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1 year ago

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ABC is translated 6 units up and 3 units left to crest A’B’C’. If vertex A is at (-1,2) and vertex B is at (1, 5) then vertex A’

is at (5, 1) or (-4, 8) and vertex B’ is at (-2, 11) or (-7, -1).

1 answer:

jekas [21]1 year ago

3 0

The translation is

... (x, y) ⇒ (x -3, y +6) . . . . . 3 units left, 6 units up

Then

... A(-1, 2) ⇒ A'(-1-3, 2+6) = A'(-4, 8)

... B(1, 5) ⇒ B'(1 -3, 5 +6) = B'(-2, 11)

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The sum of two consecutive even integers divided by four is 189.5

Andre45 [30]

The sum of two consecutive even integers is a+(a+2) and divided by four is
(a+(a+2))/4 = 189.5
(2a+2)/4 = 189.5
2a+2 = 189.5 * 4
2a+2 = 758
2a = 758 - 2
2a = 756
a = 756/2 = 378
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How<br> How many solutions does the nonlinear system of equations graphed below<br> have?

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1 year ago

Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is beh

Gwar [14]

Answer:

11 km/hr.

Step-by-step explanation:

Given information:

Simulated speed = 20/km/h

Time = 15 mins = 1/4 hr = 0.25 hr

Distance Covered as per simulated speed = $20\times \frac{1}{4}=5km$

Position of Julian according to the app = $-2\frac{1}{4}=-2.25$ .

Actual distance covered by the bike is

$Distance= 5 - 2.25 = 2.75km$

Formula for speed:

$\text{Average Speed}=\frac{Distance}{Time}$

$\text{Average Speed}=\frac{2.75}{0.25}$

$\text{Average Speed}=11$

Therefore, the average speed of Julian is 11 km/hr.

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2 years ago

Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist

Lera25 [3.4K]

Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

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1 year ago

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Andrej [43]

Answer:

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Step-by-step explanation:

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2 years ago