been trying to solve this, need help

Answer:

To factor the polynomial y = x³ + 2x² - 5x - 6 by dividing by (x + 1), we can use synthetic division:

-1  |   1   2   -5   -6

        |_______-1___-1___6

        | 1   1   -6   0

The result of the synthetic division is: x² + x - 6.

Therefore, we can write the polynomial as:

y = (x + 1)(x² + x - 6)

To factor it completely, we can factor the quadratic expression x² + x - 6:

y = (x + 1)(x + 3)(x - 2)

Therefore, the polynomial function y = x³ + 2x² - 5x - 6 can be factored completely as y = (x + 1)(x + 3)(x - 2).

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We can write an exponential function as:

The value that determines if it corresponds to growth or decay is the coefficient "b": if b is less than 1, the function represents an exponential decay, and if it is bigger than 1 it represents an exponential gorwth.

In this case, f(x) = 3 * (3/4)^x, the value of b is b=3/4 and it is less than 1, so it represents an exponential decay:

Answer: Exponential decay

Answer:

No

Step-by-step explanation:

Hope this helps!

The composite function (G o h)(0) is equal to -5.

To find (G o h)(0), we need to first evaluate h(0) and then substitute the result into g(x).

Let's start by evaluating h(0).

h(x) = x² - 1

h(0) = (0)² - 1

h(0) = 0 - 1

h(0) = -1

Now that we have h(0) = -1, we can substitute this value into g(x).

g(x) = 5x

g(h(0)) = 5(-1)

g(h(0)) = -5

Therefore, (G o h)(0) is equal to -5.

In simpler terms, we first find the output of h(0), which is -1. Then, we take this value and substitute it into g(x), resulting in -5. This means that when we apply the composed function (G o h) to the input 0, the result is -5.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

Your answer is 9

Step-by-step explanation:

√9=3

3-7=-4

Answer:

21

Step-by-step explanation:

A prime number has only two factors: 1 and itself.

A composite number has more than two factors. The number 1 is neither prime nor composite.

Answer:

B. 21

Step-by-step explanation:

31 is the only number that can be made by multiplying another number other than 1 and itself.

1x21=21

3x7=21

all the other options only have 2 factors

The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

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The surface area of a horse with the mass  is 4.5 x 10^6 square centimeters,

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

S = 10mi

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

m =  4.5 x 10^5 grams

substitute the known values in the above equation, so, we have the following representation

S =10 * 4.5 x 10^5

So, we have

S =4.5 x 10^6

Hence, the surfave area is 4.5 x 10^6

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Answer:

Anna

Step-by-step explanation:

she was the fastest

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Write down the percent divided by 100 like this:

25% = 25/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As 25 is an integer, we don't have numbers after the decimal point. So, we just go to step 3

(or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(25,100) = 25. So,

(25÷25)/(100÷25) = 1/4 when reduced to the simplest

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer: The answer is 1.62.

Explanation: It is in the image.

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

Answer: 1. {a, b, c, d, e}

2. {a, b, d}

3. {c, f, g, h}

4. {a, c}

Step-by-step explanation:

1. AUC ==> Means take all parameters from A and C.

A+C=

{a, b, c, d}+{a, e}={a, b, c, d, e}

2. B∩A ==> Means take the common parameters from B and A

B: {b, e, a, d}

A: {a, b, c, d}

Both B and A have a, b, and d.

So answer is {a, b, d}.

3. B' is every parameter that isn't in B

Reminder: B={b, e, a, d}.

All parameters: {a, b, c, d, e, f, g, h}

Remaining Parameters(B'): {c, f, g, h}

4. A-B∩C'

First, let's find C'.

C' is every parameter that isn't in C.

Reminder: C={a, e}

All parameters: {a, b, c, d, e, f, g, h}

Remaining Parameters(C'): {b, c, d, f, g, h}

Then lets find B∩C'

B: {b, e, a, d}

C': {b, c, d, f, g, h}

Both B and C' have b and d, so B∩C' is {b, d}

A-{b, d}=

{a, b, c, d}-{b, d}={a, c} ==> Answer for 4

Answer:

\(\sf 1) \quad \sf A \cup C = \{a, b, c, d, e\}\)

\(\sf 2) \quad B \cap A = \{a, b, d\}\)

\(\sf 3) \quad B' = \{c, f, g, h \}\)

\(\sf 4) \quad A -(B \cap C') = \{a, c \}\)

Step-by-step explanation:

Set Notation

\(\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}\)

Given sets:

Therefore:

Question 1

\(\begin{aligned}\sf A \cup C & = \sf \{a, b, c, d\} \cup \{a,e\}\\& = \sf \{a, b, c, d, e\}\end{aligned}\)

Question 2

\(\begin{aligned}\sf B \cap A & = \sf \{b, e, a, d\} \cap \{a, b, c, d\}\\& = \sf \{a, b, d\}\end{aligned}\)

Question 3

\(\begin{aligned}\sf B' & = \rm U - \sf B\\& = \sf \{a, b, c, d, e, f, g, h \}-\{b, e, a, d\}\\& = \sf \{c, f, g, h \}\end{aligned}\)

Question 4

\(\begin{aligned}\sf A -(B \cap C') & = \sf \{a, b, c, d \}- \left( \{b, e, a, d \} \cap \{b, c, d, f, g, h \} \right)\\& = \sf \{a, b, c, d \}- \{b, d \} \\& = \sf \{a, c \}\end{aligned}\)

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As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

Let JK be = x.

GF/GH = JI/JK

⇒ 11/18 = 36 /x

⇒ x = 36 × 18/11

⇒ x = 63.8.

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The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

You end up at point (7,5).

Step-by-step explanation:

Starting point:

The coordinates of the starting point are: x = 4, y = 6.

So

(4,6).

Move 3 units right:

Moving 3 units right is adding 3 to the x-coordinate. So

x = 4 + 3 = 7

(7,6).

Move 1 unit down:

Moving 1 unit down is subtracting 2 from the y-coordinate. So

y = 6 - 1 = 5.

You end up at point (7,5).

Answer:

157.41

Step-by-step explanation:

It can be identified that, given the figure, there is a rectangle and 2 semicircles.

Let's find the area of the rectangle first: A=L*w

Plugging in the given values => A=7.5*15.1 which equals 113.25.

Now the area for the semicircles: 1/2(3.14*r^2)

First, we need to find the radius. To find the radius, you just have to divide the diameter by 2. So, 7.5/2=3.75.

We can plug square the radius which is 3.75 and plug it into the formula: 1/2(3.14*3.75^2)=>22.078125.

22.078125 is the area of only one semicircle so we need to multiply it by 2 because we have two semicircles. So, we get 44.15625.

Finally, we can add them all up to find the total area of the figure: 113.25+44.15625=157.40625.

Rounding to the nearest hundredth=>157.41

Answer:

504 arrangements are possible

Step-by-step explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by:

\(A_{n} = n!\)

Arrangements of n elements, divided into groups:

The number of arrangements of n elements, divided into groups of \(n_1, n_2,...,n_n\) elements is given by:

\(A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}\)

In this case:

9 pens, into groups of 5, 3 and 1. So

\(A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504\)

504 arrangements are possible

It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.

Find the radius of the pool:

Since the diameter is 115 cm, the radius (r) will be half of that:

Radius (r) = Diameter / 2

r = 115 cm / 2

r = 57.5 cm

Calculate the volume of the pool when filled to a depth of 20 cm:

Since the pool is round and assuming it has a cylindrical shape, we can use the formula for the volume of a cylinder:

Volume = π × r² × h

where π (pi) is approximately 3.14159, r is the radius, and h is the height (or depth, in this case).

Volume = 3.14159 × (57.5 cm)² × 20 cm

Evaluate the volume:

Volume ≈ 3.14159 × 3306.25 cm² × 20 cm

Volume ≈ 3.14159 × 66125 cm³

Volume ≈ 207354.2 cm³

Calculate the time it takes to fill the pool to a depth of 20 cm:

We are given that the hose fills the pool at a rate of 34,000 cm³ per minute. To find out how long it will take to fill the pool, we can use the following formula:

Time = Volume / Fill Rate

Time ≈ 207354.2 cm³ / 34,000 cm³/min

Time ≈ 6.1 minutes

It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.

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Answer:

Perimeter = 2(5x-2)+2(3x-7)

Step-by-step explanation:

The perimeter (P) of any rectangle can be represented in terms of length (L) and width (W) with the equation P=2L+2W.

You multiply the length and width of the rectangle by two, since it's only giving one expression for the length and width.

Hope this helps!

Given:

Customers can pick their own blueberries at Blueberry Hill. They pay $5 to enter the patch and $4 per pound for the blueberries they pick.

Required:

We have to write an equation to model the given expression.

Explanation:

Let the total cost be y,

And x denotes the amount in pounds of blueberries.

Since, Given to enter the patch customers pay $5 (fixed)

and Given the customers pay $4 per pound for the blueberries they pick so for x pounds of blueberries cost 4x

Thus, total cost y = 4x + 5

Thus, Option (a) is correct.

Answer

Thus, Option (a) is correct.

Answer:

9.6 repeating

Step-by-step explanation:

Answer:

7 in by 6 in

Step-by-step explanation:

divide 28 and 24 by 4

Step 1: Let's recall that the midpoint of a line segment is the middle point and it is equidistant from both endpoints.

Step 2: Upon saying that, we have that:

ST = TU

Replacing with the values given in the exercise:

4x = 3x + 16

4x - 3x = 16

x = 16

Step 3: Now you can find the value of ST and TU easily:

ST = 4x

TU = 3x + 16