using the rectangle below calculate the values of x and y

Answer:

1.  y = 5|x|   ⇒vertical stretch

2. y = ⅓|x|  ⇒vertical compression

3. y = 3|x|   ⇒vertical stretch

Step-by-step explanation:

Given the parent absolute value function, f(x) = |x|:

The transformed function, y = a|x|, where |a| > 1, represents the vertical stretch of the parent graph by a factor of a.  

Therefore, the absolute value equation, y = 5|x|, represents a vertical stretch of the parent function by a factor of 5. The graph of y = 5|x| is narrower than the parent function, f(x) = |x|.  

The transformed function, y = a|x|, where 0< |a| < 1, represents the vertical compression of the parent graph by a factor of a.  

Therefore, the absolute value equation, y = ⅓|x|, represents a vertical stretch of the parent function by a factor of ⅓. The graph of y = ⅓|x| is wider than the parent function, f(x) = |x|.  

Similar to question 1, the absolute value equation, y = 3|x|, represents a vertical stretch of the parent function by a factor of 3. The graph of y = 3|x| is narrower than the parent function, f(x) = |x|.  

Attached are the graphs of the given absolute value functions, where it shows the transformations to the parent function, f(x) = |x|.  

Answer:

[tex]y=-\frac{2}{5} x+\frac{36}{5}[/tex]

Step-by-step explanation:

→ Find the gradient

[tex]\frac{4-6}{8-3}= \frac{-2}{5} =-\frac{2}{5}[/tex]

→ Write into y = mx + c format

[tex]y=-\frac{2}{5} x+c[/tex]

→ Substitute in ( 3 , 6 )

[tex]6 = -\frac{6}{5} +c[/tex]  ∴ [tex]c = 6+\frac{6}{5} =\frac{36}{5}[/tex]

→ Rewrite into y = mx + c format

[tex]y=-\frac{2}{5} x+\frac{36}{5}[/tex]

Answer:

6

Step-by-step explanation:

[tex]45 \: min = 0.75 \: hour[/tex]

[tex]0.75 * 8 = 6 \: hours[/tex]

Answer:

8

Step-by-step explanation:

turn 2/4 into fraction by dividing 2 by 4  equals to 0.5 then divide 4 by 0.5 equals 8

Answer:

[tex]2[/tex]

Step-by-step explanation:

Let [tex][n][/tex] denote the area of some polygon [tex]n[/tex].

The sum of the area of quadrilaterals BCDE and MNDE is equal to [tex][ABC]-([MBE]+[NDC]+AMN])[/tex] (big triangle subtracting the three smaller triangles that aren't part of BCDE or MNDE).

Let the area of triangle ABC be [tex]\alpha[/tex].

Triangle AMN is similar to triangle ABC. Because their side lengths are in ratio 1:2 respectively, the ratio of the area of triangle AMN to triangle ABC is [tex]1:2^2=1:4[/tex].

Therefore, [tex]\displaystyle [AMN]=\frac{1}{4}[ABC]=\frac{1}{4}\alpha[/tex].

Now for triangle NDC, NDC is similar to triangle AMC. Since M is the midpoint of AB, AMC is half the area of ABC. The ratio of the side lengths between triangle NDC and triangle AMC is [tex]1:2[/tex] because the D is the midpoint of MC, so it follows the ratio of their areas must be [tex]1:4[/tex], respectively.

Therefore, [tex]\displaystyle[NDC]=\frac{1}{4}[AMC]=\frac{1}{8}[ABC]=\frac{1}{8}\alpha[/tex].

We can use the same concept for triangle MEB. Triangle MEB is similar to triangle ANB, and the ratio of their sides is also [tex]1:2[/tex], since E is the midpoint of BN. Their areas are in the ratio [tex]1:2^2=1:4[/tex] and we have [tex]\displaystyle [MBE]=\frac{1}{4}[ANB]=\frac{1}{8}\alpha[/tex].

Thus,

[tex]\displaystyle \frac{[ABC]}{[BCDE]+[MNDE]}=\frac{\alpha}{\alpha-\frac{1}{4}\alpha-\frac{1}{8}\alpha-\frac{1}{8}\alpha}=\frac{\alpha}{0.5\alpha}=\frac{1}{\frac{1}{2}}=\boxed{2}[/tex]

Answer:

[tex]5^{\frac{5}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponent

[tex]\sqrt[3]{a}[/tex] = [tex]a^{\frac{1}{3} }[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

[tex]\frac{25}{\sqrt[3]{5} }[/tex]

= [tex]\frac{5^2}{5^{\frac{1}{3} } }[/tex]

= [tex]5^{\frac{6}{3}-\frac{1}{3} }[/tex]

= [tex]5^{\frac{5}{3} }[/tex]

(a) The rate at which the bag is draining is 75mL/h.

(b) After 6 hours, the remaining fluid is =0 mL.

Rate is a measurement of change of a quantity with respect to another quantity.

Given that,

Initial volume of bag=750 mL,

After 4 hours later, the volume of bag= 450.

(a)

To determine the rate of draining,

The change of volume in 4 hours= 750-450=300

The change of volume in 1 hour = 300/4=75

So, the rate of draining= 75mL

(b)

To determine the remaining volume of bag after 6 hours,

The volume drains in 1 hour=75 mL

The volume drains in 6 hours = 75×6=450

The remaining fluid = 450-450=0

The fluid remains after 6 hours is 0mL.

To know more about Rate on :

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Answer:

54 wrapping papers sold

Answer:

(7) 3 2 2x 23 xy y - 10 0 Solution The equation 2x2 23xyy2-100 has A2,B 23, and (1 13) as p3 (Example 2). 13: 271279. 2 m) long and 6 ft Step-by-step explanation:

i dont know :))))))))))))))))))))))

Answer:

148

Step-by-step explanation:

sorry, im not sure how to solve it, but its 148

hope this kinda helped :)

mark me brainliest :D

Answer:

completing the square

Step-by-step explanation:

You can change a quadratic equation from standard form to vertex form by completing the square!

Answer:

7/1000

Step-by-step explanation:

Step-by-step explanation:

you should add the equation for one to answer

Answer: Varies

Step-by-step explanation:

It involves any that is not concerned with making a profit.

Answer:

5

Step-by-step explanation:

I'm not so sure with the number's you submited but I assume it's 7,8m and 1,56 m

1. convert them to cm (780 cm and 156 cm )

2. 780/156 = 5

Answer:

1. (-2,-5) (-1,-1) (0,3) (1,7) (2,11)

2. (-8,-4) (-4,-3) (0,-2) (4,-1) (8,0)

3. (-4,3) (-2,2) (0,1) (2,0) (4,-1)

4. (-2,-1) (-1,2) (0,5) (1,8) (2,11)

Step-by-step explanation:

1. Slope = (11-7)/(2-1) = 4/1 = 4/1

y-intercept: 7 - (4)(1) = 3

Start in the vertical line (y) on 3, 4 up and 1 to the right (you need to points to trace a line)

2. Slope = (0- - 2)/(8-0) = 1/4

y - intercept = -2-(1/4)(0) = -2

Start on -2 vertical line, 1 up and 4 to the right.

3. Slope = (1-0)/(0-2 = -1/2

y-Intercept: 0 - (-1/2)(2)=1

Start on 1 vertical line then 1 down and two to the right (the slope is negative, the line goes downhill)

4. Slope: (8-1)/(1-0) = 7/1

y-intercept = 1 - (7)(0) = 1

Start on 1 vertical line (y) , seven up and 1 to the right.

Answer:

DE = 30

Step-by-step explanation:

Let X be the measure of side DE.

You can write this equation to represent the problem:

[tex]x *\frac{2}{3} =20[/tex]

The measure of DE (x) is multiplied by the scale factor of [tex]\frac{2}{3}[/tex] to become 20.

Solve for x:

[tex]x *\frac{2}{3} =20\\\frac{2x}{3} =20\\2x=60\\x=30[/tex]

DE = 30

Answer:

[tex]x=-6\frac{1}{2}[/tex]

Step-by-step explanation:

I hope this help you

Answer:

B. x = -6 1/2

Step-by-step explanation:

13 3/4 + x = 7 1/4

55/4 + x = 29/4

x = -26/4 ~ -6 1/2

Answer:

$16.65

Step-by-step explanation:

To turn percentages into coefficients divide by 100, so 85% become .85. She marks them up or adds a cost of 85% so instead of using .85 we use 1.85. so 1.85 times initial cost of candle is 1.85*9=16.65

Answer:

3 and-2

Step-by-step explanation:

The point of intersection

Answer:

x=-2, x=3

Step-by-step explanation:

x²-x-6=0

x²-3x+2x-6=0

x(x-3)+2(x-3)=0

(x+2)(x-3)=0

Answer:

X-intercept: (25,0)

Y-intercept: (0,55)

Step-by-step explanation:

Answer:The volume of the soup pot is of 226.19 cubic inches.

Step-by-step explanation:

Format of a soup pot:

A soup pot has a cylindrical format.

Cylinder volume:

The volume of a cylinder, with radius r and height g is given by:

The soup pot is 8 inches tall with a radius of 3 inches.

This means that

What is the volume of the soup pot?

The volume of the soup pot is of 226.19 cubic inches.

Answer:

Socratic app

Step-by-step explanation:

it will help you

Answer:

it is 5.5 inches wide, 1.5 inches thick and 3 feet long

Answer: Im not really sure if this is correct but it's what I put so I hope it is. If it's incorrect please let me know.

Step-by-step explanation:

We first need to find its mass and volume.

Mass: 8.05

Volume: Turn 3 feet into inches: 36

36in × 1.5in × 5.5in =297

Density : 8.05lb ÷ 297 cubic inches = 0.027 cubic inches

b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5  20/5 = 4    4×4 = 16   so 4/5 is equivalent to 16/20

2/4   20/4 = 5    5×2 = 10   so  2/4 is equivalent to 10/20  

Add:    16/20 + 10/20 = 26/20

brainliest me

Answer:

1  11/24

Step-by-step explanation:

5 1/8= 41/8  

3 2/3 = 11/3

41/8 -11/3 = (41*3)/(8*3)   -(11*8)/(3*8)

              =123/24 -88/24

               = (123-88)/24

              =35/24

              =1  11/24

Answer:

650

Step-by-step explanation:

822-72=650