If p:q=3:4 and q:r=14:9, find p:r

Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are

a(2) = a(1) + d = a + d

a(3) = a(2) + d = a + 2d

a(4) = a(3) + d = a + 3d

and so on, up to

a(n) = a + (n - 1) d

We're given that the 30th term is 98, so

a(30) = a + 29d = 98

The sum of the first 30 terms is 1635, so that

[tex]\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2[/tex]

so that

30a + 435d = 1635

Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.

-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635

-30a - 870d + 30a + 435d = -2940 + 1635

-435d = -1305

d = 3

Then

a + 29 (3) = 98

a + 87 = 98

a = 11

Step-by-step explanation:

45 >= 4x + 5

40 >= 4x

10 >= x (x <= 10)

and

53 > 4x + 5

48 > 4x

12 > x (x < 12)

so, both conditions need to be true (that is the meaning of "and").

how can that be achieved ? well, the harder, narrower condition beats any other.

so, when x <= 10, then it is automatically also smaller than 12.

so, the solution (inequality notation) is

x <= 10

and the graph just shows a line that starts at 10 (with a full, black dot at 10, as the point is included) and goes all the way to the left (to infinity and beyond ...)

Answer:

I'm pretty sure it's the 3rd option

Answer:

first option is correct

Step-by-step explanation:

because there are less no. on negative side than on positive one

Step-by-step explanation:

We have

1-cot²a + cot⁴a = sin²a(1+cot⁶a)

First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.

We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have

1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.

sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

We can then factor cos²a out of the numerator

sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so

sin²a = (1-cos²a)

sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1

sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1

sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

=  sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a

= sin²a + cos⁶a/sin⁴a

= sin²a(1+cos⁶a/sin⁶a)

= sin²a(1+cot⁶a)

Answer:

x=9

Step-by-step explanation:

.5x+.7 = .3x+2.5

     -.7   -.3x

.2x=1.8

/.2    /.2

x=9

.5(9)+.7=5.2

.3(9)+2.5=5.2

Answer:

13

Step-by-step explanation:

[2×1+6×4]÷2

[2+24]÷2

26÷2

13

Answer:

Below

Step-by-step explanation:

First we can find the volume of the box

v = lwh

v = (20)(16)(16)

v = 5120 in^3

Find the volume of the cylinder using this formula

   V = πr^2h

   V = π(5)^2(20)

   V = 1570.79633 (plug this into the final equation, not the rounded one in case it screws up the final value)

   V = 1570.8 in^3

Now we can find the volume of the shaded region by subtraction

5120 - 1570.7963= 3549.2037

Rounding to the nearest 10th and you get....

V = 3549.2

Hope this helps!

11 is the mystery number

Answer:

The mystery number is 11

Step-by-step explanation:

→ Set up an equation

( 10 + 4 + 7 + x ) ÷ 4 = 8

→ Multiply both sides by 4

21 + x = 32

→ Minus 21 from both sides

x = 11

Answer:

66

Step-by-step explanation:

since BD and BC are congruent, angle C and angle D are equal. this means 6x-9=3x+24. If you solve this equation you get x=11. If you plug it into either 6x-9 or 3x+24 you get 57. 180-(57+57)=66

Answer: Choice A

Explanation:

Since -3/5 > -0.8, this means -3/5 is to the right of -0.8

Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.

Any negative value is always to the left of 0, so -3/5 is to the left of 0.

That's why the answer is choice A.

Answer: Option 4 (Hexagon)

Step-by-step explanation:

A equilateral triangle, square and hexagon can be used to form a tessellation.

Please click thanks and mark brainliest if you like

Answer:

1 tens and 5 ones

Answer:

13x^2 - xy

Step-by-step explanation:

4x^2-3xy+2xy+9x^2

=13x^2-xy

Answer:

0.861

Step-by-step explanation:

Answer:

31/36

Step-by-step explanation:

3/4 + 1/9

= 31/36 --> this is the simplest form, you can't simplify any further.

Step-by-step explanation:

Step 1:  Write the equation using point-slope form

Point-Slope Form:  [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

[tex]y-0=m(x-3)[/tex]

[tex]y = m(x-3)[/tex]

Step 2:  Find the slope

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-2-0}{-2-(-3)}[/tex]

[tex]m=\frac{-2}{1}[/tex]

[tex]m=-2[/tex]

Step 3:  Combine them together

[tex]y = m(x - 3)[/tex]

y = -2(x - 3)

IF NEEDED:  Completely factor

[tex]y = (-2 * x) + (-2 * -3)[/tex]

y = -2x + 6

The volume of the new cone would be 1331 times more than the volume of the original cone. Thus, The volume of the original cone is multiplied by 1331

The volume of the cone can be calculated by the given formula:

                       The volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

where r = radius of the cone

           h = height of the cone

Solution:

The volume of the original cone= .......1

It is given that the height and radius of a cone are multiplied by 11.

then volume

= [tex]\frac{1}{3} \pi (11r)^{2} (11h)[/tex]

= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex] .........2

The change in volume of the cone after multiplying 11 to r and h would be

dividing equation 2 by equation 1

=  [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex]/[tex]\frac{1}{3} \pi r^{2} h[/tex]

= 121*11

= 1331

Thus, The volume of the original cone is multiplied by 1331

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Answer:

Kazan also SOS jz zks zj sj aka always zks. aiwow

Answer:

5x+1=6.136

5x=6.136-1

5x=5.136

x=5.135/5

x=1.03

x=1

Answer:

y=-3x+5

Step-by-step explanation:

concepts: y=mx+b is slope intercept equation formula

m=slope

b= y intercept

Therefore we need to find the slope and y intercept

first find slope

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

let y2 be 2

let y1 be -4

let x2 be 1

let x1 be 3

[tex]\frac{2-(--4)}{1-3}[/tex]

6/-2 = -3

m=-3

slope is -3

y= -3x+ b

we need find y intercept now

just plug in (1,2) into that equation

2=-3(1)+b

b=5

y=-3x+5

Answer:

x = 24.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 43 = x /34

34 cos 43 = x

x=24.86602

To the nearest tenth

x = 24.9

Answer:

3 a) solution:-

Discount=Rs 1,200

S .P =RS 4,000

M P=?

we know that,

Discount= M.P - S.P

or, Rs 1,200= M.P - Rs 4,000

or, M.P = RS (4,000-1,200 )

M.P = RS 2,800

In no. 3 all we have to make like this .........

Hope it helps

Answer:

Step-by-step explanation:

2)a) M.P =₹ 5000

S.P = ₹4000

Discount amount = M.P - S.P

                            = 5000 - 4000

                            = ₹1000

Discount percent = [tex]\frac{discount \ amount}{M.P}*100[/tex]

                             [tex]= \frac{1000}{5000}*100\\[/tex]

                             = 20%

3)a) Discount = ₹ 1200

S.P = ₹ 4000

M.P = S.P + discount

      = 4000 + 1200

      =  ₹ 5200

4)a ) Discount rate = 15%

S.P= ₹ 4000

[tex]M.P = \frac{100+Discount rate}{100}*S.P\\\\=\frac{115}{100}*4000[/tex]

= ₹ 4600

Answer:

b is 7 units from 0.

Step-by-step explanation:

[tex]|b|[/tex] = 7 means that the absolute value of b is 7. This means that b can be -7 or 7, so it will always be 7 units from 0.

Hope this helps!

  [tex]y=0[/tex] allows you to determine the x-intercept of a graph.

Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.

Know more about x-intercept and y-intercept here:

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#SPJ2

Answer:

x³ (4x + 1)(4x - 1)

Step-by-step explanation:

Answer:

x^3 (4x-1)(4x+1)

Step-by-step explanation:

16x^5-x^3

Factor out x^3

16* x^2*x^3 - x^3

x^3(16x^2 -1)

The term inside the parentheses is the difference of squares

a^2 - b^2 = (a-b)(a+b)

x^3 ( (4x)^2 -1^2)

x^3 (4x-1)(4x+1)

Answer:

90

Step-by-step explanation:

c is perpendicular to b

That means angles 5,6,7,8 are 90 degrees

a is parallel to c

That means b is perpendicular to a

That means that 1,2,3,4 are 90 degrees

<1 = 90 degrees

Answer:

the answer is 90

Step-by-step explanation:

simpliy because c and b make a right angle

Answer:

10 levels

Step-by-step explanation:

Ralph is on level 7

Mike level 5

Don level 10 and is playing the last one of game

The game has 10 levels

Leo is playing the first level and Ralph is sex levels above Leo. This means that Ralph is playing level:

= 1 + 6

= 7

Mike is two levels below Ralph which means that Mike is playing level:

= 7 - 2

= 5

Don is playing the last level and is five levels above Mike which means that Don is playing level:

= 5 + 5

= 10

Don is playing level 10 which is the last level so the game has 10 levels.

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Answer:

(x, y ) → (x + 7, y + 5 )

Step-by-step explanation:

Consider the coordinates of R and R'

R (- 5, 0 ) and R' (2, 5 )

x- direction : - 5 → 2 is + 7 units

y- direction : 0 → 5 is + 5 units

Translation rule is (x, y ) → (x + 7, y + 5 )

Answer:

h(x)=\sqrt(x+6)

Step-by-step explanation:

I just did the test for a p e x