A system of linear equations is given by the tables. one of the tables is represented by the equation . x y 0 5 3 6 6 7 9 8 x y -6 9 -3 8 0 7 3 6 the equation that represents the other equation is y = x . the solution of the system is ( , )

Step-by-step explanation:

1. Not neccesarily true

2. Not necessarily true

3. True because angles in a triangle add to 180°

4. Not necessarily true

5. True because the medians are being constructed, and the three medians of a triangle are always concurrent.

6. Not necessarily true

The statements that are true about the triangle are:

Option C: m∠P + m∠Q + m∠R = 180°

Option E: PT, QU, and RS intersect at the same point.

1. m∠Q = m∠R: This is not true because there is no indication that the angles are equal.

2.The length of QU is half the length of RP: This is not true because there is no length given to show that measurement.

3. m∠P + m∠Q + m∠R = 180°:

This is true because the sum of angles in a triangle add to 180°

4. QU ≅ RS:

This is not true because we are not told that they are congruent

5. PT, QU, and RS intersect at the same point:

This is true because the medians are being constructed, and the three medians of a triangle are always concurrent.

6. The sum of the lengths of QU and RS is equal to the length of PT: This is not true because we are not told that.

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The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.

The net change in latitude of the helicopter can be evaluated as follows;

x = |-6.20° - 22.27°| = |-28.47°|

x = 28.47°

The net change in longitude of the helicopter can be evaluated similarly as follows;

y = |106.80° - 114.15°| = |-7.35°|

x= 7.35°

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Answer: 0=-4.9t²+19.6t+24.5

Step-by-step explanation:

[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]

A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

From the question, we have the following highlights:

From the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph

This is so because the points on the graph are connected by a straight line.

Linear graphs have constant rate

Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

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Complete question

The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?

Answer:

1. 3 terms; degree 5

2. 2 terms; degree 3

3. 9mn³ + 14mn²

4. 9a^4b^3

Step-by-step explanation:

Problems 1 - 2:

Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.

The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.

The degree of the polynomial is the same as the degree of the term with the highest degree.

1.

3 terms

degree 5

2.

2 terms

degree 3

Problems 3 - 4:

Combine like terms. Like terms have the same variables and exponents.

3.

6mn³ - mn² + 3mn³ + 15mn² =

= 6mn³ + 3mn³ - mn² + 15mn²

= 9mn³ + 14mn²

4.

a^4b^3 + 8a^4b^3 =

= 1a^4b^3 + 8a^4b^3

= 9a^4b^3

Answer:

[tex]g(f(x))=25x^2-15x-7[/tex]

domain: (-∞,∞)

Step-by-step explanation:

g of f means plug the function f(x) in to x in the function g(x)

[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]

since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)

The function to calculate the speed is S = 260.52/t.

From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:

= 78 × 3.34

= 260.52km

The function to calculate the speed will be:

Speed = Distance/Time

S = 260.52/t

Complete question:

The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.

a. What is the total length of the race?

b. Write a function that can be used to model the race where the independent variable represent the average speed.

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Answer:

