15÷7500
what is the answer
​

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

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{13}{15}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{-13}{15})²}[/tex]

Solving numerical

[tex]Sin\theta_{1}=\sqrt{1-(\frac{169}{225})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{56}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{56}}{\sqrt{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*14}}{\sqrt{15*15}}[/tex]

[tex]Sin\theta_{1}=\frac{2\sqrt{14}}{15}[/tex]

Since

In III quadrant sin angle is negative

Answer:

Step-by-step explanation:

In the quadrant III both the sine and cosine get negative value.

Use the identity:

And consider negative value as mentioned above:

9514 1404 393

Answer:

  m∠H = 38°

Step-by-step explanation:

External angle GFD is the sum of internal angles G and H.

  14x +1 = 89° +(5x -7)

  9x = 81°

  x = 9°

Then the measure of angle H is ...

  angle H = 5(9°) -7° = 38°

Answer:

The answer is $82.46 sales tax

$1,260.46 Total

Step-by-step explanation:

Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46

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:

[tex]\|a\| = 5\sqrt{13}[/tex].

[tex]\|b\| = 3\sqrt{29}[/tex].

Step-by-step explanation:

Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:

[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].

[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].

[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].

The question states that [tex]\| a + b \| = 34[/tex]. In other words:

[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].

[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].

[tex]289\, k^{2} = 34^{2}[/tex].

Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].

[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].

[tex]k^{2} = 2^{2}[/tex].

The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].

Therefore:

[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].

[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].

[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].

Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].

[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].

Hence:

[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].

[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].

Answer:

119.43 cm²

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of rectangle - area of circle

   = (11 × 12) - π × 2²

  = 132 - 4π

  ≈ 119.43 cm² ( to the nearest hundredth )

Answer:

2x - 19

Step-by-step explanation:

Perimeter = sum of sides

First let's simplify each side

We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.

2(x + 5)

Distribute by multiplying x and 5 by 2

2 * x = 2x and 2 * 5 = 10

2x + 10

1/2(4x + 8)

Distribute by multiplying 4x and 8 by 1/2

1/2 * 4x = 2x and 1/2 * 8 = 4

2x + 4

-3(2x + 11)

Distribute by multiplying 2x and 11 by -3

-3 * 2x = -6x

-3 * -33

-6x - 33

Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )

2x + 10 + 2x + 4 - 6x - 33

Combine like terms

2x + 2x - 6x = -2x

10 + 4 - 33 = -19

Perimeter: -2x - 19

Answer:

Perimeter = - 2x - 19

Step-by-step explanation:

[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]

So, the perimeter is - 2x - 19.

Answer:

Irrational

Step-by-step explanation:

It's an irrational number since both of them are irrational

Answer:

h=6

Step-by-step explanation:

Answer:

13x^2 - xy

Step-by-step explanation:

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

=13x^2-xy

Answer:

0.75, 1.25

Step-by-step explanation:

first we bring the line equation into the same format as the parabola equation (y = ...)

3x - y = 1

=>

y = 3x - 1

now we can say for the intersection points both equations must have the same result.

4x² - 1 = 3x - 1

4x² - 3x = 0

x(4x - 3) = 0

there are only 2 possible cases to make this true :

x = 0

and 4x - 3 = 0

4x = 3

x = 3/4 = 0.75

for the y value let's use the easier equation (line) :

y = 3×3/4 - 1 = 9/4 - 4/4 = 5/4 = 1.25

Answer:

[7]

[8]

[9]

Step-by-step explanation:

according to your question

your answer is

[7]

[8]

[9]

you must be write this answer in one bracket

Answer:

1

Step-by-step explanation:

1

Answer:

x is 7

EF is 10

FG is 12

Step-by-step explanation:

[tex]EF + FG = EG \\ (4x - 18) + (3x - 9) = 22 \\ 7x - 27 = 22 \\ 7x = 49 \\ x = 7[/tex]

then substitute:

[tex]EF = 4x - 18 \\ EF = 4(7) - 18 \\EF = 28 - 18 \\ EF = 10[/tex]

[tex]FG = 3x - 9 \\ FG = 3(7) - 9 \\FG = 21 - 9 \\ FG = 12[/tex]

First question:

BC + BA = CA

BC = CA - BA

BC = 36 - 9

BC = 27

Step-by-step explanation:

Put the numbers as the value is given

So,

(6+5)= 11 Answer

Answer:

see below

Step-by-step explanation:

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

cos theta = adj / hypotenuse

cos x = 13/20

Taking the inverse cos of each side

arccos ( cos x ) = arccos( 13/20)

x = arccos ( 13/20)

x =49.45839

x = 49  to the nearest whole number

sin theta = opp/ hyp

sin y = 13/20

Taking the inverse sin of each side

arcsin ( sin y ) = arcsin( 13/20)

y = arcsin ( 13/20)

y=40.5416

y = 41 to the nearest whole number

Answer:

Option A, systematic sample

Answer:

dddddd=666=7777

Step-by-step explanation:

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)

Assuming you want to do a cartesian product, then you basically form items (x,y)  such that x is in set A, and y is in set A

More generally, A * B will consist of items of the form (x,y) such that x is in A and y is in B. However, we have B = A.

So,

A * A = {

(a,a), (a,b), (a,c)

(b,a), (b,b), (b,c)

(c,a), (c,b), (c,c)

}

I broke things up into separate rows to show that we can form a 3x3 table. Each row is a different x value from the set {a,b,c}. Each column is a different y value from the set {a,b,c}

In my opinion, this helps organize things much better than rather have it all on one single line like this

A * A = { (a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c) }

which in all honesty looks like a bit of a cluttered mess.

Answer:

Step-by-step explanation:

A={a,b,c}

A×A={a×a,a×b,a×c,b×a,b×b,b×c,c×a,c×b,c×c}

Answer:

If 4 flower pots cost 4.08 dollars, then 1 flower pot costs 4.08/4 dollars.

4.08/4 = 1.02.

So the unit price is $1.02.

Let me know if this helps!

Answer:

7

Step-by-step explanation:

Concepts:

Solving:

1. First, let's set up the equation:

7/8 ÷ 1/8

2. We can get the reciprocal of 1/8 by doing the opposite of division; multiplication. 1/8 becomes 1 · 8, and that's equal to 8.

3. Now, since we know dividing a fraction by another one is exactly the same as multiplying the fraction by the reciprocal of the other, let's multiply 7/8 by the inverse of 1/8, which is 8.

7/8 · 8 = 56/8 = 7

Therefore, 7/8 divided by 1/8 is equal to 7.

Answer:

Value is 57

Step-by-step explanation:

sin 33

= sin (90-57)

= cos 57

Answered by GAUTHMATH

Answer:

there is always a y-intercept in all graphs.

Step-by-step explanation:

be it a line graph, quadratic graph or cubic graph. all graphs will definitely have a y-intercept. and in this case, since y=mx + c where c is the y-intercept. the y intercept of this graph is 10

Answer:

5x+1=6.136

5x=6.136-1

5x=5.136

x=5.135/5

x=1.03

x=1

Answer:

A. 132 + 22h > 264

Step-by-step explanation:

Hourly sales = 22 glasses of fruit punch

Sales by 4 p.m = 132 glasses

Goal = more than 264 glasses

h = number of hours they must stay open to make their goal

The inequality:

132 + 22h > 264

22h > 264 - 132

22h > 132

h > 132/22

h > 6 hours

This means, the number of hours they must stay open to make their goal of more than 264 glasses is more than 6 hours