10. Find the area of the shaded region.
17 yd
5 yd
7 yd
6 yd
7 yd
4 yd

Following is the proof of BC||ED using alternate interior angles.

According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent.

We are given the ∠ABD = ∠FDB

and

∠1 = ∠4

using the above-given conditions we need to prove that line BC is parallel to line BD (i.e. BC || BD)

∠ABD = ∠FDB...................................(i)

∠ABD= ∠1 +∠2

and

∠FDB= ∠3+∠4

now subsituting these values of ∠ABD and ∠FDB in equation(i)

we get,

∠1 +∠2=∠3+∠4

we are also given that ∠1 = ∠4,  substituting that,

∠1 +∠2=∠3+∠1

= ∠2=∠3+∠1-∠1

= ∠2=∠3

through the given fig we know,

∠2=∠CBD

and

∠3=∠EDB

i.e.

∠CBD=∠EDB

∠CBD and ∠EDB make alternate interior angles of the lines BC and ED,

and since both the alternate interior angles are equal(∠CBD and ∠EDB) both the lines are parallel (||).

therefore we have BC||ED, hence proved.

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The constant proportionality is 3

What is Proportionality Constant ?

The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.

Now, We have the equation is:

y = 3xy

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k = y/x  or y = kx

To get the constant of proportionality,

we will derive both sides of the equation by x.

y/x = 3x/x

y/x = 3

Hence, The constant proportionality is 3

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4) The reason for the second step is division property of equality.

5) The reason for the second step is Multiplication property of equality.

6) The reason for the third step is because of substitution property of equality.

4) We are given that;

4x = -24

x = -6

Thus, the reason for the second step is division property of equality because both sides were divided by 4.

5) We are given;

(3x + 5)/2 = 7

Multiply both sides by 2 to get;

3x + 5 = 14

The reason is due to Multiplication property of equality.

6) We are given;

x = 4

y = 3x + 7

y = 3(4) + 7

The reason is because of substitution property of equality.

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The required coordinates are

Q'(-8, -9)

R'(-8, -1)

S'(-1, -10)

What is coordinate?

In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.

You want the coordinates of Q', R', and S' after rotating figure QRS 90° CCW. You are given Q(-9, 8), R(-1, 8) and S(-10, 1).

Rotation CCW 90°

The transformation that maps coordinates to their image after rotation 90° CCW is

 (x, y) ⇒ (-y, x)

The image points are

 Q(-9, 8) ⇒ Q'(-8, -9)

 R(-1, 8) ⇒ R'(-8, -1)

 S(-10, 1) ⇒ S'(-1, -10)

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Emma can play video games for 3 minutes using the available credits

Credit available with Emma = 3/4 credits

Credits required to play a video game for one minute = 1/4

Credits: In an electronic gaming setting, a value earned through the exchange of cash or currency equivalents is referred to as "gameplay credits." It can also be obtained through gaming as a prize. You can exchange gameplay credits for money or money equivalents.

Time Emma can play video games with the credits:

Credit available with Emma/Credits required to play video game for one minute

= (3/4)/(1/4)

= 3/4*4

= 3

So, she can play for 3 minutes

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The distance traveled by the tip of the minute hand in 45 minutes is approximately 256.77 mm, while the distance traveled by the tip of the hour hand in 1 hour is approximately 267 mm.

A) The hour needle completes a complete rotation of 12 hr, in 45 min = 0.75 hours, it will be 0.75 ÷ 12 of a complete rotation.

Given that the hour arrow's tip touches the rim of a clock, the radius of the clock is equal to the distance of the pointer.

The circumference of a circle is:

C=2 × π × radius

The span crossed by the hand in 12 hours is:

2 × 36=76π mm

The space traversed in 45 min is:

0.75 ÷ 12 × 72π=4.5π mm

in 45min, the min hand will make 45 ÷ 60=3 ÷ 4. If the min hand is 150% of the hour hand, then its length is 150 ÷ 100 × 36 = 54 mm.

As a result, the point of the minute will go around the complete circumference of a circle with a radius of 54 mm, implying that for a full circle, we will have:

2 × π × 54mm = 108π mm.

As a result, the minute hand's tip will have moved 45 minutes in 45 minutes, 108 × 3 ÷ 4 × π = 81π mm.

B) The clock's hour hand measures 30 mm.

As a result, the radius of the minute hand is,

1.5 × 30 = 45mm

And the minute hand moves after one hour 2π × ( r )²:

2 × 3.14 × 45 × 45 = 90π mm

And the minute hand moves,

π ÷ 6 × 30 = 5π mm

As a result, the minute hand moves,

90π - 5π = 85π mm

= 267 mm

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Answer:

P'   (3, 1)

Q'  (5, 1)

R'   (5, 4)

S'   (3, 4)

T'   (3, 3)

U'   (1, 3)

V'   (1, 2)

W'   (3, 2)

Step-by-step explanation:

What does it mean when a point is translated horizontally to the right by 6 units? That means its x coordinate is increased by 6 units, the y-coordinate is unchanged

(If it was translated 6 units to the left, it's x coordinate would decrease by 6 units)

So if we had a point say (1, 1) then its new x-coordinate will be (1+6, 1) or (7,1) The y-coordinate stays unchanged if the translation is horizontal

When a point is translated vertically by 6 units, its x-coordinate is unchanged but the new y coordinate is increased by 6 units (-6 units if the translation is vertically down)

So with a point (1, 1), an up translation will result in a new point (1, 7)

If both translations are applied both x and y coordinates will change to
(7, 7)

To figure out the new coordinates denoted by P'Q'R'S'T'  of each of the points PQRST of the  given figure:

Add 6 to the x-coordinate of each point and at the same time add 6 to the y-coordinate of that point

If you look at the graph, the original points and translated points for 6 units to right and 6 units up are
P(-3, -5)  which translates to P'(-3 + 6, -5 + 6) or P'(3, 1)

The other new points are calculated the same way by adding 6 to both x and y coordinates

Q(-1,  -5)  ==>  Q'(5, 1)

R(-1,  -2)   ==>  R'(5, 4)

S(-3,  -2)  ==>  S'(3, 4)

T(-3,  -3)   ==>  T'(3, 3)

U(-5,  -3)  ==>   U'(1, 3)

V( -5, -4)  ==>   V'(1, 2)

W(-3,  -4)  ==>  W'(3, 2)

The attached graph shows the translated figure with the translated points. Essentially the original figure has been shifted 6 units to the right and 6 units up

Answer:

29,340

Step-by-step explanation:

978 x 30 =29,340

Answer:20 in * (12 in - 2X in) * (X in) = 360 in3

This can be simplified by dividing both sides by 20 in:

20 in * (12 in - 2X in) * (X in) = (360 in3/ 20 in)

After dividing both sides by 20 in:

(12 in - 2X in) * X in = 18 in2

Distribute X in. across (12 in -2X in):

12X in2 - 2X2 in2 = 18 in2

1.Subtract 18 in2 from both sides:

12X in2 - 2X2 in2 - 18 in2 = 0

2. Rearrange the equation:

-2X2 in2 + 12X in2 - 18 in2 = 0

This for matches the form for a quadratic equation (Ax2 + Bx +C = 0)

You can then plug these values into the quadratic formula to solve for X

so your answer is X=3

Let's call a to the length of a side on the original polygon.

Let's call b to the length of the corresponding side to side a in the first photocopy. The length of b is: 0.3a (30% of a).

Similarly, c the length of the corresponding side in the second photocopy is: 0.3b = 0.3x0.3a = 0.09a

Then, the ratio of the corresponding sides of the second photocopy of the original to the sides of the original is 0.09:1

Answer:

Step-by-step explanation:

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y and an x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system. To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.  For example In algebra, 2-dimensional coordinate graphs have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a range of values cross these axes are called intercepts. The y-intercept is the place where the line crosses the y-axis and the x-intercept where the line crosses the x-axis. For simple problems, it is easy to find the x-intercept by looking at a graph. You can find the exact point of the intercept by solving algebraically using the equation of the line.

Hope this helped out!

If Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet

The gravel will be spread 3 inches deep

Here we have to convert the depth in inches to the depth in feet

To convert the inches to feet, we have to divide the inches by 12.

Then,

3 inches = 3/12 feet

= 0.25 feet

Hence, if Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet

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Answer:

24=24 ( associative property )

x + 210  = 1.15x        where x is the amount in their accounts in March....subtract x from both sides 210 = .15x   divide both sides by .15 x = $ 1400 Hope you get an A+ :))

Answer:

4x+3=12

Step-by-step explanation:

Let's evaluate the statements:

Supplementary angles: that means the sum of ∠K and ∠J is 180°.

Adjacent angles: that means that ∠K and ∠J common side and a common vertex.

So, let's observe the angles:

Given:

Linear pairs of angles are those two adjacent angles whose sum is 180°.

