(x^2-x-12)/(x+5)=x-6

Answer: x=16, y=9

Step-by-step explanation:  Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)

So the two angles add up to 180°

x+19 + 9x + 1 = 180°

combine like terms

10x + 20 = 180

subtract 20

10x = 160

divide by 10

x = 16

Now you can find the measure of the angle marked 9x+1.

9(16) + 1

= 144 + 1

= 145

Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°

3y + 8 + 145 = 180

combine like terms

3y + 153 = 180

subtract 153

3y = 27

divide by 3

y = 9

-Hope this helps! Thanks, have a good day :-)

Answer: 13,708 ft

Step-by-step explanation:

To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:

13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft

Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.

Answer: The difference is 13,708 ft.

Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].

Given that a valley is 390 feet below sea level.

So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].

So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]

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Answer:

Step-by-step explanation:

|x-3|=x-3,if x-3≥0,or x≥3

|x-3|=-(x-3),if x-3<0 ,or x<3

Answer:

The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay.

We can use the following formula to calculate the half-life (t1/2) of a substance with a decay rate of r:

t1/2 = (ln 2) / r

where ln 2 is the natural logarithm of 2 (approximately 0.693).

In this case, the decay rate is 2.5% per year, or 0.025 per year. Plugging this into the formula, we get:

t1/2 = (ln 2) / 0.025

t1/2 = 27.73 years (rounded to two decimal places)

Therefore, the half-life of the substance is approximately 27.73 years.

1. Begin the program by including the header file <iostream> which includes basic input/output library functions as well as the <vector> library which is needed for this program.

2. Declare a vector of integer type named 'ageGroups' which will store the age groups and the corresponding membership fee and reductions.

3. Create a void function named 'calculateFee()' which will take a parameters age and activities attended.

4. In the calculateFee() function, use the switch statement for the age group and store the corresponding membership fee and reduction value in variables.

5. Use an if statement to check that the number of activities attended is non-negative.

6. Calculate the membership fee using the variables and store it in a variable named 'fee'.

7. Use an if statement to check if the fee is less than 1 and if yes, assign the fee to 1.

8. Print the fee to the user.

9. End the program.

Answer:

g

Step-by-step explanation:

The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.

Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2

However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.

In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:

sin(π - π/3) = sin(2π/3) = √3/2

This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:

sin(π + π/3) = sin(4π/3) = -√3/2

This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.

Let me know if this helped by hitting brainliest! If you have a question, please comment and I"ll get back to you ASAP!

Answer:

We know that sin(π/3) = √3/2, so we can write:

arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ

where n is an integer.

Therefore, the values of arcsin(-√3/2) are:

a. π/3 + 2nπ

c. 11π/6 + 2nπ

e. 2π/3 + 2nπ

f. 7π/6 + 2nπ

So, options a, c, e, and f are all correct.

Answer:

Step-by-step explanation:

Area = 8 x 4 =24

Area doubled = 48

Let x be the amount we increase width and length to get area =48.

  [tex](6+x)\times (4+x)=48[/tex]

       [tex](x+6)(x+4)=48[/tex]

       [tex]x^2+10x+24=48[/tex]

       [tex]x^2+10x-24=0[/tex]

     [tex](x+12)(x-2)=0[/tex]

[tex]\text{gives }x=-12,2[/tex]

But [tex]x=-12[/tex] is not a practical solution.

So [tex]x=2[/tex] is the required solution.

We must increase the length and width by 2.

Hi Martin,

To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.

The total purchase cost of all three items is:

Snow shovel: $28.61

Winter coat: $23.27

Rock salt: $7.96

Total purchase cost: $59.84

Now, we apply the applicable taxes:

State tax: 5% of $59.84 = $2.99

County tax: 0.5% of $59.84 = $0.30

City tax: 2.5% of $59.84 = $1.49

Total taxes: $2.99 + $0.30 + $1.49 = $4.78

Therefore, the total purchase price is:

Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62

Answer:

The shaded region in all of the answers are equal.

Step-by-step explanation:

Since squares have equal sides, the area of each square is 12 squared or 144.

The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.

The area of the shaded region of A is 144-36pi.

In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.

The area of the shaded region of B is 144-36pi.

In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.

The area of the shaded region of C is 144-36pi.

The equation of the tangent line to the graph of the function at x = 7 is:    y = -1/49 x + 50/343, the equation of the normal line to the graph of the function at x = 7 is: y = 49x - (2402/7) and  slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.

a) To find the tangent line to the graph of the function at x = 7, we need to find the slope of the function at that point. We can use the derivative of the function to find the slope:

f(x) = 1/x

f'(x) = -1/x^2

So, at x = 7, the slope of the tangent line is:

m = f'(7) = -1/7^2 = -1/49

To find the equation of the tangent line, we also need a point on the line. We know that the point (7, 1/7) is on the graph of the function, so we can use that as our point. Using the point-slope form of a line, we have:

y - 1/7 = -1/49(x - 7)

Simplifying this equation, we get:

y = -1/49 x + 50/343

So the equation of the tangent line to the graph of the function at x = 7 is:

y = -1/49 x + 50/343

b) To find the normal line to the graph of the function at x = 7, we need to find a line that is perpendicular to the tangent line we found in part (a). The slope of the normal line is the negative reciprocal of the slope of the tangent line:

m(normal) = -1/m(tangent) = -1/(-1/49) = 49

Using the point-slope form of a line again, we can find the equation of the normal line that passes through the point (7, 1/7):

y - 1/7 = 49(x - 7)

Simplifying this equation, we get:

y = 49x - [(2402)/7]

So the equation of the normal line to the graph of the function at x = 7 is:

y = 49x - (2402/7)

Problem 42:

We can use the limit definition of the derivative to find the slope of the tangent line to the graph of y = 5x^3 at the point (2,40).

Using the formula for the derivative:

dy/dx = lim(h→0) [(f(x+h) - f(x))/h]

we can calculate the slope of the tangent line at x = 2.

Plugging in the given function, we get:

[tex]\frac{dy}{dx} = \lim_{h \to 0} [(5(2+h)^3 - 40) / h][/tex]

[tex]= \lim_{h \to 0} [(40 + 60h + 30h^2 + 5h^3 - 40) / h]\\= \lim_{h \to 0} [60 + 30h + 5h^2]\\= 60[/tex]

Therefore, the slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.

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Answer:

The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.

The total number of students in the survey is:

50 + 75 + 125 + 50 = 300

The number of students who voted for the Republican party is:

75 + 50 = 125

Therefore, the probability of selecting a student who voted for the Republican party is:

125/300 = 0.4167 (rounded to four decimal places)

So, the answer is option D: 125/300

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Check the picture below.

[tex]\measuredangle G=\cfrac{\stackrel{far~arc}{148}-\stackrel{near~arc}{106}}{2}\implies \measuredangle G=21^o \\\\\\ \hspace{6em}\measuredangle F=\cfrac{106}{2}\implies \measuredangle F=53^o\hspace{8em}\measuredangle G=106^o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle FGH\textit{ is not an isosceles}~\hfill[/tex]

Answer:

Step-by-step explanation:

[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]

Answer:

B

Step-by-step explanation:

5^2 is the small square, 4(3x4x1/2) are the 4 triangles

Answer: The answer would be B.

Step-by-step explanation:

Hello.

First, we know that the smaller square is 5, and to find the area of the big square, we need to square 5 to get the area. We also know that C wouldn't  be a viable option, so, our only remaining choices are A and B. We know that without the smaller square, there are 4 triangles, and the Area of a Triangle is: 1/2*b*h. So, this also takes A out as an option as well. After this, you will have your answer as B; 5^2 + 4(3 * 4 * 1/2)

(Or, you could have found the Area of the Triangles, and realize that neither A, nor C have those options, making B the answer by default.)

Hope this helps, (and maybe brainliest?)

The documentation "Prints all positive odd integers that are less than or equal to max" is the most appropriate documentation for the printNums procedure, as it accurately describes the behavior of the procedure. so, the option C) is correct.

This procedure uses a loop to display all positive odd integers less than or equal to the input parameter max. It starts by initializing a count variable to 1, and then uses a repeat-until loop to display the current value of count and increment it by 2 until count is greater than max.

The documentation provided is concise, clear, and accurately describes what the procedure does, making it easy for users to understand the purpose and behavior of the procedure. So, the correct answer is C).

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_____The given question is incomplete, the complete question is given below:

In the following procedure, the parameter max is a positive integer.

PROCEDURE printNums(max)

{

count ← 1

REPEAT UNTIL(count > max)

{

DISPLAY(count)

count ← count + 2

}

}

Which of the following is the most appropriate documentation to appear with the printNums procedure?

a, Prints all positive odd integers that are equal to max.

b, Prints all negative odd integers that are less than or equal to max.

c, Prints all positive odd integers that are less than or equal to max.

d, Prints all negative odd integers that are less than or equal to max.

To find the experimental probability for each outcome, we divide the number of times the cup lands in that position by the total number of tosses:

What is a outcome?

An outcome refers to a possible result of an experiment or event that is used to calculate the probability of that result occurring.

What is meant by experimental probability?

Experimental probability is the probability of an event based on actual, repeated trials or experiments rather than theoretical or mathematical calculations.

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The value of local maximum and local minimum for the function f(x) = x^2/(x -1 ) is equal to f(0) = 0 at x = 0 and f(2) = 4 at x = 4 respectively.

Local maximum and minimum values of the function

f(x) = x^2 / (x - 1),

Use both the first and second derivative tests.

First, let's find the critical points of the function,

By setting its derivative equal to zero and solving for x,

f'(x) = [2x(x - 1) - x^2] / (x - 1)^2

⇒ [2x(x - 1) - x^2] / (x - 1)^2 = 0

Simplifying this expression, we get,

x(x - 2) = 0

This gives us two critical points,

x = 0 and x = 2.

These critical points correspond to local maxima, local minima, or neither.

Use the second derivative test,

f''(x) = [2(x - 1)^2 - 2x(x - 1) + 2x^2] / (x - 1)^3

At x = 0, we have,

f''(0) = 2 / (-1)^3

       = -2

Since the second derivative is negative at x = 0, this critical point corresponds to a local maximum.

f(0) = 0^2/ (0 -1 )

      = 0

At x = 2, we have,

f''(2) = 2 / 1^3

       = 2

Since the second derivative is positive at x = 2, this critical point corresponds to a local minimum.

f(2) = 2^2/ (2 - 1)

     = 4

Therefore, at x = 0, the local maximum value is f(0) = 0, and at x = 2, the local minimum value is f(2) = 4.

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Answer:

Step-by-step explanation:

Number of cats = 8 - 3 = 5

Fraction that are cats [tex]=\frac{5}{8}[/tex]

Step-by-step explanation:

Hey mate, if there are no red balls inside the bag then the probabililty will be obviously 0

When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12

The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.

According to the intermediate value theorem,

since g(x) is a continuous function on the closed interval [1, 6]

since g(1) = 18 is greater than 12, and

g(6) = 11 is less than 12,

there must be at least one value c between 1 and 6 where g(c) = 12.

Therefore, we can conclude that a value of c does exist such that g(c) = 12.

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Answer:

9. $18  

10. 68

Step-by-step explanation:

$8 + $2 + $3 + $5= $18

104 - 36= 68

Answer:

A. 1/2 ÷ 2 = 1/4 is true.

B. 1/3 ÷ 4 = 1/12 is true.

C. 1/2 ÷ 6 = 1/12 is true.

D. 1/5 ÷ 2 = 1/10 is true.

E. 1/8 ÷ 3 = 1/24 is true.

Therefore, all the quotients are true.

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Answer:

0.38

Step-by-step explanation:

There are a total of 38 pescatarians and 35 vegetarians. This is obtained by looking at the column totals for those categories and includes both males and females

There are a total of 190 participants in the survey

P(pescatarian) = 38/190

P(vegetarian) = 35/190

P(pescatarian or vegetarian)

= P(pescatarian)  + P(vegetarian)

= 38/190  + 35/190

= 73/190

= 0.3842

= 0.38 (rounded to hundredths place)

The relationship between AB and BC is given as follows:

AB > BC.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

The supplementary angles for this problem are given as follows:

By the law of sines, we have that:

AB/sin(110º) = BC/sin(70º).

As sin(110º) > sin(70º), the inequality for this problem is given as follows:

AB > BC.

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Answer:

AB>BC

Step-by-step explanation:

AI-generated answer

Based on the given information, the relationship between AB and BC depends on the measure of angle ZADB. If mZADB is 110°, we can determine the relationship as follows:

Since triangle ABD and triangle CBD share side AB, the larger the angle ZADB, the longer the side AB will be compared to side BC. Therefore, if mZADB is 110°, we can conclude that AB is greater than BC.

In summary, when mZADB is 110°, the relationship between AB and BC is:

AB > BC.

Work Shown:

A = P*(1+r/n)^(n*t)

6700 = 5500*(1+0.045/1)^(1*t)

6700/5500 = (1.045)^t

1.218182 = (1.045)^t

log( 1.218182 ) = log(  (1.045)^t )

log( 1.218182 ) = t*log( 1.045 )

t = log(1.218182)/log(1.045)

t = 4.483724

t = 4.5

It takes about 4.5 years to reach $6700

Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex]                              [break the cube root as power [tex]1/3[/tex]]

Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex]                    [break [tex]875=125\times7[/tex]]

                                                                     [tex]125=5^3[/tex]

Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex]       [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]

Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]]

Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]

Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]

Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]

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Answer:

5/3

Step-by-step explanation:

1×3=3

3+2=5

So answer is 5/3