MATHEMATICS HIGH SCHOOL

What is the sum of all integers x that satisfy 1 < (pi -1 )x < 10?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

pi - 1 = 3.14 - 1 = 2.14

x has to be an integer, and the result must be greater than 1.

1 works.

1 < 2.14*1 < 10 2.14 is between 1 and 10.

2 works

1 < (2.14)*2 < 10

1 < 4.28 < 10

3 works

1 < 2.14 * 3 < 10

1 < 6.42 < 10

4 might work

1 < 2.14*4 < 10

1 < 8.56 < 10

and it does work.

5 can't work

1 < 5 * 2.14 < 10

1 < 10.7 < 10 is not true.

Answer: 1,2,3,4

Answer 2

Answer:

Answer:

Step-by-step explanation:

pi is 3.14...

pi - 1 is 2.14...

question becomes 1<2.14x and 2.14x < 10

1/2.14 < x, 0.46... < x

x < 10/2.14, x < 4.67...

combining

0.46< x < 4.67

x can be 1, 2, 3, 4

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In march, a customer spent $8.55 at an office-supply store for some 12-packs of pens. At that time, the store was selling packages of one dozen pens for $1.35. Any customer who bought more than 4 packages, received a discount of $0.30 on the price of each package in excess of 4 packages. In september, the same customer went back to the store to buy the same number of pens. By then, the price per 12-pack of pens had been raised to $1.50 each, with the same discount for more than 4 packages. How much more did the customer have to pay in September than in March?

Answers

We can start by making an equation from the information given on the month of March to find how many packs he bought.
$4(1.35)+x(1.05)=8.55$ This equation shows that for the first 4 packs he bought, he payed $1.35. Then, consequently, for each pack after that, he payed $0.30 less, and we don't know how many more he bought, so we set it up as shown. Finally, we set it all equal to $8.55 since that's how much he payed that month. We get that x=3, meaning that he bought a total of 7 packs of pens that month.
Knowing this, we can now make an equation for the month of September.
$4(1.50)+3(1.20)=x$ This time, we know the entire left side, that he paid $1.50 for the first 4 packs and $0.30 less for the last 3. We get x=$9.60
Knowing this, we can subtract the amount he paid in September by the amount he paid in March to get the answer... $9.60-$8.55=$1.05

I hope this helped!

2x^4=9x^2 solve by factoring

Answers

Step-by-step explanation:

2x⁴ = 9x²

2x⁴ - 9x² = 0

x²(2x² - 9) = 0

Either x² = 0 or 2x² - 9 = 0.

When x² = 0, x = 0.

When 2x² - 9 = 0, x² = 9/2, x = ± 3/√2.

Hence the solutions are

x = 0, x = 3/√2 and x = -3/√2.

A baseball team has a record of 47 wins and 39 losses. How many games must the team win, in a row, so that the winning percentage will be above 70%?A: 23 wins
B: 13 wins
C: 14 wins
D: 32 wins
E: 44 wins

Answers

A baseball team has a record of 47 wins and 39 losses, then they have to win 44 games in a row so that their winning percentage will be above 70%. Hence, option E is correct.

What is the percentage?

The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentage are fractions. To put it another way, it's the relationship here between component and a whole, in which the value of the whole is always assumed to be 100. A specific portion or amount in each hundred is referred to as the percentage. The fraction is denoted by the sign "%," and its denominator is 100.

Finding the proportion of a whole in units of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:

Through the unitary approach.
By making 100 the new denominator of the proportion.

To know more about Percentage:

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Answer:

44 wins

Step-by-step explanation:

47+39+x/100*70

What is the range of the given function? {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

Answers

range is output
(x,y)
y=mx+b aka
f(x)=somethingx

y=output
(x,range)
look at the secondn numbers

range={0,-3,-9,5,7}
arrange them in increaseing order (for nicity)
range={-9,-3,0,5,7}

Select the correct answer.The function f(x) is given by the table of values.

x 1 2 3 4
f(x) 1 8 27 64
If f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?

x 5 6 7 8
g(x) 5 12 31 68

x 1 2 3 4
g(x) 5 12 31 68

x 5 6 7 8
g(x) 1 8 27 64

x 1 2 3 4
g(x) 4 32 108 256

Answers

The solution is Option B.

x = { 1 , 2 , 3 , 4 }

g(x) = { 5 , 12 , 31 , 68 }

The function g ( x ) = x³ + 4

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

when x = 1

f ( x ) = 1

when x = 2

f ( x ) = 8

when x = 3

f ( x ) = 27

when x = 4

f ( x ) = 64

So , the equation will be y = x³ be equation (1)

Now , f(x) is shifted 4 units up to obtain g(x)

So , Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

when x = 1

g ( x ) = 1 + 4 = 5

when x = 2

g ( x ) = 8 + 4 = 12

when x = 3

g ( x ) = 27 + 4 = 31

when x = 4

g ( x ) = 64 + 4 = 68

Therefore , the function is g ( x ) = x³ + 4

Hence , the function is g ( x ) = x³ + 4

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Answer:

The second answer is correct.

Step-by-step explanation:

So g(x) = f(x) + 4

If f(x) = 1, 8, 27, and 64 then g(x) = 5, 12, 31, and 68.

Scientific notation 2/10=?
and 12 thousandth =? show the work.

Answers

12,000=12*1,000 or 12,000=12*10^3

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