What type of dilation occurs with a scale factor of 1/4?

Which explains whether or not the function represents a direct variation?

s2008m [1.1K]

Answer:

The function represents a direct variation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m

Let

$A(0,0)$ ------> the line passes through the origin

$B(2,10)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=10/2=5$

$C(4,20)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=20/4=5$

$D(6,30)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=30/6=5$

$E(8,40)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=40/8=5$

The value of k is equal in all the points of the table and the line passes through the origin

therefore

The function represents a direct variation

the equation of the direct variation is equal to

$f(x)=5x$

4 0

3 years ago

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Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t

Ilia_Sergeevich [38]

Answer: 220

Step-by-step explanation:

Children (x): $2

Teens (y): $3, $\frac{3}{4}x$

Adults: (z): $5

Quantity: x + y + z = 570 ⇒ x + $\frac{3}{4}x$ + z = 570 ⇒ 1.75x + z = 570

Cost: 2x + 3y + 5z = 1950 ⇒ 2x + 3 $(\frac{3}{4}x)$ + 5z = 1950 ⇒ 2x + 2.25x + 5z = 1950 ⇒ 4.25x + 5z = 1950

Qty: 1.75x + z = 570 → 5(1.75x + z = 570) → 8.75x + 5z = 2850

Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → -4.25x - 5z = -1950

4.50x = 900

x = 200

Teens (y): $\frac{3}{4}x$

y = $\frac{3}{4}(200)$

= $\frac{600}{4}$

= 150

Quantity: x + y + z = 570

200 + 150 + z = 570

350 + z = 570

z = 220

6 0

3 years ago

In a geometric sequence, A1 = 0.3 and r=3.Find A12, to the nearest integer

soldi70 [24.7K]

Step-by-step explanation:

We have,

First terms of geometric sequence, a = 0.3

Common ratio, r = 3

It is required to find the 12th term of a GP. The formula of the nth term is given by :

$T_n=ar^{n-1}$

Here, n =12

So,

$T_{12}=0.3\times 3^{12-1}\\\\T_{12}=0.3\times 3^{11}\\\\T_{12}=53144.1$

or

$T_{12}=53144$

So, the 12th term of the GP is 53144.

8 0

4 years ago

Can I have help with this one asap?

sasho [114]

Answer:

In Δ CFD , CD is the LONGEST side.

Step-by-step explanation:

Here, the given Δ CSD is a RIGHT ANGLED TRIANGLE.

Now, as we know in a right triangle, HYPOTENUSE IS THE LONGEST SIDE.

So, in Δ CSD SD is the longest side as SD = Hypotenuse.

Now, an altitude CF is drawn to hypotenuse SD.

⇒ CF ⊥ SD

⇒ Δ CFD is a RIGHT ANGLED TRIANGLE with ∠ F = 90°

and CD as a hypotenuse.

⇒ In Δ CFD , CD is the LONGEST side.

Hence, CD is the longest side in the given triangle CFD.

6 0

3 years ago

Please help me, I can't get this question, its for 5th graders, please

Serggg [28]

The two numbers in each column have to add to 23
So under 7 you write 16, above 4 you write 19, etc

The rule will say x + y = 23

8 0

3 years ago

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