Using Cramer’s Rule, what is the value of x in the solution to the system of linear equations below?
x+3y=16
3x+y=8

Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:

[tex]tan(45)=\frac{x}{\sqrt{2}}[/tex]

Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:

We multiply the denominator of the fraction by [tex]\sqrt{2}[/tex]. [tex]\sqrt{2}[/tex] multiplied by itself is simply 2. Try it! We also want to multiply the numerator by [tex]\sqrt{2}[/tex], but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:

[tex]tan(45)=\frac{x\sqrt{2} }{2}[/tex]

Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.

[tex]\frac{x\sqrt{2} }{2*2} =x\sqrt{2}[/tex]

[tex]tan(45)*2=2[/tex]

We can plug 2 in for the x in the numerator now:

[tex]\frac{2\sqrt{2} }{2}[/tex]

2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of [tex]x=\sqrt{2}[/tex]

Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)

Answer:

A

Step-by-step explanation:

There are 8 consonants (not including y) and only 6 vowels (not including y), so Rosa has a higher probability of winning.

The game is not fair because the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.

'Probability is defined as the possibility of an event to happen is equal to the ratio of the number of outcomes to the total number of outcomes.'

According to the given problem,

There are 8 consonants (not including y) and only 6 vowels (not including y), so Rosa has a higher probability of winning.

Hence, we can conclude that the game is not fair the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.

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Answer:

Step-by-step explanation:

(x-a)² + (y-b)² = c²

Answer:

that's an adorable little baby.

Step-by-step explanation:

Answer:

its cute

Step-by-step explanation:

Answer:

The increase is 15%

Step-by-step explanation:

Hope this helps!

Answer:

Part B The manager of The Gadget Factory wants to make sure that the next shipment costs no more than $15,000. Write an inequality that shows the amount of money that can be spent. Graph the inequality on the number line. Let n=the amount of money spent.

Step-by-step explanation:

The inequality equation is n ≤ 15,000 , where n is the amount of money spent

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.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the amount of money spent be represented as n

And , the next shipment costs no more than $15,000

So , n ≤ 15,000   be equation (1)

Therefore , the value of A is n ≤ 15,000 and the graph is plotted

Hence , the inequality equation is n ≤ 15,000

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Answer:

2

Step-by-step explanation:

Let the two consecutive integers be x , x+1

Sum : x + x +1 = 2x + 1

Difference: (x +1) - 1 = x + 1 - 1 = x

Sum = 3 times their difference

2x + 1 = 3 * x

2x + 1 = 3x    

      1 = 3x - 2x

     1 = x

The numbers are 1 , 2

Answer:

The answer is (-9)

Step-by-step explanation:

The solution is, the result of the division is 1.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

(-15)-(-18)

now we have to divide this by 3

so, we get,

(-15)-(-18) /3

now,

(-15)-(-18)

= -15 + 18

=3

so, we have,

(-15)-(-18) /3

=3 /3

=1

Hence. The solution is, the result of the division is 1.

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Answer:

√{9×81×9}=√(9²×9²)=±(9×9)=±81

Answer:

your answer will be 81

Step-by-step explanation:

.......

Answer: 4 over 5 is not a whole number and so it cannot be expressed as a whole number.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

from sss axiom

we can say that they are congurqnt

Answer:

5 6 2 + 1 9 − 1 0

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

Answer:- 1/100 degrees Fahrenheit

Step-by-step explanation:

The directions say decreasing so it has to be negative, and the slope is showing how much it is decreasing every meter. y=mx+b. The mx is the slope which is where the answer is located.

Answer:

1. Baseball

2. Soccer ball

3. Football

Explantion:

Speed = Distance / time

Baseball --> 1270/32 = 39.69

Football --> 1199/44 = 27.25

Soccer ball --> 1270/44 = 28.86

Answer:

1. Baseball

2. Soccer ball

3. Football  

Formula= Speed = Distance / time

Baseball in fraction form is 1270/32 and in decimal form is 39.69

Football in fraction from is 1199/44 and in decimal form is 27.25

Soccer ball in fraction form is 1270/44 and in decimal 28.86

Hope this helps <3 Need thanks? Comment /hearthelp

Answer:   I'm gonna go with B. hours worked; weekly pay; 30 to 35 hours; $360 to $420, because I had something similar to this

Wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.

weekly pay; hours worked; 20 to 25 hours; $180 to $225

hours worked; weekly pay; 20 to 25 hours; $180 to $225

weekly pay; hours worked; $180 to $225; 20 to 25 hours

hours worked; weekly pay; 20 to 25 hours; $9 to $225

Step-by-step explanation:

The independent quantity is her pay and the dependent quantity is the hours she works in a week.

I believe the range would be 30 to 35 hours and the domain would be $360 to $450.

...................................................................................................................................................

Answer:

Part a) The independent quantity is the variable x (the number of hours) and the dependent quantity is the variable y (total paid)

Part b) Domain  

Part c) Range  

Step-by-step explanation:

Let

x------> the number of hours

y-----> total paid

The linear equation that represent this situation is

so

Part a)

The independent quantity is the variable x (the number of hours)

The dependent quantity is the variable y (total paid)

Part b) Find the domain

The domain is the interval-------->  

All real numbers greater than or equal to  hours and less than or equal to  hours

Part c) Find the range

For  

find the value of y

For  

find the value of y

The range is the interval------->  

All real numbers greater than or equal to  and less than or equal to  

...............................................................................................................................................

The dependent quantity would be the $12 per hour, while the independent quantities are 30 hrs/ week to 35 hours/ week.

The $12 per hour would become $360/week to $420/week.

The domain of the problem, with the unit of hrs/week, would be :30,31,32,33,34,35.

The Range of the problem, with the unit of $/week, would be : 360, 372, 384, 396, 408, 420.

...............................................................................................................................................

Answer:

Step-by-step explanation: The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph  by  finding  the change  in y and the change in x.

Answer:

r = the radius, in your case, it's 4 cm. So. Area = π ×r2. = π× (4 cm)2. = 16π cm2 ≈ 50.24 cm2.

Step-by-step explanation:

Answer:

B) 3x^2+6x+4

Step-by-step explanation:

(6x+7+x^2)+(2x^2-3)

6x+7+x^2+2x^2-3

3x^2+6x+7-3

3x^2+6x+4

The sum of the polynomials is 3x² + 6x + 4.

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

Given are two polynomials whose sum has to be found.

(6x + 7 + x ²) and (2x² - 3).

The sum of the polynomials is,

(6x + 7 + x ²) + (2x² - 3)

We have to operate the like terms together.

= (6x) + (7 - 3) + (x² + 2x²)

= 6x + 4 + 3x²

= 3x² + 6x + 4

Hence the sum of the polynomials is 3x² + 6x + 4.

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Replace x any with the given values:

x/y = 9/3 = 3

The answer is 3

Answer:

3rd one

Step-by-step explanation:

Answer:

y=3(50)×

y=3(50) 8

50×3=150

150×8=1,200

Answer:

the new discounted price is $5.85

Step-by-step explanation:

First convert 130% into a decimal: 130 ÷ 100 = 1.3

Next multiply 1.3 by 9: 9 x 1.3 = 11.7

Then convert 50% into a decimal: 50 ÷ 100 = 0.5

Last multiply 11.7 by 0.5: 11.7 x 0.5 = 5.85

Answer:

$5700 - $5500= $200

Explanation:

The total installments: 24 ($175) = $4200

The hire purchase price: $1500 + $4200 = $5700

The amount saved by paying cash: $5700 - $5500= $200

The sets of side lengths that can produce a triangle are

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

That is, in a given triangle of sides a, b and c,

a + b ≥ c

Analysing the sets of the side lengths given,

In triangle 2 cm, 7 cm, and 6 cm,

2 + 6 = 8,

Therefore 8cm which is greater than the third side being 7cm makes this side lengths possible to produce a triangle.

In triangle 2 m, 5 m, and 7 m,

2 + 5 = 7

Addition of both sides of the triangle is equal to the third side being 7m.

In triangle 6 ft, 6 ft, and 12 ft,

6 + 6 = 12

Addition of both sides of the triangle is equal to the third side being 12ft

Therefore the sets of side lengths could produce a triangle are

2 cm, 7 cm, and 6 cm

2 m, 5 m, and 7 m

6 ft, 6 ft, and 12 ft

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Answer:

Angela's mistake is in step 1, she failed to change the sign when subtracting from both sides

Step-by-step explanation:

Equation given :

The correct solution should be :

3/4 - 3/4 + m = 5/4 - 3/4

m = 2/ 4

m = 1/2

Therefore failure to change the sign will result in a obtaining a wrong answer for the exercise.

m=1/2

hope this helps!