Encuentra el área de la región coloreada.

​

Answer:

  x = 2

Step-by-step explanation:

You want x such that dividing by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10.

  (x/5) +2 . . . . the value after dividing by 5 and adding 2

  (x +22)/10 . . . . the value after adding 22, then dividing by 10

These two outcomes are the same:

  x/5 +2 = (x +22)/10

Multiplying the equation by 10 gives ...

  2x +20 = x +22

  x = 2 . . . . . . . . . . . . subtract x+20

The number is x = 2.

__

Additional comment

The outcome in each case is 2.4.

The measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

According to the question,

We have the following information:

Angle CAB = 2x

Angle CBA = 3x-20

And the given triangle is a right-angled triangle which means that one of its angle is 90°.

Now, we know that the sum of three angles of a triangle is 180°.

So, we have the following expression:

2x+3x-20+90 = 180°

5x+70 = 180

5x = 180-70

5x = 110

x = 110/5

x = 22°

Now, putting the value of x in given angles:

Angle CAB = 2x

Angle CAB = 2*22

Angle CAB = 44°

Angle CBA = 3x-20

Angle CBA = 3*22-20

Angle CBA = 66-20

Angle CBA = 46°

Hence, the measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

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The value of t using straight line angle is 24°.

What is straight line angle ?

  A straight angle in geometry is one that has a length of 180 degrees. Because it seems to be a straight line, it is known as a straight angle. In other words, it is an angle whose sides extend in the same straight line in directions opposite to the vertex.

In mathematics, a straight angle is defined as an angle with a degree value of 180. It looks to be a straight line, hence the name "straight." In essence, two rays linked end to end create an angle according to the mathematical concept of angles. As a result, the two rays of the 180-degree angle are subtended in the direction of their endpoints, which are in the opposite direction.

Here we know that sum of angle in straight line at any point is 180° .

Then,

=> (4t-7)°+83°=180°

=> 4t-7+83 = 180

=> 4t+76 = 180

=> 4t = 180-76 = 104

=> t = 104/4 = 26°

Hence the value of t=24°

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The third term of F(n)=3n-4 is 5.

Two or more expressions with an Equal sign is called as Equation.

Given,

F(n)=3n-4

F of n equal to three times of n minus four.

We need to find the third term.

To find third term we need to plug 3 in place of n.

F(3)=3(3)-4

Three times three minus four

F(3)=9-4

Nine minus four gives 5

F(3)=5

Hence, the third term of F(n)=3n-4 is 5.

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If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10

information given in the question include

FG = 10x − 10

GH = x + 4

FH = 16

The problem is solved using substitution. this involves replacement of a variable with another that are same.

An instance of this a line FH having points FG and GH

FH contains FG and GH, hence adding both FG and GH gives FH

FH = FG + GH

plugging in the values

16 = 10x - 10 + x + 4

collecting like terms

16 = 11x - 6

16 + 6 = 11x

22 = 11x

rearranging the equation

11x = 22

x = 2

FG = 10x − 10

substituting the value of x

FG = 10 * 2 − 10

FG = 20 - 10

FG = 10

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Answer:

y = 12x + 35

95 pages

Step-by-step explanation:

Let y represent the total number of pages

Let x represent the total number of months

x = 5 (months)

so..

y = 12(5) + 35

y = 60 + 35

y = 95

The double inequality describing the length of time (in minutes) that Liz spends on her phone each night is 45 ≤ f(x) ≤ 120.

Double inequality is a mathematical expression that has two inequalities.

Double inequality is also known as a compound inequality. because there is more than one inequality in the expression

The form of double inequality is always written as: a ≤ f (x) ≤ b.

This double inequality gives the value of x as more than a and less than b.

The least number of minutes spent by Liz on her phone = 45 minutes

The maximum number of minutes spent by Liz on her phone = 120 minutes

Inequality 1: 45 ≤ f(x)

Inequality 2: f(x) ≤ 120

Thus, this double inequality 45 ≤ f(x) ≤ 120 shows Liz's time on the phone every night.

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The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.

Here we have the temperature function:

T(x) = (x - 5)^3 + 9

The turning point is the point where the curvature of the function changes,  by differentiating the function two times and finding the zero, we can get the turning points.

T'(x) = 3*(x - 5)^2

T''(x) = 3*2*(x - 5) = 6*(x - 5)

This is zero when x = 5, then:

T''(5) = 6*(5 - 5) = 0

So the turning point is there.

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Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.

Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.

Since the Ms. Morgan found that​ 30% of her 120 students are athletes, the known and unknown values include the following:

Known value (whole) = 120 students.

Known value (percent) = 30%

Unknown value (part) = ?

Next, we would determine the unknown value as follows:

Number of athletes = 30/100 × 120

Number of athletes = 30 × 1.2

Number of athletes = 36 students.

Unknown value (non-athletes) = 120 students - 36 students

Unknown value (non-athletes) = 84 students.

Since Mr. Gregory found that​ 27, or​ 15%, of his student are athletes, the known and unknown values include the following:

Known value (part) = 27 students.

Known value (percent) = 15%

Unknown value (whole) = ?

For the unknown value, we have:

Let the variable T represent the total number of students.

15/100 × T = 27

0.15T = 27

Total number of students, T = 27/0.15

Total number of students, T = 180 students.

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Complete Question:

Ms. Morgan is a science teacher. She found that​ 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that​ 27, or​ 15%, of his student are athletes. Complete parts a and b below.

a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.  

b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.​

Answer:

15h >= 200

>= means greater than or equal to. Just but a horizontal line underneath the >

The required solution to the given expression is 3 which is determined by the division operation.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To determine the evaluation of expression 4 ÷ 4/3

When considering multiplying the fractions together, After that, you would multiply the denominator across and the numerator across, respectively. Your final answer should be 12/4 However, if you simplify it by 4, your final answer will be 3.

Thus, the required solution to the given expression is 3.

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Answer:

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

According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.

The final solution of the inequality –2(5 – 4x) < 6x – 4 is x < 3.

Inequalities are expressions that have the <, >, ≤ and ≥ signs.

Therefore, let's solve the given inequality as follows:

–2(5 – 4x) < 6x – 4

open the brackets on the left side

–2(5 – 4x) < 6x – 4

-10 + 8x < 6x - 4

add 10 to both sides of the inequality

-10 + 8x < 6x - 4

-10 + 10 + 8x < 6x - 4 + 10

8x < 6x + 6

subtract 6x from both sides of the inequality

8x < 6x + 6

8x - 6x < 6x - 6x + 6

2x < 6

divide both sides of the inequality by 2

2x < 6

2x / 2 < 6 / 2

x < 3

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Answer:

y=3x+2

Step-by-step explanation:

Divide by 5 on all sides.

3x-y=-2

Step-by-step explanation:

The graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.

The given quadratic equation is h(t) = -16t² + 150t + 4.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The graph of a quadratic equation is as follows:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex: (75/16,5689/16)

Focus: (75/16,22755/64)

Axis of Symmetry: x=75/16

Directrix: y=22757/64

Plot the points (4, 348), (75/16, 5689/16), (6, 328) on graph

Therefore, the graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.

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The amount that should be invested to the nearest ten dollars is $930.

When an amount is compounded daily, it means that the investment increases in value everyday over the investment period.

In order to determine how much should be invested today, the present value of $1890 has to be determined.

The formula for determining the present value is:

PV = FV ÷ (1 + r)^nm

Where:

PV = 1890  ÷ (1.00016)^(12 x 365) = 930

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Answer:

See below

Step-by-step explanation:

You can pull  one y   and 6 n's out to start

then   4/5 = 24/30     and 5 / 6 = 25/30

and you can factor out a   -1

- y n^6 /30  ( 24  + 25 y^3n^2 )

The statement that accurately describes the difference between short-term and long-term capital gains in terms of taxes is A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.

A capital gains tax is a tax levied on profits made from the sale of a non-inventory asset. Capital gains from the sale of stocks, bonds, precious metals, real estate, and property are the most common.

Short-term capital gains are profits made from selling assets held for a year or less. Long-term capital gains, on the other hand, are gains from assets held for more than a year.

In conclusion, based on the information illustrated, the correct option is A.

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The surface area of the cone is  282.6 [tex]in^2[/tex].

What is surface area of cone?

  The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.

Here the given ,

=> Height h= 12in

=> Radius r = 5 in

Using surface area of cone formula,

=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.

=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])

=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)

=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]

Therefore surface area of the cone 282.6 [tex]in^2[/tex].

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Answer:

103 N

Step-by-step explanation:

we use the equation: w = mg

where m is mass, W is weight and g is gravitational field strength

w = ?

m= 10.5 kg

g = 9.81 ms‐² (for earth)

so,

w = 10.5 × 9.81

w = 103.005

w ≈ 103 Newtons

Answer:

b= -2

Step-by-step explanation:

This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2

-Hope this helped

Answer: x=6.

Step-by-step explanation: First go to the Algebra Calculator.

Rewriting all numbers in base 5

1000 = 13000

1001 = 13001

1002 = 13002

2000 = 31000

The base 5 number whose digits have least sum are 13000 and 31000

The decimal notation of the numbers are 1000 and 2000

Define unit number.

The rightmost point in a number or the number one are both acceptable definitions of the word "unit" in mathematics. A unit can also be an item or a person that is seen as distinct and whole but is actually a component of a whole or group. An identification number for a unit in a declaration is referred to as a unit number.

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The table of the equivalent ratios is:

Toss     Dollars  

5             2

30           12

45           18

The points are plotted in the diagram below.

Applying the knowledge of ratios we can create a table of equivalent ratios, given that it cost $12 to toss 30 rings.

Therefore, the ratio of dollars to toss is: 12:30 = 2:5.

Number of toss = x

Amount in dollars = y

Substitute k = 2/5 into y = kx to derive an equation to use to create a table of equivalent ratios:

y = 2/5x.

Therefore, wheny = 2:

2 = 2/5(x)

10 = 2x

x = 5 toss

When x = 45:

y = 2/5(45)

y = 18 dollars

The table of equivalent ratios is completed as:

Toss     Dollars  

5             2

30           12

45           18

(5, 2), (30, 12), and (45, 18), which are the points of the equivalent ratio table are plotted as shown in the diagram below.

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Answer:

log(mn^2) = 50

Step-by-step explanation:

assuming base a for the logs

log(mn^2) = log m + 2log n

Using the Quotient Rule, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

In the given question,

We have to differentiate the given function with respect to x.

The given function is [tex]y=\frac{x^4+1}{3x^4+4}[/tex]

We have differentiate with respect to x.

The given function is in fraction format. So solving the given expression we use Quotient Rule

According to Quotient Rule

"A method for recognizing issues where one function is divided by another is the quotient rule."

The formula of Quotient Rule is

[tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}[/tex]....................(1)

As we see in our function then f(x) = x[tex]^4+[/tex]1 and g(x) = 3x[tex]^4+[/tex]4

Before solving the function we find the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex]

Now solving the f(x) for f'(x) with respect to x.

f(x) = x[tex]^4+[/tex]1

[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(x^4+1)[/tex]

[tex]f'(x)=\frac{d}{dx}x^4+\frac{d}{dx}1[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

So [tex]f'(x)=4x^{(4-1)}+0[/tex]

[tex]f'(x)=4x^3[/tex]

Now solving the g(x) for g'(x) with respect to x.

g(x) = 3x[tex]^4+[/tex]4

[tex]\frac{d}{dx}g(x)=\frac{d}{dx}(3x^4+4)[/tex]

[tex]g'(x)=3\frac{d}{dx}x^4+\frac{d}{dx}4[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

[tex]g'(x)=3(4x^{(4-1)})+0[/tex]

[tex]g'(x)=3(4x^{3})[/tex]

[tex]g'(x)=12x^{3}[/tex]

Now finding the value of (g(x))[tex]^2.[/tex]

g(x) = 3x[tex]^4+[/tex]4

[tex](g(x))^4=(3x^4+4)^2[/tex]

Now using the formula of [tex](a+b)^2=a^2+2ab+b^2[/tex].

Now solving

[tex](g(x))^4=(3x^4)^2+2\times(3x^4)\times4+(4)^2[/tex]

Simplifying

[tex](g(x))^4=9x^8+24x^4+16[/tex]

Now putting the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex] in the equation (1)

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4+4)(4x^3)-(12x^3)(x^4+1)}{9x^8+24x^4+16}[/tex]

Simplifying

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4(4x^3)+4(4x^3))-((12x^3)x^4+1(12x^3))}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{(4+3)}+16x^3)-(12x^{(3+4)}+12x^3)}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{7}+16x^3)-(12x^{7}+12x^3)}{9x^8+24x^4+16}[/tex]

Now solving the bracket

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{12x^{7}+16x^3-12x^{7}-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{16x^3-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{4x^3}{9x^8+24x^4+16}[/tex]

Hence, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

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The vertex of the parabola is (-1,-1)

What is vertex of parabola?

The vertex of a parabola is the highest point or the lowest point, also known as the maximum or minimum of the parabola. The vertex is the point of intersection of the parabola and its line of symmetry.

The vertex is the maximum or minimum point of a parabola.

The vertex is the point where the parabola changes direction.

Here, the point where the parabola changes it direction is (-1,-1).

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y = -18(x-7)² + 1 is the vertex form of the given equation.

y = a (x − h) 2 + k, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (-a).

Given that y = -18x² + 252x - 881, where a = -18, b = 252 and c = -881

h = -b/2a

h = -252/2*(-18) = 7

k = ah² + bh + c = -18*49 + 252*7 - 881 = 1

Therefore, putting the values in y = a (x − h) 2 we get,

y = -18(x-7)² + 1

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The regular price of the tally set is $300.

From the information Illustrated, Great by is reducing by 250% the regular price of a tally set selling it for $225.

Let the regular price be represented by x.

Therefore, x - (25% × x) = 225

x - 0.25x = 225

0.75x = 225

Divide

x = 225 / 0.75

x = 300

The price is $300.

Note that the above percentage in the question is 25% and not 250%.

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The coordinate plane that represents both lines as well as the solution of the system is shown in the diagram below.

The solution to a system of equations is the value of x and y that will make the equations of the system true if they are plugged in into either of the two equations in the system.

Thus, when the equations or functions are plotted as a line on a coordinate grid, the system intersect at a point The coordinates of this point is the solution of the system of equations.

The function for Gary, y = 2x - 5, would be a line that has a slope of 2 and cuts the y-axis at -5, while that of Genevieve y = -3x + 4 will have a slope of -3, and will intercepts the y-axis at 4.

The red line in the coordinate grid in the image below is Gary's function y = 2x - 5, while the blue line is that of Genevieve y = -3x + 4. They bot intersect at (1.8, -1.4).

The solution is: (1.8, -1.4).

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