Express x^2-5x+8 in the form (x-a)^2+b where a and b are top-heavy fractions

Please help 100 points and brainlest for all the answers

masha68 [24]

Answer:

See explanation

Step-by-step explanation:

Q1. The graph of given data is attached.

The relationship is directly proportional as the line connecting all points is straight line passing through the origin.

For every 1 unit change in x, the change of y is 16.

Therefore, the equation that represents this line is

$y=16x$

If $x=10,$ then $y=16\cdot 10=160$ square feet.

Q2. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin (see second attached graph).

For every 1 unit change in x, the change of y is 0.45.

Therefore, the equation of the line is

$y=0.45x$

Q3. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

Find the constant of proportionality:

If x = 2, y = 25, then

when x = 1, y = 12.5

so k = 12.5

and the equation of the line is

$y=12.5x$

When $x=14,$ then $y=12.5\cdot 14=175$

Hence, the cost of 14 tickets is $175

Q4. This table does not show the direct variation because

if x = 500 and y = 40, then

for x = 100, y is $40\div 5=8$

and for x = 700, y must be $7\cdot 8=56$ not 50.

Hence, this relationship does not show the direct proportionality between x and y.

Q5. This elationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

The constant of proportionality is $k=1.75$

The equation of proportionality is $y=1.75x$

When $y=28,$ then

$28=1.75x\\ \\x=\dfrac{28}{1.75}\\ \\x=16$

This means for $28 you could buy 16 ice cream scoops.

Q6. The line passes through the point (2,61), so the constant of proportionality is

$k=\dfrac{61}{2}=30.5$

The equation of proportional relationship is

$y=30.5x$

When $y=274.50,$ then

$274.50=30.5x\\ \\x=\dfrac{274.5}{30.5}\\ \\x=9$

This means you could buy 9 tickets for $274.50

Q7. The equation which represent proportional relationship should have the equation of the form

$y=kx$

Circle all equations in this form:

$y=5x\\ \\p=0.5m\\ \\y=\dfrac{1}{2}x\\ \\M=3n\\ \\y=2x$

Q8. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If y is directly proportional to x, the equation is of the form y = kx (where k is a constant).

This means that the graph of direct variation is always a straight line passing through the origin (because x = 0 and y = 0 satisfy the equation for all k).

Not all lines represent the proportional relationship. Only those, which pass through the origin.

4 0

3 years ago

Read 2 more answers

If you wanted to mix pure methane with water and end up with 70 gallons of 20% methane, how many gallons of each should you use?

PtichkaEL [24]

Answer:

You want 40% of 140 gallons to be methane,

so 60% of 140 gallons is water

methane: 0.4(140) = 56 gallons

water: 0.6(140) = 84 gallons

Step-by-step explanation:

3 0

2 years ago

What number does a Roman numerals MDC XL IX represent

Ksenya-84 [330]

Answer:

the answer is 1649

7 0

2 years ago

Verify the identity. <br> Please show your work.

m_a_m_a [10]

Step-by-step explanation:

To prove :

( 1 - sin x ) ( 1 + sin x ) = sec² x

LHS : -

( 1 - sin x ) ( 1 + sin x )

Formula / Identity : -

( a - b ) ( a + b ) = a² - b²

Here,

a = 1

b = sin x

( 1 - sin x ) ( 1 + sin x )

= 1 - sin² x

Identify : -

sin² θ + cos² θ = 1

cos² θ = 1 - sin² θ

Similarly,

1 - sin² x

= cos² x

= RHS

Hence verified.

5 0

3 years ago

If f(x)=-2x-3 find the value f(4y)

jasenka [17]

Answer:

f(4y) = -8y - 3

Step-by-step explanation:

Step 1: Define variables

f(x) = -2x - 3

f(4y) = x = 4y

Step 2: Plug in x = 4y

f(4y) = -2(4y) - 3

f(4y) = -8y - 3

4 0

3 years ago