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2 years ago

10

Write a function g whose graph represents a reflection in the y-axis followed by a translation 3 units to the right of the graph

of f(x)=|x|.
g(x)=

1 answer:

svp [43]2 years ago

6 0

Answer:

$g(x) = |x - 3|$

Step-by-step explanation:

Given

$f(x) = |x|$

Required

Translate 3 units right

The result of a right translated function is:

$g(x) = f(x - h)$

<em>Where h is the unit of translation</em>

<em></em> $h = 3$ <em></em>

<em></em>

<em></em> $g(x) = f(x - 3)$ <em></em>

Solve for f(x - 3)

$f(x) = |x|$

$f(x - 3) = |x - 3|$

Hence;

$g(x) = |x - 3|$

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Which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?

m_a_m_a [10]

Answer:

SAS Theorem

Step-by-step explanation:

It would be the SAS theorem because you know 2 sides that have an angle in common on both triangles.

5 0

3 years ago

The area (in square centimeters) of a square coaster can be represented by d^2+8d+16 .

Katarina [22]

ANSWER

a. d+4

b. 4d+16

EXPLANATION

The area of the square coaster is represented by:

${d}^{2} + 8d + 16$

We split the middle term to obtain,

${d}^{2} + 4d + 4d + 16$

We factor by grouping to get,

$d(d + 4) + 4(d + 4)$

$(d + 4)(d + 4) = {(d + 4)}^{2}$

Since area of a square is l² , it means the side length of the square is

$l = d + 4$

b) The perimeter of a square is given by

$P=4l$

We substitute the length in terms of d, to obtain;

$P=4(d + 4)$

Or

$P=4d + 16$

7 0

3 years ago

Read 2 more answers

What is the average rate of change of the function over the interval x = 0 to x = 6?

Ymorist [56]

Answer:

15 2/3, or 47/3

Step-by-step explanation:

I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5. Double check on this right now, please.

If I'm right, then evaluate f(x) at x = 0 and x = 8:

f(0) = 5

and

f(8) = 2(8)^2 - (1/3)(8) + 5 = 128 - 8/3 + 5 = 133 - (2 2/3), or: 130 1/3

Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:

130 1/3 - 5 125 1/3

a. r. c. = ------------------- = ---------------- = 15 2/3, or 47/3

8 - 0 8

6 0

3 years ago

Mari has a part time job. She earns $7 an hour. She makes at most $143.50 a week. What is the greatest number of hours that she

Readme [11.4K]

591.928571 is your answer

8 0

3 years ago

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ <u>923.558 m²</u>

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago