(1 + sin x)(1 – sin x) = cos^2x

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

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

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

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

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

Answer:

23.3 miles

Step-by-step explanation:

- convert 1hour = 60minutes

14 miles per 1 hour , is the same as

14 miles per 60 minutes

-write an equivalent fraction to keep the proportion

14 miles/60 minutes = ? miles / 100 minutes

-cross multiply , and divide by 60

? = (14*100) / 60 = 23. 3333333...

-round to 1 decimal place

23.3 miles

Answer:

r = 5

Step-by-step explanation:

Side 1: 7

Side 2: 2 + r

To determine r, we subtract 2 from both sides to get the following:

Side 1: 5

Side 2: r

5 and r are the same, so 5 must equal 5.

Therefore, r = 5.

Answer:

a=6 and b=8

Step-by-step explanation:

a^2=(9/16)b^2. Substitute this in the second equation, you get b^2+b^2*(9/16)=100, b^2=100*16/25=8 and a=6

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

Answer:

a=41  b=-9

Step-by-step explanation:

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, and3b + 40 = 13, rearranging b = -9.

Answer from Gauth math

Answer:

Hello,

Step-by-step explanation:

We are going to use identification of terms.

[tex]5(7x+8)+3(2x+b)=ax+13\\\\35x+40+6x+3b=ax+13\\\\41x+40+3b=ax+13\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\3b+40&=&13\\\end{array}\right.\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\b&=&-9\\\end{array}\right.\\\\[/tex]

Produced by myself

Answer:

obviously sus island

Step-by-step explanation:

Answer:

32 female - 23 right-handed || 9 left-handed

22 male - 18 right handed || 4 left handed

Step-by-step explanation:

I find it easiest to write all the information out and fill the gaps.

From what we're given, 32 employees are female, that means 22 are male, as 54 - 32 = 22.

We are also given that there are 41 right-handed employees, which means there is 13 left-handed employees by subtraction.

If 18 of the right-handed employees are male, then 23 of them are female, and  4 are left-handed males.

If 23 of the female employees are right-handed, then 9 female employees are left-handed.

It's quite simple if you write everything out :D

f(x) = 5x^2 + 25x + 30

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

Explanation:

The roots, aka x intercepts, of this curve are x = -3 and x =  -2. This is where the graph crosses the x axis.

Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.

So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get

y = (x+3)(x+2)

y = (-1+3)(-1+2)

y = (2)(1)

y = 2

But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)

Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)

Now let's expand everything out and simplify

y = 5(x+3)(x+2)

y = 5(x^2+2x+3x+6)

y = 5(x^2+5x+6)

y = 5x^2+5*5x+5*6

y = 5x^2 + 25x + 30

Choice C is the final answer

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

To check this, we can plug in x = -3 and we should get 0

y = 5x^2 + 25x + 30

y = 5(-3)^2 + 25(-3) + 30

y = 5(9) + 25(-3) + 30

y = 45 - 75 + 30

y = -30 + 30

y = 0

This proves that x = -3 is a root of y = 5x^2 + 25x + 30

I'll let you check x = -2. You should also get y = 0 when plugging this x value in.

Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.

Answer:

Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a = \frac{2b+1}{3b-1}[/tex]

b = 2/3

[tex]2b + 1 = 2*\frac{2}{3}+1\\\\=\frac{4}{3}+1\\\\=\frac{4}{3}+\frac{3}{3}\\\\=\frac{7}{3}\\\\3b-1 = 3*\frac{2}{3}-1\\\\=2- 1 = 1\\\\\\[/tex]

[tex]a = \frac{2b+1}{3b-1}\\\\a=\frac{\frac{7}{3}}{1}\\\\=\frac{7}{3}\\\\[/tex]

a = 7/3

b)

[tex]\frac{2b+1}{3b-1}=a\\\\[/tex]

Cross multiply,

2b + 1 = a*(3b - 1)

2b + 1 = a*3b - 3*a

2b + 1 = 3ab- 3a

2b = 3ab - 3a - 1

2b - 3ab = -3a  - 1

b(2 - 3a) = -3a - 1

[tex]b =\frac{-3a - 1}{2 - 3a}[/tex]

(33.85307637623) = 33.9m

the answer is option d

Answer:

A. {x| –4 < x ≤ 4}

Step-by-step explanation:

Answer:

{x| –4 < x ≤ 4}

Step-by-step explanation:

Edge Quiz 2023

Answer:

you have to put them in order

Answer:

13 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]20+.1x=.4\left(40+x\right)[/tex]

x=40/3 = 13 [tex]\frac{1}{3}[/tex]

Answer:

-1

Step-by-step explanation:

Remember PEMDAS! Start with distributing the parentheses -(3x+6) so you get -8x-3x-6=4-x and simplify. Then you get -11x-6=4-x and combine like terms which equals -10=10x. Simplify and you get -1.

The solution to the equation -8x - (3x + 6) = 4 - x is x = -1.

Given the equation in the question:

-8x - (3x + 6 ) = 4 - x

To solve the equation -8x - (3x + 6) = 4 - x, simplify the equation by isolating all terms with variable x:

-8x - (3x + 6 ) = 4 - x

Distribute the negative sign inside the parentheses:

-8x - 3x - 6 = 4 - x

Combine like terms on both sides of the equation:

-11x - 6 = 4 - x

Add 6 to both sides:

-11x - 6 + 6 = 4 + 6 - x

-11x = 4 + 6 - x

-11x = 10 - x

Next, add x to both sides:

-11x + x = 10 - x + x

-10x = 10

Divide both sides of the equation by -10:

x = -10/10

x = -1

Therefore, the value of x is -1.

Learn more about equations here: brainly.com/question/14686792

#SPJ6

Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

Answer:

7

Step-by-step explanation:

if the bases of the exponents are the same then we can add the powers. so 2^3 * 2^4 = 2^7 = 128.

Answer:

7

Step-by-step explanation:

2^3⋅2^4= 2^7

2^7=2^x

since it had the same base you wouldn't need to worry about it you can just focus on the exponent.

7=x

swap it over

x=7

Answer:

Step-by-step explanation:

By applying tangent rule in the given right triangle AOB,

tan(30°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{BO}{OA}[/tex]

[tex]OA=BO(\sqrt{3})[/tex]

By applying tangent rule in the given right triangle BOC,

tan(60°) = [tex]\frac{OC}{BO}[/tex]

OC = BO(√3)

OA + OC = AC

[tex]BO(\sqrt{3})+BO(\sqrt{3}) =60[/tex]

2√3(BO) = 60

BO = 10√3

OC = BO(√3)

OC = (10√3)(√3)

OC = 30

By applying tangent rule in right triangle DOC,

tan(60°) = [tex]\frac{OD}{OC}[/tex]

OD = OC(√3)

OD = 30√3

Since, BD = BO + OD

BD = 10√3 + 30√3

BD = 40√3

      ≈ 69.3

Answer:

Step-by-step explanation:

11t= tina

Rita= 11r+32

Answer:

[tex]\displaystyle x=-\frac{1}{6}, 3[/tex]

Step-by-step explanation:

Hi there!

[tex]y = 6x^2 - 17x - 3[/tex]

Factor by grouping:

[tex]y = 6x^2 - 18x+1x - 3\\y = 6x(x- 3)+1x - 3\\y = 6x(x- 3)+(x - 3)\\y = (6x+1)(x- 3)[/tex]

Let y=0. Apply the zero product property:

[tex]0 = (6x+1)(x- 3)[/tex]

[tex]6x+1=0\\6x=-1\\\\\displaystyle x=-\frac{1}{6}[/tex]

AND

[tex]x-3=0\\x=3[/tex]

I hope this helps!

The ratios of oxygen atom and sulfur atom is an illustration of equivalent ratios.

There are 12 oxygen atoms, when the number of sulfur atom is 6.

From the diagram, we have:

[tex]S = 1[/tex]

[tex]O_x = 2[/tex]

So, the ratio is:

[tex]S : O_x = 1 : 2[/tex]

When there are 6 sulfur atoms, the equation becomes

[tex]6 : O_x = 1 : 2[/tex]

Express as a fraction

[tex]\frac{O_x}{6}= \frac{2}{1}[/tex]

Multiply both sides by 6

[tex]O_x = 2 \times 6[/tex]

[tex]O_x =12[/tex]

Hence, there are 12 oxygen atoms

Read more about equivalent ratios at:

https://brainly.com/question/18230617

Answer:

$445.20

Step-by-step explanation:

First, find his pay after the 5% raise:

400(1.05)

= 420

Find his pay after the 6% raise:

420(1.06)

= 445.2

So, his weekly pay is now $445.20

Answer:

6ft by 8ft

Step-by-step explanation:

12 / 2 is 6 and 16 / 2 is 8

[tex]\it L_{arc}=\dfrac{2\pi R\cdot angle}{360^o}=\dfrac{2\pi\cdot10\cdot126^o}{360^o}=\dfrac{2520^o}{360^o}\cdot \pi=7\pi\approx7\cdot3,14 \Rightarrow\\ \\ \\ \Rightarrow\ L_{arc}\approx21,98\ cm\approx22\ cm[/tex]

Answer:

MO= 5x +3

NO= 6x

MN= ( collect light terms) 5x+ 6x = 11x +3

ans= 11x+3

If points {M,N,O} are collinear, and N is between M and O, then this would allow us to use the segment addition postulate like this:

MO = MN + NO

MN = MO - NO

MN = (5x+3) - (6x)

MN = (5x-6x) + 3

MN = -x + 3

Answer:  -x+3

Answer:

m/0.1

Step-by-step explanation:

--

we want to find it

-----

10%*x=m

OF means multiply

IT is any variable

IS is equal

10%*x=m

0.1*x=m

x=m/0.1 IN THE ANSWER DO NOT INCLUDE x