If f(x) = √x + 12 and g(x) = 2√x, what is the value of (f-g)(144)?

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The difference between 90 pence and 3 pounds 25 pence is 235 pence, or 2 pounds 35 pence.

The question is asking for the difference between two amounts of money, 90 pence (90p) and 3 pounds 25 pence (£3.25). To find the difference, you would subtract the smaller amount from the larger amount. In this scenario, since both amounts are in British currency, it is a straightforward subtraction.

£3.25 is equal to 325 pence (since there are 100 pence in a pound). Now, subtract:

325p - 90p = 235p

Therefore, the difference between 90p and £3.25 is 235 pence, which can also be expressed as £2.35.

slope = growth during 1 year y-intercept = their original height i.e. the height when they were born

The standard linear equation is given by :-

[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.

Given equation to predict the average height of boys anywhere b/w birth and 15 years old:

[tex]y=2.79x+25.64[/tex], where x is the age(in yrs) and y is the height (in inches).

By comparing this equation to the standard linear equation, we have

Slope = 2.79 and y-intercept = 25.64

The slope tells that the rate of change of average height of boys with respect to age is 2.79 .

The y-intercept tells that the initial average height of boys =25.64 inches

the following is a conjunction

p∧q: An isosceles triangle has two congruent sides and a right angle measures 90°.

this statement is true because both p and q are true.

The following is a disjunction :

r∨s:  Four points are always coplanar or A decagon has 12 sides.

this statement is false besause  both statemens r and s are false: You could have four points in the three dimensional space that are not in one plane, and a decagon is a figure with 10 sides (not 12).

Answer: 4 days and 18 hours

Step-by-step explanation:

The continuous compound interest of a $3,000 deposit with an annual rate of 28% over 5 years would be approximately $9,156.58.

The question pertains to continuous compound interest, which is represented by the formula A = P  imes ert, where A is the final amount, P the principal amount, r is the interest rate (written in decimal), t is the time in years, and e is the base of natural logarithms.

Given that P=$3,000, r=28/100=0.28 and t=5 years, you would substitute these values into the formula to get A = $3000  imes e(0.28  imes 5).

Computing this, gives:
A = $3000  imes e1.4 = $3000  imes 4.0552 (approximately).
So, A = $12156.58 (rounded to the nearest cent).

The interest earned would therefore be: A - P.
Thus, the interest would be $12156.58 - $3000 = $9156.58.

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To find out how much interest a deposit of $3,000 would earn over 5 years with an interest rate of 28% compounded continuously, we would need to use the formula for continuously compounded interest, which is A = P*e^(rt).

Here,
A represents the total amount of money accumulated after n years including interest,
P is the principal amount, which is the initial amount of money,
r refers to the annual interest rate expressed in decimal form, and
t is the time the money is invested for in years.

Given in the problem we have P = $3000, r = 28% = 0.28, and t = 5 years.

Substituting these values into the formula we get:

A = 3000 * e^(0.28*5)

Solving this would yield the total amount accumulated after 5 years.

Next, we would need to calculate the accrued interest. This is done by subtracting the principal amount (the initial deposit) from the total amount.

So, the interest earned would be calculated as:

Interest Earned = Total Amount - Initial Deposit.

The numerical calculation of these formulas provides us the result that the total amount after 5 years would be approximately $12,165.60 and the interest earned would be approximately $9,165.60.

Thus, a deposit of $3000, with an interest rate of 28% compounded continuously over 5 years, would earn you interest of about $9,165.60.

This is of course rounded to the nearest cent as required.

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Answer:

[tex]12x^8-3x^9+6x^4[/tex]

B is the correct option.

Step-by-step explanation:

We have to multiply the expression

[tex]3x^4(4x^4-x^5+2)

Using the distributive property a(b+c)=ab+ac

[tex]3x^4\times4x^4+3x^4\times(-x^5)+3x^4\times2[/tex]

Now, using the exponent rule [tex]x^a\times x^b=x^{a+b}[/tex]

[tex]12x^{4+4}-3x^{4+5}+6x^4[/tex]

On simplifying, we get

[tex]12x^8-3x^9+6x^4[/tex]

B is the correct option.

1. The vertices B, D and R have coordinates (9,9), (1,5) and (11,5), respectively. Then

[tex] BR=\sqrt{(11-9)^2+(5-9)^2}=\sqrt{4+16} = 2\sqrt{5} ,\\BD=\sqrt{(1-9)^2+(5-9)^2}=\sqrt{64+16} = 4\sqrt{5}. [/tex]

The ratio

[tex] \dfrac{BR}{BD}= \dfrac{2\sqrt{5}}{4\sqrt{5}} =\dfrac{1}{2}. [/tex]

2. The vertices K, E and Y have coordinates (13,9), (14,10) and (14,2), respectively. Then

[tex] KE=\sqrt{(13-14)^2+(9-10)^2}=\sqrt{1+1} = \sqrt{2} ,\\KY=\sqrt{(13-14)^2+(9-2)^2}=\sqrt{1+49} = 5\sqrt{2}. [/tex]

The ratio

[tex] \dfrac{KE}{KY}= \dfrac{\sqrt{2}}{5\sqrt{2}} =\dfrac{1}{5}. [/tex]

Answer: correct answer is C (they are not similar because segment BR to segment DB is 1:2 and segment KE to segment YK is 1:5.)

Answer:

its a

Step-by-step explanation:

Answer:

distribute the radicals, simplify the radicals, combine like terms

Step-by-step explanation:

(-5sqrt[2]-sqrt[6])(sqrt[3]+2sqrt[2])

[tex](-5\sqrt{2})-\sqrt{6} )(\sqrt{3} +2\sqrt{2} )[/tex]

To multiply it , we apply FOIL method

Distribute the radicals inside the second parenthesis

After distributing the radicals inside the second parenthesis we multiply and simplify the radical as much as we can

Then we combine like terms to simplify further

distribute the radicals, simplify the radicals, combine like terms

After 7 month, the population of insects are 12800.

Here,

A population of insects doubles every month.

There are 100 insects to start with.

We have to find the population of insects after 7 month.

What is exponential form?

A way of writing repeated multiplication involving base and exponents, is called exponential form.

Now,

A population of insects doubles every month.

There are 100 insects to start with.

Let the population is P.

Hence, The situation is express in exponential form as;

[tex]P = 100 (2)^n[/tex]

Where, n is the number of month.

So, The population after 7 month is calculate as;

[tex]P = 100 (2)^7=100*128= 12800[/tex]

Therefore, After 7 month the population of insects are 12800.

Learn more about the exponential form visit:

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In mathematics, specifically geometry, we can determine whether three given numbers can be the sides of a triangle by applying the Pythagorean theorem (a² + b² = c²). For instance, the sides with lengths 3, 4, and 5 can form a right triangle because 3² + 4² equals 5².

The subject question is about determining whether three given numbers can form the sides of a triangle. This is an area of Mathematics that deals with geometry, specifically triangles.

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Answer:

75%

Step-by-step explanation:

Answer:  4 slices

Step-by-step explanation:

They divided the pizza into 10 slices and Ivan ate 40% of the pizza. Each piece of pizza is 10% because a full pizza is 100% and there are 10 pieces, so 10% per each slice. So, he ate 4 slices

Answer:

50

Step-by-step explanation:

So 8 percent equals to 4 so just multiply the reciprocal of 8/100 and you get 50

Answer: The economy box will hold 112 ounces.

Step-by-step explanation:

Since we have given that

A regular box of cereal holds = 14 ounces

Let the dimesion of regular box be x .

so, Volume of regular box is given by

[tex]x\times x\times x =x^3= 14[/tex]

According to question, if the box is made by doubling all the dimensions of the regular sized box.

So, volume becomes

[tex]2x\times 2x\times 2x\\\\=2^3\times x^3\\\\=8\times x^3\\\\=8\times 14\\\\=112\ ounces[/tex]

Hence, The economy box will hold 112 ounces.

Answer:

$98,636.72

Step-by-step explanation: