Help. I don't understand this.. thanks

Using the formula for finding area of a rectangle we can get the area of the shaded region = 106 sq. meters.

Given,

Dimension of rectangle .

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter.

The area of a rectangle is determined by multiplying its length by its width (breadth).

Hence, the area of a rectangle is equal to length × width

Here, in the given figure,

area of the small rectangle = length × breadth

= 7 × 2

= 14 sq. meters

Now area of the shaded region

12 × 10

=120 sq. meters.

Therefore, area of the shaded region = 120 - 14

= 106 sq. meters

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The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

$324

Step-by-step explanation:

8.10 x 40 is 324, meaning she'll have 324 dollars in the 40 hours of working.

Answer:

324

Step-by-step explanation:

If Eve is paid 8.10 an hour, and she works for 40 hours, then it will be 8.10 x 40 = 324

Answer:

7y

Step-by-step explanation:

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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Sylvia and Patrick gathered information on the weight of cars and the mileage they get, and then proceeded to plot the data on a graph.

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use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

Answer:

18

Step-by-step explanation:

2×(4 - 1) ^2

2 ×3 ^2

2 ×9

18

Answer:

y = 3/4x - 8/3

Step-by-step explanation:

y = 3/4x + b

1/3 = 3/4(4) + b

1/3 = 3 + b

-8/3 = b

Answer:

y=3/4x-8/3

Step-by-step explanation:

y-y1=m(x-x1)

y-1/3=3/4(x-4)

y-1/3=3/4x-12/4

y-1/3=3/4x-3

y=3/4x-3+1/3

y=3/4x-9/3+1/3

y=3/4x-8/3

Answer:

The correct option is;

An isosceles trapezoid with legs of length 8

Step-by-step explanation:

The correct option is an isosceles trapezoid with legs of length 8

The given properties of the quadrilateral are;

1) One pair of equal opposite sides

2) One pair of parallel opposite sides

From the given options, the two options which are not parallelograms are the kite and the trapezoid

However given that the option of the kite has a pair of adjacent side of length 8, with the given pair of equal length opposite side of length 8, we have that all the sides of the quadrilateral will be of length 8, and the figure cannot be a kite

An isosceles trapezoid of leg length 8 has one pair of equal length opposite sides of length 8 and one pair of parallel sides of unequal length

Given that the length of the lines that make up the pair of opposite parallel sides in the figure are not specified, the figure can be described by as being an isosceles trapezoid.

Answer:

I think its $1000

Step-by-step explanation:

if she earned $12 the 1012-12=1000

Answer:

I really don't know much but this is what I know

If she has $12 dollars in interest and a year later she has $1012 making it so she earned EXACTLY $1,000 in the time being.

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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In the figure, the value of m∠ABE is 115.5 and the value of  m∠DBE is 25.5

In geometric term, right angle, tells us of an angle that precisely measures 90 degrees. A square corner is formed when two lines or line segments meet at a 90-degree angle, signifying their perpendicularity within a right angle.

Note that  90 is right angle

ABE = 180-64.5

= 115.5

DBE = 90-64.5

= 25.5

Or it can still be obtained by:

90 - 64.5 = 25.5  for angle DBE

90 + 25.5 = 115.5  for angle  ABE

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The interger is closest to 20 is 19 or 21

BIM  is isosceles. So, MB = MI.

What is the Isosceles triangle ?

The other confines of the triangle, similar as its height, area, and border, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of harmony along the vertical bisector of its base.

The two angles opposite the legs are equal and are always acute, so the bracket of the triangle as acute, right, or blunt depends only on the angle between its two sides.

This is just angle chasing. Let A equal to angle BAC, B equal to angle CBA, C equal to angle ACB,

and note that A, I, M are collinear (as L is on the angle bisector). We are going to show that MB = MI,  the other cases being similar.

First, notice that

∠MBI = ∠MBC + ∠CBI = ∠MAC + ∠CBI = ∠IAC + ∠CBI = 12 A + 12 B.

However,

∠BIM = ∠BAI + ∠ABI =12 A + 12 B.

Hence,  BIM  is isosceles.

So,  MB = MI.

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Triangle BIM is isosceles, so, MB = MI.

Given that I denote A1, which is the mid point of BC.

An isosceles triangle is a triangle that contains two equal sides. Sometimes it's specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The two equal sides are known as the legs and the third side is known as the base of the triangle.

The two angles opposite the legs are equal and are always acute, so the bracket of the triangle as acute, right, or blunt depends only on the angle between its two sides.

This is just angle chasing. Let A equal to angle BAC, B equal to angle CBA, C equal to angle ACB,and note that A, I, M are collinear (as L is on the angle bisector). We are going to show that MB = MI,  the other cases being similar.

First, notice that

∠MBI = ∠MBC + ∠CBI = ∠MAC + ∠CBI = ∠IAC + ∠CBI = 12 A + 12 B.

However,

∠BIM = ∠BAI + ∠ABI =12 A + 12 B.

Hence,  BIM  is isosceles.

So,  MB = MI.

Hence triangle BIM is isosceles, so, MB = MI.

Question is incomplete. The question should include:

Prove that MB=MI.

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Answer:

x = 5

Step-by-step explanation:

The diagram shows that the rhombus is split into two isosceles triangles, LKM and NMK.  

Thus, the three angles in triangle LKM are 110, (8x - 5), and (8x - 5).

