If y varies directly as x and y=8 when x=2, find x=6.

Answer:

x=29/8

Step-by-step explanation:

3 5/8=29/8

7 1/4=29/4

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

x+29/8=29/4

x=29/4-29/8

x=58/8-29/8

x=29/8

The first step in solving the inequality is to distribute –4 to get -8x + 4 > 5 - 3x

Solution:

Given inequality is:

[tex]-4(2x - 1) > 5 - 3x[/tex]

The first step in solving the inequality is to distribute -4 to terms inside the bracket in left side of equation

This is done according to BODMAS rule

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

Thus in given inequality, brackets has to solved first

This is done by using distributive property

a(b + c) = ab + bc

Therefore,

[tex]-4(2x - 1) = (-4 \times 2x) +(-4 \times -1) = -8x + 4[/tex]

Thus, the inequality becomes,

[tex]-4(2x - 1) > 5 - 3x\\\\-8x + 4>5-3x\\\\-5x>1\\\\x<\frac{1}{5}[/tex]

Thus solution to given inequality is found

Answer:

0.13 tax

Step-by-step explanation:

0.044*3=0.132

Final answer:

To create the equation representing the situation, calculate the total meal cost by multiplying each friend's share by four and then add four times the tip to equal the final bill of $61. The equation is 4 times $12.75 + 4  imes t = $61.

Explanation:

To solve the problem using an equation, we need to consider the cost of each meal and the tip each friend left. Four friends each paid $12.75 for their meal, which gives us the cost of the meals alone: 4 times $12.75 = $51. The tip, t, needs to be added four times (once for each friend) to the total cost of the meals to reach the final bill of $61.

Therefore, the equation to represent the situation would be: 4 times $12.75 + 4 times t = $61.

Once we have the equation, we can solve for the tip, t, to find out how much each friend left for the tip.

Incomplete Question the complete Qs is

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m = 1/2?  

a: y=1/2x+2

b: y=-2x+1/2

c: x-2y=-4

d: y-1=1/2(x+2)

Answer:

The Correct option is c. x-2y=-4

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

Step-by-step explanation:

Given:

[tex]Slope = m =\dfrac{1}{2}[/tex]

point A(x₁, y₁)=(-2,1)  

To Find:  

Equation of Line  =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2 , 1) we get

[tex](y-1)=\dfrac{1}{2}(x-(-2))\\\\2y-2=x+2\\x-2y=-2-2=-4\\x-2y=-4[/tex] As required

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

Answer:

4 im not 100% but i think so

Step-by-step explanation:

Answer:

Step-by-step explanation:

4(x + 8) + 5(y + 3) =

4x + 32 + 5y + 15 =

4x + 5y + 47

total of 3 terms : 4x, 5y, and 47

Answer:

see attached picture.

Answer:

4

Step-by-step explanation:

5(1/5)+(1/5)15

1+3

4

Answer:

4

Step-by-step explanation:

when c = 1/5 and d =15

5c + cd = c×(5 + d) = (1/5)×(5+15) = 1/5×(20) = 20/5 = 4

Answer:

C. 15 and 35

Step-by-step explanation:

3 x 15=45-10= 35

15+35=50

So C. is correct

Answer:

C

Step-by-step explanation:

Let the two no.s be x and y

x+y=50 -------(I)

Condition 2:

x=3y-10 -------(2)

Putting eq 2 into 1

3y-10+y=50

4y-10=50

4y=50+10

4y=60

Dividing both sides by 4

y=15

Putting the value of y in 2

x=3(15)-10

x=45-10

x=35

Answer:

x = 41

Step-by-step explanation:

To solve this problem, we want to find the value of 'x' by isolating it (separating 'x' from all other numbers).

First, simplify the expression by using the distributive property, where you multiply the number outside the brackets with each term inside the brackets.

Then isolate 'x' by doing reverse operations (on both sides) for every number that is on the same side as 'x'. Reverse operations are opposites (addition and subtraction, multiplication and division) and "cancel out" a number, which "moves" it to the other side.

7(x - 5) = 252        Use the distributive property

7x - 35 = 252        Result of 7 times x and 7 times -5

7x - 35 + 35 = 252 + 35        Add 35 to both sides

7x = 252 + 35        -35+35 on the left side cancelled out. Simplify right side

7x = 287        Continue to isolate 'x'

7x/7 = 287/7        Divide both sides by 7

x = 287/7        Left side cancelled out to be 'x'. Simplify the right side

x = 41        Answer

Check your answer:

Substitute 'x' for 41 in the original equation. Then, make sure that the equation is still balanced. Keep in mind BEDMAS order (brackets, exponents, division, multiplication, addition, subtraction).

7(x - 5) = 252

7(41 - 5) = 252        Simplify inside the brackets first

7(36) = 252        Multiply

252 = 252        Same answer

LS = RS

Since left side (LS) equals (=) right side (RS), the equation is still balanced and we got the correct value for 'x'.

Answer:3

Step-by-step explanation:

Answer:

-3/7

Step-by-step explanation:

x-5=1

+5   +5

x=6

x-5=-1

 +5  +5

x=4

Answer: x= 6, 4

Answer:

50 persons

Step-by-step explanation:

Given:

Aaron’s dad rents out the local skating rink for a party for = $150

Food will cost per person = $3

Question asked :

how many people can Aaron invite = ?

Solution:

Total budget = $300

Rent of skating rink = $150

Remaining money for food = 300 - 150

                                             = $ 150

Each person's food cost = $3

Number of people can Aeron invite = Remaining money divided by each person's food cost

Number of people can Aeron invite = [tex]\frac{150}{3}[/tex]

                                                            = 50 persons

Answer:

Let's look again at the amount of money spent. They bought $15 game tokens and 3 admission tickets. If t is the cost of one admission ticket, as given, then the total money they spent can be written as:

$15 + 3 • t

making the statement a) false.

If the admission ticket costs $2.50, then, using the expression above, they spent:

$15 + 3 • $2.50

$15 + $7.50

$22.50

making the statement b) true.

From the table, we see that number of feet is always three times the number of yards.

So, if we label the number of yards with y and number of feet with f, we get:

f = 3y

which means that the number of feet in y yards is 3y.

When using decimal numbers we should know that the digit before the decimal point is integer and the digits after the point are decimals.

When adding two numbers, one of which isn't decimal number, sometimes it's helpful to write it in that manner. In this case, we could write 7 as 7.0.

Now, adding these two numbers should be easier:

7.0 + 0.8 = 7.8

Note that we simply add up decimal numbers and integers independently.

Here, it's important to remember one of the key features of multiplication; any number multiplied with one equals to that same number. It doesn't matter whether that number is integer, decimal number, a fraction or an expression.

So, in this case, we have:

8.3 • 1 = 8.3

We can write expressions for both girls. Samantha ran five miles each day for seven days, so her distance is:

S = 5 • 7 = 35

Mariska, on the other hand, ran seven miles each day for five days, meaning that her distance is:

M = 7 • 5 = 35

So, this means that they ran the same distance, but let us explain why. Another important feature of multiplication is that if you change the order of the numbers multiplied, you still get the same value. So, if we write:

a • b = c

then:

b • a = c

which was the case in this question (5 • 7 = 7 • 5).

Let's define the number of balls on the playground as b. Then, one more ball than that would be b+1.

Let's define the number of cookies in the jar as c. Then, three more cookies than that would be c+3.

Let's define the number of the questions on the first test as q. Then, twelve fewer then this would be q-12.

Let's define the cost of the shirt as s. Then, eight dollars more then this would be s+8.

Let's define number of drinks on the tray as d. Then, eight times as much would be 8•d.

Let's define Yumi's pay as y. Then, five dollars less would be y-5.

Let's define the number of students in math class as m. Then, half as many would be m • 1/2 = m/2

Let's define Emily's age as e. Then, third of her age would be e • 1/3 = e/3.

Let's define minutes spent exercising as x. Then, ten times this would be 10•x.

So, Spencer bought three books of stamps and spent $4.50 on mailing a package. The total amount Spencer spent at the post office is the amount spent on the books plus mailing of the package. If we mark the price of one book as b, since he bought three books, he spent 3•b. So, the total amount he spent in the post office is:

3•b + $4.50.

Morton will give 3 cookies to each student and 6 cookies to each friend

Solution:

Let "x" be the cookies given to each student

Let "y" be the cookies given to each friend

Each friend will get 3 more cookies than each student

Therefore,

cookies given to each friend = 3 + cookies given to each student

y = x + 3 -------- eqn 1

She has a total of 112 students  and 12 friends and made of total of 408 cookies for everyone

Therefore, we frame a equation as:

112x + 12y = 408 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

112x + 12(x + 3) = 408

112x + 12x + 36 = 408

124x = 372

x = 3

Substitute x = 3 in eqn 1

y = 3 + 3

y = 6

Thus Morton will give 3 cookies to each student and 6 cookies to each friend

Ms. Morton predicts that she will give each friend 4 cookies and each student 7 cookies. So this is incorrect

Answer:

11 and 23

Step-by-step explanation:

Answer:

Step-by-step explanation:

-x (4x^2 - 6x + 1).....distribute the -x through the parenthesis

- 4x^3 + 6x^2 - x <===

Answer:

b

Step-by-step explanation:

Answer:

D) -30

Step-by-step explanation:

4(-5)+7(3)+3(-5)-2(3)+2(-5)

-20 + 21 - 15 - 6 - 10

1 - 21 - 10

-20 - 10

= -30

Hope this helps

-Amelia

Answer:

x=24

Step-by-step explanation:

Here, you need to make proportion and find x.

12:16=18:x

We multiply 12 by x and 16 by 18:

12x=288

Divide by 12 both sides :

x=24

Answer:

I just had this question and i believe the answer was infinitely

Step-by-step explanation:

Answer:

62.5 gallons

Step-by-step explanation:

Divide by 8

Based on the shape of the platter and the length of each side, the area of the platter must be 64 inches².

The platter is said to be a square so the area will be that of a square.

Area of a square is:

= Length x Width

A square has the same length and width so the area is:

= 8 x 8

= 64 inches²

In conclusion, the area is 64 inches ².

Find out more about area at https://brainly.com/question/2607596.

Answer:

c=13 its the square root :)

Step-by-step explanation:

Is number2  Extend  I think

The three even integers are 66, 68 and 70

Solution:

Let the three consecutive even integers be x, x + 2, x + 4

Let the first integer be x

Let the second integer be x + 2

Let the third integer be x + 4

Given that, sum of the first and third of three consecutive integers is 136

Sum of first and third integer = 136

x + x + 4 = 136

2x + 4 = 136

2x = 136 - 4

2x = 132

x = 66

Thus the consecutive integers are:

first even integer = x = 66

second even integer = x + 2 = 66 + 2 = 68

third even integer = x + 4 = 66 + 4 = 70

Thus the three even integers are 66, 68 and 70

Answer:

10

Step-by-step explanation:

because

Answer:

17.3

Step-by-step explanation:

241.5 divided by 14 is 17.25 rounded up its 17.3

Answer:

1. Using the Pythagorean theorem.

2. Using the ratio 1 : 1 : √2.

Step-by-step explanation:

There are two options to find the value of x:

1. Using the Pythagorean theorem:

Hypotenuse = 5√2 inches and legs are equal in a 90 - 45 - 45 triangle like this.

Hypotenuse² = Leg² + Leg²

(5√2)² = 2Leg²

50 = 2Leg²

50/2 = Leg²

Leg² = 25

√Leg² = √25

Leg = 5 inches ⇒ x = 5

2. Using the ratio 1 : 1 : √2, this way:

1 : 1 : √2

x : x : 5√2

x = 5√2/√2

x = 5 and let's recall that in a 90 - 45 - 45 triangle legs are equal, therefore. ratio is:

5 : 5 : 5√2