Factored form of x^2+10x+5

Final answer:

A unit of account is a standardized metric for determining the worth of items and services in an economy, facilitating comparisons, trade-offs, and accounting. It eliminates the inefficiencies of barter by providing a common denominator for value.

Explanation:

Unit of account is one of the fundamental functions of money, serving as a standardized metric for determining the worth of items and services in an economy. This function allows for the assignment of prices and the performance of accounting, which is vital for making rational economic decisions. In essence, it provides a common denominator by which value can be measured, allowing for easier comparison and exchange. For instance, if an accountant charges $100 to file a tax return, this monetary amount can also represent the value of other goods, such as two pairs of shoes priced at $50 each. This facilitates trade-offs and helps to calculate revenue, expenditure, and savings, among other economic activities.

Without a unit of account, the economic system would likely rely on barter, which is significantly less efficient due to the necessity for a double coincidence of wants. Modern economies use fiat money as their unit of account, which has no intrinsic value but is declared legal tender by the government.

Answer:

Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Step-by-step explanation:

We are given that we deal with three cards from a regular deck of 52 cards.

We are to find the probability of getting all three Jacks.

There are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Answer:

50,24cm

Step-by-step explanation:

For circumference, you can use C = πd OR 2πr = C:

3,14[16] = 50,24

2[3,14][8] = 50,24

The diameter is double the radius.

I am joyous to assist you anytime.

Answer: v = [tex]-\frac{1}{6}[/tex]

6v + 2 - 4 = -3                         Combine like terms

6v - 2 = -3                               Add 2 to both sides

6v = -1                                     Divide both sides by 6

v = [tex]-\frac{1}{6}[/tex]          Answer!

Answer:

$1.38 per pound

Solution:

1 ton = 2,000 pounds

2,000 * 3 = 6,000 pounds

8,280 / 6,000 = $1.38 per pound.

Hope This Helps ;)

Answer: 8,280 divided by 6,000   is 1.3,

Step-by-step explanation: there are 2,000 pounds in one ton so 3 tons would be 6,000 pound so divivde the pounds from the price

4. The value f issue is the quantity  of shares multiplied by the price of each share.

25,000 shares x $9.20 = $230,000.

The answer is b.$230,000

5. Total selling expense would be the commission plus all the fees.

Multiply the value of issue by the commission percentage and then add the other costs.

230,000 x 0.065 = 14,950

14,950 + 1,985 = $16,935

The answer is a. $16,935

6. Divide the total selling expense by the number of shares:

750,000 / 900,000 = 0.83

The answer is d. $0.83

Answer:

0.3(8.2 x 10^-3) = 2.46 X 10 ^ -3

Step-by-step explanation:

We need to solve the equation 0.3(8.2 x 10^-3) and write answer in scientific notation.

Solving,

= 0.3(8.2 x 10^-3)

= 0.3 * 0.0082

= 0.00246

Writing in scientific notation

= 2.46 X 10 ^ -3

So, after solving the expression 0.3(8.2 x 10^-3) the result is 2.46 X 10 ^ -3.

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

the parameter tells you something about the whole population

Step-by-step explanation:

1) The four points are:

(x₁, y₁) = (-2, -1)

(x₂, y₂) = (3, 13)

(x₃, y₃) = (15, 5)

(x₄, y₄) = (13, -11)

Using the distanced formula the four side lengths are:

d₁₂ = √((13−-1)² + (3−-2)²) = √221

d₂₃ = √((5−13)² + (15−3)²) = √208

d₃₄ = √((-11−5)² + (13−15)²) = √260

d₄₁ = √((-1−-11)² + (-2−13)²) = √325

None of the lengths are equal, so we know this isn't a rhombus, parallelogram, or kite.  Is it a trapezoid?  To find out, let's find the slopes between the two lines that look like they might be parallel.

m₂₃ = (5 - 13) / (15 - 3) = -2/3

m₄₁ = (-1−-11) / (-2−13) = -2/3

They are indeed parallel.  So this is a trapezoid.

2) Given:

PS ≅ QR

m∠P + m∠Q = 180

m∠R + m∠S = 180

∠P ≅ ∠S

By converse of Alternate Interior Angles Theorem, since ∠P and ∠Q are supplementary, line PS and QR must be parallel.

If a quadrilateral has one pair of opposite sides that are both parallel and congruent, then it is a parallelogram.

Adjacent angles of a parallelogram are supplementary, so m∠P + m∠S = 180.

Since ∠P ≅ ∠S, then by definition of congruent angles, m∠P = m∠S.

Substitution:

m∠P + m∠P = 180

m∠P = 90

Substitution:

m∠S = 90

Opposite angles of a parallelogram are congruent, so m∠Q = m∠S = 90 and m∠R = m∠P = 90.

A parallelogram with four right angles is a rectangle.

Answer:

(1,1), (-3,4)

Step-by-step explanation:

Given  x + 2y ≥ 3

Rewrite the inequality as;

x + 2y = 3

Form a table for values of x and y

x        y

3        0

1         1

-3        3

Plot the points on a Cartesian plane

From the graph, the points are; (1,1), (-3,4)

For this case we have the following inequality:

[tex]x + 2y \geq3[/tex]

We substitute each of the points and see which one is fulfilled:

Point A: (1,1)

[tex]1 + 2 (1) \geq3\\1 + 2 \geq3\\3 \geq3[/tex]

Is fulfilled!

Point B: (-3,4)

[tex]-3 + 2 (4) \geq3\\-3 + 8 \geq3\\5 \geq3[/tex]

Is fulfilled!

Point C: (-2,2)

[tex]-2 + 2 (2) \geq3\\-2 + 4 \geq3\\2 \geq3[/tex]

It is not fulfilled!

Point D: (5, -2)

[tex]5 + 2 (-2) \geq3\\5-4 \geq3\\1 \geq3[/tex]

It is not fulfilled!

Answer:

Option A and B

Answer: End behaviour is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

The graph touches, but does not cross, the x–axis at x = 4

The graph of the function crosses the x–axis at x = 0

Step-by-step explanation:

Given function is,

[tex]f(x)=x^5-8x^4+16x^3----(1)[/tex]

The degree of f(x) is 5 ( odd ) with positive leading coefficient,

Hence, the end behaviour of f(x) is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

Now, from equation (1),

[tex]f(x)=x^3(x^2-8x+16)[/tex]

If f(x) = 0,

[tex]x^3(x^2-8x+16)=0[/tex]

[tex]\implies x^3=0\text{ or }x^2-8x+16=0[/tex]

[tex]x^3=0\text{ or }(x-4)^2=0[/tex]

[tex]x^3=0\text{ or }x-4=0[/tex]

[tex]\implies x=0\text{ or }x=4[/tex]

Now, the multiplicity of 4 is 2 ( even )

Thus, the graph touches, but does not cross, the x–axis at x = 4

Also, the multiplicity of 0 is 3 ( odd )

Hence, the graph of the function crosses the x–axis at x = 0

By using the concept of end behavior of a function, the result is

f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

What is end behavior of a function?

Let the function be f(x). End behavior of a function f(x) indicates how will the function behaves as x tends to +[tex]\infty[/tex] and [tex]-\infty[/tex]

Here,

f(x) = [tex]x^5 - 8x^4 + 16x^3[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} x^5 - 8x^4 + 16x^3\\\\= -\infty[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} x^5 - 8x^4 + 16x^3\\\\= \infty[/tex]

So f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

f(x) = [tex]x^5 - 8x^4 +16x^3[/tex]  

     = [tex]x^3(x^2 - 8x +16)\\[/tex]

     = [tex]x^3(x - 4)^2[/tex]

[tex]x^3 = 0[/tex] or [tex](x - 4)^2 = 0[/tex]

[tex]x = 0[/tex] (Multiplicity 3 which is odd)

[tex]x = 4[/tex] (Multiplicity 2 which is even)

So The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

To learn more about end behavior of a function, refer to the link-

https://brainly.com/question/1365136

#SPJ2

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{4}{7}[/tex] and (a, b) = (- 6, - 6), hence

y - (- 6) = - [tex]\frac{4}{7}[/tex] (x - (- 6) ), that is

y + 6 = - [tex]\frac{4}{7}[/tex](x + 6) ← c or d

Answer:

y + 6 = -4/7(x + 6)

Step-by-step explanation:

The point-slope form of an equation for a line that passes through a point

( a, b )with a slope m is given as;

[tex]y-a=m(x-b)[/tex]

we substitute the given values into the given equation above and simplify. Our point is given as (–6, –6) while the slope is -4/7;

[tex]y-(-6)=-\frac{4}{7}(x-(-6))\\\\y+6=-\frac{4}{7}(x+6)[/tex]

Answer:

C, [tex]4e^{i(7\pi/4)}[/tex]

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

[tex]e^{ix}=\cos{x}+i\sin{x}[/tex]

Given the complex number [tex]2\sqrt{2}-2i\sqrt{2}[/tex], we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression [tex]2(\sqrt{2}-i\sqrt{2})[/tex]

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression [tex]4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)[/tex] , and now we have something to work with.

Looking back at Euler's formula [tex]e^{ix}=\cos{x}+i\sin{x}[/tex], we can map our expression inside the parentheses to the one on the right side of the formula, giving us [tex]\cos{x}=\frac{\sqrt2}{2}[/tex] and [tex]\sin{x}=-\frac{\sqrt2}{2}[/tex], or equivalently:

[tex]\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x[/tex]

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so [tex]x=\frac{7\pi}{4}[/tex], and we can finally replace our expression in parentheses with its exponential equivalent:

[tex]4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}[/tex]

Which is c on the multiple choice section.

Answer:

Complementary angles are two angles which add up to 90° or forms a right angle. First, we find the value of A and B.

A = arccosine (0.83) = 34°

B = 90 - 34 = 56°

Thus, sin A = 0.56 and sin B = 0.83.

Step-by-step explanation:

Answer: Number 4.

Since Pedro deposited $35, the line would start at 0 and go up to positive 35. However, Pedro then withdrew $50- which is more than he has in his account, so he would have $-15, which means he'd owe a fee.

Good luck,

LaciaMelodii :)

Answer:

d). or the 4th choice

Step-by-step explanation:

hope this helped!!

Answer:

4x-10y thingi 3

Step-by-step explanation:

2x

so...

2x (4t - 2 - 9)

2x (4t -  11)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

It's 2x.

Step-by-step explanation:

The GCF of 8, 4 and 18 is 2.

The GCF of xt x and x  is x.

Answer:

a = 23, b = - 14

Step-by-step explanation:

If the polynomial is divisible by (x - 1) then f(1) = 0

f(x) = x³ - 10x² + ax + b

f(1) = 1³ - 10(1)² + a + b = 0, that is

1 - 10 + a + b = 0, hence

a + b = 9 → (1)

Similarly if (x - 2) is a factor then f(2) = 0

f(2) = 2³ - 10(2)² + 2a + b = 0, that is

8 - 40 + 2a + b = 0, hence

2a + b = 32 → (2)

Subtract (1) from (2)

a = 23

Substitute a = 23 into (1)

23 + b = 9 ⇒ b = 9 - 23 = - 14

Answer:

2(1/2)(5)(12) + 11(5) + 11(12) + 11(13) =

60 + 55 + 132 + 143 = 390 m²

Answer:

(q-9) (5+c)

Step-by-step explanation:

Factor out the common factor.  In this case, q-9.

5(q-9) + c(q-9)

(q-9) (5+c)

Answer: The jacket cost $34.79

Answer:

B. -1.75 and 4

Step-by-step explanation:

f(x)=g(x)

Input the equations

x²-2x-8 = 1/4x-1

add 1 to both sides

and subtract 1/4x from both sides

x²-2 1/4x - 7 = 0  

factor

a + b = -2 1/4

a * b = -7

1.75 + -4 = -2 1/4

1.75 * -4 = -7

reverse their symbols

1.75 becomes -1.75 and -4 becomes 4.

Answer:

[tex]\boxed{\text{B. x = 4 and x = -1.75}}[/tex]

Step-by-step explanation:

ƒ(x) = x² - 2x – 8; g(x) = ¼x -1

If ƒ(x) = g(x), then

x² - 2x – 8 = ¼x -1

One way to solve this problem is by completing the square.

Step 1. Subtract ¼ x from each side

[tex]x^{2} - \dfrac{9}{4}x - 8 = -1[/tex]

Step 2. Move the constant term to the other side of the equation

[tex]x^{2} - \dfrac{9}{4}x = 7[/tex]

Step 3. Complete the square on the left-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 4. Write the left-hand side as a perfect square

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 5. Take the square root of each side

[tex]x - \dfrac{9}{8} = \pm\sqrt{\dfrac{529}{64}} = \pm\dfrac{23}{8}[/tex]

Step 6. Solve for x

[tex]\begin{array}{rlcrl}x - \dfrac{9}{8} & =\dfrac{23}{8}& \qquad & x - \dfrac{9}{8} & = -\dfrac{23}{8} \\\\x & =\dfrac{23}{8} + \dfrac{9}{8}&\qquad & x & = -\dfrac{23}{8} + \dfrac{9}{8} \\\\x& =\dfrac{32}{8} &\qquad & x & \ -\dfrac{14}{8} \\\\x& =4 & \qquad & x & -1.75 \\\end{array}\\\\\text{f(x) = g(x) when \boxed{\textbf{x = 4 or x = -1.75}}}[/tex]

Check:

[tex]\begin{array}{rlcrl}4^{2} - 2(4) - 8 & = \dfrac{1}{4}(4) -1&\qquad & (-1.75)^{2} - 2(-1.75) - 8 & = \dfrac{1}{4}(-1.75) - 1\\\\16 - 8 -8& = 1 - 1&\qquad & 3.0625 +3.5 - 8 & = -0.4375 - 1 \\\\0& =0&\qquad & -1.4375 & = -1.4375 \\\\\end{array}[/tex]

The diagram below shows that the graph of g(x) intersects that of the parabola ƒ(x) at x = -1.7 and x = 4.

Step-by-step explanation:

You need to remember that

[tex] log( \frac{a}{b} ) = log(a) - log(b) [/tex]

and

[tex] log(ab) = log(a) + log(b) [/tex]

then the solution is

[tex] log( \frac{r}{st} ) = log(r) - log(st) \\ = log(r) - ( log(s) + log(t) ) \\ = log(r) - log(s) - log(t) [/tex]

Answer:

Step-by-step explanation:

First, let's simplify the equation:

y = √(-4x - 36)

y = √(4(-x - 9))

y = 2√(-x - 9)

The 2 coefficient in front means the function is stretched by a factor of 2.

The - sign in front of the x means the function is reflected over the y axis.

The -9 constant means the function is shifted 9 units to the right.

The third one is the correct answer.

Answer:

D:  Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Step-by-step explanation:

I actually just did this and used the answer above and got it wrong, so the answer I put down is the correct answer according to edg... Good Luck!!!

Square root x=13

x=169

Hope you get it!

To solve the equation x^2√x-8+2=7, follow these steps: combine like terms, square both sides, simplify, take the cube root, and simplify again to find x = 3.

To solve the equation x2√x-8+2=7, we need to isolate the variable x. Here are the steps:

Therefore, the solution to the equation is x = 3.

https://brainly.com/question/17870110

#SPJ11

Answer:

3/5 kg of nickel, 4/5 kg of zinc and 13/5 kg of copper

Step-by-step explanation:

we know that

An alloy is composed of nickel, zinc, and copper in a ratio of 3:4:13

so

(3+4+13)=20 kg

That means

For 20 kg of alloy is needed 3 kg of nickel, 4 kg of zinc and 13 kg of copper

so

using proportion

Find the kilograms of nickel needed for 4 kg of alloy

20/3=4/x

x=3*4/20

x=12/20

x=3/5 kg of nickel

Find the kilograms of zinc needed for 4 kg of alloy

20/4=4/x

x=4*4/20

x=16/20

x=4/5 kg of zinc

Find the kilograms of copper needed for 4 kg of alloy

20/13=4/x

x=13*4/20

x=52/20

x=13/5 kg of copper

To create 4 kg of an alloy with nickel, zinc, and copper in a 3:4:13 ratio, you will need 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper.

In this problem, we are being asked to make 4 kilograms of an alloy for which the mixture ratio of nickel, zinc, and copper is given as 3:4:13 respectively.

To find the quantity of each metal needed, we first need to understand that the ratio represents parts of the whole. In this case, the whole is the total weight of the alloy, which is 4 kilograms. Therefore, the sum of the ratio numbers (3+4+13=20) represents this total weight. Each part of the ratio represents a fraction of this total weight, so for any individual metal, the weight in kilograms will be  (its ratio number / the total ratio number) * the total alloy weight.

For nickel, it would be (3/20)*4 = 0.6 kg. For zinc, the calculation is (4/20)*4 = 0.8 kg. And for copper, it will be (13/20)*4 = 2.6 kg.

So, to make 4 kg of this alloy, 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper are required.

https://brainly.com/question/32531170

#SPJ3

Answer:

The equation of the hyperbola is x²/16 - y²/1 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

# The length of the transverse axis is 2a

# The coordinates of the vertices are (±a , 0)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (0 , ±b)

# The coordinates of the foci are (± c , 0),  

# The distance between the foci is 2c where c² = a² + b²

* Now lets solve the problem

∵ The center of the hyperbola is (0 , 0)

∵ It is opening horizontally

∴ x²/a² - y²/b² = 1

∵ a = 4 , b = 1

∴ a² = (4)² = 16

∴ b² = (1)² = 1

∴ x²/16 - y²/1 = 1

∴ The equation of the hyperbola is x²/16 - y²/1 = 1

x²/16 - y²/1 = 1

Step-by-step explanation:

Answer:

A^2+B^2=C^2

-/(A^2+B^2)=C

Step-by-step explanation:

-/ means squareroot whats in the parenthese

Answer:

sin(50°) = 3/c

Step-by-step explanation:

Answer:

Step-by-step explanation:

10 contain both chocolate and caramel

There are 18 candies.

3 don't contain either chocolate or caramel

12 contain chocolate.

There are 18 - 12 - 3 that are not accounted for. So we have 3 that are not mentioned. Those 3 must contain just caramel.

So it should be filled out like this

contain caramel      Do not contain Caramel

         10                          2

          3                           3

At aphelion, the distance between Pluto and the sun is approximately 8,000,000,000 km.

The distance between Pluto and the sun at aphelion can be calculated using the formula:

Distance at aphelion = length of the minor axis / (1 + eccentricity).

Plugging in the given values, we get:

Distance at aphelion = 10,000,000,000 km / (1 + 0.25).

Calculating the result gives us a distance of approximately 8,000,000,000 km.

https://brainly.com/question/32379878

#SPJ12