For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?

Answer: 27.5

Step-by-step explanation:

[tex](x-3)2 = 49\\x-3 = \frac{49}{2} \\x-3 = 24.5\\x = 24.5 + 3\\x = 27.5[/tex]

While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. A straightforward equation shows the connection between two terms on either side of an equal sign. Additionally, simple equations incorporate one or more of the addition, subtraction, multiplication, and division arithmetic operations.

given

Let a = the cost in cents of a cheeseburger

Let b = the cost in cents of a shake

4a+2b=7 .90

2b=a+15

-a+2b=15

Subtract (2) from (1)

4a+2b=7 .90

a-2b=-15

5a=775

a=155

2b=a+15

b=170/2

b=85

While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

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The probability that either the words BAD or CAB will appear as part of the row  is 16.7%

We have 4 places where we can put the cards.

Let's count the number of possible outcomes for each place.

In the first place, we can put one of 4 cards.

In the second place, we can put one of 3 cards (because one card was taken in the first place).

In the third place, we can put one of 2 cards

In the last place, we can put one of one cards.

The total number of different combinations is the product between the number of options for each place, then we have:

4×3×2×1 = 24

Now we need to count the number of combinations such that the words BAD or CAB appear. We have:

BADC

CBAD

CABD

DCAB

That is 4 out of 24.

Thus, the probability that either the words BAD or CAB will appear as part of the row will be:

P(BAD or CAB) = 4/24 = 16.7%

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The probability is 16.7%

If six different colors of paint are available, 360 ways can the knobs be painted.

A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available,

When examining permutations and combinations, we use factorials. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.

coat hanger has four knobs

6!  / 4! ( 4!)

6 * 5 * 4* 3 / 4 * 3 * 2* 1 (4 * 3 * 2 * 1)

= 30 * 1 2

=360

360 ways can the knobs be painted.

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The graph of a line with a slope of 3/5 has an equation of y = 3/5x + 1 and the graph is attached

From the question, we have the following parameters that can be used in our computation:

Graph of a line with a slope of 3/5

This means that

Slope = 3/5

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 3/5

So, we have

y = 3/5x + c

Assume that c = 1

So, we have

y = 3/5x + 1

Hence, the equation is y = 3/5x + 1

See attachment for graph

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The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

Now, According to the question:

Let's know:

What is Horizontal lines?

If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.

The equation is y = 4.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

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Answer:

I could find the slope of a line by looking at the gradient of a graph that the line creates. If the line is linear, then the gradient will be a constant value, which I can use to find the value of the slope. If the line is not linear, then I can use a derivative to find the slope at a given point. However, if the line is concave or concave up, then I will need to take the second derivative of the equation to determine which point on the line is closest to the point that I'm trying to calculate.

Step-by-step explanation:

Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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Answer:

2 prime numbers: 31 and 37

Step-by-step explanation:

31 and 37 are the only prime numbers between 30 and 40

The numerical coefficient of xy in the given expression -7xy is -7.

The numerical coefficient of an expression is a number that is multiplied by a variable or a product of variables. The coefficient is the number that appears in front of a variable or a product of variables. In the case of a constant term, the coefficient is the constant itself.

For example, in the expression 3[tex]x^2[/tex] + 4x - 5, the numerical coefficient of [tex]x^2[/tex] is 3, the numerical coefficient of x is 4, and the numerical coefficient of the constant term -5 is -5.

Here, in the expression -7xy, the numerical coefficient of xy is -7.

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The complete question is -

What is the coefficient of XY in the expression - 7xyz?

An angle that measures 120 degrees is called an obtuse angle.

An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. It is formed by the intersection of two lines that are not collinear, that is, they do not lie on the same line, and the angle is greater than a right angle but less than a straight angle.

An obtuse angle is represented by an arc with a curved arrow on one end, pointing in the direction of the other end.

It's important to keep in mind that the term obtuse angle is just a classification based on the measure of the angle, which is greater than 90 degrees but less than 180 degrees, and it's not a specific angle measure, it could be any angle that is in that range.

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Answer:

-33

Step-by-step explanation:

Given algebraic expression:

[tex]5c-9c+3[/tex]

To simplify the given algebraic expression using c = 9, substitute the given value of "c" into the expression and solve:

[tex]\implies 5(9)-9(9)+3[/tex]

[tex]\implies 45-81+3[/tex]

[tex]\implies -36+3[/tex]

[tex]\implies -33[/tex]

Answer:

[tex] \sf \: 5c - 9c + 3 = - 33[/tex]

Step-by-step explanation:

Given information,

→ 5c - 9c + 3

→ where c = 9

Let's simplify the expression,

→ 5c - 9c + 3

→ 5(9) - 9(9) + 3

→ (5 × 9) - (9 × 9) + 3

→ 45 - 81 + 3

→ 45 - 78

→ -33 => final value

Hence, the final value is -33.

Explanation:

The equation y = 5x^2+3x^6-10x-8 is not in standard form.

Why not? Because the term with the largest exponent (6) isn't listed first.

The standard form would be y = 3x^6+5x^2-10x-8; note the exponents decrease (6, 2, 1, then 0).

After the polynomial is in standard form, we can read off the leading coefficient to be 3. This is the coefficient of the first term 3x^6.

Side note: The degree is 6 as it's the largest exponent.

The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .

What is Law Of Sines ?

The Law Of Sines states that  the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known  are Sine Law, Sine Rule and Sine Formula.

The Sine Law  is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.

Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .

So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;

Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .

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a) The total amount of pizzas that they ate is given as follows: 2.92 pizzas.

b) The difference between the number of cheese pizzas and the number of vegetarian pizzas is given as follows: 4/3, which is the amount that they ate more of cheese pizzas than vegetarian pizzas.

The fractions relative to the amount of each type of pizza eaten are given as follows:

The total amount of pizzas eaten is given by the addition of these fractions, hence:

1/4 + 2 + 2/3 = 3/12 + 24/12 + 8/12

(as the least common factor between 4, 1 and 3 is of 12).

3/12 + 24/12 + 8/12 = (3 + 24 + 8)/12

(3 + 24 + 8)/12 = 35/12

2.92 pizzas.

The difference between the number of cheese pizzas and the number of vegetarian pizzas is obtained as follows:

2 - 2/3 = 6/3 - 2/3 = 4/3.

(as the least common factor of 1 and 3 is of 3).

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There is one way to implement a function in Python that takes in an array of integers and returns the smallest positive integer that does not occur in the array.

def smallest_missing_positive(a):

   #Create a set to store the unique elements in the array

   unique_set = set(a)

   #Iterate through the positive integers starting from 1

   for i in range(1, len(a) + 2):

       #If the current integer is not in the set, return it

       if i not in unique_set:

           return i

This function first converts the input array into a set, which removes any duplicate elements. It then iterates through the positive integers starting from 1 up to the length of the array plus 2. For each integer, it checks whether it is in the set of unique elements from the input array. If it is not, the function returns that integer as it is the smallest positive integer that does not occur in the array.

For example, when the function is called with the input array [1, 3, 6, 4, 1, 2], it will return 5 as it is the first missing positive number.

You can also use a set and difference() method of set to check the missing elements from 1 to maximum element of array+1 and find the missing first one, this method is more efficient than the above one when the array is large.

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The expression (1/4 - 3/5) is equivalent to the following expressions -

Given is the expression as -

(1/4 - 3/5)

The given expression is -

(1/4 - 3/5)

1/4 - 3/5

(5 - 12)/20

-7/20

We can write the fraction : -7/20 in many ways as given below -

-7/20 = (3/20 - 10/20) = (1/4 - 3/5)

-7/20 = (13/20 - 1) = (1/4 - 3/5)

-7/20 = (23/20 - 3/2) = 1/4 - 3/5)

Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -

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If Andrew takes same amount of time to kayak 4 miles upstream and 9 miles downstream in a river with a 6 mph current, then the speed of Andrew’s kayak in still water is 15.6 miles per hour.

Therefore the answer is 15.6 mph.

We can begin solving the problem by using the equation:

Speed (relative to water) = Speed (in still water) + Speed (of the water)

Let x be the speed of Andrew's kayak in still water.

When kayaking upstream, his speed relative to the water is x - 6 mph (since the current is moving in the opposite direction at 6 mph).

When kayaking downstream, his speed relative to the water is x + 6 mph (since the current is moving in the same direction at 6 mph).

Since the problem states that it takes Andrew the same amount of time to kayak 4 miles upstream as it takes him to kayak 9 miles downstream, we can set up the following equation knowing time = distance/ speed :

4/ (x - 6) = 9/ (x + 6)

Simplifying and solving for x we get

4(x + 6) = 9(x - 6)

4x + 24 = 9x - 54

9x - 4x = 54 + 24

5x = 78

x = 15.6

So, Andrew's kayak speed in still water is 15.6 miles per hour.

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Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

The use of labels Triangle ABC is congruent to triangle DEF if the angles of triangles ABC and DEF are AB = DE, AC = DF, and A = D.

ABC=CDE: a) in accordance with the conditions BC=CD and AC=CE; b) BCA=m (DCE).

If ABC = CDE, then m(BAC) = m(DEC), and m(ABC) = m (CDE).

If m(BAC)=m(DEC), then AB || DE, or if m(ABC)=m(CDE), then AB || DE.

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The third side of a triangle can be found using the Pythagorean Theorem.

The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.

To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.

Next, plug the values into the Pythagorean Theorem and solve for c.

[tex]a^2 + b^2 = c^2[/tex]

[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]

[tex]169 = c^2[/tex]

Finally, take the square root of both sides to solve for c.

sqrt(169) = c

13 = c

Therefore, the length of the third side is 13.

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Since X is an odd number, x+2 is the following odd number. If x is an even number, the subsequent odd number is x + 1.

The vehicles that will travel on the highways on particular days are decided by the Odd-Even rule, a space rationing system. According to the plan, vehicles with odd and even numbers will travel the roads on alternate days.

In jQuery, the odd() method is used to pick elements with odd index numbers (such as 1, 3, 5, etc.). The index begins at zero. It picks odd numbers, unlike the even() function, which is comparable. From the set of chosen items, the odd() method returns the odd indexed elements.

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It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

Solve the inequities:

k^2-7k+12. 25>0

2. 25y^2-3y+1<0

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.

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The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%" (percent sign). Percentages are used to express how much of something there is in relation to the whole. For example, if a student answers 80% of the questions correctly on a test, it means they answered 80 out of 100 questions correctly.

A tax is a financial charge imposed by a government on individuals, businesses, or other entities to raise revenue for government spending. Taxes are typically based on a percentage of income or sales, and can be levied on various forms of income, including wages, salaries, and profits. The purpose of taxation is to fund government programs and services, such as roads, schools, and national defense. Taxes can also be used to redistribute wealth and influence economic behavior.

The amount withheld from the student's pay last year in federal tax is $6675 x 0.1 = $667.50

The amount withheld from the student's pay last year in state tax is $6675 x 0.03 = $201.25

The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

So the answer is A. 867.75

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The volume of the cube, given the lengths of the small cubes used to make the larger cube, is 8 cm ³

The surface area of the cube is 24 cm ²

The total length of the edges of the cube is  24 cm

The volume of a cube can be found by the formula :

= Side x Side x Side

This is because all the sides of a cube at the same and so the volume would measure them three - dimensionally.

The side length of this cube is the length of two of the smaller cubes as these make up a side of the cube :

= 2 x 1

= 2 cm

The volume is therefore :

= 2 x 2 x 2

= 8 cm ³

The surface area of a cube is:

= 6 x side ²

= 6 x 2 ²

= 24 cm ²

The total length of the edges would be:

= 12 edges on a cube x length of each edge

= 12 x 2

= 24 cm

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For this question u have to assume value of either x or y

For example

to find the value of x

side calculation (7000/35 = 200)

let x = 200

then 35(200) +60y = 7000

7000 + 60y = 7000

60y = 7000-7000

so y = 0

so value of x should be greater than or equal to 200

x >(or equal to) 200

to find the value of y

side calculation ( 7000/60 = 116.67)

let y = 116.67

then 35x + 60(116.67) = 7000

35x + 7000 = 7000

35x = 7000-7000

35x=0

so x = 0

so the value of y should be greater than or equal to 116.67

y >( or equal to 116.67)

Column A and B matching the results with the operations

Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

The width of the frame is 8 inches.

Now, According to the question:

The length of a rectangular frame is 15 inches

The diagonal length of the frame is 17 inches.

To find the width of the frame in inches.

Let's take the width of the frame is = w

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

17² = 15² + w²

289 = 225 + w²

289 - 225 =  w²

64 =  w²

w = [tex]\sqrt{64}[/tex]

w = 8

Hence, The width of the frame is 8 inches.

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The value of h is 6.

Now, According to the question:

In right triangle, ABC

Given data:

AD = 12 and DB = 3

The equivalent ratio of the triangles is:

h : 12 = 3 : h

Express as fractions

[tex]\frac{h}{12} =\frac{3}{h}[/tex]

Cross Multiply:

[tex]h^2[/tex] = 36

Take positive square roots of both sides

h = 6

Hence, the value of h is 6.

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The real earning of her could be less than $2250 during the year where their parents supported more than half.

What is linear equation ?

linear equation can be defined as the equation in which the highest degree of the exponent is one.

Given

The Tutts cannot be claimed as dependents on anyone else's tax return. Their daughter, Lavender, is 19years old,

single and a full-time student away at college.

Lavender earned $4,500 during the year

The real earning of Lavender could be

as her parents supported more than half.

so,

her real earning could be less than $2250

Hence , the real earning of her could be less than $2250 .

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