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do the following calculations

1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9 2. 11 > -2 Add 3 to both sides, then add 3, then add (-4) 3. -2 = -2 Subtract 6 from both sides, then 8, and then 2 4. -4 < 8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

Part (a)

The error happens on the 2nd step.

The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.

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Part (b)

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]

Check:

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]

The answer is fully confirmed.

You can use a graphing tool like GeoGebra to visually confirm the answer.

Answer:92

Step-by-step explanation:

[tex]\frac{64+88+92+89+81+92+x}{7} =85[/tex]

85 x 7 = 595

595 - 64 - 88 - 92 - 89 - 81 - 92 = 92

Answer:

Naomi needs to score a 92 on her seventh test to raise her mean to an 85.

Step-by-step explanation:

Let's call the score Naomi needs to get on her seventh test "x".

To find out what score she needs to raise her mean to 85, we can set up an equation:

(64 + 88 + 92 + 86 + 81 + 92 + x) / 7 = 85

We add up all her scores so far (64 + 88 + 92 + 86 + 81 + 92) and add the score she needs to get on her seventh test (x). We divide the sum by the total number of tests (7) to get the mean score of 85.

Simplifying the equation, we get:

503 + x = 595

Subtracting 503 from both sides, we get:

x = 92

The total amount of money Tegan paid for tax last year from her income of £48,300 is £4,830

Tegan's income last year before tax = £48,300

Tegan's earnings is upto £43,000 and in excess of £48,300 - £43,000

= £5,300

Assume, Tegan's tax rate is 10% since her excess is not up to £11,000

Tegan's tax = 10% of £48,300

= 0.10 × 48,300

= £4,830

Ultimately, Tegan paid a total amount of £4,830 as tax last year.

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The measure of angle m is,

⇒ m = 43°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle PQR is shown in figure.

Now, We know that;

An exterior angle of a triangle is sum of two opposite angle of that triangle.

⇒ m + 68° = 111°

Solve for m;

⇒ m = 111° - 68°

⇒ m = 43°

Thus, The measure of angle m is,

⇒ m = 43°

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The approximate measure of the slide is 20 feet.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, a slide is 15 feet high and the slides makes a 50° angle with the ground.

Let the length of the slide be x.

Now, sin50° =15/x

0.766=15/x

x=15/0.766

x=19.58

≈ 20 feet

Therefore, the approximate measure of the slide is 20 feet.

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Answer:

kg = gal × 3.7854 × density.

Step-by-step explanation:

The surfing increased by 50% from the first week to the second. His method is correct.

The amount of any product is given as if it were a percentage of a hundred. The ratio is one-quarter of one hundred. % is an abbreviation for one hundred percent. It is represented by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The Surfing 6 seconds to reach 9 seconds. Then the percentage is given as,

P = [(9 - 6) / 6] x 100

P = (3 / 6) x 100

P = 0.50 x 100

P = 50%

The surfing increased by 50% from the first week to the second. His method is correct.

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The requried, each month receives 1/12 of the calendar or about 8.33% of the total space.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
Anita can start by drawing a large rectangle on the paper to represent the entire year. Then, she can divide the rectangle into 12 equal parts, each representing a month. One way to do this is to draw four vertical lines to divide the rectangle into five equal columns, and then draw three horizontal lines to divide each column into four equal rows.

Each of the 12 parts represents 1/12 or one-twelfth of the calendar. Therefore, each month receives 1/12 of the calendar, or about 8.33% of the total space.

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Answer:

³/₂

Step-by-step explanation:

1.5 = ¹⁵/₁₀

= ³/₂

Answer:

= 43.

Step-by-step explanation:

[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]

Note// the LCM for 18 and 12 is 36.

A procedure for using sample data to find the estimated regression equation is (c) the least squares method.

The least squares method is a commonly used statistical procedure for finding the estimated regression equation by minimizing the sum of the squared differences between the observed and predicted values.

The goal of this method is to find the line of best fit that closely represents the relationship between the independent and dependent variables in the sample data. The regression equation obtained from the least squares method can be used to make predictions about the dependent variable based on the values of the independent variable.

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When sales are under $15,000, the current job pays less than the new offer. The new job offer is therefore favoured for sales below $15,000.

a)   Wc = 2000+.07S

b)  Wn =2300+.05S

c)  When the totals are similar, the sales level at which she would not care

   2000 + .07S = 2300 + .05S

   subtract .05S from both sides

    2000 +.02S = 2300

   subtract 2000 from both sides

    .02S = 300

   divide both sides by .02

   S = 300/.02 = 15000

Sales of $15,000 equate to identical pay.

If we apply the same calculation, substituting less than for the = sign... The result of our equation is

2000 + .07S < 2300 + .05S

S < 15000

The present employment pays less than the new offer when sales are under $15,000. Therefore, the new job offer is preferred for sales below $15,000.

check:  Let S = 10,000

Wc = 2000+.07(10000) = $2700

Wn = 2300 + .05(10000) = $2800

As can be seen, at sales of $10,000 the new job earns more.

The complete question is:

A salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.

a) write a linear equation for her current wage W in terms of her monthly sales S.

b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.

c) what level of sales will make her indifferent between the two jobs? Which scheme is preferred when sales are below this level?

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An algebraic expression to represent how much Xavier will have in his savings account after w weeks is; y = 15w + 43

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given that Xavier has $43 in his savings account. Thus;

y-intercept = $43

He plans to save $15 each week. Thus;

Slope = $15

Now, after w weeks, the total savings is expressed as;

y = 15w + 43

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Answer:

1) 7995.9 feet

2) 12 degrees

Step-by-step explanation:

1)

We can start by drawing a diagram of the situation. Let's label the height of the tower as "h", the distance from the airplane to the tower as "d", and the angle of depression as 56°.

  C (top of tower)

               /|

              / |

             /  |h

            /   |

           /θ   |

    A_____/_____|

        d   B

In this diagram, point A represents the airplane, point B represents the base of the tower, and point C represents the top of the tower. The angle θ is the angle of depression from the airplane to the top of the tower.

We can use trigonometry to solve for the distance "d" from the airplane to the tower. In particular, we know that:

tan(θ) = h / d

We can rearrange this equation to solve for "d":

d = h / tan(θ)

Substituting the values we know, we get:

d = 320 / tan(56°)

Using a calculator, we can evaluate this to get:

d ≈ 215.8 feet

However, the airplane is flying at an altitude of 7,450 feet, so we need to add this to the height of the tower to get the total distance from the airplane to the ground:

total distance = d + 320 + 7,450

Plugging in the value we found for "d", we get:

total distance ≈ 7995.8 feet

Rounding to the nearest tenth, we get:

total distance ≈ 7995.8 ≈ 7995.9 feet

2)

We can use the tangent function to find the angle of depression. Let theta be the angle of depression. Then:

tan(theta) = (275 / 1324)

We can solve for theta by taking the inverse tangent (or arctan) of both sides:

theta = arctan(275 / 1324)

Using a calculator, we find:

theta ≈ 11.92 degrees

Rounding to the nearest whole number, we get:

The angle of depression is approximately 12 degrees.

Answer:

[tex]\frac{4}{90}[/tex]

Step-by-step explanation:

[tex]\frac{4}{9}[/tex]  - [tex]\frac{4}{10}[/tex]

to subtract the fractions we require them to have a common denominator

the LCM of 9 and 10 is 90

= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]

= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]

= [tex]\frac{40-36}{90}[/tex]

= [tex]\frac{4}{90}[/tex]

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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Answer:

Therefore, the height of the pole is approximately 20.79 feet.

Step-by-step explanation:

the person is standing at point A, which is 36 ft away from the base of the telephone pole. The angle of elevation from the ground to the top of the pole is 30 degrees. We want to find the height of the pole, which is represented by "h" in the diagram.

To solve for "h", we can use the tangent function, which relates the opposite side (height) to the adjacent side (distance from the pole to the person) of a right triangle:

tan(30°) = h / 36

We can solve for "h" by multiplying both sides by 36 and taking the tangent of 30 degrees:

h = 36 * tan(30°)

h = 36 * 0.5774 (rounded to four decimal places)

h ≈ 20.79

Therefore, the height of the pole is approximately 20.79 feet.

Answer:

20.78460969082652752232935609807

Step-by-step explanation:

;)

To find the value of f(-1), we simply need to substitute -1 for x in the function f(x) = 2x - 1 and evaluate:

f(-1) = 2(-1) - 1

= -2 - 1

= -3

Therefore, the value of f(-1) is -3.

Answer:

f=2x-1/x

Step-by-step explanation:

I hope this helps :) <3

Integer: 12

Irrational numbers: -2√10 and √20

Rational numbers: 17/4, 0.25, and -77/11.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

There are rational and irrational numbers in the image.

The numbers can be written in the form of p/q, where q is never zero is rational numbers.

And rest of the numbers are irrational numbers.

So, the solutions are given in the image below.

√144 = 12

0.25 = 25/100 = 1/4

Therefore, the solutions are given in the image below.

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Breakeven's time is 31.7 years.

The loan term is only 25 years, so it is not a wise decision.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To determine if the purchase of negative points is a wise decision, we first need to calculate Millie's monthly payment with and without the negative points.

Without negative points:

Principal = $600,000

Interest rate = 3.49%

Loan term = 25 years or 300 months

Now,

Monthly Payment = $2,967.27

With negative points:

Millie needs to purchase 2 negative points to cover the bank's closing cost. Each negative point will increase her APR by 0.125%, so the new interest rate will be:

New interest rate.

= 3.49% + (2 x 0.125%)

= 3.49/100 + (2 x 0.125/100)

= 3.74%

Monthly Payment = $2,998.84

The breakeven time.

This is the amount of time it takes for the cost of the negative points to be offset by the savings in monthly payments.

The total cost of the negative points.

We see that,

Each negative point costs 1% of the principal.

Cost of negative points,

= 2 x $6,000

= $12,000

The breakeven time.

Monthly savings.

= $2,967.27 - $2,998.84

= -$31.57

i.e

The value is negative because the new monthly payment is higher.

So,

Breakeven time.

= $12,000 ÷ -$31.57

= 380.2 months

This is,

1 year = 12 months

so,

31.7 years

Thus,

Breakeven's time is 31.7 years.

The loan term is only 25 years, so it does not make sense to purchase the negative points.

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Answer: 4

Step-by-step explanation:

1+1=2 but  if it is 2+2 then it would = 4

Answer: The measure of RST is 124 degrees.

Step-by-step explanation:

If HJK and RST are supplementary angles, it means that their sum is equal to 180 degrees. So we can use this information to find the measure of RST.

HJK + RST = 180

Substituting HJK = 56, we get:

56 + RST = 180

Subtracting 56 from both sides, we get:

RST = 180 - 56

RST = 124

Therefore, the measure of RST is 124 degrees.

Answer:

192

Step-by-step explanation:

2x9=18

18x12=192

The value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and 5g is equal to 5 times that amount, or 5000mg.

When converting between different metric units of mass, the prefixes are used to denote the multiple of the base unit. In this case, the base unit is the gram, and the prefix we are using is 'milli', which is equal to one thousandth of the base unit. Therefore, in order to convert 5g to mg, the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.When converting between metric units, it is important to remember that the decimal point moves right by a number of places equal to the number of zeroes in the prefix. For example, if we were converting 5g to kg, the prefix 'kilo' has three zeroes, so the decimal point would move three places to the right, resulting in a value of 0.005kg.When converting from a larger unit to a smaller unit, the numerical value will increase, and when converting from a smaller unit to a larger unit, the numerical value will decrease. In this case, we are converting 5g to mg, which is a smaller unit, so the numerical value of 5g increases to 5000mg.

Overall, the value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.

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No, a matrix does not have to be symmetric to be orthogonally diagonalizable. Orthogonal diagonalization is a property of square matrices that can be used to simplify calculations and solve certain types of problems.

A square matrix A is orthogonally diagonalizable if there exists an orthogonal matrix P and a diagonal matrix D such that A = PDP^T, where D contains the eigenvalues of A and P contains the corresponding eigenvectors.

A symmetric matrix is always orthogonally diagonalizable, meaning that there exists an orthogonal matrix P such that A = PDP^T, where D is a diagonal matrix containing the eigenvalues of A. However, not all matrices are symmetric and still can be orthogonally diagonalizable.

For a non-symmetric matrix, the eigenvectors and eigenvalues may not have certain symmetrical properties that make orthogonal diagonalization straightforward, but it is still possible to diagonalize the matrix. In such cases, we can use other techniques, such as the Schur decomposition, to obtain a similar diagonal form.

In summary, a matrix does not have to be symmetric to be orthogonally diagonalizable, but symmetric matrices are always orthogonally diagonalizable. Other techniques may be used for diagonalizing non-symmetric matrices.

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1. a. The graph for the g(x) = -4x - 5 is mentioned in the image below.

1. b. The graph for the h(x) = - 4x - 12 is mentioned in the image below.

1. c. The graph for the j(x)= -4x -15 is mentioned in the image below.

2. The equation for the linear function with a gradient of - 4 and an unknown y-intercept of k is y = -4x + k.

A slope-intercept form is an equation that represents a straight line and is written as y = mx + c, where m is the gradient and c is the y-intercept. If c becomes zero, it passes through the origin.

1. a.

The function g(x) = -4x - 5 represents a straight line that has a slope of -4 and a y-intercept of -5.

When x = 0, g(x) = -5. The point is (0,-5).

When x = 1, g(x) = -9. The point is (1,-9).

When x = -1, g(x) = -1. The point is (-1,-1).

The graph of the function is given below.

1. b.

The function h(x) = -4x - 12 represents a straight line that has a slope of -4 and a y-intercept of -12.

When x = 0, h(x) = -12. The point is (0,-12).

When x = 1, h(x) = -16. The point is (1,-16).

When x = -1, h(x) = -8. The point is (-1,-8).

The graph of the function is given below.

1. c.

The function j(x) = -4x - 15 represents a straight line that has a slope of -4 and a y-intercept of -15.

When x = 0, j(x) = -15. The point is (0,-15).

When x = 1, j(x) = -15. The point is (1,-19).

When x = -1, j(x) = -11. The point is (-1,-1).

The graph of the function is given below.

2.

The slope-intercept form of a line is y = mx + c. On substituting m = -4 and c = k into the equation, it gets reduced to y = -4x + k.

Therefore, the obtained answer is y = -4x +k.

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Answer:

C

Step-by-step explanation:

It makes the most sense.

The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.

The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.

However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.

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