Write 2/3 of 4 as a fraction.

In a 3-digit number, the hundreds digit is one more than the ones digit and the tens digit is twice the hundreds digit. If the s

MaRussiya [10]

Answer:

The mentioned number in the exercise is:

362

Step-by-step explanation:

To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.

If:

x = hundredths digit
y = tens digit
z = ones digit

We can write:

x = z + 1 (the hundreds digit is one more than the ones digit).
y = 2x (the tens digit is twice the hundreds digit).
x + y + z = 11 (the sum of the digits is 11).

Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:

x + y + z = 11
(z + 1) + y + z = 11 (remember x = z + 1)
z + 1 + y + z = 11
z + z +y + 1 = 11 (we just ordered the equation)
2z + y + 1 = 11 (z + z = 2z)
2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
2z + y = 10
2z + (2x) = 10 (remember y = 2x)
2z + 2x = 10
2z + 2(z + 1) = 10 (x = z + 1 again)
2z + 2z + 2 = 10
4z + 2 = 10
4z = 10 - 2
4z = 8
z = 8/4
z = 2

Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:

x = z + 1
x = 2 + 1
x = 3

And we'll use the second equation to obtain the value of y (the tens digit):

y = 2x
y = 2(3)
y = 6

Organizing the digits, we obtain the number:

Number = xyz
Number = 362

As you can see, the obtained number is 362.

8 0

3 years ago

Martina has a circle with a diameter

klasskru [66]

Answer:

The ratio of the circumference to its diameter remains the same.

Step-by-step explanation:

Given,

diameter of circle = 6 inch

diameter is doubled.

New diameter of circle = 2 x 6 = 12 inch

We know that,

The Circumference of a circle is 2 π r or π d where r is the radius of the circle and d is the diameter of the circle.

Circumference of the circle when the diameter is 6 inches.

C₁ = 6π

Ratio of circumference to diameter

Ratio = $\dfrac{6\pi}{6}$

Ratio = π

When the diameter is 12 inches

C₂ = 12 π

Ratio of circumference to diameter

Ratio = $\dfrac{12\pi}{12}$

Ratio = π

Now, the correct statement is the ratio of the circumference to its diameter remains the same if the diameter is doubled.

4 0

3 years ago

Y=-5(x+3)^2-1 in standard form

Andre45 [30]

Answer:

$y=-5x^{2} -30x-46$

Step-by-step explanation:

$y=-5(x+3)^{2} -1$

$y=-5((x+3) (x+3))-1$

$y=-5(x^{2} +6x+9)-1$

$y=-5x^{2} -30x-45-1$

$y=-5x^{2} -30x-46$

5 0

3 years ago

Find the value of x in the isoscleles triangle sqrt45 and altitude 3

Alisiya [41]

Answer:

$c.\hspace{3}x=12$

Step-by-step explanation:

Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.

You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached. As you can see:

$x=2a$