la suma de los primeros n enteros positivos es un numero de tres digitos iguales. cual es la suma de los digitos de n?

Answer:

[tex]g(x)=|x+8|-2[/tex]

Step-by-step explanation:

The vertex is at (-8, 2), so g(x)=a|x+8|+2.

Considering g(-6),

[tex]g(-6)=4=a|-6+8|+2 \\ \\ 2=2a \\ \\ a=1 \\ \\ \therefore g(x)=|x+8|-2[/tex]

Answer:

1. 60,000

2. 80,000

3. 100,000

4. 90,000

5. 60,000

Step-by-step explanation:

Remember if the thousands digit is 5 or greater, round up, if the thousands digit is 4 or less, round down.

57342 (up) 76564 (up) 95634 (up) 85756 (up) 63526 (down)

Answer:

1647

Step-by-step explanation:

Given the following information:

Length of traffic = 8 miles

Average Length of vehicles on the road :

Cars = 14.5 feets

Trucks = 21 feets

18 Wheeler tractor = 73 Feets

% distribution of the different vehicles :

Cars = 70% = 0.7

Trucks = 20% = 0.2

18 wheeler tractor = 10% = 0.1

Distance between vehicles = 4feets

Number of vehicles stuck in the traffic :

Let number of vehicles = v

Summation of (number of vehicles * length of each vehicle) + distance between each vehicle = Length of traffic

Total distance between each vehicle = 4(v-1)

(0.7v * 14.5) + (0.2v * 21) + (0.1v * 73) + 4(v - 1) = 8 miles

1 mile = 5280

8 miles = (5280 * 8) = 42,240

10.15v + 4.2v + 7.3v + 4v - 4 = 42240

25.65v = 42240 + 4

25.65v = 42244

v =42244 / 25.65

v = 1646.939

v = 1647.

Answer:

ok

Step-by-step explanation:

The values of the functions are:

a. When x =-4 then f(x) =  -x+4

b. When x = -2 then f(x) =  -x+4

c. When x = -1 then f(x) =  -x+4

d. When x=1/2 then f(x) = 3

e. When x = 2 then f(x) =  2x-5

Given, g(x) = {-x+4 , if x≤-1

                      3 ,   if -1≤x<2

                      2x-5, if x≥2 }

a. when x = -4, f(x) = ?

-4 comes under the condition x≤-1.

therefore, when x=-4 ⇒ f(x) = -x+4

f(-4) = -4+4 = 0

b. when x=-2, f(x)= ?

Again -2 comes under the condition if x≤-1

therefore when x=-2 ⇒ f(x) = -x+4

f(-2) = -2+4 = 2

c. when x=-1, f(x) = ?

-1 comes under the condition if x≤-1

therefore, when x=-1 then f(x) = -x+4

f(-1) = -1+4 = 3

d. when x=1/2 , f(x) = ?

1/2 comes under the condition, if -1≤x<2

therefore, when x=1/2 then f(x) = 3.

e. when x=2, f(x) = ?

2 comes under the condition, if x≥2

therefore, when x=2 then f(x)= 2x-5.

hence we get the required results of the given functions.

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If the volume of the cone is 96 cm^3 and the radius is 6 cm then the height of the cone is equal to 2.55 cm.

The height of the cone can be defined as the extent of the altitude of the cone. The height of a cone can be determined using its volume and radius values. The formula for the volume of a cone can be given as:

V= πr²h/3

Here, V is the volume of the cone, r is the radius of the cone and h is the height.

This equation can be rearranged to find the value of height as follows,

h=3V/πr²

Now, add the given values to the equation,

h= 3(96)/π(6²)

h= 288/π(36)

As π = 3.14

h= 288/3.14(36)

h= 288/ 113.04

h= 2.55 cm

Thus, the height of the cone is calculated to be 2.55 cm.

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Answer:

I believe the multiplied number would be 4.

39 × 4 = 156

The number is = 4

Step-by-step explanation:

I'm not sure what is 46 at the end of the question.

The price of a banana is 0.71 (after round off) USD per pound.

Here the price of a banana in Mexico was 34 pesos per kilogram.

price of a banana in Mexico = 34 pesos per kilogram

We are provided with the following information,

1 kg = 2.205 pounds,

and 1 Peso = 0.04574USD

We have to find the price in USD per pound,

So we have,

=(34 × 0.04574 )÷ 2.205

= 0.7105 USD per pound

= 0.71 USD per pound   (after round off)

Therefore the price of a banana in UDS per pound is 0.71 ( after round off) .

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Answer:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

Step-by-step explanation:

When writing an algebraic fraction as an identity, if its denominator has repeated linear factors, the power of the repeated factor indicates how many times that factor should appear in the partial fractions.

Write out the fraction as an identity:

[tex]\begin{aligned}\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^2}\\\\\implies \dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A(x+1)^2}{x(x+1)^2}+\dfrac{Bx(x+1)}{x(x+1)^2}+\dfrac{Cx}{x(x+1)^2}\\\\\implies 5x^2+20x+16 & \equiv A(x+1)^2+Bx(x+1)+Cx\end{aligned}[/tex]

Calculate the values of A and C using substitution:

[tex]\begin{aligned}\textsf{When }x=0 \implies 16 & =A(1)+B(0)+C(0) \implies A=16\\\\\textsf{When }x=-1 \implies 1 & =A(0)+B(0)+C(-1) \implies C=-1\end{aligned}[/tex]

Substitute the found values of A and C and expand the identity:

[tex]\begin{aligned}\implies 5x^2+20x+16 & \equiv 16(x+1)^2+Bx(x+1)-x\\& \equiv 16x^2+32x+16+Bx^2+Bx-x\\& \equiv (16+B)x^2+(31+B)x+16\\\end{aligned}[/tex]

Compare the coefficients of the x² term to find B:

[tex]x^2 \textsf{ term } \implies 16+B =5\implies B & =-11[/tex]

Replace the found values of A, B and C in the original identity:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

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Answer:

nothing there

Step-by-step explanation:

Step-by-step explanation:

or,(-6)=3(3-2x)

or,(-6)=9-6x

or,-6-9=-6x

or,-15=-6x

or,-15+6=x

or,-9=x

x=-9

The remarkable thing that was made by the Mound Builders is (C) large cities

In the Ohio River Valley, Native American tribes constructed mounds and enclosures for burial, religious, and even defense purposes. For dramatic effect, they frequently constructed their mounds on or near tall cliffs or bluffs, as well as in rich river valleys.

Mound Builders were not one particular group of people; rather, they were pre-Columbian tribal groups that erected massive earthen constructions known as mounds throughout North America. These mounds were used as houses, burial grounds, and ceremonial hubs, among other things.

In conclusion, the remarkable thing that was made by the Mound Builders is large cities.

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Answer:

x = - 1 and x = 5

Step-by-step explanation:

the zeros are the values of x where the graph crosses the x- axis

the graph crosses the x- axis at x = - 1 and x = 5 , then the zeros are

x = - 1 and x = 5

Answer:

Step-by-step explanation:

2x+18=6y

2x=6y−18

(2x)/2=(6y−18)/2

x=3y−9

Answer:

Step-by-step explanation:

2x  +  18+− 18=6y  +  −18

2x  =  6y − 18

2x / 2= 6y −18 / 2

x  =  3y −9

The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

It should be noted that even numbers can be divided by 2.

The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.

Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

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Answer:

127°

Step-by-step explanation:

The angle that's represented with x and the angle with the measure 127 are alternate exterior angles because line m and line n are parallel.

And alternate angles has equal measures so if one is 127 then so is the other.

Therefore the value of x = 127

The value of the function f(x) = 2x/(2x + 3).

A function is defined as a relationship between a set of inputs that each have one output.

Now, as per the question, the functions are give as;

h(x) = (2x + 3)/x

g(x) = 2/x

And, g(f (x) ) = h(x) =  (2x + 3)/x  ......(equation 1)

To estimate the value of f (x); Substitute x for f(x)

g(f (x) ) = 2/f (x)     ......(equation 2)

Equation (equation 1 and 2).

2/f (x) =  (2x + 3)/x

f (x) = 2x/ (2x + 3)

Thus, the value of the function f (x) = 2x/ (2x + 3).

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The correct question is-

The function h (x) = StartFraction 2 (x + 3) Over x EndFraction is a result of the composition (g compose f) (x). If g (x) = StartFraction 2 over x EndFraction, what is f(x)?

The expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle is [tex]\frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

It is given that:-

Radius of circle = 2r

Length of side of equilateral triangle = 3x

We have to find the expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle.

We know that,

Area of circle = [tex]\pi R^2[/tex]

Where R is the radius of the circle.

We have R = 2r

Area of an equilateral triangle = [tex]\frac{\sqrt{3} }{2}a^2[/tex]

Where, a is the length of side of equilateral triangle.

a = 3x

Hence,

Expression = [tex]\pi R^2-\frac{\sqrt{3} }{2}a^2[/tex]

Expression = [tex]\frac{22}{7}*(2r)^2-\frac{\sqrt{3} }{2}*(3x)^2 = \frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

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The complementary solution is Ус = C₁е¯ + C₂е¯ -6x

Consider the differential equation

=y" + 7y' + 6y = 30...(1)

Rewrite the equation,(D² + 7D + 6)y = 30 where

d /D = dx

Auxiliary equation is,

f(m) = 0

3 m³ +7m+6=0

m² + 6m+m+6=0

m(m+6) +1(m+6) = 0

(m +6)(m + 1) = 0

m = −1, −6 -6

Hence,

The complementary solution is Ус = C₁е¯ + C₂е¯ -6x

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Answer:

  3/5 < 3/4   (The symbol you need is <.)

Step-by-step explanation:

The problem is asking you to compare the fractions 3/5 and 3/4. You need to supply a comparison symbol, one of {<, =, >}.

In general, when you are asked to compare two values, you are being asked which one is greater (or smaller). Sometimes, you are being asked for the amount by which one is greater than the other (their difference), and sometimes you are being asked for the factor by which one is greater than the other (their ratio).

You can do the arithmetic to find the appropriate difference or ratio, or you can use your number sense to identify the larger (or smaller) number.

As you know, the denominator of a fraction tells you how many pieces the pie has been divided into.

In the fraction 3/5, the 5 tells you each piece is 1/5 of the whole, that there are 5 equal pieces.

In the fraction 3/4, the 4 tells you each piece is 1/4 of the whole, that there are 4 equal pieces.

A pie divided into 5 pieces instead of 4 has smaller pieces. That is ...

  1/5 < 1/4

When there are 3 pieces of each, this relation still holds:

  3×(1/5) < 3×(1/4)   ⇒   3/5 < 3/4

__

Additional comment

Here, the numerators are the same, so we only need to compare the denominators to find the relationship. If the denominators are the same, we can compare the numerators.

If neither is the same, it is often useful to multiply one or the other or both of the fractions by some value so they will have a common numerator or denominator. The usual recommendation is to give the fractions a common denominator.

Here, the denominators can be made to be 20 in each case.

  [tex]\dfrac{3}{5}=\dfrac{3}{5}\cdot\dfrac{4}{4}=\dfrac{12}{20}\\\\\dfrac{3}{4}=\dfrac{3}{4}\cdot\dfrac{5}{5}=\dfrac{15}{20}[/tex]

The denominators are now the same, so we can compare values by comparing the numerators. 12 < 15, so 12/20 < 15/20 and 3/5 < 3/4.

Answer:

1/48 should be added.

Step-by-step explanation:

If you add 9/16 to -7/12 you will get -1/48. Then do -7/12 + 1/48 and it will give you 9/16.

The weighted average of the given coordinates weights is; 3

We are given that;

Coordinate of -5 has a weight of 3

Coordinate of 3 has a weight of 1

Now, we are given the formula to calculate the weighted average as;

WA = Sum of the Weighted Values/Sum of the Weights

Thus;

WA = ((-5 * 3) + (3 * 1))/(3 + 1)

WA = (-15 + 3)/4

WA = -12/4

WA = -3

We will take the absolute value which is; WA = 3

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Step-by-step explanation:

4 consecutive odd integers means we start with x, then have x+2, x+4 and then x+6.

and then we have

-24 = x + x+2 + x+4 + x+6 = 4x + 12

4x = -36

x = -9

x+2 = -7

x+4 = -5

x+6 = -3

so, in sequence from small to large these 4 numbers are

-9, -7, -5, -3

Step-by-step explanation:

if you did not leave anything out, all we can do is

T = CB - 6

T + 6 = CB

C = (T + 6)/B

The number of customers waiting in line at the bank over a 24-hour period is a discrete variable type.

A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. when triple coins are turned, the count of heads. The number of pupils, kids, the shoe size, and so forth are some typical examples of discrete data. A statistical variable is referred to as a discrete variable if it presupposes a finite collection of data and a countable number of values. Contrarily, a continuous variable is a quantitative variable that accepts an endless quantity of data and an uncountable number of values.

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The solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression ( 9y² - 4x )( 9y ² + 4x) will be solved as below:-

Use the formula:- ( a + b ) ( a - b ) = a² - b²

a = 9y²

b = 4x

( 9y² - 4x )( 9y ² + 4x ) = ( 9y² )² - ( 4x )²

Therefore, solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

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Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

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Answer:

he has $15 left

Step-by-step explanation:

$5 for each lawn

$5 * 7 lawns = $35

$20 on a video game

$35 - $20 = $15