The objective of __________ research is to gather preliminary information that will help define the problem and suggest hypotheses.

x = 20+ 3y

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

Jame = x

Brittany  = y

x = 20+ 3y

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Answer:

64

Step-by-step explanation:

[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]

Answer:

64

Step-by-step explanation:

first 3 x 4 = 12

12+52=64

There are 5354 people were in the arena.

Percentage:

The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

The formula for calculating the percentage is,

Percentage = (Actual value/Total value) x 100

Given,

Here we have that, 4550 men in the arena comprised 85% of the people in the arena.

Now we need to find how many people were in the arena.

Let p be the number of people in Arena.

So, based on the percentage formula,

It can be written as,

=> 85% = (4550 / p) x 100

=> 85/100 = 4550 /p

=> 0.85 = 4550/p

=> 4550/0.85 = p

=> p = 5354

Therefore, there are 5354 people were in the arena.

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f(x) + k will shift the graph up k units.

For example, the notation f(x) + 5 will shift the curve up by 5

If k is negative, then the curve shifts down that amount

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

f(x-h) shifts the graph to the right h units

Example: f(x-2) shifts to the right 2 units

Another example: f(x+7) shifts left 7 units. In this case, h = -7

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

y = -f(x) is a reflection over the x axis

This is because we're multiplying each y coordinate by -1

A point like (1,2) reflects to (1,-2)

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

10) -6(-5+r) = 102

     30 -6r =102

     -6r = 72

        r = -12

11) -1 = x - 4 +4

      x =-1

12) 0 = -6x -2x

     -8x = 0

 x= 0

13)5n+ 4n =9

      n =1

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The temperature at midnight is -8°C.

Let the initial temperature be x.

It should be noted that there are 7 hours between midnight and 7am.

Therefore, the equation will be:

x + (1.1 × 7) = -0.3

x + 7.7 = - 0.3

x = -0.3 - 7.7

x = -8

The temperature at midnight is -8°C.

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Answer:

length = 90

width = 55

Step-by-step explanation:

Let W = width.

Let L = length.

L = W + 35

P = 2(W + L)

290 = 2(W + W + 35)

4W + 70 = 290

4W = 220

W = 55

L = W + 35 = 55 + 35 = 90

The height of the frame is 1 m and the width is 1.5 meters.

The height and width are the two dimensions that are used to measure the perimeter of a rectangular frame.

The perimeter is defined as the sum of all sides of a polygon. For a rectangle it is equal to twice the sum of height and width.

Perimeter(p)=2×[height(h)+width(w)]

The given dimensions of the frame is that the height is [tex]\frac{2}{3}[/tex] the width.

Let us consider the width be x.

Hence height=[tex]\frac{2}{3} x[/tex]

Now perimeter =

[tex]2\times(x+\frac{2}{3}x) \\=\frac{10}{3} x[/tex]

But the given perimeter is 5 meter.

Therefore:

[tex]\frac{10}{3} x=5\\or,x=5\times 3\div 10\\or,x=1.5[/tex]

Therefore the width is 1.5 meters.

Height=[tex]\frac{2}{3} \times 1.5\\[/tex]=1 meter.

So we can conclude that the width is 1.5 meters and the height is 1 meter.

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Answer:

Answer:

Step-by-step explanation:

no. of emergency kits = x

bottles per kit = 5

total no. of bottles = 5x

which means,

5x = 125

125/5 = x

x = 25

The angles are 19;  101

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

Given:

x+4, 9x-34

As, the lines are parallel

x+4 + 9x -34 = 180

10x + 30 = 180

10x = 150

x= 150/10

x=15

Hence, the angles are x+4 = 19; 9x-34 = 135 - 34 = 101

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Answer:

[tex] \frac{ \sqrt{2} }{2} \: or \: 0.7071[/tex]

Step-by-step explanation:

[tex] \sin(135) = \frac { \sqrt{2} }{2} \: or \: 0.7071 [/tex]

Answer:0.4875.

Step-by-step explanation:

Answer:

0.48750

explanation:

There are 98.4252 inches in 2.50m.

Unit Conversion is defined as a process that involves multiplication and division by a numerical factor or a particular conversion factor.

For Example .Convert 2m into cm.

As we know that 1m=100cm

multiplying both sides by 2 we get

2m = 200 cm.

According to the question

It is given that 2.54 cm = 1 inch

[tex]1cm = \frac{1}{2.54} inch[/tex]

[tex]100cm=\frac{100}{254} inch[/tex]

[tex]1m = \frac{100}{2.54}[/tex] ( as 100cm = 1m)

we need 2.50 m So we multiply both sides by 2.50

[tex]2.50m=\frac{2.50*100}{2.54} \\\\ 2.50m=\frac{250}{2.54}[/tex]

[tex]2.50m=98.4252 inch[/tex]

Therefore , there are 98.4252 inches in 2.50m.

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Answer:

1 hour and 4 minutes

Step-by-step explanation:

Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.

As given,

Simple interest amount earned by Elsa = $37

Annual interest rate R= 4%

Time T =6 months

Let P be the principal amount she put while opening account

Simple interest = (P × R × T) / 100

⇒37 ={P × 4 × (6/12)}/100

⇒P =(37 × 100) / 2

     = $1850

Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.

The complete question is:

Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after  6 months. How much money did she put in the account when she opened it?

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The grade level is treated as categorical when a principal wants to know the number of students from each grade will be participating in a performance.

Variables can be classified into quantitative and categorical. Quantitative variables are those which carry numerical values. Even though a person's grade in school is generally identified by a number, it is a categorical variable. Categorical variables classify data into different groups as the grade level. The grade level categorizes students into different grades and each grade level represents a particular grade only.

Any variable which is partly qualitative and represents groups of data are called categorical variables. Also grade level is ordinal. An example of a situation in which grade level is treated as categorical is when a principal wants to know how many students from each grade will be participating in a performance. Other examples of categorical variables are race, gender, age group, etc.

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The equation of the line from the given points marked on the graph is:

3. 3x+y+5=0

4. 3x+y+3=0

Given,

3.The points are:

(-1,-2) and (1,-8)

let the points be :

(-1,-2) = (x₁,y₁)

and (1,-8) = (x₂,y₂)

The equation of the line passing through the points (-1,-2) and (1,-8)

x - x₁/x₂-x₁ = y - y₁/y₂-y₁

For the given points, the equation is:

x-(-1)/1-(-1) = y-(-2)/-8-(-2)

x+1/2 = y+2/-6

-6(x+1) = 2(y+2)

-6x-6=2y+4

-6x-2y-6-4=0

-6x-2y-10=0

-2(3x+y+5)=0

3x+y+5=0 is the equation of the line.

4.The points are:

(-3,6) and (3,0)

let the points be :

(-3,6) = (x₁,y₁)

and (3,0) = (x₂,y₂)

The equation of the line passing through the points (-1,-2) and (1,-8)

x - x₁/x₂-x₁ = y - y₁/y₂-y₁

For the given points, the equation is:

x-(-3)/3-(-3) = y-6/0-6

x+3/6 = y-6/-6

-6(x+3) = 2(y-6)

-6x-18=2y-12

-6x-2y-18+12=0

-6x-2y-6=0

-2(3x+y+3)=0

3x+y+3=0 is the equation of the line

Hence we get the required equations of the line.

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Work Shown:

[tex](x_1,y_1) = (-13,2) \text{ and } (x_2,y_2) = (-17,9)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{9 - 2}{-17 - (-13)}\\\\m = \frac{9 - 2}{-17 + 13}\\\\m = \frac{7}{-4}\\\\m = -\frac{7}{4}\\\\[/tex]

A slope of -7/4 means that we move down 7 and to the right 4.

Answer:

x = 1/2, y = 1

Step-by-step explanation:

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

x = ¹/₂

y = 1

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]

Multiply the second equation by 3:

[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]

[tex]\implies 18x-3y=6[/tex]

Add this to the first equation to eliminate the term in y:

[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]

Solve for x:

[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]

Therefore, the solution to the given system of equations is:

x = ¹/₂ and y = 1

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Answer:

My prediction of the sum is 0.

Hope this helps :)

Step-by-step explanation:

It is 0 because if you owe 2 dollars and you pay it back with 2 dollars then you have 0 dollars owed.

--------------------> 2nd: 2 (positive two - move right)

<-------------------- 1st: - 2 (negative two - move left)

<----------l----------l-----------l----------l----------l--------->

-2 -1 0 1 2

Answer:

f(8) = 108

Step-by-step explanation:

Hello!

Substitute 8 for x in the equation.

f(8) is 108.

Answer:

3.5 un

Step-by-step explanation:

to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7

this is basically dividing 24.5 by 7

24.5 / 7 = 3.5

that is your answer

The monthly installments need to be paid is $10995.

To determine the number of months needed to pay off the remaining balance. We need to know the monthly installment.

When you get an installment loan, you get the money you borrowed or the item you bought right away.

Now, as per the question;

Amount paid in cash = $1500

Remaining balance which is to be paid as monthly installments

= $12495 - $1500

=$12495 − $1500

=$10995

Thus, the monthly installments are $10995.

Now, to determine the number of months needed to pay off the remaining balance. The monthly installment is need to be known.

As a result, information on monthly installments is lacking.

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The complete question is-

What necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing$12,495?

The amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the amount of 5% lemon juice mixture that is needed to be mixed be represented by x, then the amount of 20% lemon juice mixture will be represented by (42-x), because the total mixture is needed to be 42 liters.

Now, given that George wants 42 liters of a mixture of water and 15% lemon juice with a mixture of 5% lemon juice, and a mixture of 20% lemon juice. Therefore, we can write,

5% of x + 20% of (42-x) = 15% of 42 liters

0.05x + 0.2(42 - x) = (0.15×42)

0.05x + 8.4 - 0.2x = 6.3

0.05x - 0.2x = 6.3 - 8.4

-0.15x = -2.1

x = -2.1 / -0.15

x = 14

Further, the amount of mixture of lemon juice that is needed to be mixed can be written as,

Hence, the amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.

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Derivatives are essential for solving calculus and differential equation problems then the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]

The rate of change of a function with respect to a variable in Mathematics. Derivatives are essential for solving calculus and differential equation problems.

Given a traditional unbent position, f(x) = kx + d, where k is the pitch and (0, d) is the y-intercept.

a) Consider our position at two distinct points first:

f(x) = kx + d

f(x + h) = k(x + h) + d = kx + kh + d

Evaluate the derivative, then

[tex]$\lim h \rightarrow x \frac{f(x+h)-f(x)}{h}[/tex]

substitute the values in the above equation, we get

[tex]$&=\lim h \rightarrow x \frac{(k x+k h+d)-(k x+d)}{h} \\[/tex]

simplifying the above equation, we get

[tex]$&=\lim h \rightarrow x \frac{k h}{h} \\[/tex]

[tex]&=\lim h \rightarrow x k \\[/tex]

= k

Therefore, the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]

b. Since the actual function is linear, its part is all real numbers by definition.

c. Since the product is a constant function, its part is all real digits by meaning.

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