In ΔGHI, the measure of ∠I=90°, the measure of ∠H=52°, and HI = 63 feet. Find the length of IG to the nearest tenth of a foot.

Since it is a ratio of two integers, 6/4 is irrational

lukranit [14]

Answer:

is this a question? also, 6/4 is not irrational, it is rational, and an irrational number is a number that cannot be expressed as a ratio of two integers, aka a simple fraction

4 0

3 years ago

2x^3-x^2-3x=210 the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

2 years ago

Read 2 more answers

Ax + bx = 0 Solve equation for x

Serga [27]

X=0 is the value....

8 0

2 years ago

Read 2 more answers

Solve for y , what is 9x+3y=4 ??

lora16 [44]

To solve for y, isolate the variable to one side.
9x+3y=4
-9x -9x
~~~~~~~~
3y= -9x+4
~~~~~~~~
3y= -9x+4 (Divide both sides by 3)

y=-3x+4

4 0

3 years ago

Which of the following is NOT true for a hypothesis test for correlation? Choose the correct answer below. A. If |r|less than

pantera1 [17]

Answer:

Answer explained

Step-by-step explanation:

From the information, the true statements for a hypothesis test for correlation is,

If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

If |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

Explanation

According to the decision rule of P-value approach, observe that if the P-value is less than or equal to the significance level, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

Similarly, if the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

According to the critical value approach, observe that if the test statistic value is greater than the critical value, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

- If |r| greater than critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

Explanation

Based on the decision rules of the hypothesis test, the false statement about the test for a correlation is, if |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

3 0

3 years ago