please help me !! :)

Answer:

[tex]\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}[/tex]

Step-by-step explanation:

The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2\pi r[/tex]. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle [tex]\theta^{\circ}[/tex] is equal to [tex]2\pi r\cdot \frac{\theta}{360}[/tex].

Formulas at a glance:

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

[tex]C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}[/tex]

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

[tex]\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}[/tex]

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting [tex]r=2[/tex] into our circumference formula, we get:

[tex]C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}[/tex]

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

[tex]\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}[/tex]

The ratio 2:3 means for every 2 inches on the original, the photocopy would be 3 inches.

3/2 = 1.5

The photocopied image is 1.5 times larger than the original.

Side BG on the original is side FG on the copy:

14 x 1.5 = 21 meters

FG = 21 meters

Answer:

FG = 21

Step-by-step explanation:

The ratio is 2:3

2               BC

----- = ----------------

3                FG

2              14

----- = ----------------

3                FG

Using cross products

2FG = 3*14

2FG = 42

Divide by 2

FG = 21

Answer:

2, 3, 5, 7, 11, 13.

Step-by-step explanation:

A prime number is a number that you don't get a whole number when divided by 2 but you do get a whole number when divided by prime numbers such as 3,5,7,11... Basically a number with two factors, it can only be divided by 1 or themselves. for example:

9/2 = 4.5 (this is not a whole number so it might be a prime.

9/3 = 3 (it works when divided by a prime number.

another:

8/2 = 4 (it gives a whole number when divided by 2 therefor, it can't be a prime number.

Answering:

There are 6 prime numbers at the top^^^^.

One possible answer is  2, 3, 5, 41, 67, 89

Another possible answer is  2, 3, 5, 47, 61, 89

Other answers may be possible.

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

Explanation:

This is a trial and error type of problem. Though with practice it's not as blind of randomly guessing.

We have 9 values here. If we paired them up, then we can form at most 4 pairs (since 9/2 = 4.5 rounds down to 4). That means we won't be able to form six two-digit primes. Some of the primes must be single digits.

We can have 3 single digit primes and 3 two-digit primes since 3+2*3 = 9.

The single digit primes are: 2, 3, 5, 7

Let's say 2 and 5 are definitely locked down to be the single digit group. I'm doing this since we can't have 2 or 5 as the units digit. If the units digit is 2, then 2 is a factor and it's not prime. Similarly, if 5 is the units digit, then 5 is a factor and that two digit value is not prime.

For good measure, we'll throw 3 in there as well and see what happens.

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

The digits we have left are: 1, 4, 6, 7, 8, 9

The number 14 isn't prime, but 41 is prime

67 is prime so that's another two values off the list

lastly, 89 is prime so that works as well.

So one possible sequence is 2, 3, 5, 41, 67, 89

Notice how we can swap the 1 and 7 to go from 41,67 to 47,61; this gets us two other primes. So another possible answer is 2, 3, 5, 47, 61, 89

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

Side note: having the list of primes on a reference sheet is a handy recommendation. You only need to go up as high as 97 which is the largest two digit prime.

Answer:

cannot be determined

Step-by-step explanation:

We do not know if any of the angles are equal and are only given two sides.

We cannot determine if the two triangles are similar

Answer:

y = 5/4x-15

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x+b

Substitute the point into the equation and solve for b

-5 = 5/4(8)+b

-5 = 10+b

Subtract 10 from each side

-5-10 = b

-15 = b

y = 5/4x-15

Step-by-step explanation:

y-y'=m(x-x')

y-(-5)=5/4(x-8)

y+5=5x/4-10

4(y+5)=4(5x/4)-10(4)

4y+20=5x-40

4y-5x=-40-20

4y-5x=-60

5x-4y-60=0

y=5x/4-15

Answer: 1:3

Step-by-step explanation:

The odds are 2/6 because you’re given 2 choices from the 6 side die you can then simplify that fraction to 1:3

Answer:

the correct answer is option 1.

The correct explanation is: All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

In an equilateral triangle, all three sides are congruent, and all three angles are congruent.

Therefore, any equilateral triangle can be transformed into any other equilateral triangle through a combination of translations, rotations, and reflections, without changing the size or shape of the triangle.

Thus, all equilateral triangles are similar, with side lengths in a 1:1 ratio, since they have the same shape but may differ in size.

To learn more about similar triangles;

https://brainly.com/question/14926756

#SPJ7

Answer:

...-243, 729, -2187

Step-by-step explanation:

-3, 9, -27, 81, -243, 729, -2187

Everytime ×(-3)

-3×(-3)=9

9×(-3)=-27

-27×(-3)=81

Etc.

Answer:

56

Step-by-step explanation:

that is the procedure above

The missing segment in the image below is 8.

The missing segment is the side length of the small triangle that is formed by the two red lines and the green line. We can find the length of this side length by using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the missing segment, and the other two sides are 4 and 5.

missing [tex]segment^2[/tex] = [tex]4^2[/tex] + [tex]5^2[/tex]

missing [tex]segment^2[/tex] = 16 + 25

missing [tex]segment^2[/tex] = 41

missing segment = √41

Therefore, the missing segment is √41.

Here are the steps in detail:

Identify the small triangle that is formed by the two red lines and the green line.

Label the sides of the triangle with the letters A, B, and C, where C is the missing segment.

Substitute the known side lengths into the Pythagorean Theorem.

Solve for the length of the missing segment.

To learn more about segment here:

https://brainly.com/question/12622418

#SPJ2

Answer:

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

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

[tex]\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

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

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

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

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

Answer:

d talking into microphone

Answer:

i can help you i know this answer

Answer:

5 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

let h be the hypotenuse , then

h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

h = [tex]\sqrt{25}[/tex] = 5

Answer:

siis  corretoed

Step-by-step explanation:

Answer:

The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"

Step-by-step explanation:

Answer:

There were 44 students in each bus.

Step-by-step explanation:

357 - 5 = 352

352/8 = 44

Answer:

Step-by-step explanation:

Total students = 357

Total buses filled = 8

No of students traveled in car = 5

Remaining students = 357 - 5 = 352

Students in each bus = 352 ÷ 8 = 44 students

Answer:

119?

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to write the equation of this line, we need to pick 2 points on the graph where the line goes right through the intersection of the grids. Actually, you only need 1 of these, because the line goes through at (0, 15). Another point then can be (6, 6). Locate this point so you know what I means when I say that the line goes right through where the grids intersect at x = 6 and y = 6 (as opposed to somewhere in the middle of one of these grids). Find the slope between these 2 points:

[tex]m=\frac{6-15}{6-0}=-\frac{9}{6}=-\frac{3}{2}[/tex]

Since there's only one choice with that slope, that is the choice you want.

Answer:

22+g=65

Step-by-step explanation:

take the 22 add (sum) to g (the variable) and have them = 65

Answer:

Step-by-step explanation:

15. = 2.39

and jus use mathaway lma

Answer:

17 lb I guess 8 don't think the question is full

Step-by-step explanation:

the question is half

Answer:

Hello,

answer B

2

Step-by-step explanation:

[tex]\dfrac{2}{x} -\dfrac{x}{x+5} =\dfrac{10}{x^2+5x} \\\\we\ suppose\ x\neq 0\ and\ x\neq -5\\\\\text{Reducing to the same denominator}\\\dfrac{2(x+5)-x^2}{x(x+5)} =\dfrac{10}{x^2+5x} \\\\Simplify\ by\ x^2+5x\\\\2x+10-x^2=10\\\\-x^2+2x=0\\\\-x(x-2)=0\\\\roots\ are\ 2 \ and\ 0\ (to\ be\ excluded)\\\\Root=2\\[/tex]

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Answer:

x = -12

Step-by-step explanation:

5x + 2(2x - 23) = -154

Distribute;

5x + 4x - 46 = -154

Collect like terms

9x - 46 = -154

Add 46 to both sides;

9x = -108

Divide both sides by 9

x = -12

Answer: When f(x)=g(x) , x equal to -2 or -1

Step-by-step explanation:

Answer:

a. 35 Kilometres.

b. 60 litres.

c. 8150 sweets.

Step-by-step explanation:

Given the following data;

a. To find how many kilometres he traveled in one day;

770 km = 22 days

X km = 1 day

Cross-multiplying, we have;

22X = 770

X = 770/22

X = 35 Kilometres.

b. To find how many litres he would need to go 840 km;

1 litre = 14 kilometres

X litres = 840

Cross-multiplying, we have;

14X = 840

X = 840/14

X = 60 litres.

c. To find how many sweets are there in his car;

Number of sweet box, Ns = 326 boxes

Number of sweets in each box, Sw = 25 sweets

Total number of sweets = Ns * Sw

Total number of sweets = 326 * 25

Total number of sweets = 8150 sweets.

Answer:

-23/9  or -2 5/9

Step-by-step explanation:

w+(-x) - 2/3

Let w = -5/9  and x = 4/3

-5/9+(- 4/3) - 2/3

Get a common denominator of 9

-5/9 - 4/3 *3/3 - 2/3 *3/3

-5/9 - 12/9 - 6/9

-23/9

-2 5/9

Answer:

-2 5/9

Step-by-step explanation: