What is the equation of the following graph in vertex form?
Y=(X-3)^2-1
Y=(X+3)^2-1
Y=(X-4)^2-2
Y=(X-4)^2+8

Answer:

Step-by-step explanation:

The answer is 4.

Once you add 4, you get:

x^2 -2x + 4 = 7.

The left side is factorable:

(x-2)^2 = 7.

There is your perfect square.

Answer:

The height above sea level at B is approximately 1,604.25 m

Step-by-step explanation:

The given length of the mountain railway, AB = 864 m

The angle at which the railway rises to the horizontal, θ = 120°

The elevation of the train above sea level at A, h₁ = 856 m

The height above sea level of the train when it reaches B, h₂, is found as follows;

Change in height across the railway, Δh = AB × sin(θ)

∴ Δh = 864 m × sin(120°) ≈ 748.25 m

Δh = h₂ - h₁

h₂ = Δh + h₁

∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m

The height above sea level of the train when it reaches B ≈ 1,604.25 m

Answer:

See graph

[tex](x +3)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = 9

(-3 , -1) is the center.

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

Step-by-step explanation:

[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex]

center (h,k)

radius = r

Answer:

54.94954839

Step-by-step explanation:

tan(70) = x/20

tan(70) times 20 = x

Answer:

700 apples

Step-by-step explanation:

Let

x = Total number of apples in the cart

Percentage of apples sold = 40%

Number of apples sold = Percentage of apples sold * Total number of apples in the cart

= 40% * x

= 0.4 * x

= 0.4x

Number of apples left in the cart = 420

Total number of apples in the cart = Number of apples sold + Number of apples left in the cart

x = 0.4x + 420

x - 0.4x = 420

0.6x = 420

x = 420/0.6

x = 700

x = Total number of apples in the cart = 700

Lawrence started with 700 apples

Answer:

63

Step-by-step explanation:

a=9

7a

7(9)

63

Answer:

(x-12)^2+(y-2)^2=4

Step-by-step explanation:

Answer:

D. [tex] \frac{15}{8} [/tex]

Step-by-step explanation:

Recall: SOH CAH TOA

Thus,

Tan A = Opposite/Adjacent

Reference angle (θ) = A

Length of side Opposite to <A = 15

Length of Adjacent side = 8

Plug in the known values

[tex] Tan(A) = \frac{15}{8} [/tex]

Answer:

Step-by-step explanation:

The rectangle has 4 corners of 90 degrees.

Here a rectangle is divided into two right triangles. In right-angled triangles, the opposite side at a 30-degree angle is half a chord...I replace x instead of length.. So x / 2 = 4--->x:8

The perimeter of a rectangle is equal to (length + width) × 2--->(8+4)×2=24m^2

Answer:

[tex]\text{(D) }16\sqrt{3}\:\mathrm{m^2}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:2x:x\sqrt{3}[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.

The rectangle shown forms two 30-60-90 triangles. The side labelled 4 meters is opposite to the 30 degree angle. Therefore, the side on top must be [tex]x\sqrt{3}\text{ for }x=4[/tex]. Let the length of the top base be [tex]w[/tex]:

[tex]w=4\sqrt{3}[/tex]

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Thus, the area of the rectangle is:

[tex]A=4\cdot 4\sqrt{3},\\A=\boxed{16\sqrt{3}\:\mathrm{m^2}}[/tex]

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K

hope this helps! feel free to clarify if unsure

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

Step 1:  Solve for x

Since there are two parallel lines and one perpendicular line through the middle, that means that all of the angles are equal.  Therefore, we can make an equation 21x + 6 = 90 and solve for x

[tex]21x + 6 - 6 = 90 - 6[/tex]

[tex]21x / 21 = 84 / 21[/tex]

[tex]x = 4[/tex]

Answer:  [tex]x = 4[/tex]

Given:

Adam's locker has a password that consists of 4 non-repeated letters from A - Z.

To find:

The number of different passwords.

Solution:

Total number of letters from A - Z is 26.

So, the number of selecting a letter for first place is 26.

The passwords consists non-repeated letters. So, the remaining numbers is [tex]26-1=25[/tex].

The number of selecting a letter for second place is 25.

Similarly,

The number of selecting a letter for third place is 24.

The number of selecting a letter for fourth place is 23.

The total number of possible different passwords is:

[tex]26\times 25\times 24\times 23=358800[/tex]

Therefore, the total number of different passwords is 358800.

Answer:

QXV=WXV

Step-by-step explanation:

Answer:

[tex]VR=5[/tex]

Step-by-step explanation:

From the question we are told that:

No of Pulleys =5

Generally Greatest VR is achieved if it has no friction to the pulleys

Therefore

[tex]W=5P[/tex]

Generally the equation for Efficiency  is mathematically given by

[tex]n=\frac{MA}{VR}[/tex]

Where

MA=mechanical advantage

Therefore  at Greatest VR

[tex]n=100 \%[/tex]

[tex]MA=VR[/tex]

[tex]VR=\frac{W}{P}[/tex]

[tex]\frac{W}{P}=5[/tex]

[tex]VR=5[/tex]

Answer:

the values of it is the first one. meaning: f(-2)

Answer:

Step-by-step explanation:

2

3

-1

Answer:

-2x-10=-2(x+5)

Step-by-step explanation:

Just multiply and find the pair that matches which happens to be the 3rd pair. you're welcome

Step-by-step explanation:

First sentence

Let the number be X

second sentence

X-5

Third sentence

X-5=14

X=19

The number is 19

Hi there!  

»»————-　★　————-««

I believe your answer is:

19

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

25.

Step-by-step explanation:

Let the number of pupils be x, then:

there are 0.6x girls and 0.4x boys.

From the given information:

0.6x - 0.4x = 5

0.2x = 5

x = 5/0.2

= 50/2

= 25.

Answer:

Para un rectángulo de largo L y ancho W, el área se define como:

A = L*W

Ahora sabemos que nuestro rectángulo tiene un área de 24cm^2

Entonces queremos encontrar 3 pares de valores L y W tal que:

L*W = 24cm

Esto es bastante trivial, podemos simplemente definir una de las dos variables, y así encontrar el valor de la otra.

Por ejemplo, si definimos L = 1cm

tenemos:

(1cm)*W = 24cm^2

W = (24cm^2)/(1cm) = 24cm

Entonces un posible rectángulo tiene un largo de 1cm y un ancho de 24cm

Si tomamos L = 3cm tenemos:

(3cm)*W = 24cm^2

W = (24cm^2)/(3cm) = 8cm

Un rectángulo con 8cm de ancho y 3cm de largo es otra opción.

Si tomamos L = 4cm tenemos:

(4cm)*W = 24cm^2

W = (24cm^2)/(4cm) = 6cm

Un rectángulo con 6cm de ancho y 4cm de largo también es un posible rectángulo.

Así, los 3 rectangulos que se piden pueden ser:

1) largo 1 cm, ancho 24cm

2) largo 3cm, ancho 8cm

3) largo 4cm, ancho 6cm

Answer:

next 3 terms are -15, -28, -41. The formula would be n= (n-1)-13 to get the nth term

Step-by-step explanation:

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

Answer:

the answer is as follows:

Step-by-step explanation:

a)

The equation has the following integer solutions:

5*x+25=-3*xy+8*y^2

Number of solutions found: 3

x1=-31; y1=-10

x2=-7; y2=-2

x3=-5; y3=-0

b)

The equation has the following integer solutions:

2*y^2+x+y+1=x^2+2*y^2+xy

Number of solutions found: 2

x1=0; y1=-1

x2=2; y2=-1

 Do not forget to give appriciation.

Answer:

1) The length of [tex]DC[/tex] is 20.

2) The length of [tex]PS[/tex] is 17.

Step-by-step explanation:

1) If [tex]DR = RE[/tex] and [tex]CS = SB[/tex], then we can use the following proportionality ratio:

[tex]\frac{DE}{DR} = \frac{32 - x}{26 - x}[/tex] (1)

Where [tex]x[/tex] is the length of segment [tex]\overline{CD}[/tex].

If [tex]DE = 2\cdot DR[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{32-x}{26-x}[/tex]

[tex]52 - 2\cdot x = 32 - x[/tex]

[tex]20 = x[/tex]

The length of [tex]DC[/tex] is 20.

2) If [tex]QV = VP[/tex] and [tex]RW = WS[/tex], then we can use the following proportionality ratio:

[tex]\frac{QP}{QV} = \frac{x-7}{12-7}[/tex] (2)

Where [tex]x[/tex] is the length of segment [tex]\overline{PS}[/tex].

If [tex]QP = 2\cdot QV[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{x-7}{5}[/tex]

[tex]10 = x-7[/tex]

[tex]x = 17[/tex]

The length of [tex]PS[/tex] is 17.

Answer:

[tex]32\:\mathrm{m^2}[/tex]

Step-by-step explanation:

When cut by a diagonal, the parallelogram will be divided into two congruent triangles. By definition, congruent polygons have equal areas. Therefore, let the area of each of the triangle be [tex]x[/tex]:

[tex]x+x=64,\\2x=64,\\x=\frac{64}{2}=\boxed{32\:\mathrm{m^2}}[/tex]

Answer:

1. 40

2. 52

Step-by-step explanation: 1. Subtract 16 from 36 then multiply by 2

2. Subtract 4 from 472 then divide by nine

yes it can be possible to do

Answer:

[see below]

Step-by-step explanation:

A functions input is assigned to exactly one output. This means that the inputs must not repeat.

{(-3, 5), (-2, 5), (0, 5), (1, 5), (2, 5)}

Since no inputs repeat, the relation given is a function.

Hope this helps.

Answer:

Yes, it's a function.

Step-by-step explanation:

X or input no repeated.

Answer:

Step-by-step explanation: