Write the equation of the parabola in vertex form. y = (x – 2)2 + 4 y = x2 – 4 y = (x – 4)2 – 4 y = (x – 2)2

Answer:

  1.08%

Step-by-step explanation:

You want to know the continuously compounded interest rate that will result in a value of $19,000 for an investment of $18,000 after 5 years.

The value of an investment of P earning continuously compounded interest at rate r for t years is ...

  A = Pe^(rt)

Using the given values, we can solve for r:

  19000 = 18000·e^(r·5)

  19/18 = e^(5r) . . . . . . . . . . . divide by 18000

  ln(19/18) = 5r . . . . . . . . . . take natural logs

  r = ln(19/18)/5 ≈ 0.0108 = 1.08%

The required interest rate is about 1.08%.

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The percent of the dance team is also on the debate team is 25%.

Number of girls = 9

Number of boys = 3

Total = 9 + 3

= 12

Number of girls in dance team also in debate team = 2

Number of boys in dance team also in debate team = 1

Total = 2 + 1

= 3

percent of the dance team is also on the debate team = 3/12 × 100

= 0.25 × 100

= 25%

Therefore, 25% of the dance team is also on the debate team.

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Answer:

c = 8.6

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]5^{2}[/tex] + [tex]7^{2}[/tex] = [tex]c^{2}[/tex]

25 + 49 = [tex]c^{2}[/tex]

74 = [tex]c^{2}[/tex]

[tex]\sqrt{74}[/tex] = c

8.60232526704 ≈ c

It can be seen that sin20, given that cos0 = 40/41, is 720/1681.

Firstly, we can determine sin0 using the Pythagorean identity:

[tex]sin^20 + cos^20 = 1,[/tex] which gives [tex]sin0 = \sqrt(1 - cos^20) = 9/41.[/tex]

Next, using the double-angle identity

sin2θ = 2sinθcosθ, we find sin20

= 2sin0cos0 = 2 * (9/41) * (40/41)

= 720/1681.

Therefore, sin20, given that cos0 = 40/41, is 720/1681.

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The area of triangle DEF is four times larger than the area of triangle ABC.

We have,

Right triangle ABC was dilated with a scale factor of 2.

When a triangle is dilated with a scale factor of 2, the resulting triangle is enlarged by a factor of 2 in each dimension.

Since area is a two-dimensional measure, it will be enlarged by a factor of the square of the scale factor.

In this case, the scale factor is 2, so the area of triangle DEF will be

=  2²

= 4 times larger than the area of triangle ABC.

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The exact value of the expression sin 585° will be - 1/√2.

Given that:

Expression, sin 585°

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The coterminal angle of angle 585° is calculated as,

⇒ 585° - 360°

⇒ 225°

The value of sin 585° is calculated as,

sin585° = sin225°

sin585° = sin(180° + 45°)

sin585° = - sin45°

sin585° = - 1/√2

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A system of equations that will determine the length l, and the width w, of the garden include the following:

D. 92 = 2L + 2W

   L = 3W + 6

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

Since the length of the garden is 6 feet more than three times the width, we have:

L = 3W + 6

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

92 = 2L + 2W

92 = 2(3W + 6) + 2W

92 = 6W + 12 + 2W

92 = 8W + 12

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The age of the watch when David's father lost it was 13. 3 years.

David found the watch 38 years after his father lost it, and the watch worked for 2 years after it was lost. That means the watch was 40 years old when David found it.

When David found it, the watch was 3 times as old as when his father lost it. This means that :

= Number of years lost / 3

= 40 / 3

= 13. 3 years

In conclusion, the watch was 13. 33 years old when David's father lost it.

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Each student will need to pay $4.8

If 2 out of 50 students lose their phone. we can say 1 out 25 students will lose their phone. That is:

2/50 = 1/25

For a class of 200 students. We have:

students that lose their phone = 1/25 * 200 = 8 students

If each phone costs $120, the total cost of replacing the lost phones will be:

 total cost = 8 * $120 = $960.

If each student pays an equal share of the cost. Thus, each student will need to pay:

pay per student = $960/200 = $4.80.

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Answer:

The answer is D.

Step-by-step explanation:

Answer: The equation of the circle can be rewritten in standard form by completing the square for both x and y terms. The standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

17 + y^2 + 6x = 6y + 63 y^2 - 6y + 6x + 17 = 63 y^2 - 6y + 9 + 6x = 63 + 9 (y - 3)^2 + 6x = 72 (y - 3)^2 + 6(x - (-6)) = 72 (y - 3)^2 + (x + 6)^2 = 72

From this we can see that the center of the circle is (-6,3) and the radius is sqrt(72) = 6sqrt(2).

I’m sorry but I’m unable to draw a graph for you.

The area of the rectangle formed by the set of points are in the order :

Area of ABCD = 50 square units, Area of EFGH = 180 square units, Area of IJKL = 80 square units, Area of MNOP = 60 square units, Area of QRST = 100 square units and Area of UVWX = 300 square units.

Given are set of points which forms a rectangle.

We have to find the area of each rectangle.

A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16)

Find the lengths of adjacent sides, that is AB OR CD and BC or AD.

Using the distance formula,

AB = [tex]\sqrt{(-5--9)^2+(5-8)^2}[/tex] = 5

BC = [tex]\sqrt{(1--5)^2+(13-5)^2}[/tex] = 10

Area of ABCD = 5 × 10 = 50 square units

E(30, 20), F(39, 29), G(49, 19), H(40, 10)

Using the distance formula,

EF = [tex]\sqrt{(39-30)^2+(29-20)^2}[/tex] = √162

FG = [tex]\sqrt{(49-39)^2+(19-29)^2}[/tex] = √200

Area of EFGH = √162 × √200 = 180 square units

I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)

Using the distance formula,

IJ = [tex]\sqrt{(2--6)^2+(2-2)^2}[/tex] = 8

JK = [tex]\sqrt{(2-2)^2+(-8-2)^2}[/tex] = 10

Area of IJKL = 8 × 10 = 80 square units

M(5, 5), N(11, 5), O(11, -5), P(5. -5)

Using the distance formula,

MN = [tex]\sqrt{(11-5)^2+(5-5)^2}[/tex] = 6

NO = [tex]\sqrt{(11-11)^2+(-5-5)^2}[/tex] = 10

Area of MNOP = 6 × 10 = 60 square units

Q(10, 0), R(15, 5), S(25,-5), T(20, -10)

Using the distance formula,

QR = [tex]\sqrt{(15-10)^2+(5-0)^2}[/tex] = √50

RS = [tex]\sqrt{(25-15)^2+(-5-5)^2}[/tex] = √200

Area of QRST = √50 × √200 = 100 square units

U(0, 5), V(15, 20), W(25, 10), X(10, -5)

Using the distance formula,

UV = [tex]\sqrt{(15-0)^2+(20-5)^2}[/tex] = √450

VW = [tex]\sqrt{(25-15)^2+(10-20)^2}[/tex] = √200

Area of UVWX = √450 × √200 = 300 square units

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The statement "The graph of f(x) has exactly two x-intercepts" cannot be true.

Linear functions are an essential part of mathematics that come with distinct properties and characteristics. For instance they always take shape in the form of a straight line when represented on any given graph.

In addition to this feature linear equations exhibit another crucial aspect - they retain an unchanging slope throughout their entire length while possessing an easily identifiable point for where they intersect with the y axis; namely at their corresponding y intercept.

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Answer:

It's C.

Step-by-step explanation:

Edge 2020;)

Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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All the triangles which are all translations of triangle x include the following:

In Mathematics and Geometry, the translation of a geometric figure to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image.

On the other hand, the translation of a geometric figure downward simply means subtracting a digit from the numerical value on the positive y-coordinate (y-axis) of the pre-image.

In conclusion, only triangles A and F are translations of triangle x because they represent a rigid transformation where the size and shape does not change since they have congruent pre-images and images.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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Expansion is the multiplying of each term in the bracket by the expression outside the bracket.  Expansion is also when we multiply to remove the ( ).

How to determine this

Given,

11. [tex](x-8)^{2}[/tex]

By expanding it

= (x-8)(x-8)

Open bracket

= [tex]x^{2} - 8x -8x + 64[/tex]

= [tex]x^{2} - 16x+64[/tex]

Therefore,  [tex](x-8)^{2}[/tex] matches with D. [tex]x^{2} - 16x+64[/tex]

12. (x+6)(x-6)

By expansion

Open bracket

= [tex]x^{2} -6x+6x-36[/tex]

= [tex]x^{2} - 36[/tex]

So, (x+6)(x-6) matches with E. [tex]x^{2} - 36[/tex]

13. (2x-5)(2x+5)

By expanding it

Open bracket

= [tex]4x^{2} +10x -10x-25[/tex]

= [tex]4x^{2} - 25[/tex]

So, (2x-5)(2x+5) matches with H. [tex]4x^{2} - 25[/tex]

14.[tex](3x+1)^{2}[/tex]

Expanding this,

= (3x+1)(3x+1)

Open bracket

= [tex]9x^{2} + 3x +3x+1[/tex]

= [tex]9x^{2} +6x+1[/tex]

Therefore, [tex](3x+1)^{2}[/tex] matches with A. [tex]9x^{2} +6x+1[/tex]

15.[tex](x+4)^{2}[/tex]

By expanding it

= (x+4)(x+4)

Open bracket

= [tex]x^{2} + 4x+4x+16[/tex]

= [tex]x^{2} +8x+16[/tex]

Therefore, [tex](x+4)^{2}[/tex] matches with F. [tex]x^{2} +8x+16[/tex]

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The length of the rope from the person on the ground to the hot air balloon is approximately 173.21 feet.

To solve this problem, we can use trigonometric functions, specifically the tangent function.

Given that the angle of depression is 30 degrees and the height of the hot air balloon is 100 feet, we can set up the following right triangle:

 |\

 |  \

 |    \

 |      \ <-- Angle of depression: 30 degrees

 |        \

 |_____\

   100 ft

Let's assume the length of the rope is represented by 'x'. We want to find the value of 'x'.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, the opposite side is the height of the balloon (100 ft), and the adjacent side is the length of the rope (x).

Therefore, we have:

tan(30°) = 100 ft / x

To find the length of the rope (x), we can rearrange the equation:

x = 100 ft / tan(30°)

Using a calculator or reference table, we can find that tan(30°) is approximately 0.577

x = 100 ft / 0.577

x ≈ 173.21 ft.

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Answer:

1. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x

2. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x

4. To predict how many shares each student's post will be received on Day 3 and Day 10, substitute the respective values of x into each function:

a) On Day 3, Amber's post will have f(3) = 3(4)^3 = 192 shares. On Day 10, Amber's post will have f(10) = 3(4)^10 = 6,291,456 shares.

b) On Day 3, Ben's post will have f(3) = 2(3)^3 = 54 shares. On Day 10, Ben's post will have f(10) = 2(3)^10 = 196,830 shares.

c) On Day 3, Carter's post will have f(3) = 10(2)^3 = 80 shares. On Day 10, Carter's post will have f(10) = 10(2)^10 = 10240 shares.

5. The graph of Amber's post with copies mailed to the assisted living facility will have the same shape and growth rate as the original function, but it will be shifted upwards by 45 units along the y-axis.

6. Ben's post travels the fastest because it has the largest growth rate of 3 (compared to Amber's 4 and Carter's 2), meaning it triples every day.

7. It depends on the specific purpose of the post. If the goal is to have a widespread influence and viral impact, then Amber's approach of starting with a smaller group of initial shares but a higher growth rate might be more effective. On the other hand, if the goal is to create a more tight-knit network of shares with a smaller number of initial friends, then Carter's approach might be more appropriate.

The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

From the question, we have the following parameters that can be used in our computation:

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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Answer:

y = -8

Step-by-step explanation:

2(y-2)- 6y-28 = 0

2y - 4 -6y - 28 = 0

-4y = 32

y = -8

Considering the expression of a line, the price of the guitar in 2011 is $354.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

Being:

the slope can be calculated as:

m= (300 - 246)÷ (2008 - 2005)

m= 54÷ 3

m= 18

Considering point 2 and the slope m, you obtain:

300= 18×2008 + b

300= 36,144 + b

300- 36,144 = b

-35,844 = b

Finally, the equation of the line is Price= 18×Year - 35,844

Now, you want to know the price of the guitar in 2011. Replacing in the linear equation, you get:

Price= 18×2011 - 35,844

Solving:

Price= 36,198- 35,844

Price= 354

In summary, the price of the guitar by 2011 is $354.

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Answer:

  $2496

Step-by-step explanation:

You want to know the cost of carpeting a 18 ft by 24 ft room with carpet that costs $52 per square yard.

The dimensions of the room in yards are (18 ft)/(3 ft/yd) = 6 yd, by (24 ft)/(3 ft/yd) = 8 yd.

In square yards, the area is ...

  (6 yd)(8 yd) = 48 yd²

The cost of one square yard of carpet is $52, so the cost of 48 square yards will be 48 times as much.

  (48 yd²)($52/yd²) = $(48·52) = $2496

The total price to carpet the floor is $2496.

__

Additional comment

We're reluctant to call this the total price, as there are usually additional charges for tax, carpet pad, delivery, installation, removal and disposal of old flooring, and possibly additional materials such as tack strips or thresholds. Repairing mold or water damage, or leveling the floor, can also add cost.

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The value of the missing sides in the parallelogram are x = 3 and y = 6

In other to solve the question posted, we use the law which relates to the sides of a parallelogram which establishes that opposite sides of a parallelogram are of equal length.

This means that the side opposite length of 3 will also be 3 and vice-versa

side x = 3

side y = 6

Therefore, the missing sides of the parallelogram are 3 and 6 for sides x and y respectively.

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Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

Step-by-step explanation:

The exponent you put in the box multiplies the exponent ' 4'    to get the exponent '1'

4 * x = 1

x = 1/4      <====this goes in the box

As mode of the date set is 21, so, the missing number will have to be 21.

In statistic, the mode is the value that appears most often in a set of data values.

To find missing number, we will calculate mode of the given data set. The mode is the value that appears most frequently in the data.

In this case, the mode is 21 as it appears twice while all other numbers appear only once. Since mode is 21, the missing number must also be 21 in order to maintain the mode.

Full question:

The mode of the data set is 21. What is the missing number? 21,17,_,25,23,13

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Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

The fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.

Let's assume the fuel efficiency of the first car is x miles per gallon and the fuel efficiency of the second car is y miles per gallon.

Given that the first car consumed 15 gallons of gas and the second car consumed 25 gallons, we can set up the following equations:

15x + 25y = 1525 -- (Equation 1) (Total miles driven by both cars)

x + y = 75 -- (Equation 2) (Sum of their fuel efficiencies)

To solve this system of equations, we can use substitution or elimination method. Let's solve it using the substitution method:

From Equation 2, we can express y in terms of x:

y = 75 - x

Substituting this value of y into Equation 1:

15x + 25(75 - x) = 1525

Expanding and simplifying:

15x + 1875 - 25x = 1525

-10x = -350

Dividing both sides by -10:

x = 35

Substituting the value of x back into Equation 2 to find y:

y = 75 - x

y = 75 - 35

y = 40

Therefore, the fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.

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