Find the value of x. Write your answer in simplest form.

Step-by-step explanation:

everything can be found in the picture

The nth term of an arithmetic sequence is expressed as Tn = a +(n - 1)d. The 157th term of the sequence is 2180

The nth term of an arithmetic sequence is expressed as:

Tn = a +(n - 1)d

where

If -4 is the first term and 10 is the third term, then;

a = -4

a + d = 10

d = 10 - (-4)

d = 14

Determine the 157th term

T157 = -4 + (157 - 1)(14)

T157 = -4 + (156*14)

T157 = 2180

Hence the 157th term of the sequence is 2180

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Answer:

AD = 6

Step-by-step explanation:

If a radius is perpendicular to a chord, then it bisects the chord.

Here XB is the radius, AC is the chord. Given XB and AC are perpendicular to each other. Therefore, XB bisects AC at D.

So,

    [tex]AD = \frac{1}{2} \times AC = \frac{1}{2} \times 12 = 6[/tex]

Answer:

-0.0390625

Step-by-step explanation:

each is cut in half

so we do this

20, 10, 5, 2.5, 1.25, .625, .3125, .15625, 0.078125, 0.0390625

Answer:

What missing side? You're missing a picture.

Answer:

It Should Be A

Step-by-step explanation:

Answer:

option D.

[tex]y \geqslant 2x + 2[/tex]

Step-by-step explanation:

we have two points on the line

using these points to find the equation of the line (shown as red in the figure)

[tex]y - y_{1} = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} (x - x_{1})[/tex]

let,

[tex]y - 0 = \frac{2 - 0}{ 0 + 1} (x + 1) \\ y = 2(x + 1) \\ y = 2x + 2[/tex]

so the equation of the required line (boundary line) is y = 2x+ 2

the shaded portion is represented by inequality :-

so, option D is the answer

Answer:

[tex] - 15[/tex]

Step-by-step explanation:

We know that,

[tex]( - ) \times ( + ) = (- )[/tex]

So,

[tex] (- 3) \times ( + 5) = - 15[/tex]

hope this helps you.

Have a nice day!

Answer:

-15

Step-by-step explanation:

(-3)*(+5) = -15

Answer:

Heptacontakaitetragon

I'm not sure though 'cause it ain't a shape, but that's the term for a shape that has 74 sides.

Answer:

Step-by-step explanation:

take lcm of (2x-1)(x+2)

lcm=(2x-1)(x+2)

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

=(2x+4)-(2x-1)/(2x(x+2)-1(x+2)

=2x+4-2x+1/2x^2+4x-x+2

=4+1/2x^2+3x+3

=5/2x^2+3x+3

Answer:

Two angles can be vertical and supplementary only if they add up to 90 degrees because there perpendicular.

Step-by-step explanation:

Answer:

90 + 90 = 180, 45 + 45 = 90

Step-by-step explanation:

Supplementary angles add up to 180 and to be vertical angles they need to be equal to each other so 2x = 180

x = 90

Hence both angles will be equal to 90

Complementary angles add up to 90 and as previously stated, to be vertical angles they need to be equal to each other so 2x = 90

x = 45

Hence both angles equal to 45

Hope this helped!

Answer:

Mean = 14.33333333

Median = 11

Mode= 9 and 11

Range  = 42

Step-by-step explanation:

To find the mean, add all the numbers

(5+1+15+43+9+9+11+11+14+12+36+6) = 172

Divide by the number of numbers

172/12 = 14.33333333

Median is the middle number when listed from smallest to largest

1,5,6,9,9,11,11,12,14,15,36,43

Split into 2 even groups

1,5,6,9,9,11,    11,12,14,15,36,43

The middle is between 11 and 11

(11+11)/2 = 11

Mode is the number that appears mode often

This has 2 modes, 9 and 11

Range is largest number minus smallest number

43-1 = 42

Answer:

x= 15

Step-by-step explanation:

Since this is an isosceles triangle, the other angle is also 5x-6

The sum of the angles of a triangle is 180

42+ 5x-6 + 5x-6 = 180

Combine like terms

10x+30 =180

Subtract 30 from each side

10x+30-30 = 180-30

10x = 150

Divide by 10

10x/10 = 150/10

x= 15

Answer:

B

Step-by-step explanation:

One good way to look at this is to graph both polynomials, as shown in the picture. A tip to help graph is to factor it out and work from there. For example, in x²+14x+48, we can gather that (x+6)(x+8) is the same thing, and it is easier to then graph it. Similarly, for x²+12x+36, we can factor it out as (x+6)² .

When x²+12x+36 approaches 6, it is getting really close to 0, but it stays positive. When x²+14x+48 approaches 6 from the negative side, it is also getting close to 0, but it's negative. When x²+14x+48 approaches 6 from the positive side, it is positive.

Therefore, on the negative side, there is one positive and one negative (dividing a negative by a positive is negative, and a positive by a negative is also negative) , and on the positive side, there are two positives, forming one answer.The answer is therefore B

Answer:

254.47

Step-by-step explanation:

Raidus of the circle is 9

Formula to find the area is pi r^2

Answer:

a) f(3) =6

b) g(-4) =16

Step-by-step explanation:

answer to a, substitute X with 3. which will be f(3)=9-3

=6

answer to b, substitute X with -4, which will be g(-4)=(-4)^2

=16

Answer:

There are no solutions

Steps :

First we expand it

[tex]-3+6b=6b+5[/tex]

Then we add 3 to both sides

[tex]-3+6b+3=6b+5+3[/tex]

Then we simplify

[tex]6b=6b+8[/tex]

Then we subtract 6b from both sides

[tex]6b-6b=6b+8-6b[/tex]

Simplify

[tex]0=8[/tex]

No solutions !

Answer:

A. y = 2/5x - 2

Step-by-step explanation:

We can use the slope formula to find the slope of the line.

[tex]m=\frac{y_1-y_2}{x_1-x_2} \\m=\frac{-2-0}{0-5} \\m=\frac{-2}{-5}\\m=\frac{2}{5}[/tex]

Now we know that the slope of the line is 2/5. By looking at the graph, the line crosses the y-axis at the point (0, -2). Therefore, the equation of the line is y = 2/5x - 2.

Answer:

25°

Step-by-step explanation:

2x - 5°  = x + 20°

2x - x = 20° + 5°

x = 25°

The correct representation of the law of cosines is A. c² = a² + b² - 2ab cos C.

Let there is triangle ABC such that |AB| = a unit, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]

(c is the opposite side to angle A)

We have been Given any triangle ABC with corresponding side lengths a, b, and c.

In the given triangle ABC, the sides are;

BC = a, AB = b and AC = c

Now we know as per the law of cosines for all three sides of the triangle;

c² = a² + b² - 2ab cosC

a² = b² + c² - 2bc cosA

b² = a² + c² - 2ac cosC

Therefore the correct representation of the law of cosines is A. c² = a² + b² - 2ab cos C.

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Answer: The longest possible length of the shelves =  18 inches

Step-by-step explanation:

Given: Lengths of two boards are  72-inches and 54 inches.

To make as many shelves as he can while using up all the wood we will find the longest possible length of the shelves = HCF ( 72, 54)

72 = 2 x 2 x 2 x 3 x 3

54 = 2 x 3 x 3 x 3

HCF(72,54) = 2 x 3 x 3 = 18

Hence, the longest possible length of the shelves =  18 inches

Answer:

C

Step-by-step explanation:

because to solve it you are seeing which number divises 52 to get you 13

so using the inverse you just need to use multiplication

Answer:

-39

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x+52=13

Step 2: Subtract 52 from both sides.

x+52−52=13−52

x=−39

Answer:

x=−39

Answer:

[tex]-\frac{1}{12}[/tex]

Step-by-step explanation:

Reduce the expression, if possible, by canceling the common factors.

Answer:

-

Step-by-step explanation:

-5/6÷-10

-5/6*1/-10

-5/-60

1/12

Answer:

An arithmetic sequence is defined by:

[tex]a_n = a_{n-1} + d[/tex]

Here, we know that:

[tex]a_3 = 14\\a_{10} = 98[/tex]

Using the recursive relation, we can write:

[tex]a_{10} = 98 = a_9 + d[/tex]

And can keep applying the recursive relation, so we will have:

[tex]98 = a_9 + d = (a_8 + d) + d = a_8 + 2*d[/tex]

And so on, until we get to a known term:

[tex]98 = a_8 + 2*d = a_7 + 3*d = a_6 + 4*d = a_5 + 5*d = a_4 + 6*d = a_3 + 7*d[/tex]

[tex]98 = a_3 + 7*d = 14 + 7*d[/tex]

Then we can solve:

98 = 14 + 7*d

for d:

98 - 14 = 7*d

84 = 7*d

84/7 = d = 12

Now we know the value of d, we can keep using the recursive relation to find the first 3 terms:

Here, we can rewrite the recursive relation as:

[tex]a_{n-1} = a_n - d[/tex]

Then:

[tex]a_2 = a_3 - d = 14 - 12 = 2\\a_2 = 2[/tex]

[tex]a_1 = a_2 - d = 2 - 12 = -10\\a_1 = -10[/tex]

[tex]a_0 = a_1 - d = -10 - 12 = -22\\a_0 = -22[/tex]

Then the first 3 terms are:

-22, -10, 2

Answer:

D

Step-by-step explanation:

In a function with x as the independent variable and y as the dependent variable, the f(x) notation replaces y in the equation.

Answer:

y=-7x-3

Step-by-step explanation:

y=-7x+b

32=-7(-5)+b

32=35+b

-3=b

y=-7x-3

Answer:

Step-by-step explanation:

Finding the 8th term of this sequence will be much easier with an explicit formula, so we will find that, find the 8th term, then write the equation for the recursive. The recursive formula is only good if you know all the terms before the one you're looking for. That means if we want the 8th term, we first have to find the 7th term, but before that we have to find the 6th term, etc...

We can find the explicit formula for this using the info we have about the 5th term and the 3rd term. The explicit formula looks like this, in general terms:

[tex]a_n=a_1*r^{n-1[/tex] where a1 is the first term and r is the common ratio. We can solve for both, one at a time. First, using the fact that the 5th term is 3888:

[tex]a_5=a_1*r^{5-1[/tex] and subbing in and simplifying:

[tex]3888=a_1*r^4[/tex] and we will solve that for a1:

[tex]a_1=\frac{3888}{r^4}[/tex]

Now the other equation we need for this system, using the fact that the third term is 108:

[tex]108=a_1*r^2[/tex] and we sub in our expression for a1:

[tex]108=(\frac{3888}{r^4})*r^2[/tex] which simplifies to

[tex]108=\frac{3888}{r^2}[/tex] and

[tex]r^2=\frac{3888}{108}[/tex] so

r = 6. Now we'll plug 6 in for r to find a1:

[tex]a_1=\frac{3888}{6^4}[/tex] so

a1 = 3. Now we have the a and r for the explicit formula:

[tex]a_n=3*6^{n-1[/tex] and we simply put in an  for n:

[tex]a_8=3*6^{8-1[/tex] and

[tex]a_8=3*6^7[/tex] which gives us the 8th term as

a8 = 839808

The recursive formula is

[tex]a_n=a_{n-1}*r[/tex] and it works, also, but again, you have to have all the terms that come before the one you want or this formula is useless. Explicit is always better, in my opinion.

The solution to the multiplication of surds (2√3) × (3√2) is; 6√6

Let us break each of them into the factors to get;

√12 × √18 = √(4 × 3) × √(9 × 2)

(√4 × √3) × (√9 × √2)

Simplifying this further gives;

(2√3) × (3√2)

a√b × p√q = ap√bq

(2√3) × (3√2) = 6√6

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Answer:

To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator.

When the denominators are not the same, we must manipulate them so that they become the same. In other words, you must find a common denominator.

Step-by-step explanation: