Question 3
If y varies inversely as x, and y = 14 when x = 8, find y when x = 7.
AVE
Blank 1:

Answer:

(0, 6)

Step-by-step explanation:

Point T has a coordinate pair of (3, 4). That is, at point T, x = 3, while y = 4.

3 points to the left of T would be a movement on the x-axis. This movement is a run across the x-axis. At T, x = 3. Therefore, 3 points to the left would be a decrease by 3 = 3 - 3 = 0.

3 points to the left of T would leave us with an x coordinate of 0.

2 points above T suggest a rise, which is on the y-axis.

Therefore, at T, y = 4. 2 points above 4 = 4 + 2 = 6. y coordinate would now be 6.

In conclusion, the ordered pair representing 3 points to the left, and 2 points above point T is (0, 6).

Answer:

Step-by-step explanation:

[tex]8 + 9x + 4(11 - 2x) \\ = 8 + 9x + 44 - 8x \\ = 8 + 44 + 9x - 8x \\ = 52 + x[/tex]

Answer:

c < 7

Step-by-step explanation:

3(6-5c)-2c>4c-129

You will first multiply 3 with 6-5c which will give you 18 and -15c.

18-15c-2c>4c-129

Then you will subtract 2c from -15c because they're like terms. That will give you -17c.

18-17c>4c-129

Next you will put all the variables to one side. To do this, you will add 17c to 4c. You add 17c because that way, you cancel out the -17c and all the variables will be on one side

18>21c-129

Then you will add 129 to both 18 and -129 so that all of the numbers without variables can go on on side.

147>13c

Finally you divide both 147 and 13c by 13. That should give you the final solution of 7>c, or c<7.

Answer and Step-by-step explanation:

We are given a coordinate :

( 3 , -4 )

The first number within a coordinate means the x axis, meaning it moves either left or right.

While the second number within a coordinate means the y axis, meaning it moves up or down.

If a number is positive, it increases, if it is negative, it decreases.

So let's take a look at the first number 3, it is positive and the x axis number, meaning you should say "Moving right on the x axis 3 times"

Now for -4, it is negative and the y axis, meaning you should say "Moving down on the y axis 4 times"

Your final phrase should be :

"(3,-4) is moving right on the x axis 3 times, and moving down on the y axis 4 times"

Answer:

80

Step-by-step explanation:

82-12+10

82+10-12

92-12

80

The number of people in the restaurant will be 80

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter.

The expression will be solved as below:-

E = 82-12+10

E = 82+10-12

E = 92-12

E = 80

Therefore, the number of people in the restaurant will be 80

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Answer:

430 cm² is right answer ✔️

Step-by-step explanation:

A=2(wl+hl+hw)

=2(5×15+7×15+7×5)

=430cm²

hope it helped you:)

Answer:

y=-3

Step-by-step explanation:

-8y=24

y= 24/-8

y=-3

Hope this helps! :)

pls mark brainliest

y = - 3

- 8y = 24 | (-)

8y = - 24

y = - 24 : 8

y = - 3

Answer:

length= 5 + x

breadth = 6 + 2x

area = 30 + 16x + 2x^2

Answer: m=6

Step-by-step explanation:

[tex]9+12m=6+15\left(m-1\right)[/tex]

[tex]6+15\left(m-1\right)=15m-9[/tex]

[tex]9+12m=15m-9[/tex]

subtract 9 on both sides

[tex]9+12m-9=15m-9-9[/tex]

[tex]12m=15m-18[/tex]

subtract 15m on both sides

[tex]12m-15m=15m-18-15m[/tex]

[tex]-3m=-18[/tex]

divide by -3 on both sides

[tex]\frac{-3m}{-3}=\frac{-18}{-3}[/tex]

since [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]

[tex]\frac{-18}{-3}=6[/tex]

[tex]m=6[/tex]

Answer:

see explanation

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

- 27 = [tex]\frac{-27}{1}[/tex] ← in rational form

Thus - 27 is a rational number

Answer:

12.34

Step-by-step explanation:

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

Answer:

The anwer is A

Step-by-step explanation:

If it is a right angle triangle we use paythagoras theorem

a ×a + b× b= c × c

1. 15× 15( square of 15) + b× b(square of b) = 17 ×17 (square of 17)

;2. 225 + b×b(square of b ) = 289

3. b×b(square of b) = 289-225

4. b × b( square of b )= 64

[tex] \sqrt{b \times b} = \sqrt{64} [/tex]

b = 8

I hope it is helpful

Answer:

(- 1, 8 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(8, - 1 ) → (- 1, 8 )

The image of (8, -1) after a reflection over the line y = x is, (- 1, 8).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

A point (8, - 1) is reflected over the line y = x.

Now, We know that;

The image of point (x, y) after reflection over the line y = x is,

⇒ (x, y) → (y, x)

Thus, The image of (8, -1) after a reflection over the line y = x is,

⇒ (8, - 1) → (- 1, 8)

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Answer:

Step-by-step explanation:

Hope it helps you..

Thanks..

Answer:

1/6

Step-by-step explanation:

The reciprocal of a fraction can be found by flipping the numerator (top number) and denominator (bottom number).

The number 6 is equivalent to the fraction 6/1.

Find the reciprocal of 6/1. Invert the numerator and denominator.

6/1 ⇒ 1/6

The reciprocal of 6 is 1/6

Answer:

length (x) = 15 or -11

Step-by-step explanation:

step-by-step in attached picture

Answer

x.x.x.x.x = 5x

Step-by-step explanation:

Answer:

(

−

∞

,

∞

)

this is a link for help

Step-by-step explanation:

Simplify  

5

(

5

x

−

5

)

.

Tap for fewer steps...

Apply the distributive property.

5

(

5

x

)

+

5

⋅

−

5

=

25

(

x

−

1

)

Multiply.

Tap for more steps...

25

x

−

25

=

25

(

x

−

1

)

Simplify  

25

(

x

−

1

)

.

Tap for fewer steps...

Apply the distributive property.

25

x

−

25

=

25

x

+

25

⋅

−

1

Multiply  

25

by  

−

1

.

25

x

−

25

=

25

x

−

25

Move all terms containing  

x

to the left side of the equation.

Tap for fewer steps...

Subtract  

25

x

from both sides of the equation.

25

x

−

25

−

25

x

=

−

25

Combine the opposite terms in  

25

x

−

25

−

25

x

.

Tap for fewer steps...

Subtract  

25

x

from  

25

x

.

0

−

25

=

−

25

Subtract  

25

from  

0

.

−

25

=

−

25

Since  

−

25

=

−

25

, the equation will always be true for any value of  

x

.

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

(

−

∞

,

∞

)

Answer:

2 right? 3 and -3?

Step-by-step explanation:

Answer:

2 numbers

Step-by-step explanation:

● -3 and 3 are both 3 units apart from 0

We can find it with calculations.

You are moving in a real numbers line.

You can move either right or left.

You starting point is 0.

When you go 3 units to the right then you are adding 3.

● 3+0 = 3

When you go back 3 units starting from 0 then you are substracting 3.

● 0-3 = -3

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{2}}}}[/tex]

Step-by-step explanation:

[tex] \sf{4x + 8 = 16}[/tex]

Move 8 to right hand side and change its sign

⇒[tex] \sf{4x = 16 - 8}[/tex]

Subtract 8 from 16

⇒[tex] \sf{4x = 8}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{8}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

An adult ticket costs £7.

A child ticket costs £2.

Step-by-step explanation:

Let a represent the cost for adults and let c represent the cost for children.

Family 1 has a total of 2 adults and 3 children. Together, it cost them £20.

In an equation, this is:

[tex]2a+3c=20[/tex]

Family 2 has a total of 1 adult and 4 children. It cost them £15. In an equation, this is:

[tex]a+4c=15[/tex]

We know have a system of equations. Solve it. We can use the substitution method.

First, subtract both sides by 4c in the second equation:

[tex]a+4c=15\\a=15-4c[/tex]

Substitute this into the first equation:

[tex]2a+3c=20\\2(15-4c)+3c=20[/tex]

Distribute:

[tex]30-8c+3c=20[/tex]

Add:

[tex]30-5c=20[/tex]

Subtract 30 from both sides. The left cancels:

[tex]-5c=-10[/tex]

Divide both sides by -5:

[tex](-5c)/-5=(-10)/-5\\c=2[/tex]

Thus, the cost of a child ticket is £2.

Substitute 2 for c into the equation we manipulated at the start:

[tex]a=15-4c\\a=15-4(2)\\a=15-8=7[/tex]

Thus, the cost of an adult ticket is £7.

Answer:

Adult ticket= $7

Child Ticker=$2

Step-by-step explanation:

Family 1: 2x+3y=20

Family 2: x+4y=15

2x+3y=20

x+4y=15

Multiply by 2

2x+3y=20

-(2x+8y=30)

Change the signs

2x+3y=20

-2x-8y=-30

Eliminate x

-5y=-10

Divide both sides by -5

y=2<---- Price per children

Substitute the value of y

x+4(2)=15

x+8=15

x=15-8

x=7 <----Price per adult

Check:

Substitute the values of x and y to family 1

2(7)+3(2)=20

14+6=20

20=20

7+4(2)=15

7+8=15

15=15

Answer:

(- 3, 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , thus

(5, 3 ) → (- 3, 5 )

Answer:

6x + 15.

Step-by-step explanation:

3(3x + 5)

= 3 * 2x + 3*5

= 6x + 15.

Hey There!! ~

The answer to this is: Apply the distributive property.

[tex]3 (2x) + 3 . 5[/tex]

Multiply. 2 by 3 [tex]6x + 3 . 5[/tex] Multiply  

Multiply 3  by 5.

[tex]6 x + 15[/tex] Thus, for the answer is: 6x + 15.

Hope It Helped!~

[tex]ItsNobody[/tex]~

Answer:

513.95

Step-by-step explanation:

First you have to divide 7776 by 343. Then you raise the answer to the second power

Answer:

que????? no entiendo??????

Answer:

y= 5 + 0.9x

Step-by-step explanation:

Giving the following information:

NYCab company charges an initial rate of $5.00 for a ride, plus $0.90 for each mile driven.

We need to structure the total cost formula:

y= total cost

x= miles driven

fixed cost= $5

Unitary variable cost= $0.9

y= 5 + 0.9x

Answer:

57

Step-by-step explanation:

all you have to do is take the 10,602 and divide it by 186

and you end up with 57. to check this just do 10,602 divided by 57 or 57 times 186.

Answer:

0.06 cubic meters per year...

Step-by-step explanation:

The rate of water flows through a pipe is 0.06 cubic meters per year.

It is the volume of fluid flows out from the container per unit time.

Given that,

Water flows through a pipe at a rate of 6 fluid ounces per day. It can be written as:

Water flows per day ⇔ 6 fluid ounces

∴ Water flows per year ⇔  365 x (6 fluid ounces)

Volume of water in milliliter,

Water flows per year ⇔  365 x (6 x 29.574 ml )

Volume of water in cubic meter,

Water flows per year ⇔  365 x ([tex]\frac{6 x 29.574}{1000000}[/tex] [tex]m^{3}[/tex]) = 0.06477   [tex]m^{3}[/tex]

Hence Water flows per year round value to the nearest hundredth is 0.06  [tex]m^{3}[/tex].

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Answer:

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Step-by-step explanation:

Let suppose that A and B have one-dimensional coordinates. GIven that [tex]A = 8[/tex] and [tex]AB = 3[/tex], there are two possible locations for B:

[tex]B_{1} = A+AB[/tex]

[tex]B_{1} =8+3[/tex]

[tex]B_{1} = 11[/tex]

[tex]B_{2} = A-AB[/tex]

[tex]B_{2} = 8-3[/tex]

[tex]B_{2} = 5[/tex]

The midpoint equations for each case are, respectively:

[tex]m_{1} = \frac{A+B_{1}}{2}[/tex]

[tex]m_{1}=\frac{8+11}{2}[/tex]

[tex]m_{1} = \frac{19}{2}[/tex]

[tex]m_{2} = \frac{A+B_{2}}{2}[/tex]

[tex]m_{2} = \frac{5+8}{2}[/tex]

[tex]m_{2} = \frac{13}{2}[/tex]

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Answer:

3n + 2

Step-by-step explanation:

[tex]−n+(−4)−(−4n)+6[/tex]

Open the parentheses

[tex] - n - 4 + 4n + 6 \\ [/tex]

Add similar elements

[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]

Answer:

[tex] - n + 6[/tex]

Step-by-step explanation:

[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]