3x + y = 4 6x + 4y = 6 equivalent equation and solution

Step-by-step explanation:

Age of dave = y

Age of Julia = x

y = 4x - 8

if y = 16

then

4x - 8 = 16

4x = 16 + 8

4x = 24

x = 24/4

x = 6

Julia is 6 years old

Answer:

Julia is 6 years old.

Step-by-step explanation:

Dave + 8 = 4 Julia

16 + 8 = 4 Julia

24 = 4 Julia

6 = Julia

Julia is 6 years old

Answer:

see attached

Step-by-step explanation:

(i) F' shown in red = Rotation 180° about point (2, 1)

(ii) F'' show in blue = Reflection of F' in x-axis

Answer:

The answer are in the file

Answer:

w= -6

w= 4

Step-by-step explanation:

w= -b sqrt(b^2-4ac)

2a

let

a=1

b=2

c= -24

substitute values~

[tex]==========================================[/tex]

In order to solve this equation for w, we need to factor it.

First, let's think of 2 numbers that multiply to -24 and add to 2.

These numbers are -4 and 6.

Check:

6×(-4)=-24 ✓

6+(-4)=6-4=2✓

Now, factor:

(     ) (    )

That's how it should look like:

(w+   )( w-   )

Now, instead of the blanks, plug in -4 & 6:

(w-4)(w+6)

Now, set each factor equal to 0:

w-4=0

w=4

w+6=0

w=-6

[tex]====================================[/tex]

Nickname:-

Answer:

1/4 feet

Explanation:

So

Hence.

Answer:

  £102,000

Step-by-step explanation:

A growth rate of 1.6% corresponds to an annual growth factor of ...

  1 +1.6% = 1.016

The house value is multiplied by this factor each year for 4 years, so the final value is ...

  £96000 × 1.016⁴ ≈ £102,293

To 3 significant figures, the house value after 4 years is £102,000.

Answer:

answer : 102293.04

3 significant figures : 102000

Step-by-step explanation:

Answer:

it is option B that is correct

Step-by-step explanation:

use BODMAS

B- Brackets

O-order

D-division

M-multiplication

Addition

Subtraction

Answer:

A.

While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.

Answer: 12 outcomes

Step-by-step explanation:

When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.

Answer: yes there are just delete the last one and replace it with the sixth one start from the start also does this happen to be K12 7th grade?

Step-by-step explanation:

The area of Square 4 is a2+2ab+b2

The area of Square 5 is 2ab+c2

Setting them equal to one another (a2+2ab+b2=2ab+c2) and simplifying yields that a2+b2=c2 (note that 2ab is what they have in common), which is Pythagoras' theorem.

Answer:

1.25 cups of diced tomatoes

Step-by-step explanation:

1.  12 1/4 ÷ 7

2. = 49/4 x 1/7

3.  =49/28

4. =7/4

5. =1 1/4 or 1.25

I hope this was helpful

The area of one lateral face of the triangular prism could be 20 ft².

a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first base, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Since the base of the prism is triangular so there will be three lateral faces.

Dimensions of rectangular lateral faces are:

1)8 feet by 2.5 feet

2)8 feet by 6 feet

3) 8 feet by 6. 5 feet

Area of the lateral face with dimension 8 feet by 2.5 feet = 8*2.5 =20 ft²

Area of the lateral face with dimension 8 feet by 6 feet = 8*6 =48 ft²

Area of the lateral face with dimension 8 feet by 6.5 feet = 8*6.5 =51 ft²

Therefore, the area of one lateral face of the triangular prism could be 20 ft².

To get more about prism visit:

https://brainly.com/question/23963432

Answer:

7g+14h

Step-by-step explanation:

hope it helped you

Answer:

7g + 14h

Step-by-step explanation:

What is an equivalent expression?

7(g + 2h)

7(g) + 7(2h) <== multipe both terms by 7

7g + 14h

Hope this helps!

Answer:

d 2.5 line is 6.9 which is 9.4

Step-by-step explanation:

because

Answer:

8/3 < 8/2

D

Step-by-step explanation:

8/3 = 2.67

8/2 = 4

So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.

There is more left if 8 is divided by 2 than when it is divided by 3

[Answer]8/3 < 8/2

[Answer] D

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

8/3 < 8/2

Step-by-step explanation:

D. When fractions have equivalent numerators, the one with the lesser denominator is the greater fraction.

8/2 = 4

8/3 = 2.667

< PGR = 61°

[tex]< FG4\ and\ < PQR\ are\ vortical\ angles.[/tex]

    [tex]< FG4=29[/tex]°

    [tex]< PQR=90\ - < FG4[/tex]

                 [tex]=90\ -29[/tex]°

                 [tex]=61[/tex]°

I hope this helps you

:)

Answer:

area of the figure: 29.92 m²

formula's:

solving steps:

area of rectangle + area of sector

5.5 * 4 + 30/360 * π(5.5)²

22 + 7.919

29.92 m²

Answer:

Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.

Rectangle

Area of a rectangle = width × length

                                = 4 × 5.5

                                = 22 m²

Sector

[tex]\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}[/tex]

                     [tex]=\dfrac{30 \cdot\pi\cdot5.5^2}{360}[/tex]

                     [tex]=\dfrac{121}{48}\pi \textsf{ m}^2[/tex]

Total area

total area = area of rectangle + area of sector

                [tex]=22 +\dfrac{121}{48}\pi[/tex]

                = 29.91943148...

                = 29.9 m² (nearest tenth)

Step-by-step explanation:

the numbers are a bit cut off at the top.

do I understand it correctly that the question is when the balloon loses 6/8 of a cubic foot of air ?

if so, I need to point out that the balloon loses 1/8 of a cubic foot per day.

so, how many days until it loses 6/8 if a cubic foot ?

well, 6 times that of 1/8 of a cubic foot = 6 days.

Answer: -27/8

Step-by-step explanation:

[tex]\left(-\frac{1}{2}\cdot \:3\right)^3[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}[/tex]

[tex]\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]

[tex]=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

[tex]\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]

[tex]=-\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]

[tex]=-\frac{1}{8}\cdot \:3^3[/tex]

[tex]=-\frac{1}{8}\cdot \:27[/tex]

[tex]=-\frac{27}{8}[/tex]

Answer:

About 260 seconds

Step-by-step explanation:

Tha rate is:

A: 8L/1.66666m

b: 10L/1m (converted to litres)

Divide 2400 by those rates above which:

2400 / (8/1.66666) = 500

2400 / (10/1) = 240

500 - 240 = 260

Answer:

The answer is B because you add up the 3 expenses

Step-by-step explanation:

Add the three expenses

The total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht

Total expense shows the overall expense for the thing we're expending for. We add all the expenses to get the total expense.

For this case, we're given that:

So, total expected expense is sum of all these expenses.

Total expected expense = 22885 + 15307 + 29071 = 67263 baht

Thus, the total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht

Learn more about addition here:

https://brainly.com/question/1709448

Answer:

area = 4x² +210x + 2250

Step-by-step explanation:

Area of a rectangle = width × length

Given:

⇒ area = (2x + 30)(2x + 75)

            = 4x² +150x + 60x + 2250

            = 4x² +210x + 2250

Answer:

x= -2
y=4

Step-by-step explanation:

Since we have an equation set equal to y, we can plug it in for either value of y.

I will be using y= x+6 in this case.

Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2

Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2

Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4

Divide both sides by 2 to get x= -2

Not plug x= -2 in back for the top (or bottom) equation and get that y=4

Hope this helps and isn't too complicated!

Answer: 0.45  and -2.74

Step-by-step explanation:

You're going to want to use the Quadratic Formula, so (-b±√(b^2-4ac))/2a.

When you plug in you should get -16 ± √16^2-4(7)(-8)/2(7)

-16± √(256+224) all divided by 2 x 7 or 14

(-16 ± 22.3607)/14

0.45  and -2.74 are your answers

Answer:

D

Step-by-step explanation:

[tex]\frac{x^2-11x+24}{(x-8)(x+2)}[/tex] ← factorise the numerator

= [tex]\frac{(x-8)(x-3)}{(x-8)(x+2)}[/tex] ← cancel the common factor (x - 8) on numerator/ denominator

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

The quotient of the given division problem is D. (x - 3) / (x + 2).

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given expression is,

(x² - 11x + 24) / (x - 8)(x + 2)

We have to first factor the numerator.

x² - 11x + 24 can be factored as (x - 8) (x - 3).

This is done using the factorization method.

Now the expression becomes,

(x² - 11x + 24) / (x - 8)(x + 2) = (x - 8) (x - 3) / (x - 8)(x + 2)

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

Hence the quotient is option D.

Learn more about Division here :

https://brainly.com/question/29193026

#SPJ2

Answer:

Should be 251.3 cm^3

Step-by-step explanation:

Use the formula for volume of cylinder

Answer:

no solution.

Step-by-step explanation:

1) in order to explain, the given system should be resolved:
[tex]\left \{ {{2y=6x+4} \atop {y=3x-4}} \right. \ < = > \ \left \{ {{y=3x+2} \atop {y=3x-4}} \right.[/tex]

2) the both equations have the same slope (it is 3), it means the given lines are parallel, then no solution.

Answer:

A. $3960

B. r=40x^2+400x+3000

C. $200

Step-by-step explanation:

A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write . R=PC

Per price increase is $20. So four price increase is $20x4=80. Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4x2=8 customers are reduced. Hence, total customers is 30-8=22

So Total Revenue is: R= 180 x 22= 3960

B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

R= (100+2x)(30-2x) = -40x^2+400x+3000

C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y).

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5 x 20= 100. So the price that gives the greatest revenue is 100+100 = 200