Thus, we can solve for x by setting the sum of the measures of the three angles in triangle LKM equal to 180:

(8x - 5) + (8x - 5) + 110 = 180

(8x + 8x) + (-5 - 5 + 110) = 180

16x + 100 = 180

16x = 80

x = 5

Thus, x = 5

Optional step:

We can check that we've correctly solved for x by plugging in 5 for x in (8x - 5) twice for both angles, adding the result to 110, and seeing if we get 180 on both sides of the equation:

(8(5) - 5) + (8(5) - 5) + 110 = 180

(40 - 5) + (40 - 5) + 110 = 180

35 + 35 + 110 = 180

70 + 110 = 180

180 = 180

Thus, x = 5 is correct.

The difference between exponential function and logarithmic function is their graph shows mirror image of each other.

A function of the form is a logarithmic function. It can be read as "y equals the log, base b, of x" or "y equals the log of x, base b." X > 0 and b > 0 and b 1 in both forms. y is not constrained in any way.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. An essential mathematical function of the form is the exponential function. f(x) = a^x.

Examples of exponential functions include 2x, 10x, and ex; they have the form axe, where an is a constant. The cube root function, for example, "undoes" the cube function: 323=2. The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo" the exponential functions.

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Answer:

4x(x+5)

Step-by-step explanation:

factor out the 4x out of the 4x^2

Answer:

196 miles

Step-by-step explanation:

To find the distance that the bus drives, we can use the formula:

distance = rate x time

where rate is the average speed and time is the duration of the trip.

In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:

3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours

Now we can plug in the values into the formula:

distance = rate x time

distance = 56 mph x 7/2 hours

We can simplify by multiplying 56 by 7 and then dividing by 2:

distance = (56 x 7) / 2 = 196 miles

Answer:

53

Step-by-step explanation:

(5x+3)+(3x+7)=90

5x+3+3x+7=90

5x+3x+3+7=90

8x+3+7=90

8x+10=90

8x=90-10

8x=80

x=80/8

x=10

----------------------

5x+3=5(10)+3=50+3=53

Given a zero of the polynomial function, find the remaining zeros. Then, write the polynomial as a product of linear factors (in completely factored form). f(x) = x^3 - x^2 + 9x - 9; zero: 1

Since 1 is a zero of the polynomial, we can use synthetic division to find the other zeros.

1 | 1  -1  9  -9
    |    1   0  9
   -----------------
      1   0  9   0

The quotient is x^2 + 9, which is a quadratic equation. To find the remaining zeros, we can set this equation equal to zero and solve:

x^2 + 9 = 0

This equation has complex roots, as there are no real numbers that will satisfy this equation. We can find the complex roots by using the square root of -1, denoted as "i":

x^2 = -9
x = ±√(-9)
x = ±3i

The remaining zeros are 3i and -3i. The polynomial in completely factored form is:

f(x) = (x - 1)(x + 3i)(x - 3i)

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Answer:

that will be 225 ... I think

Answer:

x = 3

Step-by-step explanation:

the axis of symmetry is a vertical line passing throught the vertex with equation

x = c ( where c is the value of the x- coordinate of the vertex )

vertex has coordinates (3, - 1 ) with x- coordinate 3 , then

equation of axis of symmetry is x = 3

Answer:

Your Answer is D. x = 3

Step-by-step explanation:

The axis of symmetry is x = 3.

I have copied your graph to appear to be this equation.

y = 2 * (x-3)^2 - 1

The correct option is C: Cluster around a horizontal line when graphed are distributed equally along both axes.

A level within a phase is defined as a set of observations that cluster around a horizontal line when graphed. This means that the data points tend to remain relatively constant or steady during that particular phase.

When plotted on a graph, these observations form a horizontal line, indicating little variation or change. This stability implies that the system or process being observed is in a balanced state, with minimal fluctuations or disturbances.

The horizontal line represents a steady state, indicating that the system or process being observed is maintaining a consistent level without significant fluctuations or trends.

A stable level is characterized by a consistent and predictable pattern, which can be useful in analyzing and understanding the behavior of the system or process over time.

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Answer:

9.1

Step-by-step explanation:

Let,

hypotenuse = 12.3 cm

perpendicular = 8.2 cm

base = y cm

(hypotenuse)^2 = (perpendicular)^2 + (base)^2

(12.3)^2 = (8.2)^2 + y^2

151.29 = 67.24 + y^2

151.29 - 67.24 = y^2

.: y^2 = 84.05

y = √84.05

y = 9.1

Answer:

3XY

Step-by-step explanation:

i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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The probability of machine A breaking down in a year is 0.05.

The probability that neither machine breaks down in a 10-year period is approximately 0.605.



a) Since the probability of both machines breaking down is the product of their individual probabilities, we have:

P(A and B) = P(A) * P(B) = x * 0.01 = 0.0005

Solving for x, we divide both sides of the equation by 0.01:

x = 0.0005 / 0.01 = 0.05

Therefore, the probability that machine A breaks down in any given year is 0.05.

b) The probability that neither machine breaks down in a given year is the complement of the probability that either one or both machines break down. Since the events are independent, we can multiply the probabilities:

P(Neither A nor B breaks down) = P(A' and B') = P(A') * P(B') = (1 - 0.05) * (1 - 0.01)

To calculate the probability over a 10-year period, we raise the result to the power of 10:

P(Neither machine breaks down in a 10-year period) = (1 - 0.05) * (1 - 0.01)^10 ≈ 0.605

Therefore, the probability that neither machine will break down in a 10-year period is approximately 0.605.

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