The dimensions of a rectangular prism are given in the net shown. 7 in. x4 . 3 in. 5 in. 3 in.x 4 5 in. What is the total surface area of the rectangular prism in square inches? 71 in 2​

a) The value of y₂ is 1 for the direct proportionality case.

b) The value of y₂ is 5.76 for the inverse proportionality case.

Proportionality represents a family of relationships between two variables, which can be linear and nonlinear. Direct proportionality represents a linear relationship, whereas inverse proportionality represents a kind of nonlinear relationship.

Here are two mathematical representations of the relationships described above:

[tex]y \propto x[/tex]

[tex]\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}[/tex]   (1)

[tex]y \propto \frac{1}{x}[/tex]

[tex]\frac{y_{2}}{y_{1}} = \frac{x_{1}}{x_{2}}[/tex]   (2)

If we know that x₁ = 6, x₂ = 2.5, y₁ = 2.4, then the value of y₂ for each case are, respectively:

y₂ = 2.4 × (2.5/6)

y₂ = 1

y₂ = 2.4 × (6/2.5)

y₂ = 5.76

To learn more on proportions, we kindly invite to check this verified question: https://brainly.com/question/2548537

Step-by-step explanation:

1.

a. true

b. false (the arc angles are relative to the center of the circle)

c. true (as the central angle of a circle is twice any inscribed angle subtended by the same arc)

d. true (but note that the arc angle of YE is again measured via the center of the circle and twice as large as the angle S)

2.

EGS is an isoceles triangle (that means both legs are equally long).

remember the extended Pythagoras for general triangles :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C.

let's say c is our long baseline, since we have is opposite angle 124°, and a = b = GE = GS, we have

3.8² = a² + a² - 2aa×cos(124) = 2a² - 2a²×cos(124) =

= 2a²(1 - cos(124))

2a² = 3.8²/(1 - cos(124))

a² = 3.8²/(2(1 - cos(124)))

a = GS = sqrt(3.8²/(2(1 - cos(124)))) =

= 2.151883096... ≈ 2.2 cm

3.

circumference

16pi = 2pi×r

r = 8

area = pi×r² = pi×8² = 64pi

yes, the statement is true.

4.

a half-circle has 180°.

the arc angel AD is a full half-circle (because AD is a diameter), so it is 180°.

the angle ACB is the arc angle AB = 40°. so, the arc angle BD must be the rest of the 180° = 180 - 40 = 140°.

5.

diameter = 50 ft.

so, the radius or distance from the center to the circle arc is 50/2 = 25 ft.

the length of a chord is

c = 2×sqrt(r² - d²)

with r being the radius, d being the distance of the chord from the center.

40 = 2×sqrt(25² - d²)

20 = sqrt(625 - d²)

400 = 625 - d²

-225 = -d²

225 = d²

d = 15 cm

so, the distance of the chord from the center is 15 cm.

6.

the arc angles RE and TS are equal. that means the arc lengths of RE and TS are equal.

and that means the arc lengths of RS and ET are equal. the chords between 2 points on a circle must have the same length, when the arc lengths between these 2 points are the same.

7.

they are equally long.

as we saw in 5., the length of a chord depends on the radius of the circle and the distance of the chord from the center.

since both chords are in the same circle (with the same radius), and they both have the same distance from the center, they can only be equally long, as there is no other element to name them different.

8.

the angle NPE is half of the angle NAE (= the arc angle NE).

the arc angle NE = 63×2 = 126°

the angle PET is half of the angle PAT (= the arc angle PT).

the arc angle PT = 19×2 = 38°

the arcs NP and ET cover the rest of the whole circle circumference (360°).

so, arc angle NP + arc angle ET = 360 - 38 - 126 = 196°

but arc angles NP and ET must be equal (as per the problem definition).

therefore, 2 equal arc angles = 196°

1 arc angle = NP = 196/2 = 98°

Answer:

3/16

Step-by-step explanation:

3/8 / 2 = 3/16

Therefore you and your friend will each get 3/16.

Answer:B

Step-by-step explanation:I hope it help

Answer:

Step-by-step explanation:

Let me see if I understand what you mean. Do you mean can you have 153 dollars in your pocket when all you have is 5 dollar bills?

If that is what you mean, then no that isn't possible. You can get 150 dollars or you can get 155 dollars, but you can't get 153.

In order to do the problem, using only 5 dollar bills, the number you choose must end in 0 or 5. If it ends in anything else, the task is impossible.

