What is the x value of the solution to the system of equations

4y=2x+8
Y=-x+2

Answer:

Step-by-step explanation:

This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.

The form that the parabola is currently in is

[tex]y=a(x-h)^2+k[/tex] so that means that [tex]a=\frac{1}{8}[/tex]. We can use that to solve for p in the formula

[tex]p=\frac{1}{4a}[/tex] so

[tex]p=\frac{1}{4(\frac{1}{8}) }[/tex] which simplifies to

[tex]p=\frac{1}{\frac{1}{2} }[/tex] which gives us that

p = 2. Now to find the directrix:

y = k - p becomes

y = 0 - 2 so

y = -2, choice A.

Step-by-step explanation:

my answer is an image above

Answer:

[tex]10 \frac{2}{5}[/tex]

Step-by-step explanation:

Using BODMAS

[tex]6\frac{1}{2} \times (\frac{8}{9} \div\frac{13}{18}) + ( \frac{3}{4} )\ of \ 3\frac{1}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ expression \ inside \ bracket \ ]\\\\\frac{13}{2} \times (\frac{8}{9} \times \frac{18}{13}) + (\frac{3}{4}) \ of \ \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \ ]\\\\\frac{13}{2} \times (\frac{16}{13}) + (\frac{3}{4}) \ of \frac{16}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ solving \ of \ ] \\\\[/tex]

[tex]\frac{13}{2} \times (\frac{16}{13} ) + (\frac{3}{4} \times \frac{16}{5} )\\\\\frac{13}{2} \times (\frac{16}{13} ) + \frac{12}{5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ solving \ \times \ expressions \ ] \\\\(\frac{13}{2} \times \frac{16}{13}) + \frac{12}{5}\\\\8 + \frac{12}{5}\\\\\frac{40 + 12}{5}\\\\\frac{52}{5}\\\\10\frac{2}{5}[/tex]

[tex]\displaystyle\bf 1200=12*100=3*4*(2*5)^2=3*2^2*2^2*5^2=2^4*3^1*5^2 \\\\Answer: \boxed{ A)\quad a=4 \quad ; \quad b=1 \quad ; \quad c=2}[/tex]

Answer:

Step-by-step explanation:

The standard form equation for this type of problem is

[tex]y=a(b)^x[/tex] where a is the initial value, b is the rate of depreciation, and x is the number of years in question. Because the value of the car is going down, b can also be written as (1 - r) where r is the rate of depreciation. For us, then, the equation will look like this:

[tex]y=a(1-r)^x[/tex] and filling in:

[tex]y=21000(1-.14)^3[/tex] which in simplified form is

[tex]y=21000(.86)^3[/tex] which I'm assuming is how choice 4 should look.

Answer:

42

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = 6

7x

Step 2: Evaluate

[tex]804.2\:ft^{2}[/tex]

Step-by-step explanation:

[tex]A=4 \pi r^{2}[/tex]

We are given D = 16 ft, which means that r = (1/2)D = 8 ft. Therefore, the surface area of the sphere is

[tex]A=4 \pi (8 ft)^{2} = 804.2\:ft^{2}[/tex]

The surface area of the sphere is approximately 804.2 square feet.

It is a three-dimensional figure where the volume is given as:

The volume of a sphere = 4/3 πr³

We have,

The surface area of a sphere with diameter d is given by the formula:

SA = 4πr²

where r is the radius of the sphere, which is half the diameter. In this case, the diameter is 16 feet, so the radius is 8 feet.

Plugging in the value of r, we get:

SA = 4π(8²)

SA = 4π(64)

SA = 256π

Rounding to the nearest tenth gives:

SA ≈ 804.2 square feet

Therefore,

The surface area of the sphere is approximately 804.2 square feet.

Learn more about sphere here:

https://brainly.com/question/12390313

#SPJ7

Answer:

x=3.5

Step-by-step explanation:

25÷2=12.5

12.5-9=3.5

Answer:

7/5 or 3.5

Step-by-step explanation:

2 (x+9) =25

x+9 = 25/2

x = (25/2) - 9

x = 7/2 in decimal = 3.5

Answer:

4/8 = 1/2

Step-by-step explanation:

hope it thepled u

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.

⁺˚*･༓☾✧.* ☽༓･*˚⁺‧

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

An obtuse angle

Step-by-step explanation:

Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,

acute: degree measure between (0) and (90) degrees

right: exactly (90) degrees,

obtuse: degree measure between (90) and (180) degrees

reflex: degree measure between (180) and (360) degrees

Answer: $13.90

Step-by-step explanation:

Since Susana has a budget for school stationery of $33, but has already spent $19.10 on books and folders, the inequality that shows how much she can spend on other stationery, will be represented by:

p + $19.10 = $33

p = $33 - $19.10

The inequality is p = $33 - $19.10

Then, the amount that she can spend on other stationery will be:

P = $33 - $19.10

P = $13.90

She can spend $13.90 on other stationary

Answer: 700

Step-by-step explanation: 3 x 200 + 100

Answer:

c.$700

Step-by-step explanation:

3x+100 3 per chair=3x plus the additional 100 dollar fee

3(200)+100

600+100

700

Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

7/5 is the scale factor

Step-by-step explanation:

Answer:

Part A

x + y ≤ 460...(1)

2.5·x + 1.25·y ≥ 600...(2)

Part B

The number of bottles of water the student must sell ≥ 192 bottles of water

Step-by-step explanation:

