Two different plants grow each year at different rates, which are represented by the functions f(x) = 4x and g(x) = 5x + 2. What is
the first year the f(x) height is greater than the g(x) height?

A) year 0

B) year 1

C) Year 2

D) year 3

​

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.

Answer:

8+4n=height of tree in 4 years

Step-by-step explanation:

start of with 8

then every year add N feet

4 years times n feet + what we started with(8)

and you get 8+4n

The height of the tree, in feet, 4 years from now can be calculated as 8 + 4n, where n is the number of feet the tree grows each year.

The subject of this question is a mathematical problem involving height growth over time, specifically about a tree that grows at a constant rate each year. In this case, the height of a tree in the future can be represented by a simple equation which considers the current height of the tree (8 feet), the rate of growth each year (n feet per year), and the number of years in the future we want to calculate for (4 years). The formula to calculate the height of the tree 4 years from now is:

Future Height = Current Height + Growth Rate * Time

Plug in the values we know:

Future Height = 8 feet + n feet/year * 4 years

So, the height of the tree, in feet, 4 years from now is 8 + 4n.

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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:

14/23

Step-by-step explanation:

The total number of marbles is 6 + 8 + 9 = 23.

The probability of yellow or red is:

P(yellow or red) = P(yellow) + P(red)

P(yellow or red) = 8/23 + 6/23

P(yellow or red) = 14/23

Answer:

8 in 23 chance of picking a yellow marble

6 in 23 chance of picking a red marble

Explanation:

Firstly, we must determine the total number of marbles. To do this, we add all the marbles together:

6+8+9 = 23

Since the question says we have 8 yellow marbles, that means 8/23 marbles are yellow. Therefor, you would have a 8 in 23 chance (8/23) of picking a yellow marble. Similarly, the question states that we have 6 red marbles. Meaning 6/23 marbles are red. So, one would have a 6 in 23 or 6/23 chance of picking a red marble.

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:

[tex]\bf \begin{cases} y=x^2-7x+12\\ y=-x+7 \end{cases}\implies \stackrel{y}{x^2-7x+12}=\stackrel{y}{-x+7} \\\\\\ x^2-6x+12=7\implies x^2-6x+5=0 \\\\\\ (x-5)(x-1)=0 \implies \blacktriangleright x= \begin{cases} 5\\ 1 \end{cases} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf y=-x+7\implies \stackrel{x=5}{y=-(5)+7}\implies \blacktriangleright y=2\blacktriangleleft \\\\\\ y=-x+7\implies \stackrel{x=1}{y=-(1)+7}\implies \blacktriangleright y=6 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,2)\qquad (1,6)~\hfill[/tex]

Answer:

[tex](5, 2)[/tex], [tex](1, 6)[/tex]

Step-by-step explanation:

We have a system composed of two equations

The first is a quadratic equation and the second is a linear equation.

[tex]y=x^2-7x+12[/tex]

[tex]y=-x+7[/tex]

To solve the system, equate both equations and solve for x

[tex]x^2-7x+12 = -x+7\\\\x^2 -6x +5=0[/tex]

To solve the quadratic equation we must factor it.

You should look for two numbers a and c that when multiplying them obtain as result 5 and when adding both numbers obtain as result -6.

This is:

[tex]a * c = 5\\a + c = -6[/tex]

The numbers searched are -5 and -1

So

[tex]x^2 -6x +5 = (x-5)(x-1) = 0[/tex]

Finally the solutions to the system of equations are:

[tex]x= 5[/tex], [tex]x=1[/tex]

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:

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

60 + 55 + 132 + 143 = 390 m²

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

the parameter tells you something about the whole population

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!!!

Given the expression y^3 + x, upon substituting y = 1 and x = 6 into the equation, the resultant value of the expression is 7.

The question requires finding the value of the expression y3 + x when x = 6 and y=1. Since y is equal to 1, y3 (1 cubed) is also 1. So the expression becomes 1 + 6, which equals 7. Therefore, the value of the expression y3 + x for y = 1 and x = 6 is 7.

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Final answer:

The value of the expression  [tex]y^3 + x[/tex] for x = 6 and y = 1 is 7, which is found by substituting the values into the expression and performing the arithmetic operations.

Explanation:

To find the value of the expression [tex]y^3 + x[/tex]for x = 6 and y = 1, you simply substitute the given values into the expression and perform the arithmetic operations.

Here's the step-by-step calculation:

Replace y with 1: (1)3 + 6.

Calculate 1 cubed, which is 13 = 1.

Add the result to x, where x is 6: 1 + 6.

The final answer is 7.

This means that the value of the expression [tex]y^3 + x[/tex]when x = 6 and y = 1 is 7.

Answer: The jacket cost $34.79

Answer:

0.001

Step-by-step explanation:

1/1000 is one-thousandths. As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths. That is three steps away from the decimal point. That's where we put our 1, which gives us 0.001.

1/1000 can be expressed as one-thousandths and in decimal form as 0.001

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point, then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths.

1/1000

Which is three steps away from the decimal point 1, gives us 0.001.

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Answer:

x = 8

Step-by-step explanation:

Given

6x + 4(3x - 7) = 116 ← distribute the parenthesis on the left side

6x + 12x - 28 = 116 ← collect like terms on left side

18x - 28 = 116 ( add 28 to both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

4x-10y thingi 3

Step-by-step explanation:

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:

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

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.

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The ratio of 20:1 means for every 20 inches the car is in real life, the drawing will be 1 inch.

To find the length of the drawing, divide the length of the real car by 20.

193.2 / 20 = 9.66 inches.

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:

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.

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

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^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:

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.

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:

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.

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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: 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.

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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