identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures. m∠acd

The distance from the given point to the given line is d = 13/5 units.    

Given:

To find:

So,

Let us define line L as follows:

Choose A as the fixed point on line L with the coordinates ( m, k ).

The line L now gives the coordinates of any point (x, y):

That was accomplished by subtracting the coordinates (x,y) from (m,k).

The dot product of constants (a, b) to vector coordinates between points (x,y) to (m,k):

For the above expression to be true, the dot product of two orthogonal vectors must be zero.

As a result, vector (a, b) is always perpendicular to every vector pointing in the direction of line L.

The vector is:

It could be the line connecting the points (x_1, y_1) and (m, k).

The magnitude of the scalar projection of v onto a gives the distance d from the point P 1: (x_1, y_1) to the line L because the latter is the duration of the side of a right triangle with two vertices being P_1 and (m, k), and the other vertex lying on L.

So:

In which point A (m,k) is on the line;

Then,

Given a point P (-2,3) and a line L, the equation is 3x - 4y + 5 = 0.

Where.

Now, calculate:                  

Therefore, the distance from the given point to the given line is d = 13/5 units.    

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The correct question is given below:
Use scalar projection to show that the distance from a point P1(x1,y1) to the line ax+by+c=0 is |ax1+by1+c|/underfoot(a^2 +b^2)

Use this formula to find the distance from the point (-2,3) to the line 3x-4y+5=0

Answer:

Equations

expression

inequality

equation

expression

equation

Step-by-step explanation:

An expression does not have an equal sign.

An equation does have an equal sign

Inequality has a > or< symbols

Answer: It would take the bug 26min to clime the pole

Step-by-step explanation: For me I drew a pole and labeled it like a number line.

1. use or make a number line and plot 0-10 on it.

2. jump 2 points from 0 on the number line

3. Jump backwards once to make the equation accurate

4. plot the times it takes along the way to find the answer until you get to 10

I hope

Answer: 1.29 x 104 lbs.

Step-by-step explanation:

4.23 x 103 lbs. and 8.7 x 103 lbs.

4.23 x 103 + 8.7 x 103 =

4.23 x 10^3 + 8.7 x 10^3 =

(4.23+8.7) x 10^3 =

(4.23+8.70) x 10^3 =

(12.93) x 10^3 =

1.293 x 10 x 10^3 =

1.293 x 10^1 x 10^3 =

1.293 x 10^(1+3) =

1.293 x 10^4 =

1.293 x 10^4 = 1.29 x 104 lbs.

The total weights of the two animals in scientific notation is

13.32 x 10² lbs

What is scientific notation ?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

According to the given question,

First animal weight 4.23 x 103 lbs

Second animal weigh 8.7 x 103 lbs

adding both the animal weights

= 4.23 x 103 + 8.7 x 103

= (4.23 + 8.7 ) x 103

= 12.93 x 103

= 1331.79 lbs

converting into scientific notation

= 13.3179 x 10² lbs  (rounding off)

≈ 13.32 x 10² lbs

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Step-by-step explanation:

(a)

First:

Get AE using Pythagoras

[tex] {ae}^{2} = {6}^{2} + {8}^{2} [/tex]

[tex] {ae}^{2} = 100[/tex]

AE =10

Connect OM to form Traingle AOM.

AM=5cm (AE is 10 and AM=ME meaning that they are divided into two equal parts)

AM^2=OM^2+AO^2

5^2=OM^2+4^2

OM^2=5^2-4^2

OM=3

(B) OM is parallel to BE because of midpoint theorem

The Theorem states that The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

(C) AOM is a right angled triangle at O because angle AOM is 90°. Because OM is a perpendicular Line that bisects the chord of AB

Answer: A=-1/12

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}+(-\frac{5}{6} )+\frac{1}{4}=\\\\\frac{1*6-5*2+1*3}{12} =\\\\ \frac{6-10+3}{12}= \\\\\frac{-1}{12}= \\\\-\frac{1}{12}[/tex]

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

Given,

The distance where the football landed from where it was kicked = 100 feet

The maximum height that the football reached =  125 feet

We have to write an equation that models the path of the ball while it was in the air.

The path may be parabola.

