Question 9 Multiple Choice Worth 5 points)
(02.07 HC)
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior
Step 1: m2x +mzy + mzz = 90 degrees (sum of adjacent angles)
Step 2: mzw+mzz = 180 degrees (supplementary angles)
Step 3: Therefore, mzx+may+mzz = mzw+mzz
Step 4: So, m2x + m2y = mzw
In which step did the student first make a mistake and how can it be corrected?
Step 1; it should be mex + m2y + m2z = 180 degrees (sum of angles of a triangle)
Step 1; it should be mex + m2y + m2z = 180 degrees (corresponding angles)
Step 2; it should be mzw+mzz = 90 degrees (supplementary angles)
Step 2; it should be mzw+mzz = 90 degrees (adjacent angles)

Answer:

none

Step-by-step explanation:

4x - 6 = 2(2x + 3)

4x - 6 = 4x + 6

Everything cancels out meaning there are no real solutions

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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Given:

Required:

Area of square

Explanation:

Area=

Required answer:

Answer:

Assuming no compounding, given an interest rate of 5%, after 5 years the $300 dollars become:

300*(1+5%)^5= $382.884469

By saving $250 instead,

250*(1.05)^5=319.07039

The difference is 382.8845-319.0704= 63.8141

Step-by-step explanation:

The formula is FV=PV*(1+r%)^T

Where:

FV- future value

PV- present value

r%- interest rate

T- Time (usually in years)

Answer: 2

Step-by-step explanation:

8 - 4 = 4

5 - 3 = 2

4/2 = 2

Answer:

Step-by-step explanation:

the rate of change or slope from the given two points is rise over run.

(3, 4) (5, 8)

slope = (y2 - y1) / (x2 - x1)

         = (8 - 4) / (5 - 3)

         = 4 / 2

         = 2

Answer:

13.(8p-13)

14.(5y+1)

15.(11x+12)

Step-by-step explanation:

13. So combine like terms and then you get your answer

14. Same concept as question 13, just combine like terms

15. Also this is combining like terms and it’s pretty straight forward 3x+2x+x+5x=11x and 10+2=12

Answer:

(a) Minimum red blood cells 5.744 million cells per micro liter

(b) Maximum red blood cells 5.068 million cells per micro liter.

Step-by-step explanation:

Z-score formula is = \(\frac{x-u}{Standard deviation}\)

Z-score = \(\frac{x-5.5}{0.4}\)

The value of z-score is 0.61 so then x will be;

x = 5.744

The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.

Z-score = \(\frac{x-5.5}{0.4}\)

The value of z-score is 0.14 so then x will be;

x = 5.068

The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Answer:

option C: 120

Step-by-step explanation:

total marks = 5× 100 = 500

marks he obtained = 380

marks he lost = 500 - 380 = 120

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Answer:

P = -10

5p - 8(p + 1) > 16

5(-10) - 8(-10 + 1) > 16

-50 - 8(-9) > 16

-50 + 72 > 16

22 > 16

Answer:

Eat that cookie and you will not regret about it

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The measure of line MN in the secant line using the Intersecting theorem is approximately 19.5.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

Sectant line segment QO = 48

internal line segement of QO = QP = 29

External line segement of QO =  PO = 48 - 29 = 19

Second sectant line segment MO = NO + MN = ( 22 + x )

External line segement of MO = NO = 22

Using the Intersecting secants theorem:

22( 22 + x ) = 19 × 48

Solve for x:

484 + 22x = 912

22x = 912 - 484

22x = 428

x = 428/22

x = 19.5

Therefore, line MN is approximately 19.5.

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Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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There would be 40,320 different types of burgers.

If each burger must have all of the ingredients listed (cheese, lettuce, tomato, pickles, onions, mayo, catsup, and mustard), and the order of the ingredients is important, then the number of different types of burgers would be 8! (8 factorial), which is the number of permutations of 8 items.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

So there would be 40,320 different types of burgers that can be made with all of the ingredients and the order of placement is important.

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This question is based on the given solving an equation. Therefore, the value of n for (9n) (8n+8) is 0 and -1.

Given:

(9n) (8n+8)

We need to determined the value of n.

According to the question,

It is given that, expression (9n) (8n+8).

For finding the value of n, we would be equate the given expression is equal to zero.

⇒ (9n) (8n+8) = 0

Now, calculating the value of n. We get,

⇒ (9n) (8n)+(9n) (8)

Then, solving above expression further. We get,

⇒ \(\bold{72 n^2+ 72n = 0}\)

Now, taking common 72 n. We get,

⇒ 72n (n + 1) = 0

⇒ 72 n = 0 and (n+1) = 0

We get,

n = 0 , -1

Therefore, the value of n for (9n) (8n+8) is 0 and -1.

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Answer:

314 cm³

Step-by-step explanation:

Given ::

Cone height, h = 12 cm

Diameter of cone, d = 10 cm

Hence, radius, r = diameter / 2 = 10/2 = 5cm

The volume of a cone = 1/3 πr²h

V = 1/3 * 3.14 * 5² * 12

V = 3.14 * 25 * 4

V = 314cm³

Answer:

\((r^{2*3/3^1^* ^ 3)\)

Step-by-step explanation:

Given

\((r^2/3)^3\)

Required

Determine the equivalent expression

\((r^2/3)^3\)

Apply the following law of indices:

\((a^n)^m = a^m^n\)

\((r^2/3)^3\)

\((r^2/3^1)^3\)

So, the expression becomes:

\((r^{2*3/3^1^* ^ 3)\)

Option D answers the question.

The missing x coordinate is (24/25).

What is a Circle ?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

As per the given data:

p lies on the unit circle

radius of circle = 1 unit

p is in 4th quadrant:

Let's assume p as (x, (-7/25))

equation of the circle:

x² + y² = 1

x² + (-7/25)² = 1

x² = 1 - (49/625)

x² = (576/625)

x = ± 24/25

But as point is in 4th quadrant, x will be positive.

x = (24/25)

The coordinate of point p is ((24/25), (-7/25))

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

Option 2 is correct

Step-by-step explanation:

The graphs

The inequality the determines the value of t as number of tricks Roxanne might do during a competition is t≤ 28.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Several types of inequalities are represented by a variety of notations.

Given that, she has learned a total of 28 different tricks.

If we suppose t as number of tricks Roxanne might do during a competition.

Then the inequality the determines the value of t is t≤ 28 .

Hence, the inequality the determines the value of t is t≤ 28 .

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Answer:

x + 3y – 2z = 8

-x – 2y + z = 12

2x – 7y + z =7

this answer is fake

Step-by-step explanation:

x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1x + 3y – 2z = 3

-x – 2y + z = -2

2x – 7y + z = 1

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer: y=3x-6

Step-by-step explanation:

ANSWER:y=1/(3x-6)

Step-by-step explanation:

i think you are asking for the change of subject of formula(Transposition of subjects).

x=1/3y+2

multiply both sides by 3y

x × 3y=1/3y × 3y + 2 × 3y

3xy=1+6y

collect like terms

3xy-6y=1

fractionalize

y(3x-6)=1

divide both sides by (3x-6)

y=1/(3x-6)

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

x=1, 2, 3, 4, 5, 6

Step-by-step explanation:

Let's use logic. You can not have negative pizzas, and I assume you can not have decimals of pizzas.

That means that with the coupon you can only buy whole pizzas up to 6.

So the domain or x is1, 2, 3, 4, 5, 6