Is the expression 3(x+1 1/2)-3 equivalent to 3x+1 1/2

Answer:

Step-by-step explanation:

I'm not sure I would cross multiply as my first step.

How about subtracting 7/3 first.

0.5x = 21/4 - 7/3

0.5x = 21*3/(4*3) - 7*4/(3*4)

0.5x = 63 / 12 - 28/12

0.5x = 35/ 12                      Now multiply by 2

2*0.5x = 35*2 / 12

x = 70/12

x = 5 10/12   or

x = 5 5/6      or

x = 5.8333333

There might be a slightly easier way of doing this.

Suppose you multiply by 2 to begin with

x + 14/3 = 42/4

x + 14/3 = 21/2

x = 21/2 - 14/3

x = 63/6 - 28/6

x = 35/6

x = 5 5/6

I don't think there is much difference in how you do it. The numbers are just plain ugly.  

Answer:

x = -8 , y = -2

Step-by-step explanation:

Solve the following system:

{3 x - 4 y = -16 | (equation 1)

2 x - 4 y = -8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{3 x - 4 y = -16 | (equation 1)

0 x - (4 y)/3 = 8/3 | (equation 2)

Multiply equation 2 by 3/4:

{3 x - 4 y = -16 | (equation 1)

0 x - y = 2 | (equation 2)

Multiply equation 2 by -1:

{3 x - 4 y = -16 | (equation 1)

0 x+y = -2 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x+0 y = -24 | (equation 1)

0 x+y = -2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -8 | (equation 1)

0 x+y = -2 | (equation 2)

Collect results:

Answer: {x = -8 , y = -2

the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method here.

Given equations:

1.[tex]\(3x - 4y = -16\)[/tex]

2.[tex]\(2x - 4y = -8\)[/tex]

We can see that both equations have the same term ( -4y), so we can eliminate ( y) by subtracting equation 2 from equation 1:

[tex]\[(3x - 4y) - (2x - 4y) = (-16) - (-8)\][/tex]

[tex]\[3x - 4y - 2x + 4y = -16 + 8\][/tex]

[tex]\[(3x - 2x) - 4y + 4y = -16 + 8\][/tex]

[tex]\[x = -8\][/tex]

Now that we have found ( x = -8 ), we can substitute this value into either of the original equations to find ( y ).

Let's substitute ( x = -8 ) into equation 1:

[tex]\[3(-8) - 4y = -16\][/tex]

[tex]\[-24 - 4y = -16\][/tex]

[tex]\[-4y = -16 + 24\][/tex]

[tex]\[-4y = 8\][/tex]

[tex]\[y = \frac{8}{-4}\][/tex]

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

So, the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]

Answer:

B) 5 5/9

Step-by-step explanation:

13 1/3=40/3

7 7/9=70/9

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

40/3-70/9=120/9-70/9=50/9=5 5/9

Answer:

b

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange both equations into this form

x - 6y = - 30 (subtract x from both sides )

- 6y = - x - 30 ( divide all terms by - 6 )

y = [tex]\frac{1}{6}[/tex] x + 5 ← in slope- intercept form

with slope m = [tex]\frac{1}{6}[/tex]

y = - 6x + 5 ← in slope- intercept form

with slope m = - 6

Parallel lines have equal slopes.

Clearly the lines are not parallel.

The product of the slope of perpendicular lines equals - 1, thus

[tex]\frac{1}{6}[/tex] × - 6 = - 1

Hence the lines are perpendicular → b

Answer:

6:32 is my answer to this question

so if it is three minutes to one that means it is

12:57

in 6 hours and 34 minutes will be

12:57 + 6= 6:57

if you add 34 (i didnt do it above to make it easier)  to 57 you get 91.

because minutes dont go past 60 you have to subtract..

91 - 60 = 31 and because you only subtracted 60 once you only add one hour..

so your answer is 7:31

i hope this helps you !!!

Answer:

π/4

Step-by-step explanation:

The area of the circle is A = π(2x)^2 = 4πx².

The length of one side of the square is 2(2x), or 4x, so the area of the square is A = 16x².

The ratio of the area of the circle to the area of the square is

              4πx²

ratio = -------------   and this reduces to ratio = π/4.

              16x²

Answer: I think something is missing ?? sorry comment down below

Step-by-step explanation:

Jenna has $43 and Heidi has $17.

Step-by-step explanation:

Total amount = $60

Let,

Amount of Jenna = x

Amount of Heidi = y

According to given statement;

x+y=60   Eqn 1

x=2y+9   Eqn 2

Putting value of Eqn 2 in Eqn 1;

[tex](2y+9)+y=60\\2y+9+y=60\\3y=60-9\\3y=51[/tex]

Dividing both sides by 3,

[tex]\frac{3y}{3}=\frac{51}{3}\\y=17\\[/tex]

Putting y=17 in Eqn 2

[tex]x=2(17)+9\\x=34+9\\x=43[/tex]

Jenna has $43 and Heidi has $17.

Keywords: linear equations, substitution method

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An isosceles triangle has an angle that measures 40 degrees. 70 and 100 are other angles could be in that isosceles triangle

Solution:

Given that isosceles triangle has an angle that measures 40 degrees.

If a triangle is isosceles then it has 2 identical angles and the third different one.

Let the two identical angles be "a"

We know that sum of angles in a triangle is 180 degree

a + a+ 40 = 180

2a + 40 = 180

2a = 180-40

a = 70

Thus the two identical angles are 70 degree and 70 degree

Now let the identical two angles be "40" and the third angle be "a"

Now sum of angles = 180 degree

40 + 40 + a = 180

80 + a = 180

a = 100

Thus the third angle in this case is 100

70 and 100 are other angles could be in that isosceles triangle

Answer:

70, 40, and 100

Step-by-step explanation:

I am taking the IXL and wanted to know what t was and i got it wrong because someone answered it was only 70 and 100 when it is actually 40 100, and 70. Trust me i just got it wrong and IXL gave me the right answers.

Answer:

9w+8f+46, 11m+7, 3.1p-8.37, 8+5m.

Step-by-step explanation:

9(w+6)+4f+4(f-2)

9w+54+4f+4f-8

9w+54-8+8f

9w+46+8f

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

2m+7+9m=2m+9m+7=11m+7

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

3.1(p-2.7)=3.1p-8.37

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

5(3+m)-7=15+5m-7=8+5m

Answer:

number 7 is y= [tex]\frac{-ax+c}{b}[/tex]

Step-by-step explanation:

62. If you add up all of the numbers, you get 310, then take this number and divide it by 5. you divide it by five because there are five numbers given.

Answer:

57 is the mean.

When you add up all of the numbers, you get 285.

Divide 285 by 5 and you get 57.

Answer:

A. He has to work 5,887hrs and 55 min

B. 3,504 weeks

Step-by-step explanation:

A. He earns $9 an hr. He works 9hrs a week, or 1hr 17 min a day. $11.52 per day.

The car costs $52,753, + $235(taxes, titles, and plates)= $52,988.

52,988/9=5,887:55

B.    One week= 168 hrs. 5,887:55/168=3,504 weeks

Ryan needs to work approximately 5888 hours, which translates to about 654 weeks or 12.5 years, to save enough to buy a used car and pay for taxes, title, and plates at his current wage of $9 an hour.

To determine how many hours Ryan needs to work to afford a used car plus additional costs, we first add the price of the car to the taxes, titles, and plates. The cost of the used car is $52,753, and the taxes, titles and plates amount to $235, giving us a total cost of $52,988.

Ryan earns $9 per hour. To find out how many hours he needs to work to earn $52,988, we divide the total cost by his hourly wage.

$52,988 / $9 per hour = 5887.555... hours

Ryan would need to work approximately 5888 hours to afford the car and the extra costs.

For part B, we calculate how many weeks Ryan needs to work. Since Ryan works 9 hours a week, we divide the total hours needed by his weekly hours.

5888 hours / 9 hours per week = 654.222... weeks

Ryan would need to work approximately 654 weeks, which is roughly 12.5 years, assuming he works every week without any breaks or holidays.

Answer:

Each students will get 3 tickets and 2 brownies  .

Step-by-step explanation:

Given as :

The total number of tickets issued for the school dance = 64

The number of brownies ordered for refreshment table = 96

Let the number of tickets given to each student = x

And The number of brownie given to each student = y

Now,

According to question

The tickets and brownies is distributed equally among students

So , Now, consider the tickets and brownies = n

Or, [tex]\dfrac{n}{64}[/tex] - [tex]\dfrac{n}{96}[/tex] = 1

Or, Taking LCM we get

[tex]\dfrac{3 n - 2 n}{192}[/tex] = 1

Or, [tex]\dfrac{n}{192}[/tex] = 1

∴ n = 192

Now,

The number of tickets given to each student = x = [tex]\dfrac{192}{64}[/tex]

I.e x = 3

And The number of brownie given to each student = y =  [tex]\dfrac{192}{96}[/tex]

I.e y = 2

Hence Each students will get 3 tickets and 2 brownies  . Answer

To ensure each student gets an equal number of tickets and brownies, we distribute 64 tickets and 96 brownies among the students. Each student gets 2 tickets and 3 brownies.

To determine how many tickets and brownies each student gets, follow these steps:

Hence, Each student will get 2 tickets and 3 brownies.

Answer:

5x-2y + 8 =0

Step-by-step explanation:

2y=5x+8

5x-2y + 8 =0

Answer:

Yes

Step-by-step explanation:

[tex]\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }[/tex]

If we say u = √n, then:

[tex]\sum_{u=1}^{\infty} (\frac{1}{e})^{u}[/tex]

This is a geometric series.  Since |1/e| < 1, the series converges.

More people are allergic to peanuts because the smaller the denominator, the bigger the fraction.

There are 16 years will it take for the population to quadruple i.e. four times the initial population.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

Given that a population of a country grows exponentially and continuously at a rate of 9% per year.

The number of years it takes for the population to quadruple i.e. four times the initial population.

As per the given condition, the required solution would be as:

⇒ 4p = p[tex]e^{0.09t}[/tex]

Divided by p into both sides of the above equation,

⇒ 4p/p = p[tex]e^{0.09t}[/tex]/p

⇒ 4 = [tex]e^{0.09t}[/tex]

Take the natural logarithm of both sides of the equation,

⇒ ln 4 =  ln  [tex]e^{0.09t}[/tex]

⇒ ln 4 = 0.09t ln e

∵ ln e = 1

⇒ ln 4 = 0.09t

Divided by 0.09 into both sides of the above equation,

⇒ ln 4 / 0.09 = 0.09t / 0.09

⇒ t = 16

Thus, there are 16 years will it take for the population to quadruple.

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Answer:

x=4

Step-by-step explanation:

-2(x+2)=-12

x+2=-12/-2

x+2=6

x=6-2

x=4

Answer:

Lacy is 14 and Jack is 56

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

8*17=136+20=156

11*17=187-31=156

      156=156

Answer:

8 percent

Step-by-step explanation:

When you're trying to find the percentage, first, you divide what you're trying to find over the total amount.

2/25.

What you get from this is 0.08. However, this is a decimal, not a percent. When converting from decimal to percent, you multiply the decimal by 100 to get 8 percent.

Answer:

8%

Step-by-step explanation:

2/25=8/100=0.08=8%

Answer:

0.35

Step-by-step explanation:

Answer:

it is 0.35

Step-by-step explanation:

this is because 35/100= 0.35

This problem is tricky. Let's break it down.

1/4 - book

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

1/3 of the remainder(3/4) - stationery

"OF" MEANS MULTIPLY

1/3 x 3/4 = 1/4

So, 1/4 of total allowance on stationery.

Meaning, he spent 1/2 of his allowance in all, and 1/2 of his allowance is $18.

Since the book cost 1/4 of his allowance, and (1/4)2 = 1/2, the book cost 18/2 = $9.

The correct answer is "behaviorally anchored rating scale."

Further Explanation:

This type of testing is used by employers to rate an employees patterns of behaviors or their performance. This testing is also known as BARS. They use a scale system from either 1-5 or 5-9. This helps to see how the employee or trainee will do in certain situations.

This is commonly used by Human Resource departments, supervisors, or other higher ups in a company. This is used to benefit the company in the long run in case the employee or trainee doesn't work out during the appraisal. This can also be done during a yearly review of a seasoned employee.

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Answer:

The 3 examples are given below.

Step-by-step explanation:

1. While decorating my home the  amount of paint required ([tex]A_{m}[/tex]) for the wall is proportional to the area of the wall (A),

 or [tex]A_{m}[/tex] ∝ A .

2. The no. of tiles required(T)  to fill the floor of a house is proportional to the area of the floor(F) provided area of each tile(t) is constant here,

or  T ∝ F when t is constant

3.The tuition fee (M) taken by my sister's school for her studies is proportional to the no. of months(H) she is in that school,

or  M ∝ H

Final answer:

Examples of proportional relationships include electricity bills proportionate to usage, water in a tank related to tap flow time, and pay from a job based on the number of performed tasks.

Explanation:

Proportional relationships involve constants of proportionality which indicate a direct or inverse relationship between two quantities. For example, in a household setting, the electricity bill is directly proportional to the amount of electrical usage; the higher the usage, the higher the bill. Similarly, the amount of water in a tank can be seen as directly proportional to the time the tap runs if the flow rate is constant. Additionally, the pay for a college work-study job, such as making calls for donations, can be directly proportional to the number of calls made; if you're paid $2.50 per call, doubling the number of calls doubles your pay.

The vertex form of y = x² + 16x - 71 is (x + 8)² - 135

Step-by-step explanation:

The vertex form of the quadratic function y = ax² + bx + c, is

y = a(x - h)² + k, where

∵ The quadratic function is y = x² + 16x - 17

- Compare it with the general form of the quadratic function above

∴ a = 1 , b = 16 and c = -71

∵ [tex]h=\frac{-b}{a}[/tex]

- Substitute the value of a and b is h

∴ [tex]h=\frac{-16}{2(1)}[/tex]

∴ [tex]h=\frac{-16}{2}=-8[/tex]

∵ k = y when x = h

- Substitute x by -8 in the function above

∴ k = (-8)² + 16(-8) - 71

∴ k = 64 - 128 - 71

∴ k = -135

∴ The vertex point is (-8 , -135)

∵ The vertex form is y = a(x - h)² + k

∵ a = 1 , h = -8 , k = -135

- Substitute these values in the vertex form above

∴ y = 1(x - (-8))² + (-135)

∴ y = (x + 8)² - 135

The vertex form of y = x² + 16x - 71 is (x + 8)² - 135

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Answer:

x=2, y=0. (2, 0).

Step-by-step explanation:

5x+y=10

5y=3x-6

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

y=10-5x

5(10-5x)=3x-6

50-25x=3x-6

50-25x-3x=-6

50-28x=-6

28x=50-(-6)

28x=50+6

28x=56

x=56/28

x=2

5(2)+y=10

10+y=10

y=10-10

y=0

Answer:

There may be 3 tables or 1 table.

Step-by-step explanation:

If we factorize 12 into its prime factors then we get 12 = 2 × 2 × 3

If there are an odd number of tables and each table has an equal number of chairs and there are a total of 12 chairs, then the possibilities of the number of tables are 1 and 3.

{Since 1 and 3 both are odd numbers}

Now, for 3 tables there will be 4 chairs each to make the total chairs (3 × 4) = 12 and for 1 table there will be 12 chairs in the table to make the total number of chairs (1 × 12) = 12. (Answer)

To solve using prime factorization, the factors of 12 are 2, 2, and 3. We need an odd number of tables, so only the factor 3 is used. There are 3 tables with 4 chairs each.

The question involves a scenario where there are 12 chairs in a meeting hall and an odd number of tables. Each table has the same number of chairs. The question prompts us to use prime factorization to determine how many tables there could be. Since there is a fixed total of 12 chairs, we need to find the factors of 12 that are odd numbers because the number of tables has to be odd.

Using prime factorization, 12 can be broken down into its prime factors: 2 x 2 x 3. To have an odd number of tables, we cannot include the factor of 2 because it would result in an even number of tables. Hence, we only consider the factor of 3. In this scenario, this would mean there are 3 tables with 4 chairs each because 3 (an odd number) times 4 equals 12 (total number of chairs).

Another way to use prime factorization to solve this is to look for combinations of the factors that multiply to 12 but in groups that have an odd factor. The only possible combination is again 3 tables with 4 chairs each, as any other multiplication involving the factor 2 would result in an even number of tables.

Answer:

The value are

f = 6 cm

g = 8 cm

Step-by-step explanation:

Given:

ABCE is Trapezium

AD || BC

AD = BC = f

CD = g

Area of ABCE = 60 cm²

Area of ABCD = 48 cm²

To Find :

f  = ?

g = ?

Solution:

In the figure ∠ C = 90° and AD || BC

∴ ∠ D = 90° .....Corresponding angles are equal

∴ ABCD is RECTANGLE With Length = f and Breadth = g

∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]

[tex]\textrm{Area of Triangle AED}= \textrm{Area of Trapezium ABCE}-\textrm{Area of Rectangle ABCD}\\=60-48\\=12\ cm^{2} \\\therefore \textrm{Area of Triangle AED} = \frac{1}{2}\times AD\times DE\\12 =\frac{1}{2}\times f\times 4\\ f=\frac{24}{4}\\\therefore f= 6\ cm[/tex]

Now,

∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]

[tex]\therefore 48 = f\times g\\48= 6\times g\\\therefore g =\frac{48}{6}\\ g=8\ cm[/tex]

The value are

f = 6 cm

g = 8 cm