A rectangle's width is 6 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
A. A(1)=1²-61
B. A(7)=7w
c. A(1)=12+61
D.A(7)=1-6

The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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Answer:

y = -3/2x + 13

Step-by-step explanation:

(6,4) and (2,10)

Slope:

m=(y2-y1)/(x2-x1)

m=(10-4)/(2-6)

m=6/(-4)

m =  -3/2

Point-slope intercept:

y - y1 = m(x - x1)

y - 4 = -3/2(x - 6)

y - 4 = -3/2x + 9

y = -3/2x + 13

The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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c

12 mph • 20 hrs = 240 miles

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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Answer:

4x < -8

you will need to isolate the variable to be by itself by performing the inverse property of multiplication which is division;

/4      /4(divide by 4 from both sides)

x < -2

9514 1404 393

Answer:

  4041 m²

Step-by-step explanation:

The area is the sum of the areas of the circle and the central rectangle.

  A = πr² + LW

  A = (3.14)(18 m)² + (36 m)(84 m) = 1017.36 m² +3024 m²

  A = 4041.36 m²

The field covers about 4041 square meters.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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Answer:

Step-by-step explanation:

Answer:

the answer id d.

Step-by-step explanation:

Answer:

I think it's A !maybe it is maybe not

Check the picture below.

Answer:

l and n

Step-by-step explanation:

Answer:

345,000,000 =3.45 x 10^8

Step-by-step explanation:

To convert a number to scientific notation, place or move the decimal point of a number until the coefficient of the number is greater than 1 and less than 10. This is Jordan mistake, 34.5 is greater than 10. Which is incorrect!

explanation:

you have 345,000,000

Keep moving the dot till you have 3.45

Then count how many spaces you've moved

To get to 3.45, it took you 8 moves so you would have 3.45*10^8 as your answer

Answer:

35

Step-by-step explanation:

Answer:

Step-by-step explanation:

both are prime. so multiply each other to find the common denominator. 5x7 is 35. 10/35 plus 21/35 is 31/35 which cannot be reduced any further so yes

Answer:

62.5 square miles

Step-by-step explanation:

if the scale is 1 in. = 5 mi, then 1 square in. = 25 square miles

so if 1 in^2 = 25 mi^2

then you make a proportion

25/1 = x/2.5

(the square inches on the bottom and the square miles on top)

solving for x gives you

x=62.5 square miles

Answer:

a. 14:8

b. 6:14

Step-by-step explanation:

all books on the shelf = 6+8=14

a. 14:8

b. 6:14

The value given for "8th grade Participate in Sports" is 0.22, which is the least value among all the categories in the table.

A number can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. Frequently, proportions, rates, and changes throughout time are expressed using percentages.

Based on the table provided, it appears that the category with the least portion is "8th grade Sports participators" with a value of 0.22.

For "6th grade Sports participators", the value is 3/20, which is equivalent to 0.15, and for "7th grade Sports participators", the value is 18%, which is equivalent to 0.18.

For "Other school activities" category, the least value is 0.45 for "7th grade Other school activities" and the highest value is 33% for "6th grade Other school activities". Therefore, "8th grade Sports participators" has the least portion among all the categories in the given table.

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Answer:

Product is   6x³ - 37x² + 53x + 8

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Since x = 3 since we are given that f(3) = 16, x = 3.

The equation is:

\(f(x) = x^{2} + 2x + 1\)

and x = 3, we can easily sustitute x with 3. When we do so, our equation will look like:

\(f(3) = 3^{2} + 2(3) + 1\)

Now, we will solve.

3^2 is = 9

2(3) = 6

Now, we will plug into the equation:

\(f(3) = 9 + 6 + 1\)

Combine like terms (constants)

\(f(3) = 16\)

Answer:

Step-by-step explanation:

Slope intercept form of a line is

y=mx+b, where m=slope and b=y intercept

m=(y2-y1)/(x2-x1) I chose points (0,3) and (4,4) from graph so

m=(4-3)/(4-0)=1/4 so now the line is

y=x/4+b, using point (4,4) we can solve for b

4=4/4+b

4=1+b

b=3 so the line is

y=x/4+3 or more neatly

y=(x+12)/4

402.12÷0.01 per cubic inch is written as \(40212 inch^{-3\) οr \(2.4538868 \times109 m^{-3\)

Imperial units and US custοmary units bοth use the cubic inch as a measure οf capacity. The capacity οf a cube, which is equal tο 1/231 οf a US gallοn, has three lengths that are each οne inch lοng.

Given,

402.12÷0.01 per cubic inch

We can write the equatiοn as

40212 per cubic inch

Or \(40212/ inch{^3\)

Or, \(40212 inch^{-3\)

We knοw that 1 inch 0.0254 m

Then we can write the equatiοn as 2.4538868 × 109 m-3

Hence the cοrrect answer is \(40212 inch^{-3\) οr \(2.4538868 \times 109 m-3\)

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Answer:

the perimeter is the sum of all known sides of the square, so the formula will be P= l + l + l + l, asuming l is the lenght of each side

area of the square is A = l x l

Answer:

y=2/3x+7

Step-by-step explanation:

y-y1=m(x-x1)

y-11=2/3(x-6)

y=2/3x-12/3+11

y=2/3x-4+11

y=2/3x+7

Answer: \((-1, 4)\)

Step-by-step explanation:

Do not have time

Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.

For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.

-b/2a = -4/(2(2)) = -1

Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.

h(-1) = 2(-1)^2 + 4(-1) - 10 = -12

So, the vertex is at (-1,-12)

Answer:

20.943951023932 m^3

Step-by-step explanation:

v=1/3pi(r)^2h

v=1/3pi(2)^2(5)

v=20.943951023932 m^3

Answer:

62.8

Step-by-step explanation:

2 × 2 × 3.14 × 5 = 62.8