explain why it is useful to write linear equations in equivalent form. what does each form reveal?

Answer:

[tex]h=15.73\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=1,000\ in^{3}[/tex]

[tex]r=9/2=4.5\ in[/tex] ----> the radius is half the diameter

substitute and solve for h

[tex]1,000=(3.14)(4.5)^{2} h[/tex]

[tex]h=1,000/[(3.14)(4.5)^{2}][/tex]

[tex]h=15.73\ in[/tex]

Answer:

r = 11 in V =968 pi in3

Step-by-step explanation:

got it right on edge

Answer:

  15 inches

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of its sides. A square has 4 sides, all the same length. We can either add up the side lengths, or we can recognize that multiplication of one side's length by 4 is a useful alternative.

  perimeter = 4 × (3 3/4 in)

  = (4×3 +4×3/4) in

  = 12 in + 3 in = 15 in

Answer:

The center is (-5,1)

and

the radius is 3

Step-by-step explanation:

The given equation of the circle is

[tex](x+5)^2+(y-1)^2=9[/tex]

We can rewrite this equation in the form;

[tex](x-h)^2+(y-1)^2=r^2[/tex]

This implies that;

[tex](x--5)^2+(y-1)^2=3^2[/tex]

When we compare, we get;

(h,k)=(-5,1) which is the center and r=3 the radius.

The answer is:

The center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

To determine the center and the radius of a circle from its equation, we need to look for "h" and "k", being "h" the x-coordinate of the center and "k" the y-coordinate the center, then, calculate the radius.

Since we are given the ordinary equation of the circle, we can find the radius and the center directly.

The ordinary equation is:

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

Where,

h is the x-coordinate of the center

y is the y-coordinate of the center

r is the radius.

So, we are given the circle:

[tex](x+5)^{2} +(y-1)^{2} =9[/tex]

Which is also equal to:

[tex](x-(-5))^{2} +(y-(1))^{2} =9[/tex]

Where,

[tex]h=-5\\k=1[/tex]

[tex]r^{2}=9\\\sqrt{r^{2}}=\sqrt{9} \\r=3units[/tex]

Hence, the center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

Have a nice day!

rationalized form means that the number shoudnlt be a decimal that has never ending digits.

hope this answer to your question :)

Anwer:

1/7^2

explantion:

The expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now the given expression is,

7^3 • 7-^5

Now using the exponential property,

n^a . n^b = n^(a+b)

Therefore, we can write as,

7^3 • 7-^5 = 7^(3-5)

Solving we get,

7^3 • 7-^5 = 7^-2

Since, n^-a = 1/n^a

⇒7^-2 = 1 / 7^2

Therefore, we can write

7^3 • 7-^5 = 1 / 7²

this is the required equivalent expression.

Thus, the expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

To learn more about equivalent expression :

brainly.com/question/10188283

#SPJ2

Answer:

y = [tex]-\frac{1}{3} x[/tex] + 2

Step-by-step explanation:

The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:

Slope(s) = Change in y ÷ change in x

s = [tex]\frac{0 - -6}{2 - 0}[/tex] = 3

The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = [tex]-\frac{1}{3}[/tex]

Reason: The product of slopes of lines perpendicular to each other have to be -1

So the slope of the perpendicular line that passes through (-6,4) is [tex]-\frac{1}{3}[/tex]

As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x

Taking another point (x,y) on the line,

[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x - -6}[/tex]

[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x + 6}[/tex]

y - 4 = [tex]-\frac{1}{3}[/tex]x - 2

y = [tex]-\frac{1}{3}[/tex]x + 2

To find the slope-intercept equation of a line that passes through a given point and is perpendicular to another line, we can determine the slope of the given line and use it to find the equation.

To find the slope-intercept equation of a line, we need to know the slope and the y-intercept. Since the line that this problem is referring to is perpendicular to a line with an x-intercept of 2 and a y-intercept of -6, we can determine the slope of the line we are looking for by taking the negative reciprocal of the slope of the given line.

The slope of the given line is found using the formula: slope = (y2 - y1) / (x2 - x1)

Once we have the slope, we can use the point-slope form of a linear equation to find the equation of the line that passes through (-6,4) and has the determined slope. Finally, we can rearrange the equation to obtain the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

https://brainly.com/question/13048634

#SPJ3

10 questions = 40%

X question = 100%

40x = 1000

X = 25 questions

25 questions were on the test.

There are two ways to assess observational error: accuracy and precision. Precision measures how closely spaced or widely separated a set of measurements are from one another, whereas accuracy measures how near or far off a given set of measurements are from their true value.

Given

60% accurate means 40% inaccurate.

10 inaccurate answers means 40% inaccurate

10/40 x 100 = 25

To know more about accuracy refer to :

https://brainly.com/question/5792909

#SPJ2

Answer:

26 degrees.

Step-by-step explanation:

180 - 154 = 26

Answer:

Step-by-step explanation:

A is correct answer

Answer:

30 boxes

Step-by-step explanation:

~ You begin with the bottom row, which has 10 boxes.

~ You do 10 - 2 to get the number of boxes in the next layer, which is 8.

~ You then take 8 - 2, which is 6 for the next layer up.

~ Take 6 - 2, which is 4 for the next layer up.

~ Take away another two: 4 - 2 is 2.

~ When you take 2 away from 2, you get 0, so you have no more boxes.

~ Then, you add all the different amounts of boxes for each layer:

-> 10 + 8 + 6 + 4 + 2

-> Group smaller numbers together to get two bigger ones:

-> 18 + 12

= 30

One is rational and one is exponential.

Answer:

Step-by-step explanation:

the relationship between the graphs of y=2^x and y=2^-x is : symmetry by y-axis

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=3x-2[/tex]

Plot the line

To plot the line find the intercepts

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=3(0)-2=-2[/tex]

The y-intercept is the point (0,-2)

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]0=3x-2[/tex]

[tex]x=2/3=0.667[/tex]

The x-intercept is the point (0.667,0)

Plot the intercepts and then draw the line

Answer:

To find the circumference of a circle you have to multiply Pi (3.14) with the diameter of the circle.

You need to find circumference of the circle first

Answer:

length×width

Step-by-step explanation:

Multiplying the length of a rectangle by the width will always give you the area. If one value is missing replace it with x.

Length x width should give you the answer your needing

4xk = 4K 4x4= 16 +4K + 7k = 16+ 11k ( I would double check me

Answer:

Its C

hope this helps!!

The correct answer is A .)1

Answer:

A. Use straightedge to connect vertex B to right-most vertex of the equilateral triangle.

Step-by-step explanation:

The process is to create a bisector of angle ABC... so it means cutting angle at vertex/summit B in half.

Drawing a line from the vertex B to the right-most vertex of the equilateral triangle will deliver you the bisector.

The only answer choice that includes vertex B is the answer A, all other answers are dealing with vertex A and C... which will not help you to draw the bisector or angle ABC.

Answer:

Option A is right

Step-by-step explanation:

Given in the picture is an angle B formed by line segments AB and BC

To construct bisector of angle B

First with centre at B a circle is drawn which meets AB and BC at D and E respectively. With same radius equal to DE and centres of D and E two circles are drawn which intersect at the right most point.

The next step is join B to the rightmost vertex of equilateral triangles

This will be the angle bisector of angle ABC

Hence option A is right

72 fish total. 12 fish in each tank.

_________________________

(g+t)n=f

g=Goldfish

t=Tetras

n=Number of fish tanks

*If I got it wrong, let me know*

Final answer:

The total number of fish in the tanks is 72.

Explanation:

To find the total number of fish in the tanks, we need to multiply the number of tanks by the sum of the goldfish and Tetras in each tank. Based on the information given, there are 6 tanks, and each tank has 7 goldfish and 5 Tetras.

So, the total number of fish (f) in the tanks can be calculated as:

f = (7 goldfish + 5 Tetras) * 6 tanks

f = (7 + 5) * 6

f = 12 * 6

f = 72

Therefore, the total number of fish in the tanks is 72.

Answer:

261.67 [tex]ft^{3}[/tex]

Step-by-step explanation:

The formula is 1/3 [tex]\pi r^{2}h[/tex]

Answer:

261.67 ft^3

Step-by-step explanation:

mark me brainy plz!

It’s a rational number.

Hope this helps!

Answer:

Rational

Step-by-step explanation:

Irrational numbers are numbers that are infinite and non- repeating numbers

irrational- pi, square root of 2, etc

rational- anything else.

rational- .333333..., 1/3,  2, 1, -5, .111..., .7171..., etc.

Answer:

1. .21

2. .79

Step-by-step explanation:

1. 103/490

2. 387/490

The answer is A. $18,600 because $620,000 × 3% = $18,600

Answer:

56

Step-by-step explanation:

through estimation, you can see that the lowest value is 84 and the highest value is 140. in order to calculate the range, subtract the highest value from the lowest value. 140-84=56. The range is 56.

Answer:

56

Step-by-step explanation:

Answer with step-by-step explanation:

Ordered pairs that satisfy the given equation:

x  0  1  2  3  4

y  5  3  1  -1  -3

To find the x-intercept, we will substitute y = 0 and solve for x to get:

[tex]0 = -2x + 5[/tex]

[tex] -2x = -5[/tex]

[tex]x = 5/2[/tex]

x-intercept = (5/2, 0)

To find the y-intercept, we will substitute x = 0 and solve for x to get:

[tex]y = -2(0) + 5[/tex]

[tex]y = 5[/tex]

y-intercept = (0, 5)

Answer: option d.

Step-by-step explanation:

To create a table of five ordered pairs that satisfy the equation, you need to give values to the variable "x" and substitute these into the function to find the corresponding value of "y":

For [tex]x=-2[/tex]

[tex]y = -2(-2) + 5=9[/tex]

For [tex]x=-1[/tex]

[tex]y = -2(-1) + 5=7[/tex]

For [tex]x=0[/tex]

[tex]y = -2(0) + 5=5[/tex]

For [tex]x=1[/tex]

[tex]y = -2(1) + 5=3[/tex]

For [tex]x=2[/tex]

[tex]y = -2(2) + 5=1[/tex]

Then, you can make the table:

x   -2  -1  0  1  2

y   9  7  5  3  1

To find the  x-intercept, substitute [tex]y=0[/tex] into the function and solve for "x". Then:

[tex]0 = -2x + 5\\\\x=\frac{-5}{-2}\\\\x=\frac{5}2}[/tex]

This is: ([tex]\frac{5}{2}[/tex], 0)

To find the  y-intercept, substitute [tex]x=0[/tex] into the function and solve for "y". Then:

[tex]y= -2(0) + 5\\\\y=5[/tex]

This is: (0,5)

Answer:

the number is 5

Step-by-step explanation:

we can divide 24 by 4 in order to find the number

24/4 = 6

now we need to determine what number plus 1 equals 6 by subtracting 6 - 1

6 - 1 = 5

the answer is 5

we can check this by plugging 5 into the equation:

4(5+1) = 24

4(6) = 24

24 = 24

Answer:

120 [tex]cm^{3}[/tex]

Step-by-step explanation:

6 x 5 x 4 =120

Answer:

120 cm^3

Step-by-step explanation:

volume = length * width * height

volume = 6 cm * 5 cm * 4 cm

volume = 120 cm^3

Answer:

270,000

Step-by-step explanation:

So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet).  And you need to find out how many people can fit in the whole park area.

First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.

You had the right number for calculating the area of the park:

A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet

Now, how many people can we fit in there?  Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):

[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]

By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000

So, the park could accommodate 270,000 people.

That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.

Step-by-step explanation:

[tex]a)\ 12:18:36=\dfrac{12}{6}:\dfrac{18}{6}:\dfrac{36}{6}=2:3:6\\\\b)\ 320:480=32:48=\dfrac{32}{16}:\dfrac{48}{16}=2:3\\\\c)\ 16mm:480=\dfrac{16mm}{16}:\dfrac{480}{16}=1mm:30[/tex]

To simplify the given ratios, find the greatest common divisor (GCD) and divide all terms by the GCD. The simplified ratios are 2:3:6, 2:3, and 1:30. Refer to the solution for more details.

To simplify ratios, we divide both sides by their greatest common divisor (GCD).

a) 12:18:36

Find the GCD of 12, 18, and 36. It is 6.

Divide each number by 6:

The simplified ratio is 2:3:6.

b) 320:480

Find the GCD of 320 and 480. It is 160.

Divide both numbers by 160:

The simplified ratio is 2:3.

c) 16mm:480

Find the GCD of 16 and 480. It is 16.

Divide both numbers by 16:

The simplified ratio is 1mm:30. However, if there is no importance to specify units, simply 1:30 would be enough.

Answer:

Minimum balance account requires an amount of money to left in it all times in order to avoid fees.

Step-by-step explanation:

We have "many types of account" available in the banking sectors. As per the convenience of the customer, they opt from them. The minimum balance account is the type of account in which the customer has to maintain a standard amount prescribed by the bank in his account, failing to maintain it will lead to the gathering of fine or fee.

Answer:

Minimum Balance account.

Step-by-step explanation:

A minimum balance account is an account type that requires a minimum balance as set by the bank, at all times, in order to waive maintenance fees.

Failing this, certain amount is charged when money is deposited in that account. It can range from few dollars to 500 dollars in some banks.

Answer : True

Explanation : It is according to distance formula.

The answer is True -Apex