What is the equivalent equation to the given equation?
x = x² - 20

Answer:

==============

Since both points have same x-coordinate, the distance between them is the difference of y-coordinates:

Correct choice is D

Answer:

32 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Define the two given points:

Substitute the two points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]

[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]

[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]

[tex]\implies d=\sqrt{32^2}[/tex]

[tex]\implies d=32[/tex]

Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:  

[tex]\implies 8 - (-24) = 8+23=32[/tex]

The distance from Kano to Lagos is 1200 km

The problem involves addition of fractions

The fraction required are:

let the distance form kano to Lagos be x

it was discovered that a driver has travelled 3/8 = 3x/8

another driver had travelled 3/10 of that distance = 3x/10

The drivers are still 390 km apart

total distance, x

x = 390 + 3x/8 + 3x/10

x - 3x/8 - 3x/10 = 390

0.325x = 390

x = 390 / 0.325

x = 1200 km

From the driving distance information 1200 km is the distance from Kano to Lagos

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Answer:

224 in²

Step-by-step explanation:

The formula for the area of a triangle is 0.5bh, where b is the base and h is the height. Here the base is '4t' and the height is '7t'. Subbing in 4 for t, we get

Base = 4(4) = 16

Height = 7(4) = 28

Subbing this values into our formula for the area of a triangle, and we have:

Area = 0.5(16)(28) = 224 in²

An integral graph with graph spectrum is the utility graph.The utility graph's adjacency, incidence, and graph distance matrices are displayed in the aforementioned graphs.

These technologies enable users to mathematically represent their ideas, dynamically link several representations, form hypotheses, and finally create totally new concepts.

Use a graphing utility

See attached file

 The value  of X in the interval  [0, 2π) are

X1=0

X2=π/2-----1.5708

X3=π------- 3.1416

Values of X  (0,1.5708,3.1416)

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Answer:

23/5 > (sqrt(18)

Step-by-step explanation:

there are many ways you could go about this,

I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

The total sector of a circle is 360°

The area of the sector of 270° is 37.68 square meters.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

We have,

The radius of the circle = 4 m

The total sector of a circle is 360°

The area of the sector with 270°.

= (270°/360°) x πr²

= 0.75 x πr²

= 0.75 x 3.14 x 4²

= 37.68

= 37.7 square meters

Thus,

The area of the sector of 270° is 37.68 square meters.

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Answer:   6

Step-by-step explanation:   You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.

Answer:

18

Step-by-step explanation:

using bodmas rule by working out brackets first

Answer:

Step-by-step explanation:

457-235= 222

222-125=97

97÷2= 48.5

≈49 pairs of pants and shoes

Answer:

The rate of change is -2

Step-by-step explanation:

formula we will use: G(x)= [tex]\frac{f(b)-f(a)}{b-a}[/tex]  [-1,2]

g(x)= [tex]x^3[/tex]-5x

g(-1)=[tex]-1^3[/tex]-5(-1)

g(-1)=-1+5

g(-1)=4

g(2)=[tex]2^3[/tex]-5(2)

g(2)=8-10

g(2)=-2

so g(x)= [tex]\frac{(-2)-(4)}{(2)-(-1)}[/tex]

g(x)= [tex]\frac{-6}{3}[/tex]

g(x)=-2

The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

Using changing the subject of formula to find the miles travelled;

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3

An algebraic expression consists of unknown variables, numbers and arithmetic operators.

Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.

Therefore,

(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32

2x = 2(-3) = -6

Hence,

- 32 / -6 = 5.3

Therefore,

(6x+3y) - z² / 2x when  x = -3, y = 4 and z = -6 is 5.3

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Answer:

Step-by-step explanation:

Answer:

the last one= It takes longer to fall because it experiences greater air resistance.

also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall

Answer: It takes longer to fall because it experiences greater air resistance.

A possible perimeter for the rectangular table that was built by Irene is 50 inches.

My thinking was gotten by getting the dimensions and then using the perimeter formula to solve it.

From the information given, it should be noted that the area of the rectangle is given as 114 square inches. A dimension that can give this is 19 inches and 6 inches

The perimeter of a rectangle is calculated as:

= 2(Length + Width)

= 2(19 inches + 6 inches)

= 2(25 inches)

= 2 × 25

= 50 inches

The perimeter is 50 inches.

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All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Birdseed that costs ​$0.67 a pound and sunflower seeds that cost ​$0.97 a pound. Angela​ Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for ​$0.79 per pound.

Assume that she used [x] pound and [y] pound of each type. We can write -

0.67x + 0.97y = 0.79 x 30

0.67x + 0.97y = 23.7

Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

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Step-by-step explanation:

Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.

The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].

= [tex]x^3(^\frac{8}{5}).x^4[/tex].

= [tex]x^\frac{24}{5}.x^4[/tex].

= [tex]x^\frac{24}{5}^{+4}[/tex].

= [tex]x^\frac{24 + 20}{5}[/tex].

= [tex]x^\frac{44}{5}[/tex].

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0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.

The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.

It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.

Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

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The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through    (-7, -7)

   [tex]y +7 = \frac{1}{2}(x +7)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  [tex]y = 3 \times 0 -9\\y = -9[/tex]

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   [tex]y = -9 \times 0 -68\\y = -68[/tex]

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    [tex]y = 5 \times 0 + 2\\y = 2[/tex]

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = [tex]\frac{1}{2}[/tex]

      The line passes through (5, -3)

     Point slope equation

       [tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]

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Step-by-step explanation:

your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.

and if you remember that a year has 365 days, then the rest is rant simple and straight forward :

8 cups per day

so

365 × 8 = 2920 cups per year.

2920 cups = 2920/16 = 182.5 gallons

therefore, she drinks 182.5 gallons of water per year.

Line l was translated down 8 units, is true for the transformation that took place.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,

We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.

Hence, Line l was translated down 8 units, is true for the transformation that took place.

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Solution :

[tex]\qquad \sf  \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]

( a log(x) = log(x^a) )

[tex]\qquad \sf  \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]

( log (a) + log (b) = log (ab) )

[tex]\qquad \sf  \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]

( log (a) - log (b) = log (a/b) )

A good point estimator for the population variance is: s².

A two-tailed test can be defined as a type of hypothesis test in which a rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution.

In Statistics, the basis of an inference about the population is usually used to determine statistical inference based on all of the statistics that are calculated from samples.

This ultimately implies that, the sample mean should be close to the population mean, the sample proportion should be close to the population proportion, and the sample standard deviation should be close to the population standard deviation.  

In this context, we can logically deduce that standard deviation (s²) is considered as a good point estimator for the population variance.

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.

Probability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.

For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.

Hence, there will be 99 samples left for the second draw to be made.

The probability that the second pick will be a blue marble = 15/99.

Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.

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The total amount of money Sam paid for his food, tip for the waitress and sales tax at the Texas Roadhouse is $54

Amount of tip = 15% × $45

= 0.15 × 45

= $6.75

Amount of sales tax = 5% × $45

= 0.05 × 45

= $2.25

Total amount Sam spent at the Texas Roadhouse = Sam's bill at the Texas Roadhouse + Amount of tip for the waitress + Amount of sales tax

= $45 + $6.75 + $2.25

= $54

In conclusion, the total amount of money Sam paid at the Texas Roadhouse is $54

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Answer:1341

Step-by-step explanation:

1342123