Given: circle k(O),
ED
diameter,
m∠OEF=32°, m
EF
=(2x+10)°
Find: x

Answer:

The sum of terms 12  the geometric sequence 1,3,9...   = 265720

Step-by-step explanation:

Formula:-

Sₙ = a₁(1 - rⁿ)/(1 - r)

Where Sₙ - sum of n terms in the GP

a - First term of GP

r - Common ratio

n - Number

It is given the  geometric sequence 1,3,9....

To find the sum of 12 terms

Here a = 1, r = 3 and n = 12

Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720

Answer:

The sum of the 12 terms = 265720

Step-by-step explanation:

* Lets study the geometric sequence rule

- If a1 = a , a2 = ar ,  a3 = ar² , a4 = ar³ , .........................

∴ an = a[(r)^(n-1)]

- Where a is the first term and r is the common ratio and

  n is the position of the term in the sequence

- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)

- Where n is the number of terms we want to add

* Lets check our terms in the sequence

- The terms are 1 , 3 , 9 , ..........

- To find the common ratio divide the 2nd term by 1st term

∵ the second term is 3 and the first term is 1

∴ 3/1 = 3

∴ The common ratio is 3

∵ n = 12 and a = 1

* Lets substitute the values of a , r , n in the rule of the sum to

  find the sum of the 12 terms

∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720

* The sum of the 12 terms = 265720

Here is the work along with the answer to the problem.

Answer:

Step-by-step explanation:

Look at the picture.

We have the rectangle 2πr × h and two circles.

Therefore the formula of a Surface Area is:

[tex]S.A.=2\pi rh+2\pi r^2[/tex]

We have r = 5m and h = 9m. Substitute:

[tex]S.A.=2\pi(5)(9)+2\pi(5^2)=90\pi+50\pi=140\pi\ m^2[/tex]

[tex]\pi\approx3.14\to S.A.\approx(140)(3.14)\approx440\ m^2[/tex]

Final answer:

To calculate the surface area of the cylinder, use the formula 2π(radius)(height) + 2π(radius)², with radius = 5m and height = 9m. The answer is approximately 440 square meters when rounded to the nearest square meter.

Explanation:

To find the approximate surface area of the cylinder, we can use the formula: Surface area = 2π(radius)(height) + 2π(radius)². Given a radius of 5 meters and a height of 9 meters, we can plug these values into our formula.

The area of the two circular bases is 2π(radius)² = 2π(5)² = 2π(25) = 50π square meters.

The area of the side (the rectangular part when the cylinder is unrolled) is 2π(radius)(height) = 2π(5)(9) = 90π square meters.

Adding both of these areas together gives us the total surface area:
50π + 90π = 140π square meters.

Using 3.14159 as an approximation for π, we get 140π = 140(3.14159) ≈ 439.8226 square meters, which can be rounded to the nearest square meter as 440 square meters.

8/1 or 16/2 or 24/3 or 32/4 or 40/5

Answer:

Step-by-step explanation:

If breadth =x

length =x+2

Area =length *breadth

Area =x(x+2)=80

X^2+2x-80=0

X^2 +10x - 8x - 80=0

X(x+10)- 8(x+10)=0

(X-8)(x+10)=0

X=8 or x=-10

X=8(since breadth cannot be a negative value x cannot be negative)

Answer:

35 degress

Step-by-step explanation:

Answer: 108 degress

Step-by-step explanation:

To do multiplication is to take (usually) two sets on numbers and put them together to make them one.

For example: let’s say you want to multiply 5 and 3

This means you do 5➕5➕5

Your answer would be 15.

5✖️3= 15

Now let’s say you want to multiply a two digit number

10✖️12

This means you add 10 together 12 times.

10. First do 0✖️2 which is 0 so put it at the bottom. Then 1✖️2 which is 2

x 12. Then do 1✖️0 and 1✖️1

——————

20

➕11x. You put a place holder in this case (x) which equals 0

———————

120

Then you are left with your answer

Hope this helps! :3

Multiplication is like adding but with less work.

For example 9x9 is equal to

9+9+9+9+9+9+9+9+9.

Another example would be 15x3

which is equal to

15+15+15

Or

3+3+3+3+3+3+3+3+3+3+3+3+3+3+3z

Answer:

9√3 unit^2.

Step-by-step explanation:

The area  = 1/2 6^2 sin 60

= 1/2 * 36 * √3/2

= 9√3

The area is [tex]9\sqrt{3}un^2.[/tex]

Note that: triangle AOB is an equilateral triangle because:

OA = OB (both are radius)

So ∠OAB = ∠OBA

Given that ∠AOB=60 degree.

The sum of three angles of a triangle is 180 degrees.

So,

∠OAB + ∠OBA + ∠AOB = 180

∠OAB + ∠OBA + 60 = 180

∠OAB + ∠OBA = 120

∠OAB + ∠OAB = 120

2∠OAB = 120

∠OAB = 60

It means ∠OAB = ∠OBA  =60.

Since all the angles of these triangle is 60 degree, so triangle AOB is an equilateral triangle.

Given: side length = a = 6.

The area of the triangle is: [tex]\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\left(6^{2}\right)=\frac{\sqrt{3}}{4}\left(36\right)=9\sqrt{3}[/tex]

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Answer:

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-5, 2) and (-3, 0). Substitute:

[tex]m=\dfrac{0-2}{-3-(-5)}=\dfrac{-2}{2}=-1[/tex]

Answer:

C ($6,250)

Step-by-step explanation:

25 cartons with 5 stereos per carton=125 stereos total

profit for one stereo=80-30=50

125*50= 6250

After selling all the stereos, the company's profit will be $ 6250.

Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.

Here, Ray have 25 cartons with 5 stereos per carton

          So total Ray have,  25 X5 = 125 stereos

      profit on one stereo = 80 - 30 = $50

        Total profit on 125 stereos = 125*50=  $ 6250

Thus, after selling all the stereos, the company's profit will be $ 6250.

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Answer:

Name an event that is impossible:  Drawing the name "John" out of the bag

Name and event that is certain:  Drawing a name that starts with the letter "J"

Name an event that is as likely as not:  Drawing a girl's name or a boy's name

Name an event that is more likely than not:  Drawing a name that is longer than 4 letters.

Step-by-step explanation:

Answer: 26.8 feet

Step-by-step explanation:

In the figure attached you can see two right triangles  triangle ABD and a triangle ACD.

You are located at point B and the other person at point C.

The approximate height of the lifeguard station is x.

Keep on mind that:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Therefore:

For the triangle ABD:

[tex]tan(36\°)=\frac{x}{DC+11}[/tex]    [EQUATION 1]

For the triangle ACD:

[tex]tan(46\°)=\frac{x}{DC}[/tex]    [EQUATION 2]

Solve from DC from [EQUATION 2]:

[tex]DC=\frac{x}{tan(46\°)}[/tex]

Substitute into [EQUATION 1] and solve for x:

[tex]tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x[/tex]

[tex]x=26.81ft[/tex]≈26.8ft

Answer:

40%

Step-by-step explanation:

120/300 is 0.4 convert to percentage it is 40%

Answer:

C

Step-by-step explanation:

Given

f(x) = - 5

This will result in a value of - 5 for any value of x, hence

f( - 1) = - 5

Thus (- 1, - 5) ← represents a solution

To determine the image width for Delisa's tablet, the width on the computer is divided by the ratio of the diagonals of the devices. The calculated width on the tablet is 7.4cm (74.0mm) when rounded to the nearest tenth of a millimeter.

Delisa is tasked with ensuring that the website is proportional on both computers and mobile devices.

Given the diagonal of her computer monitor (21 inches) and tablet (9.7 inches), we know that the scale of the image on the tablet should be in the same ratio as the diagonals.

Since the image is 16 centimeters wide on the computer, we can calculate the width on the tablet using the ratio of the diagonals.

The ratio of the tablet size to the computer size is 9.7/21.

To find the width of the image on the tablet, we use the proportionality:
Width on computer / Width on tablet = Diagonal of computer / Diagonal of tablet

We can then solve for the unknown width on the tablet:
16cm / Width on tablet = 21 / 9.7

By cross-multiplying and solving the equation, we get:
Width on tablet = 16cm * (9.7 / 21)
Width on tablet = 7.390476 cm

Rounded to the nearest tenth of a millimeter, the width on the tablet will be approximately 7.4cm or 74.0mm.

Final answer:

The width of the image on the tablet is calculated using a proportion based on the diagonal screen sizes of the computer and tablet. After converting the image width from centimeters to inches, and using the ratio of the diagonals (9.7 inches to 21 inches), the width on the tablet is determined and then converted back to centimeters, rounded to the nearest tenth of a millimeter.

Explanation:

Delisa is designing a website and wants to ensure that an image displayed on different devices remains proportional. The diagonal of her computer monitor is 21 inches, and the diagonal of her tablet is 9.7 inches. When scaled down, the image width on the tablet should maintain the same proportion to the tablet's screen size as the image on the computer does to the computer's screen size.

To find the proportional width of the image on the tablet, we use the ratio of the diagonals of the two devices. The ratio is the diagonal of the tablet (9.7 inches) to the diagonal of the computer (21 inches), which simplifies to 9.7/21. Since we know the width of the image on the computer is 16 centimeters, we can set up a proportion:

(Width on tablet / 9.7 inches) = (16 cm / 21 inches)
To solve for the width on the tablet, we cross-multiply and divide:

Width on tablet = 16 cm × (9.7 inches / 21 inches)
Before solving, we need to convert 16 cm to inches, since the diagonal measurements are in inches. There are approximately 2.54 cm in an inch, so:

16 cm ÷ 2.54 cm/inch = 6.2992 inches
Now, we can calculate the width for the tablet:

Width on tablet = 6.2992 inches × (9.7 inches / 21 inches)
Performing the multiplication gives us the width on the tablet in inches. To convert back to centimeters, we multiply the result by 2.54 cm/inch. Finally, we round the answer to the nearest tenth of a millimeter.

Answer:

0.266

Step-by-step explanation:

Total No of seats in class = 8+10+12 = 30

probability that first student will be assigned first row will be: 8/30 = 0.266

because there are 8 front row seats and total seats are 30.

The probability that the first student who enters the classroom will be assigned a seat in the front row is; Option D; 4/15

We are told;

Number of front row seats = 8 seats

Number of middle row seats = 10 seats

Number of back row seats = 12 seats

Thus;

Total number of seats in classroom = 8 + 10 + 12

>> 30 seats

Now, we want to find the probability that the first student who enters the classroom will be assigned a seat in the front row.

Thus;

P(1st student sits in front row) = 8/30

This can be reduced to get;

P(1st student sits in front row) = 4/15

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Answer:

[tex]\large\boxed{530^o\ and\ -190^o}[/tex]

Step-by-step explanation:

[tex]\text{Coterminal angle with}\ \alpha:\\\\\alpha+360^o\ and\ \alpha-360^o.\\\\\text{Firs\ step}\\\\1250^o:360^o=3\ and\ 170^o\ rest\\\\1250^o=170^o\\\\170^o+360^o=530^o\\\\170^o-360^o=-190^o[/tex]

Answer:

[tex]\pi[/tex] x miles

Step-by-step explanation:

Circumference, C= 2[tex]\pi r[/tex]

r=radius = x/2

C= 2×[tex]\pi[/tex] × x/2

C=[tex]\pi[/tex] x

Answer:

πx miles

Step-by-step explanation:

Given in the question,

radius of a circle = x/2 miles

To find circumference of a circle we will use following formula

2π * r

where π is constant = 3.14

            r is radius of circle

Plug values in the formula

2(3.14)(x/2)

2 will cancel out

Is 34 the diameter or radius?

product is the answer to a multiplication problem mx6=90

The sentence 'The product of Mabel's score and 6 is 90' translates into the equation 'm * 6 = 90' in mathematics, where m represents Mabel's score.

The sentence provided can be translated into an equation. In mathematics, the phrase 'the product of' means to multiply. Here, Mabel's score is represented by the variable m. The 'product of Mabel's score and 6' is the same as saying 'm multiplied by 6'. This is said to be equal to 90. Therefore, the equation that represents this sentence is m * 6 = 90.

To translate the sentence 'The product of Mabel's score and 6 is 90' into an equation using the variable m to represent Mabel's score, we can write:

6m = 90

This equation states that the product of Mabel's score (m) and 6 is equal to 90.

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Answer: 1/5

Step-by-step explanation:

Answer:

1/500

Step-by-step explanation:

if you add a %, multiply the number by 100 (or move to the right 2 decimal places)

if you remove the %, divide the number by 100 (or move to the left 2 decimal places)

example .5 to a percent is .5(100) = 50%

to make this a fraction, first change the number to a decimal, then divide by 100, or multiply by 1/100.  

.20 is the fractional number of two tenths or 2/10%.  

(2/10)(1/100)  = 2 / 1000    this can reduce to 1/500

Answer: A. 0.09

Step-by-step explanation:

So if you subtract 45% from 80% and thats when you get 0.09

Answer:

Option B. The Lateral area is 692 cm2

Step-by-step explanation:

Verify each statement

case A) The area of the base  is 384 cm2

The statement is False

Because

The area of the base is

[tex]B=\frac{1}{2}(24)(16)=192\ cm^{2}[/tex]

case B) The Lateral area is 692 cm2

The statement is True

Because

we know that

The lateral area is equal to the area of its three triangular lateral faces

so

[tex]LA=2(\frac{1}{2}(20)(22))+ \frac{1}{2}(24)(21)=692\ cm^{2}[/tex]

case C) The surface area is 740 cm2

The statement is False

we know that

The surface area is equal to the lateral area plus the area of the base

so

[tex]SA=LA+B[/tex]

we have

[tex]LA=692\ cm^{2}[/tex]

[tex]B=192\ cm^{2}[/tex]

substitute

[tex]SA=692+192=884\ cm^{2}[/tex]

case D) The area of each congruent face is 264 cm2

The statement is False

The area of  each congruent face is equal to

[tex]A=\frac{1}{2}(20)(22)=220\ cm^{2}[/tex]

Answer:

8.) x = 15

Step-by-step explanation:

8.) divide 40 by 2 = 20 to only find half the triangle..

20^2 + b^2 = 25^2

400 + b^2 = 625

-400            -400

√b^2 = √225

b = 15

Answer:

c

Step-by-step explanation:

Answer:

(-2 , -2)

Step-by-step explanation:

Solution of the system of equations is where the lines intersect

So they intersect at x = - 2 and y = -2

Answer (-2 , -2)

Answer:

Step-by-step explanation:

The solution of the system of equations is the point of the intersection of a lines.

Final answer:

To find the diameter of Monica's shirt button with a radius of 1 centimeter, we multiply the radius by 2, resulting in a diameter of 2 centimeters.

Explanation:

The question asks to determine the diameter of a button given its radius. The radius of Monica's shirt button is 1 centimeter. In geometry, the diameter of a circle is defined as twice the radius. Therefore, to find the button's diameter, you simply multiply the radius by 2.

Formula: Diameter = 2 × Radius

Calculation: Diameter = 2 × 1 cm = 2 cm.

Thus, the diameter of Monica's shirt button is 2 centimeters

Answer:

Lets firts mention that the rule presented in the question does not apply for all real numbers

But, we can see that in some cases it might be true.

Let

a = 1

b = 0

√1 + √0  = 1 + 0 = 1

Likewise,

√(1 + 0)  =  √(1) = 1

And we see that the result is the same.

tiene que sacar la raiz nena

Answer:  π and √5

Step-by-step explanation:

π is irrational

√5 is irrational

0.3333 is rational (repeating decimal)

√-4 is imaginary (equal to 2i) so is not a Real Number

1/9 is rational (repeating decimal) equal to 0.11111