All categories

3 years ago

The graph below has the same shape. what is the equation of the graph?

Mathematics

1 answer:

Nataly_w [17]3 years ago

3 0

C; A and B are incorrect because the shift is not vertical, it is horizontal. This is because 3 is in parenthesis or a 'grouping' (same thing if it is in an exponent) and is being modified. Since the graph is being translated down 3 units, D is incorrect since it is a translation up 3 units. The answer is C.

You might be interested in

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

Scientists are creating a material that may replace damaged cartilage in human joints. This hydrogel can stretch to 21 times its

Oduvanchick [21]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The length of a rectangle is 6.7 more than 2 times the width. If the perimeter of the rectangle is 57.2 cm, what are its dimensi

Gemiola [76]

From the description, you can get two equation that looks like this:

L= 2*W+6.7cm
Perimeter= 57.2cm

Using perimeter formula, you can put the first and second equation like this:

perimeter= 2L + 2W
57.2cm= 2(2*W+ 6.7)+2W
57.2cm= 4W+ 13.4+ 2W
57.2- 13.4= 6W
W= 43.8/6= 7.3 cm

L= 2W+ 6.7
L= 2*7.3 + 6.7= 21.3
Answer: A. Length=21.3 cm; width=7.3 cm

5 0

3 years ago

Read 2 more answers

[ WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST ]

lapo4ka [179]

Answer:

c!!

Step-by-step explanation:

last saturday i did a worksheet that had the sae question

7 0

3 years ago

Read 2 more answers

The image of the point (4. 9) under a translation is (9. 13). Find the coordinates

gavmur [86]

Answer:

The coordinates of the image are (10,6)

Step-by-step explanation:

Translation

A point located at (x,y), translated by (a,b) maps to the point (x+a,y+b).

If we know the location of the point (x,y) and the location of its image (x',y'), we can know the values of (a,b) by subtracting:

(a,b) = (x',y') - (x,y)

We know the coordinates of the point (4,9) and the coordinates of its image (9,13). Calculate the translation:

(a,b) = (9,13) - (4,9) = (5,4)

If the point (5,2) is translated under the same conditions, then it will map to the point (5,2) + (5,4) = (10,6).

The coordinates of the image are (10,6)

6 0

2 years ago