If four times my age is
increased by 20, the result is 80.
How old am I?

The domain of the given function is z<0 or z>0

The entire range of independent variable values is the domain of a function.

According to this definition, it means:

The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

Keep these things in mind when locating the domain:

A fraction's denominator (bottom) cannot be 0.

In this section, the integer following a square root symbol must be positive.

The domain of a function is a set of input of argument values for which the function is real or defined.

1) Finding the singularity point:

Taking the denominator 4×[tex]z^{2}[/tex] = 0 ⇒ z = 0

∴The following function will not be defined if z = 0

So the function domain is z>0 or z<0

The domain of the given function is z<0 or z>0

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The given division will give the result as (x-3) + [2/(x+3)].

Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

The given division of the two of the polynomial can be carried out as shown below,

[tex]\dfrac{x^2-7}{x+3}\\\\=x+\dfrac{-3x-7}{x+3}\\\\=x-3+\dfrac{2}{x+3}\\\\=(x-3)+\dfrac{2}{x+3}[/tex]

Hence, [tex]\dfrac{x^2-7}{x+3}=(x-3)+\dfrac{2}{x+3}[/tex].

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After solving the equation, the value of y obtained is equal to 10°.

An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol ∠.

Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.

As per the information obtained from the given figure,

Angle, C = 4y

Angle, E = 180 - 116 = 64 and,

Angle, D = 7y + 6

As we know, the sum of the angles of a triangle is 180°.

Then,

4y + 64 + 7y + 6 = 180

11y = 180 - 70

11y = 110

y = 110/11

y = 10°

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

NO

Step-by-step explanation:

Two fourths =

[tex] \frac{2}{4} = 0.5[/tex]

Two thirds =

[tex] \frac{2}{3} = 0.66667[/tex]

Therefore

0.66667 > 0.5

[tex] \frac{2}{3} > \frac{2}{4} [/tex]

or

0.5 < 0.66667

[tex] \frac{2}{4} < \frac{2}{3} [/tex]

i hope this helped

Answer: No, 2/4 is not greater than 2/3

Step-by-step explanation: To find an easy way to calculate their values we have 2 options. So, the 1st option is to turn them into a decimal. I already calculated their values which are:

2/4 = 0.5

2/3 = 0.667

Then, we compare the two decimal numbers to get the answer.

0.5 is not greater than 0.667.

The 2nd way is to find a common denominator, which would look like this:

2/4 =  6/12

2/3 =  8/12

8/12 is greater than 6/12, so that also proves that 2/4 is not greater than 2/3.

An inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to more than 70,000 steps is  32076+3x>70000.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Diego's goal is to walk more than 70,000 steps this week.

a) The mean number of steps that Diego walked during the first 4 days of this week is 8019.

So, the number of steps =4×8019

= 32076

Let x be the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps.

Now, the inequality is 32076+3x>70000

b) The mean number of steps that Diego needs to walk during the last 3 days of this week is 12642

Substitute x=12642 in the inequality 32076+3x>70000, we get

32076+37926>70000

70002>70000

Yes, Diego will reach his goal of walking more than 70,000 steps this week.

Therefore, the inequality to represent the given situation is 32076+3x>70000.

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On solving the question as said we get to know that the maximum possible length of the repeating section of the decimal representation of the given number is 10.

As 941 and 1549 are already in whole number lets assume that the question says to find the decimal repetition is 941 and 15  divided by 41 and 59 respectively.

9 divided by 41 is equal to 0.2195121951

15 divided by 49 is equal to 0.306122449.

Therefore, the maximum possible length for their repeating section is 10.

The preferred method for representing both integer and non-integer numbers is the decimal numeral system, often known as the base-ten positional numeral system and denary.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers using the decimal system.

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Answer:

552 mph

Step-by-step explanation:

414 / 3/4 = 414 * 4/3 = 1656/3 = 552

In the triangle below, ΔABE≅ΔCBD. Reason (AAS)

We should know that the postulates talk about the proofs about the given diagram or flowchart

There is an attached diagram to support our answer

Below gives the correct explanations

S/n         Statement                                     Reason

1               <ABE≅<CDE                             Given in the diagram

2            <AEB≅CED           The theory of vertical angles  are      equal        3             BE≅ED                                 Also given in the diagram

4          ΔABE≅ΔCDE            The rule of Angle, Side Angle proof

In conclusion the triangle below, ΔABE≅ΔCBD. Reason (AAS)

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Complete question:

Given AC 1 BD, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you

The profit function is 250x  and the profit earned is 375000.

What is cost?

In production, research, retail, and accounting, a cost is that the value of cash that has been spent to provide one thing or deliver a service, and thence isn't obtainable to be used any longer.

Main body:

A) Profit function = R() – TC()

                        = 750 – (300+200)x

                        = 750 – 500x

                        = 250 x

b) total profit = 250 x

                     = 250 *1500

                     = 375000

c) The zero-profit condition is that the condition that happens once AN business or kind of business has a very low (near-zero) value of entry to or exit from the business. during this scenario, some companies not already within the business tend to hitch the business if they calculate that they're going to create a positive economic profit (profit in more than the price of effort investible funds). a lot of and a lot of companies can enter till the economic profit per firm has been driven all the way down to zero by competition.

hence the profit function is 250x

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Answer: about 4:30

Step-by-step explanation:

he used the restroom starting at 4:15, he sat on the toilet and watched tt for exactly 14 minutes, He then whiped himself which took about 50 seconds. Flushing the toilet took 10 seconds and when he flushed it was 4:30.

3) The rate of change on the interval [1, 7] is -1, so the correct option is A.

4) By using the rate of change formula, we will see that h(9) = 40

We know that for a function f(x), the average rate of change on the interval [a, b] is:

r = ( f(b) - f(a))/(b - a)

Here the interval is [1, 7]

Using the graph we can see that:

f(1)= 6

f(7) = 0

Then the average rate of change is:

r = ( f(7) - f(1))/(7 - 1)

r = (0 - 6)/6 = -1

The correct option is A.

4) Which will be value of h(9)?

We know that the average rate of change of h(x) is 7 on the interval [5, 9]

Then we can write:

7 = ( h(9) - h(5))/(9 - 5)

We know that h(15) = 12, then we have the equation:

7 = (h(9) - 12)/4

Now we can solve that for h(9), we will get:

7 = (h(9) - 12)/4

7*4 = h(9) - 12

28 = h(9) - 12

28 + 12 = h(9)

40 = h(9)

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The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

The slope(m) of the line passing through two points is X1,Y1 and X2, Y2 is

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

we have (x1,y1) and (x2,y2) is (-6,1) and (-6,-4) respectively substitute the values in m=[tex]\frac{y2-y1}{x2-x1}[/tex],

we get m=[tex]\frac{-4-1}{-6-(-6)}[/tex] = -5/0 which is Undefined.

Whenever the slope of the line is undefined then the line must be vertical. Because the slope of the vertical line cannot be defined.

The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.

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Answer: To find out how many seconds it will take for the egg to hit the ground, we need to find the value of x when the height of the egg is 0 feet. We can do this by setting the height of the egg equal to 0 in the equation 27 - 16x^2 and solving for x.

The equation for the height of the egg in feet x seconds after being dropped is given as:

27 - 16x^2 = 0

Subtracting 27 from both sides of the equation gives us:

-16x^2 = -27

Dividing both sides of the equation by -16 gives us:

x^2 = 27/16

Taking the square root of both sides of the equation gives us:

x = sqrt(27/16)

Plugging this value into the equation for the height of the egg gives us:

27 - 16(sqrt(27/16))^2 = 0

Simplifying this equation gives us:

27 - 16(27/16) = 0

Which simplifies to:

27 - 27 = 0

This equation is true, so the value of x that we found is a solution to the equation. This means that the egg will hit the ground after sqrt(27/16) seconds.

I hope this helps! Let me know if you have any other questions.

Answer:

perimeter of a triangle is the total

Step-by-step explanation:

p=48cm

Length=3x

width=x

Now P= 2(L+W)

48 =2(3x+x)

48=2(4x)

48=8x

dividing both sides by 8

we have x=6

and so length=18 and width =6

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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The area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.

The given polygon is a regular hexagon with perimeter 120 m.

Thus, the length of each side,

s = 120/6 = 20 m.

The area, A, of a regular hexagon can be found given only its side length, s, with the formula:

[tex]A = \frac{3\sqrt{3} }{2} s^{2}[/tex]

Substitute s = 120 m in above formula:

[tex]A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}[/tex]

Thus, the area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².

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Step-by-step explanation:

f(x)=3x²-x-2

a) (2,8)

f(2)=3(2²)-2-2

f(2)=3(4)-4

f(2)=12-4

f(2)=8

Hence, the point (2,8) is on the graph of f(x)

b) x=-1

f(-1)=3((-1)²)-(-1)-2

f(-1)=3(1)+1-2

f(-1)=3-1

f(-1)=2

c) x=-2

f(-2)=3((-2)²)-(-2)-2

f(-2)=3(4)+2-2

f(-2)=12+0

f(-2)=12

[tex]d)\ f(x)\in(-2\frac{1}{12} ,\infty)[/tex]

e) y=0

3x²-x-2=0

3x²-x-2=0

3x²-3x+2x-2=0

3x(x-1)+2(x-1)-0

(x-1)(3x+2)=0

x-1=0

x=1

3x+2=0

3x=-2

Divide both parts of the equation by 3:

x=-2/3

f) x=0

f(x)=3(0²)-0-2

f(x)=3(0)-2

f(x)=0-2

f(x)=-2

Answer:

(x-3)²+(y-1)²=50

Step-by-step explanation:

we know,

general eqn of circle passing through a point is

r²=(x-h)²+(y-k)²------($)

then,at (-4,2) the eqn becomes

r²=(-4-h)²+(2-k)²----(1)

at (-2,6),

r²=(-2-h)²+(6-k)²-----(2)

at (4,8),

r²=(4-h)²+(8-k)²-------(3)

Now,

from (1) and(2),

(-4-h)²+(2-k)²=(-2-h)²+(6-k)²

or,16+8h+h²+4-4k+k²=4+4h+h²+36-12k+k²

or,h²-h²+8h-4h+k²-k²-4k+12k+16+4-4-36=0

or,4h+8k-20=0

or,4(h+2k)=20

or,h+2k=5------(4)

also,from (2) and (3),

(-2-h)²+(6-k)²=(4-h)²+(8-k)²

or,4+4h+h²+36-12k+k²=16-8h+h²+64-16k+k²

or,h²-h²+4h+8h+k²-k²-12k+16k+4+36-64-16=0

or,12h+4k-40=0

or,4(3h+k)=40

or,3h+k=10-------(5)

Now,multiplying eqn (5)by 2 then subtracting from (4),we get

h+2k=5

6h+2k=20

- - -

_________

-5h=-15

.:h=3

putting value of h in (4),we get

3+2k=5

or,2k=2

.:k=1

Now,putting value of k and h in eqn(1),

r²=(-7)²+(1)²

or,r²=49+1

.:r²=50

Now putting value of h,k and r² in eqn($),we get

(x-3)²+(y-1)²=50,which is required eqn of circle

The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

⇒ θ = 20° opposite = 45

Now,

Since, The values are,

⇒ θ = 20° opposite = 45

We know that;

⇒ sin θ = Opposite / Hypotenuse

⇒ sin 20° = 45 / Hypotenuse

⇒ Hypotenuse = 45 / sin 20°

⇒ Hypotenuse = 45 / 0.34

⇒ Hypotenuse = 132.35

Thus, The value of hypotenuse will be;

⇒ Hypotenuse = 132.35

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The solutions to the quadratic linear system equations are (11, 41) and (3, 9).

The given equations are y=x²-10x+30 and y=4x-3.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, y=x²-10x+30 -------(I) and y=4x-3 -------(II)

Substitute equation (II) in the equation (I), we get

4x-3=x²-10x+30

⇒ x²-10x+30-4x+3=0

⇒ x²-14x+33=0

⇒ x²-11x-3x+33=0

⇒ x(x-11)-3(x-11)=0

⇒ (x-11)(x-3)=0

⇒ x=11 and x=3

So, y=4(11)-3=41 and y=4(3)-3=9

Therefore, the solutions to the quadratic linear system equations are (11, 41) and (3, 9).

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Applying the triangle midsegment theorem, the length of CD is: 8 units.

If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.

According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.

Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:

EG is a midsegment that is parallel to a third side CD.

Therefore:

Length of CD = 2(EG)

Substitute

CD = 2(4)

CD = 8 units.

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It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches

Total width of floor = 205 inches

Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30

30 boards are required

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Answer: hope it helps

Step-by-step explanation:

2^6=64≡ -1 ( mod 13)

So 2^70=16*(2^6)^11=16*(-)^11(mod 13)

2^70 ≡-16 ( mod 13)

2^70 ≡10 ( mod 13)

Now 3^3=27≡1 ( mod 13)

So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)

≡ 3 ( mod 13)

Thus 2^70+3^70 ≡ 10+3 (mod 13)

≡ 0 ( mod 13)

The balance in the account after 4 years as interest is compounded monthly is $9,066.02.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = 8600( 1 + 0.0132/12 )^( 12 × 4 )

A = 8600( 1 + 0.0011 )^( 48 )

A = 8600( 1.0011 )^( 48 )

A = $9,066.02.

Therefore, the accrued amount after 4 years is $9,066.02.

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Answer:

Step-by-step explanation:

Therefore, C is the correct option.

Step-by-step explanation:

We have been given the equation

The GCF of the right hand side of the equation is t. Hence, factored out the GCF.

Now,  is in multiplication with 't'. So in order to isolate t, we can divide both sides by

Therefore, C is the correct option.

Answer

150000 after 4 years

Step-by-step explanation:

The required quotient is 34.2 ÷ 3.8 = 9.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given 3.8 divided by 34.2

According to the given question, we can write the quotient as:

⇒ 34.2 ÷ 3.8

⇒ 34.2 / 3.8

⇒ 342 / 38

Apply the division operation, and we get

⇒ 9

Therefore, the required quotient is 34.2 ÷ 3.8 = 9.

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