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3 years ago

Figure b is a scaled copy of figure a. help?

Mathematics

1 answer:

Natalka [10]3 years ago

4 0

The scale factor is 4 because if you multiply 4 to all the number on figure A it will equal to figure Bs numbers(sorry if it doesn’t makes sense)

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A number consist of 2 digits whose sum is 8, If 8 is subtracted from the number, the digits interchange their place. The number

Novay_Z [31]

Step-by-step explanation:

Let's say the two digit number is 10x + y, where x is the first digit and y is the second digit.

The sum of the digits is 8:

x + y = 8

If 8 is subtracted from the number, the digits switch place.

10x + y − 8 = 10y + x

Simplify the second equation:

9x − 8 = 9y

Substitute from the first equation.

y = 8 − x

9x − 8 = 9 (8 − x)

9x − 8 = 72 − 9x

18x = 80

x = 4.444

There's a problem. x isn't an integer. Are you sure you copied the problem correctly? Perhaps you meant if 18 is subtracted from the number, the digits switch place.

9x − 18 = 9 (8 − x)

9x − 18 = 72 − 9x

18x = 90

x = 5

y = 8 − x

y = 3

So the number is 53.

8 0

3 years ago

Read 2 more answers

Does anyone know how to do this?

Vlad1618 [11]

Answer:i think you have to equal them to each other

Step-by-step explanation:

8 0

3 years ago

On his outward journey, Ali travelled at a speed of s km/h for 2.5 hours. On his return journey, he increased his speed by 4 km/

den301095 [7]

Answer:

3.08 km/h.

Step-by-step explanation:

We know that,

$Speed=\dfrac{Distance}{Time}$

Ali traveled at a speed of s km/h for 2.5 hours.

Let d be the distance and t be the time.

$2.5=\dfrac{d}{t}$

$2.5t=d$ ...(1)

On his return journey, he increased his speed by 4 km/h and saved 15 minutes. So, distance is d and times is t-15.

$4=\dfrac{d}{t-15}$

$4(t-15)=d$ ...(2)

From (1) and (2), we get

$4(t-15)=2.5t$

$4t-60-2.5t=0$

$1.5t=60$

$t=40$

Put t=40 in (1).

$d=2.5(40)=100$

So, t=40 and d=100.

Now,

Total distance = d + d = 100 + 100 = 200

Total time = t + t - 15 = 40 + 40 - 15 = 65

So, the average speed is

$\text{Average speed}=\dfrac{\text{Total distance}}{\text{Total time}}$

$\text{Average speed}=\dfrac{200}{65}$

$\text{Average speed}\approx 3.08$

Therefore, the average speed is 3.08 km/h.

3 0

4 years ago

The diameter of Circle Q terminates on the circumference of the circle at (3,0) and (3,-7) . Write the equation of the circle in

Deffense [45]

Step-by-step explanation:

The center of a circle with 2 end points of a di diameter is the midpoint of the two endpoints.

The formula needed to find the minpoints is

(x,y) = (x2 + x1)/2, (y2 + y1)/2

x2 = 3

x1 = 3

y2 = 0

y1 = -7

midpoint = (3 + 3)/2, (0 - 7)/2

midp[oint = 3,-3.5

The midpoint is the center of the circle. Observe that the signs get changed when entering the values for (x,y)

So far what you have is (x - 3)^2 + (y + 3.5)^2 = r^2

To determine r^2 you need only take the distance from the center to oneof the endpoints.

r^2 = (3 - 3)^2 + (3.5 - 0)^2

r^2 = 3.5^2

r^2 = 12.25

Answer: (x - 3)^2 + (y + 3.5)^2 = 12.25

6 0

3 years ago

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

3 years ago