look at image. reflection across x=-1 ​

Answer:

C(-3,3)

Step-by-step explanation:

Given

A = (7,-1)

B = (2,1)

AB:AC = 1:2

Required

Determine the coordinates of C

Since, B is between A and C; we need to determine ratio BC as follows;

[tex]AB:AC = 1:2[/tex]

Convert to division

[tex]\frac{AB}{AC} = \frac{1}{2}[/tex]

AC = AB + BC;

[tex]\frac{AB}{AB + BC} = \frac{1}{2}[/tex]

Cross Multiply

[tex]2 * AB = 1 * (AB + BC)[/tex]

[tex]2 AB = AB + BC[/tex]

[tex]2AB - AB = BC[/tex]

[tex]AB = BC[/tex]

Divide both sides by BC

[tex]\frac{AB}{BC} = 1[/tex]

Rewrite as

[tex]\frac{AB}{BC} = \frac{1}{1}[/tex]

Write as ratio

[tex]AB:BC = 1:1[/tex]

Next is to determine the coordinates of C as follows;

Because B is between both points. we have:

[tex]B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where

[tex]m:n = AB:BC = 1:1[/tex]

[tex]B(x,y) = B(2,1)[/tex]

[tex]A(x_1,y_1) = A(7,-1)[/tex]

So; we're solving for x2 and y2

[tex]B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where

Solving for x2;

[tex]x = \frac{mx_2 + nx_1}{m+n}[/tex]

[tex]2 = \frac{1 * x_2 + 1 * 7}{1+1}[/tex]

[tex]2 = \frac{x_2 + 7}{2}[/tex]

Cross Multiply

[tex]2 * 2 = x_2 + 7[/tex]

[tex]4 = x_2 + 7[/tex]

[tex]x_2 = 4 - 7[/tex]

[tex]x_2 = -3[/tex]

Solving for y2;

[tex]y = \frac{my_2 + ny_1}{m+n}[/tex]

[tex]1 = \frac{1 * y_2 + 1 * -1}{1+1}[/tex]

[tex]1 = \frac{y_2- 1}{2}[/tex]

Cross Multiply

[tex]2 * 1 = y_2 - 1[/tex]

[tex]2 = y_2 - 1[/tex]

[tex]y_2 = 2 + 1[/tex]

[tex]y_2 = 3[/tex]

Hence, the coordinates of C are: C(-3,3)

Answer:

$37.80

Step-by-step explanation:

Add the cost of the 2 video games together to get 77.85

Subtract 77.85 from the total, $115.65

$37.80

Hope this helps :-)

Answer:

A

Step-by-step explanation:

The function that best describes the graph is y = x²-9x+1+20

A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).

Given that, a graph, we need to find its function,

The parabola is intersecting the x-axis at 4 and 5, therefore, the function in the option having value of equal to 4 and 5 is the function of the graph,

So, the first function is =

y = x²-9x+20

Put y = 0,

x²-9x+20 = 0

Factorizing the equation to get the values of x,

x²-9x+20 = 0

x²-4x-5x+20 = 0

x(x-4)-5(x-4) = 0

(x-5)(x-4) = 0

Therefore,

x = 5, 4

Since, the function is having solutions x = 5 and x = 4, therefore, the graph is of the function y = x²-9x+20.

Hence, the function that best describes the graph is y = x²-9x+1+20

Learn more about function, click;

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Total miles = number of miles per week x number of weeks:

Total = 8n

For 5 weeks, replace n with 5:

Total = 8(5) = 8 x 5 = 40 miles

Answer:

8x, 40 miles

Step-by-step explanation:

He runs 8 miles each week.

8 miles x week

8 x week

To replace week, use a variable, commonly x.

8x

For 5 weeks, plug in the numbers.

x = 5

8 x 5 = 40

40 miles

Hope this helped, please mark Brainliest for everyone to see! :)

Answer:

Step 4

Step-by-step explanation:

Paula used these steps to solve an equation:

Step 1: -4(7 + 8) - 21 = 25

Step 2: -4r – 32 - 2x = 25

Step 3: -61 – 32 = 25

Step 4: -6x = 57

Step 5: x = -9.5

Between which two steps did Paula use the division property of equality?

Step 1: -4(x + 8) - 2x = 25

Opening the parenthesis

Step 2: -4x – 32 - 2x = 25

Combining x-terms

Step 3: -6x – 32 = 25

Adding 32 to both sides

Step 4: -6x = 57

Dividing both sides by -6

Step 5: x = -9.5

The Division Property of Equality states that: when both sides of an equation are divided by the same nonzero number, both sides remain equal.

The rule applies to step 4 where both sides of the equation is divided by -6(nonzero number) giving us x = -9.5

This means from the equation, x is equal to -9.5 and -9.5 is equal to x

The correct answer is step 4

Answer:it is step 4 and 5 hope this helps

Step-by-step explanation:

Answer:

2/11

Step-by-step explanation:

Let's say our fraction is x = 0.1818181818...

The trick is to multiply x by 10²=100 in this case, since there are two repeating digits, and then subtract the original x.

So, in fact you are subtracting 0.181818 from 18.181818 which effectively cancels the entire bit after the decimal point.

You get:

100x - x = 18

Which you can solve:

99x = 18

x = 18/99 = 2/11

Answer:

7e+6

Step-by-step explanation:

7e+6 miligramos

Answer:

Step-by-step explanation:

|3x + 12| < 2 |x - 6|

|3(x + 4)| < 2 |x - 6|        ⇒  -4 and 6 are "zeros"

1°.  x∈(-∞, -4> ⇒ |3x + 12| = - (3x + 12)  and  2|x - 6| = -2(x-6)

-(3x + 12) < -2(x - 6)

-3x - 12 < -2x + 12

  -x < 24

x > -24  ∧ x∈(-∞-4> ⇒ x∈(-18, -4>

2°.  x∈(-4, 6)  ⇒ |3x + 12| = 3x+12  and  2|x - 6| = -2(x-6)

3x + 12 < -2(x - 6)

3x + 12 < -2x + 12

  5x < 0

x < 0  ∧ x∈(-4, 6)  ⇒ x∈(-4, 0)

3°.  x∈(6, ∞)  ⇒ |3x + 12| = 3x+12  and  2|x - 6| = 2(x-6)

3x + 12 < 2(x - 6)

3x + 12 < 2x - 12

  x < -24

x < -24  ∧  x∈(6, ∞)  ⇒ x∈∅

x∈1°∪2°∪3°

x∈(-24, -4>∪(-4, 0)∪∅

x∈(-24, 0)   ⇒   -24 < x < 0

Answer:B

Step-by-step explanation:

X+2 divide 3x^4-x+2=

3x^3-6x^2+12x-25=

52=

52/x+2

the answer is d. its simple,the reason of that is because you would set up the synthetic division using the coefficients of the numerator and the root of the denominator. divide using the rules for synthetic division.

3x 4 cubed- 6x3 cubed +12x 2 cubed-24x-z+48+  2(z-47)  over x+2

Answer: The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational

Step-by-step explanation:

Given the two numbers :

1.12 and 18/7

1.12 is a rational number as it is a not a non-terminating decimal and can accurately be expressed in the form a/b, where a and b are integers, thus 1.12 is equivalent to 112 / 100

18/7 on the other hand is an irrational number as it is a non-terminating decimal.

Hence, takingbthe sum of both numbers (rational and irrational) results in an irrational output.

18 / 7 = 2.57142857....

Taking the sum of both,

1.12 + 2.57142857... = 3.69142857... ; which is irrational

Answer:

The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

5a - 10b = 45

5a - (10×3) = 45

5a - 30 = 45

5a = 45 + 30

5a = 75

a = 15

Answer:

-8 I think on a graph right

Answer:

-8

Step-by-step explanation:

on a number line -1 is one unit away add we just add 7 units. To get -8!

Answer: 11 units.

Step-by-step explanation:

Given: Point O is on line segment NP.

i.e. NP is the combination of NO and OP.

i.e. NP = NO+OP                    (1)

Since , OP = 4x - 5 , NP = 3x + 4 , and NO = 2x - 3

Substitute these values in (1), we get

[tex]3x + 4 = 2x - 3 + 4x - 5[/tex]

[tex]\Rightarrow\ 3x+4=2x+4x-3-5\\\\\Rightarrow\ 3x+4=6x-8\\\\\Rightarrow\ 6x-3x=8+4\\\\\Rightarrow\ 3x=12\\\\\Rightarrow\ x=\dfrac{3}{12}=4[/tex]

i.e. x= 4

Now, OP = 4(4)-5= 16-5= 11 units

Hence, the numerical length of OP is 11 units.

Answer:

each card cost = $3.5

Step-by-step explanation:

to spent $15 = $8 + 2cards

$15 = $8 + 2C

$15 - $8 = 2C

$7 = 2C

C = $7 / 2

C = $3.5

therefore each card cost = $3.5

Answer:

$3.50 per card

Step-by-step explanation:

15 = 8 + 2x

x = 7 / 2

x = 3.50

Answer:

5 - 3y

Step-by-step explanation:

Step 1: Convert product of y and 3 into numbers

Product = multiply

y = y

3 = 3

3y

Step 2: Convert 5 minus into numbers

minus = subtract

5 - 3y

Answer:

5-3y

Step-by-step explanation:

I have same question and I need help

Answer:

the answer would be 1 happy to help ya :)

Step-by-step explanation:

Answer:

Well Written

Step-by-step explanation:

Great Job

First set the equation equal to 0 by subtracting n from both sides.

That leaves us with 8n² - 11n = 0.

Since the GCF on the left is n, we can

factor it out to get n(8n - 11) = 0.

So either n = 0 or 8n - 11 = 0.

Solving for n in the second equation, we get n = 11/8.

So our solution is {0, 11/8}.

Answer: vrey suptuidddd

Step-by-step explanation:

Answer:

  10 units

Step-by-step explanation:

We can find the length of the hypotenuse of this right triangle using the Pythagorean theorem.

  AB² = AC² +BC²

  AB² = 2² +4² = 20

  AB = √20 ≈ 4.47

Then the perimeter is ...

  P = AB +BC +CA = 4.47 +4 +2 = 10.47

  P ≈ 10 units

Answer:

x ≈ 22.1°

Step-by-step explanation:

Using the law of cosines, then

cosC = [tex]\frac{a^2+b^2-c^2}{2bc}[/tex]

with a = 19, b = 14, c = 8 and C = x, thus

cos x = [tex]\frac{19^2+14^2-8^2}{2(19)(14)}[/tex]

         = [tex]\frac{361+196-64}{532}[/tex]

         = [tex]\frac{493}{532}[/tex], thus

x = [tex]cos^{-1}[/tex] ([tex]\frac{493}{532}[/tex] ) ≈ 22.1° ( to the nearest tenth )

Step-by-step explanation:

f o g(x)

= f(x - 4)

= (x - 4) + 7

= x + 3.

Answer: 7

Step-by-step explanation: You first distribute 3, and -2. This gets you 7 = 3t -3 -2t +3. Then you add like terms which gets you, 7 = t.

If all 216 tickets sold were faculty tickets, the revenue would be 216 * 2.5, or $540

The actual revenue collected was $450. The difference between $540 and $450 is $90.

The difference between the student and faculty tickets are $2.50-$2, or .50

$90.00 / .50 = 180 student tickets sold.

That leaves 216-180, or 36 as faculty tickets.

180 student tickets at $2 = $360

36 faculty tickets at $2.50 = $90

$360 + $90 = $450

Answer:

2500 + 215d

Step-by-step explanation: