Triangle ABC has vertices A(4,5), B(8,9), and C(6,7). What are the vertices of triangle A′B′C′ if triangle ABC is translated according to the algebraic description (x, y) → (x + 3, y – 2)?

Answers

Answer 1

Answer:

A'(7,3), B'(11,7) and C'(9,5).

Step-by-step explanation:

The vertices of given triangle are A(4,5), B(8,9), and C(6,7).

Given rule of translation is

[tex](x,y)\rightarrow (x+3,y-2)[/tex]

We need to find the vertices of triangle A'B'C'.

Now,

[tex]A(4,5)\rightarrow A'(4+3,5-2)=A'(7,3)[/tex]

[tex]B(8,9)\rightarrow B'(8+3,9-2)=B'(11,7)[/tex]

[tex]C(6,7)\rightarrow C'(6+3,7-2)=C'(9,5)[/tex]

Therefore, the vertices of triangle A'B'C' are A'(7,3), B'(11,7) and C'(9,5).


Related Questions

PLEASE HELP I HAVE A TIMER
In the diagram, the measure of angle 1 is (3x)°, and the measure of angle 2 is (12x)°

A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.

What is the measure of angle 4?
36°
45°
135°
144°

Answers

Answer:

144 degrees.

Step-by-step explanation:

Draw yourself a diagram with 2 horizontal lines and a transversal cutting across it.

After labeling, you will see that angle 4 is the same as angle 1. You can also see that angle 1 and 2 add up to 180, as they are sitting on a straight line.

First, before we get to the angle of 4, we have to find the value of x:

1) angle 1 + angle 2 = 180

3x + 12x = 180

2) solve the above equation for x

15x = 180

3) divide both sides by 15 for x

x= 12 degrees

We know that angle 4 is the same as angle 2, which is 12x degrees.

So, now that we know what x is, 12 x 12 degrees =  144 degrees.

Hope this helped : )

The measure of angle ∠4 is 144°

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

The measure of angle 1 = ( 3x )°

The measure of angle 2 = ( 12x )°

Angle 1 and Angle 2 are on the straight lines

So , the sum of the measures of angles = 180°

On simplifying the equation , we get

3x + 12x = 180

15x = 180

Divide by 15 on both sides of the equation , we get

x = 12

Substituting the value of x in the equation , we get

The measure of angle 2 = measure of angle 4 ( corresponding angles )

So , the measure of angle 4 = ( 12x )°

And , the measure of angle ∠4 = 144°

Hence , the angle ∠4 = 144°

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If the diagonal distance covered by the stairs pictured is 25 feet, and the horizontal distance is 15 feet, what is the height of the stairs? Round your answer to the nearest foot if necessary

25 feet
22 feet
400 feet
20 feet

Answers

Answer: 20 feet

Step-by-step explanation:

Hi, since the situation forms a right triangle we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the diagonal distance covered by the stairs) and a (horizontal distance) and b (vertical distance) are the other sides.  

Replacing with the values given:  

25^2 = 15^2 + b^2  

625 = 225 + b^2  

625-225 = b^2

400= b^2

√400 =b

b =20 feet

Feel free to ask for more if needed or if you did not understand something.  

Answer: 20 feet

Step-by-step explanation:

From the question, the diagonal distance covered by the stairs is 25 feet, and the horizontal distance is 15 feet. To calculate the height of the stairs, we will use the Pythagoras rule

The square of the diagonal will be equal to the addition of the square of the horizontal distance and the square of the height. This will be:

25² = 15² + height²

height² = 25² - 15²

height² = 625 - 225

height² = 400

height = ✓400

height = 20 feet

The height of the stairs is 20 feet

You bought groceries last week. You used coupons and saved 25% on your grocery bill. You saved $8.80. How much was your bill before coupons?

Answers

Answer:

$35.2

Step-by-step explanation:

% saved = 25%

Money saved = $8.80

Let x be the bill before the coupon discount.

25/100 × x = 8.80

x = $35.2

PLSSSSS HELPPPP!!! A data set has a mean of 72 and a standard deviation of 3.5. The z-score for a data point is -1.2. What is the data point?

