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3 years ago

The square of two times an interger is 6 more than ten times the integer. Find the integer

1 answer:

3 0

So for this problem, you will need to write out the equation before you can solve the question. The square of two times an integer translates into 2x². In a word problem, "is" means =. Therefore, 2x² is equal to the other half of the equation. To write out the other half of the equation, you have to know that "is more than" means addition. So, 10x+6 is the other half of the equation. your final equation becomes 2x²=10x+6. Then solve the equation like in any other problem: 2x²=10x+6 becomes 2x²-10x-6=0, and then factor or use the quadratic formula.

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Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.8% compounded daily. The annual per

sweet-ann [11.9K]

Answer:

4.92%

Step-by-step explanation:

First of all, recall that if you increase a number C in x%, then you will have $C+\frac{x}{100}C=C(1+\frac{x}{100})$

So <em>increasing a number in x% is equivalent to multiply it by (1+x/100) </em>

Now, suppose you have deposited $C where C is any amount > 0

If the bank offers an APR of 4.8% compounded daily, it means that your money increases $\frac{4.8}{365}\%=\frac{0.048}{365}$ daily.

So, after 365 days you will have

C multiplied by (1+0.048/365) 356 times, that is

(1) $C(1+\frac{0.048}{365})^{365}=C(\frac{365.048}{365})^{365}$

Now, you want to find a value x, such that C increased in x% equals the amount in (1).That would be the percentage your money increased in one year (APY)

$C(\frac{365.048}{365})^{365}=C(1+\frac{x}{100})\Rightarrow x=100[(\frac{365.048}{365})^{365}-1]$

Computing this amount, we get

x = 4.92 rounded to the nearest hundreth.

And the bank is offering an APY of 4.92%

7 0

3 years ago

Tesfa is x years old his father is 4 times as old as tesfa his mother is 7 years younger than his father If their ages add up to

Sergio039 [100]

Step-by-step explanation:

his father's age= 4x

his mother's age= 4x- 7

his age= x

x+4x+4x-7=101

x+ 4x+ 4x= 101+ 7

9x= 108

$\frac{9x}{9}$ = $\frac{108}{9}$

x= 12

Tesfa is 12 years old

4 0

3 years ago

Read 2 more answers

If f(x)=x2-2x-8 and g(x)=1/4x-1 for which value of x is f(x)=g(x)

fomenos

$f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}$

6 0

3 years ago

1. Solve: 6x - 12 < 6<br> 2. Solve: 2(3x-8) >8

8090 [49]

Answer:

Step-by-step explanation:

1. here you go mate

step 1

6x - 12 < 6 equation

step 2

6x - 12 < 6 simplify

6x-12+12<6+12

step 3

6x<18 Divide both sides

$\frac{6x}{6}$

answer

x<3

2. Here you go mate

step 1

2(3x-8) >8 equation

step 2

2(3x-8) >8 simplify

6x-16+16>8+16

step 3

6x>24 divide both sides

$\frac{6x}{6} >\frac{24}{6}$

answer

x>4

4 0

3 years ago

3.2g of sugar is needed to make 8 cakes. How much sugar is needed for 12 cakes?

4vir4ik [10]

3.2s:8c

4.8s:12c

Therefore, you would need 4.8g of sugar to make 12 cakes. This was solved by using ratios.

8 0

3 years ago

Read 2 more answers