Solve these simultaneous equations and explain how you worked your answer out
а) x+y=24
y=2x

b)2x+y=100
y=2(x-10)

c)x+y=26
3x+y=56

Answer:

a. 12 sides

b. Not possible

Step-by-step explanation:

a.

[tex]d=\frac{1}{2} n(n-3)[/tex]

[tex]\frac{1}{2}n^{2}-\frac{3}{2} n=54[/tex]

multiply by 2

[tex]n^{2} -3n=108[/tex]

equation

[tex]n^{2} -3n-108=0[/tex]

factor

[tex](n-12)(n+9)[/tex]

[tex]n-12=0\\n=12[/tex]

b.

[tex]n^{2} -3n=33[/tex]

[tex]n^{2} -3n-33=0[/tex]

The roots of the equation are decimal numbers

The number of sides must be integer

So there is no polygon with 33 diagonals.

Hope this helps

The correct statement is 3000 ml<4l

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Option 3 as 3000 ml<4 liters

we know that 1 liter=1000 ml

Thus 4 liters=4000 ml

Hence, Option C is the correct statement.

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An inequality in standard form that describes this situation is 25x + 59y ≤ 495.

In order to write an inequality that represents or describes this situation, we would assign variables to the number of nails required by the small birdhouse and large birdhouse respectively, and then translate the word problem into algebraic equation as follows:

Since Tanner has a total of 495 nails on hand and a small birdhouse requires 25 nails while a large birdhouse requires 59 nails, an inequality that represents or describes this situation can be written as follows;

25x + 59y ≤ 495.

In conclusion, we can reasonably infer and logically deduce that the total number of nails required by both the small birdhouse and large birdhouse is less than or equal to 495 nails.

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Answer:

To solve this problem, we can set up a system of equations using the information given. Let x be the number of quarters, y be the number of dimes, and z be the number of nickles.

From the problem, we know that:

x:y = 8:5 (the ratio of the number of quarters to the number of dimes)

y:z = 6:11 (the ratio of the number of dimes to the number of nickles)

x+y+z = between 500 and 600 (the total number of coins)

We can start by using the first ratio to find the value of y in terms of x:

x:y = 8:5

y = (5/8)x

We can use the second ratio to find the value of z in terms of y:

y:z = 6:11

z = (11/6)y

We can substitute the value of y into the expression for z to get an expression for z in terms of x:

z = (11/6)(5/8)x

Now we can use the equation x + y + z = between 500 and 600 to find the value of x:

x + (5/8)x + (11/6)(5/8)x = between 500 and 600

Combining like terms:

(63/40)x = between 500 and 600

x = between 800 and 1000

So, x represents the number of quarters, which is between 800 and 1000.

We know that the value of a quarter is $0.25. So the total value of the quarters is between $200 and $250.

Similarly, we know that the value of a dime is $0.1 and a nickel is $0.05.

so,

y = (5/8)x

z = (11/6)(5/8)x

y = (5/8)x * $0.1 = $0.125x

z = (11/6)(5/8)x * $0.05 = $0.04166x

So, the total value of the money in the jar is $200 <= $0.25x + $0.125x + $0.04166x <= $250

Answer:

(4,2)

Step-by-step explanation:

the solution to the system of equations is the point where the 2 lines intersect:  (4,2)

Answer:

The two spaceships will meet in 4 hours.

Step-by-step explanation:

We can start solving the problem using the formula for distance, velocity, and time which is

Distance = Velocity x Time

Let x be the number of hours it will take for the two spaceships to meet.

The distance that the first spaceship travels is 110,000 x x km

The distance that the second spaceship travels is 90,000 x (x+1) km, since the second spaceship started 1 hour later.

The total distance that the spaceships travel is equal to the distance between the space stations, so we can set up the equation:

110,000x + 90,000(x+1) = 710,000

Solving for x, we can find that x = 4 hours.

So the two spaceships will meet in 4 hours.

Answer: The answer is B

Step-by-step explanation:

4( the tip) +5 (# of family) * x( unknown cost of hot dog) = 29 (total)

Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.

A 3x3 matrix is a system of three equations with three unknowns.

For a system of linear equations to have a unique solution, the determinant of the matrix must not be zero. If the determinant of the matrix is zero, then the system of equations has an infinite number of solutions.

Therefore, a 3x3 matrix can have infinite solutions if the determinant of the matrix is zero.

Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.

