A student writes down the following piece of work which contains an error in their reasoning. The equation is: y 2
−23y=0 Add 23y to each side: y 2=23y Divide each side By y : y=23 (i) Substitute y=23 into the left-hand side of the equation y 2−23y=0, and explain why this shows that y=23 is indeed a solution of the equation. (ii) Write out a complete solution of the equationy 2−23y=0. (iii) Explain, as if directly to the student, why their solution is inadequate. Solve the following equation, checking that your solution is correct: 6−x16 = x+356
​

The diameter of the circle is AB and option b is the correct answer.

The diameter of a circle is the distance along which the circumference begins at one end and terminates at the other. Its length is double that of the circle's radius. In other words, the line that splits a circle into two equal pieces and runs through its centre is the diameter of the circle. Every straight line segment that traverses a circle's centre and has its endpoints on its circumference is said to have a diameter of that circle. The diameter is also referred to as the circle's longest chord.

We know that, the diameter of the circle is the longest segment that passes through the center of the circle.

From the given figure we observe that, the segment AB passes through the center and connects with the circle on either side.

Hence, the diameter of the circle is AB and option b is the correct answer.

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Answer:

AB

Step-by-step explanation:

The completed table that proves the congruence of the triangles are presented as follows;

Statement [tex]{}[/tex]                                                 Reasons

1. ∠BAC ≅ ∠EDC  [tex]{}[/tex]                                   1. Given

[tex]\overline{BC}[/tex] ≅ [tex]\overline{EC}[/tex]              [tex]{}[/tex]                              

2. ∠ACB ≅ ∠DCE     [tex]{}[/tex]                               2. Vertical angles theorem

3. ∠ABC ≅ ∠DEC [tex]{}[/tex]              [tex]{}[/tex]           [tex]{}[/tex]          3. Angle sum property of triangle

4. ΔABC ≅ ΔDEC [tex]{}[/tex]                                   4. ASA congruence rule

8. Statement [tex]{}[/tex]                                          Reasons

1. [tex]\overline{JK}[/tex] ≅ [tex]\overline{LM}[/tex]                                             1. Given

2. ∠JKM ≅ ∠LMK [tex]{}[/tex]                                   2. Given

3. [tex]\overline{MK}[/tex] ≅ [tex]\overline{KM}[/tex]    [tex]{}[/tex]                                     3. Reflexive property

4. ΔJMK ≅ ΔLKM [tex]{}[/tex]                                   4. SAS congruence rule

Triangles are congruent if they have the same size and shape.

The details of the reasons used to prove the congruence of the triangles are as follows;

Vertical angles theorem;

The vertical angles theorem states that the vertically opposite angles formed by two intersecting straight lines are always congruent.

Angle sum property of a triangle

The angle sum property of a triangle states that the sum of angles in a triangle is 180°.

Therefore, if two angles are known in a triangle, the third angle can be calculated as the difference between 180° and the sum of the two known angles.

ASA congruence rule

The ASA (which is an acronym for Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Reflexive property of congruence

The reflexive property states that a segment is congruent to itself

SAS congruence rule

The SAS (Side-Angle-Side) congruence rule states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

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The cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

We can use the fοrmula fοr the area οf a triangle, which is:

area = (base * height) / 2

We knοw that the base AB has a length οf 16 units, sο we can find the height by rearranging the fοrmula:

height = (2 * area) / base

height = (2 * 80) / 16

height = 10

Sο, pοint B is at (4, 0) and pοint C is at (x, y) where the height frοm A tο BC is 10 units and the length οf BC is 16 units.

