A student is deriving the quadratic formula. Her first two steps are shown.

Step 1: –c = ax2 + bx

Step 2:

Which best explains or justifies Step 2?

Answer:

40 mph

Step-by-step explanation:

To find the maximum speed at which the car can travel, as the distance it requires to stop is 168 feet, we just need to use the value of d = 168 in the equation, and then find the value of s:

168 = 0.05s^2 + 2.2s

0.05s^2 + 2.2s - 168 = 0

Using Bhaskara's formula: we have:

Delta = 2.2^2 + 4*0.05*168 = 38.44

sqrt(Delta) = 6.2

s1 = (-2.2 + 6.2)/0.1 = 40 mph

s2 = (-2.2 - 6.2)/0.1 = -84 mph (a negative value does not make sense as 's' is the speed of the car)

So the maximum speed of the car is 40 mph

Answer:C 151

Step-by-step explanation:

7 * 15=105 + 46=151

Answer: 788

Step-by-step explanation:

Answer:

30.5 and 46

Step-by-step explanation:

The minimum is 30.5 and the maximum is 46

Answer:

 [tex]\frac{- 39}{70}[/tex]

Step-by-step explanation:

{[tex]\frac{3}{7}[/tex] x [tex]\frac{1}{10}\\[/tex]} - { [tex]\frac{3}{7}[/tex] }x [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{7}[/tex] x 1

We follow the BODMAS rule

=  [tex]\frac{3}{70}[/tex] -  [tex]\frac{3}{7}[/tex] x [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{7}[/tex] x 1

=   [tex]\frac{3}{70}[/tex] - [tex]\frac{3}{7\\}[/tex] x [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{7}[/tex] x 1

=   [tex]\frac{3}{70}[/tex] - [tex]\frac{3}{7\\}[/tex] x [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{7}[/tex]

=  [tex]\frac{3}{70}[/tex] - [tex]\frac{6}{35}[/tex] + [tex]\frac{3}{7}[/tex]

=  [tex]\frac{3}{70}[/tex] - [tex]\frac{6}{35}[/tex] + [tex]\frac{3*5}{7*5}[/tex]        LCM= 35

=  [tex]\frac{3}{70}[/tex] - [tex]\frac{6 + 15}{35}[/tex]

=   [tex]\frac{3}{70}[/tex] - [tex]\frac{21}{35}[/tex]

=  [tex]\frac{3}{70}[/tex] - [tex]\frac{21*2}{35*2}[/tex]             LCM= 70

=   [tex]\frac{3 - 42}{70}[/tex]

=   [tex]\frac{- 39}{70}[/tex]

Answer:

B=-5

C=3

Step-by-step explanation:

x^4-3x^3-7x^2+7x+2= x^4-3x^3-10x^2+3x^2+7x+2

=x^4-3x^3-10x^2+ 3x^2+7x+2

=x^2(x^2-3x-10)+ 3x^2+7x+2

=x^2(x^2+2x-5x-10)+ 3x^2+6x+x+2

=x^2(x(x+2)-5(x+2))+ 3x(x+2)+1(x+2)

=(x+2)(x^2(x-5)+(3x+1))

=(x+2)(x^3-5x^2+3x+1)

Answer:

B=-5

C=3

Step-by-step explanation:

Answer:

After 15 years the population will be 7,625

Step-by-step explanation:

3.5% of 5,000 = 175

175 x 15 = 2625

2625 + 5,000 = 7625

The population after 15 years should be  8,376

Since the population is 5,000 and it grows 3.5 years and the time period is 15 years

So, the population after 15 years is

[tex]= 5,000 \times (1 + 3.5\%)^{15}\\\\[/tex]

= 8,376

Therefore, we can conclude that The population after 15 years should be  8,376

Learn more about population here: https://brainly.com/question/24309536

Answer:

180 teachers

Step-by-step explanation:

In this case, we know the value corresponding to 45% of female teachers which is 81, therefore, to find the total it would be:

% teachers    #teachers

       45                 81

       100                 x

we apply the rule of three:

x = 100 * 81/45

x = 180

which means that there are a total of 180 teachers at Russell High

Answer:

the answer is 7/10

Step-by-step explanation:

cause i am in honors math 6th grade. I am EXTREMELY smart!!!

Answer:

A relation is a set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation and the set of all second components of the ordered pairs is called the range of the relation.

Step-by-step explanation:

Answer:55.7 would be the answer.

Step-by-step explanation:

Answer:

the answer is 55.7

Step-by-step explanation:

because i got it right on edge 2021

Answer:

5cm³

Step-by-step explanation:

Volume of rectangular prism formula= L×W×H

1/2×4×5/2=

2×5/2=

10/2=

5cm³

Answer: [tex]f(x)=x^{2} -9x+14[/tex]

Step-by-step explanation:

[tex]x=2,7[/tex]

[tex]f(x)=(x-2)(x-7)[/tex]

[tex]f(x)=x^{2} -9x+14[/tex]

Answer:

Step-by-step explanation:

Givens

We know that the area of a rectangle is

[tex]A= w \times l[/tex]

Where [tex]w[/tex] is width and [tex]l[/tex] is length.

We know by given that [tex]l= 7 \ in[/tex] and [tex]A= 25 \ in^{2}[/tex], replacing these values and solving for [tex]w[/tex], we have

[tex]25=7w[/tex] (this is the equation used to solve the problem).

[tex]w=\frac{25}{7} \approx 3.6 \ in[/tex]

Answer:

The equation is Area = length × width.

The width is approximately 3.57 inches.

Step-by-step explanation:

Door sign length, l = 7 inches

Area, A = 25 square inches

Width (w) is unknow.

Since the area is the product of the length and the width,

A = l×w

25 = 7×w

Dividing both sides by 7

w = 25/7

≈ 3.57 inches

Answer:

The big bang is showing that there is tiny atoms. The atoms grouped up with gravity and more and more grouped making a super dense dot. The dot exploded making gases creating stars. The stars were bigger so they got new atoms to join creating planets. One planet named was suitable for life so tiny germs. The rest nobody knows.

Step-by-step explanation:

Answer:u tell me doc

Step-by-step explanation:

The answer is 5.25

First, you need to list all of the numbers from least to greatest. Then, you remove the sides (first 3.9 and 6.2 being the least and the greatest numbers). You then have 4.9 and 5.6 so you need to add them together (getting 10.6) and divide your answer by 2 (getting 5.25).

Hope I helped and good luck :)

Answer:

$48

Step-by-step explanation:

The rectangular wall is 6.5 m long and 3 m high and needs two coats of paint. This means the wall will be painted twice.

First, we find the area of the wall. The area of a rectangle is given as:

A = L * B

where L = length and B = breadth

Therefore, the area of the wall is:

[tex]A = 6.5 * 3 = 19.5 m^2[/tex]

One litre of paint covers an area of [tex]10m^2[/tex].

The paint can only be purchased in a full number of litres.

Therefore, let us find how many litres it will take to paint the wall once:

[tex]10m^2[/tex] = 1 litre

[tex]19.5 m^2[/tex] = 19.5 / 10 = 1.95 litres

Since the paint can only be bought in full number of litres, we approximate 1.95 litres to whole number, that is 2 litres.

2 litres is needed to paint the wall once.

Therefore, we need double of that to paint the wall twice, that is:

2 * 2 = 4 litres

Paint costs $12 per litre, therefore, the price for 4 litres is:

4 * 12 = $48

The cost of paint for the wall is $48.

Answer:

+19

Step-by-step explanation:

8-(-11)= 8+11

8-(-11)=+19

Answer:

19

Step-by-step explanation:

8 - ( -11) =

8 + 11 =

19

The two negatives combine to make a positive.

Question:

What is the area of the SHADED sector of the circle?

Image of the circle is attached.

A) 400π units²

B) 20π units²

C) 180π units²

D) 40π units²

Answer:

C) 180π units²

Step-by-step explanation:

From thr circle, we can see that the given radius is 20 and the shaded part is 162°

The formula to calculate the area of the shaded sector of a circle is =

Area of the circle * fraction of the shaded part of the circle.

We know area of a circle = πr²

Therefore, area of the shaded sector =

[tex] = \pi r^2 * \frac{162}{360}[/tex]

[tex] = 20^2 * \pi * 0.45 [/tex]

[tex] = 400 * 0.45 * \pi [/tex]

[tex] = 180 \pi [/tex]

Area of the shaded sector of the circle is 180π units²

Answer:

$11.10 per gallon.

Step-by-step explanation:

There are 4 quarts in a gallon so the cost of a gallon of oil currently is 1.85×4=$7.40

If the gallon price of oil goes up 50% then our answer is: 7.40×[tex]\frac{3}{2}[/tex]=[tex]\frac{22.2}{2}[/tex]=11.1

The price of oil in March will be $11.10 per gallon.

Answer: 50% of 1.85= 11.10

Step-by-step explanation:

11.10 is the correct answer

Answer:

295.2 cm^3

Step-by-step explanation:

Volume of a prism = length * width * height.

Here the volume = 4.8 * 4.1 * 15

= 295.2 cm^3.

The volume of rectangular prism is 295.2[tex]cm^{3}[/tex]

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

According to question

Length of rectangular prism = 4.8cm

Breath of rectangular prism = 4.1cm

Height of rectangular prism = 15cm

Volume of rectangular prism = Length * Breath * height

= 4.8*4.1*15

= 295.2[tex]cm^{3}[/tex]

Hence, Volume of rectangular prism is 295.2[tex]cm^{3}[/tex]

To know more about rectangular prism here :

https://brainly.com/question/21308855

# SPJ2

Answe12800 miles

Step-by-step explanation:a year is 12 months, and mile round trip means there and back. so 532x24 for the 24 trips that equals 12768. 12768 rounded to the nearest hundreds is 12800

Answer: $8.40

Step-by-step explanation:

The problem states that Scott has deposited $40 and is earning 10% interest, annually. It asks how much interest he will earn in 2 years to the nearest cent.

First, the formula given is B=p(1+r)^t. Since Scott deposits $40, 40 would be the starting amount, p.

B=40(1+r)^t

R is the interest rate: 10%. We plug in 0.10 instead of 10% because r is the interest rate, not the percentage.

B=40(1+0.10)^t

T is time: 2 years

B=40(1+0.10)^2

Now that we have the equation filled out, we plug this into a calculator.

48.4=40(1+0.10)^2

We know that the final amount is $48.40. Unfortunately, the question is asking how much interest is earned. To find that, you would subtract the Final-Initial to get the interest.

48.4-40=8.4

Answer:

x^2(4+x)

Step-by-step explanation:

you have to factor out x^2 off both equations since that's the only thing that you can divide off the equations

Answer:

1. Median

2. Altitude

Step-by-step explanation:

Medians- Bisect the side (Split the side into two equal parts)

Altitude- Makes a right angle

1. Splits the side into two equal parts. Anwser: Median

2. Makes a right angle Answer: altitude

Answer:

$46.

Step-by-step explanation:

We plug m = 3 and c = 4 into the given expression:

Money made =  2*3 + 10*4

= $46.

33% profit

ratio: 15:45

That can be simplified into 1:3

The price is increased by $15, which is 1/3 of the original $45.

1/3 as a percentage is about 33%.

Answer:

A

Step-by-step explanation:

[tex]3x^2+5x+2=0[/tex]

[tex]x=\dfrac{-5\pm \sqrt{5^2-4(2)(3)}}{6}=\dfrac{-5\pm 1}{6}=-\dfrac{2}{3}, -1[/tex]

Therefore, the answer is choice A. Hope this helps!