How do you factorise this using DOPS/DOTS?

2(x + 3)^2-10

Answer:

  0 < x < 3/2

Step-by-step explanation:

The dimensions are positive when ...

  18 -2x > 0   ⇒   x < 9

  3 -2x > 0   ⇒   x < 3/2

  x > 0

So, the values of x where the model makes sense are ...

  0 < x < 3/2

Answer:

19

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

< DBG = 1/2 ( DG)

< DBG = 1/2 ( 360 - BD - BG)

           = 1/2 ( 360 - 172 - 150)

           = 1/2 (38)

           = 19

Answer:

Step-by-step explanation:

y = 2x + 4a/6b   y=(12xb+4b )/6b

6yb=12x+4a

a=(-12xb+6yb)/4=

a=3yb/2 -3xb

x=y/2-a/3b

b=2a/(3y-6x)

the solution is for every variable

Answer:

There is not enough information.

Step-by-step explanation:

Answer:

tan θ × sin θ

From trigonometric identities

[tex] \tan(θ) = \frac{ \sin(θ) }{ \cos(θ) } [/tex]

So we have

[tex] \frac{ \sin(θ) }{ \cos(θ) } \times \sin(θ) [/tex]

We have the final answer as

[tex] \frac{ \sin(θ)^{2} }{ \cos(θ) } [/tex]

Hope this helps you

Answer:

Step-by-step explanation:

The gray shadowed area is below descending function and the line is dashed.

It means coefficient x is m<0 and the sign of inequality is y <  

So the inequality wich  fit it is  y < -1/2x + 2

The blue shadowed area is above ascending function and the line is uninterrupted.

It means coefficient x is m>0 and the sign of inequality is y ≥

So the second inequality of system (y ≥ 3x - 1)  also match.

The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

The standard equation of a line is expressed as y = mx + b;

For the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):

m = 5+1/2-0

m= 6/2

m = 3

The equation of the line is y = 3x - 1

Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1

For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):

m = 0-2/4-0

m= -2/4

m = -1/2

The equation of the line is y = -1/2x + 2

Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2

Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

Learn more on inequality graph here: https://brainly.com/question/9774970

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

Pretty Simple!

Now that you know about ratios and all that, this is pretty tame compared to the last problem.

Now, the problem is talking 2D(2 Dimensions)

The ratio is not going to work because it has only one parameter.

Thus, we need to square it!

[tex](\frac{1}{20})^{2} =\frac{1}{400}[/tex]

Thus, we have your correct ratio.

Now, we only need to do the same thing for the triangle problem. Meaning that, we need to compare the ratios, with x as the thing we are looking for.

[tex]\frac{1}{400}=\frac{219}{x} \\x=87,600[/tex]

See? X is practically handed to us.

Hope this helps!

Answer:

Option (C)

Step-by-step explanation:

Given formula of a line passing through [tex](x_1, y_1)[/tex] and slope 'm' is,

[tex]y-y_1=m(x-x_1)[/tex]

Further solving this equation,

[tex]y-y_1=mx-mx_1[/tex] [By distributive property]

[tex]y-y_1+mx_1=(mx-mx_1)+mx_1[/tex] [By adding [tex]mx_1[/tex] on both the sides]

[tex]y-y_1+mx_1=mx[/tex]

[tex]\frac{y-y_1-mx_1}{m}=\frac{mx}{m}[/tex] [Divide the equation by m]

[tex]\frac{y-y_1}{m}-x_1=x[/tex]

Therefore, Option (C) will be the answer.

Answer:

[tex]x=0\\y=2[/tex]

Step-by-step explanation:

El método de reducción también llamado Suma y Resta, consiste en multiplicar una o ambas ecuaciones de tal manera que los coeficientes de una de las incógnitas sean iguales y de signo contrario, de tal forma que se eliminen al sumar las ecuaciones.

Nuestras ecuaciones son:

[tex]-x+3y=6\\x+y=2[/tex]

En este caso podemos observar que x y -x son iguales y de signo contrario así que no tendremos que multiplicar y podemos sumar ambas ecuaciones.

Al sumarlas tenemos que:

[tex]4y=8\\y=2[/tex]

Ahora sustituímos el valor que encontramos de y en la segunda ecuación para poder obtener el valor de x.