Nikki has to travel a total of 351 miles, and she travels the first 216 miles in 4 hours. The second part of her trip is the remainder of the distance she needs to travel, so we can calculate it by subtracting the distance she traveled in the first part from the total distance:

Second part of the trip = 351 miles - 216 miles = 135 miles

It takes Nikki 2.5 hours to travel the second part of her trip. To calculate her speed, we can divide the distance she traveled by the time it took her:

Speed = Distance / Time

Speed for the second part of the trip = 135 miles / 2.5 hours = 54 miles/hour

To compare her speed during the first and second parts of the trip, we can calculate the speed of Nikki during the first part of the trip:

Speed for the first part of the trip = 216 miles / 4 hours = 54 miles/hour

Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.

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D) In my opinion Answer is D because 0.01 is the maximum safe value for some naturally occurring human consumption. So, value cannot be maximize for the significance and alpha.

Null Hypothesis:

The null hypothesis (often called H0) is the assertion that there is no difference or relationship between the two data sets or variables being analyzed. The null hypothesis states that all experimentally observed differences are due to chance and that there is no underlying causal relationship, hence the term "null". In addition to the null hypothesis, alternative hypotheses are also developed. This claims that there is an association between the two variables.

Alternative Hypothesis:

In statistical hypothesis testing, the alternative hypothesis is one of the statements proposed in the hypothesis test. In general, the purpose of hypothesis testing is to show that, given the conditions, there is sufficient evidence to support the reliability of the alternative hypothesis rather than the sole assertion in the test (the null hypothesis). They are usually consistent with research hypotheses, as they are generated from literature reviews, previous studies, etc. However, in some cases the research hypothesis is consistent with the null hypothesis. In statistics, the alternative hypothesis is often denoted by Ha or H1. Hypotheses are formulated to compare them in statistical hypothesis testing. In the field of inferential statistics, two competing hypotheses can be compared for their explanatory and predictive power.

According to The Question:

H subscript o : mu less or equal than 0.01

H subscript alpha : mu greater than 0.01

From the given statement we think we should have to maximize the power of test because maximize the significance alpha is not true because alphas value is given according to the table that is mentioned.

Complete Option:

A. maximize the power of the test

B. maximize beta

C. minimize mu

D. maximize the significance, alpha

E. maximize 1 minus alpha

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Answer:

Chebyshev's Theorem states that for any dataset with a mean and standard deviation, at least 1 - (1/k^2) of the data will lie within k standard deviations of the mean.

In this case, we're looking for households that have between 0 and 4 televisions, which is 4 - 0 = 4 - 2 = 2 standard deviations from the mean of 2 televisions.

So, using Chebyshev's Theorem, we can calculate that at least 1 - (1/2^2) = 1 - (1/4) = 3/4 or 75% of the households have between 0 and 4 televisions.

At least 75% of the households have between 0 and 4 televisions.

Yes, it is possible to draw a right angled triangle with sides 1.5cm , 2cm , and 2.5cm.

As given in the question,

In the given triangle,

Measure of the side length of the given triangle are :

1.5cm , 2cm , and 2.5cm

In this triangle longest side is equal to 2.5cm.

Given triangle is right angled triangle check whether Pythagoras theorem satisfied the measure of the sides of the triangle.

Hypotenuse represents the longest side.

( Hypotenuse)² = ( Side 1 )² + ( Side 2)²

Right hand side

= ( 1.5 )² + ( 2 )²

= 2.25 + 4

= 6.25

= ( 2.5 )²

= Hypotenuse²

It satisfied the Pythagoras theorem.

Therefore, the given sides of the triangle represents it is a right angled triangle.

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The largest possible solution is x + y =w = 4

Now, According to the question:

Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of the cubes is 10.

Now, One way to solve this problem is by substitution. We have

[tex]x^{2} +y^2 = (x+y)^2+2xy=7[/tex]

and,

[tex]x^3+y^3=(x+y)(x^2-xy+y^2)=(7-xy)(x +y)=10[/tex]

Hence observe that we can write :

x +y = w and xy = z

This reduces the equations to [tex]w^2-2z =7[/tex] and w(7 - z) =10

Because we want the largest possible w, let's find an expression for z in terms of w.

[tex]w^2-7 =2z[/tex] => [tex]z = \frac{w^2-7}{2}[/tex]

Substituting, [tex]w^3-21w+20=0[/tex]

which factorizes as (w-1) (w+5) (w-4) = 0

Hence, The largest possible solution is x + y =w = 4

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The area of the trapezoid is 210  squared '

The area of a trapezoid be be calculated using the formula:

A = 1/2(a+b)h

where:

a is the length of one of the parallel sides of the trapezoid

b is the length of the other parallel side of the trapezoid

h is height is the distance between the two parallel sides (perpendicular to the bases)

a = 12', b = 18 + 5 = 23' and h = √(13²-5²) = 12'

A = 1/2(a+b)h

A = 1/2(12+23)12

A = (35)6

A = 210  squared '

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Answer:

(x + 8)^2 + (y - 3)^2 = 64

Step-by-step explanation:

The equation of a circle with a center of (-8,3) and radius of 8 is:

(x + 8)^2 + (y - 3)^2 = 64

You can see that the center of the circle is represented by the point (-8,3) in the equation, and the radius is represented by the value on the right side of the equation (64) which is derived from 8^2

Pat left the office at 10:50 am.

What is the relation between speed, distance, and time?

The relation between speed, distance, and time would be

distance = speed x time

We know that Pat had a 12:30 pm appointment 72 miles from his office, arrived ten minutes late, and averaged 48 mph for the trip. So we can set up the equation as:

distance = speed x time

72 = 48 x time

To solve for time, we divide both sides of the equation by 48:

time = distance / speed

time = 72 / 48

time = 1.5 hours

Since Pat arrived 10 minutes late, we need to subtract that 10 minutes from the time it took him to get to the appointment

12:30pm - 00:10 = 12:20 pm

Now, we have to subtract the time it took Pat to get to the appointment from the time he left the office

12:20 pm - 1.5 hours = 10:50 am

So Pat left the office at 10:50 am.

Hence, Pat left the office at 10:50 am.

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The value of c can be found by solving the equation yc^2 = -x^2 + 5x.

Square is a two-dimensional shape with four equal sides and four equal angles of 90 degrees each. It is a regular polygon and is one of the most common shapes in mathematics. Squares can be found in nature, architecture, and art. They are used to divide and organize space, and are often used as a form of measurement in areas such as geometry, construction, and engineering.

After rearranging the equation, we can solve for c by using the quadratic formula. c = (x^2 - 5x)/(x^2). Therefore, the value of c is (x^2 - 5x)/(x^2).

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According to the vector rule, the values of the 2u, -3v, u + v, and 3u + 4v are (-4, 18), (-18, 6), (4, 7) and (18, 19) respectively.

Here we have given the following two vector such as

u = (-2, 9)

v = (6, -2)

Then as per the following vector rule, t

=> ku = (ka , kb)

where k refers the constant in vector.

Then the value of 2u is calculated as,

=> 2u = ((-2 x 2), (9 x 2)) = (-4, 18)

And the value of -3v is calculated as ,

=> -3v = ((-3 x 6), (-3 x- 2)) = (-18, 6)

Here we have to use the following rule, that is written as,

=>  (u ± v) = (a ± c, b ± d)

Then the value of u + v is calculated as,

=> (u + v) = ((-2 + 6),  (9 + (-2)) = (4, 7)

Then the value of 3u + 4v is calculated as,

=> 3u = ((3 x -2), (3 x 9)) = (-6, 27)

And the value of

=> 4v = ((4 x 6), (4 x- 2)) = (24, -8)

Then the value of

=> 3u + 4v = (-6, 27) + (24, -8)

=>  3u + 4v = ((-6+24) , (27 + (-8))

Therefore, the resulting value is (18, 19).

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The number of cards sold by Samantha on mother's day is 70.

Total number of cards sold on mother's day = 700

Percentage of cards Samantha sold = 10 %

Fraction of cards Samantha sold  = 700 × 10/100

                                                        = 70

The number of cards Samantha did not sold, or sold by other salesman = Total cards sold - number of cards Samantha sold

                           700 - 70 = 630

Or else we can calculate by using percentages.

Percentage of the cards sold by other salespersons = 100- 10

                                                                                         = 90

90 % of 700 = 90/100 × 700

                     = 630

We can also use proportions.

    10 : 90 :: 70 : x

    10/90 = 70/x

          x = (70× 90)/ 10

              = 630.

So the number of cards Samantha sold = 70

     Number of cards others sold = 630

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If the value of 'a' changed from -a  to +a , the equation of the directrix of the parabola is x= a

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

If parabola is y² = 4ax and the equation of the directrix of the parabola is x= -a

when parabola becomes y² = - 4ax and the equation of the directrix of the parabola is x= a

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Answer:

Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.

In probability, as the number of trials increases, the experimental probability is expected to converge to the theoretical probability. This is known as the Law of Large Numbers. Since the experiment with 3,000 flips had the most number of trials, it is most likely that the experimental probability was closest to the theoretical probability in this experiment. The larger the sample size, the more likely it is to reflect the true probability of the coin being a fair coin.

The value weight of the can is 1 ounce

To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.

The total weight of the can and oil is 31 ounces .

When ½ of the the oil is poured the weight of the can and oil is 16 ounces.

Therefore the weight of ½ of oil is 31-16 = 15 ounces

if ½ of the oil weighs 15 ounces

full oil will weigh 15× 2 = 30 ounces

the weight of the can = 31-30 = 1ounce

Therefore the weight of the can is 1 ounce

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Yes , it is possible to divide the line segment in the ratio of [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] because after simplifying the ratio becomes of integers .

For a line segment to be divided in the ratio "a:b" , both the numbers "a" and "b" should be integers ,

the ratio to divide line segment is given as : [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] ;

multiplying each term of the ratio by [tex]\sqrt{3}[/tex] , we get ,

the ratio as ⇒[tex]3 :1[/tex] , where both the numbers "3" and "1" are integers .

So ,we get that ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] can be written in simplified ratio form as 3:1    .

Therefore , a line segment can be divided in the ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex] .

The given question is incomplete , the complete question is

Is it possible to divide a line segment in the ratio [tex]\sqrt{3} :\frac{1}{\sqrt{3} }[/tex]   ?

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The least possible value of n−m, expressed as a common fraction is 17/6.

By Triangle Inequality Theorem,

(x + 4) + 3x > x + 9

So 4x + 4 > x + 9

3x > 5

x > 5/3

If angle A is the largest angle, the side opposite to angle A will be the largest length, so

x + 9 > x + 4 (which is possible for all values of x)

and x + 9 > 3x

2x < 9

x < 9/2

Therefore 5/3 < x < 9/2. So m = 5/3 and n = 9/2

So calculating value of n - m

n - m = 9/2 - 5/3

= 27/6 - 10/6

= 17/6

--The question is incomplete, the complete question is as follows--

"In the triangle shown, for ∠A to be the largest angle of the triangle, it must be that m<x<n. What is the least possible value of n−m, expressed as a common fraction?"

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Two common types of ratios we'll see are part to part and part to whole.

The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.

30 numbers complete the ratio table to make an equivalent ratio.

What is equivalent ratio?

When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.

Here in this case,

for trees: 2: 12    [ 2 to 12, 6 times more ]

for plants: 5: 30  [ 5 to 30, it is also 6 times more]

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Answer:mm

Step-by-step explanation:

Answer:

Step-by-step explanation: 6 978 781 600

After finding the LCM, the sum of 8/9 and 3/4 is 59/36

In the given question, we have to find the sum of 8/9 and 3/4.

The given numbers are 8/9 and 3/4

Sum = 8/9 + 3/4

The denominator of the both number are different. So to find the sum we find the LCM of the both number 9 and 4.

So the LCM of 9 and 4 is 36.

Multiply 4 on the number 8/9 and 9 on the number 3/4. So

Sum = [tex]\frac{8}{9}\times\frac{4}{4}+\frac{3}{4}\times\frac{9}{9}[/tex]

Sum = 32/36 + 27/36

Now the denominator is same. So now we add them.

Sum = (32+27)/36

Sum = 59/36

Hence, the sum of 8/9 and 3/4 is 59/36.

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   When we say two values are equivalent, we mean that their numerical values are the same. In mathematics, transforming one value into another that is more useful in a specific context is one technique to demonstrate that two values are comparable.

  In this instance, the values of the fraction 3/4 and the decimal 0.75 are the same. This can be demonstrated by dividing the numerator (3) by the denominator (4) using long division or a calculator to represent the fraction 3/4 in decimal form.

 The following steps can be used to breakdown the conversion of a fraction to a decimal:

           Therefore, In mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value.

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Answer:

The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.

For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.

There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.

So your expected gain/loss per roll is:

(3/9) * $3 + (3/9) * (-$6) = -$1

Therefore, on average, you will lose $1 per each throwing.