Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees

The area of the parallelogram is 32 square units.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:

    |       (3,6)        (11,6)

    |         *-----------*

    |        /           /

    |       /           /

    |      /           /

    |     /           /

    |    *-----------*

    |  (0,2)        (8,2)

    |

Now,

We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.

To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.

Therefore,

The height of the parallelogram is 4 units.

Now,

The area of a parallelogram is given by the formula:

Area = base x height

Plugging in the values we found, we get:

Area = 8 x 4

Area = 32

Therefore,

The area of the parallelogram is 32 square units.

Learn more about parallelograms here:

https://brainly.com/question/1563728

#SPJ2

Tmuch of a head start should the runner on the outside get would be = 2πm.

How to calculate the length of head start for the runner outside?

To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:

The formula for circumferential of circle = 2πr

Circumference of inner circle;

= 2× π×50

= 100π

Circumference of outer circle;

= 2×π×51

= 102π

The length of head start for the runner outside = 102π-100π = 2πm

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

The explicit rule for this situation is An = 12 + n, where "n" represents the row number.

To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:

A10 = 12 + 10

A10 = 22

So, there will be 22 marbles in the 10th row.

Matching the answers:

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

for such more question on Explicit rule

https://brainly.com/question/30394385

#SPJ12

The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex]

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Here, P = $2800

         I = 1 % compounded semiannually = 0.5 % = 0.005

        Time = t years

        n = 2t semi-years

We know that,

[tex]A = P(1+i)^n[/tex]

[tex]A = 2800 ( 1 + 0.005 )^{2t}[/tex]

[tex]A = 2800 X 1.005^{2t}[/tex]

Thus, The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex].

Learn more about Compound Interest from:

https://brainly.com/question/14295570

#SPJ2

Answer:

A. 12

B. 3

C. -2

D. -5

Step-by-step explanation:

Verified on edge, just finished it

The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.

Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.

Given:

y = 3x² + 12x + 7

Now writing the equation in vertex form

y = 3x² + 12x + 7

y = 3x(x + 4) + 7

Adding and subtracting 12 on both side

y= 3(x²+ 4x) + 7 -12 + 12

y= 3(x² + 4x + 4) + 7- 12

y= 3(x+ 2)² -5

Now, Comparing it with  y = a(x - h)² + k we get

a= 3

h= -2

and, k= -12

Learn more about vertex form here:

https://brainly.com/question/11926167

#SPJ2

The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.

This refers to a statement or assertion that is made about something, which may or may not be true.

Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.

Read more about inference here:

https://brainly.com/question/25913650

#SPJ2

Answer:its (0 -26)

Step-by-step explanation:

THATS THE ANSWER NO NEED TO explain  

Answer:

A (0,-26)

Step-by-step explanation:

Answer: 600

Step-by-step explanation:

Given : The number of times Carlin laughs in each minute = 5

The number of comedy show Carlin watched = 3

The length of each comedy show = 40 minutes

Total minute she watched Comedy show will be :-

[tex]40\times3=120\text{ minutes}[/tex]

Then , the total number of times Carlin will be :-

[tex]120\times5=600[/tex]

Hence,Carlin laughs 600 times every day due to the comedy shows.

Answer:

[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]

Step-by-step explanation:

The given expresion is:

(−2x + 4y)(3x − 7y)

We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]

We expand further to obtain:

[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]

[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]

Answer:

[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]

Step-by-step explanation:

We multiply each term in the parentheses, by those of the other parenthesis:

[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]

Now, we simplify.

We have two terms that contain xy:

[tex]=-6x^2+26xy-28y^2[/tex]

Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]

Final answer:

A rectangular hyperbola is defined by the angle between its asymptotes being 90°, with its Equation represented as x'y' = a².

Explanation:

Rectangular Hyperbola: When the angle between the asymptotes of a hyperbola is 90°, it is called a rectangular hyperbola. In this case, b = a and the eccentricity is √2. The Equation to a rectangular hyperbola is x'y' = a².

All the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8  = 90°

The theory that is mainly used to find out the angles of the above diagram is that;

the sum of the internal angles of a triangle is 180°.

when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.

Next from point A to point E, the angle rotated is 68°

the addition of these 2 angles give the angle rotated from point B to point E,

that is angle no.7

m∠7 = 53° + 68° = 121°

consider ΔPBE,

PB and PE are radii therefore isosceles triangles

In isosceles triangles the angles opposite equal sides are equal

if the angle is x°, then there are 2 angles with values x each

x° +x° + 121° = 180°

2x° = 59°

x = 29.5°

therefore m∠3 = 29.5°

next connect PC and consider ΔPCB,

according to given information, C∠PB = 72°

as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal

2y° + 72° = 180°

y° = 54°

then consider ΔPCD, again an isosceles triangle

as a straight line has an angle of 180°

B∠PC + C∠PD = 180°

72° + C∠PD = 180°

C∠PD = 108°

as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)

2z° + 108° = 180°

z° = 36°

B∠CD is a sum of y and z angles

therefore m∠8 = y + z

m∠8 = 54° + 36° = 90°

there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius

this indicates that lines PD and HD are perpendicular to each other

hence, forms a right angle where it cuts each other.

therefore H∠DP / m∠4 = 90°

C∠DH /m∠5 is the difference between P∠DH and P∠DC

m∠5 = 90° - 36° = 54°

m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°

by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.

m∠1 is the acute angle therefore m∠1 = 63.5°

m∠6 is the obtuse angle therefore m∠6 = 116.5°

consider ΔDFB

D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°

D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°

116.5 + w° + 29.5° = 180°

w° = 34°

m∠2 = m∠4 + w°

       = 90° + 34°

      = 124°

finally all the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8  = 90°