There are 20 students at lunch. One-fifth of the student are in the hall. How many people are in the hall

The 13-foot string is arranged into a rectangle. Let L denote the length of the rectangle,

soldi70 [24.7K]

The expressions for the width, W, and area, A, of the rectangle in terms of L are:

W = $\frac{13}{2}$ - L
A = $\frac{13L - L^{2} }{2}$

The expression for the perimeter of a rectangle is given as:

P = 2(L + W)

where L is its length and W its width

a. Given that the perimeter of the rectangle is 13 feet, then;

13 = 2(L + W)

divide through by 2

$\frac{13}{2}$ = L + W

So that;

W = $\frac{13}{2}$ - L

The required formula for the width as a function of L is: W = $\frac{13}{2}$ - L

b. Area of a rectangle can be expressed as;

A = L * W

substitute the expression for width in that of area to have

A = L * ( $\frac{13}{2}$ - L)

= $\frac{13}{2}$ L - $L^{2}$

A = $\frac{13L - L^{2} }{2}$

The expression for the area A is: A = $\frac{13L - L^{2} }{2}$

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5 0

3 years ago

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

madam [21]

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

<h3>Which statements are true?</h3>

Here we have the quadratic function:

$f(x) = -x^2 - 4x + 5$

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

$f(x) = -x^2 - 4x + 5$

So the vertex is at:

$x = 4/(2*-1) = -2\\$

Then the y-value of the vertex is:

$f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9$

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

If you want to learn more about quadratic functions:

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8 0

2 years ago

A bag contains 8 pieces of paper, each with one of these letters written on it: A, B, C, E, K, L, M, and R. One piece of

Delvig [45]

Answer:

Below.

Step-by-step explanation:

Letter P is drawn - Impossible because there is no paper with P on it.

Letter drawn is a consonant - Likely because there are 6 out of 8 letters which are consonants.

Letter drawn is a vowel - Unlikely because there are only 2 vowels out of 8 letters.

Letter drawn is one of the first ten letters in the alphabet - Equally likely as there is 4 of these out of a total of 8.

Letter is L - Unlikely as there is only 1 piece of paper with L on it.

The paper draw has one letter on it - Certain as there is a letter on all the pieces of paper.

6 0

4 years ago

Read 2 more answers

Help please!!!!! ASAP!!! Only brainliest answer gets points. No wrong answers. Only answer if you know how to do this.

FinnZ [79.3K]

Answer:

The number of pounds of coffee in stock decreased by 9% each hour since the trend began.

There were 40 pounds of coffee in stock when the trend began.

Step-by-step explanation:

p(x)=0.4(.91)^x

= a b^x

where a is the initial value and b = 1-rate of decrease

We know that the number of pounds of coffee will decrease as time goes on.

.4 is the initial value

It is in the hundreds of pound

.4 * 100 = 40 pounds

x is the number of hours

.91 = 1- rate of decrease

Subtract 1 from each side

.91-1 =-rate of decrease

-.09 = -rate of decrease

rate of decrease = .09

rate of decrease = 9 %

That means we keep 91 % of the coffee and sell 9% of the coffee

Lets check the statements:

There were 400 pounds of coffee in stock when the trend began.

False there were 40 pounds when we started

The number of pounds of coffee in stock decreased by 9% each hour since the trend began.

True see above calculations

There were 4000 pounds of coffee in stock when the trend began.

False see above calculations

There were 40 pounds of coffee in stock when the trend began.

True see above calculations

The number of pounds of coffee in stock decreased by 91% each hour since the trend began.

False see above calculations

4 0

3 years ago

The diagonals of a rhombus are 21 m and 32 m. What is the area of the rhombus?<br> 30 POINTS

Wittaler [7]

I have included attachment below

so since a rhombus is 2 pairs of paralell sides, we can cut it into 4 triangles
we can see that we can take the bottom 2 triangles and put them on top to get a rectangle that is width 21 and height 32/2 (16=height
area of rectangle=legnth times width=16 times 21=336 m^2

answer is 336 m^2

5 0

3 years ago