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3 years ago

The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). Which describes this translation?

Mathematics

2 answers:

Leto [7]3 years ago

7 0

Answer:

Translation of 2 units to the left and 7 units up.

Step-by-step explanation:

The general rule of translation is

$(x,y)\rightarrow (x+a,y+b)$ .... (1)

If a>0, then figure translate a units right and if a<0, then figure translate a units left.

If b>0, then figure translate b units up and if b<0, then figure translate b units down

The given rule of translation is

$(x,y)\rightarrow (x-2,y+7)$ .... (2)

On comparing (1) and (2), we get

a = -2 < 0, so figure translate 2 units left.

b = 7 > 0, so figure translate 7 units up.

Therefore, the given rule describes the translation of 2 units to the left and 7 units up.

GaryK [48]3 years ago

5 0

Answer:

It shifts left two units, and up seven units.

Step-by-step explanation:

In your translation, it says X-2, this represents the shift to the left two times, next it says Y+7, this represents the upwards shift seven units. Basically, you're taking your beginning X and Y values, and changing them according to the right of the arrow.

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A tank contains 1080 L of pure water. Solution that contains 0.07 kg of sugar per liter enters the tank at the rate 7 L/min, and

allsm [11]

(a) Let $A(t)$ denote the amount of sugar in the tank at time $t$ . The tank starts with only pure water, so $\boxed{A(0)=0}$ .

(b) Sugar flows in at a rate of

(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min

and flows out at a rate of

(<em>A(t)</em>/1080 kg/L) * (7 L/min) = 7<em>A(t)</em>/1080 kg/min

so that the net rate of change of $A(t)$ is governed by the ODE,

$\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}$

$A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}$

Multiply both sides by the integrating factor $e^{7t/1080}$ to condense the left side into the derivative of a product:

$e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}$

$\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}$

Integrate both sides:

$e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt$

$e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C$

Solve for $A(t)$ :

$A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}$

Given that $A(0)=0$ , we find

$0=\dfrac{378}5+C\implies C=-\dfrac{378}5$

so that the amount of sugar at any time $t$ is

$\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}$

(c) As $t\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5$

or 75.6 kg of sugar.

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3 years ago

Write the equation of the line fully simplified slope-intercept form.

Stells [14]

Answer:

Y = -x + 8

Step-by-step explanation:

brainliest pls.

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3 years ago

4/5 divided by 6. i don't know what the answer is

NISA [10]

So you can take 4/5 and make it easier by turning it into a decimal

If you do that you need to multiple so the Denominator is 10 so 4 times 2 and 5 times 2 so 8 divided by 6 or 8/6 is 1.3 Repeating

Answer: 1.3 Repeating

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3 years ago

GEOMETRY HELP WILL MARK BRAINLIEST

daser333 [38]

Answer:

x = 5 and z = 108

Step-by-step explanation:

We have two intersection lines and since z and 108 lie opposite each other, they are called vertical angles. By definition, vertical angles are congruent to each other, so that means z = 108.

Now, notice that z and 6x + 42 lie on the same line. A line has a measure of 180 degrees, which means that these two will add up to 180 (they are supplementary angles). Then we can write:

z + (6x + 42) = 180

We already know that z = 108, so plug that in and solve for x:

108 + (6x + 42) = 180

6x + 150 = 180

6x = 30

x = 5

Thus, x = 5 and z = 108.

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The graph of the function f(x) = –(x 3)(x – 1) is shown below. which statement about the function is true? the function is posit

kondaur [170]

See attachment

positive is where it goes above x axis

so it is posittive for x where -3<x<1
it is negativive where x<-3 and x>1

answer is
the function is negative for all real values of x where x < –3 and where x > 1

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