We can use the Pythagοrean theοrem tο find the cοοrdinates οf pοint C:

[tex]x^2 + y^2 = BC^2[/tex]

[tex]x^2 + y^2 = 16^2[/tex]

[tex]x^2 + y^2 = 25[/tex]

Alsο, we knοw that the height frοm A tο BC is 10 units, sο the distance between pοint A and the line BC is 10 units. The slοpe οf the line BC is -y/x (rise οver run), sο the equatiοn οf the line BC is:

[tex]y = (-y/x) * (x - 4)[/tex]

[tex]y = (-y/x) * x + (y/x) * 4[/tex]

[tex]y + (y/x) * x = (y/x) * 4[/tex]

[tex]y(x/x + 1) = (y/x) * 4[/tex]

[tex]y + x = 4y/x[/tex]

[tex]x^2 + xy = 4y[/tex]

[tex]y = (x^2) / (4 - x)[/tex]

Nοw we can substitute this expressiοn fοr y intο the equatiοn[tex]x^2 + y^2 = 256:[/tex]

[tex]x^2 + ((x^2) / (4 - x))^2 = 256[/tex]

Sοlving this equatiοn gives twο pοssible values fοr x: x = 8 οr x = -4.

If x = 8, then y = 16/3, and if x = -4, then y = -16.

Therefοre, the cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

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Answer:

the answer is y=-2/3x+6

Answer:

The two teachers are approximately 4.1 meters apart.

Step-by-step explanation:

Let's use the following variables:

d = distance between the two teachers

Using the Pythagorean theorem:

d^2 = 4^2 + 1^2

d^2 = 16 + 1

d^2 = 17

d = sqrt(17)

d ≈ 4.1

Answer: 4.1

Step-by-step explanation:

[tex]\sqrt{1^2+4^2}[/tex]

evaluate the equation / expression

4.12311

round

4.12311 to the required place

4.1

[tex]110 = 16 + 10h[/tex]

[tex]110 - 16 = 10h[/tex]

She needs $110 for a concert ticket.

she already has $16 . She can earn the rest by working 10 hours at her job.

[tex]\bold{h = hourly \ rate}[/tex]

she needs to work 10 hours to add to the $16 she already has to get a total of $110 required for the concert ticket.

Therefore, Her hourly rate can be solved with the following equation

The measurements in order of size, starting with the smallest are: 2.3 mm, 24 mm, 2.3 cm, 21 cm, and  0.2 m.

Given the measurements in the question;

2.3 cm, 24 mm, 0.2 m, 21 cm, 2.3 mm​

To arrange the measurements in order of size, we need to convert them to a common unit of measurement.

We can convert all the measurements to meters, as it is the largest unit given.

Hence;

2.3 mm = 2.3 ÷ 1000 =  0.0023 m

24 mm = 24 ÷ 1000 = 0.024 m

21 cm = 21 ÷ 100 = 0.21 m

2.3 cm = 2.3 ÷ 100 =  0.023 m

0.2 m = 0.2 m

Now that all the measurements are in meters, we can compare them:

0.0023 m < 0.024 m < 0.023 m < 0.21 m < 0.2 m

Therefore, the measurements in order of size, starting with the smallest, are:

2.3 mm < 24 mm < 2.3 cm < 21 cm < 0.2 m

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Answer:

30mph

Step-by-step explanation:

We can use the concept of speed, distance, and time to solve the problem.

Let's assume that the bird was flying at a constant speed of "x" miles per minute.

When the bird passed the first building, Tim started the stopwatch. Let's say the time on the stopwatch was "t" minutes.

Therefore, the bird had flown a distance of "x*t" miles when Tim started the stopwatch.

In the next minute, the bird flew another 0.5 miles (the distance between the two buildings). So, the total distance traveled by the bird was:

x*t + 0.5 miles

We know that the total time elapsed was 1 minute. Therefore:

t + 1 = total time elapsed

Now, we can use these equations to solve for the speed of the bird:

x*t + 0.5 = distance traveled

t + 1 = total time elapsed

We want to find the value of x, so we can solve for t:

t = total time elapsed - 1

Substituting this value of t into the first equation, we get:

x*(total time elapsed - 1) + 0.5 = distance traveled

Simplifying, we get:

x*(total time elapsed) = distance traveled + 0.5

Substituting the given values, we get:

x*(1) = 0.5 + x*t

x = 0.5 + x*(total time elapsed - 1)

x = 0.5 + x*(59/60)

Solving for x, we get:

x = 30 miles per hour

Therefore, the bird was flying at a speed of 30 miles per hour.

The break-even point is 120 tickets, which is option A.

It is the income generated by a business, which includes all the money received from customers for the products or services sold, as well as any other sources of income. Revenue is calculated by multiplying the price of a product or service by the number of units sold. It is an important financial metric that helps businesses determine their profitability and growth potential.

Let's assume that x number of students are attending the party.

The cost for food per person is $15 and the revenue generated per person is $20, so the profit per person is $20 - $15 = $5.

The total cost of the party is $600 + $15x.

We need to find the number of tickets sold to cover the cost of the party, which is the break-even point.

So, we set the revenue generated equal to the cost of the party:

20x = 600 + 15x

5x = 600

x = 120

Therefore, the break-even point is 120 tickets, which is option A.

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The relationship is: number of dots = n + 1

The "number of dots" typically refers to the count or quantity of small, circular shapes that are arranged in a particular pattern or sequence. The term can be used in various contexts, such as in mathematical or geometric patterns, puzzles, games, or art.

Assuming you are referring to a specific pattern of dots that increases with each step, the equation to represent the relationship between the step number, n, and the number of dots at each step can be written as:

Number of dots = n + 1

In this equation, "n" represents the step number and "n + 1" represents the number of dots at each step. This equation assumes that the pattern starts with one dot at the first step, and the number of dots increases by one with each subsequent step.

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Step-by-step explanation:

To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.

y = 5x – 2 is already in slope-intercept form, so its slope is 5.

These two slopes are not equal, so the lines are not parallel.

B) x + y = 0 can be rearranged to y = −x, so its slope is −1.

y = x + 7 is already in slope-intercept form, so its slope is 1.

These two slopes are not equal, so the lines are not parallel.

C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.

4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.

These two slopes are not equal, so the lines are not parallel.

D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.

y = 2x + 2 is already in slope-intercept form, so its slope is 2.

These two slopes are not equal, so the lines are not parallel.

E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.

y = 3x − 10 is already in slope-intercept form, so its slope is 3.

These two slopes are equal, so the lines are parallel.

Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.

Answer: To find the rational roots of f(d) = 5d^3 - 6d^2 + d - 8, we can use the Rational Root Theorem, which states that any rational root of a polynomial equation must be of the form p/q, where p is a factor of the constant term (in this case, -8) and q is a factor of the leading coefficient (in this case, 5).

The factors of -8 are ±1, ±2, ±4, and ±8, and the factors of 5 are ±1 and ±5. Therefore, the possible rational roots of f(d) are:

±1/1, ±2/1, ±4/1, ±8/1, ±1/5, ±2/5, ±4/5, and ±8/5

We can try these values one by one to see if they are roots of f(d). For example, when we try d = 1, we get:

f(1) = 5(1)^3 - 6(1)^2 + 1 - 8 = 5 - 6 + 1 - 8 = -8

Since f(1) is not equal to zero, d = 1 is not a root of f(d). We can continue this process until we find all the rational roots of f(d).

Step-by-step explanation:

Answer:

We can use the formula for the area of a triangle to solve for the height of the isosceles triangle, which will then allow us to find the lengths of the other two sides.

Let h be the height of the isosceles triangle, and let s be the length of each of the two equal sides. Then the area of the triangle is given by:

A = (1/2)bh = (1/2)(10m)(h) = 5h

We also know that the area of the triangle is 60 square meters, so we can set these two expressions equal to each other and solve for h:

5h = 60

h = 12

Now that we know the height of the triangle is 12 meters, we can use the Pythagorean theorem to find the length of each of the other two sides:

s^2 = h^2 + (1/2b)^2

s^2 = 12^2 + (5^2)

s^2 = 169

s = sqrt(169)

s = 13

Therefore, the lengths of the other two sides of the isosceles triangle are both 13 meters.

The probability that the second person chosen will also be a boy is roughly 0.872, or 87.2%.

Since the first person chosen is a boy, there are now 12 boys and 15 girls left in the class. We want to find the probability that the second person chosen is also a boy.

The probability of choosing a boy for the first selection is 13/28. Then, for the second selection, there are now 12 boys and 27 students left, so the probability of choosing a boy is 12/27.

Using conditional probability, we can calculate the probability that the second person chosen is also a boy given that the first person chosen is a boy:

P(Second person is a boy | First person is a boy) = P(Both are boys) / P(First person is a boy)

P(Second person is a boy | First person is a boy) = (12/27) / (13/28)

P(Second person is a boy | First person is a boy) ≈ 0.872

Therefore, the probability that the second person chosen is also a boy given that the first person chosen is a boy is approximately 0.872 or 87.2%.

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Answer:

Step-by-step explanation:

Angle p is supplementary to the angle that measures 127 because they are same side interior. So angle p measures 180 - 127 = 53 degrees. Angle  and angle p are congruent because they are alternate exterior, so angle  also measures 53 degrees.

the answer is 53° for both p and r

The statement "rotated an angle whose measure is more than halfway around a circle" is incorrect. An angle whose measure is 60 degree is rotated more than halfway around a circle.

A rotated angle is an angle that has been moved or transformed from its original position, while an angle that measures more than halfway around a circle is called a reflex angle. A reflex angle measures between 180 and 360 degrees, which means that it has rotated more than halfway around a circle.

In contrast, an angle that measures less than 180 degrees is called an acute angle, while an angle that measures exactly 180 degrees is called a straight angle. Understanding the different types of angles is important in geometry and mathematics.

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Answer:

-3

Step-by-step explanation:

Answer:0.27 miles

Step-by-step explanation:

Answer:

The answer to your question is 7040

Step-by-step explanation:

How many yards are in 1 mile:

So 1 mile = 1760 yards

Speed = 1760 yard per minute

= 1760 yd/min

Since we have 4 miles, we are gonna multiply 4 multiplied by 1760.

So 4 miles x 1760 = 7040

I hope this helps and have a wonderful day!

Answer:

20 cm = 0.2 m

10 cm = 0.1 m

5 cm = 0.05 m

1 km = 1000 m

5 m = 5 m

50 cm = 0.5 m

The volume of each brick is:

V_brick = 0.2 m x 0.1 m x 0.05 m = 0.001 m^3

The volume of the wall is:

V_wall = 1000 m x 5 m x 0.5 m = 2500 m^3

The number of bricks required is:

N_bricks = V_wall / V_brick = 2500 m^3 / 0.001 m^3 = 2,500,000

Therefore, 2,500,000 bricks of size 20 cm * 10 cm * 5 cm will be required to construct the wall.

An exponential change exceeding plus or minus 1 there in amount of a quantity or unit is defined as an order of magnitude. The phrase is typically used in connection with scientific notation with powers of 10.

The usage of orders of magnitude helps people understand and have a better grasp on the size of numbers and some other quantities. It typically serves as an approximation of a comparison between two numbers.

How to Estimate an Order of Magnitude?

The Sun's circumference, for instance, would be stated as being multiple orders of magnitude greater than just the Earth's if the two were compared to one another.

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jrjejrjŕjwjskskskskskskksksksksksksks

The table that follows the rule that she saves twice as much as she save the day before is illustrated below.

Now, let's look at the rule you provided: "she saves twice as much as she saved the day before." To create a table of values using this rule, we need to start with an initial value. Let's say that on the first day, she saves $1. We can use this value as our starting point.

Using the rule, we can then determine how much she saves on the second day. Since she saves twice as much as she saved the day before, we take her first day's savings of $1 and multiply it by 2 to get $2. So, on the second day, she saves $2.

We can continue this process to fill out the table of values. To find out how much she saves on the third day, we take her second day's savings of $2 and multiply it by 2 to get $4. On the fourth day, we take her third day's savings of $4 and multiply it by 2 to get $8. And so on.

We can organize this information into a table, with the days listed in the left-hand column and the corresponding savings amounts listed in the right-hand column:

Day Savings

1 $1

2 $2

3 $4

4 $8

5 $16

6 $32

7 $64

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Answer:

e = - 10

Step-by-step explanation:

4e - 6e - 5 = 15

- 2e - 5 = 15 ( add 5 to both sides )

- 2e = 20 ( divide both sides by - 2 )

e = - 10

Answer: e = -10

Step-by-step explanation:

4e-6e-5=15

-2e-5=15

add 5 on both sides

-2e=20

divide 20 on both sides

e=-10

The rent of the apartment during the 9th year of living in the apartment would be approximately $3,510.45 per month.

If the rent starts at $1600 per month and increases by 9.5% each year, then we can use the formula for compound interest to calculate the rent after 9 years.

The formula for compound interest is:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the initial principal (the starting amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, P = $1600, r = 9.5% = 0.095, n = 1 (compounded once per year), and t = 9. We want to find A, the rent after 9 years.

A = 1600(1 + 0.095/1)^(1×9)

A = 1600(1.095)^9

A ≈ $3,510.45

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Answer:

Step-by-step explanation:

In a right-angled triangle, the tangent ratio of an acute angle = the ratio of the length of the opposite side to the length of the adjacent side.

Lets say angle A= 150 degrees (obtuse)

So, the tangent ratio of angle B= the ratio of the length of the opposite side to the length of the adjacent side.

So far we have:

and because angle A is obtuse, its tangent ratio is the negative of the tangent ratio of its corresponding acute angle.

Step-by-step explanation:

first of all

tan(x) = sin(x)/cos(x)

that is the tangent ratio.

so, the question is also, what happens to sine and cosine for obtuse angles.

remember the trigonometric triangle inside the circle.

sine is the up/down leg (up = positive, down = negative), cosine is the left/right leg (and extension of the leg; of left from the center = negative, if right from the center = positive).

so, for an obtuse angle (90° < angle <= 180°) sine is still up and therefore positive, but cosine is left from the center and therefore negative.

for that reason tan(angle) = sin(angle)/cos(angle) is negative.

in fact, it is -tan(180 - angle).

Answer:

a < -7

Step-by-step explanation:

18 - a > 25

-a > 7

*divide by -1 and flip sign*

a < -7

:) hope i explained it

Answer: 18-a>25

We can solve the inequality for 'a' by isolating it on one side of the inequality symbol (>).

Starting with:

18 - a > 25

Subtracting 18 from both sides:

a > 7

Dividing by -1 (which changes the direction of the inequality):

a < -7

So the solution to the inequality is a value less than -7.

The *girl* above me did a great job :D

The dilation has a scale factor of 0.075 and the coordinates of point F" are (0.9, 0.375).

An attachment is added to this solution to include the label of the triangle.

According to the given information, the length DE is equal to 12 units.

Additionally, the length of D"E" is 0.9 units.

Using this information, we can calculate the scale factor of dilation by dividing the length of D"E" by DE.

i.e. 0.9/12 = 0.075

Thus, the scale factor is 0.075.

The solution can be expressed as follows:

We compute F by multiplying the scale factor with F.

By substituting the values, we get

F" = 0.075 * (12, 5)

F" = (0.9, 0.375)

So, the coordinates of F" are (0.9, 0.375)

To find the values of sine, cosine, and tangent, we use the following formulas:

Using these formulas and the given values, we find that:

sin(D") = 0.375/1 = 0.375

cos(D") = 0.9/1 = 0.9

tan(D") = 0.375/0.9 = 0.416

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The estimated life expectancy for someone born in 2005 is approximately 85.09 years.

Life expectancy is the average number of years that a person is expected to live, based on statistical data and various demographic factors such as age, gender, health status, lifestyle, and environmental conditions. It is usually calculated from birth and is a useful indicator of the overall health and well-being of a population.

Life expectancy can vary widely between different countries and regions, as well as between different demographic groups within a population. Factors that can influence life expectancy include access to healthcare, nutrition, education, economic development, social support, and public health policies.

To estimate the life expectancy for someone born in 2005, we need to use the line of best fit equation:

y = 0.40x - 716.91

where x is the birth year and y is the corresponding life expectancy.

To find the estimated life expectancy for someone born in 2005, we substitute x = 2005 into the equation:

y = 0.40(2005) - 716.91

y = 802 - 716.91

y = 85.09

Therefore, the estimated life expectancy for someone born in 2005 is approximately 85.09 years.

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