Find the common ratio, the 8th term, the explicit formula, the recursive formula, and the three terms in the sequence after the last one given.

-1,2,-4,8

Answer: 9.19 ft

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Sin α = opposite side / hypotenuse  

Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the opposite side (x) is the height of the top of the ladder above the ground.

Replacing with the values given:  

Sin 45 = x/ 13

Solving for x  

sin45 (13) =x  

x= 9.19 ft

Feel free to ask for more if needed or if you did not understand something.  

Answer:

1/3

Step-by-step explanation:

3^2/5 x 3^-7/5

We know that a^b* a^c = a^(b+c)

3^(2/5 -7/5)

3^ (-5/5) = 3^ -1

We know that a^-b = 1/ a^b

3^-1 = 1 / 3

Answer:

the maximum value is 3

Step-by-step explanation:

The maximum value of the function y = -2+5sin(pi/12(x-2)) is determined by taking the first derivative of the function. The first derivative is equal ( 5 pi/ 12 )* sin ((pi/12) (x-2)) = 0. x is equal to 4472 through the calculator. Substituting to the original equation, the maximum value is 3.

Answer:

[tex]M.A.D = 18.9[/tex]

Step-by-step explanation:

Given: 22,26,28,35,45,63,91

Required: Mean Absolute Deviation

The first step is to solve for the mean of the given data

[tex]Mean = \frac{\sum x}{n}[/tex]

where x->22,26,28,35,45,63,91 and n = 7

[tex]Mean = \frac{22+26+28+35+45+63+91}{7}\\Mean = \frac{310}{7}\\Mean = 44.29[/tex]

Then; subtract the calculated mean from each data

[tex]22 - 44.29 = -22.29\\26 - 44.29 = -18.29\\28 - 44.29 = -16.29\\35 - 44.29 = -9.29\\45 - 44.29 = 0.71\\63 - 44.29 = 18.71\\91 - 44.29 = 46.71[/tex]

Get Absolute Values of the above results

[tex]|-22.29| = 22.29\\|-18.29| = 18.29 \\|-16.29| = 16.29\\|-9.29| = 9.29\\|0.71| = 0.71\\|18.71| = 18.71\\|46.71|= 46.71[/tex]

Calculate the mean of the above result to get the M.A.D

[tex]Mean = \frac{\sum x}{n}[/tex]

[tex]M.A.D = \frac{22.29+18.29+16.29+9.29+0.71+18.71+46.71}{7}\\M.A.D = \frac{132.29}{7}\\M.A.D = 18.8985714286\\M.A.D = 18.9[/tex]

Explanation:

Basically triangles are congruent when they have the same shape and size.

Two triangles are congruent if they have :

exactly the same three sides and

exactly the same three angles.

Tips Area :

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent too :)

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent too ;)

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent too ^^

Hope that help :)

Answer:

g(x + 4) = -4x - 11

Step-by-step explanation:

Since g(x) = -4x + 5, g(x + 4) = -4(x + 4) + 5

g(x + 4) = -4x - 11

Answer:

[tex]c + d^2 = 96[/tex]

Step-by-step explanation:

Given

[tex]c = -4\\d = 10[/tex]

Required

Find [tex]c + d^2[/tex]

To find [tex]c + d^2[/tex], we simply substitute 10 for d and -4 for c in the given expression.

The step is as follows:

[tex]c + d^2[/tex]

Substitute [tex]c = -4\\d = 10[/tex]

[tex]c + d^2 = -4 + 10^2[/tex]

[tex]c + d^2 = -4 + 10*10[/tex]

[tex]c + d^2 = -4 + 100[/tex]

[tex]c + d^2 = 96[/tex]

The expression cannot be solved any further; so, we can conclude that when d = 10 and c = -4, [tex]c + d^2 = 96[/tex]

Answer:

5x³+10x²-3x+3

Step-by-step explanation:

(4x²-3x) - (-5x³-6x²-3)

5x³+10x²-3x+3

If equations M(x)=[tex]4x^{2} -3x[/tex] and N(x)=[tex]-5x^{3}-6x^{2} -3[/tex] then M(x)-N(x)=[tex]5x^{3} +10x^{2} -3x+3[/tex].

An equation is a relationship between two or more variables expressed in equal to form. It is often equated to find the values of variables. The form of an equation is ax+by=c.

We have been given M(x)=[tex]4x^{2} -3x[/tex] and N(x)=[tex]-5x^{3}-6x^{2} -3[/tex] and we have to find the difference between M(x) and N(x) and to solve them we have to open the brackets and add the coefficients of variable.

M(x)-N(x)=[tex]4x^{2} -3x-(-5x^{3}-6x^{2} -3)[/tex]

First we have to open the brackets.

=[tex]4x^{2} -3x+5x^{3}+6x^{2} +3[/tex]

Now we have to add the coefficients of same variable having same powers.

[tex]=5x^{3}+10x^{2} -3x+3[/tex]

Hence if M(x)=[tex]4x^{2} -3x[/tex] , N(x)=[tex]-5x^{3}-6x^{2} -3[/tex] then difference between {M(x)-N(x)} =[tex]5x^{3}+10x^{2} -3x+3[/tex].

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Answer:

The slope is 3/2 and the y intercept is 4

Step-by-step explanation:

We want to write in the form

y = mx+b where m is the slope and b is the y intercept

-3x+2y = 8

Add 3x to each side

-3x+3x+2y = 3x+8

2y = 3x+8

Divide each side by 2

2y/2 = 3x/2 + 8/2

y = 3/2x +4

The slope is 3/2 and the y intercept is 4

Answer:d

its a apartment thats just one big room

Answer:

18 gray puppies

Step-by-step explanation:

Think of this as finding equivalent fractions/ratios. 3/5 puppies are gray. what over 30 puppies would be gray? to find 3/5=?/30, you multiply the numerator and denominator by 6. 3 times 6 is 18.

Answer:

we simply see 4 has multiplied by -3

-12 = 4 x -3

This becomes -300%

We then add the 100 = initial amount onto a negatove percentage = -300 +100 = -200% change.

Step-by-step explanation:

3.00 x 4 = 12

4 + 8 = 12

4 x -2.00 = -8 being the change. The answer is -2.00 = -200%

Shows part of the answer and proves the answer is -200%

Answer:

5

Step-by-step explanation:

So you divide 24 by 5 and you get 4.8 so you round it up to 5

Answer:

Option (1). 85°

Step-by-step explanation:

From the figure attached,

'l' and 'm' are the parallel lines and line 'n' is a transverse.

Since, m∠9 ≅ m∠13 [These angles are the corresponding angles]

Therefore, m∠13 = 95°

Since, m∠13 + m∠14 = 180° [Supplementary angles]

Therefore, 95° + m∠14 = 180°

m∠14 = 180° - 95°

m∠14 = 85°

Therefore, 85° will be the measure of angle 14.

Option (1) will be the answer.

Answer:

Set C

Step-by-step explanation:

Answer:

The answer is Set B

Step-by-step explanation:  

Positive linear association goes from left to right and in a straight line. If you put the information into a scatter plot, the line moves in the positive direction and is in a straight line. (In a scatter plot, x goes across the bottom and y is vertical.)

Answer:

Find the number in the middle

First list the number from smallest to greatest

6,8,10,10,12,14,14,16,16,18,18,20,20,22

Find which one is in the middle

16 and 16 are the two middle numbers. There is two middle numbers because there is an even amount of numbers

If there are two middle numbers find the average

Do (X+Y) / 2

16+16 = 32

32 / 2 = 16

16 is the median for your score

Do the same to your friend's score

2,8,8,10,10,10,12,12,12,12,14,14,14,16,16

12 is the middle because there is 7 numbers to the left and right so 12 is the median.

Your score is greater by 4 because 16 - 12 = 4.

Hope this helps

Step-by-step explanation:

Answer:

  B  5 cm

Step-by-step explanation:

The bottom leg of the shaded triangle is 1/2 of the length of the side, so is 3 cm. The vertical leg of the shaded triangle is the height of the pyramid, given as 4 cm.

The slant height is the hypotenuse of the shaded triangle, so can be found from your knowledge of the 3-4-5 triangle, or from the Pythagorean theorem.

If s is the slant height, then ...

  s^2 = 3^2 + 4^2 = 9 +16 = 25

  s = √25 = 5

The slant height is 5 cm.

Answer:

B.

Step-by-step explanation:

If you dont understand what I wrote, just ask!

Answer:

B

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{6x^2}[/tex] × [tex]\sqrt{3x}[/tex]

= [tex]\sqrt{18x^3}[/tex]

= [tex]\sqrt{9(2)x^2(x)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] × [tex]\sqrt{x^2}[/tex] × [tex]\sqrt{x}[/tex]

= 3 × [tex]\sqrt{2}[/tex] × x × [tex]\sqrt{x}[/tex]

= 3x × [tex]\sqrt{2}[/tex] × [tex]\sqrt{x}[/tex]

= 3x[tex]\sqrt{2x}[/tex] → B

Answer:

16 a^8 = 16aaaaaaaa

Step-by-step explanation:

(4a^4)^2

We know (xy)^z = x^z y^z

4^2 a^4^2

16 a^4^2

We know a^b^c = a^(b*c)

16 a^(4*2)

16 a^8

Answer:

f(5) = -8

Step-by-step explanation:

f(5) is the output value when the input value is 5

Reading the chart,

f(5) = -8

Answer:

20

Step-by-step explanation:

To find area using coordinates, you would take the y-value of the first coordinate and the x-value of the second coordinate and multiply them. Then, take the x-value of the first coordinate and multiply it with the second y-coordinate. Take the second number and subtract it from the first number. for multiple coordinates, you would multiply the first and the second, the second and the third, and so on. Once you reach the last coordinate, just multiply it by the first again. then, take all of the numbers, from multiplying your coordinates and add them together and divide them by 2 to find your area.

We would start with coordinate (8,1) here because it's letter variable is W, which is first of the others alphabetically.

(8,1) (1,1)

1 x 1 = 1

8 x 1 = 8

1 - 8 = -7

next coordinate:

(1,1) (2,5)

1 x 2 = 2

1 x 5 = 5

2 - 5 = -3

next:

(2,5) (5,5)

5 x 5 = 25

2 x 5 = 10

25 - 10 = 15

next:

(5,5) (8,1)

5 x 5 = 40

5 x 1 = 5

40 - 5 = 35

-7 - 3 + 15 + 35 = 40

40/2 = 20

Answer:

[tex]\boxed{\mathrm{view \: attachment}}[/tex]

Step-by-step explanation:

Answer:

C) S: x = 1

Step-by-step explanation:

Answer:

C) S: x = 1

explination

Answer:

B.

F.

Step-by-step explanation:

Look at the angle. It is obtuse so the triangle is obtuse.

The sides are congruent so it is an isosceles.

Answer:

B,F

Step-by-step explanation:

sides are equal.

One angle=104°>90°

so itis an isosceles obtuse triangle.

Answer:

Answer:

a(n) is equal to $45,000

(1.035)n-1

Step-by-step explanation:

Answer:

D. y = (x - 3)²

Step-by-step explanation:

The parabola formula in vertex form is:

y = a(x - h)² + k

where the vertex is located at (h, k). Replacing with vertex (3, 0) we get:

y = a(x - 3)² + 0

y = a(x - 3)²

In all possible options the leading coefficient a is equal to one. Therefore:

y = (x - 3)²

Answer:

4/15

Step-by-step explanation:

You would have to multiply the fractions, but first reciprocate the dividend.

3/5 * 4/9

Multiply

3 * 4 = 12

5 * 9 = 45

12/45

Simplify using LCM, or the factor that applies to both sides which in this case is 3

12/3 = 4

45/3 = 15

The answer is 4/15

Answer:

4/-15

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{-9}{4}[/tex]

Invert the second fraction and multiply

[tex]\frac{3}{5}[/tex]  ×[tex]\frac{4}{-9}[/tex]

= [tex]\frac{12}{-45}[/tex]

Simplify:

=[tex]\frac{4}{-15}[/tex]

Answer:

Answer C. x = 2

Step-by-step explanation:

Given:

x − 2y = 2

3 * ( x ) + y = 6

You need to group the x-coordinates of the system of equations.

Rewrite x − 2y = 2 , in such a way that it starts with x =...

x = 2y + 2

Substitute x = 2y + 2 in 3 * ( x ) + y = 6, which gives:

3 * ( 2y + 2 ) + y = 6

6y + 6 + y = 6

7y = 0

y = 0

Substitute y = 0 in x = 2(y) + 2 gives x = 2*0 + 2

So x = 2, which is answer C.

x - 6x + 2x - 2x

x - 6x + 0

-5x

The x-coordinate of the solution to the following system of equations x − 2y = 2 and  3x + y = 6 is x = 2. Option c is correct.

system of equations is given as,

x − 2y = 2    - - - - (1)
3x + y = 6  - -- - - -(2)
x coordinate of the solution to the following system of equations to be determined.

the equation is the relationship between variables and is represented as a polynomial equation.

x − 2y = 2    - - - - (1)
3x + y = 6  - -- - - -(2)
From equation 1
x = 2y +2
put x in equation 2
3 (2y + 2) + y = 6
6y + 6 + y = 6
7y = 0
y = 0
Put y = 0 in x = 2y + 2
x = 2(0) + 2
x = 2

Thus, The x-coordinate of the solution to the following system of equations x − 2y = 2 and  3x + y = 6 is x = 2.

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