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3 years ago

What is the lowest common denominator of the two fractions? An explanation would help x

Mathematics

2 answers:

slava [35]3 years ago

5 0

Answer:

Lowest common denominator are

7/10

horsena [70]3 years ago

4 0

Answer: 30

Step-by-step explanation:

9/10 = numerator 9 x 3 = 27 and denominator 10 x 3 = 30

2/15 = numerator 2 x 2 = 4 demoninator 15x 2 = 30

This is to make it easier to subtract with a common denominator

= 27-4/ 30

= 23/30

the lowest common denominator is 30

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These triangles are congruent by the triangle congruence postulate [?]

Vinvika [58]

Given:

A figure of two congruent triangles.

To find:

The triangle congruence postulate by which the given triangles are congruent.

Solution:

First label the vertices as shown below.

In triangle ABC and triangle CDA,

$AB\cong CD$ (Given)

$\angle BAC\cong \angle DCA$ (Given)

$AC\cong AC$ (Common side)

The corresponding two sides and their included angle are congruent in both triangles. So, triangles are congruent by SAS congruence postulate.

$\Delta ABC\cong \Delta CDA$ [SAS congruence postulate]

Therefore, the correct option is B.

5 0

3 years ago

Quadrilateral ABCD has side lengths of 2, 5, 7, and 12. A new quadrilateral is created, using a scale factor of 0.25. Which of t

ratelena [41]

Answer:

1, 2, and 6

Step-by-step explanation:

5*.25=1.25 7*.25=1.75 12*.25=3

3 0

3 years ago

According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and 238U at the creation of the

FromTheMoon [43]

Answer:

6 billion years.

Step-by-step explanation:

According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let $P(t)$ be the amount of $^{235}U$ and $Q(t)$ be the amount of $^{238}U$ after $t$ years.

Then, we obtain two differential equations

$\frac{dP}{dt} = -k_1P \quad \frac{dQ}{dt} = -k_2Q$

where $k_1$ and $k_2$ are proportionality constants and the minus signs denotes decay.

Rearranging terms in the equations gives

$\frac{dP}{P} = -k_1dt \quad \frac{dQ}{Q} = -k_2dt$

Now, the variables are separated, $P$ and $Q$ appear only on the left, and $t$ appears only on the right, so that we can integrate both sides.

$\int \frac{dP}{P} = -k_1 \int dt \quad \int \frac{dQ}{Q} = -k_2\int dt$

which yields

$\ln |P| = -k_1t + c_1 \quad \ln |Q| = -k_2t + c_2$ ,

where $c_1$ and $c_2$ are constants of integration.

By taking exponents, we obtain

$e^{\ln |P|} = e^{-k_1t + c_1} \quad e^{\ln |Q|} = e^{-k_12t + c_2}$

Hence,

$P = C_1e^{-k_1t} \quad Q = C_2e^{-k_2t}$ ,

where $C_1 := \pm e^{c_1}$ and $C_2 := \pm e^{c_2}$ .

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

$P(0) = Q(0) = C$

Substituting 0 for $P$ in the general solution gives

$C = P(0) = C_1 e^0 \implies C= C_1$

Similarly, we obtain $C = C_2$ and

$P = Ce^{-k_1t} \quad Q = Ce^{-k_2t}$

The relation between the decay constant $k$ and the half-life is given by

$\tau = \frac{\ln 2}{k}$

We can use this fact to determine the numeric values of the decay constants $k_1$ and $k_2$ . Thus,

$4.51 \times 10^9 = \frac{\ln 2}{k_1} \implies k_1 = \frac{\ln 2}{4.51 \times 10^9}$

and

$7.10 \times 10^8 = \frac{\ln 2}{k_2} \implies k_2 = \frac{\ln 2}{7.10 \times 10^8}$

Therefore,

$P = Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} \quad Q = Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}$

We have that

$\frac{P(t)}{Q(t)} = 137.7$

Hence,

$\frac{Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} }{Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}} = 137.7$

Solving for $t$ yields $t \approx 6 \times 10^9$ , which means that the age of the universe is about 6 billion years.

5 0

3 years ago

The lengths of a triangle are 12 and 23 meters find the range of possible lengths for the third side

sergij07 [2.7K]

Answer: 11 < x < 35

suppose: the length of the third side is x

because x is the third side of a triangle

=> 23 - 12 < x < 23 + 12

⇔ 11 < x < 35

Step-by-step explanation:

6 0

3 years ago

NEED HELP

solmaris [256]

The solutions to the systems of equations are:

1. (2, 3) (see attachment below). [one solution]

2. no solution

3. (3, 13) [one solution]

<h3>Solution to a System of Equations?</h3>

The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.

1. Using graph to solve y = 2x - 1 and y = 4x - 5:

The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]

2. Solving using substitution method:

x = -5y + 4 ---> eqn. 1

3x + 15y = -1 ---> eqn. 2

Substitute x = -5y + 4 into eqn. 2

3(-5y + 4) + 15y = -1

-15y + 12 + 15y = -1

-15y + 15y = -1 - 12

0 = -13 (this shows that there is no solution)

3. Using elimination method:

14x = 2y + 16 ---> eqn. 1

5x = y + 2 ---> eqn. 2

1(14x = 2y + 16)

2(5x = y + 2)

14x = 2y + 16 ----> eqn. 3

10x = 2y + 4 -----> eqn. 4

Subtract

4x = 12

x = 12/4

x = 3

Substitute x = 3 into eqn. 2

5(3) = y + 2

15 = y + 2

15 - 2 = y

13 = y

y = 13

The solution is: (3, 13).

Learn more about the solution of a system of equations on:

brainly.com/question/13729904

#SPJ1

5 0

2 years ago

What is the lowest common denominator of the two fractions? An explanation would help x​

What is the lowest common denominator of the two fractions? An explanation would help x