Given that sin(X+20°)=cos(2x+25°) find the value of X and hence find the value of tan x

Answer:

Number of the houses as x =35

Step-by-step explanation:

The number of houses is 1, 2, 3, ..., 49

By observation, the numbers of houses are in an A.P.

Hence

First-term, a = 1

Common difference, d = 1

Let us assume that the number of xth house can be expressed as below:

We know that sum of n terms in an A.P. is given by the formula Sₙ = n/2 [2a + (n - 1) d]

Sum of number of houses preceding xth house = Sₓ ₋ ₁

Sₓ ₋ ₁ = (x - 1) / 2 [2a + ((x - 1) - 1)d]

= (x - 1) / 2 [2 × 1 + ( x - 2) × 1]

= (x - 1) / 2 [2 + x - 2]

= [x (x - 1)] / 2 ---------- (1)

By the given information we know that, sum of number of houses following xth house = S₄₉ - Sₓ

S₄₉ - Sₓ = 49 / 2 [2 × 1 + (49 - 1) × 1] - x / 2 [2 × 1 + (x - 1) × 1]

= 49 / 2 [2 + 48] - x / 2 (2 + x - 1)

= (49 / 2) × 50 - (x / 2) (x + 1)

= 1225 - [x (x + 1)] / 2 ---------- (2)

It is given that these sums are equal, that is equation (1) = equation(2)

x (x - 1) / 2 = 1225 - x (x + 1) / 2

x² / 2 - x / 2 = 1225 - x² / 2 - x / 2

On solving further we get,

x² = 1225

x = ± 35

As the number of houses cannot be a negative number, we consider the number of houses as x = 35

35 is the correct answer

Step-by-step explanation:

Given that the houses in a row are numbered consecutively from 1 to 49. We need to show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x. Making it more simple for you; sum of (1, 2, 3, 4.... upto x - 1) is equal to sum of (x + 1), (x + 2), (x + 3).... upto 49.

→ Sum of (x - 1) terms = Sum of (49 - x) terms

"x" is the number of houses required. The sum of houses are in AP where the value of a is 1 and d is also 1; where 'a' is first term and 'd' is common difference. We know that sum of nth term of an AP is given by: T(n) = a + (n - 1)d and upto nth term by S(n) = n/2 (2a + (n - 1)d). And also by T(n) = S(n) - S(n - 1).

As per given problem:

→ (x - 1)/2 (Sum of first and last term) = (49 - x)/2 (Sum of first and last term)

→ (x - 1)(Sum of first and last term) = (49 - x) (Sum of first and last term)

Where first term and last term in LHS is 1 and (x - 1) & in RHS is (x + 1) and 49. Substitute them.

→ (x - 1) (1 + (x - 1)) = (49 - x) ((x + 1) + 49)

→ (x - 1) (1 + x - 1) = (49 - x) (x + 1 + 49)

→ (x - 1) (x) = (49 - x) (x + 50)

→ x² - x = 49x + 2450 - x² - 50x

On solving we get,

→ 2x² - 2450 = 0

→ 2x² = 2450

→ x² = 1225

→ x = ± 35

The number of houses is a positive integer. So negative value neglected. We left with x = 35. Therefore, the value of x is 35.

Answer:

[tex]9 \frac{4}{5} [/tex]

Step-by-step explanation:

[tex] \frac{7}{5} \times 7 = \frac{7}{5} \times \frac{7}{1} [/tex]

[tex] \frac{7}{5} \times \frac{7}{1} = \frac{49}{5} = 9 \frac{4}{5} [/tex]

Step-by-step explanation:

2×3=6 I think it's like this

Answer:

2x+3

Step-by-step explanation:

factor into [tex](2x+3)^{2}[/tex]

then square root it [tex]\sqrt{(2x+3)^{2} }[/tex]

We know that,

[tex]{ \longrightarrow \bf \qquad \: {(a + b)}^{2} = {a}^{2} + 2.a.b + {b}^{2} }[/tex]

Solution :

[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + 9 }[/tex]

We can also write it as,

[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + {3}^{2} }[/tex]

Now, using the formula, we'll solve the expression.

[tex]{ \longrightarrow \sf \qquad \: {2x}^{2} + 2.2x.3 + {3}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad \: (2x + 3)^{2} }[/tex]

Since,

Therefore,

Answer:

the answer is $16

Step-by-step explanation:

Answer:

here u go the answer is $16

Step-by-step explanation:

Using the normal distribution and the central limit theorem, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For each sample, they are given by:

[tex]\mu_W = 82.3, s_W = \frac{18.2}{\sqrt{9}} = 6.0667[/tex]

[tex]\mu_S = 65, s_S = \frac{17.73}{\sqrt{6}} = 7.2382[/tex]

For the distribution of differences, we have that:

[tex]\mu = \mu_W - \mu_S = 82.3 - 65 = 17.3[/tex]

[tex]s = \sqrt{s_W^2 + s_S^2} = \sqrt{6.0667^2 + 7.2382^2} = 9.4444[/tex]

The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, one subtracted by the p-value of Z when X = 0, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0 - 17.3}{9.4444}[/tex]

[tex]Z = -1.83[/tex]

[tex]Z = -1.83[/tex] has a p-value of 0.0335.

1 - 0.0335 = 0.9665.

More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24663213

The statements about the power that is true include E. I, II, and III.

Power simply means the amount of energy that is transferred or converted per unit time.

It should be noted that an increase in sample size increases power and a test with a higher power is more likely to reject false null hypothesis.

Increasing sample size will make the hypothesis test more sensitive and thus more likely to reject the null hypothesis. Thus, it increases the power of the test.

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Answer:

probably 7x + 5y

Step-by-step explanation:

Answer: 7x + 5y

Step-by-step explanation:  You combine the like terms so you would add 2x and 5x to get 7x-2+7y. Then you combine the other like terms so subtract -2y and 7y (You are subtracting because a negative and a positive is a negative).

I hope this helps :)

Answer:

Hi I'm learning the same thing and I just got it I think it's C=43.98cm

Answer:

= (y - 4x) (y - 7)

Step-by-step explanation:

y^2-4xy-7y+28x

--

factor out y from y^2 - 4x : y(y - 4x)

factor out 7 from 28x - 7y : 7(4x - y)

= y (y - 4x) + 7(4x - y)

7 (4x - y) + 7(y - 4x)

= y (y - 4x) - 7(y - 4x)

= (y - 4x) (y - 7)

Answer:

5x +9 is the least common denominator

Step-by-step explanation:

Answer:

  $35.10

Step-by-step explanation:

The discount amount is subtracted from the original price to find the discounted price. That math can be done a couple of different ways.

  discount = discount rate × original price

  sale price = original price - discount

Or, these equations can be combined:

  sale price = original amount × (1 - discount rate)

__

Using the latter equation, we get ...

  sale price = $45.00 × (1 - 0.22) = $45.00 × 0.78 = $35.10

Leia will be paying $35.10 for the jacket.

Ok, good job for posting the answer

Answer:

For me it says pmn is 63 degrees

Step-by-step explanation:

Answer:

So here we have 3 adjacent angles, and add them all up they would equal a right angle as shown in the diagram.

POT is the right angle which can be seen by the square

POQ is the first angle

QOS is the second

SOT is the third

Now solve it.

We know that it has to be equal to 90 since thats the final reasoning.

4a + 20 + 3a - 10 + a = 90

Solve.

So you’d get 10.

If you want to elaborate then just say all adjacent angles has to add put o 90 since

Answer:

3052 cm^3 (Answer C)

Step-by-step explanation:

The formula for the circumference of a circle of radius r is C = 2(pi)(r).  We know that C = 56.52 cm and want to find the model's radius:

                                       C                                                56.52 cm

Solving for r, we get ----------   so that in this case   r = ------------------  or

                                      2(pi)                                                 6.28

r = 9 cm.

The formula for the volume of a sphere of radius r is V = (4/3)(pi)(r^3), which here comes out to:

V = (4/3)(3.14)(9 cm)^3 = 3052 cm^3 (Answer C)

Answer: 4

Step-by-step explanation:

Simply divide 12 by 3 because it states she will give 3 to every class,

12/3=4!

[tex]Y=0.213x-352[/tex]  will represent this linear model shown in the data table.

Put the values of the x in the all given equations and then check the value of y if the value of y matches the given values in the option

So if we put the value x=1980 in the [tex]Y=0.213x-352[/tex]  then

[tex]Y=0.213(1980)-352[/tex]

[tex]Y=69.74[/tex]

These values are closest to 70.1 whereas other options do not satisfy the condition.

Thus [tex]Y=0.213x-352[/tex]  will represent this linear model shown in the data table.

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Explanation:

One method is to do the steps like this

15% of 60 = 0.15*60 = 9

Or you can solve like this

part/whole = percent/100

x/60 = 15/100

100x = 60*15

100x = 900

x = 900/100

x = 9

5 / ( 2 / 3 ) = 7.5

7 full jars

Answer: m<D = 30

Step-by-step explanation: In the third step of the problem, it says that E is next to itself and equals 90. However, this is not true. Angle BEA and angle CED are vertical angles and are both equal to 65°. This means that to find the measurement of angle D, subtract 65 and 85 from 180, which equals 30.

Answer:

STEP 1:Equation at the end of step 1 ((3 • (p3)) + 32p2) - 210p

STEP 2 :Equation at the end of step 2: (3p3 + 32p2) - 210p

STEP 3:STEP 4:

Pulling out like terms  4.1     Pull out like factors :   3p3 + 9p2 - 210p  =   3p • (p2 + 3p - 70) 

Trying to factor by splitting the middle term 4.2     Factoring  p2 + 3p - 70 The first term is,  p2  its coefficient is  1 .The middle term is,  +3p  its coefficient is  3 .The last term, "the constant", is  -70 Step-1 : Multiply the coefficient of the first term by the constant   1 • -70 = -70 Step-2 : Find two factors of  -70  whose sum equals the coefficient of the middle term,

which is   3 .     -70   +   1   =   -69     -35   +   2   =   -33     -14   +   5   =   -9     -10   +   7   =   -3     -7   +   10   =   3   That's itStep-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  10                      p2 - 7p + 10p - 70

Step-4 : Add up the first 2 terms, pulling out like factors :                    p • (p-7)              Add up the last 2 terms, pulling out common factors :                    10 • (p-7)Step-5 : Add up the four terms of step 4 :                    (p+10)  •  (p-7)             Which is the desired factorization

Final result : 3p • (p + 10) • (p - 7)

Step-by-step explanation:

mark me brainliest!!

Answer:

76 m^2

Step-by-step explanation:

Area of a rectangle is width*height. So to find width we will do area/height.

Answer:

a) 390

b) 239

c) 151

Step-by-step explanation:

a) 30 + 15 + 45 + 300 = 390

b) 160 + 30 + 9 + 40 = 239

c) 390 (income) - 249 (expenses) = 151 pounds (profit)

The product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

The product of the two fractions can be written as,

[tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex]

Taking 4 as the common term from both numerator and denominator of the first fraction, therefore,

[tex]\dfrac{4n}{4(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\[/tex]

Now, cancelling the common factor from the numerator and the denominator, we will get,

[tex]=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\\\=\dfrac{n}{(n+1)}[/tex]

Hence, the product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].

Learn more about Fraction:

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Answer:

23696

Step-by-step explanation:

[tex]Step1\1\\We\ know\ that:[/tex]

↓

[tex]P=15000[/tex]
[tex]r=6.75[/tex]%
[tex]n=1[/tex]
[tex]t=7[/tex]

[tex]Step\ 2:\ Formulate\ and\ substitute:[/tex]

                                [tex]P=15000[/tex]
                                [tex]r=6.75[/tex]%

[tex]Substitute[/tex]                                  [tex]into\ formula[/tex]

                                [tex]n=1[/tex]
                                [tex]t=7[/tex]

[tex]F=P\ast(1+r/n)^{nt}[/tex]

[tex]F=15000\bullet(1+6.75\bullet\frac{1}{100})^7[/tex]

[tex]Step\ 3:Evaluate[/tex]

[tex]Evaluate\ the\ equation/expression:[/tex]

[tex]23695.53098[/tex]

[tex]Step\ 4:\ Find\ the\ value[/tex]

[tex]Find\ the\ closest\ integer\ to\ 23695.53098:[/tex]

[tex]23696\ YOUR\ ANSWER[/tex]

I hope this helps you

:)

Answer:

x = 5

Step-by-step explanation:

21 - 3x = 6

21 - 6 = 3x

15 = 3x

5 = x

therefore x=5