2. Identify the relationship between the angles
given, then write and solve the equation to find
the value for the variable “x”.

Answer:

The first one . +++ --

Step-by-step explanation:

Answer:

x = 2 ± √34/5

Step-by-step explanation:

Move terms to the left side.

5x^2 - 4x = 6

5x^2 - 4x -6 = 0

Identify a, b, and c before plugging them into the quadratic formula.

a = 5

b = -4

c = -6

x = -(-4) ± √(-4)^2 - 4 * 5(-6)/2 * 5

Then simplify.

Answer:

18

Step-by-step explanation:

Answer:

if    x ≥ 2, then y = x - 1

if    x < 2, then y = -x + 3

Step-by-step explanation:

y = 1* |x - 2|  +  1

y = |x-2| + 1

*** The rule on absolute value: |a| =a, if a ≥ 0; |a| = -a, if a < 0

If       x-2 ≥ 0,   then |x-2| = x-2, so y = (x - 2) + 1 = x - 1; y = x - 1

So   if    x ≥ 2, then y = x - 1

If      x-2 < 0,    then |x-2| = -(x-2) = -x + 2, so y =  {-x + 2} + 1 = -x + 3; y = -x + 3

So   if    x < 2, then y = -x + 3

Answer:

x = 12.5

Step-by-step explanation:

Based on the interesting chords theorem, we would have the following:

2*x = 5*5

2x = 25

Divide both sides by 2

x = 25/2

x = 12.5

Answer:

98 cm squared

Step-by-step explanation:

Answer:2721

Step-by-step explanation:

Answer:

Joel had 120 dimes and 80 quarters.

Step-by-step explanation:

Given that Joel had 200 coins, which were dimes and quarters, and the total value was $ 32, to determine how many coins of each type he had, the following calculation must be performed:

0.25 - 0.10 = 0.15

200 x 0.10 = 20

32 - 20 = 12

12 / 0.15 = 80

200 - 80 = 120

(80 x 0.25) + (120 x 0.1) = X

20 + 12 = X

32 = X

Thus, Joel had 120 dimes and 80 quarters.

Step-by-step explanation:

12/15 in a calculator

0.8

Answer/Step-by-step explanation:

Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.

Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.

Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.

Answer:

Answer/Step-by-step explanation:

Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.

Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.

Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The center is halfway between vertices, at (4, -6).

It is also halfway between foci.

:::::

The vertices are vertically aligned, so the parabola is vertical.

General equation for a vertical ellipse:

 (y-k)²/a² + (x-h)²/b² = 1

with

 center (h,k)

 vertices (h,k±a)

 co-vertices (h±b,k)

 foci (h,k±c), c² = a²-b²

Apply your data and solve for h, k, a, and b.

center (h,k) = (4, -6)

h = 4

k = -6

vertices (4,-6±a) = (4,-6±9)

a = 9

foci (4,-6±c) = (4,-6±5√2)

b² = a² - c² = 9² - (5√2)² = 31

b = √31

The equation becomes

 (y+6)²/81 + (x-4)²/31 = 1

:::::

length of major axis = 2a = 18

length of minor axis = 2b = 2√31

The various parts of the question needs to be answered.

Center: (4,-6)

Standard equation: [tex]\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]

Length of major axis: 18 units

Length of minor axis: [tex]2\sqrt{31}\ \text{units}[/tex]

Graph is attached.

The Vertices are of the form

[tex](h,k\pm a)=(4,-6\pm 9)[/tex]

This means that the ellipse is symmetrical to the y axis.

The center of an ellipse is given by [tex](h,k)[/tex]

So, here the center is [tex](4,-6)[/tex]

[tex]a=\pm 9[/tex]

The foci are of the form

[tex](h,k\pm c)=(4,-6\pm 5\sqrt{2})[/tex]

So, [tex]c=\pm 5\sqrt{2}[/tex]

[tex]b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}[/tex]

The standard equation for major axis being parallel to y axis is given by

[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]

Length of major axis is

[tex]2a=2\times 9\\ =18\ \text{units}[/tex]

Length of minor axis is

[tex]2b=2\sqrt{31}\ \text{units}[/tex]

Learn more about ellipse:

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Answer:

b

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

(3, 2) is a solution to the given system of linear equations.

x - 8y = 3 - 8*2 = 3 - 16 = - 13

16x - 16y = 16(x - y) = 16( 3 - 2) = 16*1 = 16

Answer:

It doesn't show the whole picture

Step-by-step explanation:

9514 1404 393

Answer:

  7 square units

Step-by-step explanation:

There are several ways the area of triangle EBD can be found.

We choose the latter.

__

Pick's theorem says the area of a polygon can be found as ...

  A = i + b/2 -1

where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.

The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...

  A = 6 + (4/2) -1 = 7

The area of ∆EBD is 7 square units.

Answer:

expression

Step-by-step explanation:

It is expression because it is a algebraic expression.

Answer:

c

Step-by-step explanation:

A part-time seamstress made $8881.93 last year. The taxable income is $0.

We have given that,

A part-time seamstress made $8881.93 last year. If she claimed herself as an exemption for $3650 and had a $5700 standard deduction.

We have to determine, what was her taxable income last year.

Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.

Therefore the taxable income is $0.

To learn more about the taxable income vsit:

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#SPJ2

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC = [tex]\sqrt{324-81}[/tex]

AC = [tex]9\sqrt{3}[/tex] cm  

sin(C) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{AB}{BC}[/tex]

         = [tex]\frac{9\sqrt{3}}{18}[/tex]

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]

sin(B) = [tex]\frac{AC}{BC}[/tex]

         = [tex]\frac{9}{18}[/tex]

         = [tex]\frac{1}{2}[/tex]

cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

          = [tex]\frac{9\sqrt{3}}{18}[/tex]

          = [tex]\frac{\sqrt{3} }{2}[/tex]

tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

          = [tex]\frac{AC}{AB}[/tex]

          = [tex]\frac{9}{9\sqrt{3} }[/tex]

          = [tex]\frac{1}{\sqrt{3} }[/tex]

tan(C) = [tex]\frac{AB}{AC}[/tex]

          = [tex]\frac{9\sqrt{3}}{9}[/tex]

          = [tex]\sqrt{3}[/tex]

Therefore, Options (1), (3) and (4) are the correct options.

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC =

AC =  cm  

sin(C) =

        =

        =

sin(C) =

sin(B) =

        =

        =

cos(B) =

         =

         =

tan(B) =

         =

         =

         =

tan(C) =

         =

         =

Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:

Answer:

The correct answer is B. $59.05.

Step-by-step explanation:

Given that I have a restaurant bill of $ 46.32, if I am taxed 7 1/2 and decide to tip my server 20%, to determine how much is my total, the following calculation must be performed:

1/2 = 0.5

46.32 + (46.32 x 0.075) + (46.32 x 0.2) = X

46.32 + 3.474 + 9.264 = X

49.79 + 9.26 = X

59.05 = X

Thus, the total amount that I must pay is $ 59.05.

Answer:

b

Step-by-step explanation:

trust

Answer:

I do not know the answer to this question

Step-by-step explanation:

Answer:

40 in

Step-by-step explanation:

I HAVE THE POWER OF GOD AND ANIME ON MY SIDE

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Answer:

The relation is not a function.

Step-by-step explanation:

The x-values of the relation are repetitive, making it not a function.

Answer:

Not a function

Step-by-step explanation:

-1 is used more than once

Answer:

A= 90    (right angel )

E= 90 - 67 = 23

I hope im right!!

Answer:

the third option

Step-by-step explanation:

Answer:

55/4

Step-by-step explanation:

Answer:

0.125 cubic feet

Step-by-step explanation:

Since the container has a shape of a cube with a measure of its side 0.5 ft, then;

Volume of the container, V = [tex]s^{2}[/tex]

where s is the measure of its side.

s = 0.5 ft, then;

V = [tex](0.5)^{3}[/tex]

    = 0.125

V = 0.125 cubic feet

The cubic feet of slime that would fit in the container is 0.125.