What method of solving quadratic equations must be used in order to derive the quadratic formula?.

The axis of symmetry line passes through the vertex of the parabola.

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The equation for the remaining work is given by the equation  25 - (x+y)

let x be the number of pizza made by Mario and y be the number of pizza made by luigi

let z be the pizza that still need to be made

so x+y+z=25

=> z = 25 - ( x + y )

so the total remaining pizza is given by 25 - (x+y) ---(i)

given that Mario had made 11 pizza so x = 11

and Luigi had made 3 pizza so  y = 3

so total remaining work is found using equation (i)

so z = 25 - ( 11 + 3)

=> 11

so remaining work is 11

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The pair of linear equations does not have a solution when K is equal to 2.

We can solve this system of linear equations by using the process of elimination. This involves rearranging the equations to isolate one variable and then using that information to determine the values of the other variables.

The first equation should be multiplied by (k-1) and the second equation by 3.

3(3x+y)=3

(2k-1)(3x + y)=(2k-1)2k+1

Add the two equations

3(3x+y)+(2k-1)(3x+y)=(2k-1)2k+1 + 3

Simplify the equation

5kx+ (3+2k-1)y = (2k-1)2k+1 + 3

Further simplify the equation

5kx + (2k+2)y = (2k-1)2k+1 + 3

Rearrange the equation

5kx - (2k+2)y = (2k-1)2k+1 + 3 - (2k+2)

Simplify the equation

5kx - (2k+2)y = (2k-1)2k+1 -2

With the LHS set to 0 and the RHS set to a non-zero number, we can determine the value of k for which the equations cannot be solved.

5kx - (2k+2)y = 0

(2k-1)2k+1 -2 ≠ 0

Solve for k

5k = 2k +2

3k = 2

k=2

Therefore, K=2 is the value of k for which there is no solution to the pair of linear equations.

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No there is not enough information

Answer: It grew by 13,640 people

Step-by-step explanation:

First, turn 6.2% into 0.062.

Next, multiply 0.062x220,000.

You get 13,640.

The rest of the information is unnecessary.

The ratio of e:f from 2 different squares are 1.2:1.

From the case, we have 2 squares that:

Square E side = e

Square F side = f

Area of E = (1 + 44%) Area of F

Using the area of square formula, we know that:

Area of square = side x side

Area of square = side²

Area of E = e x e

Area of E = e²

Area of F = f x f

Area of F = f²

We will compare the area of both squares:

Area of E = (1 + 44%)Area of F

e² = (1 + 44%) f²

e² = 1.44 f²

√e² = √(1.44 f²)

e = 1.2 f

Hence the ratio of e : f would be:

e : f = 1.2f : f

e : f = 1.2 : 1

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Answer:

To find the speed of the boat in still water, we can use the formula:

Speed in still water = (Downstream speed + Upstream speed) / 2

We know that the speed of the current is 1.5 km/h and the boat can travel twice the distance downstream as it can travel upstream. Therefore, if the boat travels x km downstream in one hour, it travels x/2 km upstream in one hour.

We can use this information to set up the following equation:

x + (x/2) = (x + x/2) = (3/2)x = Downstream speed

And the upstream speed is x/2

Now we can substitute this value into the formula for speed in still water:

Speed in still water = ( (3/2)x + (x/2) )/2 = (3x + x)/4 = x = (3+1) km/h = 4 km/h

So, the speed of the boat in stillwater is 4 km/h.

We don't know the exact distance that the boat travels downstream in one hour, so we can't calculate the speed in still water with the given information. To find the speed in still water we need to know the distance traveled downstream or upstream.

To solve the expression 9 - 12 + 6/-3 + 3(-3) first do the operation of division, i.e. option B: 6/-3.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - 9 - 12 + 6/-3 + 3(-3)

Follow the BODMAS rule to solve the expression.

BODMAS = Bracket Of Division Multiplication Addition and Subtraction

The first step is to solve the bracket -

= 9 - 12 + 6/-3 + 3(-3)

= 9 - 12 + 6/-3 - 9

The next step is to solve the division -

= 9 - 12 + 6/-3 - 9

= 9 - 12 -2 - 9

The next step is to solve the addition and subtraction -

= 9 - 12 - 2 - 9

= 9 - 23

= -14

Therefore, the value of the expression is obtained as -14.

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Answer:

j = 46

Step-by-step explanation:

16j = 736

----    -----

16      16

j = 46

Answer:

j = 46

I did 736 divided by 16 to find the answer.

Answer:

5

Step-by-step explanation:

I assume the ratio is 1:3.

We need a total of 20 candies, and we need the number of sweet candy to be 3 times the number of sour candy.

Start guessing the number of sour candy with 1. Then find the number of sweet candy. Then find the sum. Keep going up with the guess until it works.

Sour      Sweet        Sum      Comment

1              3                4           too low

2             6                8           too low

3             9                12           too low

4             12               16          too low

5             15               20         exactly right

Answer: 5

Answer:

b

Step-by-step explanation:

If the graph doesn't go through the origin (0,0), the relationship is not a proportional one.

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Answer:

B) Sample. There are too many to count.

Step-by-step explanation:

You can only check a portion of all the fish. It would take too much work and manpower to check every single fish.

the answer should be B. 65cm

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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Contrapositive is an example for indirect proof.

Indirect proof;

When the conclusion from a hypothesis is taken to be false (or the opposite of what it states), indirect proof or proof by contradiction is achieved from the given or deduced statements.

Contrapositive method of proof;

Proof by contrapositive, also known as proof by contraposition, is an inference rule used in proofs in mathematics where a conditional statement is inferred from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."

Proof by Contrapositive method is indirect.

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Proof by contrapositive is an indirect method of proof where we assume the negation of the conclusion and show that it leads to the negation of the hypothesis. It is a powerful tool in mathematical reasoning and can be used to prove various statements and theorems.

In mathematics, a direct proof is a method of proving a statement by providing a logical sequence of steps that directly leads from the given information to the desired conclusion. On the other hand, an indirect proof is a method of proving a statement by assuming the opposite of the desired conclusion and deriving a contradiction or an absurdity.

To prove a statement using the contrapositive, we start by assuming the negation of the conclusion. Then, we proceed to show that if the negation of the conclusion is true, then the negation of the hypothesis must also be true. In other words, we prove the contrapositive of the statement.

Here is an example to illustrate proof by contrapositive:

Statement: If a number is even, then its square is also even.

To prove this statement by contrapositive, we assume the negation of the conclusion: If a number's square is odd, then the number itself is odd.

We then proceed to show that if the negation of the conclusion is true, then the negation of the hypothesis is also true. In this case, if the square of a number is odd, then the number itself must be odd.

We can prove this by considering that any even number squared will always result in an even number. Therefore, the contrapositive of the original statement is true, which implies that the original statement is true as well.

In conclusion, proof by contrapositive is an indirect method of proof where we assume the negation of the conclusion and show that it leads to the negation of the hypothesis. It is a powerful tool in mathematical reasoning and can be used to prove various statements and theorems.

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Equivalent 1/4 is equals to 4/16 in fractions.

Equivalent fractions in mathematics are ones that have the same denominator but different numerators. For instance, 2/4 and 3/6 are equivalent fractions since they both equal 1. A fraction is a piece of the total. Equivalent fractions are used to indicate identical parts of the whole.

The equivalent fraction of each fraction can be calculated by multiplying the numerator and denominator by the same integer. Equivalent fractions are ones that denote the same value despite visual disparities. You will have devoured half of a cake, for example, if you take a piece, cut it into two equal pieces, and then eat one of them.

= 1/4 is equivalent to:

= 1/4 * 4/4

= 4/16

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Correct Question:

What is 1/4 equivalent to in fractions?.

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant when the light is traveling from a denser medium to a rarer medium and the angle of incidence is greater than the critical angle.

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant under the condition of total internal reflection.

This constant is known as the refractive index of the medium in which the light is traveling. When a beam of light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is known as the refractive index of the second medium with respect to the first medium.

Total internal reflection occurs when a beam of light passes from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence exceeds the critical angle. Under this condition, the light is reflected back into the original medium, instead of passing into the second medium.

In short, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant when the light is traveling from a denser medium to a less dense medium and the angle of incidence is greater than the critical angle.

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Answer: Disagree.

Step-by-step explanation:

Dividend = 36

Divisor = 13

36 (Dividend) ÷ 13 (Divisor) = 2 (Quotient)

Remainder = 10

Rules of division indicate,

Quotient < Dividend

Here too, 2 < 36

Thus, the answer to 36÷13 does NOT represent a number greater than 36.

The total number of minutes Carter played the basketball game is 25 minutes.

The correct answer choice is option C.

Total minutes of the basketball game= 40 minutes

Minutes Carter played= 5/8 of Total minutes of the basketball game

= 5/8 × 40

= 0.625 × 40

= 25 minutes

Hence, Carter played the basketball game for 25 minutes.

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The side length SV= 13 units

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

In a parallelogram, opposite sides are congruent.

ST=VU

=> 19=4x-1

=> 4x=19+1 = 20

=> x= 20/4 = 5

SV=2x+3

=>  SV=2(5)+3 = 10+3 = 13

The side length SV= 13 units

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Answer: It would look like this, and your equation is y = 0.5x + 0 or just y = 0.5x, you are supposed to connect the dots, as it is a linear equation with a continuous run

Step-by-step explanation:

I hope this helps!

To solve nth problems we use the formula stated as  aₙ = a + (n – 1)d.

A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A formula for the nth term of the AP could be derived from this kind of progression. Because it follows a pattern where each number is acquired by adding 4 to the preceding term, the sequence 2, 6, 10, 14,... is an example of an arithmetic progression (AP). In this series, the nth term equals 4n-2. By changing the nth term to n=1,2,3,..., the sequence's terms can be obtained. i.e.,

First term when n = 1 is 4n-2 = 4. (1)

-2 = 4-2=2

second term = 4n-2 = 4 when n = 2 (2)

-2 = 8-2=6

The third term is 4n-2 = 4 for n = 3. (3)

-2 = 12-2=10

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The slope of the line perpendicular to the line y = ( -1/4 )x - 1 is m₂ = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( -1/4 )x - 1   be equation (1)

The slope of the line is m₁ = ( -1/4 )

Now , the product of the slopes of perpendicular lines is -1

So , m₁ x m₂ = -1

Substituting the values in the equation , we get

( -1/4 ) x m₂ = -1

m₂ = 4

So , the slope of the line perpendicular to the line A is m₂ = 4

Hence , the slope of the line is m₂ = 4

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A basic log graph is a line graph that plots logarithmic data points plotted on a logarithmic scale.

The x-axis of the graph is the logarithmic scale, and the y-axis is the data points.

The points are plotted in a straight line, making it easy to see how the data points change as the logarithmic scale increases or decreases.

On the exponential f, identify several locations (x). The graph will look better the more points we plot.

A  two-dimensional graph of numerical data using logarithmic scales on both the horizontal and vertical axes is known as a log-log graph or log-log plot.

In order to obtain points on the inverse, swap the x and y variables. Discover the asymptote. The ensuing logarithmic functions should be plotted. the domain and the range.

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According to the presented question, m∢PSQ = 3y - 15 and m∢PRQ = 2y + 15, then m∢PSQ equals 97.

Supplementary angles are a pair of angles that always sum to 180 degrees. These two viewpoints are referred to as complements to one another. The English word "supplementary" is derived from the Latin words "Supplere" and "Plere," which respectively mean "supply" and "fill." As a result, the term "supplementary" designates something that is added to complete a task.

In this lesson, we will study about supplementary angles and how they can be applied to various geometry problems. As we explore supplementary angles, we'll discover how they differ from complimentary angles.

We know that the measure of an angle is supplementary to its adjacent angle. That means that the measure of an angle and its adjacent angle add up to 180 degrees.

Given that m∢PSQ = 3y - 15 and m∢PRQ = 2y + 15, we can set up the equation:

m∢PSQ + m∢PRQ = 180

Plug in the values for the angles:

(3y - 15) + (2y + 15) = 180

Simplifying, we get:

5y = 180

Now we can find the value of y by dividing both sides by 5:

y = 36

Therefore, m∢PSQ = 3y - 15 = 3(36) - 15 = 97

So, the measure of angle PSQ is 97 degrees.

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According to the presented question, m∢PSQ = 3y - 15 and m∢PRQ = 2y + 15, then the measure of angle PSQ equals 97.

Supplementary angles are a pair of angles that always sum to 180 degrees. These two viewpoints are referred to as complements of one another. The English word "supplementary" is derived from the Latin words "Supplere" and "Plere," which respectively mean "supply" and "fill." As a result, the term "supplementary" designates something that is added to complete a task.

In this lesson, we will study about supplementary angles and how they can be applied to various geometry problems. As we explore supplementary angles, we'll discover how they differ from complementary angles.

We know that the measure of an angle is supplementary to its adjacent angle. That means that the measure of an angle and its adjacent angle add up to 180 degrees.

Given that m∢PSQ = 3y - 15 and m∢PRQ = 2y + 15, we can set up the equation:

m∢PSQ + m∢PRQ = 180

Plug in the values for the angles:

(3y - 15) + (2y + 15) = 180

Simplifying, we get:

5y = 180

Now we can find the value of y by dividing both sides by 5:

y = 36

Therefore, m∢PSQ = 3y - 15 = 3(36) - 15 = 97

So, the measure of angle PSQ is 97 degrees.

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Answer:

Step-by-step explanation:

To find out how much of the 100 foot roll of fencing Martin will need to enclose the garden, you need to calculate the perimeter of the rectangular garden.

The perimeter is the total distance around the garden. To find the perimeter, you add up the lengths of all four sides of the rectangle.

The formula for the perimeter of a rectangle is: P = 2L + 2W

Where P is the perimeter, L is the length, and W is the width.

In this case:

P = 2 x 10 feet + 2 x 100 feet = 20 feet + 200 feet = 220 feet

Martin will need 220 feet of fencing to enclose his rectangular garden.

If the radius of the base of the cone is 2 inches the height of the cone should be 2.1485 inches.

The volume of the cone is the capacity occupied by this. It is given by the formula,

The volume of the cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

r is the radius of the base, and h is the height of a cone.

Now, it is stated that cones hold 9 cubic inches of popcorn. Hence, the volume of a cone can be noted as,

The volume of the cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

[tex]9 * 3 = \pi r^{2} h[/tex]

[tex]\frac{9 *3}{\pi } = r^{2}h[/tex]

[tex]r^{2}h = 8.5943[/tex]

Now, let the radius of the cone be 2 inches, hence, the height of the cone is,

[tex]8.5943 = r^{2}h[/tex]

[tex]8.5943 = 2^{2}h[/tex]

h = 2.1485 in

Hence, if the radius of the base of the cone is 2 inches the height of the cone should be 2.1485 inches.

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The complete question is:

Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 9 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?

Answer:

56

Step-by-step explanation:

Take 70 and multiply 80%

70 × 80/100 = 56

Answer:

Yes, an acute angle is an angle that measures less than 90 degrees.

Step-by-step explanation: