prove that there are infinitely many primes of the form 3n 2, n eo z .

Answer:

16.   Angle 2 is 30° and angles 1 & 3 are 150°

17. Equilateral (all sides are equal)

18. A, B, D

19. A, B. (8 angles and all sides are congruent)

20. False.

Step-by-step explanation:

angle 2 is a corresponding (ish) angle to the one marked 30°, so they are the same. and then the other angle is supplementary to the 30° one, therefore they must add up to 180 degrees. 180-30= 150 so that is angle 1 and 3.

Answer:

question 1 - angle 1 and 2 the answer is 150 and angle 3 is 30

question 2 - the triangle is an equilateral

Question 3 - A,B,D

question 4 - A,B

Step-by-step explanation:

Answer:

i don t this topic because i am the secundary

Step-by-step explanation:

.

The value of rocket's distance will be 51.66.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

When a rocket is launched, it climbs 50 feet for every 13 feet it travels horizontally.

Now,

Since, When a rocket is launched, it climbs 50 feet for every 13 feet it travels horizontally.

And, The figure is shown the right triangle.

So, We can apply the Pythagoras theorem as;

⇒ x² = 50² + 13²

⇒ x² = 2500 + 169

⇒ x² = 2669

⇒ x = √2669

⇒ x = 51.66

Thus, The value of rocket's distance will be 51.66.

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12620256  different combinations of 31 balloons can be chosen

What are combinations?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

From the question, we understand that; a combination of 31 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

n= 31 +8-1 = 38

r=31

Selection =  \(^{38}C_{31}\)

Use the formula:

\(^{n}C_{r}=\frac{n!}{(n-r)! r!}\)

= > \(^{38}C_{31}=\frac{38!}{(38-31)! 31!}\)

\(^{38}C_{31}=\frac{38!}{7! 31!}\)

         = \(\frac{38*37*36*35*34*33*32*31!}{7*6*5*4*3*2*1* 31!}\)

         = 12620256

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Answer:

see derivation below

Step-by-step explanation:

Show that:

( sec(t) - cosec(t) ) ( 1 + tan(t) + cot(t) ) =

sec(t) tan(t) - cosec(t) cot(t)

Some trigonometric definitions used:

tan(t) = sin(t)/cos(t)

cot(t) = cos(t)/sin(t)

sec(t) = 1/cos(t)

csc(t) = 1/sin(t)

some trigonometric identities used:

sin^2(t) + cos^2(t) = 1 ......................(1)

rewrite left-hand side in terms of sine and cosine

(1/cos(t) - 1/sin(t) ) ( 1 + sin(t)/cos(t) + cos(t)/sin(t) )

Simplify using common denominator sin(t)cos(t)

= ( (sin(t) - cos(t))/(sin(t)*cos(t)) ) * ( ( sin(t)cos(t) + sin^2(t) + cos^2(t)) / ( sin(t)cos(t) ) )

= ( sin(t) -cos(t) ) * (1 + sin(t)cos(t) ) / ( sin^2(t) cos^2(t) )   ...... using (1)

Expand by multiplication

= ( sin(t) -cos(t) + sin^2(t)cos(t) - sin(t)cos^2(t) ) / ( sin^2(t) cos^2(t) )

Rearrange by factoring out sin(t) and cos(t) in numerator

= ( sin(t) (1-cos^2(t) - cos(t)(1-sin^2(t) )  / ( sin^2(t) cos^2(t) )

= ( sin^3(t) - cos^3(t) ) /( sin^2(t) cos^2(t) )   .........................using (1)

Cancel common factors

= sin(t)/(cos^2(t)) - cos(t)/(sin^2(t))

Rewrite using trigonometric definitions

= sec(t)tan(t) - csc(t)cot(t)   as in Right-Hand Side

The two scale degrees shared by the iii chord and the v chord are 2 and 4. Therefore, the correct option is option 2.

1: Determine the scale degrees of each chord

The iii chord consists of scale degrees 3, 5, and 7

The v chord consists of scale degrees 5, 7, and 2 (in some cases notated as 9)

2: Compare the scale degrees to find the shared ones

Both the iii chord and the v chord share scale degrees 2 and 4.

Hence, the two scale degrees which is shared by the iii chord and the v chord are option 2: 2 and 4.

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The independent variable in this experiment is the ink color used to present the test (black ink or red ink).

1. The professor is conducting an experiment where the ink color used to present the test is being manipulated.

2. The students are divided into two groups: one group receives the test in black ink, and the other group receives the test in red ink.

3. By using different ink colors, the professor is creating two distinct conditions or treatments for the students.

4. The purpose of manipulating the ink color is to examine if it has any effect on the students' test scores.

5. The professor will collect and compare the test scores of both groups to determine if there are any differences between them.

6. The ink color is the independent variable because it is the variable being deliberately changed by the professor in order to observe its potential impact on the students' test scores.

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Answer: A, B, C, and D have the same volumes:  100 units^3

Step-by-step explanation:

The details are attached.  Use the volume formula for the respective shapes.  Bear in mind that B is he area of the base (I assume).  It is the

\(\pi\)\(r^{2}\) in the formulas that have a round base, and the width x length for bases that are rectangular (or square).

Answer:

20

Step-by-step explanation:

Count the number of scores there are.

Answer:

2243x32

Step-by-step explanation:

23r4ft3gweftb3q54rvfwgeht rtg,5tjqbygucmrekv wjhqvrxerjuwqrgf4 jfy2qteg cwrhgrwe;iujihyuwgreob0uyergvbfyuwehvgboyu8erhgbhyurehgbyew8uhjrghyhbe3rjuhghbuyrehjgbyuhrejgbyuerjhghreyuhjgfhrueyhjfhgreuyhfgyurehfueirhfurehruyehgvbuyhgfhbhurjehguyhjnvdbkjhgifuejdhfguyfdhuyefhjhbgfuyvfjhgbfyugvhfnghbuhyfjvgryu78uyregyt587yuygh8ruiggh587eru5 y587urifibyutg89fhju34hr583u4 i43498iuty3894 iutu3489tu3389uyt38u

Answer:

  $12.92

Step-by-step explanation:

The total being split 3 ways is ...

  $32.85 × (1 + 0.18) = $38.76

So each pays ...

  $38.76 / 3 = $12.92 . . . amount each person pays

Answer: 222.78

Step-by-step explanation:

Answer:

x > -3

Step-by-step explanation:

Step 1: Write inequality

-5x + 6 < 21

Step 2: Solve for x

The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are: a) sin(2x) = 2sin(x)cos(x). b) cos(2x) = cos^2(x) - sin^2(x). c) tan(2x) = 2tan(x) / (1 - tan^2(x))

(a) To find the exact value of sin(2x), we can use the double angle formula for sine:

sin(2x) = 2sin(x)cos(x)

Therefore, the exact value of sin(2x) is 2sin(x)cos(x).

(b) To find the exact value of cos(2x), we can use the double angle formula for cosine:

cos(2x) = cos^2(x) - sin^2(x)

Therefore, the exact value of cos(2x) is cos^2(x) - sin^2(x).

(c) To find the exact value of tan(2x), we can use the double angle formula for tangent:

tan(2x) = 2tan(x) / (1 - tan^2(x))

Therefore, the exact value of tan(2x) is 2tan(x) / (1 - tan^2(x)).

The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are:

a) sin(2x) = 2sin(x)cos(x)

b) cos(2x) = cos^2(x) - sin^2(x)

c) tan(2x) = 2tan(x) / (1 - tan^2(x))

These formulas allow us to express the values of sin(2x), cos(2x), and tan(2x) in terms of the values of sin(x) and cos(x) without explicitly solving for x.

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Answer:

D

Step-by-step explanation:

Given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

• If a > 0 then minimum value

• If a < 0 then minimum value

For

f(x) = x² + 16x + 3

a = 1 > 0 then f(x) has a minimum value

The minimum is the value of the y- coordinate of the vertex.

The x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

Here a = 1 and b = 16 , then

\(x_{vertex}\) = - \(\frac{16}{2}\) = - 8

To find the y- coordinate of the vertex, substitute x = - 8 into f(x)

f(- 8) = (- 8)² + 16(- 8) + 3 = 64 - 128 + 3 = - 61

Thus the function has a minimum value of - 61 → D

9514 1404 393

Answer:

  (7.5, 1.7)

Step-by-step explanation:

The point of interest (P) is the weighted average of the end points. The weights are the reverse of the lengths of the associated segments.

  P = (3A +7B)/10

  P = (3(-3, -6) +7(12, 5))/10 = (-9+84, -18 +35)/10 = (75, 17)/10

  P = (7.5, 1.7)

The volume of the larger cylinder is 54 cm3.

Two cylinders are said to be similar if the ratio of their radii is equal to the ratio of their heights is equal.

Analysis:

let length of radii for  smaller and bigger cylinders to be r and R respectively.

let length of height of smaller and bigger cylinder be h and H respectively.

Base area of smaller cylinder = π\(r^{2}\) = 24

r = \(\sqrt{\frac{24}{\pi } }\)

Base area of bigger cylinder =  π\(R^{2}\) = 54

R = \(\sqrt{\frac{54}{\pi } }\)

volume of smaller cylinder = base area x height

16 cm3 = 24 cm2 x h

h = 16/24 = 2/3m

for similar cylinders, \(\frac{r}{R}\) = \(\frac{h}{H}\)

\(\sqrt{\frac{24}{\pi } }\)/  \(\sqrt{\frac{54}{\pi } }\) = 2/3/H

H = 1cm

volume of bigger cylinder = base area x height = 54 x 1 = 54 cm3

In conclusion, the volume of bigger cylinder is 54 cm3

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Answer:

54cm2

Step-by-step explanation:

Edge.2023! Good luck

Answer:

neither is right

Step-by-step explanation:

it should factorize to (8x + 12) (x + 1)

Answer:

7 laps

Step-by-step explanation:

4n = 28

n = 7

hope this helps :)

Answer:

9/25

Step-by-step explanation:

The total 460 cards are sold on Mothers day.

Given that, Bob's gift shop sold a record number of cards for Mother's Day.

One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day.

Let the number of cards sold on mothers day be x.

Here, 10% of x =46

10/100 ×x= 46

10x=4600

x=460

Therefore, total 460 cards are sold on Mothers day.

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Answer:

28

Step-by-step explanation:

im famous bro

Step-by-step explanation:

Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.

Let x = distance (mile)

let y = total charge (dollars)

Yellowcab company equation for cost calculation;  3.50 + 2.5x = y

laxicab company equation for cost calculation;  4.54+2.3x = z

the two companies charge the same amount when y = z

; 3.50 + 2.5x = 4.54+2.3x

x = 5.2 miles

COST CALCULATION

;3.50 + 2.5x = ?

if x = 5.2;

; 3.50 + 2.5(5.2) =$16.50

OR

; 4.54+2.3x = ?

; 4.54 + 2.3(5.2) = $16.50

The required answer of the word problem is the machine requires 0.051 hours to make 612000 aluminum cans.

The given question is a word problem which can be calculated as,

A machine working at a constant rate makes 3313 aluminium cans in one second.

Therefore, one aluminum can be produced in = 1/ 3313 seconds.

The machine makes 612000 aluminum cans.

Thus, 612000 aluminum cans can be produced in = (612000)*(1/3313) seconds = 184.7268336855 seconds

= 184. 72 seconds (approximately up to two decimal places)

We can convert the value in seconds to hours of the  given  problem as,

There are 3600 seconds in one hour.

That is, one second = 1/3600 hours.

Thus, the machine makes 612000 cans in = (184.72)*(1/3600) hours

= 0.0513111111 hours

= 0.051 hours ( approximately up to three decimal places)

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Answer:

Answer in explanation

Step-by-step explanation:

y = 0.752x + 4.75

The independent variable will refer to what we have on the horizontal axis which is x. It is from these x we will get the values of the y

The dependent variable is the other variable asides the independent, in this case, the dependent variable is y

When we talk of the domain, we talk of the range of values from the independent variable axis

Here, these values are 0,1,2 or 3

Lastly, the domain refers to the range of values on the y-axis

To get this, we need to input the x-values digit into the equation one after the other

At x = 0

y = 4.75

At x = 1

y = 0.752 + 4.75 = 5.502

At x = 2

y = (0.752)2 + 4.75 = 6.254

At x = 3

y = 0.752(3) + 4.75

= 7.006

The range of values is between 4.75 and 7.006

Answer:

16

Step-by-step explanation:

3 x 3 = 9 then 9 +7 = 16