Answer: ∠K and ∠J are linear pairs.

y < 2

can't be y <= 2 or y<=1 because the dot is open meaning the point is not included.

the range is talking about the y value, the point is at y = 2. The graph is also negative; therefore, range will be anything less than y = 2

Step-by-step explanation:

21+3=24

1/3x+9=24

24-9=13

1/3x=13

13×1=13

3x=13

13/3=4.33

x=4.33

Answer:

p=1

Step-by-step explanation:

6p=2(5-2p)

6p=10-4p

Add 4p on both sides

10p=10

Divide 10 on both sides

p=1

Hello!

Let's solve:

   [tex]6p=2(5-2p)\\\\\text{Multiply 2 into the function in the parentheses}6p=10-4p\\\\\text{Add '4p to both sides}\\6p+4p=10-4p+4p\\10p=10\\\\\text{Divide both sides by 10}\\\frac{10p}{10} =\frac{10}{10} \\p=1[/tex]

Hope that helps!

The other endpoint is (7,10).

Assuming that your midpoint M = (x, y) and endpoint A = (x1, y1) are both present: Coordinates of the double midpoints are 2x, 2y. To find the x-coordinate of the missing endpoint, subtract the known endpoint's x-coordinate from the first value: x₂ = 2x - x₁.

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint.

An alternate solution would be to substitute (-1, 2)  for (x1,y1) and (3,6) for (x2,y2) into the midpoint formula:

(x - 1)/2 = 3

x -1 = 6

x =7

(y + 2)/2 = 6

y + 2 = 12

y =10

Solving each equation for (x2,y2) yields the solution (7,10).

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The probability that none of the employees in the sample work at the plant in hawai is 0.0112

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

PH= 20/60 = 1/3

P(T) = 2/3

It is hypergeometric distribution

P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},

where

N = 60

K = 20 for Hawai; 40 for Texas

n = 10

P(X=0) = 0.0112

Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112

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If at noon the price of Stock B was ​$12.67. It begins to decrease at the rate of ​$0.08 each hour. If the two rates​ continue, the number of hours that the prices of the two stocks be the​ same is 3.57 hours.

Let the hours when they equalize be h

Hence,

12.17 + .06h =12.67 - .08h

Combine like terms

.06h + .08h=12.67 - 12.17

.14h=.5

Divide both sides by .14h

h = .5/ .14

h = 3.57 hours

Therefore we can conclude at the number of hours is  3.57 hours .

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The total number of students surveyed by Omar in his school is 1000.

Here, we are given that Omar conducted a survey of some students in his school about their favorite color.

650 of those surveyed said their favorite color was blue.

Further, 65 percent of the students surveyed said their favorite color was blue.

Let the total number of students surveyed be x

Then, according to the given information,

65% of x is 650

Thus, we can form the following equation-

65/ 100 × x = 650

0.65x = 650

x = 650/ 0.65

x = 65000/ 65

x = 1000

Thus, the total number of students surveyed by Omar in his school is 1000.

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The value of f(-1) when f(x) = 2x + 2 will be 0.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this situation, we want to know the value of f(-1) when f(x) = 2x + 2. This will be Illustrated as:

f(-1) = 2x + 2

= 2(-1) + 2.

= -2 + 2

= 0

The value is 0.

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Answer:idek

Step-by-step explanation:

After inspecting the picture of the given graph, the range of the function is represented by the following set:

Inequality notation: - 5 ≤ y ≤ 0

Interval notation: y ∈ [- 5, 0]

Functions are characterized by the following three features:

In this question we find the case of a function with one input variable and one output variable. That is:

x → f(x)

After inspecting the picture shown in the image we notice that the range of the graph is formed by the following set:

Inequality notation: - 5 ≤ y ≤ 0

Interval notation: y ∈ [- 5, 0]

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The function formula of the mass of the bottle to the function of the volume of the oil is M = 590 - 0.95V

The glass bottle filled with oil weighs 590 grams.  

After Sophia uses 200 millilitres of oil, the bottle of oil weighs 400grams.

Therefore, the weight M of the bottle of oil in grams is a function of V, the volume, in millimetres of oil Sophia has used.

Therefore, the formula of the function can be represented as follows

density = mass / volume

200 mm reduces the weight of the bottle by 590 - 400 = 190 grams.

V mm will reduce  it to ?

cross multiply

190 × V / 200 = 19 / 20 V = 0.95V

where

V = volume of the oil reduced from the bottle

Therefore, the function formula will be as follows:

M = 590 - 0.95V

Where,

M = weight of the oil.

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not to intrude but is that big ideas math?

The rule for the reflection is (x, y) ---> (x+6, y).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.

Given:

The coordinates of L is ( -3, 6).

Now, after the reflection

The x- coordinates increases +6 units on right side.

and, y- coordinates remains the same.

Hence, the rule for the reflection is (x, y) ---> (x+6, y).

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