I just need help on the restrictions part

Answer: x = -5

Step-by-step explanation: To solve this equation, we start by distributing the -4 through the parentheses on the left side.

So we have -4 times x which is -20x and -4 times -5 which is positive 20. So our equation now reads -20x + 20 = 120.

Solving from here, we subtract 20 from both sides of the equation and we have -20x = 100 and dividing both sides by -20, we find that x = -5.

Although I will not provide work to check our answer, the great thing about solving equations is that your can always check your answer by substituting what you got as a final answer into the original equation.

Answer:

The answer is X = -5.

Answer:

1/52

Step-by-step explanation:

4/208=1/52

Answer:

The fourth option

Step-by-step explanation:

48 is the minimum height, 42 is his current height, and h is the height he must grow. 42 +h is at least 48 so that rules out the first and third options. The second option would be around twice the required  height, so it must be the fourth option.

Answer:

A.

Step-by-step explanation:

To simplify the given expression, first perform the multiplication, then the division, and finally the addition and subtraction. The final result is 20.

To simplify the expression 3 · 32 + 8 ÷ 2 − (4 + 3), we follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication: 3 · 32 = 3 · 9 = 27. Next, we perform the division: 8 ÷ 2 = 4. After that, we simplify the addition and subtraction within the parentheses: (4 + 3) = 7. Finally, we subtract 7 from the previous result: 27 - 7 = 20. Therefore, the answer is A. 20.

Option A

It is a function because at any given time the oven was exactly one temperature.

Solution:

Given that,

At 5:00 p.m., Antonio turned on the oven

While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period

The oven remained at 400°F for 45 minutes until Antonio turned it off

It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m

From above information,

5:00  ------------ 72°F

5:10 ------------------ 400°F

5:45 ------------------ 400ºF

6:55 -------------------- 72°F

Thus at any given time (input) the oven was exactly one temperature  (a single output )

Therefore the statement that best explains is:

Option A) It is a function because at any given time the oven was exactly one temperature.

Since the definition of function states that there is a unique image corresponding to a element hence here the temperature at a given time is unique

Answer:

option a

Step-by-step explanation:

Answer:

it should be a 50:1 gas oil ratio.

Step-by-step explanation:

Answer:

8(3+4)

Step-by-step explanation:

simple use pemdas

parenthesis 3+4= 7

multiply 8x7=56 :)

Answer: 4.25 feet

Step-by-step explanation:

a-living room wall in feet

area=a²

70sqf²=a²

a=√70

a=4.248 feet

Answer:

9 lawns

Step-by-step explanation:

If she already has $25 of the $115 dollars needed for the ticket, she only needs to make $90 more. If she makes $10 each lawn, she would need to mow 9 lawns in order to get the $90 dollars.

The correct conclusion based on the data is that 10% of all eighth-grade students at the High Achievers Charter School are reading below grade level.

Based on the information provided in the question, the most accurate conclusion we can make is that 10% of all eighth-grade students at High Achievers Charter School (HACS), specifically, are reading below grade level. This is because the sample data was only collected from eighth-grade students at HACS. Therefore,

answer C

is correct. That being said, these results only apply to this specific school and grade level and cannot be generalized for all students at HACS or all other schools.

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Answer:

The solution of the given system of equations is,

[tex]x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}[/tex]

Step-by-step explanation:

The given equations are :

x + ay = b          .......(1)

ax - by = c        .......(2)

We will use 'Substitution Method' to solve the given system of equations.

In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable  and then substitute that value in the other equation to find the value of the another variable.

Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).

Consider the equation (1), that is,

   x + ay = b ⇒ x = b - ay          ........(3)

Substitute the value of 'x' from (3) in (2), we get

  a(b - ay) - by = c

⇒ab - a²y - by = c

⇒-a²y - by = c - ab

⇒-y(a²+b) = c - ab

⇒y(a²+b) = ab - c

[tex]\implies y=\frac{ab-c}{a^{2}+b}[/tex]

Now, substituting the above value of 'y' in equation (3), we get

[tex]x=b-a(\frac{ab-c}{a^2+b})[/tex]

[tex]\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}[/tex]

[tex]\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}[/tex]

[tex]\implies x = \frac{b^2+ac}{a^2+b}[/tex]

Hence, the solution of the given system of equations is,

[tex]x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}[/tex]

Final answer:

The expression 12.70 - n + 9 + n/4 is simplified by combining like terms, resulting in 21.70 + 1.25n.

Explanation:

The student's question involves simplifying the expression 12.70 - n + 9 + n/4. To simplify this expression, we first combine like terms. As 'n' and 'n/4' are like terms, we simplify by combining them which can be done by adding 1n (which is the same as n) with 1/4n. Here are the steps:

This completes the simplification process for the given expression. It is important to ensure terms are like terms before combining them and to perform accurate arithmetic operations when combining numerical values.

Answer:

Option A. $6,706

Step-by-step explanation:

we know that

To find out how much was the book profit in the entire month, subtract the number of copies at the start of the month from the number of copies at the end of the month, and the result multiply by $13.97 (each book profits)

so

[tex](1,364-885)(13.97)\\479(13.97)=\$6,691.63[/tex]

so

approximately $6,706

The composite function (f o g)(x) is found by substituting g(x) into the f(x) expression. Upon simplification, (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1) is: 1/(x² + 2x + 1) + 6/(x+1) + 5.

To find the composite function (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1), we substitute g(x) into f(x). That is, wherever you see 'x' in f(x), replace it with what g(x) is equal to.

Start with f(g(x)) = f(1/(x+1)). In f(x), replace x with 1/(x+1), which gives us: (1/(x+1))² + 6*(1/(x+1)) + 5. This is the composite function (f o g)(x).

To simplify further: the first term '(1/(x+1))²' becomes '1/(x² + 2x + 1)', the second term '6*(1/(x+1))' becomes '6/(x+1)', and the third term is just '+5'. So the composite function (f o g)(x) simplifies to: 1/(x² + 2x + 1) + 6/(x+1) + 5.

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Answer:

[tex]\$47\ per\ week[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In his problem

The amount of savings per week  is equal to the constant of proportionality k or slope of the linear equation

so

Looking at the graph

take the point (2,94)

x=2 weeks, y=$94

Find the value of k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{94}{2}[/tex]

[tex]k=\$47\ per\ week[/tex]

Answer:$90

Step-by-step explanation:

360/4=90

Answer: $90 in one week

Step-by-step explanation:

Since you earn $360 every 4 weeks, you would have to divide $360 by 4 to find the amount of money you earn in one week.

360 divided by 4 = 90

So you earn $90 in one week.

Answer: x=19°

Step-by-step explanation:

First, add 41° to 35

Next, subtract 4x from 8x, then you should have your answer from there!

Answer:

Step-by-step explanation:

R = report length

R = 40 + (3/8)R + (1/3)R

3/8 = 3*3/8*3 = 9/24

1/3 = 8*1 / 3*8 = 8/34

R = 40 + (9/24)R + (8/24)R

R = 40 + (17/24)R                         Subtract 17/24 from the left

R-17/24 R = 40

7/24 R = 40                                  Multiply both sides by 24

7R = 40 * 24

7R = 960                                       Divide by 7

R  = 960/7

R = 137.1 which breaks the rounding rule and becomes 138 because something has to be typed on page 138

Answer:

Yes, because (−1, −5) is below the line.

Step-by-step explanation:

The given inequality is [tex]y \leq  -\frac{3}{4} x - 1[/tex] .......... (1)

Now, rearranging this equality relation we get,

4y = - 3x - 4

⇒ 3x + 4y = - 4

⇒ [tex]\frac{x}{- \frac{4}{3} } + \frac{y}{- 1} = 1[/tex] .......... (2)

This equation is in intercept form and the line represented by this equation passes through the x-intercept [tex](- \frac{4}{3}, 0)[/tex] and y-intercept (0,-1).

Now, it is clear that (0,0) point is above the equation.

But (0,0) point does not satisfy the inequality equation (1).

Hence, the solution of the inequality equation (1) is below and including line (2).

Now, point (-1,-5) is below the line (2) and hence, it is a solution of the inequality (1) as it is below the line. (Answer)

Answer:

the answer is [yes, because (-1, -5) is below the solid line].

Step-by-step explanation:

I took the test and got it right

Answer:

18

Step-by-step explanation:

Find the equation for the line in slope-intercept form: y = mx + b.

x and y are points on the line. Points are written in the form (x, y).

m is the slope.

b is the y-intercept, when it hits the y-axis.

Substitute the point (4, 4) and slope. x = 4; y = 4; m = -2. Find b

y = mx + b

4 = (-2)(4) + b

4 = -8 + b

b = 4 + 8

b = 12

Get the equation of the line using slope and the y-intercept.

y = -2x + 12

Substitute -3 as x and find the missing y.

y = -2(-3) + 12

y = 6 + 12

y = 18

The point was (-3, 18)

Therefore the missing value for y is 18.

To find the y-value, you substitute the given points into the formula for slope and solve for 'y'. In this case, the required value of 'y' is 18.

The subject of your question is mathematics, specifically the concept of calculating the slope of a line. The slope (m) of the line through two points (x1,y1) and (x2,y2) is defined as m = (y2 - y1) / (x2 - x1). You are given that the points are (4,4) and (-3,y) and the slope is -2. Substituting the given points into the formula gives -2 = (y - 4) / (-3 - 4 ). Solving this equation will give you the value of 'y'.

First, simplify the denominator to get -2 = (y - 4) / -7. Afterward, multiply both sides by -7 to eliminate the fraction: -2 * -7 = (y - 4). This yields 14 = y - 4. Solve for 'y' by adding 4 to both sides of the equation, which gives that y = 18.

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Answer:

False

Step-by-step explanation:

Image (graph) of y = Sinx is attached.

First, lets understand domain and range.

Domain is the set of all x-values for which a function is defined (x axis).

Range is the set of all y-values for which a function is defined (y axis).

We are said that range of y = Sin x is the set of all real numbers.

If we look at the graph and look at the y-values for which the function is defined, we see that the Sin Curve oscillates between y = -1 and y = 1.

So the range would be:

[tex]-1 \leq y \leq 1[/tex]

It is not defined for other values, certainly not for ALL REAL NUMBERS!

So, this statement is false.

Answer:

[tex] |60| = | - 60| [/tex]

Step-by-step explanation:

They are equal. When the negative sign is inside the box the absolute value is positive, when the negative sign is outside the box THEN it is negative.

Answer: equal to

Step-by-step explanation: Absolute value means distance from zero on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number like we see in this problem.

So for the absolute value of 60, we know that 60 is 60 units from zero on a number line which means that the absolute value of 60 is just 60.

For the absolute value of -60, we know that -60 is also 60 units from zero on the number line so the absolute value of -60 is also 60.

Now we know that the absolute value of -60 is 60 and the absolute value of 60 is also 60. Since 60 is the same as 60, it means that 60 is equal to 60.

Another way of thinking about absolute value is that no matter what number you have inside the absolute value, your result will always be positive except for 0 which has an absolute value of 0.

In other words, the absolute value of any number is the positive version of that number. Again, not including zero.

18 divided by 6 is 3

when you add 3 with 4 it gives you 7

7 is your total answer

18/6 + 4

18/6 = 3

3 + 4 = 7

The answer is 7.

Answer: x=202

Step-by-step explanation:

1st: Add 98 to 104, this should give you your answer of x=202

Answer:

202

Step-by-step explanation:

x-98=104

  +98  +98  (you add because 98 is a negative)

Answer:

Commutative Property of Addition.

Step-by-step explanation:

The Commutative Property of Addition states that no matter what order you add the numbers, the outcome (answer) will all be the same.

~

Answer:

Step-by-step explanation:

5/x = 4/x+3

5 * ( x+3) =  4 * x

5x + 15 = 4x

5x - 4x =  -15

x = ( -15)

Answer:

- 30

Step-by-step explanation:

Note the common difference d between consecutive terms in the sequence

d = 34 - 40 = 28 - 34 = 22 - 22 = - 6

This indicates the sequence is arithmetic with sum to n terms calculated as

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 40 and d = - 6, thus

[tex]S_{15}[/tex] = [tex]\frac{15}{2}[/tex] [ (2 × 40) + (14 × - 6) ], that is

[tex]S_{15}[/tex] = 7.5(80 - 84) = 7.5 × - 4 = - 30

Answer:

[tex]\displaystyle -44 = s_{15}[/tex]

Step-by-step explanation:

[tex]\displaystyle -6n + 46 = a_n \\ -6[15] + 46 = a_n \\ -90 + 46 = a_n \\ -44 = a_n[/tex]

Use the Arithmetic Sequence to figure this out.

I am joyous to assist you anytime.

Answer:

C

Step-by-step explanation:

The diagram shows the system in equilibrium. Left part consists of 3 circles, 2 triangles and 6 squares. Right part consists of 2 circles, 5 triangles and 3 squares.

If this system is in equilibrium, then the mass of the left part is the same as the mass of the right part.

The mass of the left part:

[tex]3\cdot 3+2\cdot \triangle +6\cdot 2=2\triangle+9+12=2\triangle+21\ grams[/tex]

The mass of the right part:

[tex]2\cdot 3+5\cdot \triangle+3\cdot 2=5\triangle +6+6=5\triangle +12\ grams[/tex]

Hence,

[tex]5\triangle +12=2\triangle +21\\ \\5\triangle -2\triangle =21-12\\ \\3\triangle =9\\ \\\triangle =3\ grams[/tex]

The mass of the triangle is 3 grams.

Given information:

A circle has a mass of 3 grams and a square has a mass of 2 grams.

From the given diagram of a mass balance, it can be concluded that:

Now, the left and right sides are balanced. So, the mass of left side will be equal to the mass of right side.

Let x be the mass of a triangle shape.

So, the value of x can be calculated as,

[tex]\texttt{mass of left side = mass of right side} \\6\times 2+2x+3\times 3=3\times 2+5x+2\times 3\\12+9+2x=6+6+5x\\3x=9\\x=3[/tex]

Therefore, the mass of the triangle is 3 grams.

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Final answer:

Mridul will take 14.4 minutes to jog around a rectangular park for a total of 6 rounds, considering the total jogging distance of 2.16 kilometers at a pace of 9 kilometers per hour.

Explanation:

To calculate the time Mridul will take to jog around a rectangular park for 6 rounds, we need to compute the total distance he will cover and then use his speed to find the time. The perimeter of the rectangle is the sum of all its sides. Since the park is 100m by 80m, the perimeter will be (2 × 100m) + (2 × 80m), which equals 360 meters. For 6 rounds, the total distance will be 6 × 360 meters = 2160 meters or 2.16 kilometers.

Next, we use the formula for time:

Time = Distance / Speed

Given Mridul's jogging rate is 9 kilometers per hour, we can convert this speed into meters per second to match the distance units by multiplying by 1000 and dividing by 3600 (the number of seconds in an hour), which gives us 2.5 meters per second. Finally, to find the time taken:

Time = 2160 meters / (2.5 meters/second)

This calculation results in 864 seconds, which when converted to minutes is 14.4 minutes. Therefore, Mridul will take 14.4 minutes to jog 6 rounds around the park.

Answer:

Number of cheaper dresses sold  is 35

Number of expensive  dresses sold  is 15

Step-by-step explanation:

Given:

Cost of cheaper dresses = $90

Cost of  expensive dresses = $140

Total cost of  the dresses = $5250

To Find:

Number of cheaper dress = ?

Number of expensive  dress = ?

Solution:

Let

The number of  cheaper dresses be x

The number of  expensive dresses be y

(Number of cheaper dresses X cost of cheap dress) +  (Number of Expensive dresses X cost of  expensive dress)  =  $5250

[tex]x \times90 +y \times 140 = 5250[/tex]=  $5250

It is given that the 20 more of the cheaper dresses than the expensive dresses is sold

So,

number of cheaper dress  =  20  +  number of expensive dress

x = 20 + y---------------------------------------(1)

[tex](20+y) \times90 +y \times 140 = 5250 = 5250[/tex]

[tex](20 \times 90 +y\times 90) +y \times 140= 5250 [/tex]

[tex]1800 + 90y+ 140y = 5250 [/tex]

[tex]1800 + 230y = 5250 [/tex]

[tex] 230y =5250 -1800[/tex]

[tex] 230y = 3450 [/tex]

[tex]y = \frac{3450}{230}[/tex]

y = 15

Substituting y in (1)

x = 20 +15

x= 35