What is 2.394 * 7.489

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 )

(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

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

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)

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

(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>

The value for X, the measure of angle MKL, is not specifically given in the question. Since angle JKL is a straight angle of 180 degrees, X can be any value up to 180 degrees.

In mathematics, a straight angle is defined as an angle of 180 degrees. In the scenario described with angle JKL, it is mentioned that this is a straight angle. Given that angle MKL is a part of the straight angle, its degree measure X is a component of those 180 degrees. The specific value of X is not given in the question, and it can be any number less than or equal to 180, provided the other part of the angle KJM is equal to 180- X.

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The measure of angle MKL is 60 degrees.

Finding the Measure of Angle MKL

To determine the value of X in this problem, we first need to understand that a straight angle measures 180 degrees. The problem states that angle JKL is a straight angle, so:

Angle JKL = 180 degrees

Next, we have the measure of angle JKM given as 120 degrees. Since angle JKL is made up of angle JKM and angle MKL, we can set up the following equation to find the measure of angle MKL, which is X:

Angle JKM + Angle MKL = Angle JKL

Substituting the known values:

120 degrees + X = 180 degrees

To find X, subtract 120 degrees from both sides:

X = 180 degrees - 120 degrees = 60 degrees

Therefore, the measure of angle MKL is 60 degrees.

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.

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!!

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

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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(a) [tex]a_{n}[/tex] = 4n + 8

(b) row 13 has 60 seats

(a)

the sequence of seats is an arithmetic sequence whose n th term is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

where [tex]a_{1}[/tex] is the first term and d the common difference

here the sequence is 12, 16, ....

with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus

[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8

(b)

calculate the number of rows n when 60 seats

solve 4n + 8 = 60 ( subtract 8 from both sides )

4n = 52 ( divide both sides by 4 )

n = 13 ← number of rows

Answer:

The correct answer is:

New students laughing at Steve

10 × 10 = 100

Add all the students laughing at Steve

10 + 100 = 110

Add Steve

110 + 1 = 111

There were 111 students in total laughing.

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

Given P is T, q is F and r is F.

Let us find p ↔ q first.

↔ is called bi-conditional operator and is true when p and q both are matched.

Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)

~p v r = ~T v F = F v F = F

Hence (p↔q)→(~pvr) = F → F = T     (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)

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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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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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].

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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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

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

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:

$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

( 4.625, - 3.75 )

the midpoint of (x₁, y₁ ) and (x₂, y₂ ) is

[[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

here (x₁, y₁ ) = (5.5, - 4.75 ) and (x₂, y₂ ) = (3.75, - 2.75 )

[ [tex]\frac{1}{2}[/tex](5.5 + 3.75 ), [tex]\frac{1}{2}[/tex](- 4.75 - 2.75 ) ]

= (4.625, - 3.75 ) ← midpoint of HX

Answer:

y = 0.75x+20

Step-by-step explanation:

Given that there is an admission ticket fixed and extra cost of 0.75 per ticket for the rides.

This means even if there is no ride used, enterer has to pay a fixed amount for admission.

Let us find out this admission cost from the given information

If y is the total cost and x no of rides

a) x is the no of rides and y the total cost

b) y = 0.75x+20 is the linear equation to calculate the cost for anyone who only pays for festival admission and rides

(c)

Total cost = Admission charges +0.75 * no of ride tickets.

then y = 0.75x+C

where C is the admission fee

Kendall bought 18 tickets i.e. x= 18 and y = 33.50

33.50 = 0.75(18)+C

33.50=13.50+C

C = 33.50-13.50 = 20.00

Hence admission fee = 20

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

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

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.

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.

Answer:

Given: A Δ ABC in which , AB ≅ BC, BE − median of ΔABC, m∠ABE = 40°30'

To Find: ∠ABC, ∠ CE B,∠A E B

Solution: In Δ ABC , BE is the median.

So, AE= EC

Now, In Δ A E B and Δ CE B

AE = EC [ BE is median]

BE is common.

AB=BC [given]

Δ A E B ≅Δ CE B { SSS Congruency]⇒S→side

So, ∠ABE=∠C BE  [ C PCT]

∴ ∠ABC=2×∠ABE=2×40°30'=81°

∠B EA =∠C E B [ C P CT]

Also,∠B A C = ∠BC A=k° [As AB =BC , if opposite sides are equal , then angle opposite to them are equal]

∠A+ ∠B+∠C=180°[ angle sum property of triangle]

k°+81°+k°=180°

2 k°=180°-81°

2 k°=99°

k°=99°/2

k°=49°30'[1°=60']

In Δ A E B, ∠ABE=40°30',∠A=49°30',∠A E B=?

∠ABE+∠A+∠A E B=180°[ angle sum property of triangle]

40°30'+49°30'+∠A E B=180°

90°+∠A E B=180°

∠A E B=180°-90°

∠A E B=90°

As, ∠B EA =∠C E B

So,∠C E B= 90°

So, BE is perpendicular bisector.

The measure of the angle ∠ABC and ∠BCA are both 69°45'. and ∠FEC measures 99°.

∠ABE and ∠BEC are opposite angles formed by the intersecting lines AB and BE, and BC and BE respectively.

Therefore, they are congruent.

The sum of the interior angles of a triangle is always 180°. So, we can find ∠ABE by subtracting ∠BEC from 180°.

Since m∠ABE = 40°30', we have:

∠BEC = ∠ABE = 40°30'

Since AB ≅ BC, the two sides are congruent.

This means that ∠ABC and ∠BCA are also congruent angles. Let's call their measure x.

Using the fact that the sum of the angles in a triangle is 180°, we can set up an equation:

∠ABC + ∠BCA + ∠BAC = 180°

Since ∠BCA = ∠ABC = x, we can substitute these values in:

x + x + 40°30' = 180°

Adding the like terms:

2x + 40°30' = 180°

Subtracting 40°30' from both sides:

2x = 180° - 40°30'

2x = 139°30'

Dividing both sides by 2:

x = 69°45'

So, ∠ABC and ∠BCA are both 69°45'.

To find ∠FEC, we can use the fact that the sum of the angles in a triangle is 180°. Since ∠BEC = ∠ABE = 40°30', we can find ∠FEC:

∠FEC = 180° - ∠BEC - ∠BCE

Substituting the values we know:

∠FEC = 180° - 40°30' - 40°30'

Simplifying:

∠FEC = 180° - 81°

∠FEC = 99°

Therefore, ∠FEC measures 99°.

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