Solve for the unknown angles. Justify your answers with steps (do not just provide answers)

Answer:

3

Step-by-step explanation:

since the diagonal are equal in length

6x-8=2x+4

4x=12

x=3

Answer:

True

Step-by-step explanation:

When two lines are parallel, the corresponding angles formed by the transversal (intersecting line) are congruent. This is called the corresponding angles postulate. It can be used in reverse: if two corresponding angles are congruent, then the non-transversal lines are parallel.

Answer:

Step-by-step explanation:

Angles 4 and 5 are corresponding; this means that they are sitting in the same places within their angle "bunch" for lack of a better word. We are then told that they are are congruent which means that they have the exact same measure. Corresponding angles can exist without being congruent, but because they are, that means that A and B HAVE to be parallel. So true.

Answer:

That is correct

Step-by-step explanation:

To get from a to 2a we multiply by 2, so we also need to multiply -5 by 2:

2(a)=2(-5)

2a=-10

Happy learning!

--Applepi101

Answer:

1) -1

2) 3

3) 2

Answer:

Step-by-step explanation:

1a) The function will shift 5 units to the right, 4 units down,

1b).The function will shift 3 units to the left, stretched in the y direction by a scale factor of 3, and shift up 2 units.

2a). The function will shift 2 units to the left, reflect over the x axis, and shift 2 units down.

2b) The function will stretched in the y direction by a scale factor of -2 and shift the function up 3 units.

9514 1404 393

Answer:

  1a. translation right 5, down 4

  1b. vertical stretch ×3, translation left 3, up 2

  2a. translation left 2, down 2

  2b. reflect in x, vertical stretch ×2, translation up 3

  3. f(x) = -4/(x+5)+4

  4. f(x) = 1/2√(3(x +3)) -4

Step-by-step explanation:

Transformations of functions can be decoded by considering the transformation ...

  g(x) = a·f((x-h)/b) +k

The transformations here are ...

Note that either 'a' or 'b' can be a fraction less than 1, which results in a transformation usually described as a compression (not a stretch). If either of these is negative, then a reflection over the x-axis (a<0) or y-axis (b<0) is also involved. The stretch (or compression) and/or reflection is applied before the translation the way this is written.

_____

1a. translation right 5, down 4

1b. vertical stretch by a factor of 3, translation left 3, up 2

__

2a. translation left 2, down 2

2b. reflected across the x-axis, vertically stretched by a factor of 2, translated up 3

__

3. a=4, b=-1, h=-5, k=4

f(x) = -4/(x+5)+4

__

4. a=1/2, b=1/3, h=-3, k=-4

f(x) = 1/2√(3(x +3)) -4

_____

The graphs in the attachments show the various functions. (It takes a little work to verify that the graph in the last attachment has the appropriate compressions, but it does.)

Answer:

Equilibrium price for widgets = 13.22

Step-by-step explanation:

At equilibrium, quantity demand, Qd = quantity supplied, Qs

Demand

P = 14 – 0.39Q

P - 14 = - 0.39Q

Q = (P - 14) / - 0.39

Supply

P = 0.61Q + 12

P - 12 = 0.61Q

Q = (P - 12) / 0.61

Qd = Qs

(P - 14) / - 0.39 = (P - 12) / 0.61

Cross product

(P - 14) * 0.61 = - 0.39 * (P - 12)

0.61P - 8.54 = - 0.39P + 4.68

0.61P + 0.39P = 4.68 + 8.54

P = 13.22

Check

Q = (P - 14) / - 0.39

= (13.22 - 14) / - 0.39

= -0.78 / -0.39

= 2

Q = (P - 12) / 0.61

= (13.22 - 12) / 0.61

= 1.22 / 0.61

= 2

Therefore,

Equilibrium price for widgets = 13.22

Equilibrium quantity = 2

Answer:

$11,400

Step-by-step explanation:

3,000+14(600)=11,400

We know that it expands by $600 a year and we are looking for the salary during the 15th year.  During the 15th year, it could be using the salary of the 14th year since it is during not after.  We then add that to the base salary of $3,000 so then we have $11,400.

Answer:

A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , k . The value of k determines whether the dilation is an enlargement or a reduction.

In simple words, it's stretching, when you dilate with scale factor of x, means you multiply the previous value with x, say co-ordinates area -2,4, so you do (-2x,4x) to find the co-ordinates after dialation,

Here the scale factor is 3, so the new co-ordinates are,

(-2×3, 4×3) which is A' (-6, 12)

similarly,

B' (12, -3)

C' (-3, -6)

Answered by GAUTHMATH

Answer:

A’(-6;12)

B’(12;-3)

C’(-3;-6)

Step-by-step explanation:

If k is the factor then it means you have to multiply the coordinates of each point ( A, B and C).

So for example:

A’=3xA so when A(x;y) -> A’( 3x;3y)

So you have :

A’(-6;12)

B’(12;-3)

C’(-3;-6)

Then you just have to put them into a scale and rely them three to have your figure .

Hope it helps you.

Have a nice rest of your day :)

Step-by-step explanation:

A. cos4x-sin4x=2-cos2x

Answer:

A = 60 in ^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

The bottom base is 8+2+2 = 12

A = 1/2 ( 8 + 12) *6

A = 1/2( 20)6

A = 60 in ^2

Answer:

9 seconds

Step-by-step explanation:

y = -4.9t² +42t +18.9

if the ball will be on the ground then y =0 and we need to find t by solving the quadratic equation

-4.9t² +42t +18.9 = 0

t= (-b±√b²-4ac)/2a, quadratic formula

t= {-42±√[42²-4*(-4.9)(18.9)] }/ 2(-4.9) , use calculator to solve

t= (-42 ±√2134.44)/ -9.8, solve the square root

t= (-42 ±46.2)/-9.8

one t = (-42 - 46.2)/-9.8 = - 88.2/ -9.8 = 9 seconds

another t = (-42 + 46.2)/-9.8 = 4.2 / -9.8 ≈ - 0.43 seconds reject this answer

Answer:

x² - 4x - 8

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(-3 + 4x² - 4x) + (-1 - 3x² - 4)

Step 2: Simplify

Answer:

The customer will pay along with VAT = Rs 3767.4

Step-by-step explanation:

Cost price of an electric fan = 2800

Pirce after 30% above the cost price = 2800 + (30% of 2800 = 3640

Selling price after 10% discount = 3640 - (10% of 3640) = 3276

Now 15% VAT = 3276 x 15%

15% VAT = 491.4

The customer will pay along with VAT = 3276 + 491.4  

The customer will pay along with VAT = Rs 3767.4

Answer:

5

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

1=879=96889=

Answer:

x= 0

y= -2

Step-by-step explanation:

− 7x+ 9y =− 18

4x+ 9y =− 18

 7x- 9y =+ 18

4x+ 9y =− 18

11x=0

x=0

y=-2

Answer:

Habrá 100 chocolates en total en 5 cajas de chocolates.

Step-by-step explanation:

Esta pregunta es resolvida usando proporciones, con lo uso de regla de tres .

11 cajas, 220 chocolates:

Entonces:

[tex]\frac{220}{11} = 20[/tex]

20 chocolates por caja.

Calcula cuántos chocolates habrá en total en 5 cajas de chocolates.

20 chocolates por caja, entonces:

5*20 = 100

Habrá 100 chocolates en total en 5 cajas de chocolates.

Answer:

-1 5/28

Step-by-step explanation:

-3/7 + (-3/4)

Get a common denominator of 28

-3/7 *4/4 = -12/28

-3/4 *7/7 = -21/28

-12/28 + -21/28

-33/28

-28/28 - 5/28

-1 5/28

Answer:2

Step-by-step explanation: but it was real

Answer:

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Step 1

x^2 – 30x = –125

-30/2 = -15

(-15)^2 = 225

Step 2

x^2 -30x+225 = -125+225

(x-15)^2 = 100

Step 3

Take the square root of each side

sqrt((x-15)^2) = sqrt(100)

Step 4

x-15 = ±10

x-15 =10    x-15 = -10

x= 10+15    x = -10 +15

x = 25      x = 5

Answer:

DE and B⁢C are parallel line segments.

Step-by-step explanation:

Edmentum-

Answer:

DE and BC are parallel line segments.

Step-by-step explanation:

Edmentum

Answer:

42

Step-by-step explanation:

ABC + CBD = ABD

3x+33 + 5x+13 = 70

Combine like terms

8x +46 = 70

Subtract 46 from each side

8x+46-46 = 70-46

8x = 24

Divide each side by 8

8x/8 = 24/8

x=3

We want to find ABC

ABC = 3x+33 = 3*3 +33 = 9+33 = 42

Answer:

[tex]m\angle ABC+\angle CBD=m\angle ABD[/tex]

[tex]\longrightarrow (3x+33)+(5x+13)=70[/tex]

[tex]\hookrightarrow 8x+46=70[/tex]

[tex]\hookrightarrow 8x=70-46[/tex]

[tex]\hookrightarrow 8x=24[/tex]

[tex]\hookrightarrow x=24/8=3[/tex]

[tex]so, m\angle ABC=3(3)+33=42[/tex]

-----------------------

Hope it helps...

Have a great day!!

Answer:

16

Step-by-step explanation:

Her account balance on the sixth day is sixteen. This is because -54 +75 is 21 then you subtract 5 and get 16. (15 times 5 is 75)  

Answer:

16

Step-by-step explanation:

Starting balance: -54

Deposits +15

                +15

                 +15

                 +15

                +15

for a  total of +75

-54+75 = 21

Maintenance fee: - 5

21 - 5 = 16

Answer:

- 3 / 10

Step-by-step explanation:

- 9 / 10 - ( - 3 / 5 )

= - 9 / 10 + 3 / 5

= 3 / 5 - 9 / 10

= 6 / 10 - 9 / 10

= ( 6 - 9 ) / 10

= - 3 / 10

Answer:

[tex]4=1/2gt^{2}[/tex]

Multiply equation by 2/g

4(2/g) = t²

t = √(8/g)

t = 2√(2/g)

[tex]answer:t=\sqrt{\frac{8}{g} }[/tex]

OAmalOHopeO

Answer:

GHI is congruent to HGW

Step-by-step explanation:

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(x) = 21/40

x = sin^-1(21/40)

x = 32 degrees

Hope this helps!