Devaughn is 15 years older than Sydney. The sum of their ages is 107. What is Sydney's age?

Answer:

[tex]Area =55.4ft^2[/tex]

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]

Solve for x

[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]

[tex]\tan(60) = \sqrt 3[/tex]

So:

[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]

[tex]x = 4[/tex]

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

[tex]Base = 4\sqrt 3[/tex]

[tex]Height = 4[/tex]

So, the area of the rhombus is 4 times the area of 1 triangle

[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]

[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]

[tex]Area =2 * 4\sqrt 3 * 4[/tex]

[tex]Area =55.4ft^2[/tex]

Answer:

either 22/60 or .3666 recurring

Step-by-step explanation:

All you are doing is converting minutes to hours basically, so all you have to do is divide 22 by 60.

Answer:

[tex]\frac{4}{20}[/tex] or 0.2 or 20%

Step-by-step explanation:

For only two tests to be needed this means that the first test would need to come back as negative and the second test would be to come back as positive. Therefore, to find the probability of this happening we first need to find the probability of each individual test and multiply them together.

The first test needs to come back negative, there are four negative individuals out of the total 5 that are in the group. Therefore, the probability of the first test is 4/5.

Now we remove the individual that has just been tested and we are left with 4 total subjects in the group, of which only 1 is positive. Therefore, the probability of the second test is 1/4. Now we need to multiply these two probabilities together to get the probability of only needing two tests.

[tex]\frac{4 * 1}{5 * 4} = \frac{4}{20}[/tex] or 0.2 or 20%

Answer:

x = 14

Step-by-step explanation:

The polygon given has 6 sides

Sum of interior angles of a 6-sided polygon = 180(n - 2)

substitute n = 6 into 180(n - 2)

Sum of the polygon = 180(6 - 2) = 720°

Thus:

10x + 8x - 16 + 12x - 8 + 7x + 2 + 9x + 4 + 6x + 10 = 720

Add like terms

52x - 8 = 720

52x = 720 + 8

52x = 728

x = 728/52

x = 14

Answer:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ slope = \frac{10 - 5}{20 - 15} \\ = \frac{5}{5} \\ = 1[/tex]

Answer:

s = 32

Step-by-step explanation:

s - 12 = 20

s (- 12 + 12) = 20 + 12

s = 32

Step-by-step explanation:

s-12=20

s=20+12

s=32

Hope it helps.

Answer:

g(x) = f(x + 2)

Step-by-step explanation:

The x value has been translated by 2

Feel free to mark it as brainliest :D

Answer:

x = 18.4

y = 35º

Step-by-step explanation:

cos∅ = adj/hyp

cos49 = x/28

28cos49 = x

x = 18.4

tany = opp/adj

tany = 19/27

y = arctan19/27

y = 35º

Answer:  1,953,125

This is one single value and it is just a bit under 2 million.

Or more accurately, it's a bit over 1.9 million.

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

Explanation:

Note that dividing any term by its previous term gets us the common ratio

The r value must stay the same the entire time, or else the sequence isn't geometric.

The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)

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

To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.

If we tried n = 2 for instance, then we find the 2nd term is

5(-5)^(n-1) = 5(-5)^(2-1) = -25

which matches what your teacher gave you. I'll let you verify the other terms.

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

The last thing we need to do is plug in n = 9 and simplify

5(-5)^(n-1)

5(-5)^(9-1)

5(-5)^8

5(390625)

1,953,125  this is one single value (rather than 3 separate values)

Answer: b d a

Step-by-step explanation:

B

D

A

Answer:

B

Step-by-step explanation:

Answer: 1238.916

Step-by-step explanation:

A = (Bh)/3

B = 14.7 x 14.7

The area of a pyramid is the formula at the top. B in the formula at the top is the Base. The reason it is capitalized is because B is also a formula. You need to find the area of the base of the pyramid and plug it into the equation. It this case, the base is equal to the second equation above.

Answer:

10.5

Step-by-step explanation:

Answer:

the answer is a!

Step-by-step explanation:

Answer:  

f

−

1

(

x

)

=

x

−

12

5

Step-by-step explanation:

Answer:

x=28.8

Step-by-step explanation:

using cosine

cos x= adjacent/hypotenuse

cos x = 71/81

cos x = 0.8765

make x subject of the formula

x= cos^-1 0.8765

x= 28.77699973

x≈ 28.8

The required value of x is 28.8 degrees for the right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the question, as shown

We have to determine the value of x for the triangle.

As we know the cosine ratio is:

cos x = adjacent/hypotenuse

As per the question, substitute the known values in the above ratio,

cos x = 71/81

Apply the division operation,

cos x = 0.8765

Solve for x, and we get

x= cos⁻¹ (0.8765)

x = 28.77699973

x ≈ 28.8

Thus, the required value of x is 28.8 degrees.

Learn more about the right triangle here:

brainly.com/question/6322314

#SPJ2

Answer:

Area of shaded part = 113 mm² (Approx.)

Step-by-step explanation:

Given:

Diameter of Semi-circle = 24 mm

Find:

Area of shaded part

Computation:

Radius of semi-cicrle = Diameter of Semi-circle / 2

Radius of semi-cicrle = 24 / 2

Radius of semi-cicrle = 12 mm

So,

Radius of small circle = 12 / 2

Radius of small circle = 6 mm

Area of shaded part = Area of semi circle - Area of small circle

Area of shaded part = [πR² / 2] - [πr²]

Area of shaded part = [(3.14)(12)² / 2] - [(3.14)(6)²]

Area of shaded part = [(3.14)(144) / 2] - [(3.14)(36)]

Area of shaded part = 226.08 - 113.04

Area of shaded part = 113.04

Area of shaded part = 113 mm² (Approx.)

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Researchers must increase the response rate to achieve a narrower confidence interval. Because we see that the trust gap is inverse to sample size. We must increase data in estimating a narrower 95-percent trust range. Since the sample has increased, its error margin has decreased, this reduces the width of the trust interval.

Answer:

8ft is the diameter so the radius would be half of that, so it's 4ft. Now substitute

[tex]\pi4 {}^{2} [/tex]

now solve 4^2=16 now multiply it by 3.14 (pi). 16×3.14= 50.24

Answer:

b

Step-by-step explanation:

because the price of money is maximum 2,500

Answer:

2pi

Step-by-step explanation:

Right on edg assignment

Answer:

step 3 didn't divide by 2

Step-by-step explanation:

in step

[tex] \frac{ - 8 + \sqrt{100} }{2} = \frac{ - 8 + 10}{2} = 1 \\ \frac{ - 8 - \sqrt{100} }{2} = \frac{ - 8 - 10}{2} = - 9[/tex]

Answer:i dont know

Step-by-step explanation:

9514 1404 393

Answer:

  (0, c)

Step-by-step explanation:

Compare the given equation to the vertex form equation ...

  y = a(x -h)^2 +k . . . .  quadratic with vertex (h, k)

You have ...

  y = ax^2 +c

Matching these forms, we see that h=0, and k=c. Then the vertex is ...

  (h, k) = (0, c)

Answer:

40-10=30

Step-by-step explanation:

x-10=30

we are going to flip the problem which would make it addition so you would do 10+30=X and we can fill in the blank of x equalling 40 because 10+30 is 40

Answer:

x = 40

Step-by-step explanation:

x - 10 = 30

=> x = 30 + 10

=> x = 40

From 2 to 101 , the perfect square numbers are ,

Total number of possible outcomes = 100.

Total number of favourable outcomes = 9 .

Hence ,

→ P ( of getting perfect square ) = 9/100

Step-by-step explanation:

tan 30°= root 3/ 3

r²=x² + y²

r²= 4root3 ² + 12²

r²= 48 +144

r²= 192

ŕ= 8root3

so the bottom is 12...

the other side is 4root3

[tex]4 \sqrt{3} [/tex]

and hypotenuse is 8root3

[tex]8 \sqrt{3} [/tex]

Answer:

LHS,

hope it helps.

Answer: 107/100x

1.07x

Step-by-step explanation:

Since the price of the model is x dollars, and she also has to pay a 7% tax, the amount that Leila will pay in total for the model will be the addition of the price of the model and the tax. This will be:

= x + (7% × x)

= x + (7/100 × x)

= x + (0.07 × x)

= x + 0.07x

= 1.07x

This can also be 107/100x

Answer:

Step-by-step explanation:

first: x+(1/4)

second: (-1/3 )x +1/4

third: (3/4)x +1/3