Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options. 5 and one-third x minus 3 and one-half x + 35 minus 12 One-sixth x + 47 1 and two-thirds x + 35 minus 1 and one-half x + 12 5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4) 1 and one-third x + 35 minus 1 and one-half x minus 12

Answers

Answer 1

The equivalent options are:

"One-sixth x + 47" ⇒ 2nd

"1 and two-thirds x + 35 minus 1 and one-half x + 12" ⇒ 3rd

"5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)" ⇒ 4th

Step-by-step explanation:

The expression is: 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) to find the equivalent to it:

Open the bracketsAdd the like terms

Multiply the bracket ( [tex]\frac{1}{3}[/tex] x + 7) by 5

∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(

Multiply the bracket ( [tex]\frac{1}{2}[/tex] x - 4) by - 3

∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{5}{3}[/tex] x + 35 -  [tex]\frac{3}{2}[/tex] x + 12

Add the like terms

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) + (35 + 12)

To add fraction with different denominators find the LCM of the two denominators and change them by it, then divide the LCM by each denominator and multiply the quotient by the corresponding numerator

∵ LCM of 3 and 2 is 6

∵ 6 ÷ 3 = 2, then multiply 5 by 2

∴  [tex]\frac{5}{3}[/tex] = [tex]\frac{10}{6}[/tex]

∵ 6 ÷ 2 = 3, then multiply 3 by 3

∴ [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{6}[/tex]

∴ ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) =  [tex]\frac{10}{6}[/tex] x -  [tex]\frac{9}{6}[/tex] x = [tex]\frac{1}{6}[/tex] x

∵ 35 + 12 = 47

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{1}{6}[/tex] x + 47

The 1st option is "One-sixth x + 47"

In the step 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12

∵  [tex]\frac{5}{3}[/tex]  = [tex]1\frac{2}{3}[/tex]  and  [tex]\frac{3}{2}[/tex] = [tex]1\frac{1}{2}[/tex]

∴  [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12 = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12

The 2nd option is "1 and two-thirds x + 35 minus 1 and one-half x + 12"

∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(

∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = 5(

The 3rd option is "5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)"

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Answer 2

Answer:

[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]

[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]

[tex]\frac{1}{6}x+47[/tex]

Step-by-step explanation:

The given expression is [tex]5(\frac{1}{3}x+7)-3 (\frac{1}{2}x- 4)[/tex]

We expand to get:

[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]

[tex]\frac{5}{3}x+35-\frac{3}{2}x+ 12[/tex]

As mixed number coefficients:

[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]

This simplifies to:

[tex]\frac{1}{6}x+47[/tex]


Related Questions

PLZ HELP WILL GIVE BRAINLIEST
A new juice stand is serving free drinks at a community festival. It offers the following drink options.
Fruit: apple, mango, orange, lime
Cup size: small, regular, large
Ice: cubed, crushed

If drinks are randomly passed out from each of the options, what is the probability that the next drink given out will be a regular apple juice with cubed ice?
a. 1/9
b. 1/12
c. 1/24
d. 1/4
THX SO MUCH!!!!

Answers

The correct answer is 1/24

Fruit: apple, mango, orange, lime

Cup size: small, regular, large

Ice: cubed, crushed

If you count every variation you'll get to 24.

The chances are 1 in 24.

1/24 since there’s 24 options

what is the value of x? enter in the box.​

Answers

Answer:

x=39° bc you add 102 +39 then subtract the total by 180

Answer: i think its 39 cause

180-(39+102)= 39

4.5 percent of what number is 33.5

Answers

The answer is 7.4 .
The answer to the question is 745

A population mean of 360, a standard deviation of 4, and a margin of error of 2.5%

Answers

Answer:

(351.04, 368.96)

Step-by-step explanation:

Given that population mean= 360

Std devitaion = 4

margin of error = 2.5%= 0.025

Since population std deviation is known we can use Z critical value

For two tailed critical value for 2.5% would be

2.24

Margin of error = ±Critical value*std deviation

= ±2.24(4)

