HELP ASPPP SHOW UR WORK PLEASE

Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]

[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex

Apply completing the square method to find vertex

[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]

Lets take half of coefficient of x is -6

divide by 2 that is -3

square it [tex](-3)^{2}[/tex] that is 9

Add and subtract 9

[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]

Take out -9 and multiply by -2

[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]

Now factor the parenthesis part

[tex]f(x) = -2(x-3)^{2} +23[/tex]

The value of h=3  and k=23

So vertex is (3,23)

The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum

Hence the answer is the vertex is maximum at (3,23)

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The gallons of milk were in each container originally is 2.4 and 4.8 gallons respectively.

Let us say that:

V₁ = initial gallons in the first container

V₂ = initial gallons in the second container.

From the problem statement, we can create the expression:

V₁ = 2 V₂

V₁ – 3 = 45 (V₂ – 2)

Combining the two expressions:

2 V₂ – 3 = 45 (V₂ – 2)

2 V₂ – 3 = 45 V₂ – 9

2.5 V₂ = 6

Divide

V₂ = 6 / 2.5

V₂ = 2.4 gallons

V₁ = 2 V₂:

= 2 × 2.4

= 4.8 gallons

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Complete question

The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 4.5 times as much milk as the second, How many gallons of milk were in each container originally?

Answer:

Step-by-step explanation:

an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:

4x - 8 = 22 + x

4x -x = 22 + 8      

3x = 30

x = 10          

Answer: 5:1

Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1

Answer:

[tex] \sf \: \frac{7}{12} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

[tex] \sf \rightarrow \: \frac{(1) \times 3}{(4) \times 3} + \frac{(1) \times 4}{(3) \times 4} [/tex]

[tex] \sf \rightarrow \: \frac{3}{12} + \frac{4}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(3 + 4)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{7}{12} [/tex]

Hence, the answer is 7/12.

The rectangle with the sides 4 and 3 is the required rectangle.

The correct option is third shape.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 6 x 4

= 12 square millimeters.

And rectangle has the same area as the triangle.

The rectangle with the sides 4 and 3 is the required.

Therefore, the rectangle with the sides 4 and 3 is the required rectangle.

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The unit rate of three dollars for 2 1/2 hours of work is 1.2.

The rate is a ratio of change in one quantity with respect to other. The unit rate is a rate such that the denominator of the rate must be one. An item's unit rate is its rate for one of them. How many units of the first type of quantity are needed to make up one unit of the second type is expressed using a unit rate (or unit ratio).

Now, finding the unit rate for three dollars for 2 1/2 hours of work,

Unit rate [tex]=\frac{3}{2.5}[/tex]

= 1.2

Therefore, the unit rate of three dollars for 2 1/2 hours of work is 1.2.

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The sequence of transformations that we should apply is the one that appears on the top left option:

Reflection across the y-axis followed by a rotation of 90° counterclockwise.

We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.

First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.

Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.

Concluding, the sequence of transformations is:

Notice that this is equivalent to:

Then the correct option is the one in the top left corner.

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The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.

Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).

Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.

The given expression is

[(1.3^3)/(1.2^4)]^-6

Apply the indices power law to the above expression.

[(1.2^4)/(1.3^3)]^6

The exponents are then expanded using the power law of indices.

(1.2^[4x6])/(1.3^[3x6])

(1.2^[24])/(1.3^[18])

Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])

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Answer:

#0.85

Step by step:

13.60/16 = #0.85

pls give me brainliest

pls:(

Answer:

[tex]y=\frac{1}{2}x-5[/tex]

B: smaller rate of change but night y intercept

Step-by-step explanation:

y intercept is -5 because when x is zero y is -5

Now to find slope

-1-(-3)/8-4

-1+3/4

2/4

1/2

Now we can put it in an equation

y=1/2x-5

2nd question

-6-4/0-2

-10/-2

5

-6 is greater then -10 so the y intercept is bigger

So B is correct

Answer: i'm writeing this so you can mark the other person brainliest

Step-by-step explanation:

The vector <5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

Vectors are described by two features: (i) magnitude, (ii) direction. The magnitude is the quantity associated with a vector and determine by Pythagorean theorem, and the direction indicates the "distribution" of the magnitude along the ortogonal axes of the vector. Unit vectors are vectors of magnitude 1 and we can determine it by using the following definition:

[tex]\vec u[/tex] = <x, y> / ||<x, y>||

Where ||<x, y>|| = √(x² + y²)

Please notice that [tex]\vec u[/tex] represents the unit vector.

If we know that <x, y> = <5, - 7>, then the unit vector is:

Magnitude

||<x, y>|| = √[5² + (- 7)²]

||<x, y>|| = √74

Unit vector

[tex]\vec u[/tex] = <5, - 7> / √74

[tex]\vec u[/tex] = <5 / √74, - 7 / √74>

[tex]\vec u[/tex] = <5√74 / 74, - 7√74 / 74>

<5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

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If the steps follow an arithmetic series, the concrete required for the first 12 steps is 140.4.

Given, the first term of the arithmetic series, a=1.8 and the sum of first five terms that is s5=27, we have to find the sum of first 12 steps.

The formula to calculate the sum of the terms in AP is

Sn = n/2 {2a + (n - 1) d}

S5=5/2(2(1.8) +(5-1)d)

27=2.5(3.6+ 4d)

27=9+10d

27-9=10d

18=10d

d=18/10

d=1.8

The common difference d is 1.8.

Now we have to find S12,

S12=12/2(2(1.8) +(12-1)1.8)

= 6(3.6+19.8)

=6(23.4)

=140.4

S12=140.4

Therefore, the concrete required for the first 12 steps is 140.4.

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Answer: r = 19.35 ft

Step-by-step explanation:

[tex]Volume = V = \pi r^{2} \frac{h}{3} \\235.5 = \pi r^{2} 15/3\\r^{2} = \frac{235.5}{\pi} 5\\r = \sqrt{374.8} = 19.35[/tex]

Answer:

ok

Step-by-step explanation:

By evaluating a linear equation, we will see that after two seconds there are 93 gallons of fuel.

We know that the tank initially has 103 galons of fuel, and we know that it releases 5 gallons per second at a constant rate.

So, after x seconds, the amount of fuel inside the container is:

F(x) = 103 - x*5

so we have a linear equation.

The amount of fuel in the tank after 2 seconds is given by:

F(2)=  103 - 2*5 = 103 - 10 = 93

After 2 seconds there are 93 gallons of fuel.

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Answer:

  1 1/2

Step-by-step explanation:

You want the other number when one of the two numbers that have a product of 7 is 4 2/3.

Let x represent the unknown factor. Then we have ...

  (4 2/3)x = 7

  (14/3)x = 7 . . . . . . write as improper fraction

  x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x

  x = 3/2 = 1 1/2

The other number is 1 1/2.

Answer:

B

Step-by-step explanation:

Alright, to start off... we need to find a range of value that sqr 74 is between.

To do that, we can check by just trying some random numbers.

Let's try 8 -- 8^2 is 64. Let's try 9 -- 9^2 is 81. So the sqr 64 is 8 and sqr 81 is 9.

sqr 74 is between sqr 64 and sqr 81, so the statement is true. However, the multiple-choice has decimal numbers, meaning that they want us to be more specific.

First, we can cross out 9.5, because we don't want to expand our range, we want to keep it as accurate as possible.

That leaves us 8.5

To find if 8.5 fits the criteria, meaning that it can't be larger than sqr 74, we can use two methods.

The first method is preferred, you simply need to multiply them. I hope you know how to do that by hand. We get 72.25

The second method is less preferred but works. We need to approximate the value by finding the mean of 64 and 81, because 8.5 is the mean of 8 and 9. The approximate value should be very close to the true value. By doing (81+64)/2, we get 72.5

Now, double-check: is the 74 between 72.25 and 81? Yes, it is!
Hence, that gives us the answer that sqr74 is between 8.5 (sqr 72.25) and 9 (sqr 81)

Answer:

x = 139°

Step-by-step explanation:

The sum of the internal angles of a triangles is 180°

a + 59 + 80 = 180

a = 180 - 139

a = 41°

a and x are supplementary angles. Supplementary angles sum 180°.

Then:

a + x = 180

41 + x = 180

x = 180 - 41

x = 139°

slope = m = (4 - 0) / (1 - 0) = 4

y = mx + b

y = 4x + b

substitute (0, 0) to find b

b = 0

y = 4x

A quadratic equation in one unknown;

has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.

If we apply discriminant for the above equation, we obtain the following expression;

If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.

Now let's remember our formula for finding the roots and solve the problem using the discriminant value.

Therefore;

Other root is;

The rectangular coordinates are

a. (1,0,0) ⇒ (x,y,z) = (0,0,1)

b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)

Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then

x   =   r.sinΘ.cos∅      →   1

y   =   r.sinΘ.sin∅       →   2

z   =   r.cosΘ               →   3

According to the given problem,

a.)   ( 1, 0, 0 )  =   ( r, Θ, ∅ )

Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅          

           =   1.sin0.cos0

           =   1.0.1

      x   =   0

2 ⇒ y   =   r.sinΘ.sin∅

            =   1.sin0.sin0

            =   1.0.0

      y   =   0

3 ⇒ z   =   r.cosΘ

            =   1.cos0

            =   1.1

       z   =   1

∴   ( x, y, z )   =   ( 0, 0, 1 )

b.)   ( 18, π/3, π/4 )   =   ( r, Θ, ∅ )

Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅

           =   18.sinπ/3.cosπ/4

           =   18.√3/2.1/√2

      x   =   11.022

2 ⇒ y  =   r.sinΘ.sin∅

           =   18.sinπ/3.sinπ/4

           =   18.√3/2.1/√2

       y  =   11.022

3 ⇒ z   =   r.cosΘ

            =   18.cosπ/3

            =   18.1/2

       z   =   9

∴   ( x, y, z )   =   ( 11.022, 11.022, 9 )

Therefore the rectangular coordinates for the spherical coordinates of

a. ( 1, 0, 0 )   is   ( 0, 0, 1 )

b. ( 18, 1/3, 1/4 )   is   ( 11.022, 11.022, 9 )

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Step-by-step explanation:

are you sure there is no other given info? do you have to solve in terms of m and D?

Answer:

  y = 9x -78

Step-by-step explanation:

You want the equation y + 6 = 9(x − 8) written in slope-intercept form.

Solve for y and simplify.

  y +6 = 9x -72 . . . . . . . . eliminate parentheses

  y = 9x -78 . . . . . . . . . subtract 6

__

Additional comment

The given equation is written in point-slope form. It has a slope of 9 and goes through the point (8, -6).

Slope-intercept form is ...

  y = mx +b

where m is the slope and b is the y-intercept.

Answer:

[tex]f( x) = x2 - 7 x[/tex]

From the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

As given in the question,

From the given relative frequency table , answer of the following questions are as follow:

Total percentage of students completing the exam review = 65%

a. Completed the exam review with the condition that they have passed the exam = 55%

b. Completed the exam review with the condition that they have failed the exam = 10%

c. Yes, there is association between the two completing the exam review and passing the exam is only 55% and those who have completing the exam review but failed are 10%.

Therefore, from the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

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Answer: 10

Step-by-step explanation: The least common denominator is 10 because both integers 2 and 10 have a LCM OF 10. Your welcome. :’j

Answer: 10

Step-by-step explanation: The least common denominator is 10, cuz it is the lowest common multiple of 10 and 2, 2 × 5 =10, 10× 1 = 10. they r both common multiples.

The height of woman who has a shoulder width of 18.5 inches is 74 inches.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of woman = 64 inches

Shoulder width = 16 inches

So, ratio = Height :  shoulder width = 64:16

let the height of a woman who has a shoulder width of 18.5 inches be x.

So, x:18.5.

Now,

64 / 16 =  x/ 18.5

4= x/18.5

x= 74

Hence, the height of woman who has a shoulder width of 18.5 inches is 74 inches.

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The equation of the parallel line is 4x + 5y - 12 = 0

The equation is given as

4x + 5y + 2 = 0

The x-intercept is also given as

x-intercept = 3

We have

4x + 5y + 2 = 0

Make y the subject

5y = -4x - 2

Divide through by 5

y = -4x/5 - 2/5

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -4/5

This means that the slope of 4x + 5y + 2 = 0 is =4/5

The slopes of parallel lines are equal

This means that the slope of the other line is -4/5

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4/5

(x₁, y₁) = (3, 0) i.e. the x-intercept

So, we have

y = -4/5(x - 3) + 0

Multiply through by 5

5y = -4(x - 3)

Open the brackets and evaluate

5y = -4x + 12

This gives

4x + 5y - 12 = 0

Hence, the parallel line has an equation of 4x + 5y - 12 = 0

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