MATHEMATICS HIGH SCHOOL

How to solve it ...

1. 5-2x²-6x
2. (x+3) (x+4)=0

Answers

Answer 1
Answer: 1.\n5-2x^2-6x=0\n-2x^2-6x+5=0\n\na=-2;\ b=-6;\ c=5\n\n\Delta=b^2-4ac\to\Delta=(-6)^2-4\cdot(-2)\cdot5=36+40=76\n\nx_1=(-b-\sqrt\Delta)/(2a)\to x_1=(6-√(78))/(2\cdot(-2))=(6-√(4\cdot19))/(-4)=(6-2√(19))/(-4)=(√(19)-3)/(2)\n\nx_2=(-b+\sqrt\Delta)/(2a)\to x_2=(3-√(19))/(2)

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2.\n(x+3)(x+4)=0\iff x+3=0\ \vee\ x+4=0\n\nx=-3\ \vee\ x=-4

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Solve the equations: (7x+4)/5 + (4x-2)/2=27, (8x+7)/6 + (9x-2)/2=6, 2/(x-4) + 8/(2x-8)=13 and 2/(x+5) - 4/(7x+35).

Answers

We need to solve for the x in the equations given.
(7x+4)/5 + (4x-2)/2=27
[(7x+4)*2 + (4x-2)*5]/ 10 = 27
(14x+8+20x-10)/10 = 27
(14x+8+20x-10) = 270
34x = 272
x = 8
---------------------

(8x+7)/6 + (9x-2)/2=6
[(8x+7) + (9x-2)*3] / 6 = 6
(8x + 7 + 27x - 6) / 6 = 6
(8x + 7 + 27x - 6) = 36
35x = 35
x = 1
----------------------------

2/(x-4) + 8/(2x-8)=13
[(2*2) + 8] / (2x-4) = 13
12 / (2x-4) = 13
13(2x-4) = 12
26x - 52 = 12
26x = 64
x = 64/26
x = 32 / 13 
-----------------------------------

2/(x+5) - 4/(7x+35)
[(2*7) - 4] / (7x+35)
(14-4)/(7x+35)
10 / (7x+35)

0.06 or 0.06666666666 As a fraction

Answers

0.06 = 6/100
When simplified, that's 3/50 .

0.06666666666 = 6,666,666,666/10,000,000,000
When simplified, that's 3,333,333,333/5,000,000,000 .

Sam Seller offers credit at 19% interest per year. To the nearest tenth, APR =

Answers

Answer:

20.7%.

Step-by-step explanation:

We have been given that Sam Seller offers credit at 19% interest per year.

We will annual percent yield formula to solve our given problem.

APY=(1+(r)/(n))^n-1, where,

r = Interest rate in decimal form,

n = Number of times interest is compounded per year.

Let us convert our given interest rate in decimal form.

19\%=(19)/(100)=0.19

Upon substituting our given values in above formula we will get,

APY=(1+(0.19)/(12))^(12)-1

APY=(1+0.015833)^(12)-1

APY=(1.015833)^(12)-1

APY=1.207450998-1

APY=0.207450998

Let us convert APY in percentage by multiplying our answer by 100.

APY=0.207450998* 100

APY=20.7450998\%\approx 20.7\%

Therefore, the APY is 20.7%.

Answer:

\text{APR}=20.7\%              

Step-by-step explanation:

Given : Sam Seller offers credit at 19% interest per year.

To find : To the nearest tenth, APR ?

Solution :

The formula to calculate the annual percentage rate is given by

\text{APR}=(1+(r)/(n))^n-1

where, r is the interest rate i.e. r=19%=0.19

n is the number of time period for which interest is compounded per month i.e. n=12.

Substitute in the formula,

\text{APR}=(1+(0.19)/(12))^(12)-1

\text{APR}=(1+0.01583)^(12)-1

\text{APR}=(1.01583)^(12)-1

\text{APR}=1.2074-1

\text{APR}=0.2074

Into percentage,

\text{APR}=0.2074* 100

\text{APR}=20.74\%

To the nearest tenth,

\text{APR}=20.7\%

There goes my hopes for Virtuoso rank....What are the zeros of the function y = x2 + 10x – 171, and why?

A) The zeros are x = –19 and x = 9 because in factored form, the function is y = (x – 19)(x + 9)

B) The zeros are x = –19 and x = 9 because in factored form, the function is y = (x + 19)(x – 9).

C) The zeros are x = 19 and x = –9 because in factored form, the function is y = (x – 19)(x + 9).

D) The zeros are x = 19 and x = –9 because in factored form, the function is y = (x + 19)(x – 9).

Answers

y = x^2 + 10x - 171
y = (x - 9)(x + 19)

x - 9= 0 x + 19 = 0
x = 9 x = -19

Answer B covers all requirements... the factored form is
y= (x + 19)(x - 9)
and the zeros are -19 and 9

Sarah is planning to spend a week at her friend’s summer house in Miami Beach. All meals will be provided by her friend’s parents, but Sarah still needs at least $500 to pay for her airfare and personal expenses for the week. She is selling bracelets and earrings to fund her trip. A graph representing this situation is shown below.Questions:
1.This region represents the combinations of bracelets and earrings that Sarah must sell in order to get a minimum of $500 profit to pay for her trip.
2.This region represents the area where Sarah sells a lot of earrings but not enough bracelets to reach her $500 goal.
3.This region represents the area where Sarah sells a lot of earrings but not enough bracelets to reach her $500 goal.

graph below ∨↓↓↓↓

Answers

Given:
x > 50
2x + 3y > 500

Bracelet is represented by x.
Earrings is represented by y.

Since x > 50 let us assume that x = 50 to get the value of y in the inequality equation.

2x + 3y       > 500
2(50) + 3y  > 500
100 + 3y    > 500
-100             -100
         3y     > 400
          ÷3         ÷3
           y     > 133 1/3

x > 50 ; y > 133 1/3

Let us assume that no bracelet was sold. x = 0 ; y =? 

2x + 3y     > 500
2(0) + 3y   > 500
0     + 3y   > 500
       ÷ 3          ÷3
            y   > 166 2/3

Let us assume that no earrings was sold; y = 0 ; x = ?
2x + 3y   > 500
2x + 3(0) > 500
2x + 0     > 500
2x           > 500
÷2               ÷2
x             > 250

Let us assume that we sold have of each item.
x = 250/2 = 125 ; y = 166 2/3 ÷ 2 = 100

2x + 3y              > 500
2(125) + 3(100) > 500
250 + 300         > 500
550                   > 500

To get at least $500, Sarah needs to sell at least 100 bracelets and 100 earrings.

the first one is region 2 and the second is region 3 i think

Put 983 in scientific notation.

Answers

To the left of the decimal point needs to be somewhere between 1 and 9 (one place). 983 in scientific notation would be 9.83 x 10^2. Do you understand how i got that? I got the 10^2 because i am moving the decimal point over two places to the left. If i move the decimal point to the right, then the exponent would be negative. Example:
0.00983 in scientific notation would be 9.83 x 10^-3 because i moved the decimal point three places to the right.
9.83• ten to the negotiation two
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