A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 83 m long and 62 m wide.
Find the area of the training field. Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answer:

x = - 2 or x = - 4

Step-by-step explanation:

Via completing the square:

x^2 + 6x + 8  = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8

                     = (x + 3)^2 - 3^2 + 8

                     = (x + 3)^2 - 9 + 8

                     = (x + 3)^2 - 1

Since x^2+6x+8=0,

(x + 3)^2 - 1 = 0

(x + 3)^2 = 1

x + 3 = +- sqrt(1)

x + 3 = +- 1

x + 3 = 1 or x + 3 = -1

x = -2 or x = -4

Answer:

The bottle that costs R59,99 for 375 g is cheaper

Step-by-step explanation:

The given costs of the bottles of honey are given as follows;

The cost of one of the bottles of honey = R89,99 for 530 g

The cost of the other bottle of honey = R59,99 for 357 g

Let 'x' represents the bottle of honey that costs R89,99 and let 'y' represent the bottle of honey that costs R59,99, we have;

The unit cost (cost per gram) for the bottle of honey, 'x', C/gₓ = R89,99/(530 g) ≈ R 0.16979/g

The unit cost (cost per gram) for the bottle of honey, 'y', [tex]C/g_y[/tex] = R59,99/(357 g) ≈ R 0.168/g

Given that the unit cost of a bottle 'y' ≈ R 0.168/g is less than the unit cost of a bottle of 'x' ≈ R 016979/g, a bottle 'y' is cheaper than the bottle 'x'

Therefore;

The bottle that costs R59,99 for 375 g is cheaper than the bottle that costs R89,99 for 530 g.

The graph of the following equation will be a Parabola. The y=1 will be the line of symmetry.

Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.

A set of points in a plane that are equally spaced apart from a directrix or focus are known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.

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Answer:9

Step-by-step explanation:beacuse if you take 6 by 9 and 10 it will make 2 of 69

6.666666666666666 (6.6 repeating, I just don’t know how to use the sign online)

I multiplied 3 1/3 by 2

Those are vertical angles so both sides need to be equal.

2x+15 = 145

Subtract 15 from both sides:

2x = 130

Divide both sides by 2:

x = 65

Answer:

145 = 2x + 15

2x = 130

x = 65

145 and 2x + 15 are vertical angles and therefore congruent.

Answer: 32

Step-by-step explanation:              90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

The time taken to complete the rest questions is 32 minutes

Since Yan has already finished Three-fifths of the 45 math problems he was assigned today. The number remaining will be:

= 45 - (3/5 × 45)

= 45 - 27

= 18

Now, the time taken to complete the rest questions will be:

= 18 × 1 4/5

= 18 × 1.80

= 32.4

= 32 minutes.

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Answer:

SAS

Step-by-step explanation:

Answer:

k= -1/3

Step-by-step explanation:

hope this helps :)

Rotation of PQRS by 90 degree.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?

Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.

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Answer:

  1/2log₂(a-1) -log₂(9)

Step-by-step explanation:

You want the expanded form of log₂(√(a-1)/9).

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The rules are applicable for any base.

  [tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]

Answer:

sin(T)

cos(C)

Step-by-step explanation:

sine goes up or down for angles in the circle.

cosine goes left or right for angles in the circle.

consider a circle with is center at T, and it goes through C (so, the radius is 25 = TC).

then 7 = sin(T)×25

24 = cos(T)×25

so, sin(T) = 7/25

then, sin(T) = cos(90-T)

and the angle at C = 90-T.

therefore, cos(C)=sin(T)=7/25

tan(x) = sin(x)/cos(x)

and that would lead here always to a 7/24 or 24/7 ratio.

so, no tan function is right.

y=-2x-5 and y=-7x+15.75 are equations in  slope-intercept form for each line.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We need to find equation in slope-intercept form of line passing through of (-6,7) to (1,-7) and one more line passing through (1.25,7) to (3.25,-7)

Slope of line with (-6,7) to (1,-7) is m=-7-7/1+6=-14/7

=-2

y intercept we have to find

7=-2(-6)+b

7=12+b

-5=b

So slope intercept form of line passing through (-6,7) to (1,-7) is y=-2x-5

Now Slope of line with (1.25,7) to (3.25,-7) is

m=-7-7/3.25-1.25

m=-14/2=-7

y intercept we have to find

7=-7(1.25)+b

7=-8.75+b

b=15.75

So slope intercept form of line passing through (1.25,7) to (3.25,-7) is y=-7x+15.75

Hence, y=-2x-5 and y=-7x+15.75 are equations in  slope-intercept form for each line.

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Answer:

Step-by-step explanation:

6+2= 8

8×2.54= 20.32

The slope of the line is 20.

The slope represents the rate of change in the price per hour is $20.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Two coordinates from the graph.

(1, 60) and (3, 100)

Slope.

= (100 - 60) / (3 - 1)

= 40 / 2

= 20

The slope represents the rate of change in the price per hour.

Thus,

The value of the slope is 20.

The slope denotes that the rate of charge per hour is $20.

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Answer:

311 cm squared

Step-by-step explanation:

Formulas/things to know:

area of circle = pi times r^2

diameter = r * 2

pi = 3.14159

r = radius

__________________________________________________________

CIRCLE 1:

diameter 36, radius = 36/2 = 18

area of circle = pi times 18^2

3.14159 times 324

= 1017.87601976

CIRCLE 2:

diameter 30, radius = 30/2 = 15

area of circle = pi times 15^2

3.14159 times 225

= 706.858347058

__________________________________________________________

Great, now we can calculate the difference between the areas!

1017.87601976 - 706.858347058

= 311.017672702

and then round to the nearest square centimeter: 311

answer: 311 cm squared

note: make sure to round at the end, not after calculating area for the most accurate result! :) Hope this helped

Answer:

50.26548246 or 50.3 mm^2 (rounded to the tenth)

Step-by-step explanation:

[tex]\pi 8^{2} = 201.0619298[/tex]

just divide that # by 4 and you get the answer! Hope this helps!

The polynomial in terms of its simplest factors is (x + 3)(x − 6)

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

x2 − 3x − 18.

Rewrite as

x² − 3x − 18

Expand

x² − 3x − 18 = x² − 6x + 3x − 18

Factorize the expression

This gives

x² − 3x − 18 = x(x − 6) + 3(x − 6)

Factor out x - 6

x² − 3x − 18 = (x + 3)(x − 6)

Hence, the expression is (x + 3)(x − 6)

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The fraction after solving and simplifying the mixed fraction 5 3/4 ÷ 1 1/2​ is 23 / 6.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.

Given:

5 3/4 ÷ 1 1/2​

Solve the mixed fraction into improper fractions as shown below,

5 × 4 + 3 / 4 ÷ 1 × 2 + 1 / 2

20 + 3 / 4 ÷ 2 + 1 / 2

23 / 4 ÷ 3 / 2

23 / 4 × 2 / 3

23 × 2 / 4 × 3

On simplifying,  

23 × 1 / 2 × 3

23 / 6

Thus, the value is 23 / 6.

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Answer:

68, 97, 81, 96, 84.2

Step-by-step explanation:

16. The minimum of the data is the smallest value. Take the smallest stem value and find its smallest leaf value, you'll get 68.

17. Take the largest stem value and find its largest leaf value. That's 97.

18. Counting the number of values, there are 10 values here. So you need to look at the mean of the 5th and 6th values. (80 + 82) ÷ 2 = 81

19. Mode: the most frequently occurring value. All values in this dataset are unique except for the two 96s in the last row, hence 96 is the mode.

20. Add all values and divide your result by the number of values.

(68+75+77+79+80+82+92+96+96+97) ÷ 10 = 84.2

Hence 84.2 is your mean.

Answer:

55cm^2

Step-by-step explanation:

Split into 2 parts, the rectangle on the left, and triangle on the right.

Rectangle:

8 cm x 5 cm = 40 cm^2

Triangle

14 cm - 8 cm = 6cm (Height)

(5cm(base) x 6cm)/2 = 15cm ^2

15cm^2 + 40cm^2 = 55cm^2

Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

140° is an exterior angle of the triangle , then

∠ B + 90° = 140° ( subtract 90° from both sides )

∠ B = 50°

∠ ACB and ∠ DCB are a linear pair and sum to 180° , that is

∠ ACB + 140° = 180° ( subtract 140° from both sides )

∠ ACB = 40°

Answer:

C

Step-by-step explanation:

Hope this helpssss

Answer:

(-1,0)

Step-by-step explanation:

To find the x value of the vertex use the equation

-b/(2a)

-4/(2*2)= -1

this means that the x coordinate is -1

Now that we know the x value we need to find the corresponding y value

to do this we just plug in x into the equation

2(-1)²+4(-1)+2

2-4+2=0

put it all together and get (-1,0)

Answer:

-3/5

Step-by-step explanation:

from 1st point to second, you go down 3, right 5

Answer:

B

Step-by-step explanation:

This is a neat question

f(x) - g(x) = 2x           Add g(x) to both sides

f(x) = g(x) + 2x

Now you need the right hand side to have 20 added to g(x).

2x must = 20

2x = 20                    Divide by 2

x = 20/2

x = 10

So the answer must be x = 10