Can someone help it’s a little confusing


Orange traffic cones comes in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone
that has a height of 2 feet and a diameter of 16 inches. Round your answer to the nearest tenth. Use 3.14
for a.

The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Learn more about rationalization here;

https://brainly.com/question/14261303

#SPJ1

Find answers to the questions in the attached file.

Learn more about area of a regular hexagon: brainly.com/question/1601601

#SPJ1

The value of k is[tex](3\sqrt{ 10})/2[/tex]

Given:

x-y=k.............(eq i)

2x²+y²-15..............(eq ii)

We would make y the subject formula in eq ii

2x²+y²-15= 0

2x² + y²= 15

y²= 15-2x²

y= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)

Substitute the value of y into eq i

x-([tex]\sqrt{15-2x^2}[/tex]= k

x- ([tex]\sqrt{15} - 2x[/tex]= k

k= [tex](3\sqrt{ 10})/2[/tex]

Read more about simultaneous equations here:

https://brainly.com/question/16863577

#SPJ1

For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E,  the ground speed of the plane and its direction is mathematically given as

Generally, the equation for the velocity of the plane is mathematically given as

[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]

Therefore

Vp=530cos45i+530sin45j

Vp= 374.76i+374.76j

For wind speed

Vm=80cos(90+30)i+80sin(90+30)j

Vm=-40i+69.28j

Hence, there resultant is

Vr=Vm +Vp

Vr=374.76i+374.76j + 40i+69.28j

Vr=334.77i+1444.05j

In conclusion, the Ground speed is

[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]

Vg=556.10km/hr

Direction

[tex]Tan \theta=\frac{444.05}{334.77}[/tex]

[tex]\theta=52.99East[/tex]

Read more about Arithmetic

https://brainly.com/question/22568180

#SPJ1

Answer:

37.5°, 52.5°

Step-by-step explanation:

Let the two angles be 5x and 7x

Total ratio= 5+7 =12

5x = (5/12) ×90° ( sum of complementary angles = 90°)

= (5/2)×15°

75/2= 37.5°

Similarly

7x = (7/2)×15°

=105/2= 52.5°

37.5°+52.5°=90° (sum of complementary angles= 90°)

[tex]\text{Let the number be x,}\\\\~~~~~~~~x+64\leq 36\\\\\implies x \leq 36 - 64\\\\\implies x \leq -28[/tex]

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]

The arrangement of the rose plants on the triangular plot is such that they

form a series or progression that is defined.

The number of rows on Bill's plot is; 8 rows

The given parameters for the triangular plot are;

Number of plants at the corner = 1 plant

Number of additional plants per row = 6 plants

Number of rose plants = 150 rose plants

The number of rows in the plot.

The difference between successive rows, d = 6

The number rose at the top vertex, a = 1

Therefore, the rose in the garden forms an arithmetic progression

The first term, a = 1

The common difference, d = 6

The number of rows Bill's plot will have, n is given by the sum of n in terms of

an arithmetic progression, Sn, is given as follows;

[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]

When Sn = 150, we get;

[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]

150 = 3·n² - 2·n

3·n² - 2·n - 150 = 0

Taking only the positive solution for n, we have;

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]

[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]

The number of rows Bill's plot has, n ≈ 7.3965

Given that the 7th row is completed, an 8th row will be present on Bill's plot

The number of rows Bill's plot will have = 8 rows

To learn more about the arithmetic progression visit:

https://brainly.com/question/6561461

#SPJ1

Answer:

26

Step-by-step explanation:

You would add the 3 numbers and then minus that from 100

Answer:

the Area = 100in^2

Step-by-step explanation:

pls mark brainiest

Area of triangle is 10 square cm.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Given

Base = 4

Height = 5

Area of triangle = [tex]\frac{1}{2}[/tex] × b × h

=  [tex]\frac{1}{2}[/tex] × 4 × 5

= 2 × 5

= 10

Hence, area of triangle is 10 square cm.

Learn more about area of triangle here

https://brainly.com/question/19305981

#SPJ2

The height of the mountain estimated by two students is 2,467.98 meters.

The height of the mountain is calculated as follows;

tanα = h/( a + b + x)

where;

tan37 = h/(1850 + 740 + x)

tan37 = h/(2590 + x)

h = tan37(2590 + x)

h =1,951.82 +  0.7536x  ---- (1)

tanβ = h/(b + x)

tan60 = h/(740 + x)

h = tan60(740 + x)

h = 1,281.68 + 1.732x ---- (2)

Solve (1) and (2) together

1,951.82 +  0.7536x = 1,281.68 + 1.732x

1,951.82  -  1,281.68 = 1.732x  -  0.7536x

670.14 = 0.9784x

x = 684.93 m

h = 1,281.68 + 1.732x

h = 1,281.68 + 1.732(684.93)

h = 2,467.98 m

Thus, the height of the mountain estimated by two students is 2,467.98 meters.

Learn more about angle of elevation here: https://brainly.com/question/88158

#SPJ1

Height be h

[tex]\\ \rm\Rrightarrow tan\Theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \rm\Rrightarrow tan54=\dfrac{h}{60}[/tex]

[tex]\\ \rm\Rrightarrow h=60tan54[/tex]

[tex]\\ \rm\Rrightarrow h=82.6\approx 83m[/tex]

Answer:

83 m  (nearest metre)

Step-by-step explanation:

This can be modeled as a right triangle, where the base is 60 m and the height is the height of the building.

Alternate Interior Angles Theorem (Z-angles)

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Using the Alternate Interior Angles theorem, the angle between the ground and the dashed line (angle of elevation) is 54°.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula and solving for h:

[tex]\implies \sf \tan(54^{\circ})=\dfrac{h}{60}[/tex]

[tex]\implies \sf h=60 \tan(54^{\circ})[/tex]

[tex]\implies \sf h=82.58291523...[/tex]

[tex]\implies \sf h=83\:\:m\:(nearest\:metre)[/tex]

Answer:

83.08

Step-by-step explanation:

this means that they want only two numbers after the decimal point

if the number is up to five round it up and call it one the add it to the number before it

hope it helps

83.08 is the correct notation of 83.07718 to two decimal places.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To write a number correctly to two decimal places, you need to look at the third decimal place digit.

If this digit is 5 or greater than 5, you will need to round up the second decimal place digit by adding 1 to it.

If this digit is less than 5, you simply leave the second decimal place digit as it is.

In the case of 83.07718, the third decimal place digit is 7, which is greater than 5. Therefore, we need to round up the second decimal place digit (7) by adding 1 to it, resulting in 83.08. This is the number written correctly in two decimal places.

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ2

Answer:

A. -1/8 x + 3/16

Step-by-step explanation:

Distribute -1/2 over the parentheses

-1/2 ( 1/4 x - 3/8 )

-1/2 (1/4 x) - 1/2 (-3/8 )

multiply fractions to simplify

-1/8 x + 3/16

A is correct

Answer:

Step-by-step explanation:

  base = b = 7  km

  altitude or height = h = 3.8 km

     [tex]\sf \boxed{\text{\bf Area of triangle =$\dfrac{1}{2}b*h$ }}[/tex]

                                    [tex]= \dfrac{1}{2}*7*3.8\\\\= 7 * 1.9\\\\= 13.3 \ km^2[/tex]

     length = l = 8.2 cm

     width  = w = 7 cm

      [tex]\sf \boxed{\text{\bf Area of rectangle = l*w}}[/tex]

                                        = 8.2 * 7

                                        = 57.4 cm²

            base = b = 9.1 km

           height = h = 5 km

[tex]\sf \boxed{\text{\bf Area of parallellogram =b*h}}[/tex]

                                          = 9.1 * 5

                                          = 45.5 km²

           Parallel sides a = 8.9 m  & b =  2.7 m

           height = h = 4.2 m

[tex]\sf \boxed{\text{\bf Area of trapezium =$\dfrac{(a +b)*h}{2}$}}[/tex]

                                   [tex]\sf =\dfrac{(8.9+2.7)*4.2}{2}\\\\=\dfrac{11.6*4.2}{2}\\\\= 5.8 * 4.2\\\\= 24.36 \ m^2[/tex]

Answer:  

1# 13.3 Km

2# 57.4 Km

3# 45.5 Km

4# 24.36 Km

The question requires the computation of loss body fluid. The results show that Don Pedro's loss of body fluid per hour is 54,234ml/hours. See computation below.

This refer to the rate at which a human being loses water on the hour. The formula for this is given as:

The Body weight in lb x percentage rate of dehydration (given in decimal form) x 500.

Hence, Don Pedro's loss of fluid per house is:

82 x 0.6 x 500;

Recall that in the formula, the weight is given in lb. So we convert Pedro's weight to Lb.

1kg = 2.20462Lb

Hence

80kg = 80 * 2.20462 = 176.37

Hence

Pedro's loss of fluid per house =

180.779 x 0.6 x 500

= 54,233.70

≈ 54, 234 ml/h


Learn more about loss of body fluid at:
https://brainly.com/question/2060910
#SPJ1

Answer:

Question 13 of 16 Evaluate the following function at the values 2, -4, and x-1. f(x)=x2-5 = ..... f(2)= (Type an integer or a simplified fraction.) f(-4)=L(Type an integer or a simplified fraction.) f(x-1)= (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

Answer:

D

Step-by-step explanation:

with this functional definition y can never have a negative value.

so, A and C are automatically out.

and then find some core points (like x = 0 and y = 0).

for x = 0 we get y = 3. ok, that fits to both B and D.

for y = 0 x must be 3.

and that leaves only D as right answer.

Answer:

the answer is a on my test

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9

7x^4 - y^3 - 3

Answer:

28x-3y-3

Step-by-step explanation:

(-2x × 4 - 4v × 3 + 4z× 3 + 6) - (-9× × 4 - 3v× 3 + 4

Multiply the monomials

（-8×-4y×3+ 42×3+6)-（-9××4-3y×3+42×3+9

Multiply the monomials

(-8x-12y + 4z × 3 + 6) - (-9x× 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x - 12y + 12z +6) - (-9× × 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x-12y +12z +6) - (-36x -3y × 3+ 4z × 3 + 9)

Multiply the monomials

(-8x-12y + 12z + 6) - (-36x - 9y + 4z × 3 + 9)

8×-12y+122+6-（-36×-9y+122+9

Remove the parentheses for addition or

subtraction

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

Reorder and gather like terms

(-8x + 36x) + (-12y + 9y) + (12z - 12z) + (6 - 9) 3 steps

Collect coefficients of like terms

(-8+36) ××+ (-12 + 9) × y+ (12 - 12) × z+ (6 - 9)

Hi there.

[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]

What we should do here is multiply the fractions. We know this information because it says in our problem - "the product".

.

If ever we come across the word "the product of" in any mathematics problems, we should know that the operation we should use is "multiplication".

.

.

This is how we multiply fractions:

.

First, we check: Is there any way we can reduce the fractions?

.

.

We cannot divide the top and bottom of these two fractions by the same number, but there is some reducing that can be done:

.

.

Notice that 4 and 8 have a common factor - 2.

.

Since 4 and 8 have a 2 in common, we divide 8 and 4 by 2:

.

[tex]\bf{\displaystyle\frac{4}{15} *\frac{3}{8}}[/tex]

.

[tex]\bf{\displaystyle\frac{1}{15} *\frac{3}{2}}[/tex]

.

.

Now, 15 and 3 also have a common factor - 3:

.

[tex]\bf{\displaystyle\frac{1}{5} *\frac{1}{2}}[/tex]

.

.

What we should do now is multiply 1 by 1 and 5 times 2:

.

[tex]\bf{\displaystyle\frac{1}{10}}[/tex]

.

I hope that this helps clear your doubts; if any are left, please ask.

.

I wish you a nice rest of your day.

.

[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\bf{n}\sf{g}\:\bf{A\:\sf{L}\bf{e}\sf{t}\bf{t}\sf{e}\bf{r}.[/tex]

--

[tex]\huge\textbf{What does \boxed{product} mean?}[/tex]
[tex]\bullet\large\text{ Product simply means multiplication/multiply}[/tex]

[tex]\huge\textbf{So, what are we doing in the equation?}[/tex]

[tex]\bullet\large\text{ We are multiplying! :)}[/tex]

[tex]\huge\textbf{What should our equation look like?}[/tex]

[tex]\rm{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]

[tex]\huge\textbf{What are the steps?}[/tex]

[tex]\mathsf{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]

[tex]\mathsf{= \dfrac{4\times 3}{15\times 8}}[/tex]

[tex]\mathsf{= \dfrac{12}{120}}[/tex]

[tex]\mathsf{= \dfrac{12\div2}{120\div2}}[/tex]

[tex]\mathsf{= \dfrac{6}{60}}[/tex]

[tex]\mathsf{= \dfrac{6\div3}{60\div3}}[/tex]

[tex]\mathsf{= \dfrac{2}{20}}[/tex]

[tex]\mathsf{= \dfrac{2\div2}{20\div2}}[/tex]

[tex]\mathsf{= \dfrac{1}{10}}[/tex]

[tex]\huge\textbf{What is your answer to the question?}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{1}{10}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The height and the base area of both the design must be equal. Then the correct option is A.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.

Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.

The figure shows both designs.

The volume of the cylinder will be given as

V = πr² h

If the volume of the oblique cylinder and right cylinder is the same.

Then the height of both the designs must be equal and the base area of both the design must be equal.

Then the correct option is A.

More about the cylinder link is given below.

https://brainly.com/question/3692256

#SPJ1

Answer:

D

Step-by-step explanation:

did the test on edmentum

Answer:

( we know that square of perimeter is 4L now,4L=6c-4(c-5),4L=6c-4c+20,4L=2c+20,then L=(c+10)/2

The side of a given square is c/2+5. Therefore, option C is the correct answer.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, the perimeter of a square is 6c-4(c-5).

We know that, the perimeter of a square is 4a, where a is the side.

Now, 4a=6c-4(c-5)

4a=6c-4c+20

4a=2c+20

a=c/2+5

Therefore, option C is the correct answer.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ2

Answer:

3

Step-by-step explanation:

because there are only three pictures

Answer:

  7.2 cm

Step-by-step explanation:

The height of the trapezium can be found by making use of the area formula with known values filled in.

__

The area of a trapezium is given by ...

  A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height

Using the given values, we have ...

  90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values

  (90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h

The height of the trapezium is 7.2 cm.

To write this sum as a fraction, you can use the following formula: 5x/4 + 3/4.

To transform a fraction into a sum we must perform the following procedure:

According to the above, all we have to do is divide the fraction using each digit of the numerator and put the same denominator.

Learn more about fractions in: https://brainly.com/question/10354322

#SPJ1

Answer:

14 divided by 9 = 1.5

The result of 14/9 is a non-terminating, repeating decimal.

Answer:

1.56 [?]

this question's wording was slightly confusing but I think this is what you meant

Step-by-step explanation:

by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as [tex]\frac{14}{9}[/tex], actually divide

14 by 9) you will end up with a number:

1.55555556

(repeating decimal)

So, you can either write this as 1.5 with a little dash over the 5

Or, you can round the decimal to 1.56 .

(method: by actual division)