Choose the best initial step in solving the following system by substitution.
2x + 3y = –12
6x + y = 18
Answers:
1.Solve the first equation for x.
2.Solve the first equation for y.
3.Solve the second equation for x.
4.Solve the second equation for y.

Answer: 43.47517

Step-by-step explanation:

Considering orders of magnitude, we see that Option 2 is the only reasonable answer.

The entrance fees is 13 dollars charges by the paintball court.

Let us assume that the entrance fees is $X and the actual cost of using one ball is $Y charged by the paintball court.

According to one situation,

Total cost of using to ball = Cost of entry fees + actual cost of using two ball.

So, we can write,

X + 2Y = 18

Let us say that this is our equation 1,

Also, it is provided,

Total cost of using 4 balls = cost of entry fees + actual cost of using four balls.

X + 4Y = 23

Let us say that this is our equation 2,

Both of our equations are linear equations with two variables,

Now, substracting equation 1 from equation 2,

X + 4Y -(X + 2Y) = 23 - 18

2Y = 5

Y = $2.5.

Putting the value of Y = 2.5 in equation 1,

X + 2(2.5) = 18

X = 18 - 5

X = $13.

So, the entry fees is 13 dollars.

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Rewriting the words mathematically:

Next we will write in standard decimal form:

1st step. Calculate the area of the parallelogram

We can use the following formula:

where,

base, b = 9 km

height, h = 5 km

Therefore,

The area of the parallelogram is 45 km^2

2nd step. Calculate the area of the triangle

Let's use this formula:

where,

base, b = 6 km

height, h = 3 km

Therefore,

The area of the triangle is 9 km^2

3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle

Answer: the area of the parallelogram is 5 times greater than the area of the triangle.

A variable is a symbol and a stand-in for any mathematical object in mathematics.  A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable. Independent, dependent, and controlled variables are typically found in experiments. A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

The ladder's position would serve as an illustration.

Both 4x-2y=12 and -4x-9=54 are supplied to you. You are required to determine the ladder's order. But you didn't say which variable stands in for the ladder. I'll simply solve for both variables. I'll use the substitute strategy.

Let equations one and two be equivalent to 4x-2y=12 and -4x-9=54, respectively.

4x-2y=12

4x=12+2y

x=3+1/2y

Put this x in place of it in equation 2.

-4x-9y=54

-4(3+1/2y )-9y=54

Y=-6

X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0 \s.

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Answer: [tex]-\frac{x^2}{4}[/tex]

Step-by-step explanation:

The graph of g(x) is the graph of f(x) reflected over the x-axis and horizontally stretched by a factor of 2.

So, the equation is [tex]g(x)=-(x/2)^2 =-\frac{x^2}{4}[/tex]

Considering the definition of perpendicular line, the equation of a line perpendicular to 8x−5y=−9 that passes through the point ​(−8​,3​) is y=-5/8x-2 .

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 8x-5y= -9. Expressed in the form y = mx + b, you get:

-5y= -9 - 8x

y= (-8x -9)÷ (-5)

y= 8/5x +9/5

The line has a slope of 8/5. If you multiply the slopes of two perpendicular lines, you get –1. In this case:

8/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (8/5)

slope perpendicular line= -5/8

So, the perpendicular line has a form of: y= -5/8x + b

The line passes through the point (-8, 3). Replacing in the expression for perpendicular line, you get:

3= -5/8× (-8) + b

3= 5 + b

3- 5 = b

-2= b

Finally, the equation of the perpendicular line is y= -5/8x -2 .

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The required value of x is -3.6 which is determined by the substitute that equals the vertical angles.

When two lines intersect at a location, vertical angles are generated. They are always equal to each other.

Since ∠A and ∠B are vertical angles then they are congruent, thus

⇒ (x - 29) = (6x - 11)

Subtract 6x from both sides of the above equation,

⇒ x - 29 - 6x = 6x - 11 -6x

⇒ -5x - 29 = - 11

Add 29 to both sides of the equation,

⇒ -5x - 29 + 29 = - 11 + 29

⇒ -5x = 18

Divided by 5 to both sides of the equation,

⇒ x = - 18/5

⇒ x = - 3.6

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This situation can be expressed by the equation [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.

What is an equation?

Let the weekly allowance of anna be = X

Allowance spent on movies= X/2

The extra money from the car wash = 8

Allowance retained with anna = 18

This situation can be expressed by the equation,

[tex]x-\frac{x}{2} +8=18[/tex]

Solving the above equation, we get,

[tex]\frac{x+16}{2} =18[/tex]

x+16=36

x=20

Therefore, her weekly allowance is $20.

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Samuel's order will ultimately cost $39.84.

One DVD Samuel purchased cost $9.96.

He purchased four DVDs in total.

as a result, his total outlay will be 4 * 9.96 = $39.84.

The 7.75% sales tax that must be paid is disclosed to us.

Adding 7.75% to $39.84 yields

39.84 x 7.75/(100) (100)

= $3.0876

Consequently, the total amount of tax due is $3.0876.

Using 25% of 39.84 to calculate a 25% discount,

39.84 x 25/100

= 996/100

=$9.96

Consequently, the total discount on the total of $39.84 will be $9.96.

as a result, the updated purchase price will be,

39.84-9.96

=$29.88

adding the tax to the updated price,

9.96+29.88

= $39.84

Consequently, Samuel's order will ultimately cost $39.84.

One must compute percentage in order to determine the proportion of a whole that is stated in terms of 100. A percentage can be determined using one of two methods:

using the unitary method.

by changing the fraction's denominator to 100.

It should be noted that the second method of percentage computation is not used when the denominator is not a factor of 100. In these circumstances, we make use of the unitary approach.

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The corn's height when the fertilizer was applied is 13 centimeters and it grows at a rate of 13 centimeters each day.

The equation that is given is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

A linear equation increases or decreases at a constant rate. When a linear equation is drawn on a graph, it is a straight line that curves either upward or downward.

A linear equation usually has this form y = mx + b

Where:

H = 13 + 13t

Where:

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Answer:

16.4

Step-by-step explanation:

The time is irrelevant to the problem

fraction42 *20.5= 16.4

Hope this helps

Answer: 18: 18, 36, 54, 72, 90
20: 20, 40, 60, 80, 100
16: 16, 32, 48, 64, 80

32: 32, 64, 96, 128, 160

Step-by-step explanation:

multiply each number by 1 2 3 4 5 respectivly to get the answer.

Answer:

a = h/2 would be the answer.

Step;-

Find slope:-

m = rise/run = (16-8)/(8-4) = 8/4 = 2

Now,

y = mx + b

or, 8 = 2(4) + b

so, b = 0

So,

y = mx + b

or, h = 2a + 0

so, h = 2a

hence,a = h/2.

The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age [tex]a = \frac{h}{2}[/tex]

Hello!

First, let's analyze these two quadrilaterals:

• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.

Let's try to solve it using the lines AB and AB':

• The measurement of the ,line AB is 14 units,.

• The measurement of the ,line AB' is 7 units,.

Knowing it, let's write the scale factor as:

Answer: alternative D.

The total distance from his highest point to his lowest point is 21.8 feet.

Height H climbed by Zack and Zane is 14.6 feet.

The depth D underwater that Zack got down to is 6.8 feet.

The distance between the highest and the lowest point can be found by assuming the coordinates axis.

Let us assume the origin is on the water surface,

So, going by this logic, highest point is at +14.6 feet.

The lowest point is at -6.8 feet.

The distance L between lowest and highest point is,

L = H - D

L = 14.6 -(-6.8) feet

L = (14.6 + 6.8) feet

L = 21.8 feet

So the distance L is 21.8 feets.

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Answer: x = 77 - 2y    y = -x/2 + (77/2)

Step-by-step explanation:

All pairs of parallel segments are given below.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Given,

a) Line segment = AC and FD

Parallel = AC ║FD

b) Line segment = AE and BD

Parallel = AE ║BD

c) Line segment = EC and FB

Parallel = EC ║FB

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a. Inadequate chlorine levels cause cloudy or creamy swimming pool water.

b. Even though water represents the most ample substance on the planet, it is rarely encountered in its pure form in nature.

Part a: Cloudy or milky pool water is ended up causing by seven major issues: insufficient chlorine, an imbalanced pH and alkalinity, extremely high calcium hardness (CH), a faulty or clogged filter, and the initial phases of algae, ammonia, as well as debris.

Methods for Cleaning Cloudy Pool Water

Part b: A swimming pool mixture of water as well as chlorine is made reference to as a homogenous mixture even though water and chlorine cannot be separated back to one‘s distinct materials once mixed together.

Because chlorine as well as water diffuse between each other, they cannot be kept separate into their pure forms again.

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The probability of selecting two students has 10 ways

Total number of students = 5

Only two students can be selected for the conference who are equally qualified.

The probability that the first two students selected alphabetically is derived from the combinations.

Therefore, the final probability for selecting the students randomly is,

x = ⁵C₂

x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]

x = 10

Hence, the probability of selecting two students has 10 ways.

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The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given sum of the mixed number,

1 1/4 + 4 2/3

⇒ 1 + 1/4 + 4 + 2/3

⇒ 1 + 4 + 1/4 + 2/3

⇒ 5 + 1/4 + 2/3

Take LCM of 1/4 and 2/3 as 12.

⇒ 5 + (3 + 8)/12

⇒ 5 + 11/12 = 5 11/12

Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".

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Answer:

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

Step-by-step explanation:

We have to find the GCF (Greatest common factor) of 135 , 225 and 315.

          135 = 5 * 3 * 3 * 3 = 45 * 3

          225 =  5 * 5 * 3 * 3 = 45 * 5

          315 =  5 * 3 * 3 * 7 =  45 * 7

GCF = 5 * 9 = 45

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

Answer:

Ages are as follows:
Father: 40

Mother: 37

Son: 11

Each twin daughter: 6

Step-by-step explanation:

Interesting puzzle!

Let

F denote the age of the father

M the age of the mother

S the age of the son

D the age of each of the twin daughters

Total of all ages is

F + M + S + 2D = 100  [1]

We also have

F + S = 51   ==>  S = 51- F    [2]

F - M = 3    ==>  M = F - 3    [3]

S - D = 5 ==> D = S -5  [4]

==> D = (51-F) -5  

==> D = 46 - F         [5]

Substitute this in equation [1] to get

We now have everyone's age in terms of the father's age F

Substituting each of equations [2], [3]  and [5] into [1] we get one equation in terms of F

F + (F-3) + (51-F) + 2(46-F) = 100

(F + F - F -2F ) + (-3 + 51 + 92) = 100

-F + 140 = 100

- F = 100 - 140

-F = -40

or

F = 40

From [3]

M = F - 3 = 40 - 3 = 37

From [2]

S = 51 - F = 51 - 40 = 11

From [4]

D = S - 5  = 11 - 5 = 6

Verify:

F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100

Step-by-step explanation:

a = father age

b = mother age

c = son age

d = daughters age

1. a + b + c + 2d = 100 (don't forget : twin-daughters)

2. a + c = 51

3. a = b + 3

4. d = c - 5

we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.

once we have that, we can use again the equations 2-4 to solve for the other variables.

2. tells us that

c = 51 - a

3. tells us that

b = a - 3

4. and 2. tells us that

d = c - 5 = (51 - a) - 5 = 46 - a

with that we get in 1.

a + (a - 3) + (51 - a) + 2(46 - a) = 100

a + a - 3 + 51 - a + 92 - 2a = 100

2a - 3a + 48 + 92 = 100

-a + 140 = 100

-a = -40

a = 40

b = a - 3 = 40 - 3 = 37

c = 51 - a = 51 - 40 = 11

d = c - 5 = 11 - 5 = 6

so, the father is 40 years old

the mother is 37 years old

the son is 11 years old

both of the twin daughters are 6 years old.

Step-by-step explanation:

(2x² + 3x+8) (x²-x-4)

= (2x² + 3x+8) (x² +-x²+-4)

= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)

= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32

=2x⁴ + x³ - 3x² - 20x - 32

Answer:

[tex](x-5)^2=4(y+2)[/tex]

Please note that alternative forms of this equation (vertex and standard) are in the explanation.

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

Given:

Therefore:

Calculate p:

[tex]\implies -2+p=-1[/tex]

[tex]\implies p=-1+2[/tex]

[tex]\implies p=1[/tex]

Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:

[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]

[tex]\implies (x-5)^2=4(y+2)[/tex]

In vertex form:

[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]

In ax² + bx + c form:

[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]

Graph f(x)=14.

Plot each graph on the same coordinate system.

f(x)=14x

image of graph

Step-by-step explanation:

slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

we have

2x + 3y = 15

3y = 15 - 2x

y = (-2/3)×x + 5