how to solve a system of three equations using the elimination method

Answer:

B.

Step-by-step explanation:

Let's find g(f(x)) for each choice for fun and so you can have more examples:

A) f(x)=3x and g(x)=sqrt(x)+1

so g(f(x))=g(3x)=sqrt(3x)+1

So definitely not this choice

B) f(x)=x+1 and g(x)=sqrt(3x)

so g(f(x))=g(x+1)=sqrt(3(x+1))

So this one works! :)

C) f(x)=sqrt(x)+1 and g(x)=3x

so g(f(x))=g(sqrt(x)+1)=3(sqrt(x)+1)

Not this one!

D) f(x)=sqrt(3x) and g(x)=1

g(f(x))=g(sqrt(3x))=1

Answer:

The correct answer is (-5,-5)

Step-by-step explanation:

1. Both of the equations are in standard form, so first you set them equal to each other.

2. Solve for x as a normal algebraic equation.

3. Back substitute your answer for x into one of the original equations. (back substitution is just putting the x back into the equation and solving for y.)

4. Now you have your x and y coordinates, and the point of intersection of the two lines.

The ordered pair represents the solution to the system is (-5, -5), and the correct option is A.

A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.

The given system of equation is;

y = 3x + 10

y = 5x +20

Subtraction equation 1 from 2

y - y = 3x + 10 - 5x -20

0 = -2x -10

2x = -10

x = -10/2

x = -5

Substitute the value of x in equation 1

y = 3x + 10

y = 3(-5) +10

y = -15 +10

y = -5

Hence, the ordered pair represents the solution to the system is (-5, -5), and the correct option is A.

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Answer:

420

Step-by-step explanation:

Each of the 7 appetizers can be paired with one of 10 entrees, and each entree can be paired with one of 6 desserts.  So the number of combinations is:

7 × 10 × 6 = 420

By combination property, there are a total of 420 different lunch specials that are possible.

The combination property is defined as the selection of items from a set that has distinct members, such that the order of selection does not matter.

It is given that a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts.

Thus, there are 3 different items which quantities are also mentioned. '

Thus by combination property, the total number of lunch specials that are possible -

7 * 10 * 6 = 420 .

Therefore, by combination property, there are a total of 420 different lunch specials that are possible.

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Answer: second option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]

Answer:

The correct answer is second option

6√2

Step-by-step explanation:

From the figure we can see a right angled triangle, with angles 45°, 45° and 90°

The height of triangle is 6 units

Points to remember

If the angles of a right angled triangle are  45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2

To find the value of x

From the figure we can see that, the angles are  45°, 45° and 90°

Therefore the two sides are equal and one side is x

The equal side is 6 units

Therefore 6 : 6 : x = 6 : 6 : 6√2

The value of x = 6√2

The second option is the correct answer.

Slope formula = y2-y1/x2-x1

Plug in.

4 - 7/-1 - 3 = -3/-4 = 3/4

Answer: 3/4 or Choice A

Answer:

Step-by-step explanation:

setup a proportion

                               Big Triangle             Small Triangle

corresponding              15                              3

corresponding               x                               6

so you are trying to solve 15/x=3/6

cross multiply 6(15)=3(x)

last step divide both sides by 3 giving x=30 ft

If the triangles are similar, value of x in the drawings is Option(B) 30 ft.

Similar triangles are triangles that have the same shape, but their sizes may vary. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

The given two triangles are similar .

In the diagram, it is mentioned that one side is 3 and its corresponding other side of the similar triangle is 15 .

Thus the proportion is 15/3 = 5

Therefore if the other side of the same triangle is 6 then its corresponding other side of the similar triangle will be 6*5 = 30

Thus x = 30 ft.

Therefore, if the triangles are similar, value of x in the drawings is Option(B) 30 ft.

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Answer:

-10.6

Step-by-step explanation:

-3|z| + 2(a + y) =

= -3|-4.2| + 2(-2 + 3)

= -3(4.2) + 2(1)

= -12.6 + 2

= -10.6

Answer:

0.75 and n-6= 0.75(t-8)

Step-by-step explanation:

To find the average speed of Ava's car, divide the total distance traveled by the total time taken. Ava travels 6 miles in 8 minutes, so the average speed is 0.75 miles per minute. The equation of the line representing the number of mile markers passed as a function of time is n = (3/4)t.

To find the average speed of Ava's car in miles per minute, we can use the formula:

Average speed = total distance / total time

First, we need to find the total distance traveled. Ava travels from mile marker 0 to mile marker 6, which is a distance of 6 miles.

Next, we need to find the total time it took Ava to travel this distance. Ava notes that 8 minutes have passed when she reaches mile marker 6, but it took her 4 minutes to travel from mile marker 0 to mile marker 3. This means it took her 4 minutes to travel 3 miles. Therefore, it would take her an additional 4 minutes to travel the remaining 3 miles from mile marker 3 to mile marker 6.

So, the total time taken by Ava to travel 6 miles is 4 minutes + 4 minutes = 8 minutes.

Now, we can use the formula to calculate the average speed:

Average speed = total distance / total time = 6 miles / 8 minutes = 0.75 miles per minute.

Equation of the line:

To find the equation of the line that represents the number of mile markers passed as a function of time, we can use the equation:

n = mt + b

Here, 'n' represents the number of mile markers passed, 't' represents time in minutes, 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this scenario, Ava starts checking her car's clock at mile marker 0, which means the y-intercept is 0. We also know that Ava takes 4 minutes to travel from mile marker 0 to mile marker 3, which means she passes 3 mile markers in 4 minutes. Therefore, the slope of the line is 3/4.

So, the equation of the line is: n = (3/4)t.

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Final answer:

Lily's budget scenario with her sister's charm bracelet is translated into the inequality statement 12 + 1.50c ≤ 25, where c represents the number of charms she can buy. Solving this inequality will show how many charms Lily can afford without exceeding her $25 budget.

Explanation:

The question involves translating a real-life situation into an inequality statement concerning budget and expenses. Lily has $25 to spend on her sister's birthday gift, which is a charm bracelet. The cost structure for the bracelet is $12 for the bracelet itself plus $1.50 for each charm. We let the number of charms she plans to buy be represented by c. The total cost for these charms would be $1.50c, and when added to the initial $12 for the bracelet, the sum should not exceed Lily's budget of $25.

Therefore, the inequality that represents this situation is 12 + 1.50c ≤ 25.

To find the maximum number of charms Lily can afford, we would solve for c in the inequality. This step involves subtracting 12 from both sides and then dividing by 1.50.

Answer:

263.99 m3 (i tried my best)

Step-by-step explanation:

diameter > radius= 12/2

=6 m

v. of cone: 1/3 x 22/7 x r² x h

1/3 x 22/7 x 6² x 7

=263.99 m3

Answer:84piem^3

Step-by-step explanation:AP3X

Answer: 605 candies

Step-by-step explanation:

Machine C shows a table where 150 candies are added every 2 minutes (which equals 75 candies per minute). Extend the table to show how many candies are made in 11 minutes:

     x                  y

(minutes)    (candies)

   2                 150

   4                 300

   6                 450

   8                 600

  10                 750

   11                 825    

Machine D productivity is given by the equation y = 130x

when x = 11 minutes, y = 130(11)

                                     = 1430 candies

The difference between machines C and D is: 1430 - 825 = 605

Answer:

Option A.12 square units

Step-by-step explanation:

Let

[tex]A(-2,2), B(1,2), C(0,-6)[/tex]

Plot the vertices

see the attached figure

we know that

The area of triangle is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

[tex]b=AB=(1-(-2))=3\ units[/tex]

[tex]h=(2-(-6))=8\ units[/tex]

substitute

[tex]A=\frac{1}{2}(3)(8)[/tex]

[tex]A=12\ units^{2}[/tex]

Answer:

Step-by-step explanation:

A. 12

Answer:

C.) 5.1

Step-by-step explanation:

First, solve for J's angle of degrees

180 - (120 + 40) = 20

Second, fill in all the information that you know in the equation

sin(20) / 2 and sin(120) / k

Third, cross multiply

k x sin(20) = 2 x sin(120)

Fourth, solve for k

k x sin(20) / sin(20) = [2 x sin(120)] / sin(20)

k = [2 x sin(120)] / sin(20)

k = 5.0641777.....

Fifth, round to the nearest tenth

k = 5.1

Answer:

its 5.1 on edg

Step-by-step explanation:

The answer for AB is 5.

To find this answer, you would use Pythagorean Theorem. The equation would be a² + 12² = 13². First, square 12 and 13, to get the equation to say a² + 144 = 169. Next, subtract 144 from both sides. This leaves a² = 25. Finally, square root  both sides to a = 5. Thus meaning 5 is the answer.

Here is an image to show how this answer is found. I hope this helps!

Answer:

The x-intercept are (-7 , 0) and (5 , 0)

Step-by-step explanation:

* Lets revise the general form of the equation of the parabola

- The general form of the equation of the parabola is:

  y = ax² + bx + c , a , b , c are constant

- The y-intercept is c, because the parabola intersect the y-axis at

  point (0 , c)

- The x-coordinate of the vertex point is -b/2a

* Now lets solve the problem

∵ The general form of the equation of the parabola is y = ax² + bx + c

∵ The y-intercept is -105

∴ c = -105

∴ y = ax² + bx - 105

∵ The vertex point is (-1 , -108)

∴ The x-coordinate of the vertex of the parabola = -1

∵ The x-coordinate of the vertex of the parabola = -b/a

∴ -b/2a = -1 ⇒ using cross multiplication

∴ -b = -2a ⇒ multiply two sides by -1

∴ b = 2a

- Substitute the value of b in the equation

∴ y = ax² + 2ax - 105

- Substitute the value of x , y in the equation by the coordinates of

 the vertex point

∵ The vertex point lies on the parabola

∴ put x = -1 and y = -108

∴ -108 = a(-1)² + 2a(-1) - 105

∴ -108 = a - 2a - 105 ⇒ add the like term

∴ -108 = -a - 105 ⇒ add 105 to both sides

∴ -3 = -a ⇒ multiply both sides by -1

∴ a = 3

- Substitute the value of a in the equation

∵ y = ax² + 2ax - 105

∴ y = 3x² + 2(3)x - 105

∴ y = 3x² + 6x - 105

- To find the x-intercept put y = 0

∴ 3x² + 6x - 105 = 0

- All the terms have 3 as a common factor

∴ divide all the terms by 3

∴ x² + 2x - 35 = 0

- Now factorize it into two factors

∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the

  2nd bracket

∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the    

  2nd bracket

∵ x × - 5 = -5x ⇒ means

∵ x × 7 = 7x ⇒ extremes

∵ 7x - 5x = 2x ⇒ the middle term

∴ (x - 5)(x + 7) = 0

- Equate each bracket by 0

∴ x - 5 = 0 ⇒ add 5 to both sides

∴ x = 5

OR

∴ x + 7 = 0 ⇒ subtract 7 from both sides

∴ x = -7

∴ The x-intercept are -7 , 5

* The x-intercept are (-7 , 0) and (5 , 0)

Answer:

Step-by-step explanation:

Answer:

Yep the answer is C bro. I very much appreciate your help :D

congruency statement applies to the trapezoids is CDEF ≅ NMOP.

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid

From question, we have

Hence, Trapezoid CDEF and trapezoid NMOP are congruent.

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Answer: y=3x+8

Step-by-step explanation:

The slope will be the same as the original equation, so 3. And to make the line go the points (0,8), you can plug in 0 into the original equation to find what needs to change. Hope this helps!

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be 3

y = 3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(0, 8)

8 = 3(0) + b

8 = 0 + b

8 = b

y = 3x + 8

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

the ordered pair is (2,-1)

Step-by-step explanation:

We need to solve the system of equations using elimination method

12x - y = 25     eq(1)

9x + y = 17      eq(2)

Adding eq(1) and eq(2)

12x - y = 25

9x + y = 17

___________

21x = 42

x = 42/21

x= 2

Now, putting value of x in equation 1

12x - y = 25

12(2) -y = 25

24 -y = 25

Adding -24 on both sides

24 -y-24 = 25-24

-y = 25-24

-y = 1

Multiply both sides by -1

y = -1

the value of x = 2 and y = -1

So, the ordered pair is (2,-1)

Answer:

The solution is: (2, -1)

Step-by-step explanation:

I have the following system of equations

[tex]12x - y = 25[/tex]

[tex]9x + y =17[/tex]

Note that if we add both equations, the variable y is "eliminated".

So add the first equation to the second and solve for the variable x

[tex]12x - y = 25[/tex]

[tex]9x + y =17[/tex]

----------------------------------

[tex]21x=42[/tex]

[tex]x=\frac{42}{21}\\\\x=2[/tex]

Now substitute the value of x in any of the two equations and solve for the variable y

[tex]9(2) + y =17[/tex]

[tex]18 + y =17[/tex]

[tex]y =17-18[/tex]

[tex]y =-1[/tex]

The solution is: (2, -1)

Answer:

A

Step-by-step explanation:

Because it touches the x axis 3 times as shown in your graph

Hope it helps you..☺

Check the picture below.

Answer:  -1x-11

Step-by-step explanation:

Answer:

The mean of pictures is 2

Step-by-step explanation:

To find the mean we add up all the pictures then divide it by the amount of newspapers, there are 10 and 5 newspapers. 10/5=2.

Answer:

40 - x² = 0

x² = 40

x = ±√40 = ±√4√10 = ±2√10

Answer:

I have not the slightest clue but there's an app called cam calc and I swear its the best

Answer:

-2!

Step-by-step explanation:

im just finished this exact test and i swear thats the right answer!!

Answer:

Half gallon

Step-by-step explanation:

at the least expensive price per ounce (60 cents), half gallon is the answer.

Answer:

A or (2x+1)/(x-1)

Step-by-step explanation:

Let's simplify the top of the fraction first.

1. Simplify the numerator.

2x^2 -7x-4=(2x+1)(x-4)

2. Simplify the denominator.

x^2-5x+4=(x-4)(x-1)

Now we have:

((2x+1)(x-4))/((x-4)(x-1))

We see that there is an (x-4) both on the numerator and denominator.

We can remove (x-4) by division.

Doing that, we have:

(2x+1)/(x-1) or A

Answer:

Length =12

Width= 10

Step-by-step explanation:

The difference between two consecutive integers is 2.

Thus the difference between the length and the width of the rectangle also differ by 2.

width- x

length- x+2

AREA=L×W

120=x(x+2)

x²+2x-120=0

Factorizing:

x² - 10x + 12x - 120=0

x(x-10) + 12( x-10)=0

(x-10)(x+12)=0

either x-10=0 or x+12=0

x=10 0r -12

We consider positive roots only. thus x=10

width = 10

length = 10+2 =12

Answer:

the value  of the digit 1 in the no. 13 is 10

Step-by-step explanation:

cuz it's in the tens place

tens    ones

hope u understood

and helps u

and ur welcm

:D

The value of digit 1 in the number 13 is 10 because it is located in the 'tens' place.

The value of the digit 1 in the number 13 corresponds to its place value in the number. In the number 13, 1 is in the 'tens' place, thus its value is 10. Place value is determined by the position of a digit in a number. It shows the mathematical worth of each digit at their respective places. Zeroes play a significant role in deciding the place value of digits in a number, acting as placeholders that help identify decimal points.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y< 8[/tex]

The solution is the interval -----> (-∞,8)

[tex]y\geq3[/tex]

The solution is the interval -----> [3,∞)

The solution of the system is equal to

[3,∞)∩ (-∞,8)-------> [3,8)

All real numbers greater than or equal to 3 and less than 8

The graph in the attached figure

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -3/2 and the y-intercept b = 3.

Substitute:

y = -3/2x + 3

The x-intercept is for y = 0. Substitute:

0 = -3/2x + 3           add 3/2x to both sides

3/2x = 3     multiply both sides by 2

3x = 6           divide both sides by 3

x = 2