Question number 8. Prove that 3 + √5 is an irrational number.​

Answer:

see below

Step-by-step explanation:

7x = 6x-1

Subtract 6x from each side

7x-6x = 6x-6x-1

x = -1

Check

7(-1) = 6(-1) -1

-7 = -6-1

-7  =-7

Answer:

d = 9√2

Step-by-step explanation:

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\d=\sqrt{\left(4-\left(-5\right)\right)^2+\left(-2-7\right)^2}\\\\d=\sqrt{\left(4+5\right)^2+\left(-2-7\right)^2}\\\\d=\sqrt{9^2+9^2}\\\\\mathrm{Add\:similar\:elements:}\:9^2+9^2=9^2\times\:2\\\\=\sqrt{9^2\times\:2}\\\\=\sqrt{2}\sqrt{9^2}\\\\=9\sqrt{2}[/tex]

Answer:

-16, -21, -27

The pattern is -5 every time

Step-by-step explanation:

The pattern is removing 5 every time it goes

Answer:

5

Step-by-step explanation:

You have to move all variables to the left side of the equation. It should be

5c-7c=-2-8. Notice how when 7c and 8 get moved over to their designated places, they become a negative. 5c-7c equals to -2c. -2-8 equals to -10. The equation we have now is -2c=-10. 10 divided by 2 is 5 and there ar two negatives which equal a postiive so the answer is 5.

Answer:

[tex]\boxed {c = 5}[/tex]

Step-by-step explanation:

Solve for the value of [tex]c[/tex]:

[tex]8 + 5c = 7c - 2[/tex]

-Take [tex]7c[/tex] and subtract it from [tex]5c[/tex]:

[tex]8 + 5c - 7c = 7c - 7c - 2[/tex]

[tex]8 - 2c = -2[/tex]

-Subtract [tex]8[/tex] to both sides:

[tex]8 - 8 - 2c = -2 - 8[/tex]

[tex]-2c = -10[/tex]

-Divide both sides by [tex]-2[/tex]:

[tex]\frac{-2c}{-2} = \frac{-10}{-2}[/tex]

[tex]\boxed {c = 5}[/tex]

Therefore, the value of [tex]c[/tex] is [tex]5[/tex].

Answer:

4.68

Step-by-step explanation:

Answer:

4.68

Step-by-step explanation:

i got it right on my quiz.

Answer:

Step-by-step explanation:

opposite angles are equal, o

6x = 78

x = 78 / 6

x = 13

therefore, the angle is 6x = 6(13) = 78

Answer:

Answer:

The answer is "Option a".

Step-by-step explanation:

[tex]\text{Weighted mean} = \frac{(6\times 16+10 \times 12)}{16}[/tex]

                         [tex]= \frac{( 96 +120)}{16}\\\\ = \frac{(216)}{16}\\\\ = 13.5[/tex]

[tex]\text{Weighted mean} = \frac{( 6\times 18+10\times 14)}{16}[/tex]

                        [tex]= \frac{( 6\times 18 +10\times 14)}{16}\\\\= \frac{( 108+140)}{16}\\\\= \frac{( 248)}{16}\\\\= 15.5[/tex]

Answer:

= 5/7

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 3 - -2)/(9-2)

    = ( 3+2)/(9-2)

    = 5/7

Step-by-step explanation:

y=2(x+3)² y=x²

x²=2(x²+9+6x)

x²=2x²+18+12x

0=x²+18+12x

x²+18+12x=0

Answer:

Step-by-step explanation:

shift 3 units left then stretch vertically 2 times

Answer:

141,161

Step-by-step explanation:

Answer:

940,760

Step-by-step explanation:

The question wants to if you know place value. You can write any number as long as the 2nd and 5th number is 4 and 6.

For example:

?4?,?6?

The question marks can be filled with any number.

Answer:

a'2+b'2-c'2

Step-by-step explanation:

well i wouldnt know the answer because you didnt say what a b or c was

Answer:

a

Step-by-step explanation:

Answer: (4x+24)=4⋅(x+6) =28

11x+33= 11⋅(x+3) =44

6x-6= 6⋅(x−1)=0

Step-by-step explanation:

Answer: (10x+7)/2 = -13/2

This is not the only answer possible. There are infinitely many possible answers.

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

Explanation:

We start with the given equation x = -2

Multiply both sides by some number. I'll pick 10

So if we multiply both sides by 10, we get

10*x = 10*(-2)

10x = -20

Now let's add something to both sides. Let's say we add 7 to both sides

10x+7 = -20+7

10x+7 = -13

Finally, let's divide both sides by 2

(10x+7)/2 = -13/2

You could keep going to add, subtract, multiply, or divide both sides by some number. This process can continue indefinitely. I'll stop here since we have three operations done.

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

If we were to solve (10x+7)/2 = -13/2, we would get to x = -2

To solve (10x+7)/2 = -13/2, we follow the steps done in the previous section in reverse.

So we'll undo the "divide both sides by 2" operation by multiplying both sides by 2.

Then we'll undo the "add 7 to both sides" operation to subtract 7 from both sides

Lastly, we'll undo the "multiply both sides by 10" by dividing both sides by 10.

Answer:

-5.55 - 4.20c    

Answer:

I assume that you want the answer to this question but with the values replaced

We know from trigonometry that:

Θ(in radians) = s / r

Now, we will plug our given values in this equation

2 = s / 3

s = 6 inches

Answer:

the two numbers are 21 and 63

Step-by-step explanation:

divide 84 into 4 parts = 21

21x3= 63

CHECKING OUR WORK

21 + 63 = 84

The two numbers are 21 and 63.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the first number be x.

and, the second number = 3x

and, the sum of two number is 84.

x+ 3x= 84

4x = 84

x = 84/4

x = 21

Then, numbers are 21 and 3(21)= 63.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

x≥10,460 watts

Step-by-step explanation:

1Air conditioner=3,500w

1Washing machine=500w

1Dryer=5,000w

2Computers=70x2=140w

4Light bulbs=60x4=240w

1Refridgerator=600w

2Televisions=240x2=480w

Next, add.

3,500

  500

5,000

  140

  240

  600

+ 480

10,460w    So, x has to have at least 10,460 watts. The inequality would be...

x≥10,460 watts

Hope this helps c:

Answer:

Option (d)

Step-by-step explanation:

From the given table,

Number of members in 1980 (t = 0) were 5400.

With the period of time number of members increased.

Let the number of years after 1980 = x

Therefore, line of best fit will be in the form of y = mx + b

Where b = Initial number of members = 5400

m = Increase in members in every 5 years duration

So the equation will be,

y = mx + 5400

From the given options,

Equation which matches to our equation is,

y = 310.58x + 5400

For the number of members in year 2022,

x = 2022 - 1980 = 42 years

y = 310.58(42) + 5400

y = 18445

Option (d) will be the answer.

I think the answer is 10x +37.

I hope this helps!

Answer:

-8

Step-by-step explanation:

to isolate x you have to divide both sides by 5/4 and -10/(5/4) is -8

Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

[tex] 42 + 0.72m = 70 + 0.12m [/tex]

Collect like terms

[tex] 0.72m - 0.12m = 70 - 42 [/tex]

[tex] 0.6m = 28 [/tex]

Divide both sides by 0.6

[tex] \frac{0.6m}{0.6} = \frac{28}{0.6} [/tex]

[tex] m = 46.7 [/tex]

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

Answer:

y = -4/3x - 8

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Define points

x-intercept is (-6, 0)

y-intercept is (0, -8)

Step 2: Find slope m

[tex]m=\frac{-8-0}{0-(-6)}[/tex]

[tex]m=\frac{-8}{0+6}[/tex]

[tex]m=\frac{-8}{6}[/tex]

[tex]m=\frac{-4}{3}[/tex]

y = -4/3x + b

Step 3: Find y-intercept b

We are given (0, -8)

Step 4: Write linear equation

y = -4/3x - 8

Answer:

-9/10

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

First, you must change the denominator of -2/5 to an even one. I changed it to 10 by multiplying the fraction by 2. Multiplying the fraction by 2 will give you -4/5. To add 1/2, find 1/2 of 10/10. 1/2 of 10/10 is 5/10, so add 5/10 to -4/10 and you get 1/10. Hope this helps. <3

Answer:

  -17x +2y

Step-by-step explanation:

  (-8x -8y) -(9x -10y) = -8x -8y -9x +10y

  = x(-8 -9) +y(-8+10)

  = -17x +2y