Find an equation for the surface obtained by rotating the line x = 4y about the x-axis.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]vertex \begin{cases} x=4\\ y=7 \end{cases}\implies y=a(x-4)^2 +7~\hfill \textit{we also know that} \begin{cases} x=6\\ y=19 \end{cases} \\\\\\ 19~~ = ~~a(6-4)^2 +7\implies 12=a(2)^2\implies \cfrac{12}{(2)^2}=a\implies 3=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} y=3(x-4)^2 + 7 \end{array}} ~\hfill[/tex]

Answer:

  4x² -11x +5 = 0

Step-by-step explanation:

Given α and β are roots of 4x² -5x -1 = 0, you want to find the quadratic equation that has (2-α) and (2-β) as its roots.

Factoring out the leading coefficient, we can write the factored form of the given quadratic as ...

  4(x -α)(x -β) = 0 = 4x² -5x -1

When the roots are changed from α and β to (2-α) and (2-β), the factored form of the new equation is ...

  4(x -(2 -α))(x -(2 -β)) = 0

  4(x -2 +α)(x -2 +β) = 0

Negating both factors allows us to write this in a familiar form:

  4((2 -x) -α)((2 -x) -β) = 0

Comparing to the original factored quadratic, we see that this is the original with x replaced by (2 -x). Then the quadratic we seek is ...

  4(2-x)² -5(2 -x) -1 = 0 . . . . . . . . . . . original with x replaced by (2-x)

  4(4 -4x +x²) -10 +5x -1 = 0 . . . . simplify a bit

  4x² -11x +5 = 0 . . . . . . . . . . simplify

The quadratic whose roots are (2-α) and (2-β) is 4x² -11x +5 = 0.

__

Additional comment

Effectively, the roots and the equation are reflected across the line x=1.

The length of the pieces of wire include 23.5425 inches and 75.4565 inches.

Given the total length of wire is

X+Y=100

Y=100-X

Then we bend the two pieces into squares so that the sides of each square are X/4 and (100-X)/4. Therefore

(X/4)² + [(100-X)/4]² =400

X² +10000-200X +X² =6400

X²-100X+1800=0

Solving the equation

X = 76.4565 inches and X=23.5425 inches

Therefore, the length of the pieces of wire include 23.5425 inches and 75.4565 inches.

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The triangle with vertices located at U(-5 , 5), K(-5 , -1), and L(1 , 2) has its centroid located at (-3 , 2).

The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.

To get the centroid of a triangle, use the formula given by:

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

where C is the centroid of the triangle located at (x , y)

x1, x2, and x3 are the x-coordinate of the vertices of the triangle

y1, y2, and y3 are the y-coordinate of the vertices of the triangle

Let Point 1(x1 , y1) = U(-5 , 5)

Point 2(x2 , y2) = K(-5 , -1)

Point 3(x3 , y3) = L(1 , 2)

Plug in the values in the formula.

C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

C(x ,y) = [(-5 + -5 + 1)/3 , (5 + -1 + 2)/3]

C(x ,y) = (-9/3 , 6/3)

C(x ,y) = (-3 , 2)

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The error is the symbol for the ray is not correct.

We know that opposite rays are two rays that both start from a common point and go in exactly opposite directions.

In the image attached the rays,

→

YC and

→

YE are opposite rays.

And the points E, Y, and C are colinear, that is the points E, Y, and C lie on a straight line.

In the image, the rays YC and YE just have a line on the above without the right arrow mark. This representation that is given in question indicates that YC and YE are line segments and not rays.

Hence, The correct way to represent them is

→

YC and

→

YE are opposite rays.

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Answer:

x = 2

Step-by-step explanation:

Let's solve for the value of x,

→ √2x - 1 + 3 = 4

→ √2x + 2 = 4

→ √2x = 4 - 2

→ 2x = (2)²

→ x = 4/2

→ [ x = 2 ]

Hence, the value of x is 2.

For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]

Given,

The conditions

We know,

Median is the middle number of ordered data set.

Consider the number of observations as x

Then the median is located at [tex]\frac{x+1}{2}[/tex]

Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]

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Hence, the equation of exponential function is represented by y = A(Bˣ)

The equation in exponential form

y = A(Bˣ)

Case 1 :

x =0 y = 0.02

0.02 =  A (B⁰)

A = 0.02

Case 2:

x = 1 y =0.04

0.04 =  0.02(B)

0.04 /0.02 = B

B = 2

Case 3 :

x = 2 y =0.08

0.08 = 0.02(2²)

0.08 = 0.08

Case 4 :

x = 3 y = 0.16

0.16 = 0.02(2³)

0.16 = 0.16

So, we have implemented the eqaution y = A(Bˣ)

We found the values of A & B, and also proved them in case 3 and case 4.

Hence, the equation of exponential function is represented by y = A(Bˣ)

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The simplest form of 12 to 14 is 6 to 7.

It should be noted that the information is that we should find the simplest form of 12 to 14.

In this case, it's important to look at their common factor. The common factor here is 2.

Therefore, the simplest form will be:

(12/2) / (14/2) = 6/7.

Therefore, the simplest form of 12 to 14 is 6 to 7.

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the equation formula y=2/3x+5 is (3,-3).

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

based on the available facts;

You might be wondering how, but we can start with that 5 at the end, which denotes the y-intercept.

If 0 is used in place of x, then y=2/30+5y=5

We shall receive the first coordinate as a result, which is (0,5).

Let's then consider the slope, which is 2,3. As you may already be aware, the slope is also known as

rise/run

; what do they mean by that is that the first top number tells you how many units you go up and the second one how many units you go right or how many units you go down and go left.

Now, I know this may seem complicated but let's make it clear. Since we know one coordinate, which is

(0,5)

, from that point by knowing the slope we can find a second point; this point is 2 points above and 3 to the right, which tells us that −5+2

points above gives us −3 and 3 points on the right gives us a new coordinate:

(3,−3)

And since we now know two coordinates, that is enough to draw the line and have the graph.

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Answer: False

Step-by-step explanation:

4 x 106 = 424

Answer: false

Step-by-step explanation: I'm not even going to explain it just multiply 4 x 106

Answer:

describe any eight risky situation young people are frequently exposed to

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5 = n - 3

- 5 + 3 = n

-2 = n

--------------

check

-5 = -2 - 3

-5 = -5

the answer is good

Answer:

A

Step-by-step explanation:

Point slope form is y-y1=m(x-x1)

If the point is (3, -2) then y1 is -2 and x1 is 3, then the equation should look like this y+2=m(x-3)

Then you just plug in -2 for m

Total time spend by Natalie doing her Math and English homework is 90 minutes ,equation represents the time she for math homework is a function of time she spends her English homework is y = 90-x.

As given,

Total time spend =90 minutes

Time spend on doing

English homework =x minutes

Math homework =y minutes

Equation representing the function,

y = 90-x

Therefore, total time spend is 90 minutes , equation represents the time she for math homework is a function of time she spends her English homework is y = 90-x.

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The value of the algebraic expressions is 59.

According to the statement

We have to find that the value of the expression.

So, For this purpose, we know that the

Algebraic expression is, a symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations

From the given information:

5(7-4)^2 + 3 + 11

Then we have to solve it with bodmas rule.

Then

5(7-4)^2 + 3 + 11

Firstly solve the bracket

5(3)^2 + 3 + 11

Then multiply the terms

5*9 + 3 + 11

Then add the terms

45+14

59.

So, The value of the algebraic expressions is 59.

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The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.

It follows from the task content that the mathematical expression which correctly represents the word phrase is to be determined.

Since the product of -3 and the number, a can be written as; -3 × a = -3a.

Hence, the word phrase as given in the task content can be written as;

-3a +7 < 11.

This follows from the concept of inequalities.

Ultimately, The mathematical expression, an inequality to be more specific which represents the given word phrase; -3 * a number increased by 7 is less than -11 is; -3a +7 < 11.

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The correct option is (C) 45°

The measure of angle ∠OCA = 45°.

A circle is a depiction with no sides or vertices.

It includes a radius as well as a center. The center is the point from which all other points just on circle are equidistant, and the distance between them equals the radius.

Let AC equal the tangent to the circle with center O.

OA ⊥ AC   ....(The tangent has always been perpendicular to the radius.)

As, it is given that ∠OAC = 90° and ΔOAC is isosceles triangle.

Thus, ∠O = ∠C = x (say)

Now, using the triangle's angle sum property. We have it,

90° + x + x= 180°

On simplification;

x = 45°

Thus, the value of angle ∠OCA is 45°.

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The correct question is-

'O' is a centre of a circle, AC is a tangent to a circle at point A. If ΔOAC is an isosceles triangle, then find the measure of  ∠OCA

(A) 75°

(B) 50°

(C) 45°

(D) 40°

Step-by-step explanation:

are you serious ?

1/3 of 24 means dividing 24 by 3,

means 24×1/3 = 24/3 = 8

The expression that is equivalent to negative three raised to the fourth power divided by negative three raised to the second power is (-3⁴) / (-3²)

Expression:

Expressions are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Negative three raised to the fourth power divided by negative three raised to the second power.

Here we need to find the expression for this statement.

First, we have to divide the statement into two like,

"Negative three raised to the fourth power"

It can be written as,

=> (-3⁴)

And the for the next part,

"Negative three raised to the second power."

It can be written as,

=> (-3²)

Now we have to divide these two terms, the we get,

=> (-3⁴) / (-3²)

Therefore, the expression is (-3⁴) / (-3²).

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Answer: 8 14/15

Step-by-step explanation:

2 1/3 + 6 3/5 =

2+1/3 + 6+3/5=

2+6+1/3+3/5=

8+1/3+3/5=

8+(1/3+3/5)*15/15=

8+(1*15/3+3*15/5)/15=

8+(15/3 + 45/5)/15=

8+(5+9)/15=

8+14/15=8 14/15

Answer:  -21

Step-by-step explanation:

To solve this, you must subtract either one of the numbers from the other, then take the absolute value.

The easiest way is to subtract -6 from 15, since it will allow you to work with positive numbers.

So you do 15 - (-6), which is the same as 15 + 6. The answer is -21, and since it is a positive number, no further calculations are required to find the absolute value.

Step-by-step explanation:

0.125 gallons of 35% solution are required to achieve the specified ratio.

This is further explained below.

Generally, It takes 0.125 gallons of a 35% solution to get the ratio you want.

Eli wishes to mix 0.5 gallons of a 10% acetic acid solution with a 35% solution to create a 15% acetic acid solution; thus, the calculation below must be done to calculate how many gallons of

5% solutions are required:

1 x 10 + 2 x 35 = 80

=> 80 ÷ 3 = 26.66

1x10 + 1x35 = 45

=>45÷ 2 = 2.5

1 x 10 + 0.5 x 35 = 27.5

=>27.5 ÷ 1.5 = 18.33

1 x 10 + 0.4 x 35 = 24

=>24 ÷ 1.4 = 17.14

1 x 10 + 0.2 x 35 =17

=> 17 / 1.2 = 14.16

1 x 10 + 0.3 x 35 = 20.5

=> 20.5/ 1.3 = 15.76

1 x 10 + 0.25 x 35 = 18.75

=> 18.75 / 1.25 = 15

1 / 2 = 0.5

0.25 / 2 = 0.125

In conclusion, 0.125 gallons of 35% solution are required to achieve the specified ratio.

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CQ

eli wants to combine 0.5 gallons of a 10% acetic acid solution with a 35% solution to make a 15% acetic acid solution. he needs to determine how many gallons of 35% solution are needed eli decides to let v represent the volume of 35% solution and makes a table to help solve the problem

Answer:

if yours is how mine is- i hope this helps

Step-by-step explanation:

Answer: there are 6 servings

Step-by-step explanation:

[tex]\displaystyle\\6\frac{3}{4}:1\frac{1}{8} =\\\\\frac{6*4+3}{4} :\frac{1*8+1}{8} =\\\\\frac{24+3}{4}:\frac{8+1}{8}=\\\\\frac{27}{4}:\frac{9}{8}=\\\\\frac{27}{4}*\frac{8}{9} =\\\\ \frac{27*8}{4*9} =\\\\\frac{3*9*4*2}{4*9} =\\\\3*2=\\\\6[/tex]

Answer:- 4x + 3y = 23

Step-by-step explanation: 1x=y=-7

Answer:

21

Step-by-step explanation:

The domain of the function is the set of all real values

The equation of the function is given as:

f(x) = |2x + 5| + 3

The above function is an absolute value function

All absolute value functions can take any value as their input

This means that the given function can take any value as its input

Hence, the domain of the function is the set of all real values

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Answer:43

Step-by-step explanation: