Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (hint: assume that the central point of each arc is its corresponding vertex. ).

−26am^2 + 26am + 37a

(a) The height after t years is given by

h(t) = 0.6t² + 3t + 11

(b) The shrubs are 38 centimetres tall when they are sold.

The growth rate of the shrubs during the first year of growth can be determined by setting t = 1 in the given differential equation dh/dt = 1.2t + 3. This gives us dh/dt = 1.2(1) + 3 = 4.2 centimeters per year.

Therefore, during the first year of growth, the shrubs will grow at a rate of 4.2 centimeters per year. This rate of growth is expected to increase as the shrubs age and reach the end of the 5-year growth period before they are sold by the nursery.

(a) To find the height after t years, we integrate the growth rate function with respect to t:

∫dh/dt dt = ∫(1.2t + 3) dt

h(t) = 0.6t² + 3t + 11

(b) The shrubs are sold after 5 years, so we plug in t = 5 into the function we found in part (a):

h(5) = 0.6(5)² + 3(5) + 11

= 38 cm

Therefore, the shrubs are 38 centimetres tall when they are sold.

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The expression for its distance d (measured in feet) from the intersection t seconds later is d = x + 79200 t (feet)

Since the balloon is moving due east, we only need to consider its horizontal motion, ignoring its vertical motion at a constant altitude of 95 feet.

Let's call the initial distance of the balloon from the intersection x. The distance of the balloon from the intersection t seconds later can be found using the formula for distance traveled at a constant speed:

d = x + vt

where v is the speed of the balloon (15 miles per hour) and t is the time elapsed (in hours). To convert the speed from miles per hour to feet per second, we can multiply by the conversion factor of 5280 feet per mile:

d = x + (15 miles/hour) * (5280 feet/mile) * (t hours)

d = x + (15 * 5280) t feet

d = x + 79200 t feet

So the expression for the distance of the balloon from the intersection t seconds later is:

d = x + 79200 t (feet)

Note: In this expression, x represents the initial distance of the balloon from the intersection, which is unknown.

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Answer:

c) [tex]10x<7z[/tex]

Step-by-step explanation:

[tex]5x<3y \implies 10x<6y \\ \\ \therefore 10x<6y<7z \implies 10x<7z[/tex]

Check the picture below.

so the triangles are similar by AA.

[tex]\cfrac{GI}{10}~~ = ~~\cfrac{15}{12}\implies \cfrac{GI}{10}~~ = ~~\cfrac{5}{4}\implies 4GI=50\implies GI=\cfrac{50}{4}\implies GI=12.5[/tex]

Answer:

Q(x) = 15x^2 + x - 2.

Step-by-step explanation:

To find the height of the water in a pool when both hoses are on, we need to add the values of the two functions, F(x) and P(x), at a given x value. The new function, Q(x), that determines the height of the water in the pool can be expressed as follows:

Q(x) = F(x) + P(x) = 9x^2 + 3x - 5 + 6x^2 - 2x + 3 = 15x^2 + x - 2

So the height of the water in the pool is determined by the function Q(x) = 15x^2 + x - 2.

The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.

The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need  to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.

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Answer: A) Dashed line with shading below

Step-by-step explanation:

because, as you can see the < sign is only less than not 'less than and equal to' so it will be dashed...

Answer:

A

Step-by-step explanation:

A dashed line is used if < or > is used to indicate that the boundary is not part of the solution. Then shade the appropriate region.

As in the question, y is less than 4/3x + 2 therefore, the region below the line is shaded.

Answer:

[tex]x > 7[/tex]

Step-by-step explanation:

Given the inequality

[tex]x+4 > 11[/tex]

Lets solve the inequality for [tex]x[/tex].

Subtract [tex]4[/tex] from both sides of the inequality.

[tex]x > 11-4[/tex]

Evaluate [tex]11-4[/tex].

