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29 1.2. Constructing Direct Proofs 1. Let a, b, and c be real numbers with a 0. The solutions of the quadratic equation ax 2 + bx + c = 0 are given by the quadratic formula, which states that the solutions are xi and x2. where and x2 2a 2a (a) Prove that the sum of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to -b/a . (b) Prove that the product of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to c/a.

The proving of both a) and b) has been done

Step-by-step explanation:

The step by step explanation has been given in the attachment below.

Step-by-step explanation:

Answer:5

Step-by-step explanation:

2x=10

10÷2= 5

x=5

Answer:

X = 5

Step-by-step explanation:

2x means x plus itself. if x + x is 10, what number fits that description?

5!

2.5 = 10, so X = 5

Answer:

26 guests

Step-by-step explanation:

Answer:

3.14

Step-by-step explanation:

compare 3.4 to 3.111111111111111111...

4 is bigger than 1

3.14 is bigger than 3.1 repeating.

The number 3.1 repeating (or 3.1 with an infinite number of decimal places of 1) is equivalent to the mathematical concept of the number 3.1111..., where the digit 1 repeats indefinitely.

When comparing 3.14 and 3.1 repeating, we can consider the decimal places:

3.14 has a hundredth place digit of 4, which is greater than the repeating decimal of 3.1, where the hundredth place digit is 1.

Therefore, 3.14 is bigger than 3.1 repeating.

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Answer: 600 feet per hour

Because there are 60 minutes in an hour and 10 times 60 is 600

Answer:

- 10/27

Step-by-step explanation:

Answer:

-10/27

Step-by-step explanation:

-3 1/3 divided by 9 = -10/3 divided by 9/1= -10/27

Answer:

5.35

Step-by-step explanation:

9-3.65=5.35

Answer:

1 and 3 = 84

Step-by-step explanation:

the lines are parelle meaning you will get the same agles

we know that all the even angles are equal to 96 degrees

we need to do 180- 96= 84

so know we know that 84 equalls all the odd numbers

Answer:

x = -3

Step-by-step explanation:

x + 2/x = 4/3 - 1 (collect like terms)

The rest of the steps are in the screenshot.

Answer:

11 1/4

Hope I helped

Answer:

32h (1 day and 8h )

Step-by-step explanation:

268-12=256

256:8= 32

32h

Answer:

8x+12= 268

Step-by-step explanation:

We know that Lester already has $12, so that would be: +12

Since he works for $8 an hour, x will represent each hour: 8x

*x will determine the number of hours, if you want days, then divide the amount of hours by 24.

Answer: 15

Step-by-step explanation: 60/4=15

the perimeter is the overall numbers that are on each side that add up since a square has 4 sides and the overall perimeter=60 in all then it's 60/4=15

Answer:

C

Step-by-step explanation:

It is 75 cents a game plus 5 dollars admission. You should automatically subtract 5 dollars for admissions. That would give you ten dollars. You would just multiply how many games by how much they cost.

(You can also find the number of games first, and then solve the two inequalities that match that number backwards)

Hope this helps :)

Answer:

8.8 cm , but not sure.....

Thank you ☺️

x= -66/19

Multiply 2 on both sides:

2*(5x+6)/2=3(4x+12)*2

Simplify:

5x+6=24x+72

Subtract 6 from both sides:

5x+6-6=24x+72-6

Simplify:

5x=24x+66

Subtract 24x from both sides:

5x-24x=24x+66-24x

Simplify:

-19x=66

Divide both sides by -19

-19x/-19=66/-19

Simplify:

x= -66/19

Answer: integers

Step-by-step explanation:

Answer:

no it is(7,2)

Step-by-step explanation:

Sorry. Had to redo this with the correct answer.

Here it is...

Solve for x by simplifying both sides of the equation, then isolating the variable.

Exact Form:

x = - 2/5 (fraction)

Decimal Form:

x = - 0.4 (decimal)

Answer:

The answer is 27 your welcome

Step-by-step explanation:

Answer:

the answer is none

Step-by-step explanation:

because as you can see the dots dosent match the tally's on the chart

Answer:

32h+40

Step-by-step explanation:

8*4h=32h

8*5=40

Maxwell runs faster than Hayley

In order to determine who runs faster, the average speed has to be determined

Average speed is total distance travelled divided by total time travelled.

Average speed = Total distance / Total time

Hayley's average speed = [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{6}[/tex]

=  [tex]\frac{3}{4}[/tex] x 6 = [tex]\frac{9}{2} = 4\frac{1}{2}[/tex] miles / hour

Maxwell's average speed = [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{15}[/tex]

[tex]\frac{2}{3}[/tex] x [tex]\frac{15}{2}[/tex] = 5 miles / hour

Maxwell runs faster because he has a higher average speed when compared with Hayley

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For the conditions to be fulfilled number of chocolate bars Janet bought is 35.

An equation is a statement in form of numbers and variables that both sides are equal.

Janet bought the same bars of chocolate to share equally with her friends and it is between 36 and 50.

There are two possible cases,

Let the number of chocolates be 'N' and no. of chocolates each friend gets be 'A'.

(i)  If she shares the bars of chocolate equally with 7 friends, she will have 7 bars left over,

∴ N = 7A + 7...(i).

(ii) If she shares the bars equally with 6 friends she will have 5 bars left over,

Let the number of chocolates be 'N' and no. of chocolates each friend gets be 'B'.

∴ N = 6B + 5...(ii)

Now, we have to equate these two equations,

7A + 7 = 6B + 5.

7A = 6B - 2.

A = (6B - 2)/7.

From here we have to find such integer value of B which also makes the value of A an integer and also when we put the values of either A or B in our equations it should lie between 35 and 50.

So,

A = (6B - 2)/7.

When B = 5 then A = 4. Or when B = 12 the A = 10.

But the B = 12 and A = 10 is inadmissible.

Now, we'll put the value of A or B in eqn (i) or (ii).

Which results in N = 35.

So, the number of chocolate bars she bought is 35.

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Answer:

9=4

Step-by-step explanation:

9(1)= 1+3

9(1)=9

1+3=4

9:4

Answer:

1. 10d + 5n = 85

2.  idk how to attach stuff

3. 17 nickels  

4. 8.5 thats weird tho since its not possible to get 85 with using only dimes you would have to use 8 dimes and 1 nickel but its doesn't ask for that so 8.5 ig

Step-by-step explanation:

5n = 85

5*17 = 85

10d = 85

10*8.5 = 85

Answer:

C=5+0.25m

Step-by-step explanation:

Answer:

y = -7

Step-by-step explanation:

Answer:

(a) 0.0051

(b) 0.9773

Step-by-step explanation:

Let X = prices of the car.

It is provided that [tex]X\sim N(23,000, 3,500^{2})[/tex].

(a)

Compute the value of P (X ≥ 32000) as follows:

[tex]P(X\geq 32000)=P(\frac{X-\mu}{\sigma}>\frac{32000-23000}{3500})[/tex]

                       [tex]=P(Z>2.57)\\=1-P(Z<2.57)\\=1-0.99492\\=0.00508\\\approx 0.0051[/tex]

Thus, the proportion of cars cost an equal amount or more than $32,000 is 0.0051.

(b)

Compute the value of P (X ≥ 16000) as follows:

[tex]P(X\geq 16000)=P(\frac{X-\mu}{\sigma}>\frac{16000-23000}{3500})[/tex]

                       [tex]=P(Z>-2)\\=P(Z<2)\\=0.97725\\\approx 0.9773[/tex]

Thus, the proportion of cars cost an equal amount or more than $16,000 is 0.9773.