So, equation is like:

y = a·(x - h)² + k

Where;

(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)

Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;

The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)

We have;

The coordinate of the highest point reached by the ball = (50, 125)

Therefore;

(h, k) = (50, 125)

Substituting the above values in the equation of the parabola gives;

y = a·(x - 50)² + 125

At x = 100, y = 0, which gives;

0 = a·(100 - 50)² + 125 = a·2500 + 125

0 = a·2500 + 125

a = -125/2500 = -0.05

Therefore, we have;

y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125

y  = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x

y =  -0.05·x² + 5·x

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

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Answer:

5,4

Step-by-step explanation:

According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

A parabola is an U-shaped mirror-symmetrical planar curve. It matches a variety of seemingly dissimilar mathematical formulations, all of which identify the same curves. A point and a line are two ways to describe a parabola.

Apollonius, who discovered numerous features of conic sections, is credited with the name "parabola." It signifies "application," referring to the "application of regions" notion, which, as Apollonius demonstrated, has a connection with this curve. Pappus is responsible for the focus-directrix attribute of the parabola as well as other conic sections.

given equation:  y=X² -2x+8

on solving the equation:

y==X² -2x+8

X² + 4x -2x -8

x(x - 4) -2(x - 4)

-1(x-2)(x+4)

According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

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Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.

We are given that:

Jack has 150 feet of Barb wire.

The fencing is:

35 3/4 feet that is equal to

= 140 / 3 feet

For each foot the Barb wire will be calculated by dividing the total Barb wire by the wire required for fencing.

So, we get that:

Barb wire used for each foot = 150 ÷ 140 / 3

Barb wire used for each foot = 450 / 140

Barb wire used for each foot =  = 45 / 14

Barb wire used for each foot = 3 3/14 feet.

So, Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.

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-120... I would be easier if you used a scientific calculator

Answer:   24

Step-by-step explanation:

[Solve brackets first]

[tex](-7--9)\\-7+9 = 2[/tex]

[Perform the multiplication]

[tex]8[/tex] x [tex]2 = 16[/tex]

[Finally do the Addition]

[tex]16 + 8 = 24[/tex]

General Rule:

Brackets Indices Division Multiplication Addition Subtraction

[tex]Negative + Negative = Positive \\Negative + Positive = Negative[/tex]

As we first choose a cluster of the store before surveying all of the customers present in the store, they employed cluster sampling in this instance.

A population is divided into several clusters that are representative of homogeneous traits and have an equal chance of being included in the sample using the sampling technique known as cluster sampling.

Cluster sampling using a single stage: As the name implies, sampling only happens once.

Two-stage cluster sampling: In this case, a small number of individuals are chosen from each group by means of systematic or simple random sampling rather than the entire cluster.

Multiple stage cluster sampling: Compared to two stage sample, multiple stage cluster sampling goes one or more steps beyond. Complex clusters must be formed in order to conduct effective research across several geographies, and this can only be done by employing the multiple-stage sampling technique.

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Answer: 97°

Step-by-step explanation:

∠XWY = 153°

∠2 = 56°

∠1 = ?

∠XWY-∠2=∠1

153°-56°=?

? = 97°

The total balance remaining on Joshua's game card is $4.5. So, the correct option is (A).

In the Question, It is given that Joshua purchase a game card for $18 which makes the Balance Bal = $18 on his card.

Now, He played 2 rounds of Basketball hoop and each costs $3.25 which makes total for Basketball B = 2*3.25 => B = $6.25

And, He played 4 rounds of Air Hockey each game cost $1.75 which makes the total for Air Hockey A = 4*1.75  => A = $7

To calculate the remaining balance on his card we need to subtract these games' costs from the balance on his card :

=> T = Bal - B - A, Where T = Total, Bal = Balance on card, B = Basketball, A = Air Hockey

=> T = 18 - 6.25 - 7    => T = $4.5

Hence, the Total balance remaining on his card T = $4.5

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The equation of the line is [tex]5y+4x-35=0[/tex]

Given,

Point is (5,3)

Slope m=-4/5

so formula of  equation of line is

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-3)=-4/5(x-5)[/tex]

[tex]5y-15=-4x+20\\5y+4x-15-20=0\\5y+4x-35=0[/tex]

A line's equation can be formed using the slope of the line and a point on the line. To better understand the formation of a line equation, let us learn more about the slope of the line and the required point on the line. The slope of a line is its inclination with respect to the positive x-axis, and it is expressed as a numeric integer, fraction, or the tangent of the angle it makes with respect to the positive x-axis. The term "point" refers to a coordinate system point with the x and y coordinates.

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Answer:

23

Step-by-step explanation:

38/13 = 3

69/3 = 23

After the rotation of the point, we get the point as (5, 2)

We are given a point:

C (2, -5)

We first need to rotate it 180°.

When rotating a point 180 degrees counterclockwise about the origin our point A(x, y) becomes A'(-x, -y). So all we do is make both x and y negative.

So, we get the point as:

( - 2 , 5 )

Now, we need to rotate it 270°

The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x).

So, we get the point as:

(5, 2)

Therefore, after the rotation of the point, we get the point as (5, 2)

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We get that the absolute inequality will be | x + 16 | < 8.

We are given two inequalities:

x < - 8 and  x > 24

We need to write one inequality by combining both the inequalities.

We know that:

x < - 8 means that x can have any value less than - 8

x ∈ ( - ∞ ,  - 8 )

Also, x > 24 means that:

x ∈ ( 24 , ∞ )

So, combining these, we get that:

x = ( - ∞ ,  - 8 ) U ( 24 , ∞ )

Inequality will be:

| x + 16 | < 8

Therefore, we get that the absolute inequality will be | x + 16 | < 8.

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The area of a Dragon's kite with the given dimensions is 6 square feet.

Given that, team Dragon's kite is 4 feet long and 3 feet across.

We need to find how much fabric it takes to make their kite.

The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal.

The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is Area = ½ × d1 × d2. Here d1 and d2 are long and short diagonals of a kite.

Now, the area of Dragon's kite = 1/2 × 4 × 3=6 square feet.

Therefore, the area of a Dragon's kite with the given dimensions is 6 square feet.

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Answer:

(l) y=2x-2

(ll) y=4x+1

(lll) y=5x+13

(lV) y=-3x-6

(V) y=-5x-17

(Vl) y=(2/3)x-3

It will take the object 1/5 hour to travel 2 1/5 mi

The given parameters are

Speed = 9 4/5 mi/h

Distance = 2 1/5 mi

The time is calculated as

Time = Distance/Speed

So, we have

Time = (2 1/5)/(9 4/5)

Approximate the factors

Time = (2)/(10)

Evaluate

Time = 1/5

Hence, it will take the object 1/5 hour to travel 2 1/5 mi

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The correct sequence of the steps required to construct the bisector of [tex] \angle{A}[/tex] is presented as follows;

The game given steps and their number of appearance in the question photo are;

1. Label the intersection of the arcs in the interior of the angle as point D.

2. Without changing the opening of the compass, place the point of the compass at point C and draw another arc in the interior of the angle

3. Place the point of the compass on point B and draw an arc in the interior of the angle

4. Use the straight edge to draw [tex] \overrightarrow{AD}[/tex]

5. Place the point of the compass at point A and draw an arc that intersects the sides of [tex] \angle{A}[/tex]. Label the points of intersection as points B and C.

The correct order of the steps required to construct the bisector of [tex] \angle{A}[/tex] is as follows;

Step 5 → Step 3 → Step 2 → Step 1 → Step 4

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It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

Now,

Hence, It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

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The pharmaceutical company uses the quantitative variable to conducts an experiment.

Variables:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Given,

A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.

And  the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.

Here we need to find the kind of variable is the company​ studying.

Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.

So, the experiment uses the Qualitative Variable.

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Answer:

6 yards

Step-by-step explanation:

Answer:

[tex]5\frac{3}{4}[/tex]

Step-by-step explanation:

bottom is below, so we use a negative number

[tex]bottom = -3\frac{1}{2}\\top = 2\frac{1}{4}\\distance = top - bottom = 2\frac{1}{4} - (-3\frac{1}{2}) = 2\frac{1}{4} + 3\frac{1}{2} = 5\frac{3}{4}[/tex]

Answer:

1) 4

2) 16

Step-by-step explanation:

The total length of the bridge built is less than the total length of the bridge.

We are given;

Length of bridge to be built per day = 54 feet

Number of days they built the bridge = 9 days

Thus, to find the total length that the bridge will span, we multiply the length built each day by the number of days. Thus;

Total Length of bridge = (54 * 9)

Total Length of bridge = 486 ft

Since we want to find if the bridge is at least 490 feet long. Thus, the total length of the bridge built is less than the total length of the bridge.

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The width of the rectangular mat is 7/10 units.

We know that the area of rectangle is A = length × width

For given question,

Let w be the width of the rectangular mat and l be the length of the rectangular mat.

The length of the mat is 5/6.

⇒ l = 5/6

A rectangular mat has an area of 7/12.

⇒ A = l × w

⇒ 7/12 = 5/6 × w

⇒ w = 7/12 × 6/5

⇒ w = 7/10

Therefore, the width of the rectangular mat is 7/10 units.

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Answer:

108cm^2

Step-by-step explanation:

Find the areas of the rectangle and the two triangles. Then add all three areas together. See image.