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3 years ago

Which rule describes the transformation that is

Mathematics

1 answer:

Ne4ueva [31]3 years ago

6 0

Answer:

D. (x,y) --> (x,-y)

Step-by-step explanation:

the x number stays the same but the y number flips to a negative.

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Which sequence of transformations will map figure K onto figure K′? Two congruent kites, figure K and figure K prime, are drawn

elixir [45]

Answer:

The sequence of transformations will map figure K onto figure K′

is the first sequence option (1)

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

Step-by-step explanation:

See the attached figure

as shown in the figure the K' is the image of K by reflection over x-axis

But  We need to know which sequence of transformations will give the same result.

So, we will test the options by any point from K and its image from K'

i.e: we will test the options using the points (6,5) , (6,-5)

(6,5) ⇒ (6,-5)

option (1):

Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y)

(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (6,-5)

option (2):

Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y)

(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (-10,-5)

option (3):

Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)

(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (2,-3)

option (4):

Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)

(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (-14,-3)

As shown: The sequence of transformations will map figure K onto figure K′

is the first sequence option (1)

7 0

3 years ago

Read 2 more answers

Help me please please

aniked [119]

Answer:

The total least sale amount is $5,000,000

Step-by-step explanation:

Given as :

The base salary amount of Carmen = $125,000

The commission percentage on total sale = 4%

The performance bonus amount = $25,000

The total compensation amount last year = $350,000

Let The total sale amount = $x

According to question

Total compensation amount last year = base salary amount + percentage on total sale + performance bonus amount

I.e $350,000 = $125,000 + 4% of x + $25,000

Or, $350,000 = $150,000 + 4% of x

Or, 4% of x = $350,000 - $150,000

Or, 4% of x = $200,000

Or, × x = $200,000

Or, x =

∴ x = $5,000,000

So, The total sale amount = x = $5,000,000

Hence, The total least sale amount is $5,000,000 Answer

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Find an explicit formula that generates a sequence whose first four terms are: 24, 36, 54, 81

sattari [20]

Answer:

see explanation

Step-by-step explanation:

These are the first 4 terms of a geometric sequence with n th term

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

r = 36 ÷ 24 = 54 ÷ 36 = 81 ÷ 54 = 1.5 and a₁ = 24, hence

$a_{n}$ = 24 $(1.5)^{n-1}$ ← explicit formula

3 0

4 years ago

Read 2 more answers

Find the equation of the line that passes through points (4,5) and (-1,6).

steposvetlana [31]

First find the slope using the formula $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
Substitute the values in:
$m= \frac{6-5}{-1-4}= -\frac{1}{5}$
Point-slope form is $y=m(x-x_{1})+y_{1}$
Substitute (it doesn't matter which point you choose; I chose (4,5):
$y=- \frac{1}{5} (x-4)+5=-\frac{1}{5}x+\frac{29}{5}$
Therefore, the answer is D. $y=-\frac{1}{5}x+\frac{29}{5}$

4 0

3 years ago

The velocity of an automobile starting from rest is given by the equation below, where v is measured in feet per second and t is

maria [59]

Answer:

a. At t = 5 s

$a(5)=\frac{1785}{\left(6(5)+17\right)^2}=\frac{1785}{2209}\approx0.808 \frac{ft}{s^2}$

b. At t = 10 s

$a(10)=\frac{1785}{\left(6(10)+17\right)^2}=\frac{255}{847}\approx0.301 \frac{ft}{s^2}$

c. At t = 20 s

$a(20)=\frac{1785}{\left(6(20)+17\right)^2}=\frac{1785}{18769}\approx0.095 \frac{ft}{s^2}$

Step-by-step explanation:

We know that the velocity function is given by

$v(t)=\frac{105t}{6t+17}$

Acceleration is the rate of change of velocity so we take the derivative of the velocity function with respect to time.

$a(t)=\frac{dv}{dt}=\frac{d}{dt} (\frac{105t}{6t+17})$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\105\frac{d}{dt}\left(\frac{t}{6t+17}\right)\\\\\mathrm{Apply\:the\:Quotient\:Rule}:\quad \frac{d}{{dx}}\left( {\frac{{f\left( x \right)}}{{g\left( x \right)}}} \right) = \frac{{\frac{d}{{dx}}f\left( x \right)g\left( x \right) - f\left( x \right)\frac{d}{{dx}}g\left( x \right)}}{{g^2 \left( x \right)}}$

$105\cdot \frac{\frac{d}{dt}\left(t\right)\left(6t+17\right)-\frac{d}{dt}\left(6t+17\right)t}{\left(6t+17\right)^2}\\\\105\cdot \frac{1\cdot \left(6t+17\right)-6t}{\left(6t+17\right)^2}\\\\a(t)=\frac{1785}{\left(6t+17\right)^2}$

a. At t = 5 s

$a(5)=\frac{1785}{\left(6(5)+17\right)^2}=\frac{1785}{2209}\approx0.808 \frac{ft}{s^2}$

b. At t = 10 s

$a(10)=\frac{1785}{\left(6(10)+17\right)^2}=\frac{255}{847}\approx0.301 \frac{ft}{s^2}$

c. At t = 20 s

$a(20)=\frac{1785}{\left(6(20)+17\right)^2}=\frac{1785}{18769}\approx0.095 \frac{ft}{s^2}$

3 0

3 years ago