a box of cereal weighs 600 grams . how much is this weight in pounds ? explain or show your reasoning .

Final answer:

The student's question involving a system of equations can be solved to find that the two numbers are 17 and -5. By setting up a system of equations based on the given conditions and solving it using the elimination method, we obtain the values for the two unknown numbers.

Explanation:

System of Equations to Find Two Numbers

Let's define the first number as x and the second number as y. The problem states that x plus twice y equals 7 and twice x plus y equals 29. These statements can be turned into a system of linear equations:

x + 2y = 7

2x + y = 29

Using the substitution or elimination method, we can solve these equations for x and y. First, multiply the first equation by 2 to align the coefficients of x:

(2)(x) + (2)(2y) = (2)(7)

The equations now become:

2x + 4y = 14

2x + y = 29

Subtracting the second equation from the first gives us:

3y = -15

Divide both sides of this new equation by 3 to get the value of y:

y = -5

Now that we have a value for y, substitute it back into one of the original equations to find x:

x + 2(-5) = 7

x - 10 = 7

x = 17

The two numbers that solve the system are x = 17 and y = -5.

Answer:

$293.6

Step-by-step explanation:

Here is the complete question: A cell phone is on sale for 30% off. Find the original price if the sale price of the cell phone is $205.50.

Given: Sale price of cell phone is $205.50

           Discount= 30%

As 30% discount is given on original price or we can say 70% of original price is $205.50.

∴ Let the original price be x.

⇒ [tex]\frac{70}{100} \times x= 205.50[/tex]

Now, cross multiplying both side.

⇒ [tex]x= \frac{100}{70} \times 205.5[/tex]

∴ x= $293.6

The original price of cell phone is $293.6.

Answer:

The length of the mat is 60 in.

Step-by-step explanation:

Given :

Mats are inclined to form a triangle.

two sides of the mat are right triangles.

Hence the triangle formed is right angled triangle.

Let the length  be x.

Now,The height of the mat is 28 inches shorter than the length of the mat.

Height of mat = x - 28

Also, the hypotenuse is 8 inches longer than the length of the mat.

Hypotenuse = x + 8

Hence by using Pythagoras theorem we get ,

[tex]Hypotenuse^2= lenght^2+height^2\\[/tex]

[tex]x^2+(x-28)^2=(x+8)^2\\x^2+x^2-56x+784=x^2+16x+64\\x^2-72x+720=0\\x^2-60x-12x+720 = 0\\x(x-60)-12(x-60)=0\\(x-12)(x-60) = 0\\x-12=0\\x=12\\x-60=0\\x=60[/tex]

Now we get 2 values of length 12 and 60.

But height is 28 in less than length.

And when we take length value as 12 the height will be negative hence it can't be true.

Hence the Length of mat = 60 in.  

4x+8=7.8+5x

Subtract 4x from both sides:

8 = 7.8 +x

Subtract 7.8 from both sides:

x = 0.2

Answer:

y = 42x

Step-by-step explanation:

Answer:

The answer is y=42x

Answer:

40%

Step-by-step explanation:

30/75 = 0.4

Move decimal point back 2 places to convert to percent.

0.4 = 40%

Answer: 40%

Step-by-step explanation:

let x equal the percent

75x=30

x=2/5=40%

Answer:

Adults= 250 tickets

Children= 400 tickets

Step-by-step explanation:

Answer

250 adult tickets were sold and 400 children tickets were sold

Step by Step Explanation:

Given

Saturday Sales: $3675

Total tickets: 650

Cost of adult tickets = $7.50

Cost of children tickets = $4.50

Let A represent the adult tickets and C represent the children tickets,

if there's a total of 650 tickets, then

A + C = 650

Also,

if an adult ticket cost $7.50 and a child ticket cost $4.50 then

7.5A + 4.5C = 3675

From these, we have a simultaneous equation

A + C = 650 ------- (1)

7.5A + 4.5C = 3675 ----------(2)

Make A the subject of formula in (1)

A + C = 650  becomes

A = 650 - C

Substitute 650 - C for A in (2), we have

7.5(650 - C) + 4.5C = 3675

Open the bracket

4875 - 7.5C + 4.5C = 3675

4875 - 3C = 3675

Collect like terms

-3C = 3675 - 4875

-3C = -1200

Divide through by -3

[tex]\frac{-3C}{-3} = \frac{-1200}{-3}[/tex]

C = 400

Recall that

A = 650 - C

So, A = 650 - 400

A = 250

Hence, 250 adult tickets were sold and 400 children tickets were sold

Answer:0

Step-by-step explanation:

because once you flip all of them there all in the air and there flipped

Answer:

x=5/2, y=15/2. (5/2, 15/2).

Step-by-step explanation:

y=x+5

y=3x

---------

x+5=3x

5=3x-x

5=2x

x=5/2

y=3(5/2)=15/2

Answer:

The sign of the product is negative because a positive multiplied by a negative is a negative.

Step-by-step explanation:

Since you asked for evidence I will multiply even though the question asks you to solve without multiplying.

1×-1=-1

-1×-1=1

1×1=1

A negative multiplied by a positive is always negative. Doesn't matter which order you put it in. Meaning a positive multiplied by a negative is also always negative.

A positive multiplied by a positive is always positive.

A negative multiplied by a negative is always positive.

356,864 × −194,758 = negative sign answer

Answer:

25/12 or 2 1/12

Step-by-step explanation:

4 3/4=19/4

2 2/3=8/3

19/4-8/3=57/12-32/12=25/12

Answer:

4*6+8*6=48

Step-by-step explanation:

Answer:

The number is 4.

Step-by-step explanation:

4x+8x=48

12x=48

x=48/12

x=4

These two ratios are not equivalent, as 18 trucks and 4 cars simplifies to a ratio of 9:2, while 21 trucks and 6cars simplifoes down to a ratio of 7:2. Obviously, there is a difference between 9:2 and 7:2, so they are not equivalent.

Answer:

This cannot be done, but it can be factored as: 6(5x + 1)

Step-by-step explanation:

This expression cannot be distributed any further.

The distributive property is used when multiplying polynomials (multiplying one or more terms by two or more terms). In which case, each term in multiplied by each of the terms in the bracket, for example: .

5(x + 2)  =  5x + 10

We can factor this expression however to go the opposite direction:

30x + 6

Since 30 and 6 are both divisible by 6, we can factor it out of each term.

Divide 30x by 6 and divide 6 by 6.

6(5x + 1)

Answer

○ A. [tex]\displaystyle y - 5 = 2(x - 10)[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 7}{-10 + 4} = \frac{-12}{-6} = 2[/tex]

Then, according to the Point-Slope Formula, [tex]\displaystyle y - y_1 = m(x - x_1),[/tex]all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT signs:

[tex]\displaystyle y - 5 = 2(x - 10)[/tex]

I am joyous to assist you anytime.

Answer:

The sum of 50 and 6 is the total of 56

Answer:

Fifty plus six equals fifty-six.

Equation 5 + 5 = 10  and 5 + 5 + n = 10 + n are equivalent equation

Given that  

John wrote that 5 + 5 = 10   ------ (1)

Then wrote that 5 + 5 + n = 10 + n    ------ (2)

Need to determine are the equations written by John are equivalent.

First we need to keep in mind that whenever we apply same operation like addition, subtraction, multiplication and division on both the sides of equation that is left hand side and right hand side, we get the equivalent equation.

As in the second equation John added same value that is n on both sides of equation, we can say that equation with n is equivalent to the previous equation without n

Other way is let’s solve equation (2) and see if we can get equation (1)

5 + 5 + n = 10 + n  

On subtracting both the sides with n we get,

5 + 5 + n – n = 10 + n – n

=> 5 + 5 = 10 which is same as equation (1)

Hence we can conclude that equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation.

Final answer:

The equations 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent because adding the same number 'n' to both sides of an equation does not change the original equality.

Explanation:

Yes, the equations that John wrote are equivalent. The first equation, 5 + 5 = 10, establishes that the sum of five plus five equals ten. The second equation, 5 + 5 + n = 10 + n, simply adds n to both sides of the first equation. This does not change the equality because, according to the properties of equality, if you add the same amount to both sides of an equal sign, the two sides remain equal. This can also be seen as an application of the commutative property of addition which states that numbers can be added in any order without changing the sum, as in A + B = B + A. Therefore, the original sum of 5 + 5 on the left side remains 10 when n is added to both sides, showing that 5 + 5 + n is indeed equal to 10 + n.

(3, 6) can replace the missing value and create a function

Step-by-step explanation:

Given relation is:

{(8,5), (2, 3), (1,6), (7,4), _?_}

In order for a relation to be a function, the first condition is that there should be no repetition in domain of the function i.e. same input cannot map to multiple outputs.

In the form of ordered pairs, the first element of each ordered pair represents the elements of domain set

So,

From all the option given, only (3,6) is suitable to be put in the blank space as it will create no repetition in the domain while other ordered pairs will cause repetition.

Hence,

(3, 6) can replace the missing value and create a function

Keywords: Relations, functions

Learn more about functions at::

#LearnwithBrainly

Answer:

A=F

Step-by-step explanation:

It's the congruency

Answer:

x = 2y

x + 4 = 3y + 1

2y + 4 = 3y + 1

y = 3, x = 6

Answer:

Part A) The reasonable domain to plot  the growth function is the interval [0,5]

Part B) The average rate of change is [tex]0.21\ \frac{cm}{day}[/tex]

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

[tex]f(n)=10(1.02)^n[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^x[/tex]

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

[tex]a=10\ cm[/tex] ----> initial value or y-intercept

[tex]b=1.02\\r=b-1=1.02-1=0.02\\r=2\%[/tex]

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

[tex]11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n[/tex]

Apply log both sides

[tex]log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days[/tex]

so

The reasonable domain to plot  the growth function is the interval -----> [0,5]

[tex]0 \leq x \leq 5[/tex]

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

In this problem we have

[tex]f(a)=f(1)=10(1.02)^1=10.2\ cm  f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\[/tex]

Substitute

[tex]\frac{11.04-10.2}{5-1}=0.21\ \frac{cm}{day}[/tex]

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval

"Part A) The reasonable domain to plot  the growth function is the interval [0,5]

Part B) The average rate of change is

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

This is a exponential function of the form

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

----> initial value or y-intercept

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

Apply log both sides

so

The reasonable domain to plot  the growth function is the interval -----> [0,5]

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

In this problem we have

Substitute

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval"quoted from

Answer:

D: is the answer  

Step-by-step explanation:

A. +   add

B. −   subtract

C. ×   multiply

D. ÷  divide (can also be written with a "/") as in 3/2 vs 3÷ 2

The symbol used to write an algebraic expression for "three divided by a number" is the division symbol, ÷. We write this based off the description as '3 ÷ n' or '3/n' in fractional form.

To write an algebraic expression for "three divided by a number," you would use the division symbol which is represented as ÷. So, if our unknown number is represented by the letter 'n', the algebraic expression would be written as "3 ÷ n" or "3/n" in fractional form.

In an algebraic expression, each symbol represents a specific mathematical action. The '+' symbol is for addition, '-' is for subtraction, 'x' is for multiplication, and '÷' is for division. In this case, since the problem specifies division, the correct symbol to use would be '÷'.

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Answer:

The number is -5.

Step-by-step explanation:

x+x=x-5

2x=x-5

x-2x=5

-x=5

x=-5

Answer: 39 loaves were sold in the afternoon

Step-by-step explanation: So basically what you do here is divide 60 by 100. That makes 0.6, 0.6 equals 1%. (60 equals 100% and that why you divide by 100) Now, you multiply 0.6 by 65. the answer is 39. 65% of the bread is 39 loaves. So 39 loaves were sold in the afternoon.

Have an amazing day! :)

Answer:

60 x 65% = 39

So 39 were sold in the afternoon

Step-by-step explanation:

Answer:

The ratio of 1 by 5 is to 1 by 6​  is   Rs 176  :   Rs 146.67

Step-by-step explanation:

The given amount here = Rs 880

Now let us assume the 1 by 5 of Rs 880 = m

and assume 1 by 6 of the amount Rs 880 =n

To Find  m : n

Now, [tex]\frac{1}{5}  \times 880 = m\\\implies m =176[/tex]

or, 1 by 5  = 176

Similarly: [tex]\frac{1}{6}  \times 880 = n\\\implies n =146.6666[/tex]

or, 1 by 6  = 146.67

⇒ m  : n  = 176  : 146.67

Hence, the ratio of 1 by 5 is to 1 by 6​  = Rs 176  :  Rs 146.67

Answer:6i-6

Step-by-step explanation:

9i-3i=6i

1+5=6

Answer:

12.22

Step-by-step explanation:

I don't know if 12.22 is an answer for you but if it's not I would round to 12. What you do is multiply 9.32 by 16 3/4 which gives you 156.11. Take 156.11 and subtract 150 since Garth is putting that in the bank which leaves you with 6.11. Lastly you will divide 6.11 by .5 which will give you 12.22. So Garth can buy 12 raffle tickets.

Answer:

Garth can buy 12 raffle tickets.

Step-by-step explanation:

This is because when you multiply 9.32 with 16, it is 149.12.

Then, each quarter an hour, or 15 minutes, he earns 2.33 dollars.

Multiply by 3 and you get 6.99.

Add 6.99 with 149.12 and you get 156.11

Get rid of 150$ and you have 6.11

Each dollar you can get 2 raffle tickets.

So 6 dollars or 6, multiplied by 2 is 12.

Hope this helps you!

P.S If I may, can I please have brainliest, I would greatly appreciate it.

Answer:

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

Step-by-step explanation:

Answer:

error pecentage is 5.5% i think because 1.8 divde by 32.7 is 0.5504... * 100 is 5.504

Step-by-step explanation:

The percent error in Charlie's guess regarding his dog's weight is 5.5%, calculated using the difference between the actual and estimated values divided by the actual value, times 100%.

To calculate the percent error in Charlie's guess, we use the formula for percent error which is:

Percent Error = (|Actual Value - Estimated Value| / Actual Value) × 100%

Substitute the values into the formula:

Percent Error = (|32.7 - 34.5| / 32.7) × 100%

Percent Error = (1.8 / 32.7) × 100%

Percent Error = 0.054983922826 × 100%

Percent Error = 5.5% (rounded to the nearest tenth)

Therefore, the percent error in Charlie's guess is 5.5%.