Does the following system have a unique solution? Why?

3x+2y= 9
14x + 10y = 14

Answers

Answer 1

Answer: Yes, the determinant of the coefficient matrix is 2.

Related Questions

What is the value of x in 3x+7y=27
Four times the first of three consecutive even integers is six more than the product of two and the third integer. Find the integers.
Write 63.63% as a fraction
The coordinates of the point on the curve y=x²+3x+4 the tangent at which passes through the origin are - a. (-2,2)(2,14) b. (1, -1) (3,4) c. (2.14)(2,2) d. (1,2) (14,3)
Explain how to solve 3x+4=19

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16.

Answers

Answer:

x²/64 + y²/81 = 1

Step-by-step explanation:

Standard form of an equation for the ellipse is $(x^(2) )/(a^(2))+(y^(2) )/(b^(2) )=1$

Here b is the length of vertical major axis = 9

and minor axis of length a = 8

Therefore the equation of the ellipse will be

$(x^(2) )/(8^(2) )+(y^(2) )/(9^(2) ) =1$

$(x^(2) )/(64)+(y^(2) )/(81)=1$

So the answer is x²/64 + y²/81 = 1

Let us assume then that the center is the origin. If the major axis is 18, then a = 9 and a^2=81. If the minor axis is 16, then b = 8 and b^2=64. Now you can write the equation. Remember that this ellipse is vertical and so a^2 goes under y^2

Irina predicted that she would sell 75 books, but she actually sold 95 books. Which expression would find the percent error? Use the table below to help answer the question.

Answers

There is no image of the table given.

Given:
approximate number = 75
exact number = 95

error = |approximate number - exact number| ÷ exact number
error = |(75-95)| / 95 = |20| / 95 = 0.21

percentage of error = 0.21 x 100% = 21%

Answer:

Given:

approximate number = 75

exact number = 95

error = |approximate number - exact number| ÷ exact number

error = |(75-95)| / 95 = |20| / 95 = 0.21

percentage of error = 0.21 x 100% = 21%

Triangle PQR ~ triangle PꞌꞌQꞌꞌRꞌꞌ.Which two transformations were performed on triangle PQR to produce triangle PꞌꞌQꞌꞌRꞌꞌ?

Choose exactly two answers that are correct.

A.Triangle PQR was reflected across the y-axis to produce triangle PꞌQꞌRꞌ.

B.Triangle PQR was reflected across the x-axis to produce triangle PꞌQꞌRꞌ.

C.Triangle PꞌQꞌRꞌ was dilated by a scale factor of to produce triangle PꞌꞌQꞌꞌRꞌꞌ.

D.Triangle PꞌQꞌRꞌ was dilated by a scale factor of 2 to produce triangle PꞌꞌQꞌꞌRꞌꞌ.

Answers

The correct answer for the question that is being presented above is this one: D.Triangle PꞌQꞌRꞌ was dilated by a scale factor of 2 to produce triangle PꞌꞌQꞌꞌRꞌꞌ; C.Triangle PꞌQꞌRꞌ was dilated by a scale factor of to produce triangle PꞌꞌQꞌꞌRꞌꞌ.

ten brothers receive 100 gold coins between them . Each brother receives a constant number more than the next oldest . The seventh oldest brother receives 7 gold coins . How much does each brother receive ? Show all your calculations

Answers

let's set 'a' as the coins the first brother recieves (the youngest) and for every older brother, we will add 'x' (the constant number)
Since we know the sum has to be equal to 100, our equation is:
100=a+(a+x)+(a+2x)+(a+3x)+...+(a+8x)+(a+9x)

the 7th oldest brother is the 3rd youngest, therefore, if we look at our equation, he gets (a+2x) - we know now that 7=a+2x

We can now simplify the first equation by summing up our 'x' and 'a'
we get: 100=10a+45x

In order to resolve the equation (since we have 2 variables), we can use the subtraction method

100=10a+45x
-10(7=a+2x)

100=10a+45x
-(70=10a+20x)

30=25x
1.2 = x

and for 'a' -> 7 = a +2(1.2)
a=4.6

Therefore, the youngest gets 4.6 coins (a), the second 5.8 (a+x) ...

Final answer:

The question involves arithmetic sequences. The first brother gets 5.5 gold coins with subsequent brothers getting 1 more coin than the brother before them. This gradually increases to the tenth brother who gets 14.5 gold coins.

Explanation:

This problem involves the concept of arithmetic sequences where each term is a constant amount different from the previous term. Given the seventh oldest brother receives 7 gold coins, we can denote the amount of money the first brother gets as x. The increment in each sequential brother's amount is then 1.

Firstly, denote the amount of money the first brother gets as x. Since each subsequent brother gets 1 more gold coin, we can denote the amount the other brothers receive as follows: x, x+1, x+2, ..., x+6 (for the seventh brother), ..., x+9 (for the tenth brother).

As the problem states that the total gold the brothers receive is 100, you would set up the equation: 10x + 45 = 100, where 45 is the sum of the increments from 1 to 9. Solving this equation for x, we get x=5.5. This means the first brother received 5.5 gold coins and each subsequent brother received 1 more than his immediate predecessor.

Learn more about Arithmetic Sequences here:

brainly.com/question/32830972

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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x5 – 3x

Answers

5 roots
...............................

It really is five roots in e2020

The solution to 2 * 27 will be what kind of number?A. Prime
B. Odd
C. Perfect square
D. Even

Answers

Answer: Even

Step-by-step explanation:

The given product is $2*27$

When we solve the given product we get, $2*27=54$

Now, 54 is not a prime number since it has more than two factors such as 2 and 27.

[ ∵ A prime number is a whole number greater than 1 and it has only two factors which are 1 and itself. ]

It is even not odd since its last digit is an even number.

54 cannot be written as $n* n$ , for any natural number n, therefore, it is not a perfect square.

Answer: Hello mate!

Let's analyze the options:

A) prime, a prime number is a number that only can be divided by 1 and itself, if you look at the number 2*27, you can see that this number can be divided by 2 and 27, then this number is not prime.

B) An odd number has the form m= 2*n + 1 where n is an integer number.

in this case, we have 2*27, so this number is not odd.

C) perfect square, 2*27 = 54, we know that 7*7 = 49, and 8*8 = 65

so 2*27 lays in between two consecutive perfect squares, so 2*27 can not be a perfect square.

D) an even number has the form 2*n, where n is an integer.

n = 27 is this case, so 2*27 = 54 is an even number.

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1.What is the value of p – (–3.5) when p = 8.2?