Three whole numbers have an HCF of 3 and an LCM of 180. Two of the numbers are 45 and 60. Find the third number.

Answer:

The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;

S + 429 = 85 × 6

Step-by-step explanation:

The parameters given are;

The scores earned by Mele on the first five test in Economics II are;

75, 70, 92, 95, and 97 points

The total test points = 429 points

Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;

From the definition of average, μ = (Sum of data values)/(Number of data)

Sum of data values = S + 429

The number of data = 5 test + 6th test =  6

μ = 85 = (S + 429)/6

Therefore;

S + 429 = 85 × 6

Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.

Answer:

( 0,0) is the x intercept

Step-by-step explanation:

y = (2x)/(x-1),

To find the x intercept set y = 0 and solve for x

0 =  (2x)/(x-1)

Multiply by x-1 on each side assuming x does not equal 1

0 = 2x

x = 0

The x intercept is 0

( 0,0) is the x intercept

Answer: g(x) f(x) h(x)

Step-by-step explanation:

The order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is is g(x) >f(x) > h(x)

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

It is a measure of how much the function changed per unit, on average, over that interval.

Given,

[tex]f(x) = 16(\frac{1}{2})^{x}[/tex]

interval = [0,3]

[tex]f(0)= 16(\frac{1}{2})^{0} =16 \\f(3)= 16(\frac{1}{2})^{3} =2[/tex]

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change= [tex]\frac{2-16}{3-0}=-4.67[/tex]

Consider the function g(x)

g(0)=21

g(3)=1

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change =[tex]\frac{1-27}{3-0}=-8.67[/tex]

Consider the exponential function

at x=0 the exponential function h =4

at x=0 the exponential function h =-3

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change =[tex]\frac{-3-4}{3-0}=-2.33[/tex]

Hence, the order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is g(x) >f(x) > h(x)

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Answer:

7x+14

Step-by-step explanation:

The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.

In this case it will be 7×x and 7×2

7(x+2)=7x+14

Answer:

B. (6,-2)

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2=r^2

The center of the circle is (h,k)

So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).

Answer:

Step-by-step explanation:

Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA

Starting with the expression

4sinB= 3sin(2A+B)

Let us re write angle B = (A + B) - A

and 2A + B = (A + B) + A

Substituting the derived expression back into the original expression ww will have;

4Sin{(A + B) - A } = 3Sin{(A + B)+ A}

From trigonometry identity;

Sin(D+E) = SinDcosE + CosDSinE

Sin(D-E) = SinDcosE - CosDSinE

Applying this in the expression above;

4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}

Open the bracket

4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA

Collecting like terms

4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA

Sin(A+B)CosA = 7Cos(A+B)sinA

Divide both sides by sinA

Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA

Since cosA/sinA = cotA, the expression becomes;

Sin(A+B)cotA = 7Cos(A+B)

Finally, divide both sides of the resulting equation by sin(A+B)

Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)

CotA = 7cot(A+B) Proved!

Answer:

Hey... Ans is in the pic..

Hope it helped u if yes mark me mark me BRAINLIEST!

Tysm!

:)

Answer:

y = 5

Step-by-step explanation:

−x+y=0   −2x+y=−5

Multiply the first equation by -2

-2(-x+y=0)

2x-2y =0

Add this to the second equation

 2x-2y =0

−2x+y=−5

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

0x -y = -5

-y =-5

Multiply by -1

y = 5

Answer:

Started- 1200BC

Moses wrote the book of Torah.

Ended- 96 CE

John wrote the last book, The book of 'revelation'

Step-by-step explanation:

It took 1400 years to write it.

40 people around 38 people wrote the Bible even though the main author of the book is Holy Spirit.

The Bible has 2 sections:

Old testament

Consists of 39 books.

Also referred to as taNaK which means the 'old testament' in Hebrew.

Based on the first five books of the testament (Torah or Pentateuch)

Written before the birth of Jesus Christ.

New testament

Consists of 27 books.

Written after the birth of Jesus Christ.

Based on the teachings and life of Christ (The Gospel).

Apocrypha:

Written between the Old testament and the New Testament.

Some denominations of Christianity don't believe in the Apocrypha.

Took 400 years to write it.

Hope this helps ;) ❤❤❤

Answer:

k Nishant

Step-by-step explanation:

The Old Testament is the original Hebrew Bible, the sacred scriptures of the Jewish faith, written at different times between about 1200 and 165 BC. This your answer

Answer:

This is poorly written, so i will answer it as it was:

"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of  A, followed by a translation 2 units up of the graph of f."

I don't really know what you do mean by I2), so i will answer it in a general way.

First, we do a vertical shrink of factor A.

A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:

g(x) = A*f(x)

As 0 < A < 1

We will have that the graph of g(x) is a vertical compression of the graph of f(x)

Now we do a vertical shift of 2 units up.

A general vertical shift of N units up is written as:

g(x) = f(x) + N

Where N is a positive number.

So in our case, we have:

g(x) = A*f(x) + 2.

Where you will need to replace the values of A and f(x) depending on what the actual question says,

Answer:

Pregunta 1: Opcion D. 8

Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)

Pregunta 3: 28 años (no está como opción)

Pregunta 4: Opción D. 1/3

Step-by-step explanation:

Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.

Fracciones irreductibles con común denominador 24.

Como máximo divisor tenemos el 24 y como mínimo el 1

entre 1/24 y 1 estarán nuestras fracciones o sea:

1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x

1/24 < x/24 < 24/24

Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23

Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos

5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24

Mismo procedimiento para el 25:

1/25 es una de las fracciones irreductibles. Pensamos en los valores de x

1/25 < x/25 < 25/25

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:

1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de

20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)

26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25

Próxima pregunta:

Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.

Plantiemos la siguiente ecuacion donde x es la edad de la novia

4/5x + x = 63

9/5x = 63

x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)

x = 35

Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad

4/5 .35 = (35 .4) /5 = 28

Es raro porque no está la respuesta como tal.

Próxima pregunta:

Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día

y el día tiene 24 horas.

8 horas transcurridas / 24 horas totales = 1/3

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

5x - 2(2x-2) = 2(3x - 1) + 7/2

= 5x - 4x + 4 = 6x - 2 + 7/2

= 5x + 4 = 10x - 2 + 7/2

= 5x + 6 = 10x + 7/2

= 5x + 2.5 = 10x

= 2.5 = 5x

Thus, x = 1/2 or 0.5

Hope this helps!

Answer:

Question 1: d ≥ 4  or  d ≤ -8

Step-by-step explanation:

Question 1 Solve the inequality. |d + 2| ≥ 6

d + 2 ≥ 6  or  d + 2 ≤ -6

d ≥ 4  or  d ≤ -8

Answer: do do that you need a firm understanding of trig. once you do, you can see all the steps and solve a trig proof problem easily. So go back to solving regular trig questions, and keep asking yourself why this formula works. once you have understanding of that, you can solve trig proof problems with ease.

Step-by-step explanation:

Answer:

0.46 feet

Step-by-step explanation:

Length = 5/6 feet (or 0.254 m)

Width = 3/8 feet (or 0.114 m)

(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)

The answer is 200 cm³

The volume of the rectangular prism (V1) is:

V1 = l · w · h                       (l - length,  w - width,  h - height)

It is given:

h = 12 cm

w = l = 5 cm (since it has a square base which all sides are the same size).

Thus: V1 = 12 · 5 · 5 = 300 cm³

The volume of pyramid (V2) is:

V2 = 1/3 · l · w · h                   (l - length,  w - width,  h - height)

It is given:

h = 12 cm

w = l = 5 cm (since it has a square base which all sides are the same size).

V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³

The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):  

V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³

Answer:

28

Step-by-step explanation:

[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]

Answer:

[tex]\huge \boxed{28}[/tex]

Step-by-step explanation:

The trinomial is a perfect square.

Take the square root of the first term and the last term.

[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]

[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]

[tex](2x+7)^2[/tex]

Expand to find the second term of the trinomial.

[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]

The second term of the trinomial is 28x.

Hey there! I'm happy to help!

To find the surface area of a sphere, here is what you do.

You square the radius.

4²=16

You multiply by 4.

16×4=64

And you multiply by pi!

64×π=64π

Therefore, the surface area of the sphere is A. 64π units². It's that easy!

Now you can find the surface area of a sphere! Have a wonderful day! :D

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]

[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]

Therefore :-

[tex]\\[/tex]

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Answer:

The points for this will be:

A: (1, -4)

B: (-4, -2)

C: (-5, 4)

D: (-2, 1)

Step-by-step explanation:

If we reflect a shape over the x-axis, all of it’s points y values will be negated.

So, (1, 4) becomes (1, -4)

(-4, 2) becomes (-4, -2)

(-5, -4) becomes (-5, 4)

and (-2, -1) becomes (-2, 1)

Hope this helped!

New coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of quadrilateral ABCD are A is (1, 4), B is (-4, 2), C is (-5, -4) and D is (-2, -1)

After reflecting across the x-axis , the x-coordinates of the vertices will remain the same, but the signs of their y-coordinates will change.

Therefore, the new coordinates of the vertices will be:

A' is (1, -4)

B' is (-4, -2)

C' is (-5, 4)

D' is (-2, 1)

Hence,  new coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)

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Answer as an inequality:  [tex]x > 0[/tex]

Answer in interval notation:  [tex](0, \infty)[/tex]

Answer in words: Set of positive real numbers

All three represent the same idea, but in different forms.

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

Explanation:

Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]

For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.

Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.

The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.

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

The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.

So,

[tex]\log_e(x) = \text{Ln}(x)[/tex]

allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.

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

In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.

Answer: It is false, the diameter is not 16 m.

Step-by-step explanation:

P 4m are 8 m are 32 m away. The diameter= 32 m.

(I hope its rights!!!)

Answer:

[tex]\Large \boxed{\mathrm{( - \infty, \frac{17}{3}) }}[/tex]

Step-by-step explanation:

[tex]2x-5\leq -x+12[/tex]

Add x and 5 on both parts.

[tex]2x+x\leq 12+5[/tex]

Combine like terms.

[tex]3x\leq 17[/tex]

Divide both parts by 3.

[tex]\displaystyle x \leq \frac{17}{3}[/tex]

Answer:

Sin

Step-by-step explanation:

Sin < = opposite/hypotenuse

Answer:

2/5 ±i4/5sqrt(6)= t

Step-by-step explanation:

20= 4t -5t^2

Rewriting

20 = -5t^2 +4t

Divide by -5

20 = -5t^2 +4t

20/-5 = -5/-5t^2 +4/-5t

-4 = t^2 -4/5 t

Complete the square

Take the coefficient of t

-4/5

Divide by 2

-4/10 = -2/5

Square it

(-2/5)^2 = 4/25

Add to each side

-4 +4/25 = t^2 -4/5 t + 4/25

-100/25+4/25 = ( t-2/5)^2

-96/25 = ( t-2/5)^2

Take the square root of each side

sqrt(-96/25) = sqrt(( t-2/5)^2)

±isqrt(96/25)=( t-2/5)

±i4/5sqrt(6)=( t-2/5)

Add 2/5 to each side

2/5 ±i4/5sqrt(6)= t

Answer:

8, 19

Step-by-step explanation:

let group 1 have x students and group 2 have y students

x + y = 27

but group 2 has 2x + 3 students

the sum of students from both groups is 27

x + 2x + 3 = 27

3x + 3 = 27

3x = 24

x = 8

y = 2x + 3

y = 19

Answer:

Intersects; intersection point: (-2,3)

Step-by-step explanation:

Substitute -1.5x for y into y=0.5x+4:

-1.5x = 0.5x +4

-1.5x - 4 = 0.5x

-4 = 2x

x = -2

Plug in -2 for x into y=-1.5x

y = -1.5(-2)

y = 3

Organize the x and y values into an ordered pair:

(-2,3)

Answer:

y=0.5x+4 intersects y=-1.5x.

The intersection point is (-2,3)

Step-by-step explanation:

First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.

So we have the equation:

[tex]y=-1.5x[/tex]

Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5

The equation given to us is:

[tex]y=0.5x+4[/tex]

As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.

To find the x-value of their intersection, simply set the equations equal to each other and solve for x.

[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]

Now, plug -4 into either of the equations:

[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]

Therefore, the point of intersection is (2,3).

Answer:

The coordinates of A'C'S'T' are;

A'(-7, 2)

C'(-9, -1)

S'(-7, -4)

T'(-5, -1)

The correct option is;

B

Step-by-step explanation:

The coordinates of the given quadrilateral are;

A(-3, 1)

C(-5, -2)

S(-3, -5)

T(-1, -2)

The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward

Therefore, we have;

A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)

C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)

S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)

T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)

Therefore, the correct option is B

Answer:

70%

Step-by-step explanation:

To find the total percentage of his $60 dollars that he spent on fruit, we simply take the amount of money spent on fruit divided by the total spent.

% spent on fruit = 42 / 60

% spent on fruit = 0.7

% spent on fruit = 70 %

Cheers.

Answer:

70%

Step-by-step explanation:

so he spent 42/60

lets simplify by dividing on both sides by 2

21/30

then divide by 3

7/10

which is also 70/100

so 70%

yaaaaayyyy we r done!!!!!!!!!

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

  ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                 PEACE!