What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=|x|:
a) compress horizontally by a factor of 2
b) shift right 1 unit
c) shift up 3 units

Answer:

384 m²

Step-by-step explanation:

The formula to find the surface area of a cube is:

S.A. = 6a²

Here,

a ⇒ length of a side ⇒ 8m

Let us solve it now.

S.A. = 6a²

S.A. = 6 × 8 × 8

S.A. = 48 × 8

S.A. = 384 m²

Jordan can now hear the math teacher, whose classroom instruction was crucial in addition to what Jordan read in his textbook.

A hearing aid is a small electronic device that you wear in or behind your ear. It is used by people who cannot hear properly. Wearing this device makes sounds louder so that a person who cannot hear can listen, and talk to other people. A hearing aid can help people hear in every situation.

SCD is nothing but a specific learning disorder.

An SLD is specific to underachievement in academic skills that are not attributable to intellectual disability, developmental delay, or physical cause.

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Using the completing the square method, for the equation, we have the zeros as x = √26 + 4 and x = 4 - √26

The given equation is presented as follows

[tex]7 = \mathbf{ {x}^{2} - 8x - 3}[/tex]

Which, by completing the square, gives;

[tex] {x}^{2} - 8x - 3 - 7 = 0[/tex]

[tex] {x}^{2} - 8x - 10 = 0[/tex]

[tex] {x}^{2} - 8x + {\left(\frac{8}{2} \right) }^{2} - 10 - {\left(\frac{8}{2} \right) }^{2} = 0[/tex]

[tex] \mathbf{{(x - 4)}^{2} } =26[/tex]

The zeros of the equation;

[tex]7 = {x}^{2} - 8x - 3[/tex]

are;

[tex] \underline{x = \pm \sqrt{26} + 4}[/tex]

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Answer:

A quadratic function

Step-by-step explanation:

Answer:

f(x) = 2|x – 2|  + 6

Step-by-step explanation:

On edg 2022

Answer:

m = 2/3

Step-by-step explanation:

Rewrite in slope-intercept form.

y = -3/2x + 7/2

Using the slope-intercept form, the slope is −3/2.

m = -3/2

The equation of a perpendicular line to y=−3/2x + 7/2 must have a slope that is the negative reciprocal of the original slope.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

• First rewrite the original equation in the form y = mx + c ,

where m = gradient:

[tex]3x + 2y = 7[/tex]

⇒ [tex]2y = -3x + 7[/tex]

⇒ [tex]y = \frac{-3}{2}x + \frac{7}{2}[/tex]

• From this equation, we can see that the gradient, m = [tex]\frac{-3}{2}[/tex] .

The gradient of a line perpendicular to another line with gradient m,  = [tex]\frac{-1}{m}[/tex].

∴ gradient of perpendicular = -1  ÷   [tex]\frac{-3}{2}[/tex]

                                              = [tex]\frac{2}{3}[/tex]    

The inequality is x + 5274 ≥ 10,000.

The total number of steps I have to take to reach my goal is 4726.

Here are inequality signs and what they mean:

Number of steps I have to take + number of steps I have taken ≥Total steps

X + 5274 + x ≥ 10,000

x ≥ 10,000 - 5274

x ≥ 4726

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Answer: -1

Step-by-step explanation:

I assume the points are (-3, r) and (9,2).

Substituting into the slope formula,

[tex]\frac{r-2}{-3-9}=\frac{1}{4}\\\\\frac{r-2}{-12}=\frac{1}{4}\\\\r-2=-3\\\\r=-1[/tex]

The energy of the photon in each case is;

1. 2.97 * 10^-27 J

2. 3.2 * 10^-19 J

3. 6.6 * 10^-19 J

4. 2.64 * 10^-29 J

5. 8.6 * 10^-19 J

The energy of a photon is obtained form the Plank's equation; E = hf

1) E = hf

E =  6.6 × 10^-34 J s  *  4.5 × 10^6 Hz

E = 2.97 * 10^-27 J

2)E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/615  * 10^-9

E = 3.2 * 10^-19 J

3) E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/300 * 10^-9

E = 6.6 * 10^-19 J

4) E = hf

E = 6.6 × 10^-34 J s  * 4 × 10^4 Hz

E = 2.64 * 10^-29 J

5) E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/230  * 10^-9

E = 8.6 * 10^-19 J

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When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

      Distances                     Time

             0                              0

             1                               3

             2                              6

             3                               9

             4                               12

             5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

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Answer:

Step-by-step explanation:

f(2x) means that we have to substitute x with 2x

So, the answer is

2x + 3

The computation shows that the number of flowers will be 10.

The information illustrates the flowers that were brought for the nursery.

Based on the information given, the total number of flowers bought for the nursery will be:

= 5 freesias + 3 rosebrushes + 2 calls lilies

= 10

In conclusion, the total number of flowers is 10.

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Answer:

The following lines is perpendicular, y=-x+6 and y=x+1

Step-by-step explanation:

(ex. slope of 2 stays 2 )

(ex. slope of 2 becomes -1/2)

y = -x + 6 and y = x + 1

the slope for y = -x + 6 is -1    (-1/1)

the slope for y = x + 1 is 1

the slope -1 is the negative reciprocal of 1

hence, the definition of perpendicular fits the given

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Hello,

Answer:

x = 20

Step-by-step explanation:

    3x + 10 = 4x - 10

⇔ 4x - 3x = 10 + 10

⇔ x = 20  

Answer:

20

Step-by-step explanation:

Since l ll m

( 3x + 10 ) and ( 4x - 10 ) are alternate exterior angles,

Property of parallel lines ( ll ) : -

Alternate exterior angles are equal.

4x - 10 = 3x + 10

4x - 3x = 10 + 10

x = 20

Answer:

[tex] \beta = 28.610[/tex]

Step-by-step explanation:

in this case we have a right angled triangle, whenever you see this triangle think of the TRIG RATIOS * sin, cos & tan* but if it was another triangle besides right angled triangle you use SINE RULE OR COSINE RULE

SOLUTION

[tex] \tan( \beta ) = \frac{opposite}{adjecent} \\ \tan( \beta ) = \frac{6}{11} \\ \beta = tan(inverse)( \frac{6}{11} ) \\ \beta = 28.61045[/tex]

Triangle JKL is transformed to create triangle J'K'L'. It can be a rigid or a non rigid transformation depending on whether the corresponding side lengths have the same measures.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

A rigid transformation such as reflection, rotation and translation preserve the shape and size, hence the pre-image and image have the same corresponding angle and side measures.

A non rigid transformation such as dilation preserve the shape and not size, hence the pre-image and image have the same corresponding angle measures.

Triangle JKL is transformed to create triangle J'K'L'. It can be a rigid or a non rigid transformation depending on whether the corresponding side lengths have the same measures.

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Answer:

C

Step-by-step explanation:

2023

The correct answers are option an x>2 for inequality 17x-16>18 and option b x>(4/3) for an inequality 3x-91>-87.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

Given inequalities are:-

The inequalities will be solved as:-

i ) 3x - 91 > -87

3x > -87 + 91

3x > 4

x > ( 4 / 3 )

ii) 17x-16>18

17x > 18 + 16

17x > 34

x > 34 /17

x > 2

Therefore the correct answers are option an x>2 for inequality 17x-16>18 and option b x>(4/3) for an inequality 3x-91>-87.

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The distance of the road junction form Timpson is given as 21.57 miles.

We have AT = [tex]\sqrt{TN^{2}+AN^{2} }[/tex]

√60² + 12² = 12√26

∠TMG = LN = 90 degrees

Therefore we have the system

[tex]\frac{TM}{60} = \frac{22}{12\sqrt{26} }[/tex]

When we cross multiply we would have to solve for TM

TM = 21.57 miles

Hence the distance of the road junction form Timpson is given as 21.57 miles.

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Answer:

12/25

Step-by-step explanation:

total number of possible outcomes =50

number of possible outcomes =24

probability of not selecting odd or prime numbers

=24/50

=12/25

The unit rate per minute is 2/3.

In order to determine the unit rate, divide the temperature by the time. Division is the mathematical operation that is used to determine the quotient of a number.

Unit rate = temperature / time

10 / 15  = 2/3

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The equation has no solutions when m = 0, and when m ≠ 0, the equation has only one solution.

Here we have the equation:

m*x = 5

If we solve for x, we get:

x = 5/m

So, as long as m is different than zero, we will have one solution.

We can't have m = 0 because we can't divide by zero.

Then:

m > 0 or m < 0.

We have no solutions when m = 0, the equation becomes:

0*x = 5

0 = 5

This equation has no solution

And we never can have infinite solutions.

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Answer:

Step-by-step explanation:

We can calculate a few points, such as when x = 0, y = 0 (which sometimes doesn't happen), and the lowest point (where y is the smallest)

When x = 0, y = 3, so (0,3) is one of the points, and is also the y intercept

When y = 0, x = -3, and it also happens that 0 is the lowest point that y can be, since no value of x would make y negative.

Now, we have two points, (0,3) and (-3,0)

Graph B is the one one which has both the points (0,3) and (-3,0) on it, and indeed, y never reaches below the x axis since y can't be negative

Answer:

$420

Step-by-step explanation:

100.80/x = 24/100

with x being the regular price

x = (100.8*100)/24

x = 420

The angular speed of the wheel is calculated as 52.36 radians per second

The revolution of this wheel is said to be at 500 in a minute

This is also called the frequency of this wheel.

This can be written as

500rev in 60 seconds. 500/60 = 8.333 per second

Angular speed is given as

pi = 22/7

f = 8.333

Formular for angular speed = ω = 2*pi*f

w = 2 * 22/7 * 8.333

= 52.36 radians per second

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Step-by-step explanation:

The equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8

The equation of a line in point slope form is expressed as:

y - y1 = m(x-x1)

Given the equation y = -x + 2, the slope of the line parallel to the line is -1

Substitute the slope and point (-3, -5)

y -(-5) = -1(x - (-3))

y+5 = -(x + 3)

y+5 =-x - 3

y = -x - 3 - 5

y = -x - 8

Hence the equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8

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Answer:

Step-by-step explanation:

The interval where f is positive is [tex]0 \le x < 1.5[/tex]

The missing function is added as an attachment

From the attached graph, the function f(x) is positive from x = 0 to x = 1.5

As an interval notation, this can be represented as:

[tex]0 \le x < 1.5[/tex]

Hence, the interval where f is positive is [tex]0 \le x < 1.5[/tex]

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