In the rhombus, m1 = 18x, m2 = x + y, and m3 = 30z. Find the value of the variables x, y, and z. The diagram is not drawn to scale.

Answers

Answer 1

Answer: None of the angles are 90 degrees. The sides of the rhombus that are across from each other are parallel. would add up to 180 degrees, When we have a rhombus, that bit of info really helps.
4X+X=180
5x=180
x=36

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Kyle has 125 marbles. Fifty of these marbles are red and the reat are other colors. What is the ratio of the nunber of red marbles to the total of marbles expressed in simplest terms?

Answers

Answer:

The required simplest form is: $(2)/(5)$

Step-by-step explanation:

We have been given Kyle has 125 marbles.

And 50 out of total 125 are red and rest of them are other colours

that means other colour marble are 125-50=75

we need to find ratio of the number of red marbles to the total of marbles

The ratio is: $(50)/(125)=(2)/(5)$

The required simplest form is: $(2)/(5)$

Answer:

Step-by-step explanation:

2/5

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.f(x) = 3(x2 – 8x) + 10

(-8/2)^2 = 16

What is the function written in vertex form?
A.f(x) = 3(x + 4)2 – 6
B.f(x) = 3(x + 4)2 – 38
C.f(x) = 3(x – 4)2 – 6
D.f(x) = 3(x – 4)2 – 38

Answers

Following the steps already shown to transform the given function into the vertex form, we have:

f(x) = 3(x2 - 8x + 16) + 10 - 3(16)
f(x) = 3(x - 4)(x - 4) + 10 - 48
f(x) = 3(x - 4)2 - 38

Therefore, the function written in vertex form is:
D.f(x) = 3(x – 4)2 – 38

The vertex form has the general form of:

y = a(x-h)^2 + k

We have the given equation:

f(x) = 3x^2 – 24x + 10

f(x) - 10 + 3(16) = 3(x^2 -8x + 16)
f(x) + 38 = 3(x - 4)^2
f(x) = 3 (x-4)^2 -38

Then, the correct answer is D.

radium has a half life of 1660 years. If the initial amount of radium is 200 grams, how much will remain in 500 years?

Answers

Amount remaining = (original amount) x (2)^-(years/1660)

Amount remaining = (200) x (2)^-(500/1660)

= (200) x (2)^-(0.3012)

= (200) x (0.8116) = 162.3 grams (rounded)

Simplify.7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54A) 11 square root of 6 end root minus 7 square root of 12
B) 11 square root of 3 end root minus 7 square root of 6
C) negative 3 square root of 9
D) 4 square root of 9

Answers

The simplest form of the expression ''7 square root of 3 end root minus 4 square root of 6 end root plus the square root of 48 end root minus the square root of 54'' would be, ''11 square root of 3 end root minus 7 square root of 6''. Hence, option B is true.

Used the concept of the square root of a number that states that,

The square root of a number is the number that, when multiplied by itself, gives the original number.

Given that the expression is,

7 square root of 3 end root minus 4 square root of 6 end root plus the square root of 48 end root minus the square root of 54.

Now, the mathematical form of the expression is,

$7√(3) - 4√(6) + √(48) - √(54)$