Can someone help me out with this?

Answers

Answer 1

Answer:

9) obtuse 10) isosceles

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Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a depth of 4 in., how many cubic yards of dirt does he need? If dirt costs $25 per yd3, how much will the project cost? (Hint: 1yd3=27 ft3).

Answers

Find the volume of the rectangular prism.

V = lwh

V = (9)(16)(4)

V = 756 ft^3

Convert to cubic yards:

1 ft^3 = 0.037037037 yd^3

756 * 0.037037037 = 28

So there are 28 cubic yards of dirt he needs.

Multiply this to 25 to find the total cost of the dirt:

28 * 25 = 700

So the project will cost $700

A school wishes to enclose its rectangular playground using 480 meters of fencing.Suppose that a side length (in meters) of the playground is , as shown below.

(a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x.

(b) What side length x gives the maximum area that the playground can have?

(c) What is the maximum area that the playground can have?

Answers

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\nL=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\nW=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\nW=(240-x)\ m$

substitute

$A=x(240-x)\nA=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

Final answer:

The width of the playground is 120 meters, the side length that gives the maximum area is 120 meters, and the maximum area the playground can have is 14400 square meters.

Explanation:

(a) Let's assume the width of the rectangle is x meters. Since the playground is rectangular and has two equal sides, the length will also be x meters. The perimeter of the rectangle, which is also the amount of fencing needed, is given as 480 meters. This can be expressed as: 2(length + width) = 480. Using this equation, we can solve for the width: 2(x + x) = 480 ⇒ 4x = 480 ⇒ x = 480/4 = 120. Therefore, the width of the playground is 120 meters.

(b) To find the side length that gives the maximum area, we can use calculus. The area function is A(x) = x * x = x^2. To find the maximum of this function, we can take the derivative and set it equal to zero: dA/dx = 2x = 0 ⇒ x = 0. So, x = 0 is a critical point, but since we are dealing with a physical situation where the length cannot be zero, we disregard this critical point. Thus, x = 120 is the value that gives the maximum area.

(c) Now that we know the side length, we can calculate the maximum area. Plugging in x = 120 into the area function, we find: A(120) = 120 * 120 = 14400 square meters. Therefore, the maximum area the playground can have is 14400 square meters.

Learn more about Area of a rectangle here:

brainly.com/question/15218510

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What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)?
0
-8

Answers

Answer:

Step-by-step explanation:

The given function is $f(x)=-(x-3)(x+11)$ .

We expand to get:

$f(x)=-x^2-8x+33$

We complete the square to obtain the vertex form as follows:

$f(x)=-(x^2+8x)+33$

$f(x)=-(x^2+8x+16)--16+33$

$f(x)=-(x^2+8x+16)+16+33$

$f(x)=-(x+4)^2+49$

This function is now of the form:

$f(x)=a(x-h)+k$ , where (h,k)=(-4,49) is the vertex.

The y-value of the vertex is therefore 49

a community bike ride offers a short 5.7 mile ride for children and families. the short ride is followed by a long ride, 5 2/3 times as long as the short ride, for adults. if a woman bikes the short ride with her children, and then the long ride with friends. how many miles does she ride together?

Answers

38 miles

Further explanation

Given:

A community bike ride offers a short 5.7-mile ride for children and families.

The short ride is followed by a long ride, 5²/₃ times as long as the short ride, for adults.

A woman bikes the short ride with her children, and then the long ride with friends.

Question:

How many miles does she ride together?

The Process:

Let us make a pattern for the short ride:

$\boxed{5.7} \rightarrow in \ miles$

Let us do a multiplication on a fraction at first.

$\boxed{ \ = (2)/(3) * 5.7 \ }$

$\boxed{ \ = (2)/(3) * 5(7)/(10) \ }$

$\boxed{ \ = (2)/(3) * (57)/(10) \ }$

We crossed out 3 and 57.

$\boxed{ \ = 2 * (19)/(10) \ }$

$\boxed{\boxed{ \ = 3.8 \ }}$

Then we make a pattern for the long ride, 5²/₃ (five and two third) times as long as the short ride:

$\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{5.7}\boxed{3.8} \rightarrow in \ miles$

A woman bikes the short ride with her children, and then the long ride with friends. Let's calculate how many miles does she ride together.

The short ride: $\boxed{5.7 \ miles}$
The long ride: $\boxed{(5.7 * 5) + 3.8 = 28.5 + 3.8 = 32.3 \ miles}$

$\boxed{ \ 5.7 + 32.3 = 38}$

Thus, she rides 38 miles together.

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Keywords: A community bike ride, offers, a short 5.7-mile ride, for children and families, followed by, 5 2/3 times, for adults, a woman, with friends, how many miles, she ride together

First multiply 5.7 by 5 2/3 to figure out how long the adult ride is: 5.7/1 X 17/3= 32.3. Then add the adult ride and the children's ride together: 5.7+32.3=38 (7+3=10 which adds 1 to the whole number). The mom would ride 38 miles :)

Mia has a rectangle clothShe dips 5/8 of it in blue dye
She dips 9/20 in yellow
The part of the cloth that is dipped in both colours turns green.
Work out the fraction of cloth that turns green.
plz show working

Answers

Answer:

Fraction of cloth that turns green = $(3)/(40)$

Step-by-step explanation:

Let total cloth be of length = 1 unit

Given $(5)/(8)$ of it is dipped in blue dye.

Fraction which is not dipped in blue is given as:

⇒ $1-(5)/(8)$

Taking LCD to subtract fractions.

⇒ $(8)/(8)-(5)/(8)$

⇒ $(3)/(8)$

She dips $(9)/(20)$ in yellow.

Comparing the fraction dipped in yellow which is $(9)/(20)$ and fraction which is not dipped in blue i.e. $(3)/(8)$

$(9)/(20),(3)/(8)$

Taking LCD between 8 and 20 = 40

We have:

$(9* 2)/(20* 2),(3* 5)/(8* 5)$

$(18)/(40),(15)/(40)$

Thus, we can say $(9)/(20)>(3)/(8)$

Since $(9)/(20)>(3)/(8)$ , so the part dipped in yellow will also cover some part which is blue.

Thus, fraction dipped in yellow and blue which turns green will be given as:

⇒ $(9)/(20)-(3)/(8)$

Subtracting by taking LCD =40.

⇒ $(9* 2)/(20* 2)-(3* 5)/(8* 5)$

⇒ $(18)/(40)-(15)/(40)$

⇒ $(3)/(40)$ (Answer)

HELP ME FAST PLEASE, PLEASE

Answers

Vcone=(1/3)hpir^2
base=diameter=2rdaius=6
diameter/2=3=radius
height=9.2

Vcone=(1/3)(9.2)pi(3^2)
Vcone=9.2pi3
vcone=27.6pi cm^3
aprox pi=3.141592
vcone=86.707 cm^3

round
86.7 cm^3

Vcone=(1/3)hpir^2

base=diameter=2rdaius=6

diameter/2=3=radius

height=9.2

Vcone=(1/3)(9.2)pi(3^2)

Vcone=9.2pi3

vcone=27.6pi cm^3

aprox pi=3.141592

vcone=86.707 cm^3

round

86.7 cm^3

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