The given parameters are;

The selling price of each can of lemonade = $2.50

The selling price of each bottle of water = $1.25

The amount of money the club needs to raise = $600

The maximum number of cans and bottles the students can accept = 460

Part A

Let 'x' represent the number of cans of lemonade the students accept, and let 'y' represent the number of bottles the student accept, the system of inequalities that can be used to represent the situation can be presented as follows;

x + y ≤ 460...(1)

2.5·x + 1.25·y ≥ 600...(2)

Part B

The number of cans of lemonade the club sells, x = 144

The number of bottles of water the student must sell to cover the cost of costumes, 'y', is given from the second inequality as follows;

2.5 × 144 + 1.25·y ≥ 600

1.25·y ≥ 600 - 2.5 × 144 = 240

1.25·y ≥ 240

y ≥ 240/1.25 = 192

y ≥ 192

The number of bottles of water the student must sell = 192 bottles of water

Answer:, Joey will pay $117.18 for sneakers.

Step-by-step explanation:

Given: original price = $155

Discount rate = 30%

Tax rate = 8%

Price after discount = Original price - (Discount) x (original price)

[tex]= 155-0.30\times 155\\\\=155-46.5\\\\=\$\ 108.5[/tex]

Tax = Tax rate x (Price after discount)

[tex]= 0.08 \times 108.5[/tex]

= $ 8.68

Final price for sneakers = Price after discount + Tax

= $ (108.5+8.68)

= $ 117.18

Hence

Answer:

The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.

Step-by-step explanation:

Let be the following system of equations:

[tex]2\cdot x + 3\cdot y = 12[/tex] (1)

[tex]x\cdot y = 6[/tex] (2)

Then, we solve both for [tex]x[/tex] and [tex]y[/tex]:

From (1):

[tex]2\cdot x + 3\cdot y = 12[/tex]

[tex]2\cdot x = 12- 3\cdot y[/tex]

[tex]x = 6 - \frac{3}{2}\cdot y[/tex]

(1) in (2):

[tex]\left(6-\frac{3}{2}\cdot y \right)\cdot y = 6[/tex]

[tex]6\cdot y-\frac{3}{2}\cdot y^{2} = 6[/tex]

[tex]\frac{3}{2}\cdot y^{2}-6\cdot y + 6 = 0[/tex]

The roots of the polynomial are determined by the Quadratic Formula:

[tex]y_{1} = y_{2} = 2[/tex]

By (1):

[tex]x = 6 - \frac{3}{2}\cdot (2)[/tex]

[tex]x = 3[/tex]

If we know that [tex]x = 3[/tex] and [tex]y = 2[/tex], then the final value is:

[tex]z = 8\cdot x^{3}+27\cdot y^{3}[/tex]

[tex]z = 8\cdot 3^{3}+27\cdot 2^{3}[/tex]

[tex]z = 432[/tex]

The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.

Answer:

4 + (1/3)w + w = 24

subtract 4 from both sides

(1/3)w + w = 20

multiply both sides by 3 to clear the fraction

w + 3w = 60

4w = 60

Divide both sides by 4

w = 15

Answer: a = 7.5h + bn

Step-by-step explanation:

Since Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.

where,

a = total amount earned,

h= hours worked in one week,

n = number of bouquets she arranged

b= bonus amount for bouquets

Then, the formula that will help her determine how much she will make in a week will be:

a = (7.5 × h) + (b × n)

a = 7.5h + bn

The formula is a = 7.5h + bn.

Answer:

36.87°

Step-by-step explanation:

Given the right angle triangle :

To obtain the value of Cosθ ; we use the trigonometric relation :

Cosθ = Adjacent / Hypotenus

The adjacent angle isn't given :

Opposite = 9 ; hypotenus = 15

Adjacent = √(hypotenus ² + opposite ²)

Adjacent = √(15² - 9²)

Adjacent = √(225 -81)

Adjacent = √144 = 12

Hence,

Cos θ = 12/15

θ = Cos^-1(12/15)

θ = 36.87°

Answer:

−3x^2+2x /x−2

Step-by-step explanation:

4x−9x^3/ 3x^2−4x−4

=  −9x^3+4x /3x^2−4x−4

=  x(−3x+2)(3x+2) /(3x+2)(x−2)

=  −3x^2+2x /x−2

Answer:

D

Step-by-step explanation:

D on edg

Answer:

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Step-by-step explanation:

sorry di ko po alam yung sagot pasensiya na po

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]

From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]

Solve the second equation for y and find out y intercept

[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]

Answer:

The distance between the parallel lines = 1.5

Reference:

https://brainly.com/question/24145911

Answer:

38.92 dollars

Step-by-step explanation:

Answer:

B. (7b – 9)(7b + 9)

Step-by-step explanation:

got 100% on my quiz

Answer:

19

Step-by-step explanation:

Conditional probability formula: A|B (A given B)= (A∩B)/B

So cold drink | large (cold drink given large)=  (Cold∩Large)/Large

cold∩large= 5

large= 22+5= 27

5/27=.185185185

which i guess rounds to 19%

Answer:

5%

Step-by-step explanation:

Percent error = (actual - estimated) / actual x 100

(240 - 228) / 240 x 100 = 5%

Answer:

-.985

Step-by-step explanation:

Answer:

.25

Step-by-step explanation:

there are 13 clubs

13/52= 1/4