Decide if the following biconditional statement
is true or false:
An angle is a right angle if and only if the angle
measures 90 degrees.
True
False

If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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Answer:

6.68 hours

Step-by-step explanation:

Answer:

[tex]\frac{10}{\pi}[/tex] or 3.183

Step-by-step explanation:

[tex]C=2\pi r[/tex]

If the circumference is 20 inches, plug 20 into C and solve for r.

[tex]20=2\pi r[/tex]

Answer:

Sure! Here's a system of equations we can set up to represent this situation:

Let x be the price of a bag of popcorn and y be the price of a drink.

Then we can set up the following system of equations:

x + 3y = 16.50 (equation for Jack's purchases)

2x + 5y = 29.75 (equation for Jill's purchases)

To solve this system of equations, we can use the substitution method.

First, we can solve for x in equation 1:

x = 16.50 - 3y

Then, we can substitute this expression for x into equation 2:

2(16.50 - 3y) + 5y = 29.75

Simplifying this equation, we get:

33 - 6y + 5y = 29.75

Combining like terms, we get:

33 - y = 29.75

Subtracting 29.75 from both sides, we get:

33 - 29.75 - y = -y

Simplifying, we get:

3.25 - y = 0

Subtracting 3.25 from both sides, we get:

-y = -3.25

Dividing both sides by -1, we get:

y = 3.25

So, the price of a drink is $3.25.

Now we can substitute this value for y back into equation 1 to solve for x:

x + 3(3.25) = 16.50

Simplifying, we get:

x + 9.75 = 16.50

Subtracting 9.75 from both sides, we get:

x = 6.75

So, the price of a bag of popcorn is $6.75.

To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.

Step-by-step explanation:

Tyler drove 40 miles in one hour.

To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.

So, we have:

(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour

                                                = (52 21/32) * (3/32)

                                                = (52 213/3232)

                                                = (52 63/32) miles/hour

                                                = 40 miles/hour

So, Tyler drove 40 miles in one hour.

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No, Misha is not correct in her statement that the equation will be positive.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

No, Misha is not correct. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. A line can cross the x-axis before it crosses the y-axis, and the values of m and b in its equation can still be either positive, negative or zero.

For example, a line with the equation y = -2x + 1 will cross the x-axis at x = 1/2 and y-axis at (0,1) , so it crosses x-axis first but both m and b have negative values (-2 and 1 respectively).

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Answer:

they are proportionate

Step-by-step explanation:

1560/100 = 15.6

312/100 = 3.12

Answer: Because they're based off the power of 10.

Step-by-step explanation:

I think the answer is correct because, to make 15.6 to 1560 you just need to multiply by 100, and to get 3.12 to 312 all you have to do is multiply by 100. So if you divided 1560 and 312 which is 5, all you have to do is divide by 100 and you get the same answer thats why its basically considered the same because of the power of tens.

Hope This Helps!

Answer:

6

Step-by-step explanation:

I counted

Answer:

Para el punto a. tenemos 312 elementos en el espacio muestral

Para el punto b. la probabilidad pedida es [tex]\frac{1}{26}[/tex]

Step-by-step explanation:

Comencemos explicando el principio de multiplicación. Supongamos que se tiene un experimento por etapas, es decir, una primera etapa que se puede llevar a cabo de '' [tex]x_{1}[/tex] '' maneras distintas, una segunda etapa que se puede llevar a cabo de '' [tex]x_{2}[/tex] '' maneras distintas y así sucesivamente hasta una etapa final que se puede llevar a cabo de '' [tex]x_{n}[/tex] '' maneras distintas. La cantidad total de formas de desarrollar todo el experimento se puede calcular como el producto de las distintas maneras en que se puede ejecutar cada etapa :

Formas de desarrollar todo el experimento = [tex]x_{1}x_{2}[/tex] ... [tex]x_{n}[/tex]

Para el punto a. del ejercicio vamos a utilizar este principio para calcular la cantidad de elementos del espacio muestral. La primera etapa del experimento sería el lanzamiento del dado y una segunda etapa el sacar una carta de una baraja de poker (52 cartas distintas). Entonces, para un dado tenemos 6 posibles opciones y cuando sacamos una carta podemos obtener 52 resultados distintos. Por lo tanto ⇒

[tex](6)(52)=312[/tex]

Tenemos un total de 312 elementos en el espacio muestral (todos distintos) y con la misma probabilidad de ocurrencia ya que suponemos que en el dado tenemos la misma probabilidad de obtener un uno, un dos, etc; así como en la baraja tenemos la misma probabilidad de sacar cada una de las cartas.

Para el punto b. utilizaremos el hecho de que estamos frente a un espacio muestral equiprobable y calcularemos la probabilidad del evento ''sale un número par en el dado y un AS en la baraja'' contando los casos favorables a este evento y dividiendo por la cantidad de elementos totales del espacio muestral. Podremos hacerlo de esta manera ya que el espacio muestral es equiprobable. Definimos para ello

[tex]A:[/tex] ''Sale un número par en el dado y un AS en la baraja''

[tex]P(A)=\frac{CasosFavorablesAlEventoA}{CasosTotales}[/tex]

Los casos totales son 312 (calculados en el inciso a.)

Los casos favorables al evento A se pueden escribir utilizando el principio de multiplicación como

[tex](3)(4)=12[/tex]

El 3 es por los tres números pares que podemos obtener del dado (estos números son el dos, cuatro y el seis).

El 4 se debe a la cantidad de ases en una baraja de Póker de 52 cartas (estos son el as de corazones, el as de picas, el as de trébol y el as de diamantes).

Reemplazando en la expresión de [tex]P(A)[/tex] obtenemos :

[tex]P(A)=\frac{12}{312}=\frac{1}{26}[/tex]

Otra forma de haber calculado esta probabilidad es utilizando el hecho de que tirar el dado y sacar una carta de la baraja son dos eventos independientes. Por ende, la probabilidad se puede calcular como el producto de la probabilidad parcial de cada evento. Esto es :

B : ''Sale un número par en el dado''

C : ''Saco un as en la baraja''

[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]

Tres casos favorables a que salga un número par de seis posibles.

[tex]P(C)=\frac{4}{52}[/tex]

Cuatro casos favorables a obtener un as de la baraja de 52 casos posibles.

Ahora escribimos

P ( B ∩ C ) = P(B).P(C)

Por ser B y C dos eventos independientes. Entonces

[tex]P(B)P(C)=(\frac{1}{2})(\frac{4}{52})=\frac{1}{26}[/tex]

Obteniéndose la misma probabilidad ya calculada.

Answer:

perimeter of the rectangle=2(12m+3m)

=30m

area of the rectangle=12m×3m

=36m

▬▬▬▬▬▬▬▬▬▬▬▬▬

→ Perimeter of Rectangle = 2(l + b)

= 2(12 + 3)

= 2 × 15

= 30m

→ Area of Rectangle = l × b

= 12 × 3

= 36m

∴ The Perimeter and area of Rectangle are 30m and 36m respectively.

▬▬▬▬▬▬▬▬▬▬▬▬▬

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

f of G in a pair of functions ,

Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2

To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).

f(x) = x2

f(g(x)) = g(x)2

= (√x + 2)2

= x + 2√x + 4

To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

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Answer:

y = -x + 5

Step-by-step explanation:

The equation is y= mx + b

m = the slope or rise/run or (y2 - y1) / (x2 - x1)

b = y-intercept

The slope here is -1, and the y-intercept is 5, so our equation is

y = -x + 5

Answer:

6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

a^2+b^2=c^2

6^2+6^2=c^2

36+36=c^2

72=c^2

square root 72 is the hypotenuse

Or simplified 6[tex]\sqrt{2}[/tex]

Or decimal form 8.48528137424

Rounded 8.49

Answer:

hectogon or hecatontagon or 100-gon

Step-by-step explanation:

It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.

Answer:

Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.

Step-by-step explanation:

Answer:

x = 3.25 m

Step-by-step explanation:

First, find the height of the triangle using sin31:

sin 31 = h/9 ---> h = 9sin31 = 4.64 m

Next, we can now solve for x using tan55:

tan 55 = h/x --> x = (4.64 m)/(tan 55) = 3.25 m

Answer:

4 maybe I don't understand what or how to do this but W is similar to M. I don't really know.

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

a) -1535.5

b) 0

Step-by-step explanation:

A) We do this problem according to its parenthesis. First, let's evaluate the first half, -2[(-1/4)-12(-1)^2]. We have to do (-1)^2 first, because of PEMDAS. (-1)^2 is just 1. Now, our equation is -2[(-1/4)-12*1]. Thus, we get -2[(-1/4)-12] because 12*1 is just 12. Then, we do (-1/4)-12, giving us -12.25. Our equation becomes -2(-12.25). Then, we just get 24.5.

The next half, -5[24+2(-12)^2] is similar. We first evaulate (-12)^2 because of PEMDAS, giving us 144. Then, we have -5[24+2(144)]. 2 times 144 is 288, so we get -5[24+288]. 24 + 288 is 312, so we have -5(312). This finally gives us -1560.

Putting the two together, we get 24.5 - 1560, which is -1535.5.

--------------------------------------------------------------------------------------------------------------B) We substitute a = -1/3 and b = -1 into the equation, -a^2b^2 - 3a^3b^2.

We plug in -1/3 where a is and -1 where b is. So:

-(-1/3)^2(-1)^2 - 3(-1/3)^3(-1)^2.

The tricky part of this problem is making sure you follow PEMDAS. We evaluate the exponents first.

-1/9 * 1  - 3(-1/27) * 1

= -1/9 + 1/9

= 0

Step-by-step explanation:

good answer .qanda app Also use

The required graph of the system of linear equations has been attached below.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The system of linear equations is given in the question, as follows:

2x + y = 8      .....(i)

-x + 2y = 6    .....(ii)

To graph the equations using the slope and y-intercept,

1) To determine the slope m and the y-intercept, write the equation in the form y = mx + b. (0, b).

Plot the y-intercept next.

3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

Thus, the required graph of the system of linear equations.

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[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]

In order to divide two fractions, you will need to use the KCF method.

Keep

Change

Flip

This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

Multiply:

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

[tex]\dfrac{15\times8}{4\times5}[/tex]

[tex]=\dfrac{120}{20}[/tex]

Simplify:

[tex]120\div20[/tex]

[tex]=\fbox{6}[/tex]

Answer: 6

Step-by-step explanation:

1. 15/4 divided by 5/8 = 120/20

15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20

2. 120/6 = 6

Answer:

630

Step-by-step explanation:

you can search it up if you want.

Answer:

630

Step-by-step explanation:

If measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.

Angles that really are identical to each other are referred to as congruent angles (and to themselves).

Thus, if measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.

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Answer:

B should be 3 inches long because the area of the square above is 48 inches squared, so that long side is probably 8. B is 3 inches long. As for A, this should be simple. since we know the longer side of the room has the area of 27, we can tell the length(longest side) is 9. 14 minus 9 is equal to 4. A's width is 4 inches long.

Step-by-step explanation:

for the rest, since we know one of the widths is 6 inches, we know that the length of the room with an area of 32 inches is 8. therefore, since 8 times 4 equals the number 32, C is 4 inches long. back to B. since we know that c is 4 inches long and that there is a length of 11 inches, we can tell the longest side of room A is 7. 4 Times 7 equals 28, so B is 28 inches squared.

Answer:

9x+7y+13

Step-by-step explanation:

add all the x's, y's, and no exponents together

Answer:

I think 1/6

Step-by-step explanation:

A die has 6 sides so every side has 1/6 chance to land on

Whatever the case a quadrilateral has always a sum of interior angles = 360°.

A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.

A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.

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