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STALIN [3.7K]
3 years ago
7

Which statements are true about triangle ABC and its translated image, A'B'C'? Check all that apply.

Mathematics
2 answers:
Natasha_Volkova [10]3 years ago
4 0
This is the concept of translation;
Given that triangle A (-1,3), B(-1,1), C(3,1) has been translated to A'(2,-1), B'(2,-4), C(6,-4)
the from the diagram we see that the coordinates of the triangle ABC have been moved by 3 units to the right while the y coordinates have been moved by 5 units down to form A',B',C'.
We therefore conclude that the correct statement is:
Triangle ABC has been translated 3 units to the right and 5 units down.


adelina 88 [10]3 years ago
3 0

Answer:

The rule for the translation can be written as T3, –5(x, y).

Triangle ABC has been translated 3 units to the right and 5 units down.


Step-by-step explanation:

Just took the test.

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Y=4x-6 and passes through point 8,12
umka2103 [35]

Answer:

Slope of required line if both lines are parallel: y=4x-20

Slope of required line if both lines are perpendicular: y=-1/4x+14

Step-by-step explanation:

We need to find equation of line while we are given another line having equation y=4x-6 and passes through point (8,12)

<u><em>Note: Since it is not given if the required line is parallel or perpendicular to the given line. I will solve for both cases.</em></u>

If Both lines are parallel the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are parallel there slopes are same

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=4

Now finding y-intercept

Using slope m=4 and point (8,12) we can find y-intercept

y=mx+b\\12=4(8)+b\\12=32+b\\b=12-32\\b=-20

y-intercept of new line is: b=-20

Equation of required line having slope m=4 and y-intercept b=-20 is

y=mx+b\\y=4x-20

If Both lines are perpendicular the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are perpendicular there slopes are opposite of each other

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=-1/4

Now finding y-intercept

Using slope m=-1/4 and point (8,12) we can find y-intercept

y=mx+b\\12=-\frac{1}{4} (8)+b\\12=-2+b\\b=12+2\\b=14

y-intercept of new line is: b=14

Equation of required line having slope m=-1/4 and y-intercept b=14 is

y=mx+b\\y=-\frac{1}{4} x+14

8 0
2 years ago
Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1
belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

            F(x) = \int\limits^a_b {f(x)} \, dx

By using integration formula

\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

 \int\limits^6_^-6} (x^{5}  + 8 x^{4}  + 2 x^{2}  + 5 x + 15) )dx

<em>On integration , we get</em>

=   (\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}

F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)

= (\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))

After simplification and cancellation we get

 =  \frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6

on calculation , we get

= \frac{124,416}{5} + \frac{864}{3} + 180

On L.C.M  15

= \frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}

= 25 351.2 units²

<u><em>Conclusion</em></u>:-

<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>

6 0
2 years ago
WILL MARK BRAINLIEST A satellite is to be put into an elliptical orbit around a moon as shown below. A vertical ellipse is shown
Radda [10]

Answer:

a=567 km+900 km

a=1,467 km

b=567 km+169 km

b=736 km

x^2/a^2+y^2/b^2=1

x^2/(1,467)^2+y^2/(736)^2=1

Step-by-step explanation:

7 0
3 years ago
What is the answer for <br> x^2-5x+6=0?
faltersainse [42]
The answer for that is
x= 3,2
5 0
3 years ago
A survey was done that asked people to indicate whether they preferred to swim in a pool or in an ocean. The results are shown i
posledela
Given:
                                 Pool swimming        Ocean swimming    Total
Age 30 and younger             228                         54                 282
Over 30 years old                142                        185                 327
total                                    370                        239                609

Frequencies:
                                Pool swimming        Ocean swimming    Total
Age 30 and younger     228/609 = 0.37         54/609 = 0.09       282/609 = 0.46
Over 30 years old        142/609 = 0.23       185/609 = 0.30       327/609 = 0.54
<span>total                           370/609 = 0.61       239/609 = 0.39       609/609 = 1.00</span>

<span>The relative frequency (rounded to the nearest hundredth) of a person over 30 years old who prefers to swim in the ocean is 0.30</span>    
8 0
3 years ago
Read 2 more answers
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