Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than Lana. When the four sisters' ages are added together, the result is $45$. If the youngest sister is $n$ years old, what is $n$?

Formula for the volume of a sphere: V = 4/3 x pi x r^3

V = 4/3 x pi x 6^3

V = 4/3 x pi x 216

V = 288 pi in^3

Hope this helps!

Answer:

288 pi in ^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3 where r is the radius

V = 4/3 pi *( 6)^3

V = 4/3  pi (216)

V = 288 pi in ^3

Answer:

11.3 feet

Step-by-step explanation:

let x= answer

x²+4²=12²

x²=128

x=11.3137085

which rounds to

11.3

Answer:

≈ 11.3 ft.

Step-by-step explanation:

In order to solve this, we must use some trigonometry, in this case, SOH-CAH-TOA. If you don't know what it is, here's a quick explanation:

- SOH: Sin(θ) = Opposite / Hypotenuse

- CAH: Cos(θ) = Adjacent / Hypotenuse

- TOA: Tan(θ) = Opposite / Adjacent

(Remember, SOH-CAH-TOA can ONLY be used for right triangles. If the problem does not clearly show a right triangle, meaning that there's no box in the corner, you cannot use it)

When using SOH-CAH-TOA, we first must choose an angle, either the top one or the bottom one. We can't use the right angle as, well, you just can't :). First, we have to find the bottom angle, so circle it. Literally, just circle the angle, you'll thank me later. I'll explain why we don't solve the top angle later on.

After that, we just do some labeling on the sides of the triangle. First, label the shortest side that forms the circled angle, which is the floor (4 ft), as the Adjacent side. Then label the longest side of the triangle, which is the ladder (12 ft), as the Hypotenuse. Finally, label the side that doesn't form the circled angle as the Opposite side. This is why the circling comes in handy :)

Then, out of SOH, CAH, and TOA, we choose the one that has the sides that forms the circled angle. In this case, it's CAH, or cosine, as the adjacent and hypotenuse form the circled angle.

Next, we write out the formula and solve:

Cos(m∠Circled Angle) = Adjacent/Hypotenuse

Cos(m∠Circled Angle) = 4/12

Cos(m∠Circled Angle) x Cos^-1 = 1/3 x Cos^-1

m∠Circled Angle ≈ 70.5288 (Rounding to the nearest ten-thousandth)

Note: Pay attention to the 3rd line. 'Cos^-1' is basically the equivalent of '÷ Cos'.

The reason why we did the bottom angle first is because you cannot have two unknown variables when solving for one of them. That would've been the case if we did choose the top angle as we wouldn't know the measure of the wall nor the angle. Now that we have solved the bottom angle, we can move onto solving the length of the wall.

Looking at SOH-CAH-TOA, we can either use sine or tangent as we have the measures for both the adjacent and hypotenuse. I'll use sine cause why not? Anyways, let's move on!

Just like last time, we write out the formula and solve:

Sin(m∠Circled Angle) = Opposite/Hypotenuse

Sin(70.5288) = Opposite/12

0.9428 = Opposite/12

0.9428 x 12 = Opposite/12 x 12

11.3137 ≈ Opposite (Wall)

Wall ≈ 11.3 ft. (Rounding to the nearest tenth, as asked to do so by the problem)

Note: Be careful with SOH-CAH-TOA because I've messed up multiple times with my calculator while typing out my explanation, so just make sure you go over it several times before submitting your answer when solving trig problems :). But I'm confident with my answer, so just submit it without hesitation as I've already double-checked my work.

9514 1404 393

Answer:

  +24

Step-by-step explanation:

The number of steps run can be represented by the integer +24.

The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex]  gives - 335.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

[tex]xy-5x+y^2xy-5x+y ^2[/tex]

Substitute x = -3 and y = 5.

[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]

= -15 + 15 - 375 + 15 + 25

= -335

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Answer:

5

Step-by-step explanation:

[tex]5^{2}[/tex] = 25

25 * 2 = 50

50 - 3 = 47

Hope that this helps!

Answer:

Step-by-step explanation:

let the number be x

Square of a number: x²

Twice the square of a number = 2*x² = 2x²

Three less than twice the square of a number = 2x² - 3

2x² - 3 = 47     {Add 3 to both sides}

2x² = 47 + 3

2x² = 50        {Divide both sides by 2}

 x² = 50/2

x² = 25          Take square root

x = √25

x = 5

Answer:

10x² + 11x - 6

Step-by-step explanation:

The area (A) is the product of the sides, that is

A = (2x + 3)(5x - 2) ← expand using FOIL

   = 10x² - 4x + 15x - 6 ← collect like terms

   = 10x² + 11x - 6

Answer:

Step-by-step explanation:

a). In ΔABC and ΔEDC,

Since, AB and DE are parallel and AE is a transversal,

Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]

m∠D = m∠B = 90°

ΔABC ~ ΔEDC [By AA property of similarity of two triangles]

b). Therefore, by the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]

[tex]\frac{60}{200}=\frac{40}{AB}[/tex]

AB = [tex]\frac{40\times 200}{60}[/tex]

     = 133.33

     ≈ 133.3 ft

Answer:

4x+11

Step-by-step explanation:

you have to add the like terms,in this case the like terms are 7 and 4.4x isn't a like term cause it has a variable.

so you just have to add 7+4

4x+11

I hope this helps

Step-by-step explanation:

hope this may help you tq

Answer:

B. SAS

Step-by-step explanation:

Ratio of sides equal:

• 4/2= 6/3

So the 2 sides are congruent and also share same angle between.

• B. SAS is the similarity reason

Answer:

8= coefficients.

4ab=constant term

5b=number of terms

Step-by-step explanation:

when terms are being added and substrated in algebra expression, we can sometimes simplify the expression to produce an expression with fewer terms

LET ME KNOW IF IT HELPS

Step-by-step explanation:

Product property

Quotient property

Power property

Negetive exponent property

Answer:

Graph is attached below with coordinated points of (3,3),  (-3,2),  (-2,-3),  (-3,-2),  (0, -4),  (-2,0),  (4,0), and (0,0)

Step-by-step explanation:

Answer:

1.

= Here,

cost of pen = 3+4 ( x ) = 7x

costs of two pen = 7x

cost of three pencils = 71 - 7x = 64x

cost of 1 pencil = 64/3

= 21.333334

c

Answer:

3

Step-by-step explanation:

The value of x is 3 if the volume of the triangular prism is 54 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that  volume of the triangular prism is 54 cubic units.

We have to find the value of x

The volume of the prism with triangular base is 54 unit³.

The base is a triangle with,

base = 4 units

height = x units

height of the prism = 3x

V= 6x²

54= 6x²

Divide both sides by 6

x² = 9

x=3

Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.

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Answer:

B.

Step-by-step explanation:

Table B has x values that go to multiple y values. A function has inputs that only go to one output.

Answer:

Rs.6420

Step-by-step explanation:

we know that A=P(1+r/100)

7488=P(1+8/100)2

7488*10000/108*108=P

P=Rs.6420

Answer:

Principal=Rs.45000 ; And Amount=Rs.52488.

Step-by-step explanation:

For finding Principal i used the formula:[ x(1+8/100)^2-x] =C.I ( where x = P)

And for Amount : Sum of principal and interest.

Hope so, you liked my solution.

Answer:

x = -1

Step-by-step explanation:

14x + 2 = 9x -3

Transpose

14x -9x = -3 -2

5x = -5

x= -5/5

x = -1

Answer:

x = -1

Step-by-step explanation:

[tex]14x+2=9x-3\\\\5x+2=-3\\\\5x=-5\\\\x=-1[/tex]

Answer:

B: 1/6

Step-by-step explanation:

The probability a boy will get picked who owns what is 5 on the picture, out of 30 choices.  So divide 30 by 5 and get your answer :)

Please mark brainiest

Answer:

195.06

Step-by-step explanation:

area of circle = πr^2 = π8^2 = 64π

area of triangle = 1/2 x 4 x 3 = 6

area of shape = 64π-6 = 195.061929 = 195.06

Answer:

sum of the interior angles x and y gives the exterior angle z

(4n-18)°+(n+8)°=(133-6n)°

4n°-18°+n°+8°=133°-6n°

4n°+n°-18°+8°=133°-6n°

5n°-10°=133°-6n°

5n°+6n°=133°+10°

11n°=143°

11°n/11°=143°/11°

n=13

exterior angle=133-6×13

=133-78

=55

Answer:

The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1

Step-by-step explanation:

all you have to do is replace the x in "G" with the "F" function

F(x) = x+4  and  G(x) = x^3-1

===========================================================

Explanation:

Let's try choice A to see if it works or not

G(x) = (x+4)^3

G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)

G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1

G( F(x) ) = (x+3)^3

This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.

------------

Let's try choice B

G(x) = x+4

G( F(x) ) = F(x)+4

G( F(x) ) = x^3-1 + 4

G( F(x) ) = x^3 + 3

Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.

--------------

Now choice C

G(x) = x^3 - 1

G( F(x) ) = ( F(x) )^3 - 1

G( F(x) ) = (x+4)^3 - 1

We found the final answer.

Answer:

The third one

Step-by-step explanation:

Just took the quiz

Answer:

15x + 7

Step-by-step explanation:

x + (7 + 14x)

x + 7 + 14x

15x + 7

Answer:

15x + 7

Step-by-step explanation:

Remove parenthesis:

x + 7 + 14x

Combine like terms:

14x + x = 15x

Add the seven:

15x + 7

Hope this helped.

Answer:

Step-by-step explanation:

Find the slope of the line AB.

The slope:

Since the altitude is perpendicular to AB, it has a slope of -2.

The line with the slope of -2 and passes through point C(6, 16).

Use point-slope equation to find the line:

A = 2, B = 1, C = 28

Answer:

Solution given:

A(7,9)

B(11,11)

C(6,16)

Slope of AB=[tex]\frac{11-9}{11-7}=\frac{2}{4}=½[/tex]

since altitude is perpendicular to it .

so its slope becomes negative reciprocal to the slope of base

so

slope of altitude(m) =-2

now

equation of a line passing through C(6,16) perpendicular to its base is:

By using formula

[tex]y-y_{1}=m(x-x_{1})[/tex]

y-16=-2(x-6)

solve it

y-16=-2x+12

y+2x=12+16

in the form of Ax +By=C is:

2x+y=28

:.

B=1

C=28

Answer:

<2 = 75°

<3 = 75°

Step-by-step explanation:

<2 = <6

2x+15 = 45+x

or, 2x-x = 45-15

or, x = 30

so, <2 = 30×2+15 = 75

<6 = 45+30 = 75

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

i. 5/12

ii. 1/8

iii. 11/24

iiii. 7/8

Answer:

29.4 m/s

Step-by-step explanation: