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3 years ago

What is the intermediate step in the form (x+a)^2=b(x+a)

Mathematics

1 answer:

Step2247 [10]3 years ago

7 0

Answer:

The intermediate step are;

1) Separate the constants from the terms in x² and x

2) Divide the equation by the coefficient of x²

3) Add the constants that makes the expression in x² and x a perfect square and factorize the expression

Step-by-step explanation:

The function given in the question is 6·x² + 48·x + 207 = 15

The intermediate steps in the to express the given function in the form (x + a)² = b are found as follows;

6·x² + 48·x + 207 = 15

We get

1) Subtract 207 from both sides gives 6·x² + 48·x = 15 - 207 = -192

6·x² + 48·x = -192

2) Dividing by 6 x² + 8·x = -32

3) Add the constant that completes the square to both sides

x² + 8·x + 16 = -32 +16 = -16

x² + 8·x + 16 = -16

4) Factorize (x + 4)² = -16

5) Compare (x + 4)² = -16 which is in the form (x + a)² = b

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Minor surgery on horses under field conditions requires a reliable short-term anesthetic producing good muscle relaxation, minim

iren [92.7K]

Answer:

We accept H₀

Step-by-step explanation:

Normal Distribution

size sample n = 69

sample mean 18.94

standard deviation 8.3

Is a one tailed-test to the left we are traying of find out is we have enough evidence to say that the mean is less than 20 min.

1.-Test hypothesis H₀ ⇒ μ₀ = 20

Alternative hypothesis Hₐ ⇒ μ₀ < 20

2.- Critical value

for α = 0.1 we find from z Table

z(c) = - 1.28

3.-We compute z(s)

z(s) = [ ( μ - μ₀ ) / (σ/√n) ⇒ z(s) = [( 18.94 - 20 )*√69)/8.3]

z(s) = ( -1.06)*8.31/8.3

z(s) = - 1.061

4.- We compare

z(c) and z(s) -1.28 > -1.061

Then z(c) > z(s)

z(s) in inside acceptance region so we accept H₀

5 0

3 years ago

An aeroplane at an altitude of 200m observes the angle of depression of opposite points on the two banks of a river to be 45 and

blagie [28]

Answer:

84.5 m

Step-by-step explanation:

It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.

The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:

Tan = Opposite/Adjacent

Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:

tan(30°) = OB/OA

OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m

Likewise, we have ...

OC = (200 m)·tan(45°) = 200 m

Then the width of the river is the difference between these values:

BC = OC -OB = 200 m - 115.47 m = 84.53 m

4 0

3 years ago

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 (μ ± σ). He polls his class

solniwko [45]

Answer:

Step-by-step explanation

Hello!

Be X: SAT scores of students attending college.

The population mean is μ= 1150 and the standard deviation σ= 150

The teacher takes a sample of 25 students of his class, the resulting sample mean is 1200.

If the professor wants to test if the average SAT score is, as reported, 1150, the statistic hypotheses are:

H₀: μ = 1150

H₁: μ ≠ 1150

α: 0.05

$Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } ~~N(0;1)$

$Z_{H_0}= \frac{1200-1150}{\frac{150}{\sqrt{25} } } = 1.67$

The p-value for this test is 0.0949

Since the p-value is greater than the level of significance, the decision is to reject the null hypothesis. Then using a significance level of 5%, there is enough evidence to reject the null hypothesis, then the average SAT score of the college students is not 1150.

I hope it helps!

7 0

3 years ago

Smooth transitions in an informative essay_____

WITCHER [35]

The answer is connect.
hope your day is good !!

3 0

2 years ago

Read 2 more answers

A car, purchased for $20,000, loses 14% of its value in the first year. What is the car worth after one year?

OLga [1]

The car is worth 17,200.
20,000x .14=2800
20,000-2,800=17,200.

7 0

3 years ago