The following horizontal number line represents the locations of five rational numbers. Use the number line to determine whether each statement is true or false. If a statement is false, explain why it is false.

The product of Q and T is negative.
The quotient of P and S is -P.
The product of R and 0 is rational.
The quotient of T and 0 is rational.
The product of -S and Q is the same as the quotient of -Q and S.

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

[tex]\mathbf{n = 5}[/tex] --- the number of digits

[tex]\mathbf{r = 3}[/tex] ---- the number of actions

Each of the three actions can either be:

The number of ways of pressing a button is:

[tex]\mathbf{n_1 = ^5C_1}[/tex]

Apply combination formula

[tex]\mathbf{n_1 = \frac{5!}{(5-1)!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5!}{4!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}[/tex]

[tex]\mathbf{n_1 = 5}[/tex]

The number of ways of pressing a pair is:

[tex]\mathbf{n_2 = ^5C_2}[/tex]

Apply combination formula

[tex]\mathbf{n_2 = \frac{5!}{(5-2)!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5!}{3!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}[/tex]

[tex]\mathbf{n_2 = 10}[/tex]

So, the number of ways of performing one action is:

[tex]\mathbf{n =n_1 + n_2}[/tex]

[tex]\mathbf{n =5 + 10}[/tex]

[tex]\mathbf{n =15}[/tex]

For the three actions, the number of ways is:

[tex]\mathbf{Action = n^3}[/tex]

[tex]\mathbf{Action = 15^3}[/tex]

[tex]\mathbf{Action = 3375}[/tex]

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

https://brainly.com/question/4546043

Answer:

...............c

Step-by-step explanation:

Answer:

y = 6x - 42

Step-by-step explanation:

Point (7,0)

y-intercept = 0 - (6)(7) = -42

Answer:

x= 3, -4

Step-by-step explanation:

BIG BRAIN

Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then then corresponding sides are in proportion , that is

[tex]\frac{NP}{ST}[/tex] = [tex]\frac{NM}{SR}[/tex] , substitute values

[tex]\frac{x}{25}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )

30x = 450 ( divide both sides by 30 )

x = 15

Similarly

[tex]\frac{UT}{QP}[/tex] = [tex]\frac{NM}{SR}[/tex] , that is

[tex]\frac{y}{15}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )

30y = 270 ( divide both sides by 30 )

y = 9

The similarity ratio is the ratio of corresponding sides , that is

[tex]\frac{NM}{SR}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]

SRUT is [tex]\frac{3}{5}[/tex] of NMQP

Answer:

k = 6

Step-by-step explanation:

Answer:

(a² + b² + 3ab)(a² + b² - 3ab)

Step-by-step explanation:

a⁴ - 7a²b² + b⁴

= (a⁴ + 2a²b² + b⁴) - 9a²b²

= (a²+b²)² - (3ab)²

= (a² + b² + 3ab)(a² + b² - 3ab)

Answer:

The answer will be -5

You are welcome:)

Step-by-step explanation:

Answer:

y = x - 11

Step-by-step explanation:

f (x) = x + 11

y = x + 11

x = y + 11

x - 11 = y

Answer:

4 classes

Step-by-step explanation:

1. Write an equation for the cost for both members and nonmembers, in which x is the number of aerobics classes.

Cost = 3x + 6 for members

Cost = 4x for nonmembers

2. Set the equations to equal each other and solve.

3x + 6 = 4x

-3x         -3x

6 = x

3. Check your answer

4*6 = 24

(3*6) + 6 = 24

For 4 aerobics classes, the cost for members and nonmembers is the same.

Answer:

a^2 = -2a

a= -2

b=18/a

b=18/ -2

b= -9

Answer:

7/10

Step-by-step explanation:

Answer:

GOOD LUCK ON YOUR TEST YOU WILL DO GOOD

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

Hope this helps!

Answer:

point = (-3, 5)

slope = 3/4

Step-by-step explanation:

The formula for point slope is:

y - y1 = m (x - x1)

point (x1, y1)

slope m

So with your equation:

y - 5 = 3/4 (x+ 3)

point = (-3, 5)

slope = 3/4

Answer: M=0,75

Step-by-step explanation:

Answer:

y-2=2(x-12)

the alternative is

y+3=2(x-2)

Step-by-step explanation:

Answer:

the circumference of circle is 2 πr

Answer:

565.48 sq. in.

Step-by-step explanation:

Given the Slant height and radius, we are asked to find the lateral area of the cone.

Lateral area of the cone is given by  

where, 'r' is the radius of the cone.

and 'l' is its slant height.

From the figure, we see that the slant height of the cone, l = 15 in

Also, the radius of the cone, r = 12 in.

Therefore,  

= 565. 48 sq. in. which is the required answer.

Answer:

A  proportional relationship is written as:

y = k*x

where k is the constant of proportionality.

A general word problem that represents one of these relationships can be:

If each burger costs $1.50, what would be the cost of buying x burgers?

The cost of x burgers will be x times $1.50, so if we define y as the total price, we will have the relation:

y = $1.50*x

Which is a proportional relationship where the constant of proportionality is $1,50

Step-by-step explanation:

Q6

answer A, as x² is the regular parabolic curve up. and x²-3 just shifts this curve down by 3 units. and that is what we need, as the extreme point of the curve is a bit below the x-axis, and therefore has a negative y value.

Q7

answer C, as this curve is the complete opposite of the curve in Q6.

it is the regular parabolic curve but down. that means -x².

but the extreme point is a bit above the x-axis (and has therefore a positive y value). -x²+3 shifts the parabolic curve up by 3 units.

Q8

answer A again. the functional values are only positive (the whole curve is above the x-axis). so, C and D are therefore wrong.

and between A and B we need to remember, that a negative exponent means 1/...

in case of B 1/(2^x).

and that would mean for large positive x we would get very small values for y.

but we see the opposite. for large x we also get large y.

so, it is 2^x (answer A).

Answer:

1/4

Step-by-step explanation:

We know :-

Substitute ,

Answer:

450 words at a rate of 45 word per minute

Step-by-step explanation:

180 divided by 4 equals 45

times 10 equals 450

Answer:

450 words in 10 minutes

Step-by-step explanation:

To set this up you need to put it like this:

[tex]\frac{180}{4} =\frac{x}{10}[/tex]

From here, you need to cross multiply, which will get you to: 180(10) = 4x

Multiply 180 and 10: 1,800

The equation will now be: 1,800 = 4x

Now, divide both sides by 4:   450 = x

Answer:

KL = 6 units.

Step-by-step explanation:

Congruent means the same or similar.

Hope this helps!

Answer:

Width = 125 m

Length = 375 m.

Step-by-step explanation:

If the width = w then length l = 3w.

Perimeter = 2(w + l)

= 2(w + 3w)

2(w + 3w) = 1000

2 * 4w = 1000

w = 1000/8 = 125m

l = 3*125 = 375.

Step-by-step explanation:

width = x

length= 3x

perimeter of triangle =2( l + b)

1000 = 2( 3x + x )

1000÷ 2 = 4x

500=4x

x= 500÷ 4 = 125

width = 125

length = 125×3= 375

recheck by filling value

width= x = 125

length = 3x =375

perimeter = 2( l+ b)

= 2(375 + 125)

= 2× 500 = 1000

hence proved

hope it helps : )

Answer:

1.) 40 degrees

2.) 75 degrees

3.) 105 degrees

4.) 140 degrees

Step-by-step explanation:

Straight lines are = 180 degrees. Each of the angles you must solve have a given exterior angle. All you have to do is subtract the exterior angle from 180 to find the interior angle

1.) angle = 180-140

2.) angle = 180-105

3.) angle = 180-75

4.) angle = 180-40

Answer:

Measure of angle 1 is: 40 degrees

Measure of angle 2 is: 75 degrees

Measure of angle 3 is: 105 degrees

Measure of angle 4 is: 140 degrees

Step-by-step explanation:

Answer:

you got the answer right there

Step-by-step explanation:

Answer:

-14/25

Step-by-step explanation:

7x +2 / 2 - 5x = -2 / 5

First you can cross multiply (shown in the picture):

Next, expand the brackets:

5(7x + 2) = -2(2 - 5x) → 35x + 10 = -4 + 10x

Now, simplify:

35x + 10 = -4 + 10x → 35x - 10x = -4 - 10 → 25x = -14 → x = -14/25

Hope this helps!

Answer:

this problem is  Non-proportional

Step-by-step explanation:

hope this helps