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Answer: 180 degrees rotation, center (1.5, -0.5)

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Explanation:

Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)

Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2

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Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11

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We have this system of equations

[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]

Equate the right hand sides and solve for x

7x-11 = x-2

7x-x = -2+11

6x = 9

x = 9/6

x = 3/2

x = 1.5

which leads to

y = x-2 = 1.5-2 = -0.5

or

y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5

Either way, x = 1.5 leads to y = -0.5

We get the ordered pair (x,y) = (1.5, -0.5)

This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)

Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that

AD = A''D

BD = B''D

CD = C''D

Answer:

0.4069 ; 1.843

Step-by-step explanation:

Given:

Base of parallelogram, b = (2x - 1)

Height = (4x - 7)

Area = 1

Area of parallelogram = Base * height

Area of parallelogram = (2x - 1) * (4x - 7)

(2x - 1) * (4x - 7) = 1

8x² - 14x - 4x + 7 = 1

8x² - 18x + 7 - 1 = 0

8x² - 18x + 6 = 0

Divide through by 2

4x² - 9x + 3 = 0

Solving the quadratic equation :

Using the formula

-b ± √(b² - 4ac) / 2a

a = 4 ; b = - 9 ; c = 3

Plugging in the values :

-(-9) ± √((-9)² - 4(4)(3)) / 2(4)

9 ± √(81 - 48) / 8

9 ± √33 / 8

(9 ± 5.7445626) / 8

(9 - 5.7445626) / 8) = 0.4069

(9 + 5.7445626) / 8 = 1.843

Answer:

The slope is 7/4 and the y intercept is -10

Step-by-step explanation:

y=7/4x-10

This equation is written is slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 7/4 and the y intercept is -10

Answer:

x = 12 , y = 7

Step-by-step explanation:

Let the numbers be x and y

Sum of the numbers,         x + y = 19 -------- ( 1 )

Difference of the number , x - y = 5 -------- ( 2)

( 1 ) + ( 2 ) => 2x = 24  

                    x = 12

Substitute : x in ( 2 ) => 12 - y = 5

                               => 12 - 5 = y

                              => 7 = y

Answer:

64km/h

Step-by-step explanation:

Average speed= 48km÷45 minutes

= 48km÷0.75h

= 64km/h

Answer:

x=-1

Step-by-step explanation:

the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1

Answer:

1/24

Step-by-step explanation:

13/6x = 52

1/6x = 52/13

1/6x = 4

1 = 4(6x)

1 = 24x

24x = 1

x = 1/24

Step-by-step explanation:

5(x + 7) = 15

x+7=3

x=-4!!!!!!

Answer:

x = -4

Step-by-step explanation:

Solve for x

Divide each side by 5

subtract 7 from both side

Answer:

(a) Tree (see diagram)

(b)   (i) 9/64   (ii) 3/8

Step-by-step explanation:

3 black, 5 white, picks two at random with replacement.

SEE DIAGRAM FOR EXPLANATIONS

(a) Tree (see diagram)

(b)

(i) 9/64

(ii) 3/8

In the given problem we have 3 black ball and 5 white ball, the probability tree be constructed as per ball picks from bag.

(a) Refer the attached figure for the probability tree.

(b)

(i) The probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii) The probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Given:

The bag contain 3 black and 5 white balls.

(a)

Refer the attached figure for the construction of probability tree.

(b)

(i)

Since the getting two black ball are independent event so multiply the branch B ( refer attached figure)

[tex]P(\rm two\: black)=\dfrac{3}{8}\times\dfrac {3}{8}\\P(\rm two\: black)=\dfrac{9}{24}[/tex]

Thus, the probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii)

There should be two outcomes either (B,B) or (W, B).

From the attached figure,

[tex]P(\rm B,B)=\dfrac{9}{64}[/tex]

[tex]P(\rm W, B)=\dfrac{15}{64}[/tex]

Calculate the probability of second ball black.

[tex]P(\rm second\: ball\: black)=P(B, B) + P(W, B)\\P(\rm second\: ball\: black)=\dfrac{9}{64}+\dfrac{15}{64}\\P(\rm second\: ball\: black)=\dfrac{3}{8}[/tex]

Thus, the probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Learn more about probability here:

https://brainly.com/question/11234923

Answer:

10. Where was the medical mission held? A. At Barangay Tatalon Marikina B. At Barangay Almanza Las Piñas City C. At Barangay Pamplona Las Piñas City D. At Barangay CAA BF INT'L Las Piñas City

Answer:

3/4 ft / second

Step-by-step explanation:

15 ft / 20 seconds

Divide the top and bottom by 5

3/4 ft / second

Answer:

[tex] \frac{3}{4} [/tex]ft/sec

Step-by-step explanation:

[tex] \frac{feet}{sec} = \frac{15}{20} [/tex]

[tex] \frac{15}{20} \frac{ \div 5}{ \div 5} = \frac{3}{4} [/tex]

Answer:

(last part)

25%

27.8%

290%

300%

67%

Step-by-step explanation:

Answer:

x = 1/2

hope it helps

have a nice day

Answer:

maybe  x=3.5

Step-by-step explanation:

6x= 1/2 (2x+5)

we take the 1/2 and distribute it into (2x+5) so we end up with

6x= 1x (or just x) + 2.5

We subtract 2.5 from both sides of the equation and we end up with

3.5x= 1x

we then need to isolate the x, so we divide both sides of the equation by x

and then we end up with

3.5= x/x, which ends up just being

3.5=x

Answer:

54

Step-by-step explanation:

Angle 2 and Angle 3 are vertical angles

Vertical angles are congruent ( equal to each other )

So if angle 2 = 54 then angle 3 also equals 54

Answer:

∠3 = 54°

Step-by-step explanation:

54° and ∠3 are vertical angles, which means they are equal .

54° = ∠3

Answer:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

49 dollars

Step-by-step explanation:

14 times 3 is 42 and 3.50 times 2 is 7, so 42 plus 7 is 49.

Total cost with 2 snacks = $35

Total cost with x  snacks = 28+3.50x

Given :

Carson is going to see a movie and is taking his 2 kids. Movie ticket costs $14 and snacks cost $3.50.

Explanation :

Carson buys 2 snacks . we need to find the total cost that Carson have to pay where he buy 2 snacks.

Total cost = cost of ticket (2 kids) + cost of 2 snacks

[tex]Total \; cost = 14(2) + 2(3.50)=35[/tex]

Total cost with 2 snacks = $35

Total cost with x snacks = cost of ticket (2 kids) + cost of x snacks

[tex]Total \; cost = 14(2) + 3.50(x)\\Total \; cost = 28+3.50x[/tex]

Total cost with x  snacks = 28+3.50x

Learn more :  brainly.com/question/17565961

Given:

The two sets are:

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

To find:

The [tex]A\times B[/tex] and the number of relations from A to B.

Solution:

If A and B are two sets, then

[tex]A\times B=\{(x,y)|x\in A, y\in B\}[/tex]

We have,

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

Then,

[tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex]

If number of elements in set A is m and the number of element in set B is n, then the number of relations from A to B is [tex]2^{m\times n}[/tex].

From the given sets, it is clear that,

The number of elements in set A = 2

The number of elements in set B = 3

Now, the number of relations from A to B is:

[tex]2^{m\times n}=2^{2\times 3}[/tex]

[tex]2^{m\times n}=2^{6}[/tex]

[tex]2^{m\times n}=64[/tex]

Therefore, the required relation is [tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex] and the number of relations from A to B is 64.

Answer:

a) correct

b) 70 degrees

Step-by-step explanation:

since in the triangle BXC the sides BX and XC have the same length, they must also have the same angles with the baseline BC.

so, we know, XBC = 55 degrees.

and therefore BCX = 55 degrees.

the sum of all angles in a triangle is always 180 degrees.

so,

BXC = 180 - 55 - 55 = 70 degrees

Answer:

because one pair of congruent corresponding angles is sufficient to determine similar triangles.

Answer:

C

Step-by-step explanation:

Answer:

7 hours

Step-by-step explanation:

9 : 30 to 17:00 = 7 hours 30 minutes

Minus 30 minutes = 7 hours

Answer:

2025 is not a perfect cube

Answer:

[tex]R = \frac{x(x+1)}{2x+1}[/tex] --- total resistance

Step-by-step explanation:

Given

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Required

Find R when

[tex]R_1 = x[/tex]

[tex]R_2 = x+1[/tex]

So, we have:

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Substitute values for both R's

[tex]\frac{1}{R} = \frac{1}{x} + \frac{1}{x+1}[/tex]

Take LCM

[tex]\frac{1}{R} = \frac{x+1+x}{x(x+1)}[/tex]

Collect like terms

[tex]\frac{1}{R} = \frac{x+x+1}{x(x+1)}[/tex]

[tex]\frac{1}{R} = \frac{2x+1}{x(x+1)}[/tex]

Inverse both sides

[tex]R = \frac{x(x+1)}{2x+1}[/tex]

Answer:

y = 6/5x -7

Step-by-step explanation:

Answer:

9-4+(5x3)

Step-by-step explanation:

9-4+15

24-4

20

Solution :

Assuming [tex]$\sigma_1^2=\sigma_2^2$[/tex]

We have to test

[tex]$H_0:\mu_1=\mu_2$[/tex]

Against [tex]H_a: \mu_1 \neq \mu_2[/tex]

Level of significance, [tex]$\alpha = 0.05$[/tex]

[tex]$s_p=\sqrt{\frac{(n_1-1)s_1^2+ (n_2-1)s_2^2}{n_1+n_2-2}}$[/tex]

[tex]$s_p=\sqrt{\frac{(25-1)(425)^2+ (20-1)(415)^2}{25+20-2}}$[/tex]

   = 420.6107

Under [tex]H_0[/tex], the t-statistics is as follows:

[tex]$t=\frac{(\overline{x_1} - \overline{x_2})}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \sim $[/tex]             [tex]$\text{t with }(n_1+n_2-2) \ DF$[/tex]

[tex]$t=\frac{(7200-7087)}{(420.6107)\sqrt{\frac{1}{25}+\frac{1}{20}}}$[/tex]

 = 0.90

DF = (25 + 20 - 2)

    = 43

P-value of the test = 0.375

Since the p value is more than 0.05, we fail to reject our null hypothesis.

There is no difference between then mean tensile strength of the ropes that is produced in the Bozeman and Challis.

the answer for this question is A

Answer:

option B

Step-by-step explanation:

Given :

 [tex]y = 7x^2 - 10[/tex]

Replace x and y :

  [tex]x = 7y^2 - 10 \\[/tex]

Now solve for y :

[tex]x = 7y^2 - 10 \\\\x + 10 = 7y^2 - 1 0+ 10[/tex]                               [tex][ \ adding \ 10 \ on \ both \ sides \ ][/tex]

[tex]x + 10 = 7y^2\\\\\frac{x + 10 }{7 } = \frac{7y^2}{7}[/tex]                                              [tex][ \ dividing\ by \ 7 \ on \ both \ sides \ ][/tex]

[tex]\frac{x+ 10}{7} = y^2\\\\\pm \ \sqrt{\frac{x+ 10}{7}} = y[/tex]

I think the choose (2)

[tex]y = - + \sqrt{ \frac{x + 10}{7} } [/tex]