please answer dont just do this for points >:(

Given:

Perimeter of a football field = 920 feet.

The width is 60 feet more than one-third of the length.

To find:

The dimensions of a football field.

Solution:

Let the length of the field be x.

Then, width = [tex]\dfrac{1}{3}x+60[/tex]

We know that,

[tex]Perimeter = 2( length + width)[/tex]

[tex]920 = 2(x+\dfrac{1}{3}x+60)[/tex]

[tex]920 = 2(\dfrac{4}{3}x+60)[/tex]

[tex]920 =\dfrac{8}{3}x+120[/tex]

Subtract both sides by 120.

[tex]920-120 =\dfrac{8}{3}x+120-120[/tex]

[tex]800 =\dfrac{8}{3}x[/tex]

Multiply both sides by 3.

[tex]2400 =8x[/tex]

Divide both sides by 8.

[tex]300 =x[/tex]

Now,

[tex]Length = 300\text{ feet}[/tex]

[tex]Width=\dfrac{1}{3}(300)+60[/tex]

[tex]Width=100+60[/tex]

[tex]Width=160\text{ feet}[/tex]

Therefore, the length and width of the football field are 300 feet and 160 feet respectively.

Answer: a + b = 40

[tex](3+\sqrt{5})(7-6\sqrt{5})=3.7+7\sqrt{5}-3.6\sqrt{5}-6\sqrt{5}.\sqrt{5}\\\\=21+6.5-11\sqrt{5}\\\\=51-11\sqrt{5}[/tex]

because [tex](3+\sqrt{5})(7-6\sqrt{5})=a+b\sqrt{5}[/tex]

=> a = 51

    b = -11

=> a + b = 51 -11 =40

Step-by-step explanation:

Answer:

[tex]a = -9 - 11\sqrt{5} - \sqrt{5}b[/tex]

a = 51

b= -11

Answer:

0.094

Step-by-step explanation:

I hope this helps!

Answer:

61

Step-by-step explanation:

nth=5n+1

.: 12th=5(12)+1 =60+1

=61

Answer:

d = - 1/5

Step-by-step explanation:

slope form: m= y2-y1/x2-x1

m= -5-(-7)/-6-4

m= 2/-10

m= - 1/5

Answer:

[tex]\huge\boxed{-32a^2b+7a^2+3b^2-35ab-a+40b+3}[/tex]

Step-by-step explanation:

[tex]7b(2a^2+5a-7)\qquad|\text{use the distributive property}\\\\=(7b)(2a^2)+(7b)(5a)+(7b)(-7)=14a^2b+35ab-49b\\\\\\(7a^2-a+3)-3b(6a^2-b+3)\qquad|\text{use the distributive property}\\\\=7a^2-a+3+(-3b)(6a^2)+(-3b)(-b)+(-3b)(3)\\\\=7a^2-a+3-18a^2b+3b^2-9b[/tex]

Substraction

[tex](7a^2-a+3-18a^2b+3b^2-9b)-(14a^2b+35ab-49b)\\\\=7a^2-a+3-18a^2b+3b^2-9b-14a^2b-35ab+49b\\\\\text{combine like terms}\\\\=(-18a^2b-14a^2b)+7a^2+3b^2-35ab-a+(-9b+49b)+3\\\\=-32a^2b+7a^2+3b^2-35ab-a+40b+3[/tex]

Answer:

I hope I helped :)

Step-by-step explanation:

a. The y-intercept represents b. (y = mx + b) also b is 20 because that's where the line touches the y-axis.

b. The slope represents Sam's monthly fee.

c. Sam's monthly fee is 0.4 or 2/5

d. Every 50 minutes is $20.

Answer:

C' (4,-6)

Step-by-step explanation:

Any point being reflected over the x-axis will undergo the following transformation:

(x, y) --> (x, -y)

(4, 6) --> (4, -6)

The coordinates of C',

C(4,6) → C'(4, -6).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Quadrilateral ABCD has coordinates A(-2,0), B(0,4), C(4,6), and D(2,2).

If it is reflected over the x-axis,

The reflection rule:

(x, y) → (x, -y)

The coordinates of C',

C(4,6) → C'(4, -6).

Therefore, the image point of C is C'(4, -6).

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Answer:

m:number that is multiplied on x  b:the y-intercept

Step-by-step explanation:

In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".

In the equation y = mx + b, m represents slope and b represents y intercept.

In the equation y = mx + b, the variables "m" and "b" represent coefficients or constants. Specifically:

"m" represents the slope of the line. It determines the steepness or inclination of the line.

The slope indicates how much y (the dependent variable) changes for each unit change in x (the independent variable).

"b" represents the y-intercept of the line. It is the value of y when x is equal to zero.

The y-intercept is the point where the line intersects the y-axis.

m and b define the equation of a straight line in slope-intercept form, where "m" is the slope and "b" is the y-intercept.

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Answer:

5x+3x=8x

8x = 32

x=32/8 = 4

boys are 4 x 5 = 20

girls are 4 x 3 = 12

Step-by-step explanation:

Add the ratios together: 5 + 3 = 8

Divide total students by 8:

32 / 8 = 4

Multiply each ratio by 4 to find the number of each:

Boys = 4 x 5 = 20

Girls = 3 x 4 = 12

There are 20 boys.

Answer:

1/5

Step-by-step explanation:

A metre is 100cm, thus

20cm/100cm= 1/5

The solution of inequality 3x + 12 – 6x ≤ –9 will be greater than or equal to 7.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3x + 12 – 6x ≤ –9

Simplify the equation, then the value of 'x' is calculated as,

3x + 12 – 6x ≤ –9

6x – 3x ≥ 12 + 9

3x ≥ 21

x ≥ 21 / 3

x ≥ 7

The solution of inequality 3x + 12 – 6x ≤ –9 will be greater than or equal to 7.

The solution is shown on the number line.

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Answer:

B

Step-by-step explanation:

I just took the test

Answer:

A.

Step-by-step explanation:

Answer:

Adults =193

children=52

Step-by-step explanation:

Step one:

let the number of tickets adults be x

and the number of tickets children be y

x+y=245--------1

6.5x+3y=1410.5---2

Step two:

solve the system of equation using substitution

x+y=245

x=245-y

put x=245-y in equation 2 we have

6.5(245-y)+3y=1410.5

1592.5-6.5y+3y=1410.5

-6y+3y=1410.5-1592.5

-3.5y=-182

y=182/3.5

y=52

put y=52 in x=245-y

x=245-52

x=193

Answer:

A, B, and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

True!!

Answer:

Step-by-step explanation:

Given ratio of boys and girls in the class =7:5

No of boys is 8more than the girls

So

Let no of boys in the class =7x

No of girls in the class=5x

7x=5x+8

2x=8

X=8/2

X=4.

Total strength =no of boys + no of girls

=7x+5x

=7×4+5×4

= 28+20

=48.

Total strength in the class is 48.

Answer:

Total class strength = 48

Step-by-step explanation:

Boys : Girls = 7 : 5

Number of boys  = 7x

Number of girls = 5x

7x - 5x = 8

      2x = 8      

       x = 8/2

       x = 4

Total strength = 7x + 5x = 12x = 12*4  = 48

Answer:

99<x<315

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

edg. 2021

Answer:

a

Step-by-step explanation:

just did it and got right

The required value of the trigonometric operator tan(π/12) = 2 -√3. None of them is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operation.

Let,

= [tex]tan(\pi /12) = tan((3-2)\pi /12)[/tex]
[tex]= tan[(3\pi -2\pi )/12]\\=tan(3\pi /2-2\pi /12)\\=tan(\pi /4-\pi /6)\\=\frac{tan(\pi/4)-tan(\pi/6)}{1+tan(\pi/4)tan(\pi/6)}[/tex]
= [tex]\frac{1-1/\sqrt{3} }{1+1*1/\sqrt{3} } \\[/tex]
[tex]=\frac{(\sqrt{3}-1)/\sqrt{3}}{(\sqrt{3}+1))/\sqrt{3}}[/tex]
[tex]=\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}\\=\frac{(\sqrt{3}-1)(\sqrt{3}+1)}{(\sqrt{3}+1)(\sqrt{3}+1)}\\=\frac{(3-2\sqrt{3}+1)}{(3-1)}\\\\=\frac{(4-2\sqrt{3})}{(2)}\\={(2-\sqrt{3})}\\[/tex]


Thus, the required value of the trigonometric operator tan(π/12) = 2 -√3. None of them is correct.

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Answer:

4 days

Step-by-step explanation:

because Mariana drank 2 pints a day 8 pints are in a gallon so 8 ÷ 2 = 4

Answer:

2

Step-by-step explanation:

Given:

The interval, x = -2 to x = 0.

Required:

Average rate of change from x = -2 to x = 0.

SOLUTION:

From the graph,

If x = -2, f(-2) = 0.

If x = 0, f(0) = 4

Average rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]

Where,

[tex] a = -2, f(a) = 0 [/tex]

[tex] b = 0, f(b) = 4 [/tex]

Plug in the values into the formula:

[tex] = \frac{4 - 0}{0 -(-2)} [/tex]

[tex] = \frac{4}{2} = 2 [/tex]

Average rate of change from x = -2 to x = 0 is 2.

Answer:

√33

Step-by-step explanation:

In the image .

The expression (6 + √3) (6 - √3) / √33 upon  rationalizing the denominator gives √33.

Square root of a number is the value such that upon multiplying the value by itself twice gives the original number.

The given expression is (6 + √3) (6 - √3) / √33

We have the identity,

(a + b) (a - b) = a² - b²

∴ (6 + √3) (6 - √3) / 33 = 6² - (√3)² / √33

                                     = (36 - 3) / √33

                                     = 33 /√33

Multiplying numerator and denominator by √33,

(6 + √3) (6 - √3) / 33 = (33 × √33)  / (√33 × √33)

                                   = 33√33 / 33

                                   = √33

Hence upon rationalizing the denominator in the expression (6 + √3) (6 - √3) / 33 yields √33.

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Answer:

A.) -5

Step-by-step explanation:

Slope Formula --->     [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]       m = slope

[tex]m = \frac{2 - (-3)}{-2 - (-1)}[/tex]

Eliminate negatives:

[tex]m = \frac{2 + 3}{ -2 + 1}[/tex]

Solve:

[tex]m = \frac{5}{-1}[/tex]

Simplify:

[tex]m = -5[/tex]

Answer:

Even

Step-by-step explanation:

Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  [tex](-1, 4), (0,4), (2,5), (3,-6), (-1, 7)[/tex]

ii) [tex](-1, 4), (0,4), (2,5), (3,-6), (0, 7)[/tex]

iii) [tex](-1, 4), (0,4), (2,5), (3,-6), (2, 7)[/tex]

iv) [tex](-1, 4), (0,4), (2,5), (3,-6), (3, 7)[/tex]

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  [tex](-1, 4), (0,4), (2,5), (3,-6), (-1, 7)[/tex]

ii) [tex](-1, 4), (0,4), (2,5), (3,-6), (0, 7)[/tex]

iii) [tex](-1, 4), (0,4), (2,5), (3,-6), (2, 7)[/tex]

iv) [tex](-1, 4), (0,4), (2,5), (3,-6), (3, 7)[/tex]

i think true because 0,4 on there is correct and so is 2,0

Answer:

67

Step-by-step explanation:

2b+9r

2(2)+9(7)

4+63

67

Answer:

67

Step-by-step explanation:

2(2)+9(7)

4+63=67

Have a great day

Answer:

51t^3

Step-by-step explanation:

64+3=67

67 +(-16)=51

t^2 +t= t^3

now you just add them up but they cant be combined because one is a number and the other a variable w an exponent so we just get 51t^3