11. The coordinates of AABC are A(-1,1), B(3,3),
and C(4, -2). Find the coordinates of points A', B',
and C' under the translations that take
a. P(0,0) to Q(1,3)
b. P(0, -1) to Q(4,-2)
c. P(-1,-2) to Q(-2,2)

Answers

Answer 1

Answer:

See explanation

Step-by-step explanation:

Given

[tex]A = (-1,1)[/tex]

[tex]B = (3,3)[/tex]

[tex]C =(4,-2)[/tex]

Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]

This means that:

[tex](x,y) \to (x+1,y+2)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1 + 1,1+2)[/tex]

[tex]A' = (0,3)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3 + 1,3+2)[/tex]

[tex]B'= (4,5)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C' = (4+1,-2+1)[/tex]

[tex]C' = (5,-1)[/tex]

Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]

This means that:

[tex](x,y) \to (x+4,y-1)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1+4,1-1)[/tex]

[tex]A' = (3,0)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3+4,3-1)[/tex]

[tex]B'= (7,2)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C' = (4+4,-2-1)[/tex]

[tex]C' = (8,-3)[/tex]

Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]

This means that:

[tex](x,y) \to (x-1,y)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1-1,1)[/tex]

[tex]A' = (-2,1)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3-1,3)[/tex]

[tex]B'= (2,3)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C'= (4-1,-2)[/tex]

[tex]C'= (3,-2)[/tex]


Related Questions

Six sophomores and 14 freshmen compete

Answers

Answer:

(6C1)(5C1)/20C2

Step-by-step explanation:

Was right on egde

The mathematics department of a college has 6 male​ professors, 12 female​ professors, 14 male teaching​ assistants, and 11 female teaching assistants. If a person is selected at random from the​ group, find the probability that the selected person is a teaching assistant or a female.

The probability is ___. ​
(Type an integer or a fraction. Simplify your​ answer.)

Answers

Answer:

37/43

Step-by-step explanation:

6+12+14+11=43

Males: 6+14=20

Females: 11+12=23

If the selected person is a teaching assistant or a female, then the probability is 11+12+14=37. 37/43

what is 9/10 + 7/15

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{9}{10}+\dfrac{7}{15}}[/tex]

[tex]\large\textsf{FIRST: FIND the LCD (Lowest Common Denominator) then solve}\\\large\textsf{from there!}[/tex]

[tex]\large\textsf{If you have calculated it correctly, you should have came up with \underline{\bf 30}}\\\large\textsf{as your LCD (Lowest Common Denominator).}[/tex]

[tex]\mathsf{= \dfrac{9\times3}{10\times3}+ \dfrac{7\times2}{15\times2}}[/tex]

[tex]\mathsf{9\times3=\bf 27}\\\mathsf{10\times3=\bf 30}\\\\\mathsf{7\times2=\bf 14}\\\mathsf{15\times2=\bf 30}[/tex]

[tex]\mathsf{= \dfrac{27}{30}+\dfrac{14}{30}}[/tex]

[tex]\mathsf{= \dfrac{27+14}{30}}[/tex]

[tex]\mathsf{27+ 14=\bf 41}\\\\\mathsf{30+0=\bf 30}[/tex]

[tex]\mathsf{= \dfrac{41}{30}}\large\textsf{ which you could convert to }\mathsf{1 \dfrac{11}{30}}[/tex]

[tex]\boxed{\boxed{\large\textsf{ANSWER: }\bf \dfrac{41}{30} \large\textsf{ or }\mathsf{\bf 1 \dfrac{11}{30}\large\textsf{ because they both equal the same thing}}}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Matematykakdbebox
Jaggbn

Answers

Answer:

theres no question....

Step-by-step explanation:

???


I need help answer asap

Answers

9514 1404 393

Answer:

  A

Step-by-step explanation:

To form the conjugate, change the sign between terms. Leave the radical alone.

  the conjugate is √(x-5) +2 . . . . matches choice A

[tex]\huge\bold\pink{ANSWER} [/tex]

===========================================

A

[tex] \sqrt{ \times - 5 + 2} [/tex]

tsurezure children

#BrainliestBunch

Armando planted a 9-inch tall magical beanstalk. The height of the beanstalk increases by 13% each day. Write a function f that determines the height of the beanstalk in inches in terms of the number of days t since Armando planted the beanstalk.

Answers

Answer:

F(t) = 9(1 + 0.13)^t

Step-by-step explanation:

Given :

Height of beanstalk = initial height = 9 inches

Percentage increase in height per day = 13%

This plant exhibits an exponential increase in growth per day, hence, the function will be modeled using an exponential function.

Using an exponential function :

F(t) = initial height(1 + percentage increase)^t

Where, t = number of days since tree was planted.

The function is :

F(t) = 9(1 + 0.13)^t

Help please guys thanks

Answers

Answer:

D

Step-by-step explanation:

sqrt_{4}(81)^5=(81^(5))^(1/4)=81^(5/4)

Answer:

D

Step-by-step explanation:

if it was properly typed, it would have been All of the above but the most correct option is D.

Compare the functions shown below:



f(x) = 7x + 3 g(x) tangent function with y intercept at 0, 2 h(x) = 2 sin(3x + π) − 1

Answers

F(x) has the greatest y-intercept=3

PLEASE HELPPPPPPPPPP

Answers

Answer: SORRY NEED AN ACCOUNT ON - 10

Step-by-step explanation:

To resolve the proposed issue, an explanation is needed in which the subject is addressed

A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water.

Answers

Speed of canoe in still water we will denote it CS and water itself has a speed we denote it WS. Downstream will be (CS + WS)*45 = 2, Upstream will be (CS - WS)*90 = 2. Solve the system you will find canoe speed in still water and the water speed as well. 90CS = 90WS +2, CS = WS+ 1/45 put it in the first function 90WS +1 = 2, WS = 1/90 miles per minute, CS =1/30 miles per minute.

Q3) He decorated the path in his garden with LED bulbs in three rows so that the bulbs in the first row blink at every 4 min, the bulbs in the second row blink at every 6 min and the bulbs in the third row blink at every 8 min. When will they blink together for the first time if he switches the lights on together at 6pm?

6.24 pm
6.30 pm
6.40 pm
They will not blink together at any time

Q4) If so, which is the next time they blink together?

 6.28 pm
6.48 pm
6.50 pm
None of these. ​

Answers

Answer:

They will blink together at 24minutes

Step-by-step explanation:

Using product of primes

4 = 2²

6 = 2 × 3

8 = 2³

Prime numbers with highest power

2³ × 3

8 x 3

24 minutes.

You $12 for a day, and plan to spend your time feeding the Lorakeets. $2 per feed (f), and drinking ICEE's (I), $4 each. What is the equation for the total number f times you can feed the lorakeets and icees you can drink with your total amount of money you brought?

Answers

Answer: 85 i think

Step-by-step explanation:

What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?

Answers

Answer:

a.

[tex] \frac{36}{40} [/tex]

Can you provide a solution or a formula?

Answers

144 x 1.25 = 180

Answer: 144

Answer:

144

Step-by-step explanation:

144 × 1.25 = 180

We add the 1 to .25 to represent the original value plus the 25% increase.

Or you could have divided 180 by 1.25 to find original price.

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 401 drivers and find that 294 claim to always buckle up. Construct a 90% confidence interval for the population proportion that claim to always buckle up. Use interval notation, for example, [1,5].

Answers

Answer:

[0.6969, 0.7695]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 401 drivers and find that 294 claim to always buckle up.

This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]

The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]

14. A quadratic equation is graphed above.
Which of the following equations could be
paired with the graphed equation to create
a system of equations whose solution set is
comprised of the points (2,-2) and (-3, 3)?
A. y = x + 6
B. y = x - 6
C. y = X
D. y = -x

Answers

Answer:

D.

Step-by-step explanation:

2=-2,3=-3

2²=-2²,3²=3²

billy joe purchased a 60 gallon pool. at 1 pm he stared filling the pool at the rate of 3 gallons per hour. after 10 hours the horses started drinking the water at the rate of 1 gallon per hour. five hours after that he notices the animal and place a second hose in the pool which filled at the rate of 2 gallons per hour. at what time was the pool finally filled

Answers

Answer:

3*10=30 gallons after 10 hours

minus 1 gal/hr for 5 hours=25 gallons.

If the animals are still drinking, the pool is effectively filling at 1 gal/hr, 2-1, and it will take 35 more hours to fill.

If the animals aren't drinking, the pool will fill at 2 gal/hour and it will be full in 35/2 hours or 17.5 hours.

Step-by-step explanation:

Which side of XYZ is the longest?

A. xy
B. xz
C. yz
D. cannot be determined​

Answers

Answer:

the answer is x because its small

Answer:

Step-by-step explanation:

It’s Xy

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it.

[infinity]
â« e^-1.3x dx
1

Answers

divergent is the correct answer goodluck!

Solve for the value of x

Answers

x= 55°

according to the picture .........

Please help me with the question?

Answers

Answer:

<a=55° ,< b=55° and <c=70°

How much wrapping is needed to cover a cubed gift box that is 9 inches high? (Include the bow which takes 115 sq. inches.)

Answers

Answer:

601 in²

Step-by-step explanation:

To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow

Area of bow = 115 in²

Surface area of cube shaped box = 6a²

a = side length of cube = 9

Hence,

Surface area of gift box = 6 * 9²

Surface area = 6 * 81 = 486 in²

Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²

how many distinct permutations can be formed using the letters of the word robberies

Answers

Answer:

45360 arrangements

Step-by-step explanation:

Given the word 'robberies'

Number of letters = 9 letters in total

Repeated letters ; r = 2 ; b = 2 ; e = 2

Therefore, the number of distinct arrangement of letters is :

(total letters)! / repeated letters!

The number of distinct arrangement of letters is :

9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)

362880 / 8 = 45360 arrangements

PQRS is a parallelogram of area 18 cm. if PQ = 5 cm & QR = 4 cm. calculate the lengths of corresponding heights ?​

Answers

Answer:

2cm

Step-by-step explanation:

area of parallelogram=b*h=18cm

5*4=20

length of corresponding heights=20-18

=2cm

the length of corresponding height of the parallelogram is : 2cm

Meaning of a parallelogram

A parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.

A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.

In conclusion, the length of corresponding height of the parallelogram is : 2cm

Learn more about  parallelogram : https://brainly.com/question/970600

#SPJ2

What is the point slope equation of a line with slope -3 that contains points (-8,-4)

Answers

Answer:

y+4=-3(x+8)

Step-by-step explanation:

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x)= sqrt of x [0,9]
c =

Answers

Answer:

9/4

Step-by-step explanation:

f(x) is continuous and differentiable on (0,9).

We want to find c using the following equation.

f'(c)=(f(9)-f(0))/(9-0)

This will require us to find f'(x) first.

f(x)=sqrt(x) is the same as   f(x)=(x)^(1/2)

Using power rule to differentiate this gives f'(x)=(1/2)(x)^(1/2-1) or simplified f'(x)=(1/2)x^(-1/2) or f'(x)=1/(2x^(1/2)).

So we want to solve:

(1/2)c^(-1/2)=(f(9)-f(0))/(9-0)

Simplify denominator on right:

(1/2)c^(-1/2)=(f(9)-f(0))/9

This will require us to find f(9) and f(0).

If f(x)=sqrt(x), then f(9)=sqrt(9)=3 and f(0)=sqrt(0)=0.

So we have the following equation so far:

(1/2)c^(-1/2)=(3-0)/9

Simplify numerator on right:

(1/2)c^(-1/2)=3/9

Multiply both sides by 2:

c^(-1/2)=6/9

Raise both sides to the -2 power:

c^(1)=(6/9)^(-2)

Note c^1=c:

c=(6/9)^(-2):

Note negative exponent means to find reciprocal of base to change exponent to opposite

c=(9/6)^2

Apply the second power:

c=81/36

Reduce by dividing top and bottom by 9:

c=9/4

This means the slope of the tangent to the curve f at x=9/4 is the same value as the slope of the secant line going through points (0,0) and (9,3).

Also 9/4 is between 0 and 9... According to the theorem we were suppose to get a value c between x=0 and x=9.

Confirmation:

Slope of the secant line is (3-0)/(9-0)=3/9=1/3.

Slope of the tangent line to curve f at x=9/4.

f'(x)=(1/2)x^(-1/2)

f'(9/4)=(1/2)(9/4)^(-1/2)

f'(9/4)=(1/2)(3/2)^(-1)

f'(9/4)=(1/2)(2/3)

f'(9/4)=1/3

They are indeed equal values (talking about the 1/3 from the secant and the tangent.)

Solve the triangle. round your answer to the nearest tenth

Answers

Answer:

∡A =41°

~~~~~~~~~~~~

BC=21

~~~~~~~~~~~~~~

sin(24)/AC=sin(41)/21

AC=13

~~~~~~~~~~~~~~

sin(115)/AB=sin(41)/21

AB=29

Step-by-step explanation:

Which is the graph of the equation y- 1 =} (x 3)?
10
06
6 4
(9,5)
3.1)
1
-10-A-22
2 4 6 8 10 x
4
od
wo
10
6

Answers

slope: 2/3
y-intercept(0,-1)

Determine the dimension of the vector space. M4,2
STEP 1: Determine the number of linearly independent vectors needed to span M4,2. The basis for M4,2 has linearly independent vectors.
STEP 2: Using the result from Step 1, determine the dimension of M4,2.

Answers

Answer:  

STEP 1  

M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.  

Hence its basis has 8 linearly independent vectors.  

STEP 2  

Dimension= cardinality of basis = 8.

I really need help!!!​

Answers

Answer:

the third option (a=1, h=0, k=6)

Step-by-step explanation:

if I understand correctly what your teacher wants from you, then you need find a (the factor of x² in the equation) and the vertex (turnaround point) of the parabola represented by such a quadratic equation.

the vertex point coordinates are called (h, k).

the general form of such an equation equation is

y = ax² + bx + c

so, we have a right away : a=1

now we can make this quickly by using common sense, or a bit more complex by going through mathematical formulas.

the fast, practical way is to know that y=x² is the very basic parabola with its vertex at (0, 0).

y = x² + 6 is simply the same parabola just lifted up (y direction) by 6 units, that makes the vertex (0, 6).

in pure theory, though, we need to find the transformation from the general y = ax² + bx + c form to

y = a(x - h)² + k

we see right away that k = f(h) = h² + 6

y = a(x² - 2xh + h²) + k

a=1

y = x² - 2xh + h² + k = x² - 2xh + h² + h² + 6 =

= x² - 2xh + 2h² + 6

comparing with y = x² + 6

we know that

-2×h = 0

as we have no term with just x.

=> h = 0

2h² + 6 = k

2×0² + 6 = 6 = k

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