Factor the expression below. x2-10x+25

A doorway is 7 1/2 feet tall. How many inches tall is the doorway?

neonofarm [45]

Answer:

6.07/212

Step-by-step explanation:

5 0

2 years ago

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Is 9.521521521 rational or irrational

enyata [817]

If the numbers after the decimal terminate, yes, it's rational.

9.521521521 = 9,521,521,521 / 1,000,000,000

If they don't terminate, but the pattern continues (which I suspect is the case here), yes, it's still rational.

If x = 9.521521521…, then

1000x = 9521.521521521…

Subtract x from this to eliminate the fractional part:

1000x - x = 9521.521521521… - 9.521521521…

999x = 9512

x = 9512/999

If they don't terminate, but the pattern does not continue, meaning the next few digits could be something random like

9.52152152119484929271283583457…

then the number would be irrational.

7 0

2 years ago

An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted t

7nadin3 [17]

Answer:

A

The test statistics is $t = -1.7$

B

The Null and Alternative hypothesis are

$H_o : \mu = 47.2$ and $H_a : \mu \ne 47.2$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 47.2 miles/gallon(MPG)$

The sample size is $n = 250 \ van$

The sample mean is $\= x = 47.0$

The sample standard deviation is $\sigma = 1.9$

The level of significance is $\alpha = 0.02$

Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then

The Null Hypothesis is

$H_o : \mu = 47.2$

The alternative Hypothesis is

$H_a : \mu \ne 47.2$

The test statistics can be mathematically evaluated as

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

substituting values

$t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }$

$t = -1.7$

7 0

2 years ago

Solve the simultaneous equations 4x+3y=1 4x^2+3xy+y^2=2

Fantom [35]

Notice that the second equation,

4x ² + 3xy + y ² = 2

can be written as

x (4x + 3y) + y ² = 2

and the first equation says 4x + 3y = 1, so this reduces to

x + y ² = 2

Solve the first equation for x :

4x + 3y = 1

4x = 1 - 3y

x = (1 - 3y)/4

Substitute this into the reduced second equation to get a quadratic equation in y, which happens to be easily factorized and solved:

(1 - 3y)/4 + y ² = 2

1 - 3y + 4y ² = 8

4y ² - 3y - 7 = 0

(4y - 7) (y + 1) = 0

4y - 7 = 0 or y + 1 = 0

y = 7/4 or y = -1

Solve for x :

x = (1 - 3 (7/4))/4 or x = (1 - 3 (-1))/4

x = -17/16 or x = 1

So the two solutions are (x, y) = (-17/16, 7/4) and (x, y) = (1, -1).

8 0

2 years ago

- x - x + 11 - 2x = 83 please show step by step!!

m_a_m_a [10]

Answer:

$x=-18$

Step-by-step explanation:

Given

$-x-x+11-2x=83$

Step 1: Combine Like Terms on LHS

$-x-x+11-2x=83\\-2x+11-2x=83\\-4x+11=83$

Step 2: Subtract 11 on both sides

$-4x+11=83\\-4x+11-11=83-11\\-4x=72$

Step 3: Divide both sides by -4 to isolate the x-variable

$-4x=72\\\\\frac{-4x}{-4}=\frac{72}{-4}\\ \\ x=-18$

Final Answer

$x=-18$

7 0

2 years ago

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