The first six steps of the derivation of the Quadratic Formula are listed below.
b
x
lo
=
a
a
+
1. ax2 + bx +c=0
2. Cx2 + x + =
3. x2 + x+8 = 0
b
4. x2 +
X=
a
b2
5. x2 + x +
4a2
6. (x + )2
4a2
a
+
a
b2
4a2
b2-4ac
2a

Answer:

y= -60x+ 200

Step-by-step explanation:

Given: Initial distance from Kingston = 200 miles

Distance from Kingston after 2 hours= 80 miles

Step 1:

The general model for linear equations is given as:

y= ax+ b

where

a= slope

b= y-intercept

Step 2:

The y-intercept represents the initial value: 200 miles from the Kingston

b= 200

Therefore,

y= ax+ 200

Step 3:

As the car gets closer to Kingston, the distance keeps decreasing.

The car having covered 80miles need to cover another 120 miles after 2 hours

Hence, the slope would be negative

Slope:

a= -120 miles/2 hours

a=-60

The model therefore is:

y= -60x+ 200

Final answer: Option (D)

The model is : y= -60x+ 200

Answer:

13

Step-by-step explanation:

to round to nearest whole number if its .5 or above you go up 1. If it's .4 or below you go down 1.

2.414=2

8.160=8

2.621=3

add

2+8+3=13

if you just added the decimals you would get: 13.195. (This shows you have a good estimate.)

HCF for both I believe!

Answer:

d is about 8.6 feet.

Step-by-step explanation:

We have similar triangles, so we can set up and then solve this proportion:

[tex] \frac{d}{10} = \frac{6}{7} [/tex]

[tex]7d = 60[/tex]

[tex]d = 8.6[/tex]

Answer:

Kenya is trying to find matching

socks. There are 4 red socks, 6 blue

socks, and 2 white socks in her

drawer. What is the probability that

Kenya will pull out a blue sock, put it

on, and then pull out another blue

sock to put on?

Kenya is trying to find matching

socks. There are 4 red socks, 6 blue

socks, and 2 white socks in her

drawer. What is the probability that

Kenya will pull out a blue sock, put it

on, and then pull out another blue

sock to put on?

Kenya is trying to find matching

socks. There are 4 red socks, 6 blue

socks, and 2 white socks in her

drawer. What is the probability that

Kenya will pull out a blue sock, put it

on, and then pull out another blue

sock to put on?

Kenya is trying to find matching

socks. There are 4 red socks, 6 blue

socks, and 2 white socks in her

drawer. What is the probability that

Kenya will pull out a blue sock, put it

on, and then pull out another blue

sock to put on?

Kenya is trying to find matching

socks. There are 4 red socks, 6 blue

socks, and 2 white socks in her

drawer. What is the probability that

Kenya will pull out a blue sock, put it

on, and then pull out another blue

sock to put on?

Answer:

A

Step-by-step explanation:

it's a geometric sequence since it is continuously being multiplied by the same number which in this case is 2.

Answer:

A. 3, 6, 12, 24

Step-by-step explanation:

In A, you're multiplying by 2 each time.

Answer:

It will gain $120, making it $620 in all.

Step-by-step explanation:

A = 500(1 + (0.06 × 4)) = 620

Considering the confidence interval, the interpretation regarding wheter 60% of Skyline College students say math is their favorite subject is:

A. No, 0. 60 is not contained in the interval.

B. Yes, all the interval values are greater than 0.60.

C. No, all the interval values are greater than 0.60.

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

In this problem, the confidence interval for the proportion of students who say math is their favorite subject is (0.6358, 0.7532).

Since the entire interval is above 0.6, and it does not contain 0.6, the correct answer for each question is given as follows:

A. No, 0. 60 is not contained in the interval.

B. Yes, all the interval values are greater than 0.60.

C. No, all the interval values are greater than 0.60.

More can be learned about confidence intervals at https://brainly.com/question/25890103

To find the lengths of a right triangle, we can use what is called Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse.

13^2 + b^2 = 17^2

169 + b^2 = 289

b^2 = 120

b = 11.0 cm

The length of the other leg of the triangle is 11.0 cm (rounded).

Hope this helps!

The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

[tex]a^2 + b^2 = c^2[/tex]

Given that One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm.

To find the lengths of a right triangle, we can use Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex],

where; a and b are the legs of the triangle and c is the hypotenuse.

[tex]13^2 + b^2 = 17^2\\169 + b^2 = 289\\b^2 = 120[/tex]

b = 11.0 cm

Therefore, The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.

Learn more about Pythagoras theorem;

https://brainly.com/question/343682

#SPJ2

Answer:

4x+3=2x+27

4x-2x=27-3

2x=24

x=24/2

x=12

Answer:

51

Step-by-step explanation:

2x+27=4x+3

    -3       -3

__________

2x+24=4x

___________

         2

x+12=2x

-x      -x

___________

12=x

now plug in/check answer

2(12)+27=4(12)+3

24+27=48+3

51=51

true

Step-by-step explanation:

From how Bert, his sister and older brother are standing, they form a triangle. Since we are not told anything else we can assume they form a right angled triangle. Use theorem of pythagoras to get the missing side.

Bert and his sister are 4 meters apart.

Answer:

24

Step-by-step explanation:

4x=12

x=12/4

x=3

8×=?

8(3)=24

therefore, 8 pieces will cost 24.

another way is:

since 8 is 4×2

you could double the amount of money

12x2

which would also give you $24

If charged per cut, it will cost 24 dollar to cut a log into eight pieces if cutting it into four pieces costs $12

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that to cut a log into eight pieces if cutting it into four pieces costs $12.

Thus,

4x=12

x=12/4

x=3

Hence, for 8 pieces

8(3)=24

therefore, 8 pieces will cost 24.

If charged per cut, it will cost 24 dollar to cut a log into eight pieces if cutting it into four pieces costs $12

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

14.5 hours

Step-by-step explanation:

Take the return trip situation.

From town to village

That is equal to the sum of t, the time taken from the village to the city and 30 minutes.

⇒ t + 30 minutes = 15 hours

⇒ t + 0.5 hours = 15 hours

⇒ t = 14.5 hours

Answer:

9 in × 5 in

Step-by-step explanation:

the area of a rectangle :

length × width

and this is 45 in² in our case.

the perimeter of a rectangle is

2×length + 2×width

and this is 28 in in our case.

l×w = 45

l = 45/w

2×l + 2×w = 2×(45/w) + 2w = 28

45/w + w = 14

45 + w² = 14w

w² - 14w + 45 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = w

a = 1

b = -14

c = 45

w = (14 ± sqrt((-14)² - 4×1×45))/(2×1) r

= (14 ± sqrt(196 - 180))/2 = (14 ± sqrt(16))/2 =

= (14 ± 4)/2 = 7 ± 2

w1 = 7 + 2 = 9 in

w2 = 7 - 2 = 5 in

l1 = 45/w1 = 45/9 = 5 in

l2 = 45/w2 = 45/5 = 9 in.

so, we see, length and width are interchangeable. it is only important to make one 9 in and the other 5 in.

Answer:

7.62

Step-by-step explanation:

To calculate the distance we can set up a right triangle and use the pythagorean theorem to calculate the distance.

A^2 + B^2 = C^2

Keep in mind that the A and B in this theorem (and my proceeding work) does not correlate to the labels for the points in the problem and are the standard variables used in the theorem.

First lets find the lengths of the sides A and B of our triangle by determing the distance on each axis that seperates the points.

On the x-axis we have

A = 5 - 2

A = 3

The y-axis has

B = 4 - (-3)

B = 7

Plugging these values into the equation from earlier we get:

3^2 + 7^2 = C^2
Where C is the hypotenuse of the right triangle we have created, and the distance between the two points.

9+49 = C^2

sqrt(58) = C

7.615773106 = C

Rounded the the nearest hundredth:

C = 7.62

Answer:

less

Step-by-step explanation:

3 km is 1.864 miles therefore, less than 5,000 m

Answer:

18

Step-by-step explanation:

no. of boys=2x

no.of girls=x

total no. of pupils=2x+x

27=3x

27/3=x

x=no.of girls=9

no.of boys =2x=2*9=18

Answer: 18 Boys

Step-by-step explanation: make first 27 divided by 3 equals 9 and then 9 times 2 equal 18 . We multiply by 2 to make it twice

Answer:

a) Class D - lowest variability/range

b) Class C - highest average/mean

Hope this helps!

Answer:

X= -27

Step-by-step explanation:

X+12= -15

X= -15 -12

X= -27

Answer: 64x + 30

Step-by-step explanation:

         Since this is an expression, we will simplify. Let � be x.

    Given:

32 + 4 * (16 * x) -2

    Simplify:

32 + 4(16x) -2

    Distribute / multiply:

32 + 64x - 2

    Combine like terms

64x + 30

Answer:

850m^2

Step-by-step explanation:

Look at the formula SA=L*W*H. And plug in the numbers pertaining the question! hints on to what to add is stuff like "long" for length, "wide" for width, and "high" for height! And use a calculator, or scetch it out to find your total answer!

Hope this helps!

Answer:

Point C

Step-by-step explanation:

because the number is 0.3 you need to start at zero on the number line and go forward 3 marks. That will lead you to your answer of 0.3

Answer: it’s C because it’s the one that’s closer to 3 if u need help just ask

Step-by-step explanation:

Hope this helps

-3

Answers:  

Exponential decay model is y = 500*0.88^x

There is roughly 0.0000000000237 mL of the original air left.

There are 10 zeros between the decimal point and the '2'

The number in scientific notation is [tex]0.0000000000237 = 2.37 \times 10^{-11}[/tex]

=============================================================

Further Explanation:

A general exponential equation is

y = a*b^x

We start with 500 mL of air which is the value of 'a'

If 12% of the air is replaced, then 88% of it remains because 12% + 88% = 100%

Convert 88% to the decimal form 0.88 and this represents the base of the exponent. This is the value of b.

-------------

Since a = 500 and b = 0.88, we have

y = a*b^x

y = 500*0.88^x

Now we plug in x = 240 to estimate how much of the original air is in the lungs after that many breaths.

y = 500*0.88^x

y = 500*0.88^240

y = 0.0000000000237

This number is very small and to be expected since quite a bit of breaths have occurred. Nearly all of the original air particles should be replaced by this point. A very small trace amount remains.

Notes:

Step-by-step explanation:

it seems we are dealing with multiplication, as the distances between the numbers get bigger and bigger.

and then I see

7 × 2 = 14

14 × 2 = 28

28 × 2 = 56

ok, so the sequence is created by always multiplying by 2.

a1 = 7

a2 = a1 × 2 = 7 × 2 = 14

a3 = a2 × 2 = a1 × 2 × 2 = 7 × 2 × 2 = 28

an = an-1 × 2 = a1 × 2^(n-1) = 7 × 2^(n-1)

a14 = 7 × 2¹³ = 7 × 8192 = 57,344

[tex] \huge\fbox\green{ANSWER} [/tex]

Surface Area = 2×(8.25×1.5 + 8.25×3 + 1.5×3) = 83.25 centimeters^2

[tex] \mathsf \blue{83.25 {cm}^{2} }[/tex]

Answer:

10 is the answer for this

please mark me as brilliant

Answer: x=4. PS=QR=15

Step-by-step explanation: