Let a and b be rational numbers. Is a – b rational or irrational?

Answer:

See below.

Step-by-step explanation:

Since the two triangles are similar, this means that their corresponding sides are proportional. In other words:

[tex]\frac{PQ}{XY}=\frac{QR}{YZ}=\frac{RP}{ZX}[/tex]

Part A:

We already know PQ, RP, XY, and YZ.

To find XZ, we can use the first and third proportions:

[tex]\frac{PQ}{XY} =\frac{RP}{ZX} \\=\frac{7.2}{18}=\frac{6.5}{ZX}[/tex]

Cross multiply:

[tex]117=7.2(ZX)\\ZX \text{ or } XZ = 16.25[/tex]

Part B:

The same thing as Part A, but with the first and second proportions:

[tex]\frac{PQ}{XY}=\frac{QR}{YZ}\\\frac{7.2}{18}=\frac{QR}{7}\\50.4=18(QR)\\QR=2.8[/tex]

Answer:

x^2+3x-4

Step-by-step explanation:

(x-1)(x+4)

x^2+4x-x-4

x^2+3x-4

Hope this helps ;) ❤❤❤

Answer:

y = x² + 3x -4

Step-by-step explanation:

we can use the FOIL formula

(x-1) (x+4)

x² + 4x - x -4

x² + 3x -4

therefore, the standard form would be y = x² + 3x -4

Answer:

He is currently reading 7 pages per night

Step-by-step explanation:

We can simply the question a little by finding what percent of the original Wesley is currently reading. Instead of saying 65% fewer, we can say he is reading 35% of what he used to read

Now we need to set up a proportion to solve the problem.

35% of 20

35/100=x/20

Cross multiply

35x20=700

700/100=7

He is currently reading 7 pages per night

Answer:

1. [tex]c = \sqrt{2}[/tex].

2. b = 4.

Step-by-step explanation:

To solve these two questions, keep the Pythagorean Theorem in mind: [tex]a^2 + b^2 = c^2[/tex]. Also remember that measurements cannot be negative, so we will disregard the negative answers.

1. a = 1, and b = 1. c = ?

[tex]1^2 + 1^2 = c^2[/tex]

[tex]1 + 1 = c^2\\[/tex]

[tex]c^2 = 1 + 1\\c^2 = 2\\\sqrt{c^2} = \sqrt{2}\\c = \sqrt{2}[/tex]

2. a = 3, c = 5. b = ?

[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\\sqrt{b^2} = \sqrt{16}\\b = 4[/tex]

Hope this helps!

Step-by-step explanation:

Given,

distance =420 miles

time 6.5 hrs

now,

420miles took 6.5 hrs.

1mile took 6.5/420hrs

=0.015476hrs

Therefore, 0.015476hrs to cover 1 mile distance.

Hope it helps...

Answer:

64.6153846 miles/hour

0.0154761905 hours/mile

Step-by-step explanation:

If we want to find the miles driven in one hour, we must divide the total miles by the total hours.

miles / hours

We know that 420 miles were driven in 6.5 hours

420 miles/ 6.5 hours

Divide 420 by 6.5

420/6.5=64.6153846

64.6153846 miles/hour

In one hour, 64.6153846 miles are driven.

If we want to find the time to drive one mile, divide the time (hours) by the miles.

hours / miles

We know that 420 miles were driven in 6.5 hours.

6.5 hours/420 miles

Divide 6.5 by 420

6.5/420=0.0154761905

0.0154761905 hours/ mile

It will take 0.0154761905 of an hour to drive one mile.

Answer:

Step-by-step explanation:

 [tex]\left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7[/tex]                          

Answer:

  5 19/20 or 5.95

Step-by-step explanation:

You can add these numbers as decimal numbers or as mixed numbers.

Decimal

  2.2 +3.75 = 5.95 . . . hours spent studying

Mixed Numbers

  (2 1/5) +(3 3/4) = (2 4/20) +(3 15/20) = (2 +3) +(4/20 +15/20)

  = 5 19/20 . . . hours spent studying

Answer:

A.) As x increases, the rate of change of g exceeds the rate of change of f

Step-by-step explanation:

Let's take the options given and look at them to actually know which is true.

Option A

We notice that as x increase in value the rate of change of g starts exceeding the rate of change of f.

Then it's exceeds it from the value x = 5

Option B

At x= 4.39

F= 2616.689

G= 2606.657

They are different values

Option C

That's opposite of option A

But option A is true which signify option C to be false

Option D

Not true also.

We can see from x= 0 to 4 the rate of change of F exceeds that of G

Answer:

Step-by-step explanation:

6):

Take the small right triangle with the sides 25 and 7.

☆ The Pythagorian theorem ☆

Let x be the third side.

● 25^2 = x^2 + 7^2

Substract 7^2 from both sides

● 25^2 -7^2 = x^2 +7^2 -7^2

● x^2 = 25^2 -7^2

● x^2 = 576

● x = 24 inches

The third that we find is the half of the side of the square.

Multiply it by 2 and get the side of the square.

● 24 × 2 = 48 inches

The perimeter of the square is the side times 4.

● P = 48 × 4

● P = 192 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

7):

Both triangles are righr and they have a khown angle.

Start with the small one and calculte the third angle.

The sum of a triangle angles is 180°

Let B be the third angle.

● B = 180-(90+51) = 39°

That's equal to the second angle of the second's triangle.

So it's an AA similarity.

So:

● x/24 = 7/15

● x = (7/15)×24

● x = 11.2

Answer:

The answer can be interpreted by the distance moved by each gallon :))

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

Answer:

20π cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( where r is the radius )

Here r = 10 , thus

C = 2π × 10 = 20π cm

Answer:

hope it helps

Step-by-step explanation:

circumference of a circle = 2*pi*r = 2*pi*10 =20picm

Answer:47 is a prime and 81 is a composite

Step-by-step explanation:47={1,47}

81={1,3,9,18,27,81}

1. The number 47 is prime. The only factors are 1 and itself. We can check by dividing 47 over the list of primes smaller than 47. To be more efficient, we can stop once we reach sqrt(47) = 6.85. So we only need to check the primes {2, 3, 5} to show they are not factors of 47 to show that 47 is prime.

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

2. The number 81 is composite. It is not prime because it has factors other than 1 and itself.

There are 5 factors and they are

1, 3, 9, 27, 81

Note how each factor listed is a power of 3 (1 = 3^0, 3 = 3^1, 9 = 3^2, 27 = 3^3, 81 = 3^4)

The prime factorization of 81 is

81 = 3*3*3*3 = 3^4

Answer:

b

Step-by-step explanation:

Answer:

B. The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

Step-by-step explanation:

I just have an educated guess out of the info that you gave me.

Answer:

8.94~9.0

Step-by-step explanation:

If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!

The required length of the hypotenuse of the triangle is 16√5.

Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

Here,
Applying the Pythagorean theorem,
Hypotenuse²  = perpendicula² + base²
Hypotenuse²  = 8² + 4²
Hypotenuse²  = 64 + 16
Hypotenuse²  = 80
Hypotenuse  = √80
Hypotenuse  =  16√5

Thus, the required length of the hypotenuse of the triangle is 16√5.

Learn  more about Pythagorean triplets here:

https://brainly.com/question/10174253

#SPJ2

Answer:

B. $18.00

Step-by-step explanation

160/4 divide 160 by 4 to see how much Miss Adams makes and hour

She makes $4 an hour

multiply this ($4) by her idle time (4.5) hours to get $18

Answer:

54

Step-by-step explanation:

i put in the calculator 50+36×54= and got this 1,994

Answer:

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

Answer:

[tex]\frac{1}{9^4}[/tex].

Step-by-step explanation:

[tex]9^{-4}[/tex]

= [tex]\frac{1}{9^4}[/tex]

= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]

= [tex]\frac{1}{81 * 81}[/tex]

= [tex]\frac{1}{6561}[/tex]

= 0.0001524157903.

Hope this helps!

Answer:

x = -67/15 = -4-46667

Step-by-step explanation:

4(-3x+1) - 3x = 71

4*-3x + 4*1 - 3x = 71

-12x + 4 - 3x = 71

-15x = 71-4

-15x = 67

x = 67/-15

x = -4.46667

check:

4(-3*-4.46667 + 1) - 3*-4.4666= 71

4(13.4+1) + 13.4 = 71

4*14.4 + 13.4 = 71

57.6 + 13.4 = 71

Answer: Answer is the steps

Step-by-step explanation:

If they are down by seven points then it means that they are losing by 7 points.And fortunately they made  two-point field goal so they will now be down by 5 points. Which means that they need 5 more points to tie the game.

For example,

-7 represents the points that they are down by and they made 2  points so

-7 + 2 = -5   which means that they are now down by 5 points to make a tie game.

Answer:-7+2+5=0

Step-by-step explanation:

Answer & Step-by-step explanation:

Take the last  expression:

[tex](3*3)*(4*4)[/tex]

This can be simplified using exponents. [tex]x*x=x^2[/tex] :

[tex]3^2*4^2[/tex]

So, take the two numbers within the parentheses from the first expression and write separately, including the exponent with each. Do this with the next problem:

[tex](5*6)^3=5^3*6^3[/tex]

:Done

Answer:

=2x+3/4=5.50

x=19/8 or 2 3/8

hope this helps

Step-by-step explanation:

Long piece is 81 inches

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

Explanation:

x = length of short piece

3x = length of the longer piece (3 times longer)

x+3x = 4x = total length

total length = 108

So 4x = 108 is the equation which solves to x = 27 after dividing both sides by 4.

The short piece is x = 27 inches and the long piece is 3*x = 3*27 = 81 inches. Adding the two pieces gives 27+81 = 108 which helps confirm the answer.

Answer:

(-5) ^ 11

Step-by-step explanation:

(-5) ^5 / (-5) ^ -6

We know that a^ b / a^ c = a^ ( b-c)

(-5)^ (5 - -6)

(-5) ^ (5+6)

(-5) ^ 11

Answer:

-5

Step-by-step explanation:

Mathaway

Answer:

5 hours

Step-by-step explanation:

Scott's delivery rate = 10 pizzas per hour

Kenneth's delivery rate = 12 pizzas per hour

Combined delivery rate

= Scotts delivery rate + Kenneth's delivery rate

= 10 + 12

= 22 pizza's per hour  (take reciprocal to find the rate in "hours per pizza")

= 1/22 hours per pizza

Given that they both deliver 110 pizzas combined, the will take

= 1/22 hours per pizza x 110 pizzas

= (1/22) x 110

= 5 hours

Answer:

7/40 is the fraction filled with water

Step-by-step explanation:

Here we start by calculating the volume of the cylindrical tank.

Mathematically, that would be;

V = π * r^2 * h

From the question

r = 80 cm = 80/100 = 0.8 meters

h = 1.4 meters

π = 22/7

Plugging these values into the volume equation, we have;

V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3

But mathematically;

1 m^3 = 1000 liters

So 2.816 m^3 = 2.816 * 1000 = 2816 liters

So the fraction filled with water will be;

492.8/2816 = 0.175 = 175/1000 = 7/40

Answer:

4 to the power of 10.

Step-by-step explanation:

A rule is that x to the power of y + x to the power z of must equal x to the power of z+y.

Answer:

Option B

Step-by-step explanation:

4²×4^8

4^(2+8)

4^10

4 to the 10th power

Answer:

Step-by-step explanation:

[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]

Answer:

one fifth

Step-by-step explanation:

42

Answer:

The graph of g is one-fifth as steep as the graph of f.

Step-by-step explanation:

Answer:

D. m = 43

Step-by-step explanation:

Answer: D. m=43

Step-by-step explanation: