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2 years ago

Which rule was used to translate the image?

Mathematics

2 answers:

Korvikt [17]2 years ago

7 0

Answer: $(x,y)\rightarrow(x-8,y+11)$

Step-by-step explanation:

Given: Right triangle LMN has vertices L(7,-3), M(7,-8) and N(10,-8).

The triangle is translated on the coordinate plane so the coordinates of L' are (-1,8)

The difference in the x coordinates of L and L' (corresponding vertices) = $-1-7=-8$ ...............→ translated 8 units left.

The difference in the y coordinates of L and L' = $8-(-3)=11$ ...............→ translated 11 units upwards.

Thus, triangle LMN translated 8 units left and 11 units above the coordinate plane .

So the rule used to translate the image will be :_

$(x,y)\rightarrow(x-8,y+11)$

damaskus [11]2 years ago

3 0

Answer:

Step-by-step explanation:

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Damien , Jake , and Makayla shared a bowl of grapes . Damien ate x grapes . Jake ate 1 more than twice the number of grapes that

vivado [14]

Answer:

There were (4x + 2) grapes in the bowl

Step-by-step explanation:

Here, we are interested in calculating the total number of grapes in the bowl.

We have 3 people sharing the total

Damien are x grapes

Jake ate 1 more than twice what Damien and that is (1 + 2x) grapes

Makayla ate 5 fewer grapes than Damien: So what Makayla ate is (x-5) grapes

And now, we have 6 grapes left.

To find the total number of grapes in the bowl, we need to add up all what they ate plus what is left.

Mathematically, that would be;

x + 1 + 2x + x -5 + 6

= 4x + 2

8 0

2 years ago

Read 2 more answers

Easy question.

Nimfa-mama [501]

Answer:

Pia

Step-by-step explanation:

The smaller the number of pencils in a bundle the greater the number of bundles.

For example if the number of pencils each has is 60,

Then the number of bundles for Pia = 60/10 = 6,

and ...................................................Gauri = 60/12 = 5,

and .....................................................Yasmin = 60/20 = 3.

3 0

2 years ago

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16

jolli1 [7]

To find the time at which both balls are at the same height, set the equations equal to each other then solve for t.
h = -16t^2 + 56t
h = -16t^2 + 156t - 248
-16t^2 + 56t = -16t^2 + 156t - 248
You can cancel out the -16t^2's to get
56t = 156t - 248
=> 0 = 100t - 248
=> 248 = 100t
=> 2.48 = t
Using this time value, plug into either equation to find the height.
h = 16(2.48)^2 + 56(2.48)
Final answer:
h = 40.4736
Hope I helped :)

6 0

2 years ago

Read 2 more answers

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles

Ugo [173]

By definition, the average rate of change is given by:

$AVR = \frac{f(x2)-f(x1)}{x2-x1}$

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

$f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2$

Evaluating for x = 3:

$f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18$

Then, the AVR is:

$AVR = \frac{18-(-2)}{3-(-2)}$

$AVR = \frac{18+2}{3+2}$

$AVR = \frac{20}{5}$

$AVR = 4$

For f (x) = 3x - 8:

Evaluating for x =4:

$f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4$

Evaluating for x = 5:

$f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7$

Then, the AVR is:

$AVR = \frac{7-4}{5-4}$

$AVR = \frac{3}{1}$

$AVR = 3$

For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

$f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15$

Evaluating for x = 4:

$f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8$

Then, the AVR is:

$AVR = \frac{8-15}{4-(-3)}$

$AVR = \frac{-7}{4+3}$

$AVR = \frac{-7}{7}$

$AVR = -1$

For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

$f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4$

Evaluating for x = 1:

$f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4$

Then, the AVR is:

$AVR = \frac{-4-(-4)}{1-(-1)}$

$AVR = \frac{-4+4}{1+1}$

$AVR = \frac{0}{2}$

$AVR = 0$

Answer:

from the greatest to the least value based on the average rate of change in the specified interval:

f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]

4 0

1 year ago

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the he

Tamiku [17]

Answer:

5 feet

Step-by-step explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

$y=-0.4x^2+3x$

where y is the height above water and x is the horizontal distance in feet.

If a beam of light is shone upward at an angle modeled by the equation

$x+y=10$

A beam of light hit the dolphin.

So, line must be intersect path of dolphin.

Using substation method,

Substitute y=10-x into dolphin equation.

$10-x=-0.4x^2+3x$

$-0.4x^2+4x-10=0$

$x=\dfrac{-4\pm\sqrt{4^2-4(-10)(-0.4)}}{2(-0.4)}$

$x=5\text{ feet }$

$y=5\text{ feet }$

Hence, The beam hit dolphin at 5 feet.

8 0

2 years ago