so much

Step-by-step explanation:

I am so bored by the way...

Answer:

daaslkfnsdlfknsdfnsdnfsdf

Step-by-step explanation:

The expected time for the activity in the network diagram is 7 weeks, and the variance is 1 week.

In project management, the expected time and variance of an activity can be calculated using the PERT (Program Evaluation and Review Technique) formula. The formula takes into account the optimistic time estimate (O), the most likely time estimate (M), and the pessimistic time estimate (P).

To calculate the expected time (TE) for the activity, the formula is as follows: TE = (O + 4M + P) / 6. In this case, the optimistic time estimate is 5 weeks, the most likely time estimate is 7 weeks, and the pessimistic time estimate is 12 weeks. Plugging these values into the formula, we get (5 + 4 * 7 + 12) / 6 = 7 weeks.

The variance (V) of the activity can be calculated using the formula: V = ((P - O) / 6)^2. Substituting the values, we have ((12 - 5) / 6)^2 = 1 week squared.

Therefore, the expected time for the activity in the network diagram is 7 weeks, and the variance is 1 week.

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Answer:

Step-by-step explanation:

Let the length be x and the width be y

The perimeter of a rectangle is give as ; 2 ( L + B) , that is

We know the perimeter formula would be 440=2x+2y. And the area will be A=x*y

We can to take the derivative of the area formula to find where it is a max but we must first substitute something in from the first formula so we only have one variable.

440-2x=2y

220-x=y

A=(x)*(220-x)

A=220x-x^2

Now we take the derivative:

A'=220-2x (set equal to 0 and solve)

0=220-2x

2x=220

x=110 

Then when we plug this into the perimeter formula, we can solve for y

440=2x+2y

440=2(110)+2y

440=220+2y

220=2y

y=110

So both the length and width are 110 yards, and the area would be 12,100 square yards

Answer:

Step-by-step explanation:

Answer:

b. 0.225

Step-by-step explanation:

tan = opposite / adjacent

opposite of A is 9

adjacent of A is 40

9/40=0.225

The simplification of the given fraction which is solved as a fraction would be =-13/12

A fraction is defined as the expression that represents the whole of a value in the form of a numerator and denominator.

The fraction given;

-8/24+ -18/24

The Lowest common denominator of the given fraction is 24

= -8-18/24

= -26/24

= -13/12

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The sequence of Transformations involved to form ∆A′B′C′ is a reflection over the y-axis, followed by a translation to the right 6 units.

The graph shows two triangles plotted on a coordinate plane.

One triangle is at A (minus 4, 2), B (minus 6, 2), and C (minus 2, 6).

Another triangle is at A prime (2, 2), B prime (4, 2), and C prime (0, 6). ∆ABC goes through a sequence of transformations to form ∆A′B′C′.

The sequence of transformations involved is a reflection over the y-axis, followed by a translation to the right 6 units. The steps to get from ∆ABC to ∆A′B′C′ are as follows:

Step 1: Reflection over y-axis: This transformation can be done by replacing the x-coordinates of each point with their opposites, or by drawing perpendiculars from each point to the y-axis and reflecting them across the y-axis. In either case, the new points are A(-(-4),2) = A(4,2), B(-(-6),2) = B(6,2), and C(-(-2),6) = C(2,6).

Step 2: Translation to the right 6 units: This transformation involves adding 6 units to each of the x-coordinates of the reflected triangle. The new points are A'(2+6,2) = A'(8,2), B'(4+6,2) = B'(10,2), and C'(0+6,6) = C'(6,6).

Therefore, the sequence of transformations involved to form ∆A′B′C′ is a reflection over the y-axis, followed by a translation to the right 6 units.

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Answer:

50

Step-by-step explanation:

because 250 g = 20 cookies

500g = 40 cookies

625 = 50 cookies

120 g = 20 cookies

240 g = 40 cookies

360 g = 60 cookies

but you only able to make 50 from butter so the answer is 50

The number of cubes Lucy should add is 8.

In mathematics, an equation is a formula that expresses the equivalency of two expressions, by connecting them with the equals sign = .

Given that, a visage balance has 3 cells on one visage and 11 cells on the other visage.

The equation to represent the situation is 3 c = 11

The result of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, c = 11- 3

c = 8

thus, the number of cells Lucy should add is 8.

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The average is approximately 49.56.

To find the average of the given numbers, we add them up and divide the sum by the total count of numbers. Let's calculate it:

45.97 + 61.32 + 57.89 + 39.04 + 51.44 + 41.67 = 297.33

There are 6 numbers in total.

Now, we divide the sum by 6 to find the average:

297.33 / 6 = 49.555

Rounding to the nearest hundredth, the average is approximately 49.56.

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Answer:

See below ~

Step-by-step explanation:

Let :

Two inequalities created are :

Solving

Let the people paying $15 be "x" and $25 be "y"

1st inequality

15(x) + 25(x) ⩾ $1500

2nd inequality

x + y ≤ 100

Allow the adhesive to cure for a few minutes.7. If the patch is still visible, dye it or cover it with fabric paint to conceal it.

The best method of repair for a fabric-covered surface which has an L-shaped tear, each leg of which is approximately 14 inches long, is to use a patch, as the tear is too long to repair using a simple needle and thread.What is a patch?A patch is a piece of fabric or other material that is used to repair a hole or other damage in a larger piece of fabric. When it comes to covering holes or tears, patches can be quite useful.Patching processIt's time to patch the fabric once you've gathered all of the supplies. It's a fairly straightforward operation. Here's how to do it.1. Take a scrap piece of the same material as your torn fabric, making sure it's a few inches larger than the tear.2. Trim the patch down to the size of the tear, allowing for a margin of error of about half an inch on all sides.3. Apply adhesive to one side of the patch, making sure it's evenly distributed and covers the whole area.4. Put the patch on the wrong side of the torn fabric, ensuring that the adhesive side is facing the fabric.5. Smooth out the patch, working from the center outwards, to eliminate any air bubbles and ensure that the edges are fully adhered.6. Allow the adhesive to cure for a few minutes.7. If the patch is still visible, dye it or cover it with fabric paint to conceal it.

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Answer:

10s-14

Step-by-step explanation:

Perimeter of rectangle = 2s+2(4s-7)

                                      = 2s+8s-14

                                      = 10s-14

= > Perimeter of rectangle = 2(l + b)

= > 2(s + 4s - 7)

= > 2(5s - 7)

= > 10s - 14...ans

Step-by-step explanation:

There is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

In two- or three-dimensional space, a curve is a mathematical object that symbolises a continuous, smooth path. Curves can be derived from geometric operations, parametric equations, or mathematical equations. They are commonly used to simulate real-world processes in physics, engineering, mathematics, and many other disciplines.

To find the level curve of value c for the given surface \(z = f(x, y) = (x^2/4) + (y^2/25) = c\), where c < 0, follow these steps:

Step 1: Write down the equation of the surface.
\(z = f(x, y) = (x^2/4) + (y^2/25)\)

Step 2: Replace z with the constant c.
\(c = (x^2/4) + (y^2/25)\)

Step 3: Rearrange the equation to isolate \(y^2\).
\(y^2 = 25(c - (x^2/4))\)

However, note that we're given that c < 0. This means that the value inside the parentheses (c - (\(x^2/4\))) must also be negative. Since y^2 can't be negative, there's no real solution for this equation.

In conclusion, there is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

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It is the picture down below

Answer:

Step-by-step explanation:

The value of P is approximately $94,759.68 for the present value (P) that amounts to $310,000 after 18 years, invested at an annual interest rate of 7% compounded semi-annually.

We can use the formula for the future value of an investment compounded semiannually, FV = P(1 + r/n)^(n*t), where FV is the future value, P is the present value, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, FV is $310,000, r is 7%, n is 2 (compounded semiannually), and t is 18.

Rearranging the formula to solve for P, we have

P = FV / (1 + r/n)^(n*t). Plugging in the given values, we get

P = $310,000 / (1 + 0.07/2)^(2*18), which simplifies to P ≈ $94,759.68.

Therefore, if $94,759.68 is invested at an annual interest rate of 7% compounded semiannually for 18 years, it will accumulate to approximately $310,000. This is the present value required to achieve the desired future value.

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Answer:

The area of the room is 432 square feet

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The scale drawing of the room is 1 inch: 3 feet

→ That means each 1 inch in the drawing represents 3 feet in real

∵ The drawing is 8 inches long by 6 inches wide

∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→  inches  :  feet

→  1            :  3

→  8           :  L

→  6           :  W

→ By using the cross multiplication

∵ 1 × L = 8 × 3

∴ L = 24

∴ The actual length of the room is 24 feet

∵ 1 × W = 6 × 3

∴ W = 18

∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

∵ Area of rectangle = length × width

∴ Area of the room = 24 × 18

∴ Area of the room = 432 feet²

∴ The area of the room is 432 square feet

She ran faster on Thursday running at 7.5 mph which is 0.3 mph faster than 7.2 mph speed on Wednesday

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Speed is the ratio of total distance travelled to total time taken. It is given by the equation:

Speed = distance / time

1 hour = 60 minutes

She ran 6 miles in 50 minutes.

50 minutes = 50 min * 1 hr per 60 min = 5/6 hr

Speed on Wednesday = distance / time = 6 miles / (5/6)hr = 7.2 mph

She ran 4 miles in 32 minutes.

32 minutes = 32 min * 1 hr per 60 min = 8/15 hr

Speed on Thursday = distance / time = 4 miles / (8/15)hr = 7.5 mph

Difference in speed = 7.5 mph - 7.2 mph = 0.3 mph

She ran faster on Thursday

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