= ±8.96

Confidence interval =(Mean - margin of error, mean + margin of error)

=[tex](360-8.96, 360+8,.96)\\= (351.04, 368.96)[/tex]

Answer:

368 is the answer

Tim said that to solve the equation x - 2 = 9, he would
need to subtract 2 from both sides of the equation.
Is Tim correct? Explain. Step by step please :D

Answers

No he would have to add 2 to both sides
Once added you will have x=11

_____ life insurance is for a specific time period and is the cheapest way to buy life insurance.

Answers

Term life insurance is insurance that insures you for a certain time period like 5 years for example.

Usually in months and years is how its done.

Term life insurance is for a specific time period and is the cheapest way to buy life insurance.

Unlike permanent life insurance policies, which cover an individual for their entire life, term life insurance offers protection for a predetermined period, such as 10, 20, or 30 years. Because it does not accumulate cash value and only pays out a death benefit if the insured passes away during the specified term, premiums for term life insurance tend to be lower compared to permanent policies.

The affordability of term life insurance makes it an attractive choice for individuals seeking to secure financial protection for their loved ones during specific critical periods, such as the years when children are growing up or when a mortgage is being paid off.

It's a straightforward and efficient way to provide a death benefit for beneficiaries in case the insured passes away within the chosen term, offering financial security without the long-term commitment and higher premiums associated with permanent life insurance options.

Select the correct answer from each drop down menu the cross-section is the intersection of a Solid or point and a plain in line

Answers

Answer:

Solid / plane

Step-by-step explanation:

Final answer:

A cross-section is a geometric concept, representing the intersection of a solid and a plane. The shape of the cross-section depends on how the plane intersects with the solid. A related physics concept is the continuity equation which states that the amount of incompressible liquid entering a cross-sectional area must equal the amount leaving it.

Explanation:

In mathematical terms, a cross-section is usually the intersection of a 3-dimensional solid with a plane. This concept is often used in Geometry. For instance, if we intersect a cylinder with a plane perpendicular to the base of the cylinder, the cross-section will be a circle which is the same size as the base of the cylinder. On the other hand, if the plane is parallel to the axis of the cylinder, the cross-section would be a rectangle.

A related concept, from the field of Physics, as described in Figure 14.28, is the continuity equation, usually applied when analyzing fluid dynamics. The equation posits that the volume of fluid entering a cross-sectional area of a duct or pipe must equal the volume of fluid leaving it, assuming the fluid is incompressible. This is because the mass of liquid cannot change within a closed system.

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Which of the following is a solution to this inequality? y>1/2x+2

Answers

The only solution to the inequality is point A, (1,4). Thus, the correct answer is A. To find the solution to the inequality [tex]\( y > \frac{1}{2}x + 2\),[/tex] we need to determine which of the given points satisfy the inequality. Let's test each point by substituting its coordinates into the inequality and checking if it holds true.

A. (1,4):

When [tex]\(x = 1\)[/tex] and [tex]\(y = 4\),[/tex] we have:

[tex]\(4 > \frac{1}{2}(1) + 2\)[/tex]

[tex]\(4 > \frac{1}{2} + 2\)[/tex]

[tex]\(4 > 2.5\)[/tex]

This is true, so point (1,4) satisfies the inequality.

B. (-1,1):

When [tex]\(x = -1\)[/tex] and [tex]\(y = 1\)[/tex], we have:

[tex]\(1 > \frac{1}{2}(-1) + 2\)[/tex]

[tex]\(1 > -\frac{1}{2} + 2\)[/tex]

[tex]\(1 > 1.5\)[/tex]

This is false, so point (-1,1) does not satisfy the inequality.

C. (2,3):

When [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex], we have:

[tex]\(3 > \frac{1}{2}(2) + 2\)[/tex]

[tex]\(3 > 1 + 2\)[/tex]

[tex]\(3 > 3\)[/tex]

This is false, so point (2,3) does not satisfy the inequality.

D. (0,2):

When [tex]\(x = 0\)[/tex] and [tex]\(y = 2\)[/tex], we have:

[tex]\(2 > \frac{1}{2}(0) + 2\)[/tex]

[tex]\(2 > 2\)[/tex]

This is false, so point (0,2) does not satisfy the inequality.

Therefore, the only solution to the inequality is point A, (1,4). Thus, the correct answer is A.

The complete question is:

Which of the following is a solution to this inequality? y>1/2x+2

A. (1,4)

B. (-1,1)

C. (2,3)

D. (0,2)

Johanna rode her bike 7 miles to a lake. She rode 3/4 of the distance to the lake before lunch. How many miles did Johanna ride before lunch?

Answers

Answer:

5.25 miles

Step-by-step explanation:

In Long division please divide 9 by 243

Answers

Answer:

27

Step-by-step explanation:

Answer:27

Step-by-step explanation: 9 goes into 2 zero times. Put a zero on top. 9 goes into 24 two times. Put a 2 on top. Now multiply 9 by 2 and get 18. Put 18 under the 24 and subtract. This gives 6. Bring down the 3 and have 9 into 63 which is 7. Put a 7 on top. The top is the answer of 027, cancel the zero and get 27.


At a restaurant, the bill comes to $62. If you decide to leave a 10% tip, how much total do you need to pay? Give your
answer to the nearest dollar.

Answers

Answer:the tip itself will be $6.20 but in total it will all cost $68.20

Step-by-step explanation:

Much HELP needed here!! If you can id appreciate it so much ):

Answers

Answer:

OPTION D: (-1, 10)

Step-by-step explanation:

The equation of a line in standard form is given by: [tex]$ \textbf{y} \textbf{-} \textbf{y}_\textbf{1} \hspace{1mm} \tetxbf{=} \hspace{1mm} \tetxtbf{m}(\textbf{x - x}_{\textbf{1}}) $[/tex]

Here, m is the slope of the line.

[tex]$ (x_1, y_1) $[/tex] is the point on the line.

Therefore, comparing it with the given data:

[tex]$ y - 2= -\frac{2}{3}(x - (-1)) $[/tex]

[tex]$ \implies y_1 = -2 $[/tex]

[tex]$ \& \hspace{2mm} x_1 = -1 $[/tex]

Hence, the point on the line is: (-1, 2).

Hence, the answer.

Angle C and P are


PLEASE HURRT!

Answers

Answer:

Same side interior angles

They are also supplementary (add up to 180 deg)

Step-by-step explanation:

see attached

What percentage of 7.7 billion is 15 million?

Answers

Answer:

64.94% or as a decimal .65

Step-by-step explanation:

7.7 billion (x)=15 million

7.7x /7.7 and 15/7.7

is about .... 64.94% which is about .65

x- represents the unknown percentage.

Sorry if incorrect :(

What is the solution to the system of equations graphed on the coordinate plane? (4, 3) (3, 4) (2, 0) (5, 0)

Answers

Answer:B. (3,4)

Step-by-step explanation:

because looking at the x-axis we see that the 3 is pointing to that point, and looking at the y-axis we can see that the 4 is pointing to the same point as the 3. Therefore the answer is B (3,4)

Answer:

(3,4)

Step-by-step explanation:

when looking at the x and y axis on the graph you see where the lines intersect. when on the x-axis at 3 you go up 4 times and on the y-axis 4 you go to the right 3 times showing both lines intersecting each other.  

took the quiz on edg :)

Select all ratios equivalent to 3:4.
11:16
11:16
18:24
18:24
15:20
15:20
T

Answers

Answer:

18:24

18:24

15:20

15:20

Step-by-step explanation:

Because 18/3:24/3 = 3:4

Also, 15/5:20/5 = 3:4

18:24
18:24
15:20
15:20

Solve this proportion. Show your work. 7/12 = 42/x

Answers

Answer:

42/72

Step-by-step explanation:

42/7=6

12*6=72

This is the answer to a problem or an equation.

Example: For 3x+6=27, this is x=7

Answers

Answer:

x=7 is the answer

3x+6=27 is the equation

x=7 is the correct answer for the equation.

To solve the equation 3x + 6 = 27, subtract 6 from both sides and then divide by 3 to get x = 7. Verify by substituting x = 7 back into the original equation. This confirms the solution is correct by making a true statement.

Step by Step Solution:

When solving an algebraic equation, the goal is to find the value of the variable that makes the equation true. For example, consider the equation 3x + 6 = 27. To solve for x, follow these steps:

Subtract 6 from both sides of the equation: 3x + 6 - 6 = 27 - 6, which simplifies to 3x = 21.

Next, divide both sides by 3: 3x / 3 = 21 / 3, which gives x = 7.

To verify the solution, substitute x = 7 back into the original equation: 3(7) + 6 = 27. Simplifying this, we get 21 + 6 = 27, which is a true statement, verifying our solution.

Note that an identity in algebra is an equation that is true for all values of the variable, such as 6 = 6. In our example, the solution x = 7 makes both sides of the original equation equal, thus satisfying the equation.

The isosceles triangle has a perimeter of 7.5 m.

Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?

2 x minus 2.1 equals 7.5
4.2 plus y equals 7.5
y minus 4.2 equals 7.5
2.1 plus 2 x equals 7.5

Answers

The equation 2.1 plus 2 x equals 7.5 can be used to find the value of x ⇒ 4th answer

Step-by-step explanation:

In an isosceles triangle:

Two sides are equal ⇒ the angle between them is called the vertex angle of the triangleTwo angles are equal ⇒ they called the base angles

∵ The triangle is isosceles

- That means it has two equal sides

∵ The shortest side is y

∵ The length of the other two sides is x

The perimeter of the triangle = y + 2 x

∵ The perimeter of the triangle = 7.5 m

- Equate the expression of the perimeter by 7.5

y + 2 x = 7.5

∵ The shortest side measures 2.1 m

∴ y = 2.1

- Substitute y by 2.1 in the equation above

2.1 + 2 x = 7.5

The equation 2.1 plus 2 x equals 7.5 can be used to find the value of x

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Answer:

D

Step-by-step explanation:

A car travels on a highway at a constant speed of 67 miles per hour. Which equation and table shows the correct relationship between , the number of hours, and , the distance traveled

Answers

Answer:

Theres no tables but y=67x would be the equation

since 67 is the constant which =m in y=mx+b

if sin F = 3/5 , what is cos G ?

Answers

Answer:

D

Step-by-step explanation:

side HG is 3

side FG is 5 hypotenuse

sin F = 3/5 = opposite/hypotenuse

cos G is adjacent/hypotenuse

adjacent side is HG which = 3

hypotenuse is 5

Final answer:

Without additional context, we cannot give a direct answer for cos G based only on sin F = 3/5. If F and G are complementary angles in a right triangle, cos G would also be 3/5. Otherwise, more information about the relationship between F and G is needed.

Explanation:

To solve this question, we need a bit more context because there is not enough information provided to directly determine the value of cos G. However, typically, if sin F is given as 3/5 for a right triangle, then by the Pythagorean theorem, we know cos F = √(1 - sin^2 F), which calculates to 4/5, assuming F is an angle in a right triangle in standard position with F between 0 and 90 degrees.

This doesn't directly give us cos G, but if we assume G is the complementary angle to F in a right triangle (F + G = 90 degrees), then cos G = sin F and we could say cos G is also 3/5. If sine and cosine relate to different triangles or different contexts, we would need the relationship between angles F and G or additional information to solve for cos G.

how do you solve y=1/2x-4

Answers

Answer: x = 2y + 4

Step-by-step explanation:

y=1/2x-4

multiply both sides by 2

2y=x-4

substract from both sides 2y

0=x+–2y-4

substract from both sides x

-x=-2y-4

multiply both sides by -1 to get positive x

x=2y+4

Find the seventh term in the sequence: 11, 13, 15,...

Answers

The seventh term is 23.

Step-by-step explanation:

Step 1: This is an Arithmetic Progression 11, 13, 15...

Given, First term, a = 11

Step 2: Find Common difference, d =   13 - 11 = 2Step 3: Formula for nth term in an AP, a(n) = a + (n-1) d Step 4: Substitute for 7th term, a(7) = 11 + (7 - 1) 2

= 11 + (6*2)

= 11 + 12 = 23

The product of twice a number and six is the same as the difference of eleven times the number and 8/5. Find the number

Answers

Answer:

-1.6

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ!

Your equation will be 2x*6=(11*x)-(8/5)

12x=11x-1.6

-11x -11x

x=-1.6

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

The number that satisfies the given condition the product of twice a number and six is the same as the difference of eleven times the number and 8/5 is -1.6.

Let's assume the number we are looking for is "x."

The problem states that the product of twice the number and six is the same as the difference of eleven times the number and 8/5.

Step 1: Express the given statement as an equation.

The product of twice the number and six is 2x * 6 = 12x.

The difference of eleven times the number and 8/5 is 11x - 8/5.

Now, we can set up the equation:

12x = 11x - 8/5

Step 2: Solve for x.

To solve for x, we need to isolate x on one side of the equation. Subtract 11x from both sides of the equation:

12x - 11x = 11x - 11x - 8/5

x = -8/5

The number we are looking for is x = -8/5 or -1.6.

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Solve the inequality. Graph the solution set.
5x - 6 > 4x - 8

Answers

Answer:

Step-by-step explanation:

sorry

no graph paper to graph

What is
4+27÷(4+5) = ??

Answers

The answer is 7 hope I answered In time

Answer:

7

Step-by-step explanation:

To solve this equation you have to use PEMDAS

Because of PEMDAS, we start with parenthesis.

4+27 ÷(4+5)= ?     4+5 = 9     4+27 ÷ 9 = ?

There are no exponents or multiplication so we skip to division.

4+27 ÷ 9 = ?   27 ÷ 9 = 3    4+3=?

Then we do addition

4+3 =7

Find the quotient 1/5 divided by 2

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

A line segment has endpoints j(2,4) and l(6,8) the point k is the midpoint of ja what is an equation of a line perpendicular to ja and passing through k

Answers

Answer:

An equation of a line perpendicular to ja and passing through k is:

y = -x + 10

What equals to 2/3 the answers denominator is 9

Answers

the answer would be 6/9

explanation:

2/3 ?/9

if you multiply 3 and 3, it gives you 9, which is the denominator. then you also have to multiply the numerator by the same thing you multiply the denominator with. therefore, 2x3 would give you 6, which makes your answer:

6/9

a rectangle has a length of 6cm, and an area of 18cm aquared. what is the width of the rectangle?

Answers

Answer:

  3 cm

Step-by-step explanation:

The formula for the area of a rectangle is ...

  A = LW . . . . . . area is the product of length and width

Fill in the given values and solve for the width (W).

  18 cm² = (6 cm)W

  (18 cm²)/(6 cm) = W = (18/6) cm²/cm . . . . . . divide by the coefficient of W

  W = 3 cm

The width of the rectangle is 3 cm.

Final answer:

The width of a rectangle, with a length of 6 cm and an area of 18 cm squared, is 3 cm.

Explanation:

The question is asking for the width of a rectangle which we can find using the formula for the area of a rectangle. The formula is: Area = Length x Width. From the given question, we know that the area is 18 cm2 and the length is 6 cm. So, we can set up the equation: 18 = 6 x Width. To solve for width, we divide both sides of the equation by 6. This gives us Width = 18 ÷ 6 which equals 3 cm.

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