Determine the type and number of solutions of 7x^2+3x+8=0

Answers

Answer 1

Answer: $7x^2+3x+8=0 \n \na =7, \ b=3 ,\ c=8 \n \n\Delta =b^2 - 4ac = 3^2 -4\cdot 7\cdot 8=9-224=-215\n \n Answer : \ \Delta \ is \ negative,\ this \ gives \ two \ imaginary \ solutions$

Answer 2

Answer: $7x^2+3x+8=0\n\n \Delta=3^2-4\cdot7\cdot8=9-224=-115\ \ \Rightarrow\ \ \ no\ real\ solution\n\n\ two\ complex\ solutions\n\n\Delta=-115=115\cdot i^2\ \ \ \Rightarrow\ \ \ √(\Delta) = √(115)\ i\n\nx_1= (-b- √(\Delta) )/(2a) = (-3- √(115)\ i)/(2\cdot 7) = (-3- √(115i))/(14)\n\nx_2= (-b+ √(\Delta) )/(2a) = (-3+ √(115)\ i)/(2\cdot 7) = (-3+ √(115)\ i)/(14)$

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For her birthday Lucy received $20 from her aunt , $15 from her grandmother , and $32 from her cousins. She bought an e- book for $10.85 . How much birthday money does Lucy have left ?

Frankie paid $11.75 for the movie ticket and $4.75 for popcorn and a drink. How much did Frankie spend?
a. $7.00
b. $15.50
c. $15.75
d. $16.50

Answers

He spent $16.50. Add the two amounts up.

Its 16.50

11.75 + 4.75

add them and you have your answer :) hope that helped

Please show all work.

Answers

Answer:

wait where is the photo?

Step-by-step explanation:

After making a deposit,puja had $264 in her savings account.She noticed that if she noticed that if she added $26 to the amount originally in the account and doubled the sum,she would get the new amount.How much did she originally have in the account.

Answers

Answer:

Let the original deposit be

Add $26 to original deposit

→

And doubled the sum

→

(

)

You get the new amount

→

(

)

264

Multiplying out the bracket

264

Subtract 52 from both sides

264

−

212

Divide throughout by 2

106

So the original amount was $106.00

Which of the following equations is an equation formed when completing the square on y 2 - 12y = -27?(y - 6) 2 = -27
(y - 6) 2 = 9
(y + 6) 2 = 9

Answers

Answer: The correct option is

(B) $(y-6)^2=9.$

Step-by-step explanation: We are given to select the equation that is formed when completing the square on the following equation :

$y^2-12y=-27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula :

$a^2-2ab+b^2=(a-b)^2.$

From equation (i), we have

$y^2-12y=-27\n\n\Rightarrow y^2-2* x*6=-27\n\n\Rightarrow y^2-2* x* 6+6^2=-27+6^2\n\n\Rightarrow (y-6)^2=-27+36\n\n\Rightarrow (y-6)^2=9.$

Thus, the required equation that is formed is $(y-6)^2=9.$

Option (B) is CORRECT.

Hello,

You should write y²-12y=-27 or y^2-12y=-27

y²-12y=-27
==>y²-2*6y+6²=-27+36
==>(y-6)²=9
(second answer)

There are two bottles of tomato ketchup, one weighs 720 g and costs £1.79, while the other weighs 460 g and costs £1.00. Which bottle gives better value for money? (Hint: you have to use ratios)

Answers

$To\ find\ better\ value\ for\ money\ you\ can\ find\ price\ of\ 100g:\n\n720:100=72\n460:100=46\n\n1.79:72=0.025\n1.00:46=0.022\n\n460g\ ketchup\ is\ more\ profitable.$

The better value would be the one that weighs 720 g and costs $ 1.79.

You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, and granola costs $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredients should you buy?

Answers

Answer:

8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts

Step-by-step explanation:

Lets form equations first.

->Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, granola costs $4.00 per pound

2.50p + 2.00r + 4.00g= 80 -->eq(1)

-> bought ingredients to make 30 pounds of trail mix

p+ r+ g= 30 -->eq(2)

->If you use twice as many pounds of peanuts as raisins

2r=p

eq(1)=> 2.50p + 2.00r + 4.00g= 80

2.5(2r) + 2r +4g =80

5r + 2r + 4g =80

7r + 4g =80

eq(2)=>

2r+ r+ g= 30

3r + g =30

-4(3r + g =30)

7r + 4g =80

_______________

-5r = -40

r= 40/5 =>8

For 'g':

3(8) + g =30

g= 6

For 'p':

2r=p

p=16

therefore, 8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts should be bought

Final answer:

The solution to the problem is to buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.

Explanation:

This problem requires the use of algebra. Let's denote the amount of peanuts as x, the amount of raisins as y and the amount of granola as z. We have certain constraints according to the problem that need to be satisfied. These are:

2*y = x (since the amount of peanuts is twice that of raisins)
x + y + z = 30 (total weight should equal 30 pounds)
2.5x + 2y + 4z = 80 (total price should not exceed $80)

First, substitute x = 2y from the first equation into the other two equations. This gives you the new equations y + z = 10 and 9y + 4z = 80. Next, solve these simultaneous equations. The solutions are y = 4, z = 6. Substituting y into the first equation gives us x = 2*4 = 20. So, you should buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.

Learn more about Simultaneous Equations here:

brainly.com/question/30319215

#SPJ3

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