The ratio of the number of laps Andy swam to the number of laps Ben swam
on the first day of a swimming lesson was 5: 6. The ratio of the number of
laps Andy swam to the number of laps Ben swam on the second day of the
swimming lesson was 9: 5. If Ben swam 33 laps on both days, how many laps
did Andy swim on the second day of the swimming lesson?

Answer:

26.85%

Step-by-step explanation:

first you find the difference in price increase

633-499=134

*percentage increase=increase value/original value x100

so;=134/499x100=28.85%

hope it helps you.please don't forget to give me a thanks

Usando relaciones en un triángulo rectángulo, se encuentra que el valor del lado c es c = 35.5 unidades.

Las relaciones en un triángulo rectángulo se dan de la siguiente manera:

El lado opuesto de el ángulo de 26º48' = 26.8º es de 16, de esa forma, puede-se encontrar el lado c de la siguiente manera:

[tex]\sin{(26.8^\circ)} = \frac{16}{c}[/tex]

[tex]c = \frac{16}{\sin{(26.8^\circ)}}[/tex]

c = 35.5º.

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Answer:

x-intercept is (-1,0)

y-intercept is (0,-3)

Step-by-step explanation:

An intercept is where the graph crosses the axis.

Here the graph crosses the x-axis (numbered horizontal line that goes left and right) at the point (-1,0)

The graph crosses the y-axis (numbered vertical line that goes up and down) at the point (0,-3). These are what are called intercepts.

Answer: m x H = [ -9  36  - 9/2 ]

Step-by-step explanation:

Step-by-step explanation:

[tex]f(x) = 5x - 1[/tex]

[tex] \: [/tex]

[tex]y = 5x - 1[/tex]

[tex]5y - 1 = x[/tex]

[tex]5y = x + 1[/tex]

[tex]y = \frac{x + 1}{5} [/tex]

[tex] {f}^{ - 1} (x) = \frac{x + 1}{5} [/tex]

Answer: It is not a right angle.

Answer:

72

Step-by-step explanation:

I got it right .......

The maximum number of spherical balloons that can be held in the canopy will be 30.

The canopy is the fabric cover that hangs above a bed. It is a covering that is fastened to or carried over a dignitary or a holy item.

The base layer of spheres in a square pyramidal arrangement has n2 balls, where n is the number of balls that make up a square's side.

n=4 inch

The total number of spheres in the pyramid is;

⇒n(n+1)(2n+1)/6

⇒4(4+1)(2×4+1)/6

⇒(4×5×9)/6

⇒30

Hence, in the canopy, 30 spherical balloons are the most that may be accommodated.

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The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have an equation that represents the circle:

4x² + 8x + 4y² + 32y +52 = 0

Divide by 4 on both the sides:

x² + 2x + y² + 8y + 13 = 0

x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0

x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13

(x + 1)² + (y + 4)² = 4

(x + 1)² + (y + 4)² = 2²

Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

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Answer:

.

Step-by-step explanation:

.

Answer:

2:9 or 2/9

Step-by-step explanation:

I guess this question asks the simplest form of ratio 4:18

so I divided it by two and since they cannot be divided further that's the answer

you can either choose to write it in ratio form or fraction form that's your choice good day.

The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:

f(x) = (x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is:

f(x) = x² + 2x + 3

Completing the squares, we find the equation in vertex form, as follows:

f(x) = (x + 1)² + 2

As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.

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The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

We have

(x₁, y₁) ⇒ (-4, -5)

(x₂, y₂) ⇒ (3, -3)

(x₃, y₃) ⇒ (3, -7)

Then the area will be

Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]

Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]

Area = 1/2[-18 + 4]

Area = 1/2 × 14

Area = 7 square units

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The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is:   (0, ∞) - {0, 2, -2} or [tex]\:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: [tex]\rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: [tex]\:\left(0,\:\infty \:\right)[/tex]

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

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Answer:

[tex]\textbf {B}[/tex]

Step-by-step explanation:

f(x) = 2x²

f [f(x)]

f [2x²] = 2(2x²)²

f[f(x)] = 2(4x⁴)

f[f(x)] = 8x⁴

Answer:

sub(2，-6)into y=mx+C

-6=-1(2)+C

C=-4

equation=y=-x-4

Answer:

y = -x - 4

Step-by-step explanation:

Given:

a line with a slope of -1, passing through the point (2,-6)

Point-Slope Form: y - y₁ = m(x - x₁)

where:

(x₁, y₁) is the given point

m is the slope

Substitute the given values into the formula:

⇒ y - y₁ = m(x - x₁)

⇒ y - (-6) = -1(x - 2)

⇒ y + 6 = -1(x - 2) [distribute -1 through the parentheses]

⇒ y + 6 = -x + 2 [subtract 6 from both sides]

⇒ y + 6 - 6 = -x + 2 - 6

⇒ y = -x - 4

Check your work:

⇒ y = -x - 4 [substitute 2 for x, and -6 for y]

⇒ -6 = -2 - 4 [simplify]

⇒ -6 = -6 ✔

Therefore, the equation of the line is: y = -x - 4

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Answer:

3x^{2} -16x-19

Step-by-step explanation:

If we are going to be simplying this problem, then we need to take it step by step.

Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.

Answer:

(3x - 19) • (x + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3•((x-5)2))+14•(x-5))-24

STEP

2

:

Equation at the end of step 2

(3 • (x - 5)2 + 14 • (x - 5)) - 24

STEP

3

:

Trying to factor by splitting the middle term

Factoring 3x2-16x-19

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -19

Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57

Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .

-57 + 1 = -56

-19 + 3 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3

3x2 - 19x + 3x - 19

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (3x-19)

Add up the last 2 terms, pulling out common factors :

1 • (3x-19)

Step-5 : Add up the four terms of step 4 :

(x+1) • (3x-19)

Which is the desired factorization

Answer:

48/49

Step-by-step explanation:

divison and multiplcation

The method for calculating how many arrangements are feasible when only a few items are chosen from a collection of items that are unique is as follows:

[tex]^nC_k=\frac{n!}{k!(n-k)!}[/tex]

Where:

n – the sum of all the elements of a set

k – the number of selected objects (the order of the object may change)

! – factorial

For instance, 3!=1×2×3

So, according to the problem, there are [tex]^7C_3[/tex] possible groups of 3 women out of 7 women. And [tex]^5C_2[/tex] possible groups of 2 men out of 5 men.

Combining we get that there are [tex]^7C_3 ~^5C2[/tex] groups of 3 women and 2 men out of 7 women and 5 men.

Therefore, there are [tex]^7C_3 ~^5C2=\frac{7!}{3!4!}\frac{5!}{2!3!}= 350[/tex] possibilities.

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Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Given, that a hyperbola centred at the origin has vertices at (0, ±9)  and foci at  (0, ±10).

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]

Where (h, k) is the center = (0, 0)

Distance from centre to vertices a = 9 ⇒ a² = 81

Distance from centre to vertices which is given from the foci c = 10

⇒ c² = 100

Using the Pythagorean formula, c²= a²+ b²

Substituting the values 100 = 81 + b²

So we get, b²= 100 - 81 = 19

Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

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Answer:

-3

Step-by-step explanation:

/= negative slope; \= positive slope

The y-intercept is 2 because this is where it crosses the y-axis

Then you find the next point that touches the graph on an exact point which is (-2,-4)

So, your points are (0,2) and (-2,-4) then you do the slope formula of y2-y1 divided by x2-x1

-4-2/-2-0 = 3 and because the line is / then it is -3

The only problem is you may also go bankrupt before you're able to double your bet enough times.

If the game's events are independent,  similar to flipping a coin,  then the probability never changes, it's still a 1 out of 5 chance of winning each time.

The coin has no memory,  so it will always have the same probability on each flip.

If the games' events are like that,  a losing streak doesn't mean a win is now more likely.

But if the events are not independent,  it may make sense to increase the bet.  

for example,  a bag has 10 coins and 2 are worth 100.  You reach in and pull out 5 coins, all worth only a penny each.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Your odds of getting one of the 2 $100 coins is now much greater than the original 1 out of 5 chance.

 You originally had a 2 out of 10 chance on the first draw.  But now it's up to 2 out of the remaining 5 or 40% chance of winning.  

There is another reason someone may wish to double their bet.  If you doubled your bet each time you lost,  you would eventually recoup all your losses.  It can work.

The only problem is you may also go bankrupt before you're able to double your bet enough times.

That risk is usually considered too great to double your bets on independent events.

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Answer:

0.5km or 500m

Step-by-step explanation:

Given Distance = Speed x Time

In this case, we should use the difference in speed and time of the 2 scenarios.

Difference in Time = 20 mins(late) + 10 mins(early)

= 30 mins or 0.5 hour

Difference in Speed = 4km/h - 3km/h = 1km/h

Distance = 1km/h x 0.5 hr = 0.5km or 500m.

After all the conditions you applied from the statement given you will get the original number as 16.08.

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

Given that, if you subtract 0.3 from a certain number, add 0.4 times the original number to the result and then add another 2.78, you'll get 25.

We need to find the original number.

Let us take the original number as x.

Now, subtract 0.3 from the original number.

That is x-0.3.

0.4 times the original number is 0.4x.

Add 0.4 times the original number to the result.

That is, x-0.3+0.4x=1.4x-0.3

Now, add 2.78 to the result. That is 1.4x-0.3+2.78=1.4x+2.48.

As a result, you'll get 25. That is 1.4x+2.48=25

⇒1.4x=22.52

⇒x=16.08

There, the original number is 16.08.

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Answer:   for all values of x

Step-by-step explanation:

[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]

Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.

Answer:

The answers to different parts for ratio are - 3:5,3:5,3:5,9:25,graph C respectively .

Step-by-step explanation:

A ratio is a relationship between two quantities, normally expressed as the quotient of one divided by the other, or the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

a) The ratio of the median weekly earnings of the holder of a high school diploma only to the median weekly earnings of the holder of a bachelor's degree - 750/1250 = 3:5

b) The ratio of the area of the red rectangle  to the area of the blue rectangle - 750 x 1 / 1250 x 1 = 3:5

c) The ratio of the area of the red square to the area of the blue square in graph B - 3:5

d) the ratio of the volume of the red cube to the volume of the blue cube in graph C - 750 x 750 /1250x 1250 =9:25

e) The most misleading graph is graph B  because the distribution of values , depth, and shapes differ.

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Answer:

[tex]f(4)=e^{4}-3[/tex]   or   [tex]f(4)\approx51.5981500331...[/tex]

Step-by-step explanation:

The following is a general explanation of functions, what they mean, and how to evaluate them.  The simplifications and calculations at the end are based on the clarification from your comments that [tex]f(x)=e^{x}-3[/tex] .  If [tex]f(x)[/tex] is equal to something else, the simplifications/calculation will obviously be a little different, and the answer will likely be different, but the general process will be the same.

In the equation [tex]f(x)=e^{x}-3[/tex] , the left side of the equation is saying several things at once.

Names

The first character, "f", is the name of the function.

The name of a function tells you which set of directions you should look for to apply to an input.  Some functions have names that are more than one letter, and even might give a hint as to what they do, for instance I might name a certain function [tex]squareroot[/tex], and based on the name, you might guess what the equation for [tex]squareroot(x)[/tex] might look like.

Mathematicians often use "f" as a function name between different problems over and over and over again, unless they come up with a special function that is worth giving a special name to.  

Input

The rest of the characters after the name of the function, are "(x)" which is a pair of parentheses to contain the input, and the input itself.

Again, mathematicians often use "x" as a generic input over and over and over again, until we actually know which number we want to put into the function.

Output

Even though we've already discussed every character in the notation on the left, there is actually one more thing that the left side of the equation is saying:  Altogether, "f(x)" is the output of the function, when the input "x" is put in.  I feel it's worth stating, because it's often glossed over.

The equation itself

Next in the equation is the equals sign, which means that the left side of the equation, which is the output "f(x)", is equal to the stuff on the right.

The right side of the equation is the rule to follow describing what f(x) does to an input, and can help you calculate the output.

For instance, if I asked what p(4) was, it is clear that there is an input of 4, but without knowing what the function "p" does, there's no way to know what the function will give as an output when one inputs "4".  This is why the right-hand side of the equation for a function is important.

To evaluate any function, we take an input, apply the function, and simplify/calculate the output.

In this case, the question asks for [tex]f(4)[/tex], meaning that the "input" is "4".  

In this case, the question gives an explanation of what the function does through a rule given in equation form.

Given your clarification of the given function,  [tex]f(x)=e^{x}-3[/tex] , meaning a generic input (in this case "x") is put into the function "f" and the output is found by doing the arithmetic on the right side of the equation (exponentiating the number by "e", and then subtracting 4)

Notice that in the expression  [tex]f(4)[/tex], the "x"  was replaced with "4".  So, we need to substitute "4" where we see an "x" in the rule on the right hand side of the equation rule, and simplify and/or calculate (calculate, like with a calculator)

So, to evaluate the expression [tex]f(4)[/tex], simply substitute, and simplify/calculate.

Simplifying (no calculator)

To simplify without a calculator, we substitute "4".  Any time you make a substitution, use parentheses.  Then, try to simplify.

[tex]f(4)=e^{(4)}-3[/tex]

[tex]f(4)=e^{4}-3[/tex]

As it turns out, this is as much as we could simplify things here (without a calculator).  So, if an exact answer is needed, this would be it.

Calculating (with a calculator)

To calculate with a calculator, we substitute "4".  Any time you make a substitution, use parentheses.  Then, try to simplify.

[tex]f(4)=e^{(4)}-3[/tex]

[tex]f(4)=e^{4}-3[/tex]

[tex]f(4)=54.5981500331...-3[/tex]

[tex]f(4)=51.5981500331...[/tex]

So calculating with a calculator, the output of the function "f", for an input of "4", is approximately 51.598.