Which quantity is best modeled by a linear function?
A the area of a square as a function of the side length
the height of a ball thrown into the air as a function of time
the number of seconds as a function of the number of hours
the height of a reflector on a rotating bike tire as a function of time

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

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 10th score should be 9.5 for the mean to be 5.

The mean value is the average value of the given data.

According to the given question  the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.

The total average score for 9 games is

= ( 9 × 4.5 )

= 40.5.

The total average score for the mean to be 5 in 10 games is

= ( 10 × 5 )

= 50.

∴ The 10th score must be ( 50 - 40.5 ) which is

= 9.5.

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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)

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?

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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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

Step-by-step explanation:

they are different because the first equation only ax is in absolute but in the second equation both ax and b are in absolute, so we could solve them differently.

Answer:

it should be b.

Step-by-step explanation:

2 rare coins will make them $100 each month. There are 12 months in a year.

12 × 2 = 24 months

so $100 × 24 months will give us 2400.

Then Mario purchases 3 coins making it cost $150 ($50 + $50 + $50)

2400 + 150 = 2550

Brainliest plss :,)

The equation of a line in slope-intercept form is  [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .

The equation of the line is given below using the slope-intercept method:

y = mx + c

where,

m = the slope of the line

c = y-intercept of the line

(x, y) represent any point on the line

To find the Slope of a line that passes through the points (2, 4) and (3, -4).

m₁ = change in y/change in x

    = y₂ - y₁ / x₂ - x₁

    = Δy/Δx

   = [tex]\frac{-4-4}{3-2}[/tex]

   = [tex]\frac{-8}{1}[/tex]

   = -8

Now, we find the slope of the line perpendicular to the line with the slope -8.

m₂ = -1 / m₁

    = -1 / -8

    = 1/8

So, the slope of the line is 1/8.

Next, we find the equation of a line that passes through the point (1, -5) and has a slope of 1/8.

⇒ y - y₁ = m( x- x₁)

⇒ y + 5 = [tex]\frac{1}{8}[/tex] (x - 1)

Multiplying by 8 on both sides of the equation we get and then solving

⇒ 8y + 40 = x - 1

⇒ 8y = x - 41

 ⇒ [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex]

Therefore, the equation in slope intercept form is  [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .

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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: domain is x and range is y

Step-by-step explanation:

Answer:

Domain: {2, 8, 30, 46}
Range: {-1, 9, 16}

Step-by-step explanation:

The domain of a function y = f(x)  is the set of all values that the input values (x) that the function can accept. The range of a function is the set of all output values that the function can produce from the domain values ie the set of all  values

Looking at the figure, the set of all x values that the function y can take are
{2, 8, 30, 46} and this is the domain

The output values produced from this domain are {-1, 9, 16} and that is the range

An inflationary gap occurs when the  SRAS curve and the AD curve intersect Right of the potential GDP line.

With the help of the short-run aggregate supply curve (SRAS), we can understand how each firm in an economy reacts to price stickiness. The SRAS curve will slope upward when prices are volatile. The SRAS curve illustrates that higher price levels lead to increased output.

The demand for and supply of every good and service an economy produces are the main topics of discussion. As a result, the demand for all distinct goods and services is also combined and is known as aggregate demand.

The price level of goods and services would then rise (naturally or as a result of government intervention) to compensate for the increased demand as well as an insufficient supply when an inflationary gap occurs. This price increase is known as demand-pull inflation.

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Answer:

The debt-equity ratio is  0.726 : 1 or 72.64%

Debt is the product of debt ratio and total equity

Debt = debt ratio × total equity

We have been given that

Asset turnover = 1.84

Profit margin = 5.1%

Return on equity of 16.2 percent

Let we have to assume that sales are $100.

Therefore net Income = 100×0.051 = 5.1

Total Assets = 100/0.84

Total Assets = 54.35

⇒ 0.162 = 5.1 / Total equity

⇒ Total Equity = 5.1 / 0.162

⇒ Total Equity = 31.48

Total assets = Total debt + Total equity

⇒ 54.35 = Total debt + 31.48

⇒ Total debt = 54.35 - 31.48

⇒ Total debt = 22.87

The debt-equity ratio = 22.87 / 31.48

The debt-equity ratio = 0.72649 : 1 or 72.649%

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The equation of the sphere is

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

The standard form of the equation of the sphere is :

[tex](x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}[/tex]

Where A (a, b , c) is the center and r is the radius.

From the question we should first find the radius

r = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}[/tex]

Point = (x , y , z) = (8 , 3 , -3)

Center = (a, b , c)= (5 , 6 ,5)

Substituting it in the formula

r = [tex]\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }[/tex]

By further calculation

r = [tex]\sqrt{9+9+64}[/tex]

So, we get

r =[tex]\sqrt{82}[/tex]

Substituting it in the standard form

[tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}[/tex]

[tex](x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82[/tex]

[tex]x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82[/tex]

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0[/tex]

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

Therefore, the equation of the sphere is

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

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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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Answer:

f(8) = 108

Step-by-step explanation:

Hello!

Substitute 8 for x in the equation.

f(8) is 108.

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

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]

The equation is simplified as [tex]x^{16}=x^{16}[/tex].

The given equation is [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex].

We need to simplify and explain the equation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Use the exponent rule [tex]a^m . \ a^n=a^{m+n}[/tex] to simplify the given equation.

Now, [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex]

⇒ [tex]x^{12+4}=x^{8+8}[/tex]

⇒ [tex]x^{16}=x^{16}[/tex]

The exponents of both the sides of equation are the same.

Therefore, the equation is simplified as [tex]x^{16}=x^{16}[/tex].

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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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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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Step-by-step explanation:

1/2 + 1/4

2/4 + 1/4= 3/4

1 - 3/4 = 1/4 is left

Answer:

There is 1/4 left

Step-by-step explanation:

Find the amount of cake left.

The entire cake is 1

1-1/2 - 1/4

Get a common denominator of 4

1 *4/4 = 4/4

1/2 *2/2 = 2/4

Using the common denominator

4/4 - 2/4 - 1/4

2/4 - 1/4

1/4

There is 1/4 left

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:

Starting paragraphs:

My name is _______. I was born on a cloudy night on the ___ of _______, _____ in ___________ . My parents were very happy as they had been blessed with a baby boy/girl, and that girl/boy is me!

1 year passed by and my 1st birthday was celebrated with much joy and it turned out to be a super extravagant event.

I do not remember much of my early childhood but my parents said that I was a very active, curious and a communicative child. I would ask dozen of questions each minute, without waiting for the answers. I suppose that's why my parents offered me books as early as my third birthday.

Ending paragraph:

I am thankful for my parents, teachers and friends for making me the person who I am today.

Explanation:

Compose your autobiography with the help of the following points:

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:0.4875.

Step-by-step explanation:

Answer:

0.48750

explanation:

The money in dollars that must be put in this cd in order to have $5,000 in 3 years is $4,081.63

The formula for simple interest and procedure we will use to solve this exercise is:

A = P {1 + [(R/100) * T]}

Where:

Information about the problem:

Applying the simple interest formula and isolating the principal (P), we get:

A = P {1 + [(R/100) * T]}

$5,000 = P {1+[(7.5/100) * 3]}

$5,000 = P [1+(0.075*3)]

$5,000 = P (1+0.225)

$5,000 = P (1.225)

P = $5,000/ 1.225

P = $4,081.63

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

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