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3 years ago

Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.

1 answer:

3 0

Hello Melissamv9321, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a2.

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Prove that if one solution for a quadratic equation of theform x2 + bx + c = 0 is rational (where b and c are rational),then the

Elenna [48]

Answer:

The other solution of the given equation x² + bx + c = 0 is also rational number.

Step-by-step explanation:

Here, given: ax² + bx + c = 0 is a quadratic equation

Also, one solution (r) of equation is RATIONAL.

To show: The other solution (s) is also RATIONAL

Now, here: as x² + bx + c = 0

Since r and s are the two given solutions, the given equation can be factorized as:

x² + bx + c = (x -r) (x - s)

Simplifying LHS, we get:

(x -r) (x - s) = x x - r (x) - s (x) + (r)(s)

= x² + x(-r - s) + rs

or, x² + bx + c = x² + x(-r - s) + rs

Comparing the related terms, we get:

b = (-r - s)

⇒ b + s = - r

or, s = -r - b

Now, given : r = Rational and the negative of a rational is also rational.

⇒ -r is also rational

Also, difference of two rational number is also rational.

⇒ -r - b is also rational

⇒ s is a RATIONAL NUMBER

Hence, the other solution of the given equation x² + bx + c = 0 is also rational number.

7 0

3 years ago

What is the solution to the system of equations below? 3x+4y-2z=-1 -x+6y+2z=7 4x-2y+3z=27

matrenka [14]

Answer:

(3x+4y-2z=-1)= x=-1/3-4/3y+2/3z

(-x+6y=2z)= x=-7+6y=2z

(4x-2y+3z=27)= x=27/4+1/2-3/4z

Step-by-step explanation:

6 0

2 years ago

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportat

madreJ [45]

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is $H_o : \mu = 122$

the alternative hypothesis is $H_a : \mu \ne 122$

The test statistics is $t = - 1.761$

The p-value is $p = P(Z < t ) = 0.039119$

$p \ge 0.01$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 122$

The sample size is n= 38

The sample mean is $\= x = 116 \ feet$

The standard deviation is $\sigma = 21$

Generally the null hypothesis is $H_o : \mu = 122$

the alternative hypothesis is $H_a : \mu \ne 122$

Generally the test statistics is mathematically evaluated as

$t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }$

substituting values

$t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }$

$t = - 1.761$

The p-value is mathematically represented as

$p = P(Z < t )$

From the z- table

$p = P(Z < t ) = 0.039119$

$p \ge 0.01$

4 0

2 years ago

M. 4.96)2,9.76 Need Answer to how much does 4.96 go into 2976

Oxana [17]

Answer:600

Step-by-step explanation:2,976/4.96=600

3 0

3 years ago

What is the answer 7-2(3x+2)

melisa1 [442]

Step-by-step explanation:

Do distributive property

7 - 6x - 4

8 0

3 years ago

Read 2 more answers