Lines c and d are parallel lines cut by transversal p.


Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.
Which must be true by the corresponding angles theorem?
A. ∠1 ≅ ∠7
B. ∠2 ≅ ∠6
C. ∠3 ≅ ∠5
D. ∠5 ≅ ∠7

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

[tex] {x}^{2} + 4 = 4x[/tex]

[tex] {x}^{2} - 4x + 4[/tex]

Find the discrimant.

[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]

This means there is one real solution. Since the discramnt equal 0.

Answer:

[tex]y=-2(sin(2x))-7[/tex]

Step-by-step explanation:

1. Approach

Given information:

What conclusions can be made about this function:

Therefore, one has the following information figured out:

[tex]y=-n(sin(ax))+b[/tex]

Now one has to find the following information:

2. Midline

The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:

y = -7

2. Amplitude

The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline: [tex]y=-7[/tex]

Amplitude: 9 - |-7| = 9 - 7 = 2

3. Period

The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline intersection: [tex](0, -7)[/tex]

Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]

However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).

[tex]a=\frac{2\pi}{\pi}=2[/tex]

4. Assemble the function

One now has the following solutions to the variables:

[tex]n =-16\\a=2\\b=-7\\[/tex]

Substitute these values into the function:

[tex]y=-2(sin(2x))-7[/tex]

Answer:

the constant is the number without an x attaches to it.

Ex:

y = 2x + 9

9 is a constant because it is not attached to any x

y = x^3 + 2x^2 + 10x + 19

19 is a constant because it is not attached to any x

Answer:

True

Step-by-step explanation:

Both pairs of opposite angles are congruent. parallelogram, rectangle, rhombus, square. Both pairs of opposite sides are congruent. parallelogram, rectangle, rhombus, square. All consecutive angles are supplementary. parallelogram, rectangle, rhombus, square. diagonals bisect each other. parallelogram, rectangle, rhombus, square.

Answer:

true

Step-by-step explanation:

any 2 consecutive angles are supplamentary

Answer:

100 mm

Step-by-step explanation:

Square root the area to find the length of each side

[tex]\sqrt[]{625} =25[/tex]

Multiply 25 by 4 to get the sum of all four sides for the perimeter

25 x 4 = 100

Answer:

θ = 60.34

Step-by-step explanation:

[tex]\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}[/tex] = 16.177

[tex]\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}[/tex] =  θ = .869

[tex]arcsin\left(.869\right)[/tex] = 60.34

Answer:

60.4°

Step-by-step explanation:

There are two right triangles.

One right triangle (on the left side) has an acute angle measuring 52.3°.

Its opposite leg measures 12.8 cm.

We can find the length of its hypotenuse, x.

sin 52.3° = opp/hyp

sin 52.3° = 12.8 cm/x

x * sin 52.3° = 12.8 cm

x = 12.8 cm/sin 52.3°

x = 16.2 cm

Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.

For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.

sin Θ = opp/hyp

sin Θ = 16.2/18.6

sin Θ = 0.8698

Θ = sin^-1 0.8698

Θ = 60.4°

Answer:

D

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² + 7x - 3 + 6x³ - 7x² - 5 ← collect like terms

= 6x³ - 3x² + 7x - 8

Answer:

D. (f + g )( x ) = 6x³ - 3x² + 7x - 8

Step-by-step explanation:

Given :-

To Find :-

Solution :-

(f + g )( x ) = 4x² + 7x - 3 + 6x³ - 7x² - 5.

Arranging like terms.

(f + g )( x ) = 6x³ - 7x² + 4x² + 7x -5 - 3

Combine like terms.

(f + g )( x ) = 6x³ - 3x² + 7x - 8

Answer:

there is only one way to to roll a 3

1/36 = .044 = 4.4%

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

substitute the x- coordinate 5 into the equation and if the result is equal to the y- coordinate 0 then it is a solution

y = 5 + 5 = 10 ≠ 0

Then (5, 0 ) is not a solution to the equation

Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(

Answer:

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Step-by-step explanation:

C = 2P  .....equation 1

4C + 2P = 20  .....equation 2

Substituting eqn 1 into eqn 2, we have;

4(2P) + 2P = 20

8P + 2P = 20

10P = 20

P = 20/10

Pie, P = $2

Next, we would determine the cost of a cake;

From equation 1;

C = 2P

Substituting the value of "P" we have;

C = 2 * 2

Cake, C = $4

Therefore, we would have the following answers;

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Check:

From equation 2;

4C + 2P = 20

4(4) + 2(2) = 20

16 + 4 = 20

20 = 20

Answer:

its letter a

Step-by-step explanation:

I hope you help

Answer:

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.

Answer:

The answer is 80

Step-by-step explanation:

we know that

the outlier is 50, as it is not around the other numbers in the data set.

therefore

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80

Answer:

80

Step-by-step explanation:

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80

Answer:

ratio 2 : 3 : 5

size of smallest angle

[tex]180 \times \frac{2}{10} \\ = 36[/tex]

Answer:

The smallest angle of a triangle is 36°.

Step-by-step explanation:

Given, the ratio of angles of a triangle is 2 : 3 : 5

Let the angles of a triangle be ∠A, ∠B and ∠C.

∠A = 2x, ∠B = 3x, ∠C = 5x

∠A+∠B + ∠C= 180°

[sum of all the angles of a triangle is 180°]

2x + 3x + 5x = 180°

10x = 180°

x=180°/10 =18°

∠A=2x=2 x 18° = 36°

∠B = 3x = 3 x 18° = 54°

∠C = 5x = 5 x 18° = 90°

Hence, the smallest angle of a triangle is 36°.

HOPE IT HELPS!!!

Answer:

4.67×10

4

=4.67×10000=46700

[tex]4.67 \times {10}^{4} [/tex]

[tex] = \: 4.67 \times 1000[/tex]

[tex] = \: 46700[/tex]

Answer:

The answer is -13.

Step-by-step explanation:

The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.

So the 7th term will be a+6d= -1  ---(1)

The 16th term will a+15d=17  ---(2)

Subtract (2) and (1)

a+15d-(a+6d)=17-(-1)

=a+15d-a-6d=17+1

9d=18

d=18/9

d=2.

Substitute d in eq (1)

a+6(2)= -1

a+12=-1

a= -1-12= -13

Thus the general term of the ap is -13

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

Answer:

A=128 cm²

Step-by-step explanation:

Hi there!

We are given a trapezoid and we want to find the area of it

The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height

The bases are the parallel sides

They are the sides marked as 10 cm and 22 cm in this case

The height is the distance between the bases

In this case, it is the side marked as 8 cm

We know everything needed for the area, let's just label everything to avoid any confusion

a=10

b=22

h=8

Now substitute into the formula

A=[tex]\frac{a+b}{2}h[/tex]

A=[tex]\frac{10+22}{2}*8[/tex]

add the numbers on the numerator together

A=[tex]\frac{32}{2}*8[/tex]

Divide 32 by 2

A=16*8

multiply

A=128 cm²

Hope this helps!

Answer:169

Step-by-step explanation:13 x 13 = 169

You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.

Answer:

Un número decimal exacto es algo de la forma:

3.27

Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.

Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)

así obtenemos:

3.27*(100)/(100) = 327/100

Entonces la fracción 327/100 genera un decimal exacto.

Así, encontrar 10 fracciones es trivial, 10 ejemplos son:

7/10 = 0.7

314/100 = 3.14

27/10 = 2.7

27/100 = 0.27

2/10 = 0.2

25/100 = 0.25

31/10 = 3.1

12/10 = 6/5 = 1.2

131/10 = 13.1

142/100 = 1.42

Ahora, un decimal inexacto puro es algo de la forma:

3.33...

donde el 3 se repite infinitamente.

Tratemos de reescribir este número como una fracción:

primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:

3.33*10 = 33.33...

Ahora, podemos restar el numero original:

33.333... - 3.333... = 30

Entonces tenemos que:

3.33*9 = 30

3.33 = 30/9

La fracción:

30/9 nos da in decimal inexacto puro.

Ahora que sabemos construirlas, 10 ejemplos pueden ser:

30/9 = 3.33....

1/3 = 0.33...

40/9 = 4.44...

50/9 = 5.55...

60/9 = 6.66...

70/9 = 7.77...

20/9 = 2.22...

55/9 = 6.11...

544/99 = 5.5959...

10/9 = 1.11...

Finalmente, un periódico mixto es algo de la forma:

1.2343434...

Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.

Para construirlos, podemos tomar una fracción exacta, como

1.1 y una periódica, como 1.11...

Si las sumamos, obtenemos:

1.1 + 1.11... = 2.211...

donde el uno se repetirá infinitamente.

Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:

7/10 + 55/9 = 613/90 = 0.7 +  6.11... = 6.8111....

7/10 +  10/9 = 163/90 = 0.7 + 1.11... = 1.811....

31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...

31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...

31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...

27/10 + 20/9 =  443/90 = 2.7 + 2.22... = 4.922...

37/10 + 20/9 =  533/90 = 3.7 + 2.22... = 5.922...

4/10 +  10/9 = 136/90 = 0.4 + 1.11... = 1.511....

3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...

4/10 +  20/9 = 236/90 = 0.4 + 2.22... = 2.622....

Answer:

there is no diagram ......

Answer:

Since this number is small we know that the exponent will be negative.

In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.

1.2 x 10 ^-11

Step-by-step explanation:

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Answer:

C = 37.6991

Step-by-step explanation:

The equation for the circumference of a circle is given: C = π · d

where, d is the diameter of the circle.

Plug in the value of d = 12 and use the π button on the calculator.

C = π · 12

C = 37.6991

Answer:

a)2x-3y

b)4(9a-4)

Step-by-step explanation:

we want to expand the following expression:

[tex] \displaystyle - \frac{1}{4} ( - 8x + 12y)[/tex]

well to do so we consider distributive property thus distribute:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y)[/tex]

reduce fraction which yields:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y) \\ \\ \displaystyle 2x + ( - 3y)[/tex]

simplify Parentheses:

[tex] \displaystyle \boxed{ 2x - 3y}[/tex]

in the expression there's a common factor of 4 therefore factor it out:

[tex] \displaystyle 9.4a - 4.4 \\ \\ \displaystyle \boxed{4(9a - 4)}[/tex]

Answer:

d = 8t

Step-by-step explanation: