A circle has an area of 324π cm2. What is the radius?

(1, 3 )

to determine if the given points are a solution to the equation

They must lie on the given line to be a solution

the only one that is on the line is (1, 3 ) and is therefore the only solution

32 mm = length × 100

(32 mm)/100 = length . . . . . divide both sides by 100

0.32 mm = length

The actual length of the organism is 0.32 mm.

Let L be the actual length.  Then 100 L = 32 mm, and so L = 3 1/8 mm or 3.125 mm.

I would say K and M

By eye this looks like the line would pass through points with approximately an equal amount of points above and below the line of best fit

K and M are  pair of points which should be used to find the line of best-fit for the scatterplot, option d is correct.

To choose the pair of points that should be used to find the line of best fit, we look for two points on the scatterplot that are representative of the general trend and capture the spread of the data.

The pair of points K and M should be used.

By selecting these two points, we can establish a line that best approximates the overall relationship between the variables.

These points are typically chosen from the extremes of the scatterplot or from points that are evenly distributed across the range of the data. Choosing K and M allows us to incorporate a range of data points, providing a more accurate representation of the overall trend.

By using these two points, we can calculate the slope and intercept of the line of best fit using various regression techniques, such as linear regression.

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Answer:

$21,000

Step-by-step explanation:

The cost of car=$ 28,000

A car is depreciated by 25%

Now, the price of car=$28000(1-)[tex]\frac{25}{100}[/tex]

The price of the car= $28000([tex]\frac{100-25}{100}[/tex])

The price of the car= $28000([tex]\frac{75}{100}[/tex])

The price of the car= $280×75

The price of the car= $21,000

The car worth today $21,000

Hence the correct answer is $ 21,000

Answer:

B) y = 10x

Step-by-step explanation:

It should not be too hard for you to determine that every number on the bottom row is the same as the number on the top row with a zero appended.

Appending a zero to a number is the same as multiplying it by 10. For example, ...

... 90 = 10·9

... y = 10x

_____

In case that observation doesn't work out for you, you can always solve the given equation for k, then choose values from the table to fill in.

... y = kx

... k = y/x . . . . . divide by the coefficient of k, which is x

Fill in values from the table

... k = 20/2 = 10 . . . . . . from the second column

Now put this value where k is in the equation. After you do that, you know ...

... y = 10x

slope = (30 - 20)/(3 - 2) = 10 /1 = 10

equation

y = 10x

Answer

B) y = 10x

B

since both equations express y in terms of x we can equate the right sides

2x + 7 = 25 - x ( add x to both sides )

3x + 7 = 25 ( subtract 7 from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

substitute x = 6 into either of the 2 equations for y

y = 2x + 7 = ( 2 × 6 ) + 7 = 12 + 7 = 19

solution is (6, 19 )

Let us assume Doreen rate = x miles per hour.

Sue travels 19 miles per hour faster than Doreen.

Therefore,

Rate of Sue = (x+19) miles per hour.

We know time, rate and distance relation as

Time = Distance / rate.

Therefore, time taken by Doreen to travel  42 miles at the rate x miles per hour =

[tex]\frac{42}{x}[/tex].

And time taken by Sue to travel  100 miles at the rate (x+19) miles per hour =

[tex]\frac{100}{(x+19)}[/tex].

Sue takes 3 hours less time than it takes Doreen.

Therefore,

[tex]\frac{42}{x}-\frac{100}{(x+19)}=3[/tex]

We need to solve the equatuion for x now.

[tex]\frac{42}{x}-\frac{100}{\left(x+19\right)}=3[/tex]

[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x,\:x+19:\quad x\left(x+19\right)[/tex]

[tex]\mathrm{Multiply\:by\:LCM=}x\left(x+19\right)[/tex]

[tex]\frac{42}{x}x\left(x+19\right)-\frac{100}{x+19}x\left(x+19\right)=3x\left(x+19\right)[/tex]

[tex]42\left(x+19\right)-100x=3x\left(x+19\right)[/tex]

[tex]-58x+798=3x^2+57x[/tex]

[tex]3x^2+57x=-58x+798[/tex]

[tex]3x^2+57x-798=-58x+798-798[/tex]

[tex]3x^2+57x-798=-58x[/tex]

[tex]\mathrm{Add\:}58x\mathrm{\:to\:both\:sides}[/tex]

[tex]3x^2+57x-798+58x=-58x+58x[/tex]

[tex]3x^2+115x-798=0[/tex]

[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex]

[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-115+\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad 6[/tex]

[tex]x=\frac{-115-\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad -\frac{133}{3}[/tex]

[tex]x=6,\:x=-\frac{133}{3}[/tex]

We can't take rates as negative numbers.

So, the rate of Doreen (x) = 6 miles per hour.

Rate of Sue = x+19 = 6+19 = 25 miles per hour.

Time taken by Doreen @ 6 miles per hour to cover 42 miles = 42/6 = 7 hours.

Time taken by Sue @ the rate 25 miles per hour to cover 100 miles = 100/25 = 4 hours.

A

the equation of a line in ' slope-intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = 5x + 3 is in this form with slope m = 5

function Q has equation y = 2x + 4

the slope of function P is 3 more than function Q

Hey there!!

Given equation :

... 3 ( 2k - 9 ) + 4 = 5 - 2 ( k + 7 )  

Using the distributive property :

... 6k - 27 + 4 = 5 - 2k - 14

Combining the like terms :

... 6k - 23 = -2k - 9

Adding 2k on both sides :

... 8k - 23 = -9

Adding 23 on both sides :

... 8k = 24

Dividing by 8 on both sides :

... k = 24 / 8

... k = 3

The required answer is 3.

Hope my answer helps!!

The Pythagorean theorem is used for finding the distance between two points. You can consider the line from the origin to (12, 5) to be the hypotenuse of a right triangle with sides 12 and 5 (parallel to the x- and y-axes, respectively). Then the relation between these and the hypotenuse length is

... d² = 12² + 5² = 144 + 25 = 169

... d = √169 = 13

The point (12, 5) is 13 units from the origin.

Okay...... so for this problem you need to use the Pythagorean Theorem. So...

12^2 + 5^2

144+25

169

this = square root of 13

so.... The point (12,5) is 13 units from  the origin.

For this case we have:

Let [tex]y = f (x)[/tex] be a given function, where:

By definition, the domain of a function is represented by the values associated with the independent variable, that is, the values of x.

Therefore, the domain of the given function is represented by:

[tex]{x | x = -6, -1, 0, 3}[/tex]

Answer:

[tex]{x | x = -6, -1, 0, 3}[/tex]

Answer:

Its A for Edgenuit

The equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip.

The equation will be written as:-

S = 150m + 650

Here, 650 is how much she already saved and 150 is how much per month.

Therefore, the equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

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We can see that

there are six sides

so, n=6

so, firstly we will find total angle

total angle =(n-2)*180

total angle =(6-2)*180

total angle =720

so, sum of all angles must be 720

so, we get

[tex]x+120+100+128+133+112=720[/tex]

now, we can solve for x

[tex]x+593=720[/tex]

[tex]x=127[/tex].............Answer

the answer is b and d!

The examples of the Law of Detachment are:

1. If it snows tomorrow, then my dentist appointment will be canceled.

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

3. If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.

It states that if a conditional statement (if-then statement) is known to be true and its hypothesis (the "if" part) is true, then the conclusion (the "then" part) can be validly inferred as true.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true. In both the first and third examples, the statements follow this pattern.

So, the examples of the Law of Detachment are:

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

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100

let the number of football cards be x then she has 5x baseball cards

the total cards she has is 120, hence

x + 5x = 120

6x = 120 ( divide both sides by 6 )

x = 20

Allison has 20 football cards and 5 × 20 = 100 baseball cards

b=baseball cards

f=football cards

b=5f    she has 5 times as many baseball cards as football cards so we multiply the football cards by 5 to make them equal

b+f=120   there are 120 football and baseball cards total

5f+f = 120  substitute 5f everywhere you see a b

6f = 120  combine like terms

f=20  divide by 6

there are 20 football cards

b=5f

b=5(20)

there are 100 baseball cards

Answer:

[tex]F(x)=3x^2-1[/tex]

Step-by-step explanation:

We have been given the function [tex]G(x)=3x^2[/tex], it is shifted down 1 unit. Now, whenever a function is shifted up or down we just the idea of vertical shift which says:

To shift a function up by 'k' units we use:

[tex]g(x)+k[/tex]

To shift a function down by 'k' units we use:

[tex]g(x)-k[/tex]

Here, in our case we have to shift the function down by 1 unit, so we will subtract 1 from the function:

[tex]F(x)=G(x)-1=3x^2-1[/tex]

So the required function is [tex]3x^2-1[/tex].

In order to solve this problem, we the cost of both to equal each other, so we need to set up two expressions that will equal each other.

Let t = time in months.

The cost of Fab Pool can be represented by the expression 35t + 50

The cost of Perfect Pools can be represented by the expression by 40t + 35.

Now that we have the cost for each, we need to find when they are the same, so we set the expressions equal to each other.

35t + 50 = 40t + 35

Now we solve like a regular equation

50 = 5t + 35

15 = 5t

t = 3

At three months, the cleaning costs will be the same.

Hey there!!

Fab pool service costs $35 per month, this is a variable, the number of month could change and $50 for equipment. And perfect pools cost $40( a variable ) and $35 for equipment.

Let's take the number of month as 'm'.

The question asks us to find the number of months at which both of these costs become equal.

As the question states, we will have to equate both the sums or the values.

Total cost = Cost  for month + Cost for equipment.

Fab pool :

Cost per month = $35

Cost for equipment = $50

Total cost = 35 × ( the number of months ) + 50

Perfect pools :

Cost for month = $40

Cost for equipment = $35

Total cost = 40 × ( the number of months ) + 35

We have taken the number of months as 'm'.

Now, plugging in the values :

Fab pools : 35m + 50

Perfect pools : 40m + 35

Equating this :

... 35m + 50 = 40m + 35

Subtracting 35m on both sides :

... 50 = 5m + 35

Subtracting 35 on both sides:

... 15 = 5m

Dividing by 5 on both sides :

... m = 3

Hence, the number of months is 3.

Hope it helps!!

Assuming you require the measure of the angles

let x represent each equal  base angle then vertex = 7x

The sum of the angles in a triangle = 180°, hence

x + x + 7x = 180

9x = 180 ( divide both sides by 9 )

x = 20

the base angles = 20° and the vertex = 140°

The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1:7. The measure of the base angle is 1/7 times the measure of the vertex angle.

In an isosceles triangle, the base angles are congruent, meaning they have the same measure. Let's denote the measure of the base angle as x degrees and the measure of the vertex angle as y degrees. According to the given ratio, we have the equation:

x : y = 1 : 7

To find the exact measures of the angles, we can set up the equation:

x/y = 1/7

Multiplying both sides by y, we get:

x = y/7

Therefore, the measure of the base angle is 1/7 times the measure of the vertex angle.

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Hi

Here is the solution.

To find how much sand is in each bag we have to divide the weight of the sand by number bags.

Each bag hold = 48/12 = 4 pounds.

That's the answer.

Solution: The given random experiment follows Binomial distribution with [tex]n=10,p=0.44[/tex]

Let [tex]X[/tex] be the number of adults who use their smartphones in meetings or classes.

Therefore, we have to find:

[tex]P(X<3)[/tex]

We know the binomial model is:

[tex]P(X=x)=\binom{n}{x} p^{x} (1-p)^{n-x}[/tex]

[tex]\therefore P(X<3) = P(X=0)+P(X=1) +P(X=2)[/tex]

                       [tex]=\binom{10}{0}0.44^{0}(1-0.44)^{12-0}+\binom{10}{1}0.44^{1}(1-0.44)^{10-1}+\binom{10}{2}0.44^{2}(1-0.44)^{10-2}[/tex]

                       [tex]=1 \times 1 \times 0.0030 + 10 \times 0.44 \times 0.0054 + 45 \times 0.1936 \times 0.009672[/tex]

                       [tex]=0.0030+0.0238+0.0843[/tex]

                       [tex]=0.1111[/tex]

Therefore, the probability that fewer than 3 of them is 0.1111

400/16= 25

answer: it's a 16 to 25 ratio

one worker covers 25 dogs

25 : 1

the ratio of dogs : employees = 400 : 16

to simplify the ratio divide both parts by 16

400 : 16 = 25 : 1 ← in simplest form

Answer:

-5.27

Since when multiplying a positive and negative integer the answer will become negative

The product of -1.24 and 4.25 is -5.27, found by performing the mathematical operation of multiplication.

Given the question, you are asked to calculate the product of -1.24 and 4.25.

Which in this case, -1.24 * 4.25 equals -5.27

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Since the answer choices differ in their first coordinate, it is sufficient to determine that one. The 2:5 ratio means the distance from A to the point is 2/(2+5) = 2/7 of the total distance A to B.

The x-distance from A to B is 20 -1 = 19 units. 2/7 of that is (2/7)·19 = 38/7 = 5 3/7. Adding this value to the x-coordinate of A gives the x-coordinate of the point of interest: 1 +5 3/7 = 6 3/7.

The appropriate answer choice is ...

... (6 3/7, 12 2/7)

Answer:

(6 3/7, 12 2/7)

Step-by-step explanation: because I got it right

Yes, you're right! The first step is rewriting the equation as

[tex] \ln(a) + \ln(b^x) = M [/tex]

Subtract [tex] \ln(a) [/tex] from both sides:

[tex] \ln(b^x) = M-\ln(a) [/tex]

Use the property [tex] \ln(a^b) = b\ln(a) [/tex] to rewrite the equation as

[tex] x\ln(b) = M-\ln(a) [/tex]

Divide both sides by [tex] \ln(b)[/tex]

[tex] x = \dfrac{M-\ln(a)}{\ln(b)} [/tex]

Alternative strategy:

Consider both sides as exponents of e:

[tex] e^{\ln(ab^x)} = e^M [/tex]

Use [tex] e^{\ln(x)} = x [/tex] to write

[tex] ab^x = e^M [/tex]

Divide both sides by a:

[tex] b^x = \dfrac{e^M}{a} [/tex]

Consider the logarithm base b of both sides:

[tex] x = \log_b\left(\dfrac{e^M}{a}\right) [/tex]

The two numbers are the same: you can check it using the rule for changing the base of logarithms

To solve ln(a*b^x) = M, apply the log properties to get ln(a) + x*ln(b) = M, isolate x to get x*ln(b) = M - ln(a), and divide by ln(b) to find x = (M - ln(a))/ln(b).

To solve the equation ln(a*b^x) = M for x, begin by applying the property that the logarithm of a product is equal to the sum of the logarithms. That is, ln(xy) = ln(x) + ln(y). Therefore, we can write:

ln(a*b^x) = ln(a) + ln(b^x)

The logarithm of a power allows us to move the exponent to the front of the log, hence:

ln(b^x) = x * ln(b)

Now, our equation becomes:

ln(a) + x * ln(b) = M

We can isolate x by subtracting ln(a) from both sides:

x * ln(b) = M - ln(a)

Finally, divide both sides of the equation by ln(b) to solve for x:

x = (M - ln(a)) / ln(b)

Your answer would be

10330.9

answer:  3767.74

work:

(1.18 × 103) ⋅ (9.1 × 10 − 6)

121.54 ⋅  (91 − 60)

121.54 ⋅  31

3767.74

hope this helps! comment if the problems seems wrong :) ❤ from peachimin

Answer:

(a) 1825 = 2.25x + (2.25-1)(x -108)

(b) 560 mi/h

Step-by-step explanation:

(a) distance = speed·time

The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.

The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).

The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...

... 1825 = 2.25x + (2.25 -1)(x -108)

(b) Simplifying the equation gives ...

... 1825 = 3.50x -135

To solve this 2-step equation, we add 135, then divide by 3.50.

.. 1960 = 3.50x

... 1960/3.50 = x = 560

The first airplane's speed is 560 mph.

Check

In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.

In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.

Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.

The first plane's average rate is 560 mph. The equation that can be used to solve this problem is 2.25x + 1.25(x - 108) = 1825

To solve this problem, we need to set up an equation based on the information given.

Simplifying the equation gives us:

2.25x + 1.25x - 135 = 1825

3.5x - 135 = 1825

Adding 135 to both sides:

3.5x = 1960

Dividing by 3.5:

x = 560

Therefore, the first plane's average rate was 560 mph.

Try this option:

According to the properties of the quadratic equation the sum of its roots is '-b', in other words x₁+x₂= -b

Answer: -b

if we were to use the quadratic formula, we would get that the roots are

[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

or that the 2 seperate roots are

[tex]\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

if we sum these, then the [tex]\sqrt{b^2-4ac}[/tex] bits will cancel and we wil be left with

[tex]\frac{-b-b}{2a}[/tex] or [tex]\frac{-2b}{2a}[/tex] or [tex]\frac{-b}{a}[/tex]

the sum of the solutions is [tex]\frac{-b}{a}[/tex]

(A) Is the first factor of this form?

[minus sign] <digit> [<decimal point> [<digit> ...]]

where square brackets show optional items, and "..." shows items that repeat as much as you may like.

(B) Is the second factor of this form?

10^<integer>

You can start with the 2-point form of the equation for a line:

... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁

Filling in the given values, you get

... y = (0 -7.5)/(-1 -2)·(x -(-1)) +0

... y = 2.5(x +1) . . . . . simplify a bit

... y = 2.5x +2.5 . . . . slope-intercept form

First you find the slope with the 2 points: (2, 7.5) and (-1, 0)

y1-y2/x1-x2 so  7.5-0/2-(-1) which equals 2.5

Next you solve the slope intercept form equation to get b

y=m*x+b (m is the slope and b is the intercept)

7.5=2.5*2+b

b=2.5

So the equation is y=2.5x+2.5

Using Rise/Run, the answer would be y= -3/4x + 3.

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

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-interceot )

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0 ) ← 2 points on line

m = [tex]\frac{0-3}{4-0}[/tex] = - [tex]\frac{3}{4}[/tex]

the line crosses the y- axis at (0, 3 ) → c = 3

y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope-intercept form