[tex]x > 7[/tex]

[tex]x[/tex] is greater than 7

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On solving the provided question, we can say that  In decimals r = 3.8799 and d = 7.7598

Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.

A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.

the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.

Area  = πr²

47.25 = 3.14 × r × r

r × r = 15.0541401274

In decimals

r = 3.8799

d = 7.7598

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The amount of interest paid will be $396.6.

The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.

Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.

The simple interest will be calculated as:-

SI = ( P x R x T ) / 100

SI = ( 1100 x 9 x 4 ) / 100

SI = 39600 / 100

SI = $396

Therefore, $396 will be paid in interest.

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Answer:

Below

Step-by-step explanation:

(2x+15) / ( 3x+15)  =  11/14    cross multiply to get

28x + 210 = 33x + 165

45 = 5x

x = 9       so the larger number is   3 X 9 = 27  

                       (smaller number is 2 x 9 = 18)

7/12 can be written as a mixed number as follows:

7/12 = 7 ÷ 12/12 = 0 and 7/12.

So 7/12 can be expressed as "zero and seven twelfths" or simply "seven twelfths."

Answer: Let's call the number of hours it takes for Rayna and Desi to build the fence together as "h". During this time, Rayna will build 10h feet of fence line, and Desi will build 2h feet of fence line.

Together, they will build 10h + 2h = 12h feet of fence line in h hours.

To build 80 feet of fence line, they will need h hours such that:

12h = 80

So,

h = 80 / 12 = 6.67 hours

So it will take Rayna and Desi 6.67 hours to build 80 feet of fence line together.

Step-by-step explanation:

Answer:

f-g= 3x²+1-(1-x)

3x²+1-1+x

3x²+x=0

x(3x+1)=O

x=0, 3x+1=0

So, x=0 or -1/3

Answer:

The set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}

Step-by-step explanation:

Set builder notation is a way of expressing a set of elements in mathematical terms. The syntax of set builder notation is {x | <condition>}, where x represents an element in the set and the condition specifies the properties that the element must satisfy to be included in the set.

In this case, the set consists of all numbers less than 17 and greater than or equal to -8. The condition for the set is -8 <= x < 17, where x is a real number. This means that x must be greater than or equal to -8 and less than 17 in order to be included in the set.

Therefore, the set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}.

➡ There are 22 hundredths. That is enough to make a tenth.

What is the arithmetic operations?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional  operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find the total volume of the slime, we need to add 1.5 and 0.72:

1.5 + 0.72 = 2.22

There are 22 hundredths, which is enough to make a tenth.

Hence, the answer is:

➡ There are 22 hundredths. That is enough to make a tenth.

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Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

Step-by-step explanation:

Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.

First, let's find P(A):

P(A) = 0.3

Next, let's find P(B|A):

P(B|A) = (3/10) * (3/10) = 9/100

Finally, let's find P(A and B):

P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027

So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

Let's assume the width of the rectangular pool is w. According to the problem, the length of the pool is 12 feet shorter than the width, so the length can be represented as w - 12.

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the pool is 640 square feet, so we can set up the equation:

A = L x W

640 = (w - 12) x w

Simplifying the equation:

640 = [tex]w^{2}[/tex] - 12w

[tex]w^{2}[/tex] - 12w - 640 = 0

We can solve for w by using the quadratic formula:

w = [-(-12) ± [tex]\sqrt{-12}^{2}[/tex]- 4(1)(-640))] / (2 x 1)

w = [12 ± [tex]\sqrt{(12^{2}+2560)[/tex]] / 2

w = [12 ± [tex]\sqrt{2596}[/tex]] / 2

w = [12 ± 51] / 2

We can ignore the negative solution, so:

w = (12 + 51) / 2

w = 31.5

Therefore, the width of the pool is 31.5 feet. We can use this value to find the length:

L = w - 12

L = 31.5 - 12

L = 19.5

Therefore, the length of the pool is 19.5 feet.

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The equation for the function graphed is g(x) = -1/4(x + 2)^2 -  1

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

f(x) = x^2

First the function is reflected across the x-axis

This gives

f'(x) = -x^2

Next,  the function is stretched vertically by 4

Using the above as a guide, we have the following:

f'(x) = -1/4(x)^2

Lastly the function is translated 2 units left and 1 units dows

This is represented as

g(x) = -1/4(x + 2)^2 -  1

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The Total Surface Area for given prism will be 166 [tex]cm^2[/tex].

The entire surface area of a rectangular prism may be computed by adding the areas of its six sides. A rectangular prism's surface area may be determined using the following formula:

[tex]Surface Area = 2(l*w) + 2(l*h) + 2(w*h)[/tex]

where:

l = length of the rectangular prism

w = width of the rectangular prism

h = height of the rectangular prism

Using this formula for given problem,

Given,

l=5cm

w=4cm

h=7cm

[tex]\text{Total Surface area}=2.(5.7)+2.(4.5)+2.(4.7)\\\\=70+40+56\\\\=166\;cm^2[/tex]

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The length of

KL = 7.8units

LM = 7.1 units

MN = 8.5 units

NK = 7.8units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

KL = √1-(-4)²+3-(-3))²

KL = √5²+6²

KL = √ 25+36

KL = √ 61 = 7.8 units

To find the length KN

KN = √ 1-7)²+ 3(-2)²

KN = √ 6²+5²

KN = √ 36+ 25

KN = √ 61 = 7.8 units

to find LM

LM = √-4-1)²+-3(-8)²

LM = √25+25

LM = √50

LM = 7.1 units

to find MN

√ 7-1)²+ -2-(-8)²

MN= √ 6²+6²

MN = √ 36+36

MN=√ 72

MN = 8.5 units

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sum of two complementary angle is 180•

[tex]180 - 49 = y = 131[/tex]

B) h = 38p

An equation represents a proportional relationship if the ratio of the dependent variable to the independent variable is constant. In this equation, h is directly proportional to p, meaning that if p increases, h increases, and if p decreases, h decreases. The constant of proportionality is 38.

In other words, the equation h = 38p can be written as h/p = 38, which shows that the ratio of h to p is always equal to 38. This means that the equation represents a proportional relationship.

The other equations listed do not represent a proportional relationship because the ratio of the dependent variable to the independent variable is not constant. For example, in equation A, h is not directly proportional to p because the constant of proportionality changes as p changes. In equation C, h and p are inversely proportional because h decreases as p increases, and h increases as p decrease. And in equation D, the equation is not in the form of a proportion because there is an additional constant term on the right-hand side.

Answer:

(-4, -1)

Step-by-step explanation:

The system has one solution

Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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For the information provided the x- and y-components of the vector are 1.5 km and 2.6 km, respectively.

To find the x- and y-components of the vector, we can use trigonometry.

The x-component of vector is given by:

d_x = d × cos(θ)

where d is the magnitude of the vector and θ is the angle between the vector and the x-axis.

In this case, d = 3.0 km and θ = 60 degrees (since the vector is 30 degrees to the left of the y-axis).

So, d_x = 3.0 km × cos(60°) = 1.5 km.

The y-component of vector is given by:

d_y = d × sin(θ)

In this case, d_y = 3.0 km × sin(60°) = 2.6 km.

Expressing the answer using two significant figures gives:

d_x = 1.5 km, d_y = 2.6 km.

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Horizontal lines have a slope of zero, since the "rise" is; zero.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.

If the slope has a value of zero, the line is horizontal, neither increases nor decreases.

Therefore,

Horizontal lines always have an equation of the form; y = a

Vertical lines always have an equation of the form; x = b

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Answer:

15^4

Step-by-step explanation:

An exponent refers to the number of times a number is multiplied by itself,

so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.

[tex]15^{4} .[/tex]

When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].

As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:

[tex]15^{4} .[/tex]