Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x

Answer:

-2

Step-by-step explanation:

Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).

The required measure of supplymentary angle m∠2 is 58°.

Here, two supplymentary angles are given ∠1 and ∠2 where m∠1 = 32°, m∠2 is to be determined.

The angle can be defined as the one line inclined over another line. Unit of the measure of angle are degree and radians.

Here,
For supplymentary angles, the sum of the angle is equal to 90°. So,
m∠1 + m∠2 = 90
From the given,
32 + m∠2 = 90
m∠2 = 90 - 32
m∠2 = 58°

Thus, the required measure of supplymentary angle m∠2 is 58°.

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Answer:

  see attached

Step-by-step explanation:

An amortization schedule is conveniently prepared using a spreadsheet. It has the formula built in for computing the payment value.

__

The amount of the payment going to interest is the product of the outstanding balance and the monthly interest rate (=6%/12). In the attached, the amount of interest due is rounded to cents. The remaining amount of the payment reduces the outstanding balance.

The attachment shows the payment calculation and the amortization schedule for the first 5 payments.

Answer:

No.

Step-by-step explanation:

When trying to make this into a proportion, the left and right sides of the equation are unequal, therefore this is invalid.

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Answer:

a) \( s^2 =30^2 =900\)

b) \(\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}\)

\( 567.28 \leq \sigma^2 \leq 1690.224\)

c) \(23.818 \leq \sigma \leq 41.112\)

Step-by-step explanation:

Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in  the variability in the number of rooms occupied per day during a particular season of the  year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per  day and a sample standard deviation of 30 rooms

Part a

For this case the best point of estimate for the population variance would be:

\( s^2 =30^2 =900\)

Part b

The confidence interval for the population variance is given by the following formula:

\(\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}\)

The degrees of freedom are given by:

\(df=n-1=20-1=19\)

Since the Confidence is 0.90 or 90%, the significance \(\alpha=0.1\) and \(\alpha/2 =0.05\), the critical values for this case are:

\(\chi^2_{\alpha/2}=30.144\)

\(\chi^2_{1- \alpha/2}=10.117\)

And replacing into the formula for the interval we got:

\(\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}\)

\( 567.28 \leq \sigma^2 \leq 1690.224\)

Part c

Now we just take square root on both sides of the interval and we got:

\(23.818 \leq \sigma \leq 41.112\)

The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

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Answer:

You did not provide the tables to choose from, but the relationship between number of books and total price is that each book is 14.25. Hope that helps at least.

Answer:

1) 5y + 5z

2) 10x⁴ - 10x³ + 2x² + 18x - 11

Step-by-step explanation:

Given the subtraction of the following polynomial expressions:

In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the subtrahend by alphabetical order.

-3x - 4y + 11z  

-3x - 9y + 6z  ⇒ This is the subtrahend.

Now, we can finally perform the subtraction on both trinomials:

\(\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}} \right.}\)

In the subtrahend, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.  

\(\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}}\right.} \\\qquad\sf {\qquad\:\:\:0x\:+\:5y\:+5z\)

The difference is: 5y + 5z.

Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.

3x⁴- 4x³ + 7x - 2           ⇒  Already in descending order (degree).

9 - 7x⁴ + 6x³- 2x² - 11x​   ⇒  -7x⁴ + 6x³- 2x² - 11x​ + 9

In subtracting polynomials, we can only subtract like terms, which are terms that have the same variables and exponents.  

\(\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.}\)  

In the minuend, I added the "0x²" to make it less-confusing for us to perform the subtraction operations.  

The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x​ ⇒  their coefficients turn into positive when performing subtraction.  

\(\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.} \\\qquad\sf {\qquad\:\:10x^4-10x^3+2x^2+18x\:-11\)  

Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.

Answer:

515$

Step-by-step explanation:

Because 20$=1 month

1 year=12 months

12 months=240$

2 years=24 months

20x24=480+35$ for the hotspot in the first place=415

Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

Answer: (√2)(2) = 2√2

Step-by-step explanation:

To simplify the expression 3√2 - √2, you can factor out the common term √2:

3√2 - √2 = (√2)(3 - 1)

Now, subtract the numbers in parentheses:

(3 - 1) = 2

(√2)(2) = 2√2

Answer:

2

Step-by-step explanation:

terms are separated by addition or subtraction signs so this expression can be simplified to be \(\frac{m}{5}\) + 24, therefore two terms:

m/5 and 24

The maximum height of the firework is; 387.78 ft

The time for which the firework is in the air before it explodes is; 1 second

We are given the function;

h = -(500/9)t² + (1000/3)t + 10

where;

h is height after time of t seconds

At height of zero, the firework would either be about to launch or when it has come down.

Thus, let us set h = 0 to find the times.

0 = -(500/9)t² + (1000/3)t + 10

Using quadratic equation calculator, we have;

t ≈ 2 seconds

Now the  firework explodes at the highest point which will be the mid point of where the launching started and the endpoint where it stopped.

This means time at midpoint = (0 + 2)/2 = 1 sec

It explodes after 1 second.

Thus maximum height at this time is;

h = -(500/9)(1)² + (1000/3)(1) + 10

h = 387.78 ft

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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Using the normal distribution, it is found that the correct option is:

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

P(Y < 16) is the p-value of Z when X = 16, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{16 - 20}{2.3}\)

\(Z = -1.74\)

\(Z = -1.74\) has a p-value of 0.041.

This is valid for the entire population, hence, the correct interpretation is:

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Answer: x = -3

Step-by-step explanation:

2 x 2 + x - 1 = 0

4 + x - 1 = 0

3 + x = 0

x = -3

Answer:

X=-3

Step-by-step explanation:

See steps below:)

Answer:

12

Step-by-step explanation:

pythagoras thereom

a^2 +b^2=c^2

13^2-5^2=144

144 square root = 12

Answer:

12

Step-by-step explanation:

13^2 - 5^2 = 144

square root of 144 = 12

Step-by-step explanation:

28.4 g there are 110 calories

1 g there are 110/28.4 = 3.87 calories

39.76 g there are 3.87 × 39.76 = 153.87

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.04 cm. He knows that the population standard deviation is 0.26 cm.

Assuming a level of significance of 0.02, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?

Step 1: Null and Alternative HypothesisThe null hypothesis (H0): The machine does not need recalibration after testing 196 bolts.The alternative hypothesis (H1): The machine needs recalibration after testing 196 bolts.

Step 2: Determine the level of significance level of significance (α) = 0.02

Step 3: Find the critical valueThe level of significance is 0.02, which indicates that the critical value is zα/2 = ±2.33 using the z-table.

Step 4: Calculate the z-test statistics = (x - μ) / (σ/√n) = (4.04 - 4.00) / (0.26 / √196)z = 4.0

Step 5: Determine the p-values-value = P (Z > 4) ≈ 0Using the p-value approach, if the p-value is less than the level of significance, reject the null hypothesis.

In this case, the p-value is almost 0, indicating that there is a statistically significant difference between the sample mean and the hypothesized population mean of 4.0 cm.

Step 6: Conclusion Since the p-value is less than the level of significance, we can reject the null hypothesis and accept the alternative hypothesis. It implies that the machines need recalibration as there is sufficient evidence to suggest that the bolts' mean length is more significant than the required specification of 4.00 cm.

Therefore, the manufacturer should recalibrate the machine to ensure that the bolts' length is within the required specification.

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The checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

The fertilizing techniques that would be most effective for each example are as follows:

1. Farm with numerous workers and sensitive crops:

a. UDP (Unchecked )

b. Precision management (Checked)

2. A gardener raising produce for a family:

a. UDP (Checked).

b. Precision management (Unchecked )

3. Company that delivers corn to 10 states:

a. UDP (Unchecked)

b. Precision management (Checked)

Please note that the checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

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Answer:

33.

Step-by-step explanation:

75%   x

100   44

x = (44 * 75 ) / 100 = 33.

Answer:

B) 0.15 Pr (B)

Step-by-step explanation:

A is the event that a policyholder is classified as low-risk.

B is the event that a policyholder suffered a loss.

P(A∩B) is the probability that a low risk policyholder suffered a loss is 15%.

P(A∩B)= 15%= 15/100= 0.15

P(B∩A) is the  probability that a policyholder who suffered a loss is low-risk is = 5%= 5/100= 0.05

Intersection means finding those elements which are common to both sets. Now we have to find those elements of A which are common to B. This is already given in the statement above and is 15 %.

Hence

P(A∩B)= 15%= 15/100= 0.15

Choice B is the correct answer.

Answer:

Yes.

Step-by-step explanation:

To solve this, simply substitute the points into the equation:

7 = 4 + 3

7 = 7

Therefore, (4,7) is on the line.

Answer:

450cm²

Step-by-step explanation:

The area of the kite is made up of two pairs of congruent triangles. Find the area of these and add to get the kite's area. (area of triangle = (1/2)(base)height))

2(0.5*15*20)+2(0.5*15*10)

300+150

450

Answer:

See below.

Step-by-step explanation:

Problem 2.

Left figure: 2 sides and included angle: SAS

Middle figure: 2 angles and included side: ASA

Right figure: 3 sides: SSS

Problem 3.

CPCTC = corresponding parts of congruent triangles are congruent

The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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