The equation of a parabola is y=18x2−4x+41. What is the equation of the directrix?

Answers

Answer 1

The equation of the directrix for the parabola y = 18 · x² - 4 · x + 41 is y = 2935 / 72.

How to determine the equation of the directrix related to a parabola

In this question we find the case of the equation of a parabola in standard form:

y = a · x² + b · x + c

Where:

a, b, c - Real coefficientsx - Independent variable.y - Dependent variable.

This equation must be changed into vertex form:

y - k = C · (x - h)²

Where:

(h, k) - Coordinates of the vertex.C - Vertex constant.

Where the vertex constant is:

C = 1 / (4 · p)

Where p is the distance between focus and vertex.

And the equation of directrix is:

y = k - 1 / (4 · C)

First, write the quadratic equation in standard form:

y = 18 · x² - 4 · x + 41

Second, use algebra properties until vertex form is obtained:

y = 18 · [x² - (2 / 9) · x + 41 / 18]

y = 18 · [x² - (2 / 9) · x + 1 / 81] + 18 · (367 / 162)

y = 18 · (x - 1 / 9)² + 367 / 9

y - 367 / 9 = 18 · (x - 1 / 9)²

Third, find the equation of the directrix:

y = 367 / 9 - 1 / (4 · 18)

y = 2935 / 72

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Related Questions

The graph shows the amount of a chemical in a water sample. It is decreasing exponentially.

Find the coordinates of the points labeled A, B, and C.

Answers

The coordinates of the exponential equation are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the first point be A ( 0 , 1000 )

Let the second point be B ( 1 , 800 )

Now , the exponential equation be represented as A

y = abˣ   be equation (1)

Substitute the value of x = 0 and y = 1000

1000 = ab⁰

So , the value of a = 1000

Substitute the value of x = 1 and y = 800

800 = ab¹

b = 800/1000

b = 0.8

So , the equation is y = 1000 ( 0.8 )ˣ  

Now , at the point A , the value of x = 2

So , y = 1000 ( 0.8 )²

y = 1000 x 0.64

y = 640

So , the point is A ( 2 , 640 )

Now , at the point B , the value of x = 3

So , y = 1000 ( 0.8 )³

y = 1000 x 0.512

y = 512

So , the point is B ( 3 , 512 )

Now , at the point C , the value of x = 4

So , y = 1000 ( 0.8 )⁴

y = 1000 x 0.4096

y = 409.6

So , the point is C ( 4 , 409.6 )

Hence , the coordinates are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

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What are the tools used in constructing parallel lines and perpendicular lines?.

Answers

The 45-degree set square contains an angle of 90 degrees, and also 30/60 degree set square contains a right angle. The 45 degrees set square is utilised to draw vertical lines. With the help of set squares, we can sketch parallel lines and perpendicular lines, construct some standard angles, and so on.

Geometric tools are instruments utilised to draw different kinds of geometric shapes. In Maths, geometry is the most critical topic, in which we learn about the shapes of things. Different types of tools with different names are utilised to draw these geometric shapes while solving geometry problems.

Some of the most generally utilised geometric tools are:

Ruler

Compass

Protractor

Divider

Set-squares

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The mass of a cube, M (kg), is
proportional to the cube of the length of
its edge, L (m).
The mass of the cube is 100 kg when
the length of its edge is 20 cm.
Work out L (to 2 DP) when M = 1900
kg

Thanks

Answers

Answer:

L = 53.37 cm

Step-by-step explanation:

We have the relationship

M ∝ L³

We can rewrite this as an equation:
M = k · L³

where k, a constant, is known as the constant of proportionality

Given M = 100 kg when L = 20, we get

100 = k · 20³

100 = k · 8000

k = 100/8000 = 0.0125

If M = 1900 kg and k = 0.0125 we can plug in these values to get

1900 = 0.0125 L³

==>  L³ = 1900/0.0125

==> L³ = 152000

Therefore L = ∛152000

L = 53.36803 or

L = 53.37 cm  rounded to 2 DP


Answer:

380.00

Step-by-step explanation:

M=KL

100=20K

K=5

M=5L

1900=5L

L=380

Find the length of the third ide. If neceary, round to the nearet tenth. 8 and 12

Answers

The length of the third side is 14.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

Given that,

a = 8

b = 12

Let the length of the third side be c,

Applying the Pythagorean theorem:

a² + b² = c²

8²+ 12² = c²

c² = 64+144

c² = 208

c = √208 = 14.42

Thus, the length of the third side is 14.

