What rational number represents a drop of ​ 4/14

In the picture, there is a graph. The equation of the line y=2x+4. Option-B is correct.

Given that,

In the picture, there is a graph.

We have to find the equation of the line.

From the graph we can see there are points.

The point are (1,6) and (-2,0)

So,

The formula for equation of the line is y-y₁=m(x-x₁)

We have to find the m value

The slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=(0-6)/(-2-1)

m=-6/-3

m=2

Now,

Take a point (-2,0)

y-0=2(x+2)

y=2x+4

Therefore, the option-B is correct, the equation of the line is y=2x+4.

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The height of tulip can be expressed by expression f(n)=3n-1

A mathematical expression is made up of a statement, at least one arithmetic operation, and at least two integers or variables.

Mathematical expression components:

a) Constant: a fixed numerical value

b Variables: They don't accept any predetermined values. Values are assigned based on the criteria.

c)Terms: Constants, variables, or constants multiplied by variables are all acceptable terms (s).

d) Operators:The four operations of addition (+), subtraction (-), multiplication (-), and division (-) are referred to as operators because they are employed to combine the components in an equation.

Given:

1. f(n)=3n-1

after 1 week (n=1)

f(1) = 3*1-1

f(1) = 2 in

After 2 week (n=2)

f(2) = 3*2-1

f(2) = 5in

After 3 week (n=3)

f(3) = 3 *3-1

f(3) = 8in

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Answer:

Thats nice

Step-by-step explanation:

We are given that Mike has $36, if he spends 1/3 of this amount, the amount spent is the product of 36 and 1/3, that is:

Therefore, he spends $12 on the movie.

Now we are told that he spends 2/9 of the money, therefore, he spent:

In total, he spent $8 on the sandwich.

The money he has left is:

Therefore, he can't buy an $18 dollars book.

The system represents a straight graph.

The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.

Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross). * Before you begin, rearrange the equations so they will read "y =".

The given system of equations indicate a linear equation .

This means that after solving this we will get a straight line slope whose value can be calculated by the formula tan theta = height / base

Thus the system represents a straight graph .

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Answer:

B

Step-by-step explanation:

Step-by-step explanation:

answer is explained in my working. hope it helps

The amount of savings Oscar will save is $30.00

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Oscar wants to spend and save money he earns

For every $ 7 , The amount of money Oscar saves = $ 3

So ,

For every $ 70 , the amount of money Oscar saves =
For every $ 7 , The amount of money Oscar saves x 10

And ,

For every $ 70 , the amount of money Oscar saves = $ 3 x 10

                                                                                     = $ 30

Hence , for every $ 70 Oscar puts in his wallet he saves $ 30

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Answer:

  a) 21,600 square miles

  b) the map will be reduced to 50% of its original size. 1 in = 60 miles

Step-by-step explanation:

You have a 4-in by 6-in map of a park with a scale of 1 in : 30 miles, and you want to know the actual area of the park, the reproduction factor to fit the map in 6 square inches, and the new scale of the map at that size.

The 4-inch dimension of the map corresponds to an actual length of ...

  (4 in)(30 mi)/(1 in) = 120 mi

Similarly, the 6-inch dimension represents ...

  (6 in)(30 mi)/(1 in) = 180 mi

The area of the park is the product of its dimensions:

  (120 mi)(180 mi) = 21,600 mi²

The area of the park is 21,600 square miles.

The area of the current map is (4 in)(6 in) = 24 in². The ratio of the reduced area to this original area is the square of the reduction scale factor:

  k² = (6 in²)/(24 in²) = 1/4

  k = √(1/4) = 1/2

The map must be reproduced at 1/2 its original size.

At this scale, the scale of the map is ...

  (1/2 in) : (30 mi) = (1 in) : (60 mi)

It will be 1 inch for every 60 miles.

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The value of the ratio (6/12) is 0.5, of (32/10) is 3.2 and that of (225/150) is 1.5.

As per the question statement, we are provided with three ratios, (6/12), (32/10) and (225/15).

We are required to calculate the values of the above mentioned ratios.

To solve this question, we need to simplify the ratios, and then divide their numerators by their denominators, to obtain our desired answers.

Therefore, (6/12) = [6/(6 * 2)] = (1/2) = 0.5

Similarly, (32/10) = [(16 * 2)/(5 * 2)] = (16/5) = 3.2

And finally, (225/150) = [(75 * 3)/(75 * 2)] = (3/2) = 1.5

       (a : b), or as a fraction of (a/b) both of which are equivalent.

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You have to plug 30 in for x

13.00 + 0.10(30)

13 + 3

$16

Answer:

125=50+25n

Step-by-step explanation:

The inequalities are solved below

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. The notation a b indicates that an is less than b, while a > b indicates that an is more than b, among other distinct notations used to denote various types of inequalities. The notation a b indicates that a and b are not equal; this inequality is occasionally referred to as a type of stringent inequality. It doesn't even specify that a and b must be members of an ordered set, nor does it state that one is superior to the other.

The inequalities are

13y>9

or, y>9/13

and

2y-6>2

or, 2y>2+6

or, y>8/2

or, y>4

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It will take Mary 3.6 months (The period will occur in April.) from January to pay off her bill of $70 if she continues to pay $20 per month.

The period Mary will take to pay off her credit card balance is determined using an online finance calculator.

The input data required includes the interest rate, the present value of the bill, and the periodic payments.

I/Y (Interest per year) = 16%

PV (Present Value) = $70

PMT (Periodic Payment) = $-20

FV (Future Value) = $0

Results:

N = 3.608

Sum of all periodic payments = $-72.16

Total Interest = $2.16

Thus, Mary requires 3.6 months to pay off her credit card balance, which will occur in period 4 from January.

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Analyzing the square and finding expressions for length, area, and volume.

A. Expression for length = (20-2x)cm

B. Expression for area = [tex](20-2x)^{2}[/tex]

C. Expression for the area of tray base if x=3 : 196 cm^2

D. Volume of the tray if x=3: 2744 cm^3

A square piece of a tin of side length 20 cm has four squares of side length x cm removed from each corner. the sides are folded up to form a tray.

Since the side of x has been removed from each corner, that means, 2x length has been removed from 20 cm.[tex](20-2*3)^{2} =(20-6)^{2} = 14^{2} = 196[/tex]

So, the length of the tray base will be ( 20 - 2x ) cm.

The area of the square is given by [tex](side)^{2}[/tex]

So, the area of the base of the tray = [tex](20-2x)^{2}[/tex]

Expanding the expression, [tex](a+b)^{2} =a^{2} + b^{2} + 2ab[/tex]

Now, [tex](20-2x)^{2} = 400 + 4x^{2} -80x[/tex]

Area of the tray base if x=3, Area (x=3) =[tex]400 + 4(3)^{2} -80*3 = 400 +36- 240 = 196 cm^{2}[/tex]

Now, Volume = [tex](side)^{3}[/tex]

Volume = [tex](20-2x)^{3}[/tex]

Volume (when x = 3) = [tex](20-2x)^{3}= (20-2*3)^{3}=(20-6)^{3} = 14^{3} =2744 cm^{3}[/tex]

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Answer:

The correct answer is D. -8<535

Step-by-step explanation:

In a math perspective, -8 < 535. Done

Otherwise, the elevations of the lowest and highest points start from below sea levels up to land and so on. Since negative numbers here are feet below the sea level, we went from New Orleans up. So D.

If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75

Ronald sold 52 packages of home-made brownies.

He earns a total profit of $195.00

Profit from 52 packages = 195

Profit from 1 brownie package = 195/52 = 3.75

If he sells all 125 brownie packages

Total profit he can expect = profit from one brownie x 125 brownie packages

= 3.75 x 125

= 468.75

Therefore, If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75

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Infinitely many solutions

1) Given the equations, y =2/3x +6 and 2/3x +6

y=2/3x +6

y= 2/3x +6

2) As we have the same equation, then there will be infinitely many solutions since each and every point of line I belongs to line (II)

3) Hence, the answer is Infinitely many solutions

It would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.

Speed is the rate at which an object moves along a path in time, whereas velocity is the rate and direction of an object's movement. In other words, speed is a scalar value, whereas velocity is a vector.

For example, 50 km/hr (31 mph) describes the speed at which a car travels along a road, whereas 50 km/hr west describes the velocity at which it travels.

We have given the speed 20km/h

the distance to cover is 18km

The formula for time is

t = D/S

where,

t is time

D is distance

S is speed

Substituting the values we get

t = 0.9 hours

t = 54 minutes

Thus, it would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.

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A year ago: 80 pounds

This year: 92 pounds

Yearly increase: 92 - 80 = 12 pounds

The percentage increase in weight will be taken with respect to 80 pounds. Then:

y = 1/2x + 8



y = cx + 10

In the system of equations above, c is a constant. If

the system has no solution, what is the value of c?

so, y=y

this equation is indefinde when 1/2 - c= 0, there is not value for x that makes the equation true

so, the value of c =0.5

The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.

Based on the given conditions, formulate,

The speed, s, is measured in miles per hour, and distance, y, is measured in yards.

The regression line is given by,

Å = 5.32 + 46.73s       (Equation-1)

Then find,

The slope and y-intercept of the regression line.

The general form of linear regression line is

A linear regression line has an equation of the form Y = a + b x, where x is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

y = a + b x            (Equation-2)

where x is variable. In the given equation the variable is denoted by s.

On comparing Equation-1 and Equation-2,

We can write,

a = 46.73

b = 5.32

It means slope is 5.32 and y-intercept is 46.73.

The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed.

The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.

Therefore,

The slope, b = 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. The y-intercept, a = 46.73, is the distance estimated by this model if the speed is zero miles per hour.

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By the concept of quadratic equation the oldest parent has 49 years and the other is 43 years.

Any equation that can be written in standard form as where x stands for an unknown, a, b, and c are known values, and a 0 is an algebraic term is known as a quadratic equation. A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible. A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. A curve known as a parabola makes up the quadratic function graph.

Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.

We know that:

x + y = 92

x × y = 2107

Now we have a system of equations that we need to solve:

The first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:

x = 92 - y

Now we can replace it in the second equation and find the value of y.

x × y = 2107

y × (92 - y) = 2107

92y - y² = 2107

Now we need to solve a quadratic equation!

-y² + 92y - 2107 = 0

so we have two solutions:

y = (-92 + 6)/(-3) = 43

y = (-92 - 6)/(-2) = 49

Because y is the oldest one, we need to take the biggest solution, this is y = 49.

So the oldest parent has 49 years.

If you want to find the age of the other parent, replace this in the first equation:

y + x = 92

49 + x = 92

x = 92 - 49

= 43

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(a) Recall the definition of the step function,

[tex]\theta(t) = \begin{cases} 1 & \text{if } t \ge 0 \\ 0 & \text{if } t < 0 \end{cases}[/tex]

Then we have

• [tex]\theta(t-2) = 1[/tex] if [tex]t-2\ge0[/tex], or [tex]t\ge2[/tex]

• [tex]\theta(t-3) = 1[/tex] if [tex]t-3\ge0[/tex], or [tex]t\ge3[/tex]

and we can combine these to get

[tex]\theta(t-2) - \theta(t-3) = \begin{cases} 1 & \text{if }2\le t < 3 \\ 0 & \text{if }t<2 \text{ or } t\ge3 \end{cases}[/tex]

then scale up by 4 to get the value we want over [2, 3].

[tex]f(t) = \boxed{4\bigg(\theta(t-2) - \theta(t-3)\bigg)}[/tex]

At least that's what I get using the aforementioned definition of "step function". I don't see a way to have both [tex]f(2)=4[/tex] and [tex]f(3)=4[/tex] with this definition...

(b) No function was given...

Answer:

8

Step-by-step explanation:

Vertical angles are congruent.  That means that they have the same measurement.  Set them equal to each other and solve for x

x = 4x - 24  Subtract x from both sides of the equation

o = 3x - 24  Add 24 to both sides

24 = 3x  Divide both sides by 3

8 = x

m<A is 8

Answer:

D

Step-by-step explanation:

av= absolute value

av of 238 = 238

av of -28 = 28

av of -14 = 14

238 (+) 28 (-) 14 = 252

238 + 28 = 266

266 - 14 = 252

therefore 252 is the correct answer

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