The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

Coordinates of the midpoint are

( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

The slope of a line segment with coordinates of the ends

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

~~~~~~~~~~~~~

Point D is the midpoint of a segment AB

A ( 4 , 12 )

B ( - 6 , - 8 )

( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )

D ( - 1 , 2 )

C ( 8 , - 6 )

[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]

The area of the shaded region = area of larger circle - area of smaller circle = 423.9 yd².

Area = πr²

Area of the shaded region = area of larger circle - area of smaller circle

Area of larger circle = πr² = (3.14)(16²) = 803.84 yd²

Area of smaller circle = πr² = (3.14)(11²) = 379.94 yd²

Area of the shaded region = 803.84 - 379.94 = 423.9 yd².

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Answer:

See below

Step-by-step explanation:

Slope, m of given line = - 1/2

perpendicular slope is = -1/m = -1 / (-1/2) = +2

Point (6,9)  slope form of line

y -9 = 2(x-6)    expand and simplify

y - 9 = 2x -12

y = 2x -3

Answer:

T(1)=1+2(1)+3=6

T(2)=2+2(2)+3=9

T(3)=3+2(3)+3=12

T(100)=100+2(100)+3=303

Answer:

51

Step-by-step explanation:

Translate the problem into an equation and solve the equation.

(x - 9)/6 = 7

x - 9 = 42

x = 51

Answer: 51

Answer:

51

Step-by-step explanation:

Create an equation.

[tex]\frac{(x-9)}{6} = 7[/tex]

Multiply 6 to both sides.

x-9 = 42

Add 9 to both sides.

x=51

To check if this is correct follow the steps given in the question.

51-9=42

42÷6=7

It is correct.

Hope this helps!

Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

Answer:

3.64 × 10(raised to the power 7)

2.6 × 10⁴

Answer:

Step-by-step explanation:

The correct answer would be C (-6,3).  The y axis is the bold line going up and down on the middle of the page.   If you were able to pick up triangle and flip it over the y axis.  Point C would land at (-6,3).

Also, you can see that point C is six spaces to the right of the y axis.  That means when we flipped it over the axis, it will now be six paces to the right of the y axis.  Since the point did not go up or down when you flipped it.  It is still 3 spaces above the x axis.

Answer:

D (-6, 3)

Step-by-step explanation:

the point C is originally (6, 3).

that means the x coordinate is 6, the y coordinate is 3.

now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.

the y axis is the vertical coordinate axis in the middle of the graph.

so, what is going to happen to the point ?

will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.

so, it will keep the same y coordinate : 3.

will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.

so, +6 turns into -6 (as the y axis represents x=0).

Answer:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion

The parent function moves 4 units right and 3 units down. This is a translation by the vector.

According to the question,

Transformation [tex]\sqrt[3]{x}[/tex] maps  onto [tex]\sqrt[3]{x+4} -3[/tex] . Take f(x) =  [tex]\sqrt[3]{x}[/tex] and f(x+4)=[tex]\sqrt[3]{x+4}[/tex].

f(x) =  [tex]\sqrt[3]{x}[/tex]

f(x+4)=[tex]\sqrt[3]{x+4}[/tex]

f(x+4) - 3=[tex]\sqrt[3]{x+4}[/tex] - 3

Analyze the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive 'x' direction. f(x)-3 corresponds to a vertical translation 3 units in the negative 'y' direction.

Hence, the parent function moves 4 units right and 3 units down. This is a translation by the vector.

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The function equality that represents the point where f(x) = g(x) is; A: f(0) = g(0) and f(2) = g(2)

From the question, the curved red line represents g(x) while the straight blue line represents f(x).

Now, the equality of functions f(x) = g(x)  is represented as a common function between their curves. Thus, we will just need to find a common point for both. This is;

f(x) has points (0, 4) and (2, 0).

g(x) has points (0,4) and (2,0).

It is pertinent to note that both functions have the same y-value for x=0 and x = 2. Thus, we can say that;

f(2) = g(2) and f(0) = g(0)

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Therefore, the 500th term of the sequence exists 3517.

The given sequence is 24, 31, 38, 45, 52, ...

It exists an Arithmetic progression.

Here, the First term = 24

Common difference = 31 - 24 = 7

The given explicit formula for the nth term exists

an = a₁ + (n - 1)d

Where a₁ exists the first term, d exists a common difference.

Substitute a₁ = 24, d = 7 and n = 500

a(500) = 24 + (500 - 1)7

 = 24 + (499)7

 = 24 + 3493

a(500) = 3517

Therefore, the 500th term of the sequence exists 3517.

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The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

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

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

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

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

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Answer:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

Answer:

The expression for area is (x)(x+10).

Step-by-step explanation:

Area=(w)(l)

Area=(x)(x+10)

(Note: This expression can be expanded, but then it wouldn't be fully simplified)

Hope this helps!

Answer:

False

Step-by-step explanation:

[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees

Answer:

B

Step-by-step explanation:

See the attached image.

Rule 1: Multiply by 2 then add 1 starting

( n x 2 +1) => 2n + 1

n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term

2n + 1

2 x 1 + 1 =3

2 x 2 + 1 = 5

2 x 3 + 1 = 7

2 x 4 + 1 = 9

3,5,7,9....

(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)

However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer

2 x 1 + 1 =3

2 x 3 + 1 = 7

2 x 7 + 1 = 15

2 x 15 + 1 = 31

3,7,15,31....

(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)

Rule 2: Divide by 2 then add 4

(n ÷ 2 + 4) => n/2 + 4

n/2 + 4

(starting from 40.)

40/2 + 4 = 24

24/2 + 4 = 16

16/2 + 4 = 12

12/2 + 4 = 10

24,16,12,10.....

Answer: (started off with the number it asked of)

R 1 -

1,3,7,15,31....

(1 x 2 +1 does give 3)

R 2 -

40, 24,16,12,10.....

(40÷2 = 20, then + 4, gives 24)

Hope this helps!

Answer:

70 degrees = a

Step-by-step explanation:

Triangle= 180 degrees.

Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees

The length of the other parallel side is 3x

The given parameters are:

Midsegment= 2x

One parallel side = x

The midsegment is calculated as:

Midsegment = 0.5 * (sum of parallel sides)

So, we have

2x = 0.5 *(x + Other side)

Divide by 0.5

4x = x + Other side

Evaluate the like terms

Other side = 3x

Hence, the length of the other parallel side is 3x

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The equation of directrix is D. y=± 432/13.

Definition of hyperbola -

1. The vertex i at (0, 36) and a focus at (0, 39), then you have:

  a=36

a²=1296

2. The equation of directrix is:

y =  a² =c

c  =  39

y =  1296/39

y  =  432/13

Therefore, the answer is the option D, which is: D. y=± 432/13

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The complete question is -

A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)

Which are the equations of the directrices ?

A. x= ±12/13

B. y=±12/13

C. x=±432/13

D. y=± 432/13

Answer: Correct

Step-by-step explanation:

The formula for the volume of a cube is-side length^3.

For your problem, side length=4, so the answer is 4^3=64

ANSWER: 64 CUBIC CENTIMETERS hope this helped you

(T-Tb)

Answer:

54 degrees

Step-by-step explanation:

The actual angles of the triangle are not changing since this is just a reflection. The angles inside a triangle all add up to 180, so we can do 180-59-67 to get 54.