Five runners are entered into a competition. Four of the runners have had their turns. Their
completing times are 7.4 s, 7.75 s, 7.09 s, and 7.86 s. What time must the last runner get in order to win
the competition?

First off, we factor out the expression:

[tex] \displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }[/tex]

In the bracket, separate 8 out of the expression.

[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}[/tex]

In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

[tex] \displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}[/tex]

So we add +9 in x^2-6x.

[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}[/tex]

Convert the expression in the small bracket to perfect square.

[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}[/tex]

Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.

[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}[/tex]

Then we distribute 2 in.

[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ [/tex]

[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }[/tex]

Remember that negative multiply positive = negative.

Hence the vertex form is y = 2(x-3)^2-2 or first choice.

Answer:

The forest will cover an area of approximately 2994 square kilometers after 10 years.

Step-by-step explanation:

A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).

Since the original area is 5000 square kilometers, let a = 5000.

Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.

Thus, our function is:

[tex]\displaystyle f(x) = 5000(0.95)^x[/tex]

Then after 10 years (x = 10), the area will be:

[tex]\displaystyle f(10) = 5000(0.95)^{(10)}= 2993.6846...\approx 2994\text{ km}^2[/tex]

In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.

Answer:

Step-by-step explanation:

The midpoint formula is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the coordinates of the midpoint and the coordinates of one endpoint. Filling that in we have:

[tex](-5,-4)=(\frac{-4+x_2}{2},\frac{-7+y_2}{2})[/tex] and we will solve for the missing values one at a time. x first:

[tex]-5=\frac{-4+x_2}{2}[/tex] and

-10 = -4 + x₂ so

-6 = x₂ and do the same for y:

[tex]-4=\frac{-7+y_2}{2}[/tex] and

-8 = -7 + y₂ so

-1 = y₂

Thus, the coordinates of point g are (-6, -1)

Hi! I'm happy to help!

This expression is an exponent, or repeated multiplication. 3^3 is three multiplied by itself (3), 3 times, or 3×3×3

So, our non-exponent expression will be 3×3×3.

I hope this was helpful, keep learning! :D

Answer:

$150.60

Step-by-step explanation:

$984.20-$381.80= $602.40

Take $602.40 and divide by 4 which equals $150.60 which is the 1/4 $ Charlie has in his savings account.

Your answer is in the attachment .

Note: I have only done upto q.n d because you haven't clearly uploaded question of no. e. stay blessed !!!!!!

Answer:

Step-by-step explanation:

23550=15000(1+.0475t)

t=12

Answer:

3/7

Step-by-step explanation:

21w - 21 = -12

21w = -12 +21

21w = 9

w = 9/21

i.e w= 3/7

Step-by-step explanation:

21w-21= -12

21w= -12 + 21

w=9/21

(92.50-55)/15 =2.5 hours

Step-by-step explanation:

92.5 (total) -55 (trip charge) = 37.50(hour charge)

37.50(hour charge)/15{per hour charge)=2.5(hours)

Insert grouping symbols to make each number sentence true 3+8-2*5=45

Answer:

3+2+8×5

Answer:

x = 10

Step-by-step explanation:

AC = AB + BC

Substitute the values for the line segments:

50 = (2x) + (x + 20)

50 = 2x + x + 20

Combine like terms:

50 = 3x + 20

Subtract 20 from both sides:

30 = 3x

Divide both sides by 3:

10 = x

Check your work:

50 = 2(10) + 10 + 20

50 = 20 + 30

50 = 50

Correct!

Answer:

Your final grade will be 78.67 %

Step-by-step explanation:

67% of your grade will be from your test average which is 79 (higher)

33% of your grade will be from your homework average which is 78.

Calculating:

(67×79+33×78) / (67+33) = 7867 / 100 = 78.67

Answer:

Hi, There! Leah Is Correct

Step-by-step explanation:

A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all.

____________________________________________________________

-Darkspirit-

Answer:

Both are correct.

Step-by-step explanation:

Repeating decimals are rational.

Answer:

The answer is in the image above

Answer:

Step-by-step explanation:

The antiderivative for b is definitely incorrect, as stated in the comments section.

[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex]  That's a bit more simplified. One more important simplification and then we can integrate one term at a time:

[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex]  and here we go:

[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and

[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,

[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]

Answer:x+20

Step-by-step explanation:

Answer:

-13=5×1+5×4m-2m

-13=5+20m-2m

-13-5=18m

-18=18m

18m=-18

m=18÷18

m=1

Answer:

[tex]\frac{55}{4}[/tex]

Step-by-step explanation:

let the number be n the multiply by - 4 is - 4n and add 5 gives

- 4n + 5 = - 50 ( subtract 5 from both sides )

- 4n = - 55 ( divide both sides by - 4 )

n = [tex]\frac{-55}{-4}[/tex] = [tex]\frac{55}{4}[/tex]

The number is [tex]\frac{55}{4}[/tex] or 13.75 if you prefer

Answer:

-15.1

Step-by-step explanation:

Two negative numbers add the same way as positive numbers, so it is -(7.5 + 7.6) or -15.1.

Answer:

137027.1 Rupees

Step-by-step explanation:

(125200+5302) * 0.05 = 6525.1

130502+6525.1 =  137027.1

Answer:

h(-5) = (-2)^2 + 5 = 9

h(-1) = (2)^2 + 5  = 9

(9-9)/4 = 0

average rate of change is 0

Step-by-step explanation:

Answer:

10.71

Step-by-step explanation:

0.15*71.40

Answer:

Step-by-step explanation:

Answer:

n+2 represemts the number of sides in the polygon for the nth member of the sequence

Answer:

Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.

Answer:

8x-16y

Step-by-step explanation:

Answer:

8x - 16y and a + 3b - 2c

Step-by-step explanation:

(a)

8(x - 2y) ← multiply each term in the parenthesis by 8

= 8x - 16y

(b)

[tex]\frac{6a+18b-12c}{6}[/tex] ← factor out 6 from each term in the numerator

= [tex]\frac{6(a+3b-2c)}{6}[/tex] ← cancel the 6 on numerator/ denominator

= a + 3b - 2c

Answer:

y = -1/2x + 6

Step-by-step explanation:

The slope of a parallel line will remain the same. The only thing that is different is the y-intercept but we can solve that using the point given, the slope, and the slope intercept form equation [ y = mx + b ].

0 = -1/2(12) + b

0 = -6 + b

6 = b

Now input the data we were given and solved for back into the formula.

y = -1/2x + 6

Best of Luck!

Answer:

AB= AC+CB

50 = (2x – 2 ) + 4(x+1)

50 = (2x – 2) + ( 4x+4)

50 = 6x +2

6x = 50 – 2

6x = 48

x= 48/6

x= 8

So; x=8 Q.E.D.

I hope I helped you^_^