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3 years ago

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Mathematics

1 answer:

earnstyle [38]3 years ago

7 0

Answer:

$\frac{4}{3}$ $\sqrt{3}$

Step-by-step explanation:

the ratio of sides of a 30-60-90° triangle, respectively, are 1 : $\sqrt{3}$ : 2

we can solve for 'x' using this proportion:

x/4 = 1/ $\sqrt{3}$

now cross-multiply:

$\sqrt{3}$ x = 4

x = 4/ $\sqrt{3}$

we don't want to leave a radical in the denominator so we can multiply numerator and denominator by $\sqrt{3}$ to get:

4 $\sqrt{3}$ / 3 or $\frac{4}{3}$ $\sqrt{3}$

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How do you solve the system of linear equations by graphing<br> X+y=7<br> -x+y=-7

morpeh [17]

Answer:

x = 7 and y = 0

Step-by-step explanation:

We can either solve by substitution method or by elimination method or both method . We will solve by both the elimination and substitution method.

X+y=7 ---------------------------------------------------(1)

-x+y=-7 -------------------------------------------------(2)

Subtract equation (2) from equation(1)

2x = 14

Divide both-side of the equation by 2

2x/2 = 14/2

x = 7

Substitute x = 7 into equation (1)

x+y=7

7 + y = 7

Subtract 7 from both-side of the equation

7-7 + y = 7-7

y = 0

x = 7 and y =0

8 0

4 years ago

Let p be "it is raining" and q be "the track meet will be canceled."<br> write p->q in words

trasher [3.6K]

The statement for the logic $\text{p}\rightarrow\text{q}$ is $\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

Further explanation:

The logic given in the question is $\text{p}\rightarrow\text{q}$ .

The logic $\text{p}\rightarrow\text{q}$ is a symbol of implication.

Statement p is “It is raining” and the statement q is “The track meet will be canceled”.

The statement formed for the logic $\text{p}\rightarrow\text{q}$ is called a compound statement.

The truth table for the logic $\text{p}\rightarrow\text{q}$ is attached below.

From the table attached below it is observed that there are four cases for the compound statement.

Case1:

If p statement is true and the q statement is true then the compound statement for $\text{p}\rightarrow\text{q}$ is also true.

Case 2:

If p statement is true and the q statement is false then the compound statement for $\text{p}\rightarrow\text{q}$ is false.

Case 3:

If p statement is false and the q statement is true then the compound statement for $\text{p}\rightarrow\text{q}$ is true.

Case 4:

If p statement is false and the q statement is false then the compound statement for $\text{p}\rightarrow\text{q}$ is true.

For a true statement it can also be said that it is a positive statement and for a false statement it can be said that it is a negative statement.

Statement p is given as “It is raining”, which is a positive statement or a true statement.

Statement q is given as “The track meet will be cancelled”, which is a positive statement or a true statement.

As per the table attached for the logic $\text{p}\rightarrow\text{q}$ it is observed that the given statements p and q resembles with the case $1$ as both of the statement are true.

So, the compound statement for $\text{p}\rightarrow\text{q}$ is also a true statement.

The compound statement for the logic $\text{p}\rightarrow\text{q}$ is as follows:

$\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

Therefore, the compound statement for the logic $\text{p}\rightarrow\text{q}$ is $\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}$

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