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3 years ago

Fine the perimeter of this rectangle

Mathematics

1 answer:

frosja888 [35]3 years ago

6 0

Answer:

(z) + (z) + (z-1) + (z-1) = 4z-2

Step-by-step explanation:

Perimeter is the sum of all the sides

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The vertices of ΔABC are A(−3,4), B(−2,4), and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image ΔA'B'C

Mumz [18]

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ .

<h3>How to calculate the coordinate of point by reflection</h3>

A point if reflected across the line $y = -2$ by means of the following formula:

$P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)]$ (1)

Where:

$P(x,y)$ - Original point
$x_{P}$ - x-Coordinate of point P
$P'(x,y)$ - Resulting point

If we know that $P(x,y) = (-2,4)$ and $x_{P} = -2$ , then the coordinates of the vertex is:

$P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)]$

$P'(x,y) = (-2, 4) +2\cdot (0, -6)$

$P'(x,y) = (-2, 4) + (0,-12)$

$P'(x,y) = (-2, -8)$

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ . $\blacksquare$

To learn more on reflections, we kindly invite to check this verified question: brainly.com/question/1878272

3 0

2 years ago

A cup of coffee with temperature 155degreesF is placed in a freezer with temperature 0degreesF. After 5 minutes, the temperatur

Leviafan [203]

Answer:

45.50° F

Step-by-step explanation:

As per Newton's law,

$T(t) = T_{s}+(T_{0} + T_{s})e^{-kt}$

When T(t) is the final temperature

$T_{s}$ = Temperature of surrounding

$T_{0}$ = Initial temperature

t =duration of cooling

k = constant

$103=0+(155-0)e^{-k\times 5}$

$103=155e^{-5k}$

Now take natural log on both the sides

$ln(103)=ln(155e^{-5k})$

$ln(103)=ln(155)+ln(e^{-5k})$

$ln(103)=ln(155)=-5k$

4.6347 - 5.0434 = -5k

$k=\frac{0.40872}{5}$

k = 0.0817

$T(t)=0+(155-0)e^{(0.0817\times 15)}$

= $155e^{-1.226}$

= 155 (02935)

= 45.49 ≈ 45.50° F

8 0

3 years ago

A Ferris wheel travels in a circular motion and measures 40 meters from the top car to the bottom car. What is the length of the

Romashka-Z-Leto [24]

Answer:

20 m

Step-by-step explanation:

the distance from the top car to the bottom car is equal to the diameter of the wheel. The diameter is 40 m, and that is twice the radius. The radius of the Ferris wheel is (40 m)/2 = 20 m.

7 0

3 years ago

Read 2 more answers

Simplify the expression completely.

ivolga24 [154]

You can’t simplify it any further. 288 1/4 is already simplified.

6 0

3 years ago

Read 2 more answers

1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

$m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}$

7 0

3 years ago