MATHEMATICS HIGH SCHOOL

Alan has forgotten his 4-digit PIN code.He knows the first digit is 3, and last digit is larger than 3.
How many different sets of 4 digits could it be?

Answers

Answer 1
Answer: If Alan knows one already, there is 3 more left for him to possibly know
Answer 2
Answer: the first number obviously is 3 and the next number has to be bigger so its 6 .

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A father is four times as old as his daughter. In 18 years he will be two times as old as she. How old is the daughter now?

Answers

Let's say x to the daughter's age, since the father's age is four times the daughter's age, his age will be 4x. 18 years later, the daughter's age will be x+18 and the father's will be 4x+18. And we know that 18 years later the father's age will be twice the daughter' so , 4x+18 = 2(x+18) and 4x+18=2x+36 then, 4x-2x=36-18,
2x=18 then divide both sides by 2, x = 9. The daughter's age was x, so she is 9 years old.

Simplify 81^1/2
Please simplify and show steps

Answers

a^(n)/(m)=\sqrt[m]{a^n}\n\n\n81^(1)/(2)=√(81)=9\n\n\n81^(1)/(2)=(9^2)^(1)/(2)=9^{2\cdot(1)/(2)}=9

The expression 81⁽¹/²⁾ simplifies to 9.

To simplify the expression 81¹/², we can evaluate the squareroot of 81.

The square root of a number x is a value that, when multiplied by itself, gives x. In this case, we're looking for the number that, when squared, equals 81.

The square root of 81 is 9 since 9 x 9 = 81.

Therefore, 81⁽¹/²⁾ simplifies to 9.

In terms of steps, we can represent the process as follows:

1. Recognize that 81⁽¹/²⁾ represents the square root of 81.

2. Evaluate the squareroot of 81, which is 9.

3. Thus, 81^(1/2) simplifies to 9.

By simplifying the expression, we find that 81⁽¹/²⁾is equal to 9.

To learn more about the expression;

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Which of the following expressions is not equivalent to:4(3x2 + 6x)

A. 12x2 + 24x B. 2x(6x + 12) C. 6x(2x2 + 4x)

Answers

Answer=C

4(3x^2+6x)
can be simplified to...
12x^2+24x

To find out which expression isn't equivalent, you have to simplify them...

a=12x^x+24x

b=2x(6x+12)
b=12x^2+24x

c=6x(2x^2+4x)
c=12x^3+24x

a moving company charges a flat rate of $85 plus and additional $0.17 per mile driven. How far must the company drive to earn at least $100? Round to the nearest mile.

Answers

Answer:

Atleast 88 miles

Step-by-step explanation:

We are given that

A moving company charges a flat rate=$85

Cost of 1 mile driven=$0.17

We have to find the distance drive by the company to earn at least $100.

Let x  mile drive by company .

According to question

85+0.17x\geq 100

Subtract 85  on both sides of inequality

85+0.17x-85\geq 100-85

0.17x\geq 15

Divide by 0.17 on both sides

x\geq (15)/(0.17)

x\geq 88.23

x\geq 88 (round to nearest mile)

Hence, the company must drive atleast  88 miles to earn atleast $100.
They get $85 for just getting in the truck and starting the engine.

To earn $100, they need another $15 for mileage.

$15 / 0.17 = 88.2 miles

Rounded to the nearest mile, it's 88 miles (but that still leaves them 4¢ short).

The focus of a parabola is (3,-7) and the directrix is y = -4.What is an equation of the parabola?

Answers

Answer:

  (a)  (x -3)^2 = -6(y +5.5)

Step-by-step explanation:

The equation of a parabola can be written as ...

  (x -h)^2 = 4p(y -k)

where (h, k) is the vertex, and p is the distance from the focus to the vertex.

The vertex is half-way between the focus and directrix, so is ...

  (h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)

The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...

  -7 -(-5.5) = -1.5

Then the equation for the parabola is ...

  (x -3)^2 = 4(-1.5)(y -(-5.5))

  (x -3)^2 = -6(y +5.5) . . . . matches the first choice

Round off 4252 to one significant figure

Answers

The answer is 4000 because in sig fig, you don't count the zeros after the number unless there is a decimal after 0.
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