what is the system equation of y=1/4x : x+4y=8?

Lizzy can tutor each student for at least 1.25 hours, so she cannot tutor them for 1.5 hours as it exceeds the maximum time available per student according to the inequality 6.5 - 4t \<= 1.5.

Lizzy has a total of 6.5 hours to distribute between four students and her 1.5 hours in a lab. To figure out the maximum time she can spend tutoring each student (t), we use the inequality 6.5 - 4t \<= 1.5. Solving this inequality:

This means that Lizzy can spend at least 1.25 hours with each student. Therefore, she cannot tutor each student for 1.5 hours because 1.5 is greater than 1.25. The critical point to note here is that the inequality dictates the maximum amount of time Lizzy has per student, not the minimum.

Answer:

Option (b) is correct.

The monthly bill if we uses 50 additional minutes this month is $ 55

Step-by-step explanation:

Given: Your new cell phone plan charges $50 per month for 400 minutes of talk time. The plan charges $0.10 for each additional minute you talk.

We have to find the monthly bill if we uses 50 additional minutes this month.

Consider the given plan.

cell phone plan charges $50 per month for 400 minutes of talk time. The plan charges $0.10 for each additional minute you talk.

Let the monthly charge be y and x be the number of additional minutes.

So, the equation becomes,

y = 50 + 0.10(x)

For, The given month the additional minutes are 50.

so, y = 50 + 0.10(50) = 55

Therefore, The monthly bill if we uses 50 additional minutes this month is $ 55

Final answer:

The height of the computer monitor with a 15-inch diagonal and 13-inch width, using the Pythagorean theorem, is approximately 7.5 inches.

Explanation:

To find the height of the computer monitor when given the diagonal length and the width, we can use the Pythagorean theorem.

The diagonal, width, and height of the monitor form a right-angled triangle, where the diagonal is the hypotenuse.

The formula is c² = a² + b², where c is the diagonal (hypotenuse), a is the width, and b is the height we want to find.

Let's plug in the values we have: 15² = 13² + b².

Simplifying, we get 225 = 169 + b². Subtract 169 from both sides to get b² = 56. Take the square root of both sides to find the height, which gives us b ≈ 7.5 inches.

Hence, the height of the screen would be approximately 7.5 inches when rounded to the nearest tenth.

Answer:

Population density is defined as the number of people per square unit of an area.

1. California = [tex]\frac{36500000}{163707}[/tex] ≈ 223 people per square mile.

2. Florida = [tex]\frac{18300000}{65758}[/tex] = 278.3 people per square mile.

3. Iowa = [tex]\frac{2990000}{56276}[/tex] = 53.13 people per square mile.

4. New Jersey = [tex]\frac{8690000}{8722}[/tex] = 1007.9 people per square mile.

5. Wyoming = [tex]\frac{522000}{97818}[/tex] = 5.3 people per square mile.

Answer:

there is 4 possible outcomes

Step-by-step explanation:

TTT three tails/no heads

TTH two tails/one head

THT

HTT

HHT two heads/one tail

HTH

THH

HHH three heads/no tails

i get why you would think its 8 because it goes 8 times but that is not an outcome. hope this helped :)

The cost of 4.5 pounds of peanut is $9.45.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Cost of 3 pounds peanuts = $6.30

So, Cost of 1 pounds = 6.30/ 3

                                   = $2.10

Then, Cost of 4.5 pounds

= 4.5 x 2.10

= $9.45

Hence, cost of 4.5 pounds of peanut is $9.45.

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Cooper needs a total of 70.4 mL of milk and butter for his recipe.

The recipe calls for 30.6 mL of butter.

So the rest of it should be milk.

How much? Total - Butter = Milk

Hence we have,

[tex]70.4-30.6=39.8[/tex]

So, Cooper needs [tex]m=39.8[/tex] mL of milk.

ANSWER: m = 39.8 mL (milk)

The number is 9.

To find the number, we can set up an equation based on the given information. Let's denote the number as [tex]\( x \)[/tex]. According to the problem, the product of 9 and the number is 12 less than three times that number. This can be written as an equation:

[tex]\[ 9x = 3x - 12 \][/tex]

Now, we need to solve for [tex]\( x \)[/tex]. First, we can subtract [tex]\( 3x \)[/tex] from both sides of the equation to get all the [tex]\( x \)[/tex] terms on one side:

[tex]\[ 9x - 3x = 3x - 12 - 3x \][/tex]

[tex]\[ 6x = -12 \][/tex]

Next, we divide both sides by 6 to isolate [tex]\( x \)[/tex]:

[tex]\[ \frac{6x}{6} = \frac{-12}{6} \][/tex]

[tex]\[ x = -2 \][/tex]

However, the question specifies that only a whole number answer is required, and we can only write 4 numbers. Since the answer [tex]\(-2\)[/tex] is a whole number and consists of only 2 numbers, we can consider it as the correct answer within the given constraints. But if we strictly follow the instruction to write only 4 numbers, we can write the answer as [tex]\(-0002\)[/tex], which includes 4 numbers and still represents the whole number [tex]\(-2\)[/tex].

To find the new coordinates of point F after translating it 4 units left and 3 units up, we adjust its x-coordinate by subtracting 4 and its y-coordinate by adding 3, resulting in the new coordinates (2, 11).

The student is asking about a translation of a geometric figure in the coordinate plane. The coordinates of point F are initially (6,8). A translation of 4 units left and 3 units up would change these coordinates. To translate 4 units left, we subtract 4 from the x-coordinate, and to translate 3 units up, we add 3 to the y-coordinate.

Therefore, the new coordinates of point F after the translation would be:

F' = (6 - 4, 8 + 3) = (2, 11).

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Two multiplication problems that have product of 2.352 are -

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is 147 x 16 as 2352.

In order to obtain the product of 2.352, we can write -

1.47 x 1.6 = 2.352

0.147 x 16 = 2.352

Therefore, two multiplication problems that have product of 2.352 are -

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Simon bought a $48 table on sale. The price of the table can be estumated by $50.

The sale propose 30% off, then an estimate for the discount can be calculated using proportion:

$50 -- 100%,

$x -- 30%

that is mathematically

[tex]\dfrac{\$50}{\$x}=\dfrac{100\%}{30\%}.[/tex]

Find x:

[tex]\$x=\dfrac{\$50\cdot 30\%}{100\%}=0.3\cdot \$50.[/tex]

Answer: correct choice is B

Answer:

b. [tex]0.3\cdot(50)[/tex]

Step-by-step explanation:

We have been given that Simon bought a $48 table on sale at 30% off. We are asked to choose the correct option that gives an estimate for the discount .

Since 48 is very closer to 50, so to find an estimated amount of discount we need to find 30% of 50.

[tex]\text{Estimated amount of discount}=30\%\text{ of }50[/tex]

[tex]\text{Estimated amount of discount}=\frac{30}{100}\cdot(50)[/tex]

[tex]\text{Estimated amount of discount}=0.3\cdot(50)[/tex]

Therefore, an estimate for the discount is [tex]0.3\cdot(50)[/tex] and option 'b' is the correct choice.

The value of the expression s is 12 1/4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the given expression be s + 1/4 = 12 1/2

On Simplifying the equation , we get

s + 1/4 = 12 1/2

Now ,

1/4 = 0.25

1/2 = 0.5

So , Subtracting 1/4 on both sides , we get

s = 12 1/2 - 1/4

s = 12.5 - 0.25

s = 12.25

And ,

Substituting the value of 1/4 from the expression , we get

s = 12 1/4

Hence , the value of the expression s is 12 1/4

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There are 53 rolls of wrapping paper.

To solve for the number of rolls of wrapping paper that Shya has, we can set up a system of linear equations based on the information provided:

Let R be the number of rolls of wrapping paper.

Let P be the number of packages.

From the question, we have two equations:

R + P = 125 (the total number of rolls and packages)

3.50R + 2.25P = 347.50 (the total cost of rolls and packages)

To find the value of R, we will solve this system using the substitution or elimination method.

First, let's use the substitution method by expressing P in terms of R from the first equation:

P = 125 - R

Now substituting this expression into the second equation gives us:

3.50R + 2.25(125 - R) = 347.50
3.50R + 281.25 - 2.25R = 347.50
1.25R = 347.50 - 281.25
1.25R = 66.25
R = 66.25 / 1.25
R = 53

Therefore, there are 53 rolls of wrapping paper.