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2 years ago

If g(x)=4x^2-16 were shifted 5 units to the right and 2 down, what would the new equation be?

Mathematics

2 answers:

koban [17]2 years ago

6 0

Answer:

A. $h(x)=4(x-5)^2-18$

Step-by-step explanation:

We have been given an equation of a function $g(x)=4x^2-16$ . We are asked to find the formula of the function our g(x) is shifted 5 units to the right and 2 units down.

Let us recall the transformation rules.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}$

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}$

Upon shifting our function to the right by 5 units our function would be:

$g(x)=4(x-5)^2-16$

Let us shift our given function downwards by 2 units.

$g(x)=4(x-5)^2-16-2$

$g(x)=4(x-5)^2-18$

Therefore, option A is the correct choice.

Eduardwww [97]2 years ago

4 0

Try this, pls:
When any line on graph is moved to the right, for 'x' must be '-'.
When one is moved down, for 'y' must be '-'.
Finaly: y=4(x-5)²-18.
Answer: A.

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A boat on the ocean is 2 mi from the nearest point on a straight? shoreline; that point is 15 mi from a restaurant on the shore.

Sladkaya [172]

Answer:

a) x = 0,70 miles

T = 1/2* (√4 + x²) +( 15 - x )/3 Objective Function to minimize

b) V(min) = 2.59 m/hr

Step-by-step explanation:

Let assume the boat is in Point A, she lands in point B, and R is the restaurant

Let call x distance between the point O in which perpendicular line from the boat get to shoreline, and the point were she land.

We know distance is

d = v*t ⇒ t = d/v

She rows at 2 miles/hr and walk at 3 miles /hr

According to that she takes

c (hypotenuse) of right triangle AOB/ 2 rowing

and 15 - x /3 walking

Total time is:

T = c/2 + ( 15-x )/3 c =√(2)² + x² ⇒ T = [√(2)² + x² ] /2 + ( 15-x )/3

T = 1/2* (√4 + x²) +( 15 - x )/3 (1)

And that is the Objective function to minimize

a) Taking derivatives on both sides of the equation we get

T´(t) = x /( √4 + x²) - 1/3 ⇒ T´(t) = 0 x /( √4 + x²) - 1/3 = 0

3*x - √( √4 + x²) = 0 ⇒ 3*x = √( √4 + x²)

Squaring both sides

9x² = 4 + x² ⇒ 8x² = 4 x² = 1/2 x = 0,70 miles

If we plug this value in the Objective function we will get the minimum time

1/2* (√4 + x²) +( 15 - x )/3 ⇒ [√ 4 + 0,5] /2 + 14,3/3 = T (min)

T(min) = 1.06 + 4.77 = 5.83 hr

Distance L (hypotenuse of right triangle AOR)

L = √(2)² + (15)² L = 15,13 miles

And that distance have to be traveled at least in 5.83 hr rowing

Then as v = d/t V(min) = 15.13/ 5.83 ⇒ V(min) = 2.59 m/hr

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2 years ago

A recipe for casserole calls for 2 cups of rice. The recipe makes 6 servings of casserole. how many cups of rice will you need t

ss7ja [257]

You will need 3.333.... cups of rice to make 10 servings of casserole.

Explanation

The recipe which makes 6 servings of casserole, needs 2 cups of rice.

Suppose, you need $x$ cups of rice for making 10 servings of casserole.

Now, the equation according to the ratio of "cups of rice" to the "servings of casserole" will be.....

$\frac{x}{10}=\frac{2}{6}\\ \\ 6x= 2*10=20\\ \\ x=\frac{20}{6}=3.333.....$

So, you will need 3.333.... cups of rice to make 10 servings of casserole.

5 0

2 years ago

EAB and DCB are two right triangles. The figure has BED≅ BDE. Point B is the midpoint of segment AC. Prove: EAB≅ DCB

aleksklad [387]

See the attached picture.

you are given that ABCE is an isosceles trapezoid. 

you are given that AB is parallel to EC. 

this means that AE is congruent to BC. 

you are given that AE and AD are congruent. 

triangle EAD is an isosceles triangle because AE and AD are congruent. 

this means that angle 1 is equal to angle 3. 

since angle 1 is equal to angle 2 and angle 3 is equal to angle 1, then angle 3 is also equal to angle 2. 

this means that AD and BC are parellel because their corresponding angles (angles 3 and 2) are equal. 

since AB is parallel to EC and DC is part of the same line, than AB is parallel to DC. 

you have AB parallel to DC and AD parallel to BC. 

if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. 

that might be able to do it,depending on whether all these statements are acceptable without proof. 

they are either postulates or theorems that have been previously proven. 

if not, then you need to go a little deeper and prove some of the statements that you used.. 

here's my diagram.

this is not a formal proof, but should give you some ideas about how to proceed. 

you can also prove that angle 4 is equal to angle 2 because they are alternate interior angles of parallel lines. 

you can also prove that angle 6 is equal to angle 5 because they are alternate interior angles of parallel lines.

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2 years ago

A rectangle has a length of (3.2a + 0.18b)centimeters.The width is half the length. Sasha writes the expression (12.8a + 0.72b)

jeka94

The width is half the length, so is
width = (1/2)*length
width = (1/2)*(3.2a + 0.18b) cm
width = (1.6a +0.09b) cm

The perimeter of the rectangle is twice the sum of length and width.
perimeter = 2*(length + width)
perimeter = 2*((3.2a +0.18b) cm + (1.6a +0.09b) cm)
perimeter = 2*(4.8a +0.27b) cm)
perimeter = (9.6a +0.54b) cm

Sasha did not get this answer, so apparently ...
her reasoning was not correct.

8 0

2 years ago

3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from p

Marrrta [24]

Answer:

The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer

Step-by-step explanation:

* Lets explain the meaning of the vertical angles

- Vertical angles are the angles opposite to each other when two lines

are intersected

- The vertical angle are equal in measures

- Look to attached figure which represents the lines

∵ Line TW intersects line SV at R

∴ ∠ WRV and ∠ SRT are vertical angle

∴ ∠ WRS and ∠ VRT are vertical angle

∵ RU is between the rays of angle VRW

∴ RU intersects the lines TW and SV at R

∴ No vertical angles between RU and the other two lines because

it intersects them its endpoint R

* Now lets look to the answer to chose the right one

- ∠ WRU and ∠ SRT are not vertical angles

- ∠ WRS and ∠ VRT are vertical angles 

- ∠ VRU and ∠ TRS are not vertical angles

- ∠ VRT and ∠ SRT are not vertical angles

4 0

2 years ago

Read 2 more answers