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The shape below is made of two rectangles joined together.
3 cm
4 cm
6 cm
6 cm
15 cm
Find the total area of the shape.
Optional working
Answer:
+
cm²

Answers

The total area of the shape is equal to 102 cm².

How to calculate the area of a rectangle?

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.

Next, we would determine the area of this irregular shape in parts as follows;

Area of rectangle 1 = 15 × 6

Area of rectangle 1 = 90 cm²

Area of rectangle 2 = 4 × 3

Area of rectangle 2 = 12 cm²

Total area of irregular shape = 90 + 12

Total area of irregular shape = 102 cm²

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Each pair of points is on the graph of an inverse variation. Find the missing value.
(3.5,16) (x,8)

Answers

The missing value for x is 7.

How to find the missing value

The inverse variation relationship between two variables x and y is described by the equation y = k/x,

where k is a constant.

We can use this equation to find the missing value, using the information given.

First, we'll use the first set of points to find the constant k:

y = k/x

16 = k/3.5

16 * 3.5 = k

56 = k

Next, we'll use the constant k and the second set of points to find the missing x value:

y = k/x

8 = 56/x

8 * x = 56

x = 56/8

x = 7

hence x is 7

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please help :)

Given f(x) = -x² + 9x − 17, find f(−5)

Answers

Answer: -87

Step-by-step explanation:  -(−5)² + 9(−5) − 17 =

-25 - 45 - 17  = -87

Answer:

f(x)= 3

Step-by-step explanation:

If f(x) is equal to -[tex]x^{2}[/tex]+9x-17 and f(-5)

You will substitute -5 where you see all the x's

-(-5)[tex]^{2}[/tex]+9(-5)-17

That will equal to

-25+45-17

Combine all the like terms

This will lead you to answer 3

So, f(x) =3

An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x . Another side is 5 more than four times the length of the bottom of the triangle. The last side is 14 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.

Answers

Answer

6x + 19

Step-by-step explanation:

First, set up the equation

x + 4x + 5 + 14 + x

Now simplify the like terms

6x + 19

What are the 12 identities in Maths?.

Answers

The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

In mathematics, an identity is a statement or equation that is true for all values of the variables involved. For example, the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is an identity.

In summary, identities in mathematics are statement that are true for all values of variables, they are used to simplify expressions, solve equations and prove theorems, and they play an important role in the study of mathematical structures.

The 12 algebraic identities in mathematics are:

Commutative property of addition: a + b = b + a

Commutative property of multiplication: a x b = b x a

Associative property of addition: (a + b) + c = a + (b + c)

Associative property of multiplication: (a x b) x c = a x (b x c)

Distributive property: a x (b + c) = (a x b) + (a x c)

Identity property of addition: a + 0 = a

Identity property of multiplication: a x 1 = a

Additive inverse property: a + (-a) = 0

Multiplicative inverse property: a x (1/a) = 1

Transitive property: a = b and b = c then a = c

Substitution property: a + b = b + a

Reflexive property: a = a

It's worth noting that these are some of the algebraic identities which are frequently used in algebra and other related mathematical branches.

The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

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a trader has two beverages A & B in buckets of 24l and 27l .She repacks the beverage in bottles of the same sizes. Calculate the least number of bottles she can obtain

Answers

Answer: The least number of bottles the trader can obtain is the greatest common divisor (GCD) of the number of liters in the two buckets.

We can use the Euclidean algorithm to find the GCD:

First find the remainder of 24 divided by 27, which is 24 % 27 = 0.

Since the remainder is 0, we know that the GCD of 24 and 27 is 27.

Therefore, the trader can obtain at least 27 bottles from the two buckets of beverages A and B.

Note that the GCD represents the size of the bottle and this is the least number of bottles that the trader can obtain.

Step-by-step explanation:

please view the image and answer the questions.

Answers

The values of a and b  for the given equation  are 25,-25

What is Quadratic equation ?

Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .

Given ,

equation x^3 - 625 x  = 0

x^3 - 625x = 0

taking x common

x(x^2 - 625 ) = 0

x^2 - 625 = 0

(x+25 ) (x-25) = 0

It is in the form of a2-b2

hence it is equals to a+b * a-b

x = 25,-25 .

Hence, The values of a and b are 25,-25 respectively for the given equation.

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Find the following areas under the normal curve

A. -1.43
B. 0.58
C. -1.55
D. z> 1.34

2 find the standardized score (z-score) closest to the following percentiles

A. 35th percentile

B. First Quartile QI

C. The observation with 12% of the data falling above it


3. Given a normal distribution of heights of 5 year olds (in inches) with a mean of 36 and a standard deviation of 10, find the following areas under the curve:

A. x< 31 inches

B. x> 49 inches

C. 40
D. 70% of 5 year olds are below what height?

Answers

Answer:

1. A. -1.43 corresponds to an area of approximately 0.0637 under the normal curve.

B. 0.58 corresponds to an area of approximately 0.7295 under the normal curve.

C. -1.55 corresponds to an area of approximately 0.0633 under the normal curve.

D. For z>1.34, the area under the normal curve is approximately 0.0916.

--------

2. A. The 35th percentile corresponds to a z-score of approximately -0.48

B. The first quartile (Q1) corresponds to a z-score of approximately -0.67

C. For 12% of the data to fall above it, the z-score would be approximately 1.28

----------

3.  A. To find the area under the curve for x< 31 inches, we need to convert 31 inches to a z-score using the formula: z = (x - mean) / standard deviation. For this case, z = (31 - 36) / 10 = -0.6, the area under the curve for this is 0.2744

B. To find the area under the curve for x> 49 inches, we need to convert 49 inches to a z-score, the z-score is (49 - 36) / 10 = 1.3, the area under the curve for this is 0.0968

C. The area under the curve for x = 40 inches is 0.3520

D. To find the height at which 70% of 5 year olds are below it, we need to use the inverse standard normal calculator, which gives us a z-score of 0.84162, we can then use this z-score to find the corresponding x value by using the formula x = mean + (z-score * standard deviation) which in this case would be 36 + (0.84162*10) = 42.4 inches

There are 1490 students at Cypress Middle School. 30% of the students are enrolled in PE. How many students are enrolled in PE?

Answers

The number of students are enrolled in PE be 447.

What is the decimal form of a percentage called?

A percentage expressed in decimal form is a proportion, but a proportion is not always a % expressed in decimal form.

A fraction expressed in a specific way is called a decimal. For example, you can write the fraction as 0.5 instead of 1/2, with the zero in the ones place and the five in the tenths place. The word decimal is derived from the Latin word decimus, which means tenth, and the number 10 (or decem).

From the given information, we get 30% of 1490

Convert 30% into a decimal and multiply by 1490

Convert 30 % into a decimal form: 0.3

Multiply 0.3 by 1490

= 0.3 × 1490

Simplifying the values, we get

0.3 - 1490

= 447

Therefore, the number of students are enrolled in PE be 447.

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Is Xsquare 2 2 Xsquare a polynomial?.

Answers

No, it is not. X square 22 X square is not a polynomial because it does not have the standard form of a polynomial which is ax^n + bx^n-1 + cx^n-2 + ... + z.

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power.

Leading term and leading coefficient are terms used to describe the first term and its coefficient, respectively, in the polynomial's standard form.

A polynomial's standard form is denoted by the formula f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

According to the definition of a polynomial in standard form, exponents must be written in decreasing order.

The standard form of polynomials is used to facilitate calculations.

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how would you solve the following equation: x - 10 = 90

Answers

To solve the equation x - 10 = 90, you can add 10 to both sides of the equation to get:

x - 10 + 10 = 90 + 10

x = 100

Therefore, the solution to the equation is x = 100.

You can also check this solution by substituting it back into the original equation:

x - 10 = 90

100 - 10 = 90

90 = 90

This confirms that x = 100 is a valid solution to the equation.

9. You are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x, by adding 10 to both sides of the equation:

[tex]x - 10 = 90\\x - 10 (+10) = 90 (+10)\\x = 90 + 10\\x = 100[/tex]

a. Add 10 to both sides.

10. You are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x, by multiplying 5 to both sides of the equation:

[tex]\frac{x}{5} = 5\\ (\frac{x}{5}) (* 5) = 5 (*5)\\x = 5 * 5\\x = 25[/tex]

d. Multiply both sides by 5.

~

PLEASE HELP ASAP!!

Look at the screen shot for the question, thank you!

Answers

Answer:

read my explanation because this will take a while to put in an answer and explain.

Step-by-step explanation:

slope: 3x

y-intercept: 48.

equation: y=48-3x

we get this from reading the question.

y=48-3x is your equation! it initially starts at 48, and everytime the hour changes it decreases by 3.

for the table:

0 - 48           5 - 33

1 - 45            6 - 30

2 - 42            7 - 27

3 - 39            8 - 24

4 - 36

the graph you could have filled by yourself, but here:

and when you are done, don't forget to connect the points! i didn't do it because i had to plot them and the line would override it.

“growth or decay right” it cut out the picture


Help! i’ve been stuck on these problems for a bit now

Answers

Answer:

Growth

Growth

Decay

Decay

how to find the GCF and re write a sum using GCF and the distributive property?

Answers

To find the greatest common factor (GCF) of a sum, list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

How to find the GCF and re write a sum using GCF and the distributive property?

To find the greatest common factor (GCF) of a sum, you can first list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

For example, to find the GCF of 36x² + 18x² + 12x², you would list the prime factors of each term:

36x² = 2² × 3² × x²

18x² = 2 ×  3² ×  x²

12x² = 2² ×3 × x²

The GCF is 2 × 3 ×  x² = 6x²

To rewrite the sum using the GCF and the distributive property, you divide each term in the sum by the GCF, and then multiply the GCF by the sum of the quotients:

(36x² + 18x²  + 12x²) / (6x² ) = 6 + 3 + 2

6x² × (6 + 3 + 2) = 6x² ×  11

So the sum can be rewritten as 6x² × 11

You can also use the same method to find GCF of numbers as well.

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What is the zero of PX x2 6x9?.

Answers

On Solving the given quadratic equation , we get the zeros of the equation is x = 3 .

A quadratic equation is an algebraic equation of second degree in x. The standard form of a quadratic is written as ax² + bx + c = 0  , where "a" and "b" are coefficients, x is variable, and c is constant term.

The given equation is : p(x) = x² - 6x + 9 ;

to find the zero , we equate the given quadratic function to zero(0) .

On equating ,

we have ;  x² - 6x + 9 = 0;

⇒ x² - 3x -3x + 9 .....by split middle term method ;

⇒ x(x - 3) -3(x - 3) = 0;

⇒ (x - 3)(x - 3) = 0;

which means that x - 3 = 0 ,and x = 3 .

Therefore , the zero of the given quadratic function is x = 3 .

The given question is incomplete , the complete question is

What is the zero of p(x) = x² - 6x + 9 ?

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A wire in the hape of a citcle encloe the area of 38. 5 cm quare. If the wire i rebent to gorm a quare, find the area of a quare

Answers

The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

What is circumference of circle ?

Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

We can use the formula C = 2πr to find the circumference of the original circle, where C is the circumference and r is the radius of the circle.

Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

Now that we know the radius of the circle, we can find the circumference using the formula:

C = 2πr

Now, we can find the area of the square by squaring the length of one side of the square which is the circumference of the original circle

Area of square = C^2

Therefore, The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

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Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

C = 2πr

Area of square = C^2

The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

In the figure (not drawn to scale), m∠A = 36º, m∠B=108º, m∠D=153º. Find m∠C

Answers

Answer:

49.5°

Step-by-step explanation:

Draw a line b/w B and D, this will "cut" the angles of both down the exact middle making it much easier to work with now that you have 2 separate triangles

For example, angle A remains 36° but angle B becomes 54° and angle D becomes 76.5°. Now that you have B and D, just subtract 180 from both to get your C value. 180° - 54° - 76.5° = 49.5°

You and your friend have lunch at a diner that adds a​ 15% tip when you pay with a credit card. Your friend says the tip on the ​$ 20 bill will be ​$ 0.30 and the total amount will be ​$.20.30 Calculate the total amount that the diner will charge to your credit card using a percent greater than 100. What is your​ friend's possible​ error?

