Class 10. Trignometry. Can you solve the 1st, 4th, 7th, 9th and 10th question. Best answer will be marked brainliest.

Answer:

a) Arithmetic    yₙ = 3*(n - 1) + 13

b) Geometric   yₙ = 2*5⁽ⁿ⁻¹⁾

Step-by-step explanation:

The formula for the nth term e, of that sequence is; yₙ = 3*(n - 1) + 13 and yₙ = 2*5⁽ⁿ⁻¹⁾

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

(a) 13, 16, 19

Here,  yₙ = 3*(n - 1) + 13

This is an Arithmetic.

b) 2, 10, 50

Here, yₙ = 2*5⁽ⁿ⁻¹⁾

This is Geometric .  

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Answer:

[tex](832.156, \ 847.844)[/tex]

Step-by-step explanation:

Given data :

Sample standard deviation, s = 15

Sample mean, [tex]\overline x = 840[/tex]

n = 23

a). 98% confidence interval

[tex]$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$[/tex]

[tex]$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}[/tex]

[tex]$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$[/tex]

[tex]$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$[/tex]

∴ [tex]$E = 2.508 \times \frac{15}{\sqrt{23}}$[/tex]

  [tex]$E = 7.844$[/tex]

So, 98% CI is

[tex]$(\overline x - E, \overline x + E)$[/tex]

[tex](840-7.844 , \ 840+7.844)[/tex]

[tex](832.156, \ 847.844)[/tex]

Answer:

B

Step-by-step explanation:

We can see in the expression that there are 2 x² blocks, 4 -x blocks, and 3 -1 blocks. Therefore, we can write this as

2 * x² + 4 * (-x) + 3 * (-1) = 2x²-4x-3

Comparing this with each answer, we have

A: x²-2x-4 + x² + 2x-1 = 2x²-5. This is not correct

B: 3x²-7x+1-(x²-3x+4) = 3x²-7x+1 -x²+3x-4 = 2x²-4x-3. This seems correct but we can check the other answers to be sure

C: (2x+1)(x-3) = 2x²-6x+x-3 = 2x²-5x-3. This is incorrect

D: [tex]\frac{8x^{12} - 16x^7 - 12x^6}{4x^6} = 2x^6 - 4x - 3[/tex]. This is incorrect

Answer:

C. 2(x + 10)(x - 10)

Step-by-step explanation:

2x^2-200\\2(x^2-100)\\2(x+10)(x-10)

Answer:

domain : {3,4,6}

range: {1,5,9}

Answer:

m = 1/2

b = -5

Step-by-step explanation:

The equation of the line of the points (6,-2) and (-6,-8) is y = 1/2x — 5

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The value of m and b in the given equation is 0.5 and -5, respectively.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The given equation is the equation of a line, where m is the slope of the line and b is the y-intercept of the line. Therefore, the value of m or the slope of the equation is,

m = [-8 - (-2)] / [-6 - 6] = -6/-12 = 0.5

Now, substitute the value of x, y, and m in the given equation, therefore, the value of b can be written as,

y = mx + b

-2 = 0.5(6) = b

-2 = 3 + b

b = -2 + -3

b = -5

Hence, the value of m and b in the given equation is 0.5 and -5, respectively.

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Answer:

from left to right the second graph

Step-by-step explanation:

f(x) = 4(1/2)^x

y = 4(1/2)^x

-find the y-intercept

if x=0 then y = 4(1/2)^0 = 4*1 =4, the y-intercept is (0,4)

so is first or second graph

-look at the second graph and check if the function go trough the point (1, 2)

if x=1 then y = 4(1/2)^1 = 4/2 = 2

so the second graph it is

Answer:

x=1°.

see the IMAGE FOR SOLUTION

Answer:

5•362165924

Step-by-step explanation:

first make root of 32-6=5•099019514

then make root of 2+root2=1•84--

then divide upper by lower part answer comes

or

root32-6=root26

root 2+root 2=2root2

root26/root2root2

ans=3•0318---

Answer:

[tex] \frac{ \sqrt{32} - 6 }{ \sqrt{2} + \sqrt{2} } \\ \frac{ \sqrt{16 \times 2} - 6}{2 \sqrt{2} } \\ \frac{4 \sqrt{2} - 6}{2 \sqrt{2} } \\ \frac{2(2 \sqrt{2} - 3) }{2 \sqrt{2} } \\ \frac{2 \sqrt{2} - 3}{ \sqrt{2} } \\ thnk \: you[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Let r, c, h represent the numbers of meals eaten in a restaurant, car, and at home, respectively. The problem statement tells us of the relations ...

  r + c + h = 193

  -r + c + h = 15

  r + 0c -h = 30

Add the last two equations:

  (-r +c +h) +(r -h) = (15) +(30)

  c = 45

Add the first two equations:

  (r + c + h) +(-r + c + h) = (193) +(15)

  2c +2h = 208

  h = 104 -c = 59 . . . . solve for h, substitute for c

The last equation can be used to find r.

  r = 30 +h = 30 +59 = 89

89 meals are eaten in a restaurant; 45 meals in a car; and 59 at home.

Answer:

mine too

Step-by-step explanation:

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

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We can solve it through proportionality or ratios

Let lamps required to create 60signals be x

Now

[tex]\\ \sf\longmapsto 2:4=x:60[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{4}=\dfrac{x}{60}[/tex]

[tex]\\ \sf\longmapsto 4x=60(2)[/tex]

[tex]\\ \sf\longmapsto 4x=120[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{120}{4}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} \tt a) \ 3-2x=3(x+4)-x-1\\\\3-2x=3x+12-x-1 \\\\3-12+1=3x+2x-x \\\\4x=-8 \\\\\boxed{ \tt x=-2} \\\\\\b) \ 5x\underline{(x-1)}-4\underline{(x-1)}=0 \\\\\\(5x-4)(x-1)=0 \Longrightarrow \boxed{ \tt x_1=0.8 \ \ ; \ \ x_2=1}[/tex]

Answer:

(0, 3)

Step-by-step explanation:

(-4+4)/2 , (7-1)/2

0/2 , 6/2

0, 3

Answer:

(0,3)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2

( -4+4)/2 = 0/2 =0

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2

( 7+-1)/2 = 6/2 =3

(0,3)

Step-by-step explanation:

we see, for x=-1 we get 3³

x=0 we get 3²

x=1 we get 3¹

so the function is definitely a 3 to the power of x version.

but we need to adapt the exponent a bit and correct x, so that at least for these 3 values of x the result is "running backwards".

the easiest way : 2-x as exponent.

it fits.

for x=-1 we get 2 - -1 = 3 as exponent.

for x=0 we get 2-0 = 2 as exponent.

for x=1 we get 2-1 = 1 as exponent.

so, the exponential function passing through these 3 points is

[tex]f(x) = {3}^{2 - x} [/tex]

[tex]\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0[/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: 4[/tex]

Option ( A ) is the correct answer.

Answer:

b

Step-by-step explanation:

The triangle is an isoceles triangle since there are 2 equal angles. Hence, 2 sides would be the same length. Since its a right angled triangle, the hypotenuse (third side) would always be longer than the 2 equal sides.  

[tex] \large\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]

We know that, in ∆ABC,

∠A+∠B+∠C = 180°

But the triangle is right angled at C

ie., ∠C = 90°

Therefore, ∠A+∠B+ 90° = 180°

⇒ ∠A + ∠B = 90°

Therefore, cos(A + B) = cos 90º = 0

Answer:

A = 216.24 km²

Step-by-step explanation:

Answer:

360 in.

Step-by-step explanation:

In order to get this answer, you have to multiply 5 and 8 by 3 because the drawing is 1/3 of the actual flag.

5 x 3 = 15

8 x 3 = 24

So, 24 x 15 = 360 in.

Hope this helps! :)

Answer:

x=150

Step-by-step explanation:

x/30-x/40=5/4

or, (4x-3x)/120=5/4

or, x/120=5/4

or, x=600/4

or, x=150

Answer:

Step-by-step explanation:

None

They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.

a = - 2

b = - 4

c = - 6

D = sqrt(b^2 - 4*a * c)

D = sqrt( (-4)^2 - 4*(-2)(-6)  )

D = sqrt( 16 - 48)

D = sqrt(-32) which is negative and there are no real roots.

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

Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

Answer:

See below.

Step-by-step explanation:

[tex]3+x=ax[/tex]    (Given)

[tex]x=ax-3[/tex]    (Subtracted 3 on both sides)

[tex]x-ax=-3[/tex]    (Subtracted ax on both sides)

[tex]x(1-a)=-3[/tex]    (Factor out x from x - ax)

[tex]x=-\frac{3}{1-a}[/tex]    (Divided 1 - a on both sides)

Answer:

Step-by-step explanation:

P(A and B)=P(A)*P(B)

Answer:

9

Step-by-step explanation:

If the sine of an angle is equal to the cosine of an angle, that means that the sides adjacent and opposite to that angle are equal. One triangle that has two equal sides is an isosceles triangle. We can set this triangle to be a 45-45-90 degree triangle, which means that the angle would be 45.

Now, we have to find the value of

[tex]4\tan^2(45)[/tex]

and

[tex]5\tan(45)[/tex]

The tangent of 45 is 1, so 1 squared times 4 is 4.

We have [tex]4\tan^2(45) = 4[/tex].

Again, the tangent of 45 is 1, and 1 times 5 is 5.

We have [tex]5\tan(45) = 5[/tex]

5 + 4 = 9

Answer:

The expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Step-by-step explanation:

Recall that the volume of a rectangular solid is given by:

[tex]\displaystyle V = \ell wh[/tex]

Where l is the length, w is the width, and h is the height.

We know that the volume is given by the polynomial:

[tex]\displaystyle V = 3x^4-3x^3-33x^2+54x[/tex]

And that the length and width are given by, respectively:

[tex]\displaystyle \ell = 3x \text{ and } w =x-2[/tex]

Substitute:

[tex]\displaystyle 3x^4-3x^3-33x^2+54x=(3x)(x-2)h[/tex]

We can solve for h. First, divide both sides by 3x:

[tex]\displaystyle \frac{3x^4-3x^3-33x^2+54x}{3x}=(x-2)h[/tex]

Divide each term:

[tex]\displaystyle x^3-x^2-11x+18=(x-2)h[/tex]

To solve for h, divide both sides by (x - 2):

[tex]\displaystyle h = \frac{x^3-x^2-11x+18}{x-2}[/tex]

Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Answer:

The answer is -51146

Step-by-step explanation:

Just substract simple

Step-by-step explanation:

(-1,0),m=2

(1-7),m=12

m=-4,(-1,-4)