Is -51/5 rational or irrational

Answer:

side lengths are 96 for HI and PQ and 64 for IJ and RQ

hypothenuse is 115

Step-by-step explanation:

delta HIJ = delta PQR

HI = PQ   -->   3x = x + 64

divide both sides by x --> 3 = x/x + 64/x      *x/x = 1

3 = 1 + 64/x subtract both sides by 1

2 = 64/x --> 2x = 64 divide both sides by 2

x = 32

IJ = RQ --> x + 32 = 2x

divide both sides by x

1 + 32/x = 2 (again, x/x = 1)

subtract both sides by 1

32/x = 1

x = 32

plug in 32 for x to get the side lenghts

so 3(32) = 96

and 32 + 32 = 64

use equation a^2 + b^2 = c^2

96^2 + 64^2 = c^

9216 + 4096 = c^2

13312 = c^2        square root 13312

c = 115.378

Answer:

Khaled made 16 baskets.

Step-by-step explanation:

3 12

-- = ---

4 x

12 / 3 = 4

4 x 4 = 16

x = 16

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

Explanation:

Use the pythagorean theorem to tie together the three sides of the right triangle.

[tex]a = x-3 = \text{horizontal leg}\\b = x+5 = \text{vertical leg}\\c = 9 = \text{hypotenuse}[/tex]

[tex]a^2 + b^2 = c^2\\(x-3)^2 + (x+5)^2 = 9^2\\x^2-6x+9 + x^2+10x+25 = 81\\2x^2+4x+34 = 81\\2x^2+4x+34-81=0\\2x^2+4x-47=0\\[/tex]

From here, we use the quadratic formula to solve for x.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(4)\pm\sqrt{(4)^2-4(2)(-47)}}{2(2)}\\\\x = \frac{-4\pm\sqrt{392}}{4}\\\\x \approx \frac{-4\pm19.79898987}{4}\\\\x \approx \frac{-4+19.79898987}{4} \ \text{ or } \ x \approx \frac{-4-19.79898987}{4}\\\\x \approx \frac{15.79898987}{4} \ \text{ or } \ x \approx \frac{-23.79898987}{4}\\\\x \approx 3.94974747 \ \text{ or } \ x \approx -5.94974745\\\\[/tex]

We'll ignore the negative x value because it makes the sides x+5 and x-3 to be negative numbers. Negative side lengths make no sense.

The only practical solution is roughly x = 3.94974747; rounding to 3 sig figs leads to the final answer of x = 3.95

In this case, 3 sig figs means that we're rounding to 2 decimal places.

Answer:

x2+2x−35=0

Step 1: Factor left side of equation.

(x−5)(x+7)=0

Step 2: Set factors equal to 0.

x−5=0 or x+7=0

x=5 or x=−7

Step-by-step explanation:

Answer:

x=3-2i

Step-by-step explanation:

According to my calculations, this should be good

Answer:

Step-by-step explanation:

Value of x= `

4x+5y-6z =2

x= (2-5y+6z) divided by 4

For example : if x is 2.5

2.5 = 2 - 5x2 + 6x3

Answer:

The fraction is 13/21.

Step-by-step explanation:

The denominator of a fraction is 8 more than its numerator.

Let x be the numerator: x

So the denominator is: x + 8

[tex]\frac{x}{x + 8}[/tex]

If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2.

It will become:

[tex]\frac{x - 1}{x + 8 + 3} = \frac{1}{2}[/tex]

[tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex]

Now, by using cross multiplication, multiply (x - 1) by 2 and (x+11) by 1.

It will become:

2x - 2 = x + 11

Now transpose and combine the same values. Make sure to change the integer sign. If the integer is positive, change it to negative when you transpose it.

2x - x = 11 + 2

x = 13

So the value of x is 13. Now to check if it is correct. Go back to the equation([tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex])

Put the value of x in it.

[tex]\frac{13-1}{13+11} = \frac{1}{2}[/tex]

[tex]\frac{12}{24} = \frac{1}{2}[/tex]

12/24 is equivalent to 1/2 so that is correct.

Now, to find the main fraction. Go back to the original equation which is;

([tex]\frac{x}{x + 8}[/tex])

Put the value of x.

[tex]\frac{13}{8 + 13}[/tex]

= 13/21

Not a verified expert but I put much effort to answer your question. Hope it helps:)

Answer:

x = 32

Step 1: Solve the right-hand side of the equation.

47 - x = 50 - 35

=> 47 - x = 15

Step 2: Subtract '47' from both ends.

=> 47 - x = 15

=> -x = 15 - 47

Step 3: Solve for x.

=> -x = -32

=> x = 32.

Hoped this helped.

Answer:

12/15

Step-by-step explanation:

times 4 by 3 because 5 is timesed by 3

Answer:

100 oxygen molecules simple math

Answer:

28/4

Step-by-step explanation:

the slash is also a division sign.

Answer:

B: 28/4 should be the correct answer, correct me if I'm wrong.

Answer:

x ÷ 4 ≤ 5

Step-by-step explanation:

Answer:

232

Step-by-step explanation:

4*58=232

Answer:

$7.97

Step-by-step explanation:

98.2 Oz = 6.1375 Lbs

6.1375 Lbs times $1.30 = 7.97875

Answer:

Step-by-step explanation:

First, you have to use the law of cosines which is c² = a² + b² - 2abcosФ where Ф is the angle measure between sides a and b. So, just plug-in a = 10, b = 12, and Ф = 72 into the equation and you will get (I won't show all the calculations):

c = 13.0321

Then plug that into the area formula to get:

(0.5)(10)(12)(0.225496911)

Which is about:

13.53

Answer:

Since there is a right angle, this is a right-angled triangle and we can solve for x using Pythagoras Theorem that goes [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse (longest side of the triangle).

In this case, x would be the c.

Substitute in values of a and b:

[tex]10^2+10^2=c^2[/tex]

[tex]c^2=200[/tex]

[tex]c=\sqrt{200}[/tex]

[tex]c=10\sqrt{2}[/tex] (Option A)

Answer:

2/3

Step-by-step explanation:

     [] Since is the line is going up from bottom-left to top-right, we know it will be positive

     [] Because this graph has distinctive coordinate-points, we can use rise over run

     () The other method is to use the change in y divided by the change in x

We start at (-2, 0), then count 2 up and 3 over to get to (2, 1) which gives us a slope of 2/3

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

If the sum of first four terms in a G.P. is 30 and that of the last four terms is 960, then the sum of the first 8 terms is 990

We also know that a = 2

sum of first 4 terms

= 2(r^4 - 1)(r-1) = 30

r^4 - 1 = 15r - 15

r^4 - 15r + 14 = 0

r = 1 works for the equation , but r = 1 would make all the terms of the

GP the same, so clearly not a solution

r^4 - 15r + 14 = 0 , a bit of trial and error ....

(r-1)(r - 2)(r^2 + 3r + 7) = 0

so r = 2 or r = not real

check: sum(4) = 2(2^4 - 1)/(2-1) = 30 , as needed

so r = 2 , BUT it does not work for sum(8)

sum(8) = 2(2^8 - 1)(2-1) = 510 , not 990 as necessary according to your second part of the question.

check your question.

Answer:

a₆ = - 486

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = 3 , then

a₆ = - 2 [tex](3)^{5}[/tex] = - 2 × 243 = - 486

The recursive rule allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is

[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] with a₁ = - 2

Answer:

-5

Step-by-step explanation:

g(x)= 3x+1

g(-2)

g(-2)= 3x+1

g(-2)= 3(-2)+1= -5

Answer:

Step-by-step explanation:

(450 miles/3 inches) = 150 miles/inch

(1,250 miles)/(150 miles/inch) = 8.3333 inches

When the actual distance between two cities is 1350 miles the distance between the same cities on the map is 9 inches.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

Given that,

On scale 3 inches represents the actual distance = 450 miles.

To find the distance on scale when actual distance = 1350

Since, 3 inches = 450 miles

1 inch = 450 / 3 = 150 miles

150 miles = 1 inches

1 mile =  / 1/ 150 inches

1350 miles = 1350 / 150 inches = 9 inches

The required distance on scale is 9 inches.

To know more about Proportion on:

https://brainly.com/question/7096655

#SPJ5

Answer:

576

Step-by-step explanation:

5 + 3 = 8

5 - 2 = 3

8 x 3 = 24

24 to the second power is 576

Answer:

27x+5

Step-by-step explanation:

5+3x(5-2)^2

5+3x(3)^2

5+3x*9

5+27x

27x+5

Answer:

She can travel for 10 days

Step-by-step explanation:

first you do 1,250 divided by 1,250 will equal 0. Then you do the other side 1,700- 1,250 =450. Then you do 450 divided by 45 and you will get 10

Hope this helps you out!

Answer:

[tex]y = -6[/tex]

Step-by-step explanation:

Because is a line is of the form

[tex]y = mx + b[/tex]

and its parallel to the line

[tex]2 - y &= 7\\- y &= 5\\y = -5[/tex]

So that's meaning that the slope [tex]m[/tex] is equal to 0 then the equation now is of the form

[tex]y = b[/tex]

Then if pass for the point -6 and [tex]b[/tex] is the point of cut with the [tex]y[/tex] axis then our equation of the line is equal to

[tex]y = -6[/tex]

Step-by-step explanation:

first, we define the line.

the slope is -3 (as for every increase of x by 1 unit, y changes by -3 units, which makes the slope -3/1 = -3).

the y-intercept is 2.

so, the line is

y = -3x + 2

now the graph shows that we need to define all y values that are below (and that means smaller than) the result values of the line function.

the line is not included.

therefore the inequality is

y < -3x + 2 or 3x + y < 2

Answer:

(x+2/3) (x^2 - 2)

Step-by-step explanation:

First we can seperate the problem

(x^3 + 2/3x^2) + (-2x - 4/3)

We factor x^2 out of the first parenthesis

x^2(x + 2/3) + (-2x - 4/3)

and factor -2 out of the second

x^2 (x+2/3) +-2 (x +2/3)

then we rewrite it as

(x+2/3) (x^2 -2)

-- Gage Millar, alg1/2 tutor

Answer:

x = 35 ,y = 35

Step-by-step explanation:

x = 35

y = 35

Answer:

4 ounces each

Step-by-step explanation:

16 ounces = 1 pound

16x2=32

32/8=4

The outcomes are

Total Outcomes=3×3=9

Answer:

8x - 1 + 16x²

Step-by-step explanation:

8x - 2 + (4x - 1)(4x+1) = 0

=> 8x - 2 + 16x² + 4x - 4x - 1

=> 8x - 2 + 16x² - 1

=> 8x - 1 + 16x²

Therefore, 8x - 1 + 16x² is our answer