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Answer:

x^2 = 12 (y - 2)

Step-by-step explanation:

how to explian

The equation that represents a parabola is x^2 = 12(y-2).

Parabola is a open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is the locus of a point that is equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix.

For the given situation,

A parabola with a focus of (h,k+p) is (0, 5) and

A directrix of y = (k-p) = -1

Here,

[tex]k+p=5\\k-p=-1[/tex]

On solving these equations,

[tex]k=2, p =3[/tex]

The general equation of parabola is

[tex](x-h)^{2} =4p(y-k)[/tex]

On substituting all the values,

⇒ [tex](x-0)^{2} =4(3)(y-2)[/tex]

⇒ [tex]x^{2} =12(y-2)[/tex]

Hence we can conclude that the equation that represents a parabola is x^2 = 12(y-2).

Learn more about parabola here

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Answer:

[tex]x_{1} =-5\\and \\x_{2} =-3[/tex]

Step-by-step explanation:

Solve by using factoring ------->

rewrite the expresion

x^2+8x+15=0

x^2+5x+3x+15=0

factor out x from the expression

x^2+5x+3x+15=0

xx(x+5)+3x+15=0

xx(x+5)+3(x+5)=0

factor out x+5 from expression

(x+5)x(x+3)=0

when the product of factors equals 0, at least one factor is 0

x+5=0

x+3=0

solve the equation for x

x = -5

x = -3

the equation has 2 solutions

[tex]x_{1} =-5, x_{2} =-3[/tex]

Quadratic formula

[tex]x=\frac{-8+\sqrt{8^{2} -4x1x15} }{2x1}[/tex]

any expression multiplied by 1 remains the same

[tex]x=\frac{-8+\sqrt{8^{2}-4x15 } }{2}[/tex]

evaluate the power

[tex]x=\frac{-8+\sqrt{64-4x15} }{2}[/tex]

multiply the numbers

[tex]x=\frac{-8+\sqrt{64-60} }{2}[/tex]

subtract the numbers

[tex]x=\frac{8+\sqrt{4} }{2}[/tex]

calculate the square root

[tex]x=\frac{-8+2}{2}[/tex]

write solution with a + sign and a - sign

[tex]x=\frac{-8+2}{2} \\x=\frac{-8-2}{2}[/tex]

calculate the value

[tex]x=-3\\x=-5[/tex]

the equation has 2 solutions

[tex]x=-3\\x=-5 \\and\\x_{1} =-5\\x_{2} =-3[/tex]

Answer:

1.50

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Given expression is,

10(2x - 4) + 5 = 2x - 8

By using distributive rule,

20x - 40 + 5 = 2x - 8

20x - 35 = 2x - 8

Now we subtract 2x from both the sides of the equation

20x - 35 - 2x = 2x - 8 - 2x

18x - 35 = -8

By adding 35 on both the sides of the equation

18x - 35 + 35 = - 8 + 35

18x = 27

By diving with 18 from both the sides of the equation

[tex]\frac{18x}{18}=\frac{27}{18}[/tex]

x = [tex]\frac{3}{2}[/tex]

Therefore, Option D will be the correct option.

Answer:

Step-by-step explanation:

Y = mx + b

-1/2 x + 3y = -3

3y = 1/2 x -3

y = 1/6 x - 1

Where slope m = 1/ 6and y intercept b = -1

x+x+x+y x y= 2x+y^2

x + x = 2x

y * y = y^2

Answer= 2x + y^2.

Answer:

It's 45.78

Step-by-step explanation:

4 x 10 = 40

5 x 1 = 5

7 x 1/10 = 0.7

8 x 1/100 = 0.08

add them all together and you get 45.78

Answer:

C.

Step-by-step explanation:

Hi there!

We know that [tex]x^0[/tex] is equal to 1 because any number raised to the zero is always going to be 1.

With that out of the way, we are left with [tex]x^-^3/1[/tex], which is equivalent to [tex]x^-^3[/tex]

Using negative exponent rules,

The expression is flipped and the -3 becomes a positive 3.

It will look like this

[tex]\frac{1}{x^3}[/tex]

Your answer is C.

I hope this helps!

Answer:

4

Step-by-step explanation:

divide 9 by 3 the answer is 3 then divide 12 by 3 then the answer is 4

Answer:

4 spells can be bought with $12.00

Step-by-step explanation:

3 times 3 is 9 = 3 spells for nine dollars

3 times 4 is 12 = 4 spells for 12 dollars

Each spell costs $3.00

Answer:

= 47/21x + 132/7

hope this helps!

Step-by-step explanation:

Step-by-step explanation:

Range if third side is in between 10-22

Reason:

For the lowest value of third side 16-6= 10

For the highest value if third side 16+6= 22

⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡⚡

Answer:

10

Step-by-step explanation:

big brain B)

Answer:

25.5

Step-by-step explanation:

Put the digits in your calculator 30×85% and you will get 25.5

Answer:

evaluation : 38.5 38.5   is the answer because you simplify this term

Step-by-step explanation:

Answer:

Robert Recorde.

Step-by-step explanation:

Robert Recorde was a Welsh known for vast knowledge and experience in the field of mathematics and physics. He was born in Tenby, Pembrokeshire, Wales during the Medieval period (c. 1512).

Robert Recorde was famously known for his work in the field of mathematics and most especially, the invention of the equal to (=) sign. He introduced it in his book titled "The Whetstone of Witte."

Hence, Robert Recorde was the first english mathematician who first used the modern symbol of equality in 1557.

Answer:

it 11  IT NOT 22 NOR 2 okay 11

Step-by-step explanation:

Answer:

37

\

Step-by-step explanation:

Answer:

10 ounces

Step-by-step explanation:

5 pounds equals 80 ounces, so 80 divided by 8 is 10

Answer:

y = 147.56 - 10.78x

Step-by-step explanation:

Given :

x = 10.2 ; y = 37.6 ; Sx = 2.8 ; Sy = 30.8 ; r = - 0.98

The regression equation :

y = mx + c

Where ;

m = slope ; c = intercept

Slope = r * (Sy/Sx)

Slope = - 0.98 * (30.8 / 2.8)

Slope = - 0.98 * 11 = - 10.78

To obtain c :

y = mx + c

y - mx = c

37.6 - (-10.78)(10.2) = c

37.6 + 109.956 = c

147.556 = c

Hence, equation becomes :

y = 147.556 - 10.78x

y = 147.56 - 10.78x

Answer:

y = 147.56 + -10.78x

Step-by-step explanation:

Answer:

42 gallons

Step-by-step explanation:

Answer: 42

Step-by-step explanation:

Answer:

She needs to divide the number of students by the number of shirts that come in each box and then round to the ones place

Answer:

4(6 - 1) = 4 * 6 - 4 * 1 = 24 - 4 = 20

Step-by-step explanation:

Multiply 4 by each of the numbers inside the parentheses.

4(6 - 1) = 4 * 6 - 4 * 1 = 24 - 4 = 20

Answer: 24-4

Explanation: 4(6-1)

4x6=24

4x-1=-1

24-4

Answer:

D

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic

Answer:

inverseoperations

Step-by-step explanation:

An inequality is used to represent unequal expressions or numbers. The inequality describing the restrictions on the number of people possible in a van is [tex]160n + 200 \le 1200[/tex].

Given that:

[tex]Total = 1200[/tex] --- total pounds the van can contain

[tex]Weight = 150[/tex] --- average weight of each person

[tex]Gear = 200[/tex] -- weight of the gear in a van

[tex]Meal =10[/tex] -- weight of each meal

Assume there are n people.