What is your​ friend's possible​ error?

A. divided the amount of the bill by 15.
B. divided the amount of the bill by 1.15.
C. calculated a​ 1.5% tip, not a​ 15% tip.
D .multiplied the amount of the bill by 0.15.

Answers

Answer:

C

Step-by-step explanation:

15% is $3.00 not $0.30

Please find the value of the unknown angles; X and Y. Links are not allowed, and any answer that contains links will be reported!

First person to answer correctly with enough detail to support their answer, will be given brainliest.

Thank you.

Answers

Answer:

x = 131

y = 131

Step-by-step explanation:

x = 180 - 49 (sum of angles on a straight line)

x = 131

y = x (corresponding angles)

y = 131

formula to solve any quadratic equation

Answers

the formala is ax2 + bx + c = 0

Is 64 a square number?.

Answers

Answer:

8 X 8 = 64

Step-by-step explanation:

9b+7-6b-a
simplify the equation ​

Answers

Answer: 3b-a+7

Step-by-step explanation:

9b-6b=3b

3b-7-a

Answer: 3b+7-a

Step-by-step explanation:

9b+7-6b-a

3b+7-a

680 is the partial product of 34 and?

Answers

Answer:

64

Step-by-step explanation:

56+58497657=875845455*-88787887879=5545426464

What is the equation of a line that is perpendicular to the line y = −3x + 2 and passes through the point (6, 8)?

Answers

Answer: [tex]y=\frac{1}{3} x+6[/tex]

Step-by-step explanation:

To find the perpendicular line, we have to change the slope of the original, equation.

The slope of the perpendicular line is 1/3. We can plug in the new point. To find the equation.

[tex]8=\frac{1}{3}(6)+b[/tex]          [multiply]
[tex]8=2+b[/tex]               [subtract both sides by 2]
b=6

Final equation is [tex]y=\frac{1}{3} x+6[/tex]

Answer:

y = 1/3x + 6

Step-by-step explanation:

Because perpendicular lines have opposite and reciprocal slopes, we have to change our slope into a positive and flip it into it's reciprocal.

Now its: y = 1/3x + b

Next, we find b using slope intercept form.

8 = 1/3(6) + b

8 = 2 + b

6 = b

Place b into the equation.

y = 1/3x + 6

Find the area of the triangle below using the law of sines

Answers

The area of the triangle is 27.9 sq.cm.

What is meant by area of triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area.

We have the lengths of two sides and the measure of the included angle. So, you can use the formula R = [tex]\frac{1}{2}[/tex]pr sin(Q), where p and r are the lengths of the sides opposite to the vertices P and R respectively.

Using the formula, the area, R= [tex]\frac{1}{2}[/tex] (9) (8.4) sin (132°).

R = 37.8 sin (132°)

R = 37.8 (0.74)

R = 27.9 (approx)

Hence, the area of the triangle is 27.9 sq.cm.

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Find C and a so that f(x) = Ca* models the situation described. State what the variable x represents in your formula.
In 2000 a house was worth $300,000, and its value decreases by 7% each year thereafter.
=(Type an integer or a decimal.)
C=
a= (Type an integer or a decimal.)
What is the correct interpretation of x?
OA. The variable x represents the initial worth of the house.
OB. The variable x represents the worth of the house t years after 2000.
OC. The variable x represents the rate at which the worth of the house decreases.
OD. The variable x represents the number of years after 2000.
CECE

Answers

C = 300000

a = -0.07

The correct interpretation of x is OD. The variable x represents the number of years after 2000.

Answer:

Step-by-step explanation:

The exponential decay formula for this situation is

[tex]y=300,000(.93)^x[/tex]

where 300,000 is the initial value, .93 is decay rate (100% - 7% = 93% which is .93 as a decimal), and x represents the number of years after the year 2000. B is your answer.

Other Questions
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