1. Direct variation

A. Write an equation for the following statements.
B. Write an equation when y varies directly as x.
1. y=63 when x=9
2. y=121 when x=11
3. y=36 when x=4
4. y=224 when x=8

The correct answer is 0.1224.

In order to find this, we need to first multiply these as if they have no decimal places.

51*24 = 1224

Now, we count the number of decimals in the original equation and move the decimal place that many times. Since there are 4 numbers after decimals in the original equation, we put 4 after in the answer.

.1224

let x be the price before the discount

If you get 12% off, then you only pay the remaining 88% (since 88%+12% = 100%). This means if you take 88% of the original price (x), then you get the final price (132)

In terms of an equation, we have,

88% of (original price) = final price

(88/100)*(x) = 132

0.88*x = 132

0.88*x/0.88 = 132/0.88 <--- divided both sides by 0.88

x = 150

--------------------------------------------

Answer: The price without the discount is $150

The chance of winning is 1/9

Answer:

Step-by-step explanation:

Yes the company can hire 6 carpenters and 12 pumbers

So first lets find out how much it costs to have 6 carpenter for $220 a day.

$220 × 6 = $1320  this is how much it cost to pay 6 carpenters for one day.

Now lets find how much it cost to 12 plumbers at $260 a day.

$260 × 12 = $3120 this is how much it costs to pay 12 plumbers a day.

The total amount you have to pay to the workers is:

$3120 + $1320 = $4440

Your budget was $4500 so the total costs for the workers is $4440 which means you can hire those workers and you would still have $60.

The construction company can hire 6 carpenters and 12 plumbers as the total cost of $4440 is within the $4500 budget, and the total number of workers hired is 18, meeting both the company's requirements.

The construction company wants to hire at least 18 workers and does not want to exceed a daily budget of $4500. To determine if the company can hire 6 carpenters and 12 plumbers, we must calculate the total cost of hiring these workers for a day. The cost C for hiring carpenters and plumbers can be represented by the equation C = 6($220) + 12($260), where $220 is the daily wage for a carpenter and $260 is the daily wage for a plumber.

Let's calculate the total cost:

The total number of workers would be 6 carpenters + 12 plumbers = 18 workers, which meets the requirement of hiring at least 18 workers. Since the total cost of $4440 is also within the $4500 budget, the company can indeed hire 6 carpenters and 12 plumbers.

Answer:

Cash price using complement method id $882.8

Step-by-step explanation:

When a vendor includes terms of 4/10, n/30 , the '4' represents 4% of the amount owed , the '10' represents 10 days, the 'n' represents net and the '30' represents 30 days.

So the terms 4/10, n/30 indicate that the buyer may take an early discount of 4% of the amount owed is remitted in 10 days instead of normal 30 days.

In other words, buyer can choose any one of the following:

1) Pay within 10 days and deduct 4% of the net amount owed.

2)Pay in 30 days and take no discount.

For finding cash price using complement method, we have to find the complement of discount percentage= 100-discount percentage=100-4=96

So cash price using complement method = net price X complement of discount percentage in decimals

                                                                     = 919.6 X 0.96

                                                                     = $882.8

You can get 10 ft of ribbon for one dollar. What you need to do is divide 1 with .10 and you get 10 ft.

It seems like you may be missing some information, but:

[tex]Cost = .10x\\[/tex]

Where x is the number of feet.

x= 5

Slove for x by simplifying both sides of the equation, then isolating the variable

Hey there!!

Given equation :

... 6 - 4x = 7x - 9x - 4

Combining like terms :

... 6 - 4x = - 2x - 4

Adding 4x on both sides :

... 6 = 2x - 4

Adding 4 on both sides :

... 2x = 10

Dividing by 2 on both sides :

... x = 5

Hence, the value of x is 5.

Hope my answer helps!!

Unclear question, have is have?

Jayson saves $98 per week because half of 196 is 98. (196 divided by 2 = 98)

The solution for the given inequality is x ≥ 10.

An inequality is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression.  The solutions for inequalities can be given by: a graph in a number line or numbers.

Therefore, it is common to the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The question gives the inequality  2x+4 ≥ 24. Thus, you should follow the next steps.

2x+4 ≥ 24

2x ≥ 24 -4

2x ≥ 20

x ≥ 10

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To solve the inequality 2x+4≥24, subtract 4 from both sides, simplify the expression, divide both sides by 2, and simplify again. The solution is x≥10.

Let's solve the inequality 2x+4≥24. The first step is to isolate the term with x on one side. We can do this by subtracting 4 from both sides, which results in 2x ≥ 20. Next, we want to solve for x, so we divide both sides by 2: x ≥ 10. This means that x is greater than or equal to 10. lets solve step-by-step.

To solve the inequality 2x+4≥24, we need to isolate the variable x.

Step 1: Subtract 4 from both sides of the inequality: 2x+4-4≥24-4

Step 2: Simplify: 2x≥20

Step 3: Divide both sides of the inequality by 2: 2x/2≥20/2

Step 4: Simplify: x≥10

The solution to the inequality is x≥10. This means that any value of x that is greater than or equal to 10 satisfies the inequality.

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You add up all of the sides and the numbers that are there you pretend that they are on the other side and just add all of them up correctly and you will get your answer.

You multiply them.

4 x 4 x 3 = 48

3 x 2 x 6 = 36

First you need to figure out the formula for the line - this can be done using two obvious measurements in the plot (x,y): namely (0,0) and (2,50). The linear function that goes through these two points is [tex]y = 25x[/tex].

Now you can determine k (the function value for x=1) and that is [tex]k = 25\cdot1=25[/tex]

The meaning of k: you can find 25 grams of almonds in 1 cup of oat. (btw, if we were to take this literally it wouldn't make much sense - 1 cup of oat is 1 cup of oat and there is nothing else, but anyway).

Using a linear function, it is found that the value of k is 25, which means that for 1 cup of oats, 25 grams of almonds are needed.

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

In this problem:

[tex]m = \frac{50 - 0}{2 - 0} = 25[/tex]

The equation is:

[tex]y = 25x[/tex]

When x = 1:

[tex]k = 25(1) = 25[/tex]

The value of k is 25, which means that for 1 cup of oats, 25 grams of almonds are needed.

The point is labeled on the sketch of the graph given below.

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at this rate, he will have attempted 27 passes. we can find this by setting the problem up into a proportion: 10/18=15/?

once we solve the proportion, we get that he attempted 27 passes in order to complete 15

Final answer:

To solve for the number of passes the quarterback will attempt to complete 15 passes, we set up a proportion based on the completed 10 out of 18 passes. By cross-multiplying and solving for the unknown, we find that the quarterback would need to attempt 27 passes.

Explanation:

The question is asking us to find out how many passes the Rams' quarterback will attempt if he is to complete 15 passes, given that he completed 10 out of 18 passes in his last game. This is a proportion problem in mathematics where we set up a ratio of completed passes to attempted passes and solve for the unknown.

We know the quarterback completed 10 passes out of 18 attempts, so the ratio of completed to attempted passes is 10/18. If we want the quarterback to complete 15 passes, we can set up the proportion as:

10/18 = 15/x

where x represents the number of passes that the quarterback will attempt. To solve for x, we cross-multiply:

10(x) = 18(15)

x = (18(15))/10

x = 27

Therefore, the quarterback will have to attempt 27 passes to complete 15 passes at the same completion rate.

Answer:

the answer is 3x-5

Step-by-step explanation:

break the expression in to groups

3x^2 + 4x -15 =  (3x^2 -5x) + (9x-15)

factor out x from 3x^2 -5x: x(3x-5)

factor out 3 from 9x-15: 3(3x-5)

=x(3x-5) +3(3x-5)

factor out common terms

(x+3) (3x-5)

=((x+3) (3x-5)) / (x+3)

cancel the common factor x+3

=3x-5

The quotient for the expression is equal to 3x-5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Break the expression into groups

3x² + 4x -15 =  (3x² -5x) + (9x-15)

Factor out x from 3x^2 -5x: x(3x-5)

Factor out 3 from 9x-15: 3(3x-5)

=x(3x-5) +3(3x-5)

Factor out common terms

(x+3) (3x-5)

=((x+3) (3x-5)) / (x+3)

Cancel the common factor x+3

=3x-5

Therefore, the quotient for the expression is equal to 3x-5.

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B and E with C and G

The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches.  By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches

if the minute hand is 8 inches long, it shows the radius of the circle of the clock.

thus, the circumference of the circle (boundary)= 2πr

= 2X 3.14 X 8    ( wherein, r= radius= 8; π= 22/7 or 3.14)

= 50.27 inches.

The length between each two consecutive no.s on the clock = 50.27/12 = 4.19

Thus, the length moved n=by the tip of the minute hand= 4.19X8

= 33.44 inches

Hope that this would be correct .

The 30th term of this arithmetic sequence is 3.5 pounds. This represents the weight of the cat food bag after removing 0.5 pounds of food daily for 30 days.

The subject of this question is mathematics, particularly, a problem related to sequences. In this case, the sequence consists of gradually diminishing weights of a bag of cat food. Initially, the bag weighs 18 pounds and then 0.5 pounds are removed daily to feed the cats.

To find the weight of the bag on the 30th day (or, in other words, the 30th term of the sequence), you would subtract half a pound for each day that has passed. This is an arithmetic sequence, where each term can be found using the formula: an = a1 + (n - 1)*d, with a1 being the first term (18 pounds), d being the common difference (-0.5 pounds), and n being the term number (30).

Substituting the known values into the formula, we get: a30 = 18 + (30 - 1)*(-0.5) = 18 - 29*0.5 = 18 - 14.5 = 3.5 pounds.

Therefore, the 30th term is 3.5 pounds. This represents the weight of the cat food bag after 30 days of removing 0.5 pounds of food daily.

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To find the 30th term of the sequence representing the weight of cat food remaining each day, we can use a formula. The 30th term represents the weight of cat food remaining after 29 days of removing 0.5 pounds each day.

This question involves finding the 30th term of a sequence where 0.5 pounds of food is removed from an initial weight of 18 pounds every day. To find the 30th term, we can use the formula:

nth term = initial weight - (n-1) x rate of removal

Substituting the values, we have:

30th term = 18 - (30-1) x 0.5

= 18 - 29 x 0.5

= 18 - 14.5

= 3.5 pounds.

The 30th term represents the weight of cat food remaining after 29 days of removing 0.5 pounds each day.

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Answer: 68

Step-by-step explanation:

LM   +    MN     =   LN

x + 7  + 3x + 20 = 6x - 5

            4x + 27 = 6x - 5

           -4x         -4x      

                    27 = 2x - 5

                     +5        +5

                    32  = 2x

                    ÷2   ÷2    

                     16 = x

MN: 3x + 20

       3(16) + 20

         48   + 20

               68

This question is based on a principle in Mathematics called the Midpoint of a linelineline

Based on this question, the line = LNLN

To solve this question, we have the expression

LM + MN = LN

Step 1

We solve for x

Given that: LN= 6x-5 , LM= x + 7 , and MN= 3x + 20

Hence,

x + 7 + 3x + 20 = 6x - 5

Collect like terms

7 + 20 + 5 =6x - x - 3x

32 = 2x

Divide both sides by the coefficient of x = 2

32/2 = 2x/2

x = 16

The value of x = 16

Step 2

Find MN

Given that : MN= 3x + 20 and x = 16

We substitute 16 for x in MN

MN = 3(16) + 20

MN = 48 + 20

MN = 68

Therefore, the value of MN is 68.

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Number 3: D

Number 4: C

3.12 + (-8.5) = 11.62

Hello there!

Answer: ⇒⇒⇒⇒⇒-5.38

Step-by-step explanation:

First, remove parenthesis.

[tex]3.12-8.5[/tex]

Then, subtract by the number.

[tex]3.12-8.5=-5.38[/tex]

[tex]=-5.38[/tex]

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a  great day!

-Charlie

Answer: A & B

Step-by-step explanation:

[tex]\sqrt{5} *\sqrt{5} = \sqrt{5*5} = \sqrt{25} = 5[/tex]

The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.

Let us find area of each figure separately.

Triangle:

Area of triangle is given by:

[tex]A=\frac{1}{2}*b*h[/tex]

where b=base and h=height

Height of triangle :

h=(3x+5)-(2x+1)

h=x+4

Base = 2x-2

[tex]A=\frac{1}{2}*(x+4)(2x-2)[/tex]

Area of triangle= (x-1)(x+4) = x²+3x-4

Area of rectangle:

Area of rectangle is given by:

A=l*b

[tex]A=(2x-2)(2x+1)[/tex]

Area of rectangle = 4x²-2x-2

Area of pentagon = Area of triangle + Area of rectangle

Area of pentagon = x²+3x-4 + 4x²-2x-2

Area of pentagon = 5x²+x-6

If area of pentagon is 42 cm², then solving for x,

[tex]42=5x^{2}+x-6[/tex]

[tex]5x^{2}+x-48=0[/tex]

Factorising to get x,

x=-3.2 and x=3

If we take x as negative the side will be negative, so we neglect x=-3.2

So x=3 is the answer.

Answer 1:

[tex]\frac{x^{2} -x+1}{x^{2} +x+1}[/tex]

Here given that, x is real that is the domain

Range of the given expression is :

[tex]\frac{1}{3} \leq y\leq 3[/tex]  

Write it interval form.

[tex][\frac{1}{3},3][/tex]       Option (2)

Answer 3:

[tex]\frac{11x^{2} +12x+6}{x^{2} +4x+2}[/tex]

Here domain is all real x.

Range is :

{y ∈ R : y ≤ -5 or y ≥ 3}

In interval form:

(-∞, -5] ∪ [3, ∞)

So, y can't lies between -5 to 3                Option (2)

Answer 5 :

[tex]\frac{x^{2} -3x+4}{x^{2} +3x+4}[/tex]

Here domain is :

x is real

And range is :

{y ∈ R : [tex]\frac{-1}{7}[/tex] ≤ y ≤ 7}

We see that maximum y value is 7.

So, maximum value is 7.                      Option (4)

Answer 6:

[tex]\sqrt{9x^{2}+6x+1 } < (2 -x)[/tex]

Solve for x .

Square both the side

9x² + 6x + 1 =  4 + x² - 4x

8x² + 10x - 3 < 0

(2x + 3)(4x - 1) < 0

2x + 3 = 0                           &                    4x - 1 = 0

x = [tex]\frac{-3}{2}[/tex]      &                    x = [tex]\frac{1}{4}[/tex]

So,

[tex]\frac{-3}{2} < x < \frac{1}{4}[/tex]

x ∈ [tex](-\frac{3}{2} , \frac{1}{4} )[/tex]                     Option (1)

Answer:

Likely

Step-by-step explanation:

The answer is likely, its really close to certain but certain is 100%. Likely is the odds are for it but not confirmed.

Answer:

Likely is the answer hope this helps

Step-by-step explanation:

To test for divisibility, you look for answers that are whole numbers when you divide 59859 by either 2, 3, 5, 9, or 10.

To start divide it by each of them:

59859/2=29929.5

59859/3= 19953

59859/5= 11971.8

59859/9= 6651

59859/10= 5985.9

Now look at which of the choices are whole numbers

3 and 9 are the only non decimal numbers, therefore, C would be your answer.

Hope this helps!

Answer: C

Step-by-step explanation: The answer is C because:

You can use a lot of tricks to solve this problem. For divisibility of 2, you know that the number must be even to evenly divide by 2; 59,859 is not even, so you can scratch that out. For 3 and 9, there is a trick that says if the digits of a number add up to 3 and 9 respectively, then they are divisible by those numbers. The digits of 59,859 add up to 36, which is divisible by both 3 and 9, meaning that 59,859 is also divisible by 3 and 9. Lastly, for a number to be divisible by 5, it must end in 5 or 0, and for a number to be divisible by 10, the number must end in 0. 59,859 doesn't end in either of those giving you the final answer of:

B: 3, 9

We complete the square,

[tex]y=x^2+4x+11[/tex]

[tex]y = (x^2 + 4x + 4) + 11- 4[/tex]

[tex]y = (x+2)^2 + 7[/tex]

Answer: D

The total cost for 53 people attending the school banquet is $1,665.

Given the parameter:

The cost of a school banquet is expressed as:

$75 + 30n, as n is the number of people attending.

To determine the cost for 53 people attending the school banquet, you can plug the value of n (which is 53) into the given cost function:

Cost = $75 + 30n

Plug in n = 53

Cost = $75 + 30( 53 )

Cost = $75 + 1590

Cost = $1,665

Therefore, the total cost will be $1,665.

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Answer:

B

Step-by-step explanation:

Edge

Answer:

B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.

Statement B is true. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Equation 1;

-2x=14

Equation2;

6x=-42

Multiply equation 2 on both sides by -3.

-2x=14

-2x×3=14×3

6x= - 42

Because the second equation can be found by multiplying both sides of the first equation by 3, the equations have the same solution.

Hence, statement B is true

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The answer is 51 remainder 4      because 51* 4 =408 and 412 + 4 = 412