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The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.

The given quadratic function is f(x) = 2(x - 3)² + 4.

We need to find the key features of the given quadratic function.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.

Now, the key features of the given quadratic function as follows:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (3, 4)

Focus: (3, 33/8)

Axis of Symmetry: x=3

Directrix: y=31/8

Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.

Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.

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By using Heron's formula and standard formula for the area of a triangle, the area of the composite figure is 921006.497 square meters.

In this problem we must determine the area of a composite figure, which consists in subtracting the area of an isosceles triangle from the area of the equilateral triangle:

Big triangle

The area of the big triangle is determined by Heron's formula:

s = [3 · (520 m)] / 2

s = 780 m

A = √[(780 m) · (1560 m - 520 m)³]

A ≈936693.077 m²

Small triangle

H = (520 m) · sin 60°

H ≈ 450.333 m

h = 450.333 m - 390 m

h = 60.333 m

A = 0.5 · (520 m) · (60.333 m)

A = 15686.580 m²

Then, the area of the composite figure is 921006.497 square meters.

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Answer:

Step-by-step explanation:

if we consider mod then the negative turns to positive and positive remains positive so it will be

279 < 282 which is l279l < l-282l

Answer:

23%

Step-by-step explanation:

39.36-32=7.36

7.36/32=.23

23 percent

Answer:

they should produce 225 software programs and 225 video games per week.

Step-by-step explanation:

limit 450

there are 2 factors the software and video games.

450•2= 225

Answer:

4

Step-by-step explanation:

you do cross multiplication

you do 3x12÷9

Answer: 1. [-8, 8]

2. [-27, 27]

Step-by-step explanation:

1. |X|≤8

x≤8 or x>=-8

-8<=x<=8 ==> [-8, 8]

2. |X|≤27

x≤27 or x>=-27

-27<=x<=27 ==> [-27, 27]

Answer:

see image.

Step-by-step explanation:

Basically, what's happening here is you are adjusting one of the terms so that they both have the same exponent. Then you can factor out that 10^11 term and just add the two remaining terms.

see image.

Answer:

The coordinates of W,X,Y,Z are W= (3,4) X= (1,4) Y= (2,1) Z= (4,2)

Step-by-step explanation:

When you reflect the coordinates to the other side of the graph, you get these^^^^ coordinates.

Answer:

£8.22

Step-by-step explanation:

9x33=£297

297-24.40=£272.60

297×4%=£11.88

297+11.88=£308.88

24.40×15%=£3.66

24.40+3.66=£28.06

308.88-28.06=280.82

280.82-272.60=£8.22

Answer:

17,84,9,34,71,35,18

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

going straight across the line we can see that for $140 the demand in thousands 60

so

you can buy 60,000 units

Answer:

60 because oficial the line goes to 60

Answer:

9.25x

Step-by-step explanation:

Lindsay Bedford should embroider 73 caps.

Let us assume the number of number of caps needed to be embroidered for desired earning be x. Now, forming the equation to solve for x, thus, finding the required number of caps.

Equation -

6.50*8 + 0.45*x = 85

Now solving this equation for the value of x.

Performing multiplication of numbers on Left Hand Side

52 + 0.45x = 85

Shifting the product from Left Hand Side to Right Hand Side

0.45x = 85 - 52

Performing subtraction on  Right Hand Side to find the value of x

0.45x = 33

Shifting 0.45 to denominator on  Right Hand Side

x = 33÷0.45

Performing division to find the value of x

x = 73.3

The number of caps can not be in fraction. So, we will round off the digit to find exact number of caps.

Number of caps = 73

Therefore, Lindsay Bedford needs to embroider 73 caps.

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The complete question is -

Lindsay Bedford works at a baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders. How many caps must she embroider to earn at least $85 in an 8-hour day?

Answer:

n/10 x 10/60,000

Step-by-step explanation:

I think it's right please don't report

Answer:

N/10 x 10/60,000

Solving for the variable gives f = 100 - 2h/5

Subject of formula can be defined as the variable that is expressed in terms of other variables in a given expression, function of equation.

It is the variable worked out in an equation and left to stand on its own on one side of the equality sign

Given the equation;

5f+2h = 100

To make 'f' the subject of formula, we take the following steps;

Take '2' over the equality sign

5f = 100 - 2h

Now, let's make 'f' the subject by dividing both sides by its coefficient which is 5

We have;

5f/5 = 100 - 2h/5

Divide through

f = 100 - 2h/5

Thus, solving for the variable gives f = 100 - 2h/5

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Answer:

positive the answer is 3

Step-by-step explanation:

The length of the base will be equal to 65.99 centimeters.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The formula for the Pythagorean theorem is given below:-

H² = B² + P²

Given that in a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg.

P = 70/ 3 cm

H = 70 cm

The value of the leg will be calculated as:-

H² = B² + P²

70² = B² + (70/3)²

B² = 70² -  (70/3)²

B = √4355

B = 65.99 cm

Therefore, the length of the base will be equal to 65.99 centimeters.

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Answer:

What is 80% of 63?

50.4 is the right answer

Step-by-step explanation:

just draw what I have done

Answer:

$8.60

Step-by-step explanation:

Let x = the tip

80 - x = 9(5.85 + 1.25) + 5(1.50)

80 -x = 63.90 + 7.5

80 - x = 71.40  Subtract 80 from both sides

-x = -8.60  Divide both sides by -1

x = 8.60

The length with scale factor to form quadrilateral 1/2, A'B' is √5 units when AB is √20.

The formula to find the distance between the two points is usually given by

d=√((x2 – x1)² + (y2 – y1)²).

Given :

Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.

Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).

So, the points of the quadrilateral ABCD becomes:

So,  length of A'B'

AB = √(4-0) ² +(2 -4)²

AB = √16 + 4

AB = √20

AB = 2√5

A'B' = 1/2 AB

A'B' = √5

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Answer:

Let first angle be x

x+x+6+x-12=180°

3x-6=180°

3x=186

x=63°

First angle=63°

Second Angle=69°

Third angle=51°

Hope it helps you

Answer:1.75

Step-by-step explanation:

7x+8=3x+15

4x+8=15

4x=7

x=1.75

$72 is 4.5% of 6.25 amount. 6.25 Percentage of  72 is 4.5.

By considering the given information

[tex]72\times x=4.5\\x=\frac{4.5}{72}\times 100\\ x=6.25[/tex]

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. percent, which is a relative value used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

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$72 is 4.5% = $3.24

Solution :

The percentage is a rate or proportion per hundred,

The percentage is also used more generally to mean any proportion, as in Studies have shown that a large percentage of people love cute animals.

A percent is one one-hundredth (1/100) of something. The percentage refers to the rate or proportion of that one hundred. Usually, you will see the word percentage used in math equations or statistics or when someone is measuring the increase and decrease in rates

$72 is 4.5% =?

$72  is 10% = $7.2

$72 is 5% = $7.2 /2 = $3.6

$72 is 1/2%= $72 * .5/100 = $.72*.5 = $ 0.36

$72 is 4.5% = 5% - .5% = $3.6- $.36 = $3.24

$72 is 4.5% = $3.24

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Answer:

  angle 5

Step-by-step explanation:

Given transversal x crossing lines y and z and angles numbered 1 to 8, you want the number of the angle that is an alternate interior angle to angle 4.

In this context, "alternate" mean the angles are on opposite sides of the transversal. "Interior" means the angles are between the lines the transversal crosses.

The term "alternate interior angles" is used to refer to angles that have their vertices at the intersection points where the two lines cross the transversal. (It excludes angles that have the same vertex, or do not share a side.)

The angle that is an alternate interior angle relative to angle 4 is angle 5.

Answer:

10

Step-by-step explanation:

(21-1)/2