Answer:

[tex]a_{16}=26.5[/tex]

Step-by-step explanation:

Arithmetic series:  [tex]a_n=a+(n-1)d[/tex]

Sum of arithmetic series:  [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

(where a is the first term and d is the common difference)

Given:

[tex]\implies a_{25}=44.5[/tex]

[tex]\implies a+(25-1)d=44.5[/tex]

[tex]\implies a+24d=44.5[/tex]

[tex]\implies S_{30}=765[/tex]

[tex]\implies \dfrac{30}{2}[2a+(30-1)d]=765[/tex]

[tex]\implies 30a+435d=765[/tex]

Rewrite [tex]a+24d=44.5[/tex] to make a the subject:

[tex]\implies a=44.5-24d[/tex]

Substitute found expression for a into [tex]30a+435d=765[/tex] and solve for d:

[tex]\implies 30(44.5-24d)+435d=765[/tex]

[tex]\implies 1335-285d=765[/tex]

[tex]\implies 285d=570[/tex]

[tex]\implies d=2[/tex]

Substitute found value of d into [tex]a=44.5-24d[/tex] and solve for a:

[tex]\implies a=44.5-24(2)=-3.5[/tex]

Therefore:

[tex]\implies a_{16}=-3.5+(16-1)2=26.5[/tex]

Answer:

0.8 meters

Step-by-step explanation:

1 decimeter is 0.1 meters

so,

[tex]\frac{1}{0.1} = \frac{8}{x}\\x = 8*0.1\\x = 0.8[/tex]

Answer:

x=85/5

x= 17

y=95/5

y=19

Step-by-step explanation:

vertically opp angles are equal

Answer:

vertical angles here make an X

1. 5y and 95 are vertical

2. 5x and 85 are vertical

3. x = 17

4. y = 19

.

Step-by-step explanation:

angles MPL and NPO are equal

5x = 85

x = 17

angles MPN and LPO are equal

5y = 95

y = 19

Answer:

Pi is the number you get from dividing the circumfrence by the diameter of a perfect circle. It is important because without this, we wouldnt have perfect circles and even wheels could be disformed and cause crashes.

Answer:

Pi is an infinite number. We need it to find the area and circumference of a circle.

Step-by-step explanation:

area square= side²

= (x-6)²

= x²-12x+36

Answer:

36

Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36

Answer: 224

Step-by-step explanation:

on the white boards

Answer:

i did it

Step-by-step explanation:

Answer:

20-x

Step-by-step explanation:

you need the value of x to answer

Answer:

182

Step-by-step explanation:

We need to find 3/4 of 242.  To do this, multiply 3/4 by 242:

[tex]\sf \implies \dfrac34 \times 242=\dfrac34 \times \dfrac{242}{1}=\dfrac{3 \times 242}{4 \times 1}=\dfrac{726}{4}=181.5[/tex]

181.5 rounded is 182.

Therefore, approximately 182 students went on the field trip.

Answer:

1.28 in³

Step-by-step explanation:

Volume of Amy's cone

Volume of Don's bowl

Difference

Answer:

So obviously in the context of this question you are meant to find the volume. Since Don's bowl already has a given value of 5 cubic inches we will use that same unit when calculating amy's ice cream cone volume.

Step-by-step explanation:

You are given that amy has a cone and need to find the volume. The formula for the volume of a cone is (V=πr^2*h/3).

π = pi or 3.14......

r = radius (in this case the opening/ diameter of the ice cream cone is given as 2 inches and the radius is half of diameter so d/2 = r (r=1)

h = height (in this case it is given that height is 6 inches)

Remember all variable units must be kept the same so in this case all units are inches.

Now Plug in and solve V = [tex]3.14*(1)^{2} *\frac{(6)}{3}[/tex]

Remember order of operations / PEMDAS (in this case, do exponent first then just multiply from left to right and at the end divide that number by 3.

V= 6.28 cubic inches (since all our units were inches and we are finding cubic volume of a cone)

Now Amy volume of cone - Don volume of bowl = your answer. 6.28-5 = 1.28 cubic inches

Answer: $13.55 per shirt

Step-by-step explanation:

3 for $40.65

you must first divide 40.65 by 3 to find the cost of 1 shirt which the answer is $13.55. I hope this helps! Have a good day! :)

Since we are given the price of 3 shirts, we can work backwards to do $40.65 divided by 3 to get the unit cost per shirt, in which we get $13.55.

Glad to help!

I'd appreciate if you marked this as brainliest, if not I understand :)

Answer:

[tex]\implies (x-1)^2+(y-3)^2=10[/tex]

Step-by-step explanation:

End points of the diameter of the circle are:

[tex](-2,\:4) \implies x_1= -2, \: y_1= 4[/tex]

[tex](4,\:2) \implies x_2= 4, \: y_2= 2[/tex]

Equation of circle in diameter form is given as:

[tex](x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0[/tex]

Plugging in the values of [tex]x_1, \: y_1,\:x_2, \: y_2[/tex] in the above equation, we find:

[tex][x-(-2)](x-4)+(y-4)(y-2)=0[/tex]

[tex]\implies (x+2)(x-4)+(y-4)(y-2)=0[/tex]

[tex]\implies x^2-2x-8+y^2-6y+8=0[/tex]

[tex]\implies x^2-2x+1-9+y^2-6y+9-1=0[/tex]

[tex]\implies (x^2-2x+1)-9+(y^2-6y+9)-1=0[/tex]

[tex]\implies (x-1)^2+(y-3)^2-10=0[/tex]

[tex]\implies (x-1)^2+(y-3)^2=10[/tex]

This is the required equation of circle in standard form.

Answer:

all numbers except √34

Step-by-step explanation:

the top three are whole numbers and therefore rational

Answer:

D, n=16b

Step-by-step explanation:

There are 16 busses, each of which can hold 16 seats. There are n of those busses.

Therefore, 16*n = the total number of seats on the busses altogether.

Answer:

0

Step-by-step explanation:

since (x + 7) is a factor (aka. a multiple of) (x + 7) that means there cannot be a remainder. h(x) = n(x+7) , n being any whole number

for example

2(x+7) would be a factor of (x+7) and 2(x+7)/(x+7) = 2 will not leave a remainder

Step-by-step explanation:

I am always available to help, post your worry

The lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.

All the expenduture and charges charged by a lander and other parties is called the closing cost.

A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000.  Thus, the estimate closing cost is,

[tex]C_{ec}=\dfrac{3.75}{100}\times120000\\C_{ec}=4500[/tex]

The actual closing costs are listed below.  

The total annual cost is,

[tex]C= $300 +$600 +$1,250 +$550 +$525 +$125 +$2,000\\C=4800[/tex]

Total annual cost is $300 more than the estimate closing cost. In the percentage form,

[tex]p=\dfrac{4800-4500}{4500}\times100\\p=6.66\%[/tex]

Thus, the lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.

Learn more about the closing cost here;

https://brainly.com/question/20108287

Answer:

Its D trust me

I got it right from the other person

Answer:

Hello Camila Sofia Pazos Motta, you have to divide by pi, not 3.

Step-by-step explanation:

Answer:

Hope it helps you.

Answer:

D

Step-by-step explanation:

The equation is 4πr²

The radius is half the diameter so divide the diameter by 2

40÷2=20

4π(20)²=5026.55mm

Rounds to 5027

Answer:

27.7% of third year girls study biology

Answer

Who is your school?

Who is your class?

Who is the chapter

Answer:

1)  [tex]y=x^2+2[/tex]

2)  [tex]y=x^2-4[/tex]

3)  [tex]y=x^2[/tex]

4)  [tex]y=x^2+6x+14[/tex]

Step-by-step explanation:

Question 1

Given points:  (-2, 6)  (-1, 3)  (0, 2)  (1, 3)

This is likely to be a quadratic equation with a vertex of (0, 2) since the points (-1, 3) and (1, 3) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+2[/tex]

[tex]\implies y=ax^2+2[/tex]

To find a, input one of the points into the equation:

[tex](1, 3)\implies a(1)^2+2=3\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2+2[/tex]

Question 2

If the parabola intersects the x-axis at (-2, 0) and (2, 0) then

[tex]y=a(x+2)(x-2)[/tex]

We are told that the y-intercepts if (0, -4).  Input this into the equation to find a:

[tex]\implies a(0+2)(0-2)=-4[/tex]

[tex]\implies -4a=-4[/tex]

[tex]\implies a=1[/tex]

Therefore,

[tex]\implies y=(x+2)(x-2)[/tex]

[tex]\implies y=x^2-4[/tex]

Question 3

Given points: (-2, 4)  (-1, 1)  (0, 0)  (1, 1)

This is likely to be a quadratic equation with a vertex of (0, 0) since the points (-1, 1) and (1, 1) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+0[/tex]

[tex]\implies y=ax^2[/tex]

To find a, input one of the points into the equation:

[tex](-2,4)\implies a(-2)^2=4\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2[/tex]

Question 4

[tex]f(x) = x^2 + 5[/tex]

If we wish to move the function to the left by 3 units, we substitute x for [tex]x+3[/tex]:

[tex]\begin{aligned}\implies f(x+3) & =(x+3)^2+5\\ & = x^2+6x+9+5\\ & = x^2+6x+14\end{aligned}[/tex]

[tex]\implies y=(x+3)^2+5[/tex]

Answer:

a) Team C - lowest average/mean

b) Team A - greatest variability/range

Step-by-step explanation:

Hope this helps!