How can I figure this out?

The value of the function g(x) = 4x⁴ - 4x³ - 10x - 51

Functions are defined as those expressions or equations showing the relationship between two variables.

From the information given, we have the functions;

f(x) = 4x³ + 3x² - 12x - 32

h(x) = 4x⁴ - 3x² + 2x - 19

(f + g(x)  = h(x)

To determine the function, let us follow the expression

f(x) + g(x) = h(x)

Make g(x), the subject of formula

g(x) = h(x) - f(x)

Substitute the expressions

g(x) =  4x⁴ - 3x² + 2x - 19 -  4x³ + 3x² - 12x - 32

Now, collect the like terms, we get;

g(x) = 4x⁴ - 4x³ - 3x² + 3x² + 2x - 12x - 19 - 32

Add or subtract the values

g(x) = 4x⁴ - 4x³ - 10x - 51

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Hello!

In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23

In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.

Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.

Solve:

(-1,-4):

Plug in coordinate.

7(-1) + 4(-4) = -23

Simplify.

-7 - 16 = -23

-23 = -23

Since it is equal, (-1,-4) is a solution.

(2,6):

Plug in coordinate.

7(2) + 4(6) = -23

Simplify.

14 + 24 = -23

38 = -23

Since it is not equal, making it false, (2,6) is not a solution.

(-5,3):

Plug in coordinate.

7(-5) + 4(3) = -23

Simplify.

-35 + 12 = -23

-23 = -23

Since it is equal, (-5,3) is a solution.

(6,-7):

Plug in coordinate.

7(6) + 4(-7) = -23

Simplify.

42 - 28 = -23

14 = -23

Since it is not equal, making it false, (6,-7) is not a solution.

Answer:

The solutions to the equation are: (-1,-4) and (-5,3).

Answer:

4

Step-by-step explanation:

14 student tickets times $12 = 168

168 + $17 = 185

210-185=25

6*4=$24

so they can buy 4 pies with 1 dollar left over

sorry if I am wrong

In 2029, there will be an estimated A, 8.66 billion people in the world.

C, t = (ln(N/N₀))/k is the equation rewritten to solve for t.

Part A:

Using the given exponential growth model, find the population in 2029 as follows:

N = N₀e^kt

N₀ = 7.95 billion (present population)

k = 1.08% = 0.0108 (rate of increase)

t = 2029 - 2022 = 7 (number of years)

N = 7.95 billion × e^(0.0108×7)

N ≈ 8.66 billion

Therefore, the world's population is expected to be 8.66 billion in 2029. Answer choice A is correct.

Part B:

To solve for t, isolate it on one side of the exponential growth model equation. Taking the natural logarithm of both sides:

ln(N/N₀) = kt

Divide both sides by k:

t = ln(N/N₀)/k

Therefore, the equation rewritten to solve for t is t = (ln(N/N₀))/k. Answer choice C is correct.

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650 adult tickets were sold.

Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.

From the problem, we know that:

A + C = 1000 (the total number of tickets sold is 1000)

8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)

We can use the first equation to solve for A in terms of C:

A = 1000 - C

Substituting this expression for A into the second equation, we get:

8.50(1000 - C) + 4.50C = 7100

Expanding and simplifying:

8500 - 8.50C + 4.50C = 7100

4C = 1400

C = 350

So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:

A + 350 = 1000

A = 650

Therefore, 650 adult tickets were sold.

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The radius of the circle of the equation is 19 units

From the question, we have the following parameters that can be used in our computation:

x² + y² = 19²

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

using the above as a guide, we have the following:

Center = (a, b) = (0, 0)

Radius = r = 19

Hence, the radius of the circle of the equation is 19 units

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Answer:does anyone have the image

Step-by-step explanation:

Answer:

The numerical values of the circumference and area are equal

Step-by-step explanation:

Circumference: 12.57

Area: 12.57

12.57=12.57

Hope this helps! :)

Step-by-step explanation:

If we let A be the event that Trevor studies for at least 50 minutes, and let B be the event that he passes his Algebra test, then we know:

P(A and B) = 0.88

P(A) = 0.92

We want to find the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes, or in other words, we want to find P(B|A).

We can use Bayes' theorem to find this probability:

P(B|A) = P(A and B) / P(A)

Substituting in our values, we get:

P(B|A) = 0.88 / 0.92

Simplifying this fraction, we get:

P(B|A) = 0.9565

Therefore, the probability that Trevor passes his Algebra test given that he studied for at least 50 minutes is approximately 0.9565.

The probability of the event not happening is 5/83.

Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.

If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:

1 - 88/83

To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:

83/83 - 88/83

-5/83

Therefore, the probability of the event not happening is 5/83.

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Answer:

y=2x+3

Step-by-step explanation:

When a line is perpendicular to another line, it means that the slope is the opposite reciprocal of the other slope.

We can see that line C has a slope of -1/2, meaning that the opposite reciprocal is 2.  This overall means that line D has a slope of 2.

We can also see that line d (from the graph) has a y-intercept of (0,3).

To write this equation:

y=2x+3

Hope this helps! :)

The volume of granola a cylindrical container can hold 5451.6 cubic centimeters if containers have a diameter of 20 cm and a height of 17. 4 cm.

The number of unit cubes (cubes of unit length) that can fit inside a cylinder determines its volume.

Identifying the radius (r) and height (h)
r = 10 cm
h = 17.4 cm

Calculating the volume (V) using the formula V = πr²h
V = π × (10 cm)² × 17.4 cm
V ≈ 3.14 × 100 cm² × 17.4 cm
V ≈ 5451.6 cm³

Approximately, a container will hold 5451.6 cubic centimeters of granola.

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Answer:

This function is an exponential function because the base is a constant and the exponent is a variable.

Let's first calculate the total cost of using Green Lawns for 30 weeks. We can use the formula for the sum of a geometric series to do this:

Total cost of Green Lawns =[tex]2(1 - 0.9^30) / (1 - 0.9) + 0.9^30 * 2[/tex]

Total cost of Green Lawns = [tex]2(1.7379) / 0.1 + 0.0359[/tex]

Total cost of Green Lawns = 38.8179

Now let's calculate the total cost of using Green Thumbs for 30 weeks:

Total cost of Green Thumbs = [tex]400 + 40 * 29[/tex]

Total cost of Green Thumbs = 1160

Therefore, the Yert family would save:

$1160 - $38.8179 = $1121.18

So the Yert family would save $1,121.18 by choosing Green Lawns over Green Thumbs for 30 weeks.

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The total area of the flag is the sum of the areas of the three stripes and the percentage of the flag that is gold is approximately 0.459%

Let's call this height "h".

We also know that the side lengths of the flag are in the ratio 2:3. This means that if the shortest side is 2x, then the longest side is 3x. Since the three stripes are of equal height, each one must be h/3 in height.

Now we can use this information to find the area of the gold-colored disk and the total area of the flag. The area of a circle is given by the formula A = πr^2, where r is the radius. Since the diameter is equal to the height of the center stripe (which is h/3), the radius of the disk is h/6. So the area of the disk is:

A_disk = π(h/6)^2 = πh^2/36

The total area of the flag is the sum of the areas of the three stripes. Since each stripe is h/3 in height and the shortest side is 2x, the area of each stripe is:

A_stripe = (2x)(h/3) = 2hx/3

So the total area of the flag is:

A_flag = 3(A_stripe) = 6hx

To find the percentage of the flag that is gold, we need to divide the area of the gold-colored disk by the total area of the flag and multiply by 100.

percentage = (A_disk / A_flag) x 100

Substituting our expressions for A_disk and A_flag, we get:

percentage = (πh^2/36) / (6hx) x 100

Simplifying, we can cancel out the factor of h and get:

percentage = (π/216)x100

So the percentage of the flag that is gold is approximately 0.459% (rounded to three decimal places).

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In a circle with radius 6 and angle intercepts an arc of length 3π , the angle in radians in simplest form is π/2.

In a circle, the length of an arc is proportional to the angle that it intercepts. The ratio of the arc length to the circumference of the circle is equal to the ratio of the angle in radians to 2π. Thus, we can write:

(arc length) / (circumference) = (angle) / (2π)

In this problem, we are given that the circle has a radius of 6 and that the arc length is 3π. We can use the formula for the circumference of a circle, which is C = 2πr, to find the circumference of this circle:

C = 2πr = 2π(6) = 12π

Now we can use the formula above to find the angle in radians:

(3π) / (12π) = (angle) / (2π)

Simplifying this equation, we get:

angle = (3π * 2π) / 12π = 1/2 * π

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The coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

To find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3, we can use the concept of section formula.

Let's assume the coordinates of point P are (x, y). According to the section formula, the coordinates of P can be calculated as follows:

x = (3x2 + 1x1) / (3+1) = (37 + 1(-1)) / 4 = (21 - 1) / 4 = 20/4 = 5

y = (3y2 + 1y1) / (3+1) = (38 + 12) / 4 = (24 + 2) / 4 = 26/4 = 13/2 = 6.5

Therefore, the coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

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The expression 4 that could be used to find spaces in the game piece was moved.

Since Integers are the collection of negative, and positive numbers including zero. Then the positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on the number line.

We are given that Andi moved a game piece down 4 pieces

The expression in option 1: |-4| which is equal to 4

The expression in option 2: |4| which is equal to 4

The expression in option 3: -|4| which is equal to -4

The expression in option 4: 4 which is equal to -4

∴The correct expression is option 4

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The expression (x + 1)(x - 3) represents the Area of base of the prism.

a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.

According to question:

The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).

We can find the height of the prism by dividing the volume by the area of the base:

B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)

Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.

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To find the linearization L(x) of the function f(x) = 7cos(x) at a = 3.14159265359, we'll use the formula:

L(x) = f(a) + f'(a)(x - a)

where f'(x) is the derivative of f(x) with respect to x.

First, let's find the value of f(a) at a = 3.14159265359:

f(a) = 7cos(a)
f(3.14159265359) = 7cos(3.14159265359) ≈ -7

Next, let's find the value of f'(a) at a = 3.14159265359:

f'(x) = -7sin(x)
f'(a) = -7sin(a)
f'(3.14159265359) = -7sin(3.14159265359) ≈ 0

Now we have all the pieces we need to plug into the formula for L(x):

L(x) = f(a) + f'(a)(x - a)
L(x) = -7 + 0(x - 3.14159265359)
L(x) = -7

So the linearization of the function f(x) = 7cos(x) at a = 3.14159265359 is:

L(x) = -7

To find the linearization L(x) of the function f(x) = 7cos(x) at a specific point a, we'll use the formula:

L(x) = f(a) + f'(a)(x - a)

Given that a = 3.14159265359 (approximating π), first we need to find f(a) and f'(a).

1. f(a) = 7cos(a) = 7cos(3.14159265359) ≈ -7
2. To find f'(x), we take the derivative of f(x):
f'(x) = -7sin(x)

Now, we can find f'(a):
f'(a) = -7sin(3.14159265359) ≈ 0

Finally, we can plug these values into the linearization formula:
L(x) = -7 + 0(x - 3.14159265359)

Simplifying, we get:

L(x) = -7

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The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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F(x) and G(x) are polynomial functions in which the expression f(x) + g(x) is always a polynomial and f(x)/g(x) is sometimes a polynomial.

Let F(x) be a polynomial = 2x + 4

g(x) be a polynomial = 6x² + 12x

putting the value in the expression

f(x) + g(x) = 2x + 4 + 6x² + 12x

f(x) + g(x) = 6x² + 14x + 4

6x² + 14x + 4 is a polynomial

Now, putting the value in the equation

f(x)/g(x) = 2x + 4/6x² + 12x

Taking 3x common from 6x² + 12

We get 3x(3x+4)

f(x)/g(x) = 2x+4/3x(2x+4)

f(x)/g(x) = 1/3x

1/3x is not a polynomial

Hence, it sometimes a polynomial.

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If all the dimensions of a cube increase by a factor of 3/2, the surface area will increase by a factor of 9/2.

If all the dimensions of a cube increase by a factor of 3/2, then the new dimensions of the cube will be 3/2 times the original dimensions.

Let's say the original side length of the cube was "s". Then the new side length would be (3/2)*s.

The surface area of a cube is given by the formula 6s^2, where s is the side length.

So the original surface area of the cube would be:

6s^2

And the new surface area of the cube would be:

6(3/2s)^2
= 6(9/4)s^2
= 27/2 s^2

To find how many times greater the new surface area is compared to the original surface area, we can divide the new surface area by the original surface area:

(27/2 s^2) / (6s^2)
= (9/2)

So the new surface area is 9/2 times greater than the original surface area.

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Answer:

a = - 5 , b = 1

Step-by-step explanation:

2a = - 2 + 4(a + 3) ← distribute parenthesis

2a = - 2 + 4a + 12 ( subtract 4a from both sides )

- 2a = 10 ( divide both sides by - 2 )

a = - 5

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

- 4b = - 5(3 - b) + 6 ← distribute parenthesis

- 4b = - 15 + 5b + 6 ( subtract 5b from both sides )

- 9b = - 9 ( divide both sides by - 9 )

b = 1

Step-by-step explanation:

2a=6(a+3)

2a=6a+18

2a-6a=18

-4a=18

-4a/-4=18/-4

a=-4.5

The expression that fits perfect for the given requirement is 5z + 7.50, under the condition that a food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole.

Here we have to apply the principles of solving algebraic equations, due to the expression provided.

From the  given information, here the food truck owner charges z dollars per burrito combo along with $1.50 for a side of guacamole.

According to the information it is given that the  expression is  5(z+1.50)  which helps to state the total cost of 5 burrito combos and 5 sides of guacamole.

Lets now formulate the expression for the given required equation

= 5(z + 1.50)

= 5z + 7.50.

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A food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole. The expression 5(z+1.50) represents the total cost of 5 burrito combos and 5 sides of guacamole. What expression also represent the cost of 5 burrito combos and 5 sides if guacamole that cost 1.50 each.

To get 51 using the numbers 8, 5, 6, and 7 exactly once each, you can use the following mathematical expression:

(8 x 6) - 7 + 5 = 51

How it works:

1. Multiply 8 by 6 to get 48: (8 x 6) = 48

2. Subtract 7 from 48 to get 41: 48 - 7 = 41

3. Add 5 to 41 to get 51: 41 + 5 = 51

Therefore, (8 x 6) - 7 + 5 = 51.

Answer:

Step-by-step explanation:

8 x (7 - 5) + 6 = 51

Answer:

"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:

Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.

Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.

Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.

Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.

Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.

Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.

Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.

Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.

Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.

Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.

Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.

Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.

Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.

Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.

Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.

Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.

Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.

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The equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

To solve for x in 3/5 (30 x - 15) = 72, we can first simplify the left side by distributing the 3/5:

3/5 (30 x - 15) = 18 x - 9

Now we can solve for x by setting the right side equal to 72:

18 x - 9 = 72

Adding 9 to both sides:

18 x = 81

Dividing by 18:

x = 4.5

So we know that option E is one of the correct answers.

To check which of the other options have the same value of x, we can substitute x = 4.5 into each equation and see if it simplifies to 72:

A. 18 x - 15 = 72

18(4.5) - 15 = 72

81 - 15 = 72 (not equivalent)

B. 50 x - 25 = 72

50(4.5) - 25 = 200 - 25 = 175 (not equivalent)

C. 18 x - 9 = 72

18(4.5) - 9 = 72 (equivalent)

D. 3 (6 x - 3) = 72

3(6(4.5) - 3) = 3(24) = 72 (equivalent)

Therefore, the equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.

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The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.

To calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.

1. 112 seconds × 0.8 feet per second = 89.6 feet

2. 120 seconds × 0.6 feet per second = 72 feet

The distance from sea level is now: 89.6 feet - 72 feet

= 17.6 feet

The time, in seconds, that it will  take for the scientist to travel back to sea level at 3.5 feet per second will be:

17.6 feet ÷  3.5 feet per second

5.0 seconds to the nearest tenth.

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To find the percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race, we'll use the following formula:
Percent Error = (|(Measured Value - Actual Value)| / Actual Value) * 100

Here, the Measured Value is the stopwatch's time (32.4 seconds), and the Actual Value is the electronic touchpad's time (32.36 seconds).

Step 1: Calculate the absolute difference between the measured and actual values:
|32.4 - 32.36| = 0.04

Step 2: Divide the absolute difference by the actual value:
0.04 / 32.36 = 0.001236

Step 3: Multiply the result by 100 to get the percentage:
0.001236 * 100 = 0.1236%

The percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race is approximately 0.124%.

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The radian measure -1.7 pi is equivalent to -306 degrees.

To find the percent error of the stopwatch's measurement, we need to compare it to the more precise electronic touchpad measurement. The formula for percent error is:

percent error = (|measured value - actual value| / actual value) x 100%

In this case, the measured value is 32.4 seconds, the actual value is 32.36 seconds, and the absolute difference between them is 0.04 seconds. Plugging these values into the formula, we get:

percent error = (|32.4 - 32.36| / 32.36) x 100% = 0.124%

Therefore, the percent error for the stopwatch's measurement is 0.124%. This means that the stopwatch's measurement was very close to the actual value, with an error of only 0.124% of the actual value.

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