given that the hcf of two numbers is 16 and their product is 6,400 determine there LCM​

Answer:

These are consecutive interior angles.

Consecutive interior angles always add up to 180 degrees.

If they add up to 180 degrees, then we can use this equation:

(x + 5) + (9x - 55) = 180

And then solve for it:

10 x - 50 = 180

10x = 130

x = 13

Ta - da! works like magic

1. The entire expression, 4x² + x + 3, is a sum with: 3 terms.

2. The coefficients of the expression are: 4 and 1.

The coefficient in a polynomial expression is described as the number that is multiplied by a variable.

For example, the term 5x has a variable of x that is multiplied by 5. Therefore, the coefficient of the term is 5.

Given the expression, 4x² + x + 3 that contains three terms, namely, 4x², x, and 3 .

Therefore, we can state that:

1. The entire expression is a sum that has 3 terms.

2. The coefficient of 4x² is 4. The coefficient of x is 1.

Therefore, we can state that, the coefficients are: 4 and 1.

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Debemos tomar la integral definida de la diferencia entre las dos funciones en el intervalo dado.

Supongamos que queremos encontrar el area entre dos funciones f(x) y g(x) en un intervalo (a, b).

Vamos a suponer que f(x) > g(x) en todo el intervalo (a, b), entonces el area entre la funcion f(x) y g(x) en ese intervalo se calcula como:

[tex]\int\limits^b_a {(f(x) - g(x))} \, dx[/tex]

Si por ejemplo tuvieramos que para un valor c en el intervalo (a, b) se da que:

f(x) > g(x) en (a, c)

g(x) > f(x) en (c, b)

Entonces la integral sería:

[tex]\int\limits^c_a {(f(x) - g(x))} \, dx + \int\limits^b_c {(g(x) - f(x))} \, dx[/tex]

Y similarmente si debemos separar el intervalo mas segmentos.

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Answer:

Shipping is the conveyance of goods to a desired destination, usually through the help of transportation means

Answer:

Step-by-step explanation:

1. the act or business of sending or transporting goods. 

Example:-

To cause to go or be taken from one place to another we shipped those books out yesterday.

The lowest possible number of voters for the democratic candidate are,

3120 to 4080.

What is election?

A populace selects a person or people to hold public office through a formal group decision-making process called an election. Since the 17th century, elections have been the primary means by which modern representative democracies have been governed.

Given: A voter polling research group determined that 30% of the voters in a county would vote for the democratic candidate with a +4% margin of error.

They anticipate only 12,000 people will turn out to vote in this election.

If 12000 voters participate in the election, then 30% of them are, 3600.

Now we must add and subtract 4% of the total voters to 3600 people.

4% of the total voters = 480.

So,

3600 + 480 = 4080

3600 - 480 = 3120

Therefore, 3120 to 4080 voters represent the lowest possible number of voters for the democratic candidate.

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There are several methods to formulate a mathematical equation. A model, in its simplest basic form, is a quantitative declaration that two major theoretical findings are comparable.

A mathematical equation can be defined in a variety of ways. In its most basic form, a model is a mathematical assertion that indicates that two theoretical results are equal. 3x + 5 = 14, for example, is an equation inside which 3x + 5 and 14 are two formulas separated by an 'equal' sign. In mathematics, the most fundamental and elementary algebraic equations are comprised of one or more parameters.

Type of the mathematical equations are as follows:

A math statement is not the same as a maths problem. Between two arithmetic statements, a solution will always employ the equivalent (=) symbol.

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Answer: Equations can vary!

Step-by-step explanation: 1. Equations can be as simple as a math sentence with always an equal sign, make sure it balances, for example, 1+1=2

2. Equations can be complicated sometimes, with variables, but still you have to BALANCE both sides EQUALLY. One question is: 1+x=3

It seems simple and it is, and yeah you've actually done lots of equations throughout your life. Ever heard of algebra, it consists of equations, have you ever seen this 1+?=3? That's an equation with a variable that is represented as, or sometimes a box. You might take a look and say easy. I know, but the traditional steps are to take one on both sides first, but never forget what you do on one side you ALWAYS have to do to the other side. This is an easy equation question, there are going to be much more complex ones in the future.  

The matching angles are equivalent when the lines are parallel.

Here,

1. angles 6 and 7 are vertical angles.

2. angles 1 and 8 are alternate exterior angles.

3. angles 4 and 5 are alternate interior angles.

4. angles 2 and 6 are corresponding angles.

5. angles 6 and 8 are complimentary angles.

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Answer:

∴ He can travel 660 miles in 12 hours on the next day.

Step-by-step explanation:

Since the rate of travelling is equal on both days,

    8 hours = 440 miles travelled

    2 hours = 110 miles travelled

∴ 12 hours = 660 miles travelled

The mistake that Raquel made in simplifying the expression is given as follows:

The square is applied only to the number 3, not to the sum of 5 and 3.

Hence the correct simplified version is:

(5 + 3²) + 18 = (5 + 9) + 18 = 32.

The expression for this problem is given as follows:

(5 + 3²) + 18.

The parenthesis takes precedence, hence the first operation to be solved is of:

5 + 3².

Then the square is the operation that takes precedence, hence the expression is given as follows:

5 + 3² = 5 + 9.

Here is where Raquel's mistake lays, as only the number 3 is squared, the number 5 is not, hence 3 is squared and then added to 5.

Then the correct result of the expression is obtained as follows:

5 + 9 + 18 = 32.

The problem is given by the image shown at the end of the answer.

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Answer:

x = 4 and y = 3

Step-by-step explanation:

You are looking for the value of x and y when: 2x - 3y = -1 and y = x - 1

Because you are given y in terms of x (the second equation given), substitute that into the first equation for y:

2x - 3y = -1 when y = x - 1

2x - 3(x - 1) = -1

expand left side:

2x - 3x + 3 = -1

combine x terms on left side:

-x + 3 = -1

subtract 3 from both sides:

-x + 3 - 3 = -1  - 3

-x = -4

divide both sides by -1:

-x/-1 = -4/-1

x = 4

now use x = 4 in one of the original equations to solve for y. For simplicity sake, we will use the second equation but the answer can also be found by substituting x = 4 into the first equation.

y = x - 1 when x = 4

y = 4 - 1

y = 3

Answer:

x = 4; y = 3

Step-by-step explanation:

2x - 3y = -1

y = x - 1

Copy the first equation.

Subtract x from both sides of the second equation and multiply both sides by 3. Write it below the first equation. Then add the equations eliminating y. Solve for x.

     2x - 3y = -1

+   -3x + 3y = -3

----------------------

      -x        = -4

x = 4

Now substitute 4 for x in the second original equation and solve for y.

y = x - 1

y = 4 - 1

y = 3

Answer: x = 4; y = 3

Answer:

5.4

(use the pythagorean theorem, you get 5.39, round that to the nearest 10, you get 5.4.)

The product of 110 × 298 by rounding each factor to the nearest hundred is 30,000.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The crucial figures are preserved when numbers are rounded off. Example: When rounded to the next hundredths place, 2.786 may be converted to 2.79. If 2.786 is rounded to the nearest tenths place, 2.8 is the result.

Given,

110 × 298

Rounding to the nearest hundred:

100 × 300

30,000

The product of 110 × 298 by rounding each factor to the nearest hundred is 30,000.

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The cost of bag of popcorn is $7.5 and that of one drink is $5.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.

Assume that the cost of one popcorn bag is $[x] and one drink is $[y]. Then we can write -

6x + 4y = 65

9x + 8y = 107.5

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.

Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.

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As per the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ˣ

Population function:

Population function means  the effective population served over the course of a time

Given,

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.

Here we need to determine the population of mosquitoes in the area at any time.

Here we have to note that we have two time frames in the information given; weeks and days.

Now, we want the population after predation lets choose time in days.

We know that the population doubles every seven days (ignoring predation) so if P(t) is the population function we have IVP

So, for one week, the population function of the given situation is,

=> dP/dt = rP

=> P(0) = 200000

And we know that,

=> P(7) = 2P(0)

While we solving the IVP for P then we get

[tex]P=Ce^{rt}[/tex]

While we apply,  P(0) = 200,000 then we get the value of C = 200,000

So, the given function is rewritten as

[tex]P=200000e^{rt}[/tex]

Now we have to use P(7) = 2P(0), then we get,

400000 = 200000e⁷ˣ

Therefore, we have to use this function to find the population of mosquitoes in the area anytime.

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5)

1= 102

2= 102

3= 78

ask any questions in the comments below if needed:)

In the given number, the digit that has the greatest value is 1.

We are given a number. The number is a natural number. Natural numbers are the numbers used in mathematics for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering. The number contains five digits. We need to find the digit that has the greatest value. We know that as we go left, the place value of the digit increases by a factor of 10. So, the place value of the number is maximum for the digit that is present at the leftmost position in a number.

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The total time the ball is in the air, with an initial velocity of 19.62m/s is 3.972seconds.

What is velocity?

The rate of change in an object's position with regard to a frame of reference and time is what is meant by velocity, according to its definition. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It is measured in meters per second in the SI (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

Solution Explained:

Given,
initial velocity (v) = 19.62m/s
time taken to reach maximum height ( [tex]t_{h}[/tex]) = 2.01s

We assume, acceleration (a) = 10 m/s^2

We know,
v = at
t = v/a
t = 19.62 / 10                        (replacing with values)
t = 1.962s

total time = [tex]t_{h}[/tex] + t
                = 2.01 + 1.962
                = 3.972

Therefore, the total time the ball is in the air is for 3.972seconds.

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Step-by-step explanation:

1. First things first, the binomial tells us the zeroes.

[tex] - (x - 2) {}^{2} = 0[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

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

[tex]x = 2[/tex]

This root has a multiplicity of 2, so this root will "bounces off the x axis"

[tex](x + 4) = 0[/tex]

[tex]x = - 4[/tex]

Our x intercepts are

2 and -4

This root has a multiplicty of 1, so it will cross thorough the x axis.

Our leading degree is odd and we have a negative leading coefficient so

as x approaches ♾️, f(x) approaches negative ♾️

and as x approaches negative ♾️, f(x) approaches ♾️.

Our y intercept can be found by letting x=0,

so

[tex] - (0 - 2) {}^{2} (0 + 4) = - ( - 2) {}^{2} (0 + 4) = - (4)(4) = - 16[/tex]

So our y intercept is -16.

For Rational Functions, if the numerator and denominator share the same factor they are considered a removable discontinuity or hole.

Set it equal to 0.

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

[tex]x = - 5[/tex]

So we have a hole at x=-5.

Next, simplify the fraction.

[tex] \frac{x - 4}{x - 6} [/tex]

Now, plug in -5

[tex] \frac{ - 5 - 4}{ - 5 - 6} = \frac{ - 9}{ - 11} = \frac{9}{11} [/tex]

So we have a hole at (-5,9/11).

To find y intercept, let x=0,

[tex] \frac{0 - 4}{0 - 6} = \frac{2}{3} [/tex]

To find Vertical Asymptote, set denominator equal to 0

[tex]x - 6 = 0[/tex]

[tex]x = 6[/tex]

Draw a vertical dotted line at x=6

To find HA, this is the only case since the numerator and denominator has the same degree.

So using the leading coefficients, divide the numerator leading coefficient/ denominator leading coefficient.

The leading coefficient for both is 1 so

[tex]ha = \frac{1}{1} [/tex]

So our HA is y=1.

Draw a horizon tal dotted line at y=1

We have no slope asymptote.

The graph is above.

Part 3:

(3x-1)(2x+1)>0

[tex]3x - 1 = 0[/tex]

[tex]3x = 1[/tex]

[tex]x = \frac{1}{3} [/tex]

[tex]2x + 1 = 0[/tex]

[tex]2x = - 1[/tex]

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

We have three possible regions, when x is positive

Pick a random number less than -1/2 and plug it in the inequality to see if it true.

Let use -1

[tex](3( - 1) - 1)(2( - 1) + 1) = ( - 4)( - 1) = 4[/tex]

Since 4>0, Whenever x is less than -1/2, the function is positive (greater than zero)

Let's try the next region.

Let use 0

[tex](3(0) - 1)(2(0) + 1) = ( - 1)(1) = - 1[/tex]

So this solution won't work

Let try the next region, let use 1.

[tex](3(1) - 1)(2(1) + 1) = (2)(3) = 6[/tex]

Since 6>0, Whenever x is greater than 1/3, the function is positive(greater than zero).

Our answer is

(-oo,-1/2) U (1/3,oo).

Part 4:

We know x cannot be -2 because

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

[tex]x = - 2[/tex]

So -2 can not be in our answer.

[tex] \frac{x - 1}{x + 2} \leqslant 2[/tex]

[tex]x - 1 \leqslant 2(x + 2)[/tex]

[tex]x - 1 \leqslant 2x + 4[/tex]

[tex] - 5 \leqslant x[/tex]

So

[tex]x \geqslant - 5[/tex]

However x can not be -2. so we say

[-5,-2) U (-2,oo)

[tex]\framebox{$\dfrac{10}{x-5}$}[/tex]

10/x-5 is already in simplest form.

The image distance is 33.3 cm and the magnification is 0.333  .

In the question ,

it is given that

since the lens is diverging

the focal length (f) = -50 cm

the distance between flower and diverging lens  (u) = -100

the formula to find the image distance is given by the equation

1/f = 1/v - 1/u

Substituting the values of f and u in the equation ,

we get

-(1/50) = 1/v - (-1/100)

1/v = -1/50 - 1/100

1/v = -3/100

v = -(100/3)

v = -33.33

formula for magnification = -(v/u)

= -(-33.33/100)

= 0.33

Therefore , The image distance is 33.3 cm and the magnification is 0.333  .

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The temperature of the patient will be 99.7°F.

Temperature simply means the degree of hotness and coldness that can be found in a body.

In this case, the patient's temperature is 1.1 above normal and 98.6 Fahrenheit is considered normal.

Therefore, the temperature of the patient will be the addition of the temperature given. This will be:

= 98.6 + 1.1

= 99.7°F

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The values of x are 1, 2, ±√-3.

Step-by-step explanation:

x⁵ + 5x³ + 5x - 2 = 0

x⁵ + 5x³ + 5x = 2

x ( x⁴ + 5x² + 5 ) = 2

x(x² + 1 )(x²+5 ) = 2

x = 2

(x² + 1 ) = 2

x² = 1

x = ± 1

(x²+5 ) =2

x² = -3

x = ±√-3

Hence, the values of x are 1, 2, ±√-3.

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Answer:

x = 0.35438 (5 d.p.)

Step-by-step explanation:

Given equation:

[tex]x^5+5x^3+5x-2=0[/tex]

Solve using the Newton-Rhapson method.

[tex]\boxed{\begin{minipage}{8 cm}\underline{The Newton-Rhapson iteration for solving f$(x) = 0$}\\\\$x_{n+1}=x_n-\dfrac{\text{f}\left(x_n\right)}{\text{f}\:'\left(x_n\right)}$\\\end{minipage}}[/tex]

If f(x) = 0 then:

[tex]\text{f}(x)=x^5+5x^3+5x-2[/tex]

Differentiate f(x) to find f'(x):

[tex]\implies \text{f}\:'(x)=5x^4+15x^2+5[/tex]

This means the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{{x_n}^5+5{x_n}^3+5{x_n}-2}{5{x_n}^4+15{x_n}^2+5}[/tex]

Let x₀ = 0.

Substitute this into the formula to find x₁:

[tex]\begin{aligned}\implies x_1&=0-\dfrac{(0)^5+5(0)^3+5(0)-2}{5(0)^4+15(0)^2+5}\\&=0-\dfrac{-2}{5}\\&=0.4\end{aligned}[/tex]

Substitute x₁ into the iteration formula to find x₂:

[tex]\begin{aligned}\implies x_2&=0.4-\dfrac{(0.4)^5+5(0.4)^3+5(0.4)-2}{5(0.4)^4+15(0.4)^2+5}\\&=0.4-\dfrac{0.33024}{7.528}\\&=0.3561317747\end{aligned}[/tex]

Repeat until the solution is found:

[tex]\implies x_3=0.354380602[/tex]

[tex]\implies x_4=0.3543780551[/tex]

[tex]\implies x_5=0.3543780551[/tex]

Therefore, the solution to the given equation is x = 0.35438 (5 d.p.).

The exponential function of the given graph is y = 4ˣ

Exponential function:

the general form of the exponential function is written as,

y = aˣ

Where

a > 0 and a ≠ 1.

Here a is called the base and x is called the exponent.

Given,

Here we have the graph and the point (2,16)

Now, we have to find the exponential function form this graph and point.

We already know that the general form of the exponential function is

y = aˣ

Here we have point (2,16), now we have to apply this point value on the general form in order to find the value of a,

So, when we apply the point values, then we get,

16 = a²

Now, move the power value to the other side, then we get,

a = √16

a = 4

Therefore, the exponential function of the given graph is,

y = 4ˣ

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The probabilities are given as follows:

a) Tails and odd number: 1/4.

b) Tails or odd number: 3/4.

c) Tails or odd number, but not simultaneously: 1/2.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For each event, the probabilities are given as follows:

Hence the probability of both events is of:

p = 1/2 x 1/2 = 1/4.

The or probability is composed as follows:

Hence the ´probability is of:

3 x 1/4 = 3/4.

Removing the simultaneous event, the probability is of:

3/4 - 1/4 = 2/4 = 1/2.

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Answer:2

Step-by-step explanation:

40 is a common multiple of 6 and 10

False:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Multiples of 10: 10, 20, 30, 40...

(2) The fraction 5/6 is greater than 7/10

True:

Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.

(5/6) x (5/5) = 25/30

(7/10) x (3/3) = 21/30

25/30 > 21/30 ∴ 5/6 is greater than 7/10

(3) The fraction 42/60 is an equivalent form of 7/10

True:

Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.

(7/10) x (6/6) = 42/10

42/10 = 42/10 ∴ 7/10 = 42/10

(4) The only value that can be used as a common denominator is 60.

False:

While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.

(5) Ten is a multiple of 6.

False:

Multiples of 6: 6, 12, 18, 24, 30...

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The left-hand side of the equation becomes (x - 4)² while the right side of the equation is 25

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a quadratic equation is given by:

0 = Ax² + Bx + C

Where A, B and C are constants.

Given the quadratic equation:

x² - 8x = 9

To solve the quadratic equation using the completing square method, add to both sides the square of half the coefficient of x, hence:

x² - 8x + (-4)² = 9 + (-4)²

(x - 4)² = 9 + 16

(x - 4)² = 25

The solution to the equation is (x - 4)² = 25

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The solution of the system is, x = 9/2, y = 9/2.

System of equations?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Consider, the given system of equations,

3x - y = 9              ..(1)

x + 3y = 18            ..(2)

From equation (1),

3x = y + 9

x = (y + 9)/3

x = y/3 + 3

Plug x = y/3 + 3 in equation (2),

y/3 + 3 + 3y = 18

10y/3 = 15

10y = 45

y = 9/2

Plug y = 9/2 in equation (1).

3x - 9/2 = 9

3x = 9 + 9/2

3x = 27/2

x = 27/6

x = 9/2

Hence, the solution of the system is, x = 9/2, y = 9/2.

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Answer:

64

Step-by-step explanation:

Double the miles because you doubles the time.

Answer:

Kathryn and her mom will drive 64 miles in 1 hour.

Step-by-step explanation:

Since they can drive 32 miles in 30 minutes, 30 minutes is half of one hour. So, since it is half, we can double 32 miles as well to get 64 miles in 1 hour.

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