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Answer:

x = [tex]7\sqrt{3} [/tex] inches

Step-by-step explanation:

- 2021 Edmentum

The height x of the equilateral triangle is 7√3 inches.

Equilateral triangles are triangles that have all their sides and angles equal to each other. The three angles are 60 degrees each.

Therefore,

The side length of the equilateral triangle is 14 inches.

Therefore, To find the height of the triangle using the Pythagoras theorem.

c² = a² + b²

14² - 7² = b²

b² = 196 - 49

b² = 147

b = 7√3

Hence, The height x of the equilateral triangle is 7√3 inches.

learn more on the equilateral triangle here:

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Answer:8x5=10-x

Step-by-step explanation:

Answer:

[tex]si = \frac{p \times t \times r}{100} \\ 81.60 = \frac{510 \times 4 \times r}{100} \\ 8160 = 2040r \\ r = \frac{8160}{2040} \\ r = 4\%[/tex]

Answer: 1/14 assuming cards are nut returned back in deck

Step-by-step explanation: first is red P(1. R) = 4/8 = 1/2

Second red P(2. R) = 3/7 and P(3. R) = 2/6 = 1/3.

Multiply probabilities , you get 1/14

Answer:

4/56 simplified is 1/14

Step-by-step explanation:

nCr(8,3) = 56

4 (the number of red cards there are) / 56 = 1/14

Answer:

this goes with steps and answer

Step-by-step explanation:

hope this helped!

Answer:

( 4 , − 1 )

Step-by-step explanation:

y= (x + 3)(x + 5)

y= x^2 + 5x + 3x + 15

y= x^2 + 8x +15

Answer:

V = 540cm3 (E)

Step-by-step explanation:

Area of a square:

A = a2

Perimeter of a Square

P = 4a

Polygon diagonals of a square

q = √(2a2) = a√2

Side of a Square

a = √A

a = P/4

a = q / √2

Square Calculations

Calculate q, P, A | Given a

Given the length of a side calculate the diagonal, area and perimeter

q = a√2

A = a2

P = 4a

Calculate a, P, A | Given q

Given the diagonal length calculate the side length, perimeter, and area

a = q / √2

P = 4a

A = a2

Calculate a, q, A | Given P

Given the perimeter calculate the side length, diagonal, and area

a = P/4

q = a√2

A = a2

Calculate a, q, P | Given A

Given the area calculate the length of the sides, diagonal, and the perimeter

a = √A

q = a√2

P = 4a

Answer:

Side AH

Step-by-step explanation:

he other 3 sides only go through one face of the cube

Answer:

s√3

Step-by-step explanation:

Draw in the diagonal of the base, which is the line freom G to F.  If the side length of this cube is s, then the length of this diagonal is

d = √(s² + s²) = (√2)s.

Now draw in the diagonal of the cube:  draw a line segment from G to B.  We have already found that the length of the diagonal GF is d = s√2.  Apply the Pythagorean Theorem to the triangle whose sides are s√2 and s:

diagonal of cube = square root of the sum of the squares of s√2 and s:

= √(2s² + s²)= √(3s²) = s√3

Answer:

21 degrees

Step-by-step explanation:

The inscribed angle theorem states that when two cords (lines in a circle) make contact with the circumference of the circle (outer edge), and the two cords do not pass through the center of the circle, then the angle between the two cords is equal to half of the length of its surrounding arc. This means that the measure of arc (WV) is half of the measure of angle (WXV). Therefore, one can form an equation and solve for the length of the arc (WV).

2 (WV) = (m<WXV)

Substitute,

2 (WV) = (42)

Inverse operaitons,

2 (WV) = (42)

/2            /2

(WV) = 21

Answer:

122.46 mi^2

Step-by-step explanation:

IF ans is correct comment back for explanation

Answer:

V = 612.3

Step-by-step explanation:

d = 6

r = 3

Volume of a cylinder:

V = πr²h

V = 3.14(3²)(20)

V = 3.14(9)(20)

V = 565.2

Volume of a cone:

V = πr²(h/3)

V = 3.14(3²)(5/3)

V = 3.14(9)(5/3)

V = 47.1

Combined:

565.2 + 47.1

612.3

Answer:

1.03

Step-by-step explanation:

2015.71 = 1900(b)^2

44.896659 = 43.588989 * b

44.896659/ 43.588989 = b

1.0300000 = b

Recall ; for an exponential distribution :

b In the equation = 1 + r ; where, r = rate

b = 1 + r

1.0300000 = 1 + r

r = 1.0300000 - 1

r = 0.03

Hence, the value of b in the equation is 1.03

Answer:

Step-by-step explanation:

x=-1-2y

-2-4y-3y-12=0

-7y=14

y=-2

x=3

Answer:

slope = 1

y - intercept = (0.-4)

Answer:

c ≈ 40

Step-by-step explanation:

Using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{26}{c}[/tex] ( multiply both sides by c )

c × sin40° = 26 ( divide both sides by sin40° )

c = [tex]\frac{26}{sin40}[/tex] ≈ 40 ( to the nearest whole number )

Answer:

I'm pretty sure the answer is C

I could be wrong tho

Answer:

She will save 1.24

Step-by-step explanation:

2.65 x 4 10 .60 plus .53 x 4 equals 12.72

6.48 x 2 equals 13.96

Answer:

3

Step-by-step explanation:

28/7=4

6/3=2

4+2=6

6*1/2=3

Paraenthies

Exponets

Mulitplication

Divide

Add

Subtract

Answer: your welcome lol

Step-by-step explanation:

Answer:

m=-14/11

Step-by-step explanation:

To find the slope use the formula: y2-y1/x2-x1

(8--16)/(-1-10)

14/-11

=-14/11

From the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

What is the difference between simple and compound interests?

Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period. Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The complete question is given below.

Given,

  The principal amount deposited by both Jack and Carlie  P = $17,250

The rate of interest r = 6% = 0.06

The time period = 6.5

Jack's account earns annual simple interest and Carlie's account earns annual compound interest.

So the amount in each person's account after a time period of t = 6 years.

Jack:

Amount = P(1+rt) = 17250 ( 1 + 0.06*6) = $23,460

Carlie:

number of times compounded in a year n = 1

Amount = [tex]P(1 + \frac{r}{n})^{nt}[/tex] = 17250 ( 1+0.06)⁶ = $24,469.45

Therefore from the amounts found using simple and compound interest formulas, we found that Carlie earns more interest than Jack by $1009.45.

To learn more about the interest, follow the link.

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Step-by-step explanation:

y=57x-8y=-12

so we put the Y

y=-12

-12=57x-8y

57x-8x(-12)=-12

(-36/19,-12)<---- answer

Answer:

$375

Step-by-step explanation:

Given data

Principal= $2500

Rate= 5%

TIme = 3 years

We know that the expression for the simple interest is given as

SI=PRT/100

Substitute

SI= 2500*5*3/100

SI= 37500/100

SI= $375

Given:

Height of the Statue of Liberty = 305 feet

Angle of elevation = 9 degrees

To find:

The between the tourist and the Statue of Liberty.

Solution:

Using the given information, draw a figure as shown below.

In a right triangle,

[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]

In the triangle ABC,

[tex]\tan 9^\circ=\dfrac{305}{x}[/tex]

[tex]x=\dfrac{305}{\tan 9^\circ}[/tex]

[tex]x=1925.6942[/tex]

[tex]x\approx 1926[/tex]

Therefore, the tourist is standing 1926 feet from the Statue of Liberty.

Answer:

219

Step-by-step explanation:

let x be the number of full price tickets and y be student/ senior number , then

x + y = 465 → (1)

10x + 8y = 4212 → (2)

Multiplying (1) by - 10 and adding to (2) will eliminate x

- 10x - 10y = - 4650 → (3)

Add (2) and (3) term by term to eliminate x

0 - 2y = -438

- 2y = - 438 ( divide both sides by - 2 )

y = 219

The number of senior/ student tickets sold was 219