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3 years ago

Which absolute value function, when graphed, will be

Mathematics

1 answer:

lara [203]3 years ago

6 0

Answer: f(x) = (1/3)*IxI

Step-by-step explanation:

Ok, this is a problem of transformations.

First, if we have f(x), then:

f(x - a) is a translation of a units in the x-axis

f(x) + a is a translation of a units in the y-axis.

a*f(x) is a dilation/contraction.

if a is greater than 1, then the graph will be steeper (less wide)

if a is smaller than 1, then the graph will be wider.

Looking at the options, the correct option is:

f(x) = (1/3)*IxI

where we can see that a = (1/3)

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

2 years ago

Cuanto es (60 : 10 + 8) x 2

Nataliya [291]

Answer:

Step-by-step explanation:

4 0

3 years ago

I am thinking of a number i multiply by 11 and add 22 i get the same answer if i miltiply by 4 and add 113 whats my number

lesya [120]

Answer: 13

Step-by-step explanation:

Let the number that in thinking of be represented by x.

I multiply by 11 and add 22 will give the same answer as multiplying by 4 and adding 113. This.csn be firmed into an equation as:

(11 × x) + 22 = (4 × x) + 113

11x + 22 = 4x + 113

Collect like terms

11x - 4x = 113 - 22

7x = 91

x = 91/7

x = 13.

The number is 13

8 0

2 years ago

Graph a triangle ABC and perform a translation of (x + 4, y − 3) to create triangle A′B′C′.

LiRa [457]

Answer:

to describe the transformation in words you could say, triangle ABC was moved to the right 4 times and down 3 times.

4 0

2 years ago

What is the slope of the line determined by the equation -1/2x+3/4y=0

kvasek [131]

Answer:

The slope is 2/3

Step-by-step explanation:

-1/2x+3/4y=0

To find the slope, we need to get the equation in the form y= mx+b

Add 1/2x to each side

-1/2x+ 1/2 x+3/4y=0+1/2x

3/4 y = 1/2x

Multiply by 4/3 to isolate y

4/3 * 3/4 y = 4/3 * 1/2 x

y = 2/3 x

The slope is 2/3 and the y intercept is 0

7 0

3 years ago