On a certain map, 3 inches represents 15 miles. Briarwood and Middletown are 5 inches apart on the map. What is the actual distance between Briarwood and Middletown? A. 25 mi B. 30 mi C. 50 mi D. 75 mi

Answer:

i think it is the third one but dont know just an educational geuss

Step-by-step explanation:

The given steps from the derivation of the quadratic formula are:

Step 3:  [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.

The quadratic formula is as follows:

x = [-b ± (√b²+4ac)]/2a

This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].

The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]

Step 1: [tex]ax^2+bx=-c[/tex]

Step 2: Taking 'a' as common

[tex]a(x^2+\frac{b}{a}x)=-c[/tex]

Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides

[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]

⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: Factoring the polynomial

[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: Converting to a common denominator

[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)

⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]

⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]

⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides

⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

⇒ x = [-b ± (√b²+4ac)]/2a

Thus, step 4b best explains or justifies the property "Converting to a common denominator".

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Answer:

460256

Step-by-step explanation:

35900 books equal to 7.8% of all copies sold

Total number of books:

Answer is 460256 in whole numbers

Answer:

3x(x - 2)

Step-by-step explanation:

Both terms have a GCF (greatest common factor) of 3x so factoring that out, we get 3x(x - 2).

Answer:

3x ( x - 2 )

Step-by-step explanation:

First we hv to find wat is common in both of them.....

As we can see " 3x " is common in both of them

so....

If we take 3x from both the terms.... It will become....

3x square = 3x ( x )

-6x - 3x ( -2 )

Therefore the expression will become....

3 x square - 6x

= 3x ( x - 2 )

Hope this helps...

HAVE A GOOD DAY !!! ( no the biscuit ) (lol)

Answer:

C. 567yd^3

Step-by-step explanation:

To find the volume of the right triangular prism, it is: 1/2a c h.

In this case, 1/2✖️9✖️6✖️21=567yd^3

So this means that option C is the correct answer.

Hope this helps!

Have a nice day:)

Answer:

567 cu. yard

Step-by-step explanation:

will make it simple and short.

Vol = area of a triangle x length

Vol = (1/2 * 6 * 9 ) * 21

Vol = 567 cu. yard

Answer:

0.5 L

Step-by-step explanation:

volume of bottle: 1.5 L

amount of water = 1.5 L

volume of glass: x

3/4 full is the same as 0.75 full

vol of water in bottle + vol of water in glass = total vol of water

      0.75(bottle)          +       0.75(glass)          =           1.5

0.75(1.5) + 0.75x = 1.5

0.75x = 0.375

x = 0.5

Answer:

D. 15

Step-by-step explanation:

Both equations need the same end result because this is a square:

3x - 15 = 45 - x =

3x - 3x = 45 - x - 3x

0 = 45 - 4x

4x = 60

4x/4 = 60/4 =

X = 15

Check:

3(15) - 15 = 45 - 15

45 - 15 = 45 - 15

30 = 30

Answer:

24 students

Step-by-step explanation:

(20 + 23 + 25 + 28)/4

= 94/4

= 24

hope it helps!

Answer:

Slope = 1

Greatest value is positive infinite

Smallest value is negative infinite

Step-by-step explanation:

Function

Y=mx+c

Y=x

Answer:

v is 9

Step-by-step explanation:

it is 9 because if you simplify it is 8v=72 or 9

Answer:

v = 9

Step-by-step explanation:

3v + 5v = 72

combine like terms

8v = 72

Divide by 8

8v/8 = 72/8

v =9

Answer:

Mean

=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees

= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1

= 3+0+0+12+7+8/ 1+0+0+2+1+1

= 30 / 5

= 6

So the mean of number of hour sleep is 6 hours.

I hope this helps

if u have question let me know in comments ^_^

Answer:

Step-by-step explanation:

Mean

=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees

= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1

= 3+0+0+12+7+8/ 1+0+0+2+1+1

= 30 / 5

= 6

So the mean of number of hour sleep is 6 hours.

I hope this helps

Answer:

The lateral surface area of cone is A = π×r×l where r represents radius and l is slant height.

The formula to find slant height is l = √(h²+r²) where h represents height.

The lateral surface area of the cone is 65[tex]\pi[/tex] square cm.

Given,

The height is 12 cm and the radius is 5 cm.

We are to find the lateral surface area of a cone.

The lateral surface area of a cone:

A = [tex]\pi[/tex] x r x l

where r = radius and l = slant height.

The slant height:

l = √(h²+r²)  where h =height.

We have,

h = 12 cm and r = 5 cm

l =√(h²+r²)

l = √(12^2 + 5^2)

l = √(144 + 25)

l = √169

l = 13 cm

Now,

l = 13 cm and r = 5 cm

A = [tex]\pi[/tex] x r x l

A =  [tex]\pi[/tex] x 13 x 5 = 65[tex]\pi[/tex] square cm

Thus lateral surface area of the cone is 65[tex]\pi[/tex] square cm.

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Answer:

[tex]y = 3x-4[/tex]

Step-by-step explanation:

We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)

So right now, we have [tex]y=3x[/tex].

However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.

If we have a y-intercept of -4, the points will be:

(0, -4)

(1, -1)

(2, 2)

So our final equation is [tex]y = 3x-4[/tex].

Hope this helped!

Answer: 3x-1y=4 in Ax+By=C form

Step-by-step explanation:

the intercept form is y=3x-4

subracting 3x from both sides would get  -3x+y=-4

distributing -(-3x+y=-4) would get 3x-y=4.

Answer:

440 in²

Step-by-step explanation:

Answer:

(D) 440 in²

Step-by-step explanation:

We can find the surface area of this complex shape by breaking it down into two smaller shapes:

The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)

Let's first find the surface area of the base.

The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².

The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].

There are two of these sides.

[tex]100\cdot2=200[/tex].

Let's add up the side lengths and the base lengths.

[tex]200+80=280[/tex]

We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.

Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]

Now let's find the surface area of the top.

The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:

[tex]40\cdot4=160[/tex] in².

Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².

We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.

Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².

Finally, let's add the base and the top box surface areas together:

[tex]185 + 255 = 440[/tex]

So the total surface area of this design is 440 in².

Hope this helped (oh my god this took so long to write)

Answer:

A

Step-by-step explanation:

The first option is correct.

The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Cost of a package with 8 AA batteries = $6.32

⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79

And, cost of another package with 20 AA batteries = $16.00

⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8

Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

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Answer:

6

Step-by-step explanation:

it might be six but can you show me what the chart looks like?

Answer:

330 degrees

Step-by-step explanation:

Answer: 300deg

Step-by-step explanation:

Answer:

  P(-3) = -2

Step-by-step explanation:

Substitution

P(-3) = 4(-3)^2 +10(-3) -8 = 36 -30 -8

P(-3) = -2

__

Long Division

See the working below. The remainder is -2, so ...

  P(-3) = -2

Answer:

h(x + 1) = (x+3)(x-1)

Step-by-step explanation:

Simply plug the value of x+1 into the equation for x.

h(x) = x^2 - 4

h(x + 1) = (x + 1)^2 - 4

h(x + 1) = x^2 + 2x + 1 - 4

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

h(x + 1) = (x+3)(x-1)

Cheers.

Answer:

h(t)= t² - 2t -3

Step-by-step explanation:

h(x+1)= x²-4 is the given function

We can write it x²-4 as:

Substituting x+1  with  t. Then function is:

or

Answer:

28 - 7 = -3k

21 = -3k

21/-3 = k

k = -7

x/5 = 3 + 17

x/5 = 20

x = 5*20

x = 100

82 - 12 = 7G/10

70 = 7G/10

70*10 = 7G

700 = 7G

700/7 = G

G = 100

A-

1 box --- 6 minutes

y boxes --- 1 minute

y = 1/6

B-

1 box --- 9 minutes

t boxes --- 1 minute

t = 1/9

So...

r - used time

r(1/9 + 1/6)=100

r=(100.18)/5

r= 360 minutes

1/6 . 360 = 60 boxes

answer: 60 boxes

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.

Machine A's rate of work is 1 box of nails every 6 minutes.

Machine B's rate of work is 1 box of nails every 9 minutes.

Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.

So, the equation representing the total work is:

x (boxes filled by A) + y (boxes filled by B) = 100

Now, let's use their rates of work to form two more equations:

Rate of work of A = 1 box every 6 minutes

Rate of work of B = 1 box every 9 minutes

Since work = rate × time, we can write two equations:

x (boxes filled by A) = (1/6) * t (time in minutes)

y (boxes filled by B) = (1/9) * t (time in minutes)

Since they both worked for the same time, we can set the time for both machines as equal:

t = t

Now, we have a system of equations:

x + y = 100

x/6 = y/9

t = t

Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:

x + (x/6)*3 = 100

x + (x/2) = 100

Multiply both sides by 2 to eliminate the fraction:

2x + x = 200

3x = 200

x = 200/3

Now, let's find the value of y using the second equation:

y = (x/6)*3

y = (200/3)/6 * 3

y = 200/3

So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.

Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.

Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

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Answer:

5 Gello Pens and 12 Inko Pens.

12 Inko Pens adds up to 84.

5 Gello Pens adds up to 25.

84 + 25 = 109.

I hoped this helped :)

The type of model best fits the given situation is a quadratic equation

Quadratic equations are equation that has a leading degree of 2.

From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation

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The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The fraction numbers are given below.

1/8 and 1/5

Convert the fraction number into decimal numbers. Then we have

0.125 and 0.20

The five fractions whose values are between 1/8 and 1/5 will be given as,

0.13, 0.14, 0.15, 0.16, 0.18

13/100, 14/100, 15/100, 16/100, 18/100

13/100, 7/50, 3/20, 4/25, 9/50

The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.

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for vegetable oil, it's increasing by 120, for cornstarch by 30

Answer:

D) [tex]360 m^{3}[/tex]

Step-by-step explanation:

Let's review the formula for finding the volume of a cube or rectangular prism.

[tex]V = (l)(h)(w)[/tex] - Basically saying "Volume = length × height × width".

In this case, you can consider 9 meters as the length, 5 meters as the height, and 8 meters as the width (but it doesn't really matter which dimensions are which since you are just multiplying them all together).

Now, let's multiply our dimensions together.

[tex]9 * 5 * 8 = 360[/tex]

That's your answer! Make sure to not forget your units (in this case, meters) cubed.

Hope that helps and maybe earns a brainliest!

Have a splendid day! <3

Answer:

a(n)= 120(1/2)^(n-1)

Step-by-step explanation:

60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2

a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)

Answer:120(1/2)^(n-1)

Step-by-step explanation:

60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2

a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)

The triangle is shifted 4 units downwards and then is rotated about the origin.

Given are triangles A and B.

Transformation 1 : The triangle is shifted 4 units downwards.

Transformation 2 : The figure is rotated about the origin.

Therefore, the triangle is shifted 4 units downwards and then is rotated about the origin.

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Answer:

D, since it horizontal ellipse, a is greater than b

An ellipse has two foci. The correct option is D.

Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be:    (h±c, k) where    c² = a² - b²

If its major axis is parallel to the y-axis, then,

coordinates of its foci would be:  (h, k±c) where   c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,

[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]

Hence, the correct option is D.

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Answer:

21.5

Step-by-step explanation:

h(t) = -16t^2 + 35t + 5,

Let t = 1.5

h(1.5) = -16 (1.5)^2 + 35(1.5) + 5

        =-16 *2.25 +52.5+5

      = -36+57.5

      = 21.5