Given that a:b = 4 : 5 and a : c = 3 : 4,find the ratio of 5b : 3c

Answer:

Falso.

Step-by-step explanation:

Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:

(a) El exponente es cero.

(b) El exponente es un negativo impar.

(c) El exponente es un negativo par.

(d) El exponente es un positivo impar.

(e) El exponente es un positivo par.

(a) El exponente es cero:

Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.

(b) El exponente es un negativo impar:

Considérese las siguientes expresiones:

[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]

Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:

[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]

[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]

Si [tex]n[/tex] es impar, entonces:

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]

Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.

(c) El exponente es un negativo par.

Si [tex]n[/tex] es par, entonces:

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]

Puesto que [tex]d' = c'[/tex], la proposición es verdadera.

(d) El exponente es un positivo impar.

Considérese las siguientes expresiones:

[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]

[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]

Si [tex]n[/tex] es impar, entonces:

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]

(e) El exponente es un positivo par.

Considérese las siguientes expresiones:

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]

Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.

Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.

Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Answer:

It might be negative, I'm not sure, but I feel postive about that answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The discriminant is zero because the graph of the parabola is on the x axis.

Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as [tex]X^c[/tex]∩[tex]Y^c[/tex]∩[tex]Z^c[/tex]

By set theory, we have;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = [tex]\left | X^c \cup Y^c \cup Z^c \right |[/tex] =  [tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex]

[tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex] = [tex]\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Therefore;

[tex]\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Where;

[tex]\left | U\right |[/tex] = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

[tex]\left | X\right |[/tex] = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Y\right |[/tex] = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Z\right |[/tex] = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | X \cap Y\right |[/tex] = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Z\right |[/tex] = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | Y \cap Z\right |[/tex] = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Y \cap Z\right |[/tex] = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as [tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex]  = 1,968

Answer:

you should make the picture more clear, i cant see the answer choices

Answer:

use pythogoream theorem that is,

Step-by-step explanation:

c*2=a*2+b*2

so in order to find a*2;

a*2=c*2-b*2

Answer:

6, -5 and 6. Assume the leading coefficient of f(x) is 1. Write the equation of the cubic polynomial in standard form.

Answer: The question is not complete. the figure is attached below.

The polygon is a rectangle.

Step-by-step explanation:

Line 1 goes through (-2, 3)

hence the slope of line 1 = -3/2

Line 2 goes through (0, 3) (2, 0)

hence the slope of line 2 = -3/2

Line 3 goes through (0, 1) (-3, 1)

hence the slope of line 3 = 2/3

Line 4 goes through (3, 0) (0, -2)

Hence the slope of line 4 = 2/3

therefore -3/2 * 2/3 = -1

Line1 + Line3      Line1 + Line4       Line2 + Line3        Line2+Line4

because, the distance between Line1 and Line2 is not equal to that Line3 and Line4.

The polygon is a rectangle polygon.

Answer:

-4°C

Step-by-step explanation:

At the beginning of the chemistry experiment the temperature of the liquid was -5°C and it dropped 9°C so you do:

-5°C - 9°C = -14°C

The answer is -14°C for the first part of the question because when you are subtracting a positive number from a negative number you have to add the two numbers together but your answer will always be a negative number.

Then you add 25°C to -14°C:

-14°C + 25°C = 11

Because when adding a negative number to a positive number that is bigger than the negative number you have to subtract but your answer will always be a positive number, however if the positive number is smaller than the negative number your answer will be a negative number.

Then you subtract 11°C from 15°C:

11°C - 15°C = -4°C

Because when you subtract a number that is bigger than the first number you get a negative number.

Answer:

The b represents the people on each bus.

Step-by-step explanation:

Answer:

C.the number of students who rode on each bus.

Step-by-step explanation:

Answer:

Let that rational number to be subtracted be x.Given,-5/​6 - x = 4/9= - x = 4/9+5/6= - x = 23/18x = - 23/18.

Step-by-step explanation:

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Its area includes all Sahara's locations in North Africa, South Arabia, Iran's and Iraq's larger parts, North-Western India, California throughout the United States, South Africa but most of Australia.

Half-arid temperatures include places like the Utah, Montana, and Gulf Coastal regions of sagebrush. Also, it comprises regions in Iceland, Russia, Scandinavia, Greenland, and Northeast India. Semi-arid thankless than tube called per year of rain and up to 20 inches per year at much more than arid deserts.

Regions from of the latitude of 25° to 35° usually develop desert, because air sinks and is heated under pressures in this area. The world's dry and semi-arid desert regions are between 20°C and 35°C north latitude and between 20°C and 35°C South latitude.

9514 1404 393

Answer:

  (x, y) = (-2 12/17, -51)

Step-by-step explanation:

Here is the answer to ...

  [tex]4x+\dfrac{9}{y}+11=0\\\\\dfrac{6}{y}-3x=8[/tex]

If you mean something else, then parentheses are needed.

__

Let z = 1/y. Then the equations in general form are ...

  [tex]4x+9z+11=0\\3x-6z+8=0[/tex]

The solution (cross multiplication method) is ...

  x = (9·8 -(-6)·11)/(4(-6)-3·9) = 138/-51 = -2 12/17

  z = (11·3 -8·4)/-51 = -1/51

  y = 1/z = -51

The solution is (x, y) = (-2 12/17, -51).

Answer:

12 in 29. uou add all the number together then and it is 12 red marbles in 29 chancesso you take one marble out and put the exact marble back in having no effect.

Answer:

if you are supposed to find m<STR, then the answer is B

Step-by-step explanation:

Answer:

i thinkits c

Step-by-step explanation:

based on the info given

Answer:

α = 0.63 radians

Step-by-step explanation:

We are given;

Length of arc; L = 1.6 mm

Radius; r = 2.54 mm

The arc length equation is given by;

L = αr

Where;

L is length of arc

r is radius

α is angle in radians

Thus;

α = L/r

α = 1.6/2.54

α = 0.63 radians

Answer:

(0, 9)

Step-by-step explanation:

The y-intercept is the point when x = 0. By looking at the graph, when x = 0, y = 9. Therefore, the y-intercept of the line is (0, 9).

Answer:

1/ x = 22.5°

2/ x = 60°

Step-by-step explanation:

1/ We have: 3x + 2x + 3x = 180°

=> 8x = 180° => x = 22.5°

2/ We have: x + x + x = 3x = 180°

=> x = 60°

Answer:

1) x = 22.5

2) x = 60

Step-by-step explanation:

→ Add the angles together

1) 3x + 2x + 3x = 8x

2) x + x + x = 3x

→ Make it equal to 180

1) 8x = 180

2) 3x = 180

→ Divide both sides by 8 and 3

1) x = 22.5

2) x = 60

Answer:

the square root of 85 (so 85 is the answer)

Step-by-step explanation:

You can use the pythagorean theorem to find the height. So the sides of the triangle would contain the radius (4/2 = 2) and 9.

so, 2 squared plus 9 squared = 85

I hope this helps!

Answer:

1 / sqrt(3)

Step-by-step explanation:

tan(o) = sin(o) / cos(o)

sin(o) is the vertical distance from the x-axis. and that is in this basic circle the y-coordinate of the point.

cos(o) is the horizontal distance from the y-axis. that is the x-coordinate of the point.

so,

tan(o) = (1/2) / (sqrt(3)/2) = (2×1) / (2×sqrt(3)) = 1/sqrt(3)

Answer:

hope it helps.

=================================================

Explanation:

Consider something like 2b+6 factoring to 2(b+3). When we distribute that outer 2 back inside the parenthesis, we're multiplying that 2 by everything inside. Factoring goes in reverse of this and we divide each term of 2b+6 by the GCF 2.

The same thing applies to this current problem as well.

Divide each term by the -1.8 we want to factor out.

The results -2b and 5 will go inside the parenthesis. That's how we end up with -1.8(-2b+5)

You can use distribution to verify this

-1.8(-2b+5)

-1.8*(-2b) - 1.8*(5)

3.6b - 9

Answer:[tex]-0.802; \ 1.517[/tex]

Step-by-step explanation:

Given

[tex]3^x=x^4[/tex]

Here, two functions are given that is [tex]y=3^x[/tex] and [tex]y=x^4[/tex]

Check for the intersection of the graph of two curves

From the graph, they cut at two different points  i.e. [tex]x=-0.802\ \text{and}\ x=1.517[/tex]

Rest two roots are negative.

Answer:

1/√2

Step-by-step explanation:

The value of sin 45 is 1/√2

Answer:

Step-by-step explanation:

as angles of two triangles are equal, so they are similar.

x/17 =35/14=40/16

x/17=35/14

x=35/14×17=85/2=42.5

perimeter of ΔJKL=40+35+42.5=117.5

Answer:

C. Line

Is the correct answer