Write the equation for each translation of the graph of y=|1/2x-2| +3.

one unit to the right

Answer:

∠DBC = 155°

Step-by-step explanation:

Assuming that ABC is a straight line.

Angles on a straight line sum to 180°.

⇒ (2x² + 3x - 2) + ∠DBC = 180°

⇒ ∠DBC = 180° - (2x² + 3x - 2)

The sum of the interior angles of a triangle is 180°:

⇒ (x² + 1) + (4x + 3) + ∠DBC = 180°

⇒ ∠DBC = 180° - (x² + 1) - (4x + 3)

Therefore, we can equate the equations and solve for x:

⇒ ∠DBC = ∠DBC

⇒ 180 - (2x² + 3x - 2) = 180 - (x² + 1) - (4x + 3)

⇒ 180 - 180 = (2x² + 3x - 2) - (x² + 1) - (4x + 3)

⇒ (2x² + 3x - 2) - (x² + 1) - (4x + 3) = 0

⇒ 2x² + 3x - 2 - x² - 1 - 4x - 3 = 0

⇒ x² - x - 6 = 0

⇒ x² + 2x - 3x - 6 = 0

⇒ x(x + 2) - 3(x + 2) = 0

⇒ (x + 2)(x - 3) = 0

Therefore,  x = -2, x = 3

As angles are positive, x = 3 only

Substituting found value of x into the angle expressions:

⇒ ∠BDC = x² + 1 = (3)² + 1 = 10°

⇒ ∠DCB = 4x + 3 = 4(3) + 3 = 15°

The sum of the interior angles of a triangle is 180°:

⇒ ∠DBC  + ∠BDC + ∠DCB = 180°

⇒ ∠DBC = 180° - ∠BDC - ∠DCB

⇒ ∠DBC = 180° - 10° - 15°

⇒ ∠DBC = 155°

Sum of two interiors=exterior

Take it positive

Now

Now

<DBC=180-25=155°

The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°)   ⇒   b = 96√3 cm

Call b the base of this triangle.

The vertex angle is 120°, so the other two angles have measure θ such that

120° + 2θ = 180°

since the interior angles of any triangle sum to 180°. Solve for θ :

2θ = 60°

θ = 30°

Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

tan(30°) = h / (b/2)   ⇒   h = 48 cm

Then the area of the triangle is

1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

3072π cm² - 2304√3 cm² ≈ 5660.3 cm²

Answer:

tan is opposite over adjacent soo 12/15=4/5

Step-by-step explanation:

soo the answer is C

Answer:

4 less (less than or Equal to) X (less than or Equal to) 13

Step-by-step explanation:

Note:-

Here

we can see

Hence domain

56 - 15 = 41min

hope it helps...!!!

Answer:

41 minutes

Step-by-step explanation:

The length of time from 8:15 PM to 8:56 PM is 41 minutes (56-15 = 41)

Answer:

The answer my good friend is 7776 because if you do 6 to the 5th power  or 6x6x6x6x6 you will get 7776.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

we'll make x the number of hours and set up the following equation:

59km x + 67km x = 1008km

Now we solve for x(hours)

126x = 1008

x = 8

Answer:

53.3 somewhere like that

Step-by-step explanation:

Answer:

746

Step-by-step explanation:

i got the same question

Answer:

7x+10

Step-by-step explanation:

First, distribute the 2

2(x+5) +5x

2*x+2*5 +5x

2x+10+5x

Combine like terms

2x+5x+10

7x+10

Answer:

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20      |  10       |    50   |  100   |

Step-by-step explanation:

Formula :  y=k/x

Solve:

Before we find the answer chart =

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20     |      ?        |    ?     |      ?      |

20 = ? / 200

? = 10

Thus,

100/10 = 10

500/10 = 50

1000/10 = 100

So the chart now is:

| Drink (x ml) |   200 |       100 |    500|   1000|  

| Sugar (y g)  | 20      |  10       |    50   |  100   |

~lenvy~

Answer:

3

Step-by-step explanation:

The formula for slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], plugging in the given values, we'll have: [tex]\frac{14-8}{4-2}[/tex]

[tex]\frac{14-8}{4-2}[/tex]

[tex]\frac{6}{2}\\\\=3[/tex]

hope this helps!

Answer:

Step-by-step explanation:

You have to solve this using the slope formula in order to get the right answer.

[tex]\underline{\text{SLOPE:}}[/tex]

[tex]\Longrightarrow: \sf{\dfrac{Y_2-Y_1}{X_2-X_1} }[/tex]

y2= 14

y1= 8

x2= 4

x1= 2

Rewrite the problem.

[tex]\sf{\dfrac{14-8}{4-2}=\dfrac{6}{2}=\boxed{\sf{3}}[/tex]

I hope this helps. Let me know if you have any questions.

The root of the system of equations is x = -1

That is, the lines intersect at (x,y)= (-1,-5)

Answer:

1,000 mm³

Step-by-step explanation:

To find the volume we use the formula:

V = L×W×H   (L=length, W=width and H=height)

Since we are given all values we substitute the values to give us:

V= 10×10×10 = 1000

Units will be mm³ as this is volume.

Answer:

if it's area, it's the first one

If reflected over y = x

then use

[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right][/tex]

=====================

[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right][/tex]

similar as (x, y) → (y, x)

multiply the matrixes to get the final answer

[tex]\left[\begin{array}{ccc}(3*0+1*-3)&(6*0+1*3)&(3*0+1*3)\\(3*1+(-3*0)&(1*6+0*3)&(1*3+0*3)\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-3&3&3\\3&6&3\end{array}\right][/tex]

Answer:

[3,-3,-3] [-3,-6,3]

Step-by-step explanation:

jus got it right

The population of organisms is described by the following exponential equation:

P(t) = 18,000*(0.9966)^t

The general exponential equation is:

P(t) = A*(b)^t

Where A is the initial value, b depends on the percentage that changes, and t is the variable.

In this case, the population decreases by 3.4%, then we have:

B = 1 - 3.4%/100% = 0.9966

And the initial value is 18,000 organisms, replacing that in the general equation we get:

P(t) = 18,000*(0.9966)^t

This is the equation that represents the population.

If you want to learn more about exponential equations, you can read:

https://brainly.com/question/11832081

Answer:

Domain:  0 ≤ x ≤ 4

Range:  0 ≤ y ≤ 64

Step-by-step explanation:

Information

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

From inspection of the diagram, the minimum value of x is 0 and the maximum value of x is 4.

Therefore, the domain is:  0 ≤ x ≤ 4

From inspection of the diagram, the minimum value of y is 0 and the maximum value of y is 64.

Therefore, the range is:  0 ≤ y ≤ 64

Remember:-

If a pair be (x,y) then

hence

Here x goes from 0 to 4 so domain is

Y goes from 0 to 64 hence range is

Answer:

2/6, 1/3, 33.33%

Step-by-step explanation:

To roll a 5 or 6, meaning 2 numbers.

There are a total of 6 numbers on the die.

Therefore, it would be 2 out of 6, or 2/6.

Simplified: 1/3 or 33.33%

If we have 360 degrees and need to divide it into 12 equal angles, then all we have to do is a simple division problem.

360 / 12 = 30

There are 30 degrees in each angle.

Hope this helps!

Answer:

30 i think ???

Step-by-step explanation:

Step-by-step explanation:

area of inner rectangle = 10*8 = 80 units^2

area of outer rectangle = 12*10 = 120 units^2

area of shaded portion = 40units^2

Answer:

[tex]\frac{1}{x^2}[/tex]

Step-by-step explanation:

Hey there!

x^2 / x^4

≈ x * x / x * x * x * x

SIMPLIFY IT!

≈ 1 / x^2

Therefore, your answer should be:

1/x^2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:105

Step-by-step explanation:

A product is the outcome of multiplication. Brad can put 144 balls in the box.

A product is the outcome of multiplication or an expression that indicates the elements that will be multiplied.

Given that the bottom layer of the box has 6×6 balls, while the box has 5 layers. Since one layer is already arranged, therefore, there are only 4 layers left in which each layer will have 6×6 balls. Therefore, the total number of balls is,

[tex]\text{Total number of ball} = 4 \times 6\times 6 = 144[/tex]

Hence, Brad can put 144 balls in the box.

Learn more about Mulitplication:

https://brainly.com/question/14059007

#SPJ1

Step-by-step explanation:

The interest I per t years is 2.8% of invested amount P

Let the interest amount is same as invested amount, then our equation is

Find the value of t

Answer:

Equation:  250(1 + 0.028t) = 500

Answer:  36 years

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute given values into the formula and solve for t:

250(1 + 0.028t) = 500

⇒ 250 +7t = 500

⇒ 7t = 250

⇒ t = 250/7

⇒ t = 35.71428571...

So it will take approximately 36 years for Edward to double his money.

byAnswer: doing the trials/tests

Step-by-step explanation: Learn With Brainly

Step-by-step explanation:

The lines meet at (6,0)

That is the solution to the system of equations.

Answer:

12

Step-by-step explanation:

I am in 12th grade and make straight A;s trust me