Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)

u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.

Thus, line segment UV ≅ line segment XY i.e UV = XY and as such the side lengths are as follows:

SU = VX = 43 feet.

For the congruent angles, we have:

<J ≅ <K i.e m<J = m<K

m<S = m<V = 38°.

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The value of the car in 2014 is 154709

The given parameters are:

Initial, a = 599,99

Rate, r = 7%

The value of the car in t years is

Value = a * (1 + r)^t

This gives

Value = 59999 * (1 + 7%)^t

2014 is 17 years from 1997.

So, we have:

Value = 59999 * (1 + 7%)^14

Evaluate

Value = 154709

Hence, the value of the car in 2014 is 154709

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Question 2

1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

Answer:

197.82 m^2

Step-by-step explanation:

The area of a circle is

a = πr^2  The radius is half of the diameter.  They give us the diameter so we need to talk half of that number to use for the diameter.  The diameter is the length from the center of the circle to the edge of the circle.

We will find the area of the big circle and  subtract out the area of the little circle to bind the blue area.

Outer circle

a = πr^2

a = 3.14(12)^2

a = 3.14(144)

a = 452.16

Inner Circle:

a = πr^2

a = 3.14(9)^2

a = 3.14(81)

a =254.34

Lastly, subtract 254.34 from 452.16 to get  197.82

The height of the center of the frame has to be 15ft.

Slope of the tarp is given as 2/5

The height is said to be 10 feet

The width is given as 25

25/2 = 12.5

AB/BC = 2/5

AB/12.5 = 2/5

cross multiply to find AB

5AB = 25

AB = 5

The height = 10 feet + 5 feet

= 15 feet

Hence the center of the frame has to be 15 feet.

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Answer:

  7.7 km

Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

  t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

  7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

This can be solved in two steps. First, we find angle P, then we use that to find length j.

  sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847

  P = arcsin(0.642847) ≈ 40.0045°

Now, we can find j:

  j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km

The distance from the tower to the plane is about 7.7 km.

__

Additional comment

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

Answer: The answer is factor 3 out the variable terms

Step-by-step explanation:

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

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As currently written, solving for [tex]x[/tex], we have

[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]

[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]

[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]

I suspect you meant to write

[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]

Move one of the roots to the other side, then take squares on both sides.

[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]

[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]

[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]

[tex]12 \sqrt{3 - x} = 24[/tex]

Take squares again

[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]

[tex]144 (3 - x) = 576[/tex]

[tex]432 - 144x = 576[/tex]

[tex]144x = -144[/tex]

[tex]\boxed{x = -1}[/tex]

Answer:

Breadth=8

Length=6

OR

breadth = 6

length=8

Step-by-step explanation:

Area of 4 walls = 2(l+b)h

112=2.4(l+b)

112/8=l+b

14=l+b

l=14-b

Area of base or ceiling=l x b

48=(14-b).b

48=14b-b²

b²-14b+48=0

factorize it and we get

(b-6)(b-8)=0

taking b-6=0

b=6

l=14-6

l=8

The correct option is B. Reread the directions for each section.

If you have time left after completing the test don't reread the directions for each section.

In order to find the various problem kinds and their point values during the test preview, you must read the complete test. Mark the questions that you can answer quickly and easily.

The benefits of previewing the test are-

Therefore, resolve each issue by re-entering the solution into the equation or performing the opposing operation needed to provide the appropriate response. Do not leave the testing room until the bell has rung or after you have gone over each problem twice.

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The complete question is-

All of the following are suggestions of things to do if you have time left after completing the test except

A. Look at your answer sheet to make sure its filled properly

B. Reread the directions for each section

C. Return to the questioms you were unsure of

D. Make sure your answers correspond to the correct questions

[tex] \frac{y}{x} = \frac{1}{ - 3} \\ - 3y = x[/tex]

[tex] - 3(2) = 6 = x[/tex]

The equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2

A quadratic function is represented as:

y = a(x - h)^2 + k

Question #6

The vertex of the graph is

(h, k) = (-1, 2)

So, we have:

y = a(x + 1)^2 + 2

The graph pass through the f(0) = -2

So, we have:

-2 = a(0 + 1)^2 + 2

Evaluate the like terms

a = -4

Substitute a = -4 in y = a(x + 1)^2 + 2

y = -4(x + 1)^2 + 2

Question #7

The vertex of the graph is

(h, k) = (2, 1)

So, we have:

y = a(x - 2)^2 + 1

The graph pass through (1, 3)

So, we have:

3 = a(1 - 2)^2 + 1

Evaluate the like terms

a = 2

Substitute a = 2 in y = a(x - 2)^2 + 1

y = 2(x - 2)^2 + 1

Question #8

The vertex of the graph is

(h, k) = (1, -2)

So, we have:

y = a(x - 1)^2 - 2

The graph pass through (0, -3)

So, we have:

-3 = a(0 - 1)^2 - 2

Evaluate the like terms

a = -1

Substitute a = -1 in y = a(x - 1)^2 - 2

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

Hence, the equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2

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The equation of parabola from graph is y = a(x + 1)² - 4.

According to the statement

we have to determine the parabola equation from the graphical representation.

So,

For this purpose we know that

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

The general equation of parabola is y = a(x-h)2 + k

And The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

So, The equation of parabola from graph is y = a(x + 1)² - 4.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.

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Answer:

first option

Step-by-step explanation:

two solutions means 2 cutting points

The time it will take before your investment is worth $6000 = 7 years

The amount of money invested per month = $150

Therefore the amount principally invested yearly;

= 12 × 150 = $1,800

Simple interest = $6000

Rate = 4%

Time = ?

Using the formula for Simple interest (SI)= P×T×R/100

Make T the subject of formula,

T = SI × 100/P×R

T = $6000×100/1800×4

T = 600000/7200

T= 83 months/ 12 = 7 years

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Answer:

(x+11), (y+15)

Step-by-step explanation:

the point v gets translated 11 points to the right, so the translation is x+11.

Point v also gets translated 15 points up, so the translation is y+15

The machine produces 3000 nails in the month of April 2007.

Production of Nails in the Month of April

According to the given information,

Number of nails manufactured per day by the machine, x = 300  

And, we know that April is the fourth month of a year which has total 30 days.

Hence, number of days the machine is manufacturing nails in the month of April, y = 30

So, the number of nails that will be produced by the machine in the month of April is given by,

N = Number of nails produced per day × Number of days in April

N = xy

N = 300 × 30

N = 9000

Therefore, the machine produces 9000 nails in the April month of year 2007.

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Answer:

Shark

Step-by-step explanation:

They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.

======================================================

Further explanation:

The probability of a student taking a math class or a physics class is [tex]0.85[/tex] when the probability of a student taking a math class is [tex]0.70[/tex], the probability of taking a physics class is [tex]0.30[/tex], and the probability of taking a math class and a physics class is [tex]0.15[/tex]

How can we find the probability of taking math class or a physics class ?

Given in the question probability of the student taking class

[tex]p(M)=0.70\\p(P)=0.30\\p( M and P)=0.15[/tex]

So we use the probability union intersection formula

[tex]p(M or P)=p(M)+p(P)-p(M and P)[/tex]

Substitute the values

[tex]p(M or P)=0.7+0.3-0.15\\=0.85[/tex]

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The value of f from the given expression is 3

Given the expression below

cos(22f-1) = sin(7f+4),

This can also be expressed

cos(22f-1) = cos(90-7f-4)

cos(22f-1) = cos(86-7f)

22f - 1 = 86 - 7f

Collect the like terms

22f+7f = 86 + 1

29f = 87

f = 3

Hence the value of f from the given expression is 3

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The best that describes the type of association shown in the scatter plot is positive linear association.

Given the scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.

Amount of Food per day cups:

20

40

60

No

We are required to find the type of association shown in the given scatter plot.

It is a positive linear association. The slope is positive so the linear association is also positive and linear mean generally in a line not on a curve like a nonlinear association.

Hence the given graph is of positive linear association.

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#1

h(2.5)

After 2.5s the ball was at 47ft

#2

g(0)

g(4)

g(7)

Range

#3

Answer: (0, 3)

Step-by-step explanation:

     The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.

Answer: (3, 0)

Step-by-step explanation:

y-intercept = y=a number and x=0

So, y=3, x=0.

(3, 0)

The diagram ends at -2

The equation would be 2-4 = -2

Answer:

Step-by-step explanation:

Start on point 2

Ends on point -2

Then:

2 + a = -2

a = -2 - 2

a = -4

then the equation is:

2 + (-4) = 0

2 - 4 = 0

The missing angle of the right trapezoid is 126°.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. The trapezoid is a quadrilateral that presents at least one set of parallel sides and the sum of the internal angles is 360°. The trapezoid classifications are:

From the figure, it is possible to see that the image has two right angles. Thus, you have a right trapezoid.

Therefore, from the sum of internal angles, you can find the missing angle:

u+54+90+90=360

u=360-234

u=126

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Answer: 2x + 6y + 22 units

Step-by-step explanation:

The perimeter of a figure is the total length of all the sides of a figure.

Therefore, the perimeter can be found by adding up all the lengths of the figure.

Suppose that P is the perimeter of this figure, then

[tex]P = x+4+x+4+3y+7+7+3y\\[/tex]

Combining like terms, we get

[tex]P = 2x + 6y + 22[/tex]

Since we do not have any information on what the variables are, this is the perimeter of the figure.

The best explanation for the formula is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

The area of a sector of a circle equals measure of the central angle subtended by the sector over the angle measure of a full circle multiplied by the area of the circle.

A full circle has an angle measure of 360 degrees.

The area of a circle = pi(r²).

Therefore, the formula for the shaded sector of a circle would be represented by the formula: ∅/360 × πr².

Here, we have:

Central angle (∅) = measure of angle ZYX

Measure of full circle = 360 degrees

Area of a circle = πr². (area formula for the circle that contains the sector)

Therefore, the statement that best explains the formula, (m∠ZYX)/360 × πr², used for finding the shaded sector in the circle is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

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Answer:

its the first answer "The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector."

Step-by-step explanation: i got it right because im smort

There are 12 motorcycles in a company.

According to the statement

The ratio of cars, trucks, and motorcycles is 4:3:2.

The total number of cars and trucks is 42.

then

4x + 3x =42

7x = 42

x = 6.

now put these values in the ratio of vehicles.

Number of cars = 4*6 = 24

Number of truck = 3*6 = 18

Number of motorcycle  = 2*6 = 12

So, There are 12 motorcycles in a company.

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