Which of the equations below could be the equation of this parabola?

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5y + 2x = 12 into this form

Subtract 2x from both sides

5y = - 2x + 12 ( divide all terms by 5 )

y = - [tex]\frac{2}{5}[/tex] + [tex]\frac{12}{5}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex] → A

Answer:

a

Step-by-step explanation:

becuase you distribute the numbers

By definition of multiplication of powers of the same base we have to put the same base and add the exponents, then, we can rewrite the expression as:

[tex](2 ^ {\frac {1} {2} + \frac {3} {4}}) ^ 2 =\\(2 ^ {\frac {4 + 6} {8}}) ^ 2 =\\(2 ^ {\frac {10} {8}}) ^ 2 =\\(2 ^ {\frac {5} {4}}) ^ 2 =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, we have:

[tex]2 ^ {\frac {10} {4}} =\\2 ^ {\frac {5} {2}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So, the expression is equivalent to:

[tex]2 ^ {\frac {5} {2}} = \sqrt {2 ^ 5}[/tex]

ANswer:

Option B

Answer:

1. y=7.2

2. x=18

Step-by-step explanation:

1. Triangles CMN and CBA are similar triangles (by AAA postulate). Similar triangles have proportional corresponding sides, so

[tex]\dfrac{CM}{CB}=\dfrac{CN}{CA}\\ \\\dfrac{12}{12+y}=\dfrac{10}{10+6}\\ \\12\cdot 16=10\cdot (12+y)\\ \\192=120+10y\\ \\10y=72\\ \\y=7.2[/tex]

2. GK is angle G bisector. Use angle bisector's property:

[tex]\dfrac{GH}{GI}=\dfrac{KH}{KI}\\ \\\dfrac{40}{24}=\dfrac{30}{x}\\ \\40x=24\cdot 30\\ \\4x=24\cdot 3\\ \\x=6\cdot 3=18[/tex]

These are the formulas right?.. I hope so, anyways..

- f(n)= 2^(n-1) -1

- g(n)=3n+6  

f(7)=2^{7-1}-1  -  f(7)=2^{6}-1  -  f(7)=64-1  -  f(7) = 63

g(10)=3\X 10+6  -  g(10)=30+6  -  g(10) = 36

= f(7)>g(10)

I hope that it helped..

Answer:

The one above is right.

Step-by-step explanation:

Answer:

x = - [tex]\frac{11}{8}[/tex]

Step-by-step explanation:

Given

(x - 4) - (x + 7 ) = 8x

Distribute parenthesis noting second is distributed by - 1

x - 4 - x - 7 = 8x ← simplify left side

- 11 = 8x ( divide both sides by 8 )

x = - [tex]\frac{11}{8}[/tex]

Answer:

a) Current Interest is $75.8

b) the final payment will be $11,830

Step-by-step explanation:

Principal Amount = $9,100

Interest rate = 10% or 0.1

Time = 36 months = 3 yeras

Balance after 27 payments = $2,526.85

a) What is the CURRENT month's interest?

The formula to find interest is:

Interest = P*r*t

P= Principal

r = Interest rate

t = time in years

Interest = 9100*0.1*3

Total Interest = 2730

As total period is 36 months so, divide total interest by 36

Current Month Interest = 2730/36

Current Month Interest = 75.8

So, current month interest is $75.8

b) What is the final payment?

The formula used will be

A = P(1+r*t)

A = Final amount

r = interest rate

t = time

Putting values:

A = P(1+r*t)

A = 9100*(1+0.1*3)

A = 9100*(1.3)

A = 11,830

So, the final payment will be $11,830

to get the slope of any line, we can simply use two points off of it, for this one, say (3,12) and (4,16)

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{16}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-12}{4-3}\implies \cfrac{4}{1}\implies 4[/tex]

Answer:

18 female horses.

Step-by-step explanation:

By proportion  2 : 3 = 12 : x   where x is the number of female horses.

12 / 2 = x / 3

2x = 3*12 = 36

x = 18.

Answer: [tex]65.44\ in^3[/tex]

Step-by-step explanation:

To calculate the volume of a cone you can use this formula:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

In this case you know that this cone has a height of 2.5 inches and a radius of 5 inches. Then:

[tex]h=2.5\ in\\r=5\ in[/tex]

Finally, you need to substitute these values into the formula. Then you get that the volume of the cone is:

 [tex]V_{(cone)}=\frac{1}{3}\pi (5\ in)^2(2.5\ in)\\\\V_{(cone)}=65.44\ in^3[/tex]

Answer:

[tex]|SU|=\sqrt{13}[/tex]

Step-by-step explanation:

The given parallelogram has vertices R(1, -1), S(6, 1), T(8, 5), and U(3, 3) .

Recall the distance formula;

We use the distance formula to determine the length of the diagonals.

For diagonal R(1,-1) and T(8,5), We have;

[tex]|RT|=\sqrt{(8-1)^2+(5--1)^2}[/tex]

[tex]|RT|=\sqrt{(7)^2+(6)^2}[/tex]

[tex]|RT|=\sqrt{49+36}[/tex]

[tex]|RT|=\sqrt{85}[/tex]

For the diagonal S(6,1) U(3,3)

[tex]|SU|=\sqrt{(6-3)^2+(5-3)^2}[/tex]

[tex]|SU|=\sqrt{(3)^2+(2)^2}[/tex]

[tex]|SU|=\sqrt{9+4}[/tex]

[tex]|SU|=\sqrt{13}[/tex]

Therefore the shorter diagonal is:

[tex]|SU|=\sqrt{13}[/tex]

Answer:

V = 11

Step-by-step explanation:

All you have to do here is to multiply both sides of this equation by 13.  This will eliminate the fractions.  You'll be left with V = 11.

To solve the proportion V/13 = 11/13, we can equate V to 11 since identical denominators imply equal numerators. No further calculations or rounding needed as V is a whole number.

To solve the proportion V/13 = 11/13 for V, we can see that both sides of the equation are divided by the same number, 13. Since the denominators are equal, we can deduce that the numerators must also be equal for the proportion to be true.

Therefore, the value of V must be equal to 11, as V/13 matches 11/13. There is no need for further calculations or rounding since 11 is already a whole number.

https://brainly.com/question/14752332

#SPJ2

Answer: 720 feet

Step-by-step explanation: 120 x 6= 720

Answer:

720

Step-by-step explanation:

120/10 to find his feet per second which is 12 feet per second

12*60

since there are 60 seconds in a minute

= 720

Answer:

x= -17

Step-by-step explanation:

When we have 2 points, we can find the slope using

m = (y2-y1)/(x2-x1)

Substituting what we know

1/5 = (0-3)/(x--2)

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

Using cross products

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

x+2 = -15

Subtract 2 from each side

x+2-2 = -15-2

x=-17

Answer:

800 people

Step-by-step explanation:

We are given in the question that 2/3 of 2400 people preferred skinless chicken.

We have to find the number of people who prefer skinless chicken

[tex]So,\\= \frac{2}{3} *2400\\=1600[/tex]

1600 people prefer skinless chicken,

So,

The number of people who prefer regular chicken = 2400-1600

= 800 people

Answer: kentucky friend chicken? XD

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

The triangles are similar because  the angles marked 125 are equal and the sides either side of these angle are in the same ratio:

1.3 / 2.5 = 2.6 /5.

If we are given the length of AE we would find CF from the equation:

1.3 / 2.5 = CF / AE

CF = (1.3 * AE) / 2.5.

Answer:

-15

Step-by-step explanation:

the y-intercept would be -15

Answer:

x = - 5, x = 3

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

x² + 2x - 15 = 0

Consider the factors of the constant term (- 15) which sum to give the coefficient of the x- term (+ 2)

The factors are + 5 and - 3, since

5 × - 3 = - 15 and 5 - 3 = + 2, hence

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

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 3 = 0 ⇒ x = 3

x- intercepts at (- 5, 0) and (3, 0)

The expression that gives the number of shrimp Ariana caught will be 5C - 9.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Ariana and William go shrimping. Ariana caught nine less than five times the number of shrimp that William caught. If C represents the number of shrimp William caught.

Then the expression is given as,

⇒ 5C - 9

The expression that gives the number of shrimp Ariana caught will be 5C - 9.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

138.27 gallons

Step-by-step explanation:

Total cost = snacks + gallons * cost per gallon

387 = 35.80 + g*2.54

Subtract 35.80 from each side

387-35.80 = 35.80-38.50 + g*2.54

351.20=  + g*2.54

Divide by 3.54 on each side

351.20/2.54 = 2.54g/2.54

138.2677165 = g

Rounding to the nearest hundredth

138.27 gallons

Given : Lynn spent 387.00 on gasoline and snacks

Given : Lynn spent 35.80 on snacks for the entire trip

Money spent on gasoline :

Total money spent on gasoline and snacks - Money spent on snacks

[tex]:\implies[/tex]  Money spent on gasoline = 387.00 - 35.80

[tex]:\implies[/tex]  Money spent on gasoline = 351.20

Given : Gasoline costs 2.54 per gallon

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{Total\;money\;spent\;on\;gasoline}{Cost\;of\;gasoline\;per\;one\;gallon}}[/tex]

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{351.20}{2.54}}[/tex]

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = 138.27}[/tex]

Answer:

ln 3

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

Given

3 ln 3 - ln 9

= 3 ln 3 - ln 3²

= 3 ln 3 - 2 ln 3

= ln 3

The given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).

Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Given is the logarithmic expression as -

3 ln(3) - ln(9)

We can solve the expression as -

3 ln(3) - ln(9)

ln(3³) - ln(9)

ln(27) - ln(9)

ln(27/9)

ln (3)

Therefore, the given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).

To solve more questions on logarithmic, visit the link-

https://brainly.com/question/30085872

#SPJ7

Answer: Option C

2,400

Step-by-step explanation:

When launching the first 6-sided die there are 6 possible outcomes

When launching the 4-sided die there are 4 possible outcomes

When throwing each die of 10 faces there are 10 possible outcomes

So if all the dice are thrown together, the number of possible combinations that can be obtained is:

[tex]S = 6 * 4 * 10 * 10\\S = 24 * 100[/tex]

[tex]S = 2400[/tex] possible results

Finally the answer is the option C.

The answer to this question is option C. 104 °

(Late answer!)

2

-10 and 10 are 10 units from 0 on the number line

Answer:

D.{-4, -2, 2}  

Step-by-step explanation:

all y components

same y value are not repeated

Answer:

Option A. 20.0 square units

Step-by-step explanation:

Let

[tex]A(2, 5),B(-4, 3),C(-3, 0),D(3, 2)[/tex]

Plot the points

see the attached figure

The area of the rectangle is equal to

[tex]A=AB*AD[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance AB

[tex]A(2, 5),B(-4, 3)[/tex]

substitute in the formula

[tex]AB=\sqrt{(3-5)^{2}+(-4-2)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(-6)^{2}}[/tex]

[tex]AB=\sqrt{40}\ units[/tex]

step 2

Find the distance AD

[tex]A(2, 5),D(3, 2)[/tex]

substitute in the formula

[tex]AD=\sqrt{(2-5)^{2}+(3-2)^{2}}[/tex]

[tex]AD=\sqrt{(-3)^{2}+(1)^{2}}[/tex]

[tex]AD=\sqrt{10}\ units[/tex]

step 3

Find the area of rectangle

[tex]A=AB*AD[/tex]

we have

[tex]AB=\sqrt{40}\ units[/tex]

[tex]AD=\sqrt{10}\ units[/tex]

substitute

[tex]A=(\sqrt{40})*(\sqrt{10})[/tex]

[tex]A=20\ units^{2}[/tex]

Answer:

D. 754 m

Step-by-step explanation:

When calculating the circumference of the circle it ends up as 753.98 but rounded it's 754.

Answer: It’s 754!

Explanation: I also got this one on a test lol

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-interept (0, b)

We have the slope m = -6 and the point (0, 2) → b = 2.

Substitute:

y = -6x + 2

Answer:

180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.

Step-by-step explanation:

Please mark brainliest and have a great day!

Final answer:

The coordinates of the point are (4, 3), where 4 is the x-coordinate (horizontal direction) and 3 is the y-coordinate (vertical direction).

Explanation:

The coordinates of a point on a Cartesian coordinate system are determined by its horizontal position (x-coordinate) and its vertical position (y-coordinate). Given that the point is on the first coordinate axis (x-axis) and in the (1, 2)th coordinate plane, we understand that the x-coordinate is related to the horizontal direction and the y-coordinate is related to the vertical direction.

In the context of this problem, if the figure on the coordinate plane indicates that the point is 4 units to the right of the origin along the x-axis and 3 units above the origin along the y-axis, then the coordinates of the point are ( extbf{4},  extbf{3}). Here, the convention is that moving to the right of the origin increases the x-coordinate and moving upwards increases the y-coordinate.

Answer:

The sample standard deviation is 14.458

The population standard deviation is 13.967

Step-by-step explanation:

* Lets revise the population standard deviation (σ)

1. Work out the Mean (μ) (average of the numbers)

2. Then for each number subtract the Mean and square

   the result  (xi - μ)²

3. Then work out the mean of those squared differences

    [∑(xi - μ)²/N]

4. Take the square root of that (√[∑(xi - μ)²/N]) and to find σ

* Lets revise the sample standard deviation (s)

1. Work out the Mean (x) (average of the numbers)

2. Then for each number subtract the Mean and square

    the result  (xi - x)²

3. Then work out the mean of those squared differences [∑(xi - x)²/N - 1]

4. Take the square root of that (√[∑(xi - x)²/N - 1]) and to find s

* Now lets solve the problem

- The data are 15 numbers

  17 , 37 , 56 , 16 , 12 , 16 , 19 , 45 , 14 , 37 , 21 , 26 , 43 , 46 , 42

∵ x = μ = sum/number

∴ x = μ = (17+37+56+16+12+16+19+45+14+37+21+26+43+46+42)÷15=29.8

- Subtract the mean from each number and square the result

∵ (17 - 29.8)² = 163.84

∵ (37 - 29.8)² = 51.84

∵ (56 - 29.8)² = 686.44

∵ (16 - 29.8)² = 190.44

∵ (12 - 29.8)² = 316.84

∵ (16 - 29.8)² = 190.44

∵ (19 - 29.8)² = 116.64

∵ (45 - 29.8)² = 231.04

∵ (14 - 29.8)² = 249.64

∵ (37 - 29.8)² = 51.84

∵ (21 - 29.8)² = 77.44

∵ (26 - 29.8)² = 14.44

∵ (43 - 29.8)² = 174.24

∵ (46 - 29.8)² = 262.44

∵ (42 - 29.8)² = 148.84

∴ ∑(xi - μ)² = ∑(xi - x)² = 2926.36

∵ N = 15

∴ The sample standard deviation = √[∑(xi - x)²/(N - 1)]

∴ s = √[2926.36/(15 - 1)] = 14.458

∴ The population standard deviation = √[∑(xi - μ)²/N]

∴ σ = √[2926.36/15] = 13.967

Answer:

B

Step-by-step explanation:

Answer:

8y=-6 or 4y=-3

Step-by-step explanation:

We are given two equations

[tex]x+6y=9\\and\\-x+2y=-15[/tex]

In order to add the equations, the left hand side of one equation will be added to the left hand side of second equation. similarly, the right hand side of first equation will be added to the right hand side of the equation so,

[tex]x+6y+(-x+2y)=9+(-15)\\Combining\ alike\ terms\\x+6y-x+2y=9-15\\6y+2y=-6\\8y=-6\\Can\ also\ be\ written \ as\\4y=-3[/tex]

Answer:

The resultant equation is 8y = -6

Step-by-step explanation:

To get the system of equation that will results from adding the statement, we will follow the steps below;

x+6y=9 -------------------------------------------------------------------------------(1)

-x+2y=-15-------------------------------------------------------------------------------(2)

Adding equation (1) and equation(2), we will have;

(1-1)x + (6+2)y =(9-15)

x variable will go away

8y =-6

The resultant equation is 8y = -6