Answers

Answer:

D. The data point is 2.5 standard deviations away from 0.5.

Step-by-step explanation:

Z-score is the measure of how many number of standard deviations, the data point, is away from the mean. It also measures how many standard deviations below or above the population mean, a raw score is.

Given, a set of data has a mean (μ) of 0.5 and a standard deviation (σ) of 0.01 with a data point of the set has a z-score of 2.5.

i.e the data point is 2.5 standard deviations away from the mean 0.5.

Hope this helped!

Oh yikes this is a hard one!

Divide and answer in simplest form

A. 1/15
B. 15/1
C. 3/5
D. 5/3

Answers

Answer:

A.

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] ÷ 5 = [tex]\frac{1}{3}*\frac{1}{5} =\frac{1}{15}[/tex]

1x3 / 5x3
1/15 the answer is A

Given the original statement "If a number is negative, the additive inverse is positive," which are true? Select three options.
If p = a number is negative and g = the additive inverse is positive, the original statement is p - 9.
If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is p -9.
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~g - p.
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is perq.
Ulf g = a number is negative and p = the additive inverse is positive, the converse of the original statement is 9 - p.

Answers

Step-by-step explanation:

If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is q → p. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.

help on this translation, please :)

Answers

Answer:

1) False, the point would get flipped diagonally, to -4, 4.

2) True, the point would get flipped diagonally, to -2, 6

3) False, the point would get flipped diagonally, to -3, 1

4) True, the point would get flipped diagonally, to 5, 2

5) True, the point would get flipped diagonally, to 7, 5

6) False, the point would get flipped diagonally, to -9, 3

7) True, the point would get flipped diagonally, to -5, 4

8) True, the point would get flipped diagonally, to 2, 1

Answer:

1. true

2. false

3. true

4. false

5. false

6. true

7. false

8. false

Step-by-step explanation:

DONT TRUST ME ON THESE ANSWERS CAUSE IM NOT 100% SURE :0

One batch of cookies takes two and two-fifths cups of milk. How many cups of milk will 25 batches of cookies require?

Answers

Answer:

60 cups.

Step-by-step explanation:

2 x 25 = 50

2/5 x 25 = 10

50 + 10 = 60

Solve the equation. –3|y – 3| = 9

Answers

Answer:

 y = 0

Step-by-step explanation:

-3(y-3)=9

One solution was found :

                  y = 0

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    -3*(y-3)-(9)=0

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (0 -  3 • (y - 3)) -  9  = 0

Step  2  :

Equation at the end of step  2  :

 -3y  = 0

Step  3  :

Solving a Single Variable Equation :

3.1      Solve  :    -3y = 0

Multiply both sides of the equation by (-1) :  3y = 0

Divide both sides of the equation by 3:

                    y = 0

Answer:

No solution

Step-by-step explanation:

–3|y – 3| = 9

⇌       (Divide both sides by -3)

|y – 3| = -3  impossible

because  |y – 3| is greater than 0 and -3 is less than 0.

plz help ill mark u brainliest

Answers

Answer:

1/6

Step-by-step explanation:

P(3) = number of three's  / total number of outcomes

      = 1/6

Can someone help me asap

Answers

The right answer is 2.8

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

2.8
Sjjsjsjs jsjsjzjz jsjsjzjz!

Answer plz!
Which choices are equivalent to the quotient below? Check all that apply.

Answers

Answer:

A, C, and E are correct

Step-by-step explanation:

please help solve this

Answers

Answer:

last option

Step-by-step explanation:

We know that a₁ (or the first term) = 4 so we can rule out the second and third options. d (or the common difference) = 8 (because 4 + 8 = 12, 12 + 8 = 20 and so on) so our answer is the last option.

I think it is the last option

Which expression represents the product of 25 and 9 divided by 52

Answers

Answer:

(25*9)/52

Step-by-step explanation:

Answer:

225/9

Step-by-step explanation:

Product of 25 and 9

------------------------------ = 225/52

             52'

When you are given answer choices, please share them.  Thanks.

12. A package of 4 chocolate bars cost $3.29.
What is the price per chocolate bar? (Round to 2 decimal places)

Answers

Answer:

$0.82

Step-by-step explanation:

The full answer is 0.8225, although I believe that I was supposed to round it to the nearest hundredth, so I did that. What I did was I divided 3.29 by 4.

Answer:

.82 per chocolate bar

Step-by-step explanation:

Take the price and divide by the number of chocolate bars

3.29/4

.8225

Rounding to two decimal places

.82 per chocolate bar

Help mee pweaseeeeeee :)))

Answers

Answer: .4

Step-by-step explanation:

.


Which shows the pre-image of quadrilateral W'X'Y'Z' before the figure was rotated according to the rule (x,y) → (-x, -y)?
у
6
5
Z
Y'
4
3
X
2
1
х
1. 2. 3. 4. 5. 6
6.-5.4-3-2-11
-2
5
LE
Ty​

Answers

Answer:

W(-2, -3), X(-6, -3) , Y(-6, -4) and Z(-3, -5)

Step-by-step explanation:

In the figure attached, the quadrilateral W'X'Y'Z'  is shown. Its coordinates are W'(2, 3), X'(6, 3), Y'(6, 4) and Z'(3, 5). Transforming these points according to the rule (x,y) → (-x, -y) we can get the pre-image, quadrilateral WXYZ, as follows:

W'(2, 3) -> W(-2, -3)

X'(6, 3) -> X(-6, -3)

Y'(6, 4) -> Y(-6, -4)

Z'(3, 5) -> Z(-3, -5)

Answer:

the answer is A

Step-by-step explanation:

Mark me brainliest

What is the volume of the cylinder below?

Answers

i’m sorry, i don’t think the cylinder picture is attached

Answer:

No picture

Step-by-step explanation:

The picture isnt attached :( but the equation for the volume of a cylinder is: Hx [tex]\pi r^{2}[/tex]

H= height    R: Radius

So for example if the height was 10 and the radius was 2 you would do the following:

Hx[tex]\pi r^{2}[/tex]

= 10x 3.14x[tex]2^{2}[/tex]

= 10x 3.14x 4

= 10x 12.56

= 125.6cm^3 :)

[tex]\pi r^{2}[/tex] is the equation on finding the are of the circle (bottom circle or top circle) we then multiply is by its height because its like the circle being stacked up together until it reaches the height. :) Hope this helps

Is (–6, 6) a solution to the equation y = –x?

Answers

Answer:

Yes

Step-by-step explanation:

Yes since y is the negative of x like 6=-(-6)

Answer:

Yes.

Step-by-step explanation:

Because 6 is Y axis and -6 is the X axis. So therefore the equation is right.

Please help as quickly as possible

Answers

Answer:

The next fraction in the sequence is:

4/27

Step-by-step explanation:

How you can see, the fractions are decreasing as the sequence advance, to identify the proportion in which it decreases, we will divide the first and the second fractions:

3/4 / 1/2 = 3/2 or 1.5

Now, we just need to divide all the fractions in 3/2 to identify the next fraction, as I show below:

3/4 / 3/2 = 1/2 1/2 / 3/2 = 1/3 1/3 / 3/2 = 2/9 2/9 / 3/2 = 4/27

As you can see, all the results own to the sequence given, for this reason, the last result 4/27 is the correct fraction next to 2/9.

The area of a triangle is 17.5 square meters. The height of the triangle is 3 meters less than twice its base. The base of the triangle is x meters. Complete the equation that represents this description and fill in the values for the base and height of the triangle. The equation modeling the described triangle is x2 + x + = 0. The base of the triangle is meters. The height of the triangle is meters.

Answers

Answer:

A = ½ * base * height

A = ½ * x * (2x-3)

17.5 = ½ * (2x² - 3x)

35 = 2x² - 3x

0 = 2x² - 3x - 35

2x² - 3x - 35 = 0 .......... (the equation)

(2x + 7)(x - 5) = 0

2x + 7 = 0

2x = - 7

x = -7/2 = -3.5

x-5 = 0

x = 5

since we have two result of x, then we can choose the positive one x = 5

so the base is 5 m and the height is

h = (2x - 3) = 2*5 - 3 = 10-3 = 7 m

thomas has 4 blocks colored blue,red,green and yellow. How many different ways can he combine them on a shelf?

Answers

Answer: 24

Step-by-step explanation:

Take the factorial of that number.

4! = 4*3*2*1=24

please help me with this question (pic attached) explain if you can

Answers

Answer:

For x=1 substituting in f(x) the value of x

f(1)=-3(1)+1 = -2

For x=0 substituting in g(x) the value of x

g(0)=3^(0) =1

Finally, we have to find for what value of x the function f(x) gives -8

f(x) = -8

-8 = -3x+1

-3x=-9

x=3

Carrie and Kenny both play soccer. Kenny scored 3 times as many goals as Carrie. Together they scored 12 goals. Could Carrie have scored 2 goals? Why or why not? Yes, because 2 goals is less than the total number of goals scored. No, because 3(2) + 2 ≠ 12. Yes, because 2 goals is less than the number of goals Kenny scored. No, because 3(2) ≠ 12.

Answers

Answer:

No, because 3(2) + 2 ≠ 12.

Step-by-step explanation:

An equation is formed of two equal expressions. Carrie has not scored 2 goals, because 3(2) + 2 ≠ 12. The correct option is B.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Carrie and Kenny both play soccer. Kenny scored 3 times as many goals as Carrie. Therefore, we can write,

Number of goals scored by Carrie = x

Number of goals scored by Kenny = 3x

Now, given that Together they scored 12 goals. Therefore, the total scores can be written as,

Total score = Number of goals scored by Carrie +Number of goals scored by Kenny

12 = x + 3x

12 = 4x

x = 3

Further, the number of goals for the two can be written as,

Number of goals scored by Carrie = x = 3

Number of goals scored by Kenny = 3x = 3×3 = 9

Hence, Carrie has not scored 2 goals, because 3(2) + 2 ≠ 12.

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8-2x<4 solve inequality

Answers

Answer:

x > 2

x ∈ ( +2 ; + oo )

Step-by-step explanation:

8 - 2x < 4

8 - 4  < 2x

4 < 2x | : 2

2 < x

x > 2

x ∈ ( +2 ; + oo )

Can someone help me with this?

Answers

The right answer is 40

please see the attached picture for full solution

Hope it helps

Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs. What percentage of time was spent sprinting? please explain how you get the answer, I want to understand on my own and math is a struggle for me.

Answers

In total Lt. Bartlett spent 4.5 hours exercising. He spent a total of 1 hour sprinting so you would divide 1 by 4.5 to get .222 repeated hours which could be rounded to .22 I hope this helps, I’m not the best at explaining things.

If Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.

What is Percentage?

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given that;

Time spent on push ups = 2 hoursTime spent on sprints = 1 hoursTime spent on benching = 1.5 hoursPercentage of time spent sprinting P = ?

First we determine the total time.

T = tPUSHUPS + tSPRINT + t BENCHING

T = 2hrs + 1hr + 1.5hrs

T = 4.5hrs

Now, percentage of time spent sprinting P will be;

Percentage = ( Part / Whole ) × 100%

Percentage = ( tSPRINT / Total time ) × 100%

P = ( 1hr / 4.5hr ) × 100%

P = ( 0.2222 ) × 100%

P = 22.2%

Therefore, if Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.

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Which line segment shows the base that corresponds to the given height of the triangle?

Answers

Answer:

A

Step-by-step explanation:

The height of the triangle is always perpendicular to the base. Therefore, in this figure, the base of the triangle corresponds to segment A

the answer for this problem is A

I don’t need you to explain just answer.

Answers

Answer:

Simplify the expression.

i could not type in exponent so just open the screen shot

Step-by-step explanation:

i Hope it works

Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 15 and the x-axis on the interval [–6, 6]. Round off your answer to the nearest integer.

Question 15 options:

25,351 units2

149,473 units2

3,758 units2

2,362 units2

Answers

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

            [tex]F(x) = \int\limits^a_b {f(x)} \, dx[/tex]

By using integration formula

[tex]\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c[/tex]

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

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

On integration , we get

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

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

= [tex](\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))[/tex]

After simplification and cancellation we get

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

on calculation , we get

= [tex]\frac{124,416}{5} + \frac{864}{3} + 180[/tex]

On L.C.M  15

= [tex]\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}[/tex]

= 25 351.2 units²

Conclusion:-

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

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