[tex]x+y=2\\x+2=2\\x=2-2\\x=0[/tex]

Por lo tanto, x = 0 y y = 2

Answer:

x = 3.

Step-by-step explanation:

In this case, the x-value never changes, no matter the value of the y. So, x will always equal 3. Your equation is x = 3.

Hope this helps!

Answer:

x=3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (2, - 1), thus

y - (- 1) = - 5(x - 2) , that is

y + 1 = - 5(x - 2) → C

Answer:

Option C is the correct option

Step-by-step explanation:

The general form of point slope form of line is :

[tex]y - y1 =m ( x - x1)[/tex]

Where ( x1 , y1 ) is one point on the line and m is the slope.

In the given problem,

The slope of line ( m ) = - 5

One point on the line = ( x1 , y1 ) = ( 2 , -1 )

The point slope form of the line is:

y - ( - 1 ) = - 5 ( x - 2 )

y + 1 = - 5 ( x - 2 )

Hope this helps..

Best regards!!

Answer:

Step-by-step explanation:

The < symbol does not include the "or equal to" case, so will be graphed with an open circle at the boundary. x < 4 means that values of x less than 4 will be shaded, and there will be an open circle at x=4. Graph B shows this.

__

4 ≤ x means there will be a solid dot at x=4, and values of x greater than 4 will be shaded. Graph A shows this.

Answer: B & A

Step-by-step explanation:

Answer: 180

Step-by-step explanation:

Let the tons of ice the ship was carrying when it set sail be y.

We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.

This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:

2/3 × y = 120

2y/3 = 120

2y = 120 × 3

2y = 360

y = 360/2

y = 180

The ship was carrying 180 tons of ice when it set sail

Answer:

more explanation ?

Step-by-step explanation:

Answer:

y = 3x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x - y + 12 = 0 ( subtract 3x + 12 from both sides )

- y = - 3x - 12 ( multiply through by - 1 )

y = 3x + 12 ← in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , thus

y = 3x + c ← is the partial equation

To find c substitute (2, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = 3x - 1 ← equation of parallel line

Answer:

UV=10.5

Step-by-step explanation:

in triangle XUV it is a right angle at U

sin41=opp/hyp

sin 4` =UV/16

UV=16sin41°

UV=10.5

Answer: 1/5

Step-by-step explanation:

Given the following :

Total number of ducks in pool = 30

Mark 1 = 15 ducks

Mark 2 = 9 ducks

Mark 3 = 6 ducks

Probability of picking a duck with Mark 3:

Probability = (number of required outcomes / total possible outcomes)

Number of required outcomes = number of ducks with mark 3 = 6 ducks

P(picking a duck with Mark 3) = 6/30

6/30 = 1/5

= 1/5

Answer:

360°

Step-by-step explanation:

The sum of all the exterior angles of a triangle is equal to 360 degrees.

Answer:

It would be 360*

Step-by-step explanation:

112+129+119

Answer:

37.5 cm

Step-by-step explanation:

See attached for reference.

let the diagonal be x,

By Pythagorean formula:

x² = (22.5)² + (30)²

x = √[(22.5)² + (30)²]

x = 37.5 cm

Answer:

[tex]39x^2-416xy[/tex]

Step-by-step explanation:

To simplify, we have to distribute the 13x to 3x and -32y. To distribute, we multiply 13x with the first number, and then the second.

[tex]13x*3x=39x^2\\13x-32y=-416xy\\39x^2-416xy[/tex]

The first number is squared ([tex]39x^2[/tex]) because when two [tex]x[/tex]s get multiplied by each other, then it creates a square. We never do this: [tex]39xx[/tex]

Our answer is:

[tex]39x^2-416xy[/tex]

Hope this helps!

Answer:

[tex]\boxed{39x^2-416xy}[/tex]

Step-by-step explanation:

[tex]13x(3x-32y)[/tex]

First step into solving the problem will be to apply the distributive law.

[tex]13x(3x)+13x(-32y)[/tex]

Multiply the terms and simplify.

[tex]39x^2 +-416xy[/tex]

Answer:

$76

Step-by-step explanation:

$38 + $38 = $76

Answer:

[tex]\boxed{\sf LM = 11}[/tex]

Step-by-step explanation:

According to trapezoid mid-segment theorem:

[tex]LM = \frac{QR+ST}{2}\\ Given \ that\ QR = 9, ST = 13[/tex]

[tex]\sf LM = \frac{9+13}{2}[/tex]

LM = 22/2

LM = 11

Answer:

-2

Step-by-step explanation:

The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:

[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]

Given that a line JK, with  Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:

[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]

Line segments can be divided into equal or unequal ratios

The x coordinate of the segment is -2

The coordinates of points J and K are given as:

[tex]J = (-6,-2)[/tex]

[tex]K = (8,-9)[/tex]

The ratio is given as:

[tex]m : n =2 : 5[/tex]

The x-coordinate is then calculated using:

[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]

So, we have:

[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]

[tex]x = (\frac{2}{7}) (14) -6[/tex]

Expand

[tex]x = (2) (2) -6[/tex]

Open bracket

[tex]x = 4 -6[/tex]

Subtract 6 from 4

[tex]x = -2[/tex]

Hence, the x coordinate of the segment is -2

Read more about line ratios at:.

brainly.com/question/14382744

Answer:

This is NOT a one solution problem.

Step-by-step explanation:

Group all terms with a c in it to the left of the equal sign, and group all numbers to the right of the equal sign.

5.7c-1.5+3.2c=7.8c-1.5+1.1c

5.7c + 3.2c - 7.8c - 1.1c = - 1.5 + 1.5

8.9c - 8.9c = 0

0 = 0

No matter which number you substitute for c, it will always be true. Since you can find infinity of solutions, this is NOT a one solution problem.

Answer:

C. 1/3

Step-by-step explanation:

Given:

Number of colors listed (Successful Outcome)

Red 1

Yellow 1

Purple 1

Total or Possible outcome= 3

Required:

What is the theoretical probability that it stops on the red sector on the last spin?

Formula:

Probability= Successful outcome ÷ Possible outcome

Solution:

Probability of the spinner stoping on red.

Probability= Successful outcome ÷ Possible outcome

Probability=1÷3

Probability=1/3

Hope it helps ;) ❤❤❤

The theoretical probability that spinner stops on the red sector on the last spin is option (C)  [tex]\frac{1}{3}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given,

A spinner is separated into 3 equal parts.

Then Mary spins the spinner 6 times.

What is the theoretical probability that it stops on the red sector on the last spin.  So only last spin is important, outcomes of first 5 spin is not important and it is independent.

Probability = Number of favorable outcome / Number of Total outcome

Probability (Red sector) =  [tex]\frac{1}{3}[/tex]

Hence, the theoretical probability that spinner stops on the red sector on the last spin is  option (C)  [tex]\frac{1}{3}[/tex]

Learn more about Probability here

https://brainly.com/question/11234923

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Answer:

VX = 8.8 in

Step-by-step explanation:

By applying Sine rule in the right triangle WXV,

Sin(∠W) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

             = [tex]\frac{\text{VX}}{\text{WX}}[/tex]

Sin(34)° = [tex]\frac{VX}{15}[/tex]

VX = 15.Sin(34)°

     = 8.8379

     ≈ 8.8 in.

Therefore, measure of side VX is 8.8 in.

Answer:

false

Step-by-step explanation:

x/11 +1=7/15

x/11 =7/15 - 1

x/11 = -8/15

They are unequal .So, It is false

Answer:

C) False

D) True

Step-by-step explanation:

C. False

[tex] \frac{x}{11} + 1 = \frac{7}{15} = \frac{x}{11} = \frac{7}{15} + 1 = \frac{7 + 15}{15} = \frac{22}{15} [/tex]

We can see that they are never equal.

D. True

Both have 'x' and 'y' as they terms.

Hope this helps ;) ❤❤❤

Answer:

2,666.67 L of water

Step-by-step explanation:

Solve for W:

1) 3200 = 2400 + 0.3w

2) 800 = 0.3w

Divide both sides by 0.3 to get the variable alone

3) (800)/0.3 = (0.3w)/0.3

4) w = 2,666.67 L