The total weight (T) of the n people is:

[tex]T = Weight \times n[/tex]

Substitute [tex]Weight = 150[/tex]

[tex]T = 150 \times n[/tex]

[tex]T = 150n[/tex]

The total weight (M) of the meals is:

[tex]M= Meal \times n[/tex]

Substitute [tex]Meal =10[/tex]

[tex]M= 10\times n[/tex]

[tex]M= 10n[/tex]

Because the van cannot contain more than 1200 pounds, we use less than or equal to as the inequality.

So, the inequality is:

[tex]T + M + Gear \le 1200[/tex]

[tex]150n + 10n + 200 \le 1200[/tex]

[tex]160n + 200 \le 1200[/tex]

Hence, the inequality is: [tex]160n + 200 \le 1200[/tex]

The solution to the inequality is as follows:

[tex]160n + 200 \le 1200[/tex]

Collect like terms

[tex]160n \le 1200-200[/tex]

[tex]160n \le 1000[/tex]

Divide both sides by 160

[tex]n \le 6.25[/tex]

Remove the decimal part (do not approximate)

[tex]n \le 6[/tex]

Hence, the vehicle cannot contain more than 6 people.

See attachment for graph

Read more about inequalities at:

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9514 1404 393

Answer:

  y = 15·2.1599^x

Step-by-step explanation:

We know that the number changed by the ratio 1523/15 = 101.5333... in 6 days, so the daily multiplier is the 6th root of this:

  b = 101.5333...^(1/6) = 2.1599 . . . rounded to 4 dp

Of course, the coefficient 'a' in the equation is the initial number, 15.

Your exponential equation is ...

  y = 15·2.1599^x

  a = 15

  b = 2.1599

Answer:

mark as brainleast and fo-ll-ow me

Slide 1.

Part A.

1. Band A:  y = 600

2. Band B: y = 1.25x + 350

Part B.

200 students.

Slide 2.

Part A.

Fixed cost = $150

Rate per student served = $6

Part B.

To figure the cost/person, look at the change in cost divided by the change in attendance.

For 100 students, cost = $750.

For 150 students, cost = $1050.

Change in cost = $300

Change in students = 50

Cost per additional student = 300/50 = $6

Assuming the costs are linear, then the price charged for 100 students reflects the cost per student + a 'fixed cost' that applies to the order as a whole.

100 * 6 = $600, so the fixed cost is 750-600 = 150.

We can check this notion by substituting in the other equation.

Does 150*6 + 150 = 1050? Yes.

150*6=900

900+150 = 1050.

Slide 3.

Part A.

She can choose either band, with $9.75 per ticket, if 200 students attend

Part B.

Check the cost using band A and 200 people, including food

600 + 150 + (6*200) =

600 + 150 + 1200 = $1950

Cost per ticket: = 1950/200 = $9.75

Cost using band B, 200 people, including food:

350 + 1.25(200) + 150 + (6*200) =

350 + 250 + 150 + 1200 = $1950

Cost per ticket: 1950/200 = $9.75

This means that Paula can choose either band, and the ticket cost will be the same.

Slide 4.

Part A.

Cost per ticket: $8.50 (of Band A, since it is the cheaper one)

Part B.

Check the cost using band A and 300 people, including food

600 + 150 + (6*300) =

600 + 150 + 1800 = $2250

Cost per ticket: = 2250/300 = $8.50

Cost using band B, 200 people, including food:

350 + 1.25(300) + 150 + (6*300) =

350 + 375 + 150 + 1800 = $2675

Cost per ticket: 2675/300 ≈$8.92

Which means that in this scenario is Band A is less expensive.

Answer:

Step-by-step explanation:

Step-by-step explanation:

168 <-- quotient --- 337 2 - 13 12 -- 17 16 -- 1 <-- remainder

Answer:

168.5

Step-by-step explanation:

        ₁  ₁  ₁

2 ) 3 3 7. 0

     1 6 8.5 <--- Quoitient

first part is 2 divide  once into 3  with remainder 1

- and this 1 goes in front of the 3 to give 13.

2 into 13 goes 6 times with remainder 1

- then we get 2 into 17 giving